[User]
What is the rank of the matrix:
[[22, 20, 8, 56, -10],
 [-23, -34, 8, 2, 17],
 [10, 20, -10, -25, -10],
 [-4, 0, -6, -27, 0],
 [19, 18, 6, 45, -9]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[22, 15, 5, 11, 11],
 [-22, -16, 13, -22, 11],
 [-6, -6, 33, -24, 39],
 [-26, -17, -19, -5, -29],
 [-36, -25, 0, -23, -8]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-10, 0, 10, -25, 0],
 [2, 0, -2, 5, 0],
 [2, 0, -2, 5, 0],
 [2, 0, -2, 5, 0],
 [-2, 0, 2, -5, 0]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[19, 43, 8, -27, 52],
 [38, 34, -47, 10, 16],
 [27, -1, 25, 29, -4],
 [-49, -49, 49, -6, -31],
 [-18, -66, -12, 54, -84]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-3, -3, 29, 48, -10],
 [-12, -3, -7, -21, 5],
 [-9, -1, 7, 6, 10],
 [-54, -7, -3, -43, 55],
 [45, 10, -34, -27, -25]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[-22, 12, 32, 56, 18],
 [-12, -18, 6, -30, -18],
 [12, 3, -13, -7, 1],
 [15, 0, -18, -18, -3],
 [-21, 6, 28, 40, 11]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[11, -5, -22, 2, 28],
 [-2, 2, 8, 4, -12],
 [4, -4, -16, -8, 24],
 [3, 6, 21, 30, -39],
 [-18, 3, 17, -24, -13]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[0, 30, 0, -30, 30],
 [0, 12, 0, -12, 12],
 [0, -6, 0, 6, -6],
 [0, 24, 0, -24, 24],
 [0, 12, 0, -12, 12]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-2, -22, 27, 4, -22],
 [-18, 12, 12, -6, -30],
 [-2, -12, 16, 2, -14],
 [0, 0, 0, 0, 0],
 [11, 6, -22, 1, 29]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[49, 15, 18, -50, -4],
 [-34, -18, -3, 29, 11],
 [-1, -15, 18, -10, 16],
 [34, 6, 18, -38, 2],
 [-9, -15, 12, 0, 14]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[4, -24, 16, -12, 8],
 [-2, 12, -8, 6, -4],
 [-6, 36, -24, 18, -12],
 [-4, 24, -16, 12, -8],
 [6, -36, 24, -18, 12]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[0, 4, 1, 14, -2],
 [30, -14, -23, 2, -32],
 [-26, 15, 21, 5, 26],
 [-15, -11, 0, 2, 31],
 [36, -21, -29, -9, -36]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-20, -12, -8, 24, 12],
 [-25, -15, -10, 30, 15],
 [25, 15, 10, -30, -15],
 [10, 6, 4, -12, -6],
 [-25, -15, -10, 30, 15]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[-12, 18, 32, -31, 42],
 [36, 22, 2, -22, 2],
 [-42, -5, -7, 2, 11],
 [28, 4, 0, -1, -10],
 [6, 27, 47, -43, 51]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[9, 22, 1, -16, -4],
 [21, 38, 17, -8, -8],
 [0, 20, -22, -44, -2],
 [0, 0, 0, 0, 0],
 [9, 32, -10, -38, -5]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-36, -36, 30, 30, 36],
 [24, 24, -20, -20, -24],
 [30, 30, -25, -25, -30],
 [30, 30, -25, -25, -30],
 [24, 24, -20, -20, -24]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-9, -11, -8, 41, 15],
 [-37, -25, -34, 9, 11],
 [-15, 2, -32, -33, 12],
 [-22, -21, -6, 10, -7],
 [30, -6, 66, 24, -42]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[29, -24, 10, -9, -16],
 [1, 27, -31, -6, 34],
 [5, -30, -32, 54, -10],
 [28, -26, -62, 48, 20],
 [37, -23, -9, -4, -2]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[10, -25, 0, -10, 30],
 [0, 0, 0, 0, 0],
 [-4, 10, 0, 4, -12],
 [4, -10, 0, -4, 12],
 [-10, 25, 0, 10, -30]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[32, -20, 22, -24, -6],
 [19, -2, -5, 21, -9],
 [40, -17, 16, -24, 0],
 [48, -9, 0, 0, 0],
 [8, -7, 14, -48, 18]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[3, 7, -6, -5, 0],
 [3, 5, -18, -25, 0],
 [4, 7, -22, -30, 0],
 [-11, -27, 14, 5, 0],
 [3, 9, 6, 15, 0]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-14, 10, -2, 4, 5],
 [6, -4, -14, 6, -14],
 [8, -16, -4, -10, 4],
 [-24, 30, -6, 21, -7],
 [27, -34, -5, -18, -1]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[20, 12, -4, 4, 16],
 [30, 18, -6, 6, 24],
 [-20, -12, 4, -4, -16],
 [-15, -9, 3, -3, -12],
 [5, 3, -1, 1, 4]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[9, -12, -12, 0, -6],
 [15, -20, -20, 0, -10],
 [-6, 8, 8, 0, 4],
 [-12, 16, 16, 0, 8],
 [12, -16, -16, 0, -8]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[38, -10, -60, -50, 6],
 [-58, -28, 20, 42, -36],
 [-35, 23, 50, 63, -19],
 [-20, 5, 15, 30, -16],
 [-2, 6, -5, 30, -11]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[19, 30, 33, -15, 30],
 [5, 8, -1, 27, -8],
 [30, 60, 64, 6, 24],
 [14, 15, -9, 28, 21],
 [19, -16, -33, 21, 4]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[18, 8, 15, -4, -22],
 [-2, -2, -1, 2, 8],
 [38, -7, 53, 32, -25],
 [30, -15, 51, 42, -21],
 [28, -22, 54, 52, -2]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[30, 29, -22, 33, -34],
 [-15, 11, 21, 9, -1],
 [-14, 35, 6, 25, 18],
 [-18, 42, 14, 45, 15],
 [-40, -51, 28, -32, 51]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-46, -15, -3, -8, -11],
 [0, 36, -30, -18, 43],
 [18, 13, 1, -68, -15],
 [-3, 19, -10, -19, -18],
 [4, 25, -17, 15, 11]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-8, -18, 22, -6, 2],
 [18, 24, 44, -7, -14],
 [34, 22, 78, -13, -36],
 [-2, 80, 26, 15, 6],
 [-42, -12, 33, 2, 26]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-31, -2, -40, -14, -27],
 [82, 12, 14, 23, 0],
 [-78, 36, 3, -9, 9],
 [-44, 32, 14, -8, -12],
 [-56, 48, -22, -14, -42]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[12, -6, -6, -4, 8],
 [6, -3, -3, -2, 4],
 [0, 0, 0, 0, 0],
 [-6, 3, 3, 2, -4],
 [6, -3, -3, -2, 4]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[4, -10, 0, 6, -10],
 [8, -20, 0, 12, -20],
 [-10, 25, 0, -15, 25],
 [6, -15, 0, 9, -15],
 [-2, 5, 0, -3, 5]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[-10, -6, 2, -5, 9],
 [10, 6, -2, 5, -9],
 [30, 26, -14, 19, -23],
 [30, 24, -12, 18, -24],
 [-5, -10, 8, -6, 1]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[15, -17, -29, -7, 10],
 [19, -26, -33, -17, 5],
 [-17, 23, 27, 47, 4],
 [-11, 19, 13, 50, 13],
 [13, -24, -19, -4, -2]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[23, -17, 10, -6, 7],
 [23, -45, 2, -21, 27],
 [-30, 70, 0, 35, -45],
 [-16, -4, -12, -3, 5],
 [3, 7, 6, -1, 0]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[5, 10, 25, 30, -5],
 [6, 12, 30, 36, -6],
 [2, 4, 10, 12, -2],
 [-5, -10, -25, -30, 5],
 [4, 8, 20, 24, -4]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-30, 15, 15, -15, 5],
 [-6, 3, 3, -3, 1],
 [18, -9, -9, 9, -3],
 [-36, 18, 18, -18, 6],
 [0, 0, 0, 0, 0]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[56, -2, -14, 6, 26],
 [5, -7, -6, 10, -9],
 [-46, 6, -31, -21, 23],
 [36, -34, -49, 25, 9],
 [17, 12, -5, 9, -6]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[2, 6, -10, -10, 4],
 [-4, -12, 20, 20, -8],
 [-6, -18, 30, 30, -12],
 [-1, -3, 5, 5, -2],
 [6, 18, -30, -30, 12]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-14, 0, 4, 8, 3],
 [-15, -3, -6, -5, -14],
 [-25, 55, 30, -20, -45],
 [-54, 26, 20, 4, -26],
 [2, 4, 12, 15, 20]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[-1, 5, 4, 2, -3],
 [-6, 0, -21, -23, -13],
 [-6, 24, 15, 5, -17],
 [-11, 19, -10, -20, -27],
 [8, -10, 13, 19, 19]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[0, 0, 0, 0, 0],
 [18, -12, 12, -18, 15],
 [30, -20, 20, -30, 25],
 [12, -8, 8, -12, 10],
 [-24, 16, -16, 24, -20]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[9, -3, -12, -12, 24],
 [17, -36, -11, -11, -27],
 [42, -66, -36, -36, -12],
 [-21, 33, 18, 18, 6],
 [-22, 42, 16, 16, 24]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-2, 5, -24, -22, 2],
 [9, 14, -33, -33, 4],
 [0, -15, 24, 18, -4],
 [8, -34, 24, 4, -8],
 [22, 5, -9, -19, 1]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[18, 5, 17, 22, 6],
 [10, 4, 18, 11, -4],
 [-18, -6, -24, -21, 0],
 [-4, 4, 32, -10, -32],
 [0, -3, -21, 3, 18]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[12, -16, -24, 8, -16],
 [12, -16, -24, 8, -16],
 [0, 0, 0, 0, 0],
 [-6, 8, 12, -4, 8],
 [-3, 4, 6, -2, 4]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[0, 0, 0, 0, 0],
 [20, -8, 20, -12, -12],
 [-15, 6, -15, 9, 9],
 [20, -8, 20, -12, -12],
 [10, -4, 10, -6, -6]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[-13, 26, 30, -25, -28],
 [-7, -10, -6, -19, -4],
 [-8, 9, 12, -17, -14],
 [1, -6, -6, 1, 4],
 [15, -25, -30, 30, 30]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[16, 14, 16, 7, -13],
 [2, -2, -8, -11, -1],
 [-34, -32, -40, -22, 28],
 [1, -4, -12, -15, 0],
 [-16, -20, -32, -26, 14]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[7, -10, -13, -18, 40],
 [-13, 0, 17, 12, -20],
 [28, 12, -32, -12, 8],
 [3, -8, -7, -12, 28],
 [-13, -13, 12, -3, 18]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[-30, 20, 14, 8, -4],
 [21, 11, 8, 2, 5],
 [33, 0, 9, -2, 6],
 [3, 33, 36, 10, 3],
 [-16, -3, -11, 0, -3]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[-16, 22, 4, 41, 9],
 [58, 18, 42, -18, -33],
 [9, -18, 14, 17, -30],
 [4, -12, -28, -70, -40],
 [20, 2, 40, 51, 17]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-36, -24, -30, -24, 18],
 [18, 12, 15, 12, -9],
 [30, 20, 25, 20, -15],
 [-24, -16, -20, -16, 12],
 [0, 0, 0, 0, 0]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[30, 24, 0, -6, -36],
 [-30, -24, 0, 6, 36],
 [-30, -24, 0, 6, 36],
 [0, 0, 0, 0, 0],
 [10, 8, 0, -2, -12]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[12, 18, 3, 3, -15],
 [14, 21, 11, -19, -10],
 [6, 9, 9, -21, 0],
 [0, 0, 0, 0, 0],
 [14, 21, 11, -19, -10]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-3, -12, -33, -27, -38],
 [1, -2, -9, -7, -10],
 [-9, 9, 51, 39, 56],
 [-30, -21, 0, -6, -6],
 [-18, 0, 42, 30, 44]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-19, -9, -18, -3, -18],
 [-4, -18, 0, -21, -9],
 [14, -22, 20, -34, 4],
 [16, 4, 16, -2, 14],
 [30, -18, 36, -36, 18]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-24, 2, 2, 0, -38],
 [-36, -2, -33, 35, -19],
 [-27, 18, -34, 23, -21],
 [11, -12, 30, -21, -3],
 [3, 3, -17, 13, 18]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[8, 16, -24, 12, 20],
 [6, 12, -18, 9, 15],
 [-12, -24, 36, -18, -30],
 [-4, -8, 12, -6, -10],
 [4, 8, -12, 6, 10]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[-7, 1, -26, 6, 2],
 [6, -20, -20, -4, 34],
 [31, -12, 32, -25, 34],
 [11, 50, 6, -10, -35],
 [-41, -69, -44, 35, 33]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[-3, -12, -6, -9, -21],
 [23, 38, 19, 15, -19],
 [-10, -10, -5, 0, 30],
 [-27, -42, -21, -15, 31],
 [-9, -6, -3, 3, 37]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[17, -27, 36, -26, 12],
 [41, 29, -33, 35, -20],
 [12, -23, -5, 7, 1],
 [29, 21, -37, 35, -25],
 [-71, -28, 9, -21, 18]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[25, 60, 41, -5, 64],
 [-20, -24, -18, -2, -22],
 [-33, 12, -1, -11, 24],
 [-20, 21, 0, 3, 25],
 [-20, -18, -26, 16, -24]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[9, 5, -1, 20, -32],
 [-24, -6, -8, -34, 21],
 [51, 3, 5, 44, -10],
 [5, 11, 20, 36, -27],
 [2, 8, 8, 20, -5]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-13, -3, -13, -26, -19],
 [5, 14, 32, 34, 42],
 [-1, -8, -39, -35, -49],
 [-64, -37, -24, 4, -14],
 [-12, 6, -6, -3, -4]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[-40, -15, -53, -27, 25],
 [25, -78, -28, 24, -32],
 [0, -14, -1, -2, 36],
 [-8, -5, -23, -17, 7],
 [20, -14, -3, 4, -27]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[15, 0, -25, 15, 15],
 [15, 0, -25, 15, 15],
 [-15, 0, 25, -15, -15],
 [15, 0, -25, 15, 15],
 [0, 0, 0, 0, 0]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[0, 0, 0, 0, 0],
 [0, 0, 8, -10, -6],
 [0, 0, -20, 25, 15],
 [0, 0, -20, 25, 15],
 [0, 0, 8, -10, -6]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[0, 18, -18, 0, 15],
 [0, 12, -12, 0, 10],
 [0, -6, 6, 0, -5],
 [0, 24, -24, 0, 20],
 [0, -18, 18, 0, -15]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[-35, 30, -50, -30, 25],
 [-6, -22, 1, 2, 3],
 [-42, -30, 39, -24, 51],
 [62, -13, 53, 31, -55],
 [39, -29, 11, 43, -38]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[0, -11, -24, 2, -22],
 [0, -3, -10, 2, -8],
 [0, 11, -14, 14, 0],
 [0, -1, 3, -2, 1],
 [0, -4, -7, 0, -7]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[0, -10, -20, 25, -5],
 [0, 0, 0, 0, 0],
 [0, 2, 4, -5, 1],
 [0, 12, 24, -30, 6],
 [0, -4, -8, 10, -2]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[0, 9, 7, -16, 9],
 [9, 0, -4, -14, 9],
 [-9, 0, 4, 14, -9],
 [-21, 15, 21, 6, -6],
 [20, -4, -12, -24, 16]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[-36, -54, 7, 16, -15],
 [4, 6, 21, 20, 18],
 [-8, -12, 14, 16, 6],
 [-8, -12, 14, 16, 6],
 [24, 36, 2, -4, 15]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[-2, -14, 12, 12, -12],
 [-13, -7, -20, -54, 36],
 [-24, -9, -28, 22, -8],
 [-39, -27, -14, -15, -3],
 [-14, 1, 2, 23, -25]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-3, -9, 4, 1, 15],
 [-10, 2, 0, -6, 6],
 [-11, 31, -12, -15, -33],
 [28, -44, 16, 28, 36],
 [-12, 36, -14, -17, -39]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[13, 8, 17, -61, 25],
 [-34, -16, 18, -18, 54],
 [-30, -5, 9, 23, 19],
 [-37, -16, 11, 9, 39],
 [-1, 15, 8, 8, -8]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[-24, -8, 0, 3, 10],
 [-15, 2, 0, -13, -6],
 [27, 6, 0, 3, -6],
 [42, 4, 0, 16, 0],
 [33, 18, 0, -19, -26]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[8, 24, 12, -8, -16],
 [6, 18, 9, -6, -12],
 [8, 24, 12, -8, -16],
 [0, 0, 0, 0, 0],
 [-8, -24, -12, 8, 16]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[9, 18, 9, -3, 9],
 [0, 0, 0, 0, 0],
 [-12, -24, -12, 4, -12],
 [-12, -24, -12, 4, -12],
 [18, 36, 18, -6, 18]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-42, 16, -16, -26, -12],
 [13, -26, 8, -14, 25],
 [-59, -11, -22, -59, 16],
 [22, -29, 2, 19, 25],
 [31, 42, 24, 18, -41]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[0, 6, -6, 9, 0],
 [0, -6, 6, -9, 0],
 [0, 6, -6, 9, 0],
 [0, 0, 0, 0, 0],
 [0, 10, -10, 15, 0]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[-20, -16, -8, 12, -12],
 [15, 12, 6, -9, 9],
 [-5, -4, -2, 3, -3],
 [-30, -24, -12, 18, -18],
 [-20, -16, -8, 12, -12]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[30, 12, 30, -9, -33],
 [-6, 12, -15, 27, 21],
 [24, 16, 20, 4, -20],
 [18, 20, 10, 17, -7],
 [-28, -16, -25, 0, 26]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[19, 37, -25, 17, 17],
 [7, -15, -7, -13, -31],
 [-10, -18, 1, -6, 34],
 [-24, 16, 54, 24, 24],
 [37, -19, -16, -12, -23]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[-60, -10, 25, -37, 10],
 [-28, -16, -8, -28, 2],
 [-22, -8, 35, 1, -27],
 [-66, -19, 34, -30, -9],
 [-68, -20, 62, -18, -34]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[13, 7, -11, -10, 7],
 [64, 2, 15, -28, -33],
 [-15, 2, 20, 16, -5],
 [-24, -1, -7, -4, 7],
 [-37, -17, 21, 58, 3]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[20, -5, -55, 10, 30],
 [12, -15, -3, -20, -8],
 [-4, 37, -7, 28, 24],
 [20, 21, -4, -11, 9],
 [-16, 6, 59, -17, -33]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-1, -33, 37, -21, 8],
 [-11, -20, 17, 18, 10],
 [10, -16, 20, 16, -16],
 [-2, -21, 20, -10, 6],
 [-40, -32, 10, -1, 52]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[9, -4, -22, -10, -31],
 [48, -32, -4, 62, -24],
 [-21, 20, -6, -24, 11],
 [18, -19, -48, -12, -66],
 [35, -3, -70, 58, -41]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[31, 11, 9, -20, 25],
 [63, 25, 3, -56, 62],
 [-3, -48, -9, 30, 12],
 [33, 40, 21, -36, 14],
 [34, -39, -18, -6, 57]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[7, 14, -2, -2, 2],
 [9, 9, 13, 15, 0],
 [4, 2, 11, 0, -27],
 [-13, -41, 31, 25, -28],
 [-9, -36, 36, 24, -42]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-11, 11, -1, -3, 8],
 [19, -19, 11, -15, -16],
 [19, -19, 11, -15, -16],
 [-5, 5, -2, 2, 4],
 [39, -39, 2, 14, -28]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[30, -36, -24, 6, -24],
 [19, -12, -20, 29, 16],
 [25, -39, -16, -16, -46],
 [20, -33, -12, -17, -42],
 [3, -9, 0, -12, -18]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[26, -24, 40, -54, 14],
 [5, 14, 34, -19, 3],
 [17, 20, 50, -55, 3],
 [21, 2, 68, -67, 11],
 [-22, 31, 46, -5, -3]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-8, -8, -16, -20, 20],
 [0, 0, 0, 0, 0],
 [-8, -8, -16, -20, 20],
 [4, 4, 8, 10, -10],
 [4, 4, 8, 10, -10]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[7, 22, -10, 16, -17],
 [38, 30, 3, -2, -14],
 [9, 12, -15, -26, 11],
 [-33, -26, -10, -16, 23],
 [75, 18, 36, -36, 3]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-3, -6, -18, 5, -34],
 [-13, -17, 24, 1, 52],
 [9, 13, -12, -3, -30],
 [26, 24, -36, 14, -40],
 [15, 17, -24, 3, -42]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[17, -15, 19, -1, -18],
 [3, 3, 6, 11, 12],
 [8, 6, 9, 50, -26],
 [-11, 10, -22, -11, 2],
 [1, -16, 30, -17, 42]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-13, 53, 46, 26, 18],
 [-6, 33, 30, 20, 5],
 [-2, 18, 7, 5, 1],
 [-20, 10, 18, 28, 70],
 [9, -16, -23, -25, -26]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[30, -7, -25, -9, -3],
 [-8, 20, 31, 2, 11],
 [34, 34, 3, -16, 11],
 [3, 56, 29, -22, 12],
 [-19, 36, 16, 28, 13]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-21, 0, -30, 16, 15],
 [-18, 15, -39, -28, -22],
 [-50, 10, -78, 22, 22],
 [-7, -37, -9, -45, -3],
 [-25, -13, -39, -16, 5]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[18, -61, 38, 0, -7],
 [-4, -25, 22, 12, 10],
 [16, 2, 18, 24, -51],
 [-16, -1, 45, 72, -22],
 [13, -51, 47, 18, -19]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[6, -26, 36, 22, 22],
 [-31, -16, -15, -4, -29],
 [-23, -14, 9, 34, 21],
 [-43, -8, -21, 16, -11],
 [1, -8, -6, -26, -32]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-53, -13, 34, -26, 10],
 [13, -17, -9, 58, 19],
 [59, 1, -44, 18, -26],
 [48, 20, -31, 16, -11],
 [-35, 8, 11, -72, -28]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[4, -21, 13, 28, -23],
 [-22, 33, 39, -14, -5],
 [-7, 18, 6, 1, -26],
 [-3, -3, 17, 19, -29],
 [-5, 15, -5, -35, 49]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[0, -9, -6, -6, 18],
 [0, -6, -4, -4, 12],
 [0, 12, 8, 8, -24],
 [0, -6, -4, -4, 12],
 [0, -15, -10, -10, 30]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-3, 18, 3, 6, 3],
 [1, -6, -1, -2, -1],
 [3, -18, -3, -6, -3],
 [-3, 18, 3, 6, 3],
 [-4, 24, 4, 8, 4]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[-2, 36, 23, -44, 14],
 [0, 30, 22, -22, 4],
 [27, -19, -26, 8, 17],
 [-43, -19, 0, 4, -11],
 [33, -29, -32, 35, 24]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-30, -18, -36, 24, 30],
 [-15, -9, -18, 12, 15],
 [-15, -9, -18, 12, 15],
 [0, 0, 0, 0, 0],
 [10, 6, 12, -8, -10]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-21, -62, 5, 8, -8],
 [-8, 11, 12, -49, -25],
 [-2, 8, 52, -26, -72],
 [37, 39, -37, -10, 46],
 [-20, 23, 41, -19, -54]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[5, 15, 5, 0, -30],
 [6, 18, 6, 0, -36],
 [-12, -14, -11, -3, 35],
 [-2, 16, -1, -3, -25],
 [4, -10, 3, 3, 13]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[9, -1, -33, 19, 15],
 [-32, 1, 60, -32, -26],
 [-29, -42, 33, 17, -41],
 [-26, 2, 54, -30, -23],
 [14, -16, -26, 26, 1]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-24, 2, 22, 15, 12],
 [-8, 3, -38, 4, -14],
 [28, -55, 38, -25, 8],
 [10, -9, -23, -30, -12],
 [4, -24, 10, -4, 2]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[2, -1, 69, -52, 82],
 [51, -40, -27, 3, -66],
 [13, -15, -30, 25, -50],
 [37, -30, 11, -19, -12],
 [23, -10, 3, -19, -6]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[-21, 23, -11, -17, 16],
 [-19, 19, -17, -7, 14],
 [-10, 11, -15, -2, 7],
 [-18, 27, 9, -42, 15],
 [-20, 14, 35, -28, 18]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[-6, 0, -18, 3, 6],
 [21, -6, 36, 3, -18],
 [-36, 16, -36, -18, 28],
 [-1, -2, -12, 5, 2],
 [3, -6, -18, 12, 0]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[-45, 13, -11, -43, 0],
 [-9, 32, 14, -11, -39],
 [21, -27, -32, 46, 46],
 [-51, -10, -35, -9, 22],
 [-6, 48, 21, -48, -35]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[3, -18, -9, -6, 3],
 [-21, -18, -33, -2, 7],
 [28, -24, 12, -12, 0],
 [-3, 18, 9, 6, -3],
 [-30, 36, -6, 16, -2]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[24, 0, 16, -8, 8],
 [-30, 0, -20, 10, -10],
 [6, 0, 4, -2, 2],
 [-18, 0, -12, 6, -6],
 [-12, 0, -8, 4, -4]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-14, 12, -11, 17, -16],
 [2, -12, -19, -5, -8],
 [-6, 16, 17, 10, 4],
 [-18, 20, -5, 23, -16],
 [-4, -8, -26, 2, -16]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[-6, -3, 18, 0, 0],
 [-4, -2, 12, 0, 0],
 [2, 1, -6, 0, 0],
 [12, 6, -36, 0, 0],
 [-6, -3, 18, 0, 0]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-8, -10, -20, -16, 6],
 [-27, 8, -28, 8, 5],
 [-5, 42, -32, 8, 21],
 [-29, 26, -36, 16, 11],
 [7, 13, -8, -4, 9]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[48, 60, 24, 72, -66],
 [40, 10, 18, 2, -2],
 [-2, 3, 4, 7, -15],
 [-6, -11, -10, -17, 28],
 [58, 17, 32, 9, -19]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[15, -1, -6, -8, 1],
 [-30, 2, 12, 16, -2],
 [9, 19, 2, 12, -5],
 [3, 4, 0, 2, -1],
 [-30, -12, 8, 4, 2]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[0, 7, 5, 12, -13],
 [4, 9, 17, 9, -21],
 [42, -42, 9, 9, 6],
 [-24, 22, -2, -18, 2],
 [-8, -1, -15, -3, 13]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[-25, -10, 20, -30, 15],
 [-15, -6, 12, -18, 9],
 [10, 4, -8, 12, -6],
 [-10, -4, 8, -12, 6],
 [30, 12, -24, 36, -18]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[-36, 6, -12, -6, 36],
 [-6, 1, -2, -1, 6],
 [-12, 2, -4, -2, 12],
 [0, 0, 0, 0, 0],
 [12, -2, 4, 2, -12]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[-7, -25, 14, -37, -33],
 [-1, -35, 25, -29, -39],
 [-30, -9, 9, -24, -13],
 [9, -58, 20, -64, -25],
 [-27, 51, 6, 66, -26]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[4, -10, -60, -7, -6],
 [3, -3, -33, -6, -6],
 [-12, -42, -12, 33, 42],
 [-3, 3, 33, 6, 6],
 [5, 13, -7, -13, -16]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[-44, -4, -34, -42, 14],
 [4, 19, 7, 5, -33],
 [39, -21, 15, 18, 3],
 [-14, -11, -14, -16, 18],
 [7, 0, -3, -8, -23]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-3, -16, 7, 9, -1],
 [-8, -42, 17, 23, -4],
 [-4, -24, 16, 16, 4],
 [2, 10, -3, -5, 2],
 [0, -10, 25, 15, 20]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[4, 0, 20, -8, 24],
 [5, 0, 25, -10, 30],
 [1, 0, 5, -2, 6],
 [-6, 0, -30, 12, -36],
 [-2, 0, -10, 4, -12]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[-12, -6, 52, 30, 44],
 [12, 10, 11, -11, 7],
 [-8, -5, 60, 28, 52],
 [10, -8, -62, -29, -42],
 [12, 5, -75, -37, -63]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[22, -64, 8, -42, -4],
 [20, -28, -24, -34, -4],
 [-35, 24, 2, 47, 36],
 [-43, -44, 47, 38, 57],
 [-10, -44, 46, 8, 15]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[14, 28, 1, -15, -2],
 [14, 10, 19, 39, 16],
 [20, 6, -16, -12, 26],
 [-40, -26, 6, -6, -42],
 [0, -16, -4, 12, 14]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-25, 13, 28, -13, -36],
 [9, -6, -16, 49, 21],
 [30, -12, -16, 35, -11],
 [-37, 19, 8, -1, 40],
 [6, 51, 0, 8, -1]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[24, -4, 37, -16, 63],
 [-17, -5, 38, 18, 59],
 [33, -9, 4, -4, 23],
 [-41, 7, 11, 12, 0],
 [69, -9, -30, 15, 6]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[13, 3, -3, -18, -17],
 [2, 6, 6, -8, -6],
 [-26, 12, 27, 19, 23],
 [-1, -3, -3, 4, 3],
 [30, -18, -36, -18, -24]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[5, -7, 14, 38, -40],
 [14, 26, 14, -16, 42],
 [4, -26, 43, 28, 13],
 [-35, -71, 22, -20, 34],
 [-6, 22, -18, -24, -14]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[-18, -3, -18, 12, 6],
 [18, 3, 18, -12, -6],
 [-36, -6, -36, 24, 12],
 [-18, -3, -18, 12, 6],
 [-12, -2, -12, 8, 4]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-8, 12, 24, 16, -20],
 [8, -12, -24, -16, 20],
 [12, -18, -36, -24, 30],
 [-12, 18, 36, 24, -30],
 [-6, 9, 18, 12, -15]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[5, -4, -5, 3, -4],
 [12, -8, -12, 1, -5],
 [27, -12, -27, -21, 6],
 [-4, 8, 4, -21, 17],
 [-42, 24, 42, 12, 6]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[12, 5, 44, -2, -31],
 [10, 2, -12, 14, -28],
 [-6, -14, 4, -25, 37],
 [24, -29, -4, -23, -10],
 [9, -11, -14, -4, -5]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[-12, 4, 4, -24, 4],
 [-12, 4, 4, -24, 4],
 [18, -6, -6, 36, -6],
 [-18, 6, 6, -36, 6],
 [12, -4, -4, 24, -4]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-18, -4, 18, -6, -8],
 [-4, -6, 12, -6, -10],
 [-2, -3, 6, -3, -5],
 [-5, 4, -3, 3, 6],
 [-22, 13, -6, 9, 19]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[1, 7, -1, 4, -2],
 [-4, 19, -10, -78, 5],
 [-3, -4, -1, -26, 3],
 [4, 22, -7, -14, 1],
 [-6, -26, 14, 56, -12]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[4, 8, -6, 0, -12],
 [0, 19, 17, -32, -16],
 [-2, 34, 5, -25, -16],
 [14, -36, 11, -1, -16],
 [10, 36, 1, -29, -44]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[1, 30, 42, 2, -19],
 [67, -23, 2, 28, -43],
 [24, -62, -26, -41, -24],
 [-41, 11, 13, -36, 12],
 [-7, 42, 37, 17, 2]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[2, 24, -20, 32, -30],
 [6, -4, -2, -10, -36],
 [5, 24, -20, 26, -21],
 [18, 32, -28, 14, -9],
 [8, -12, 6, -28, -3]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[-31, 25, 4, 32, 6],
 [37, 5, 6, -10, -10],
 [15, 15, 6, 30, 18],
 [12, -50, -14, -46, 0],
 [-39, 5, -3, 11, 2]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[23, 16, 2, -10, 23],
 [20, -24, 20, -22, -12],
 [29, -20, 8, -19, -13],
 [2, -20, -10, 3, -28],
 [5, 4, -16, 7, -4]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[0, -8, -4, 0, -11],
 [-8, -24, 0, 0, -24],
 [-6, -42, -12, 0, -51],
 [-14, -10, 16, 0, 2],
 [4, -12, -12, 0, -21]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-60, 44, 11, 0, 17],
 [12, -4, -38, -26, 38],
 [65, -7, -71, -11, -5],
 [50, -22, -3, 20, -29],
 [-58, 22, 16, -16, 18]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-20, 33, 5, 3, 19],
 [4, 32, -41, 11, -21],
 [26, -15, -42, 18, -35],
 [23, 16, 2, 38, 5],
 [-46, -8, 2, -26, 18]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[9, -19, -9, -12, -6],
 [43, -7, -47, -30, -26],
 [22, -29, -24, -25, -16],
 [7, 7, -13, -8, -12],
 [-20, 40, 15, 20, 5]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[28, 60, -20, -54, -12],
 [28, 60, -20, -54, -12],
 [-6, -12, 3, 11, 4],
 [-8, -24, 16, 20, -8],
 [-24, -54, 21, 48, 6]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[-24, 24, -30, 36, 36],
 [-20, 20, -25, 30, 30],
 [16, -16, 20, -24, -24],
 [24, -24, 30, -36, -36],
 [16, -16, 20, -24, -24]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[3, -18, 3, 12, 9],
 [-1, 6, -1, -4, -3],
 [1, -6, 1, 4, 3],
 [5, -30, 5, 20, 15],
 [-2, 12, -2, -8, -6]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[7, -10, 29, -8, -51],
 [10, -38, 62, -8, -2],
 [-11, 9, 16, 25, -10],
 [3, -35, 12, -9, -10],
 [6, -7, -4, -13, -2]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[-7, -5, -4, 4, 2],
 [1, -1, -6, 0, -6],
 [35, 25, 20, -20, -10],
 [12, 0, -26, -4, -32],
 [26, 22, 28, -16, 4]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[-12, -9, 3, -20, 10],
 [48, -9, -27, 0, 0],
 [14, -6, -9, -6, 3],
 [-42, 9, 24, 2, -1],
 [18, -9, -12, -10, 5]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-3, -3, 3, -4, -6],
 [9, 9, -9, 12, 18],
 [-15, -15, 15, -20, -30],
 [-12, -12, 12, -16, -24],
 [-9, -9, 9, -12, -18]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[30, 36, -60, 51, -64],
 [-10, 41, 42, -16, -13],
 [43, 5, -13, -2, -31],
 [-67, 31, -21, 51, 31],
 [-10, -7, -9, 8, 6]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[6, -36, 19, 23, -25],
 [3, 2, -3, 44, -5],
 [26, -5, 30, -37, -20],
 [16, -33, 18, -24, -29],
 [31, -8, 38, 16, -29]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[43, 49, 31, 33, -9],
 [-12, -24, -18, -8, -6],
 [30, 56, 52, 10, -22],
 [13, 28, 34, 13, 7],
 [-21, -19, -23, -24, 3]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[-4, -3, 5, 0, 3],
 [-12, -9, 15, 0, 9],
 [-4, -3, 5, 0, 3],
 [-24, -18, 30, 0, 18],
 [-4, -3, 5, 0, 3]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[1, 3, 3, -6, 4],
 [5, 15, 15, -30, 20],
 [5, 15, 15, -30, 20],
 [6, 18, 18, -36, 24],
 [6, 18, 18, -36, 24]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-19, 3, 14, 16, 1],
 [50, 54, -31, 17, 27],
 [-17, -13, 16, 10, -31],
 [-15, -37, 1, -27, -40],
 [10, 10, -27, -21, 11]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[8, -16, -8, -12, 4],
 [0, 0, 0, 0, 0],
 [4, -8, -4, -6, 2],
 [-8, 16, 8, 12, -4],
 [-8, 16, 8, 12, -4]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[21, 17, -10, -32, -23],
 [11, -14, 17, 18, -40],
 [-31, -4, 14, 15, 25],
 [-25, 41, -3, -7, 14],
 [36, 14, 4, -58, -64]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[16, 3, 27, -4, 1],
 [-8, -18, 6, -32, -40],
 [-1, 7, -19, 18, 12],
 [8, 23, -17, 44, 49],
 [20, 3, 27, -4, -5]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[10, -2, 10, 4, 0],
 [-30, 6, -30, -12, 0],
 [0, 0, 0, 0, 0],
 [-5, 1, -5, -2, 0],
 [0, 0, 0, 0, 0]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[4, 0, 0, -6, 8],
 [-36, 36, 24, -18, 6],
 [24, -36, -24, 36, -30],
 [-8, 6, 4, 0, -3],
 [36, -36, -24, 18, -6]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[6, -30, -41, -20, -21],
 [6, 25, 36, 24, 23],
 [18, -20, -25, -4, -7],
 [-18, 25, 32, 8, 11],
 [-6, 20, 27, 12, 13]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[9, 29, 13, -26, -3],
 [1, 8, -20, -20, -13],
 [-15, 6, 12, 12, -3],
 [-15, 28, 20, -4, -9],
 [19, 56, 58, -32, 11]]

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[User]
Calculate the rank of matrix A where A =
[[-16, 9, 6, -5, -5],
 [9, -11, 11, -10, 15],
 [42, 16, -34, -74, -38],
 [8, 0, -12, 8, -6],
 [-38, 14, -2, 48, -10]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[29, -12, -35, -12, -23],
 [65, 4, 5, 26, -45],
 [57, 10, 10, 32, -34],
 [-13, -18, -45, -49, -24],
 [-50, -22, 0, -30, 38]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[-4, 8, 16, 12, 20],
 [2, -4, -8, -6, -10],
 [-4, 8, 16, 12, 20],
 [4, -8, -16, -12, -20],
 [-3, 6, 12, 9, 15]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[-4, 20, 31, 0, 20],
 [-29, -3, -26, 7, -7],
 [18, -12, -39, 12, -42],
 [-37, -7, 6, -13, 33],
 [-11, -7, -28, 7, -17]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[34, -2, -36, -8, -23],
 [-24, 6, 30, -2, 30],
 [12, 3, -9, -9, 3],
 [38, -1, -39, -11, -22],
 [0, 3, 3, -5, 9]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-4, -10, -12, -14, 4],
 [11, 18, 23, 24, -4],
 [0, 19, 20, 29, -14],
 [15, 28, 35, 38, -8],
 [-12, -11, -16, -13, -2]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[39, 42, -54, -5, -22],
 [-18, 12, 25, 15, 5],
 [17, 5, 0, 52, 26],
 [-1, 24, -2, 17, 54],
 [0, -18, -22, -60, -17]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-43, -40, -2, -5, 19],
 [-9, 32, 11, -25, -18],
 [-5, 20, 0, -15, -25],
 [14, 12, 8, 2, 10],
 [-8, -46, -13, 22, 21]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[8, -6, 8, 4, 10],
 [20, -15, 20, 10, 25],
 [-12, 9, -12, -6, -15],
 [16, -12, 16, 8, 20],
 [4, -3, 4, 2, 5]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[-3, 6, 6, 5, 6],
 [-15, 30, 30, 25, 30],
 [-6, 12, 12, 10, 12],
 [9, -18, -18, -15, -18],
 [3, -6, -6, -5, -6]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-9, -8, 6, -10, 18],
 [16, 49, -4, -32, 15],
 [-19, 8, -18, 18, 2],
 [-19, -19, -12, 30, -1],
 [-26, -83, 1, 60, -12]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[68, 31, -74, 19, 9],
 [-10, -19, -7, -23, 35],
 [-37, -21, 37, -19, -1],
 [72, 46, -72, 30, 22],
 [48, 13, -57, 45, -17]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[-25, -2, -25, 13, -45],
 [-2, 52, 50, -38, 18],
 [-20, 24, 28, -16, -20],
 [2, 6, -14, -1, -14],
 [4, -20, -40, 22, 0]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[30, 0, 18, -12, 24],
 [15, -8, 15, -22, 28],
 [25, 4, 12, -2, 12],
 [-5, 0, -3, 2, -4],
 [-25, -4, -12, 2, -12]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[12, 21, -8, -16, -28],
 [-4, -3, 2, 2, 6],
 [-16, -14, 23, 11, -1],
 [32, -8, -29, 9, 12],
 [-16, -46, 10, 36, 59]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[39, 18, -9, -3, -7],
 [54, 12, -18, -6, -10],
 [3, 24, 9, 3, 0],
 [-3, 18, 9, 3, 1],
 [23, 16, -3, -1, -4]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[-5, -25, 13, 11, -23],
 [27, 19, -35, -7, 25],
 [-15, -3, 18, 0, -9],
 [0, 12, -24, 6, 48],
 [11, 19, -14, -10, 13]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[6, -1, -9, -20, -15],
 [8, 5, 26, 5, 18],
 [-12, -2, -6, 20, 6],
 [6, -1, -9, -20, -15],
 [-12, -4, -18, 10, -6]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-60, 19, -36, -33, 26],
 [-15, 12, 69, -18, -21],
 [3, -8, -24, 23, -27],
 [-12, 32, 18, -26, -36],
 [17, 48, -16, -43, -13]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-14, -30, -17, 29, -23],
 [-18, 6, 1, 27, -27],
 [27, 1, 15, -3, 18],
 [-46, 45, 1, 9, -35],
 [35, -39, 15, 37, -4]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-36, -18, 0, 0, -6],
 [-12, -6, 0, 0, -2],
 [-12, -6, 0, 0, -2],
 [30, 15, 0, 0, 5],
 [0, 0, 0, 0, 0]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[31, 5, 19, 105, -28],
 [-10, -16, 17, 50, -8],
 [-12, -1, 7, 11, -6],
 [0, -48, 39, -21, 36],
 [-41, -26, -16, -36, 18]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[-3, 11, 5, -1, -10],
 [-18, 66, 30, -6, -60],
 [-26, 18, -2, -11, -1],
 [-17, 21, -35, -8, 17],
 [37, -3, 4, 16, -15]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[12, 0, 12, -24, -30],
 [-6, 0, -6, 12, 15],
 [8, 0, 8, -16, -20],
 [10, 0, 10, -20, -25],
 [-12, 0, -12, 24, 30]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-20, 16, 0, -2, 2],
 [-22, -16, 42, 23, 19],
 [-8, -20, 33, 19, 14],
 [40, -20, -15, -5, -10],
 [-2, 4, -3, -2, -1]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[9, 18, -42, 39, -36],
 [16, -3, -14, 4, 6],
 [-8, -6, 20, -16, 12],
 [-1, -12, 22, -23, 24],
 [6, -3, -2, -2, 6]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-23, 14, -33, 38, 9],
 [-2, 16, -12, 14, 28],
 [5, -6, 33, -44, -17],
 [57, -21, 11, 17, 37],
 [44, -16, -18, 2, 8]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[0, -12, 18, -12, -18],
 [-46, -70, 23, 10, 23],
 [21, 22, -1, 2, -20],
 [-5, -33, 27, 17, -22],
 [-28, -46, 18, 6, 10]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[1, -28, 1, 27, 0],
 [28, 7, 5, 14, -13],
 [8, 9, -17, -14, -23],
 [18, -26, -16, 25, -29],
 [-13, -5, -28, -21, -21]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[0, 0, 0, 0, 0],
 [-3, -3, 9, 18, 3],
 [-4, -4, 12, 24, 4],
 [-6, -6, 18, 36, 6],
 [0, 0, 0, 0, 0]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[-20, 22, -26, -3, -11],
 [-44, 8, -40, -10, -6],
 [-19, 23, 11, -54, -19],
 [-34, 10, -15, -32, -10],
 [-8, -20, -5, 6, 10]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[6, 4, 6, -8, -6],
 [15, 10, 15, -20, -15],
 [15, 10, 15, -20, -15],
 [3, 2, 3, -4, -3],
 [-9, -6, -9, 12, 9]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[20, 14, -24, -13, -34],
 [9, 20, -27, -34, -9],
 [22, 12, -18, -6, -34],
 [24, 12, 6, 3, -10],
 [10, -2, 12, 16, -6]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-34, -38, 11, 25, 9],
 [-12, -14, -19, 47, -27],
 [-36, -24, 48, -32, 44],
 [-36, -2, 9, 0, 16],
 [-2, 8, 16, -11, -2]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[-20, 25, 10, 0, 20],
 [-20, 25, 10, 0, 20],
 [-4, 5, 2, 0, 4],
 [8, -10, -4, 0, -8],
 [-8, 10, 4, 0, 8]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-43, -6, -12, -8, 34],
 [-18, -11, -18, 9, 29],
 [-5, -14, -34, 4, -4],
 [-23, 5, 12, -13, 15],
 [-29, -21, -26, -9, 34]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-15, 5, 5, 30, 0],
 [-3, 1, 1, 6, 0],
 [-12, 4, 4, 24, 0],
 [15, -5, -5, -30, 0],
 [3, -1, -1, -6, 0]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[5, -30, -15, 20, -15],
 [6, -36, -18, 24, -18],
 [-1, 6, 3, -4, 3],
 [6, -36, -18, 24, -18],
 [-6, 36, 18, -24, 18]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[4, -18, -2, -10, 6],
 [-10, 1, 11, -3, -7],
 [4, -18, -2, -10, 6],
 [26, -7, -28, 5, 19],
 [-16, 6, 17, -2, -12]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[10, 22, 9, -10, 2],
 [-14, -14, -27, -34, 2],
 [0, 42, 54, 60, 12],
 [34, 16, 9, -10, -10],
 [-10, -50, -54, -48, -10]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[5, 5, -6, 2, 6],
 [20, 20, -24, 8, 24],
 [15, 15, -18, 6, 18],
 [0, 0, 0, 0, 0],
 [-5, -5, 6, -2, -6]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-13, 12, -20, -5, -39],
 [-12, 36, -24, -24, -36],
 [6, -36, 16, 26, 18],
 [-3, 54, -16, -41, -9],
 [-8, 60, -24, -44, -24]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[-7, 5, -24, 12, 48],
 [-18, 13, 17, -33, -24],
 [35, 0, 22, -8, -33],
 [-3, 0, -26, 18, 27],
 [-8, -15, 18, 1, -36]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[-10, -6, 10, 10, 8],
 [10, 6, -10, -10, -8],
 [30, 18, -30, -30, -24],
 [20, 12, -20, -20, -16],
 [5, 3, -5, -5, -4]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-19, -39, -8, 4, -22],
 [31, 42, -20, -34, 27],
 [-39, -9, 66, 48, 6],
 [-1, -1, 1, 4, 3],
 [-43, -12, 27, -26, 49]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[-4, -25, 10, 33, -29],
 [8, -38, 0, 14, -33],
 [10, -4, -7, 18, 8],
 [13, 12, -8, 11, 1],
 [14, 14, -19, -44, 32]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[43, 53, 22, 27, 76],
 [-3, 15, -66, 27, -34],
 [-79, -31, 14, -20, 1],
 [-49, -9, 2, -19, 4],
 [-48, -39, 60, -39, 16]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[0, 0, 0, 0, 0],
 [-6, 8, -8, 8, -4],
 [3, -4, 4, -4, 2],
 [12, -16, 16, -16, 8],
 [-12, 16, -16, 16, -8]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[8, -10, 2, 2, 0],
 [8, -10, 2, 2, 0],
 [8, -10, 2, 2, 0],
 [-8, 10, -2, -2, 0],
 [12, -15, 3, 3, 0]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[1, 16, 11, -7, -14],
 [11, 7, 29, 24, -51],
 [13, 18, 32, -32, -27],
 [29, -63, -8, 29, 18],
 [7, -12, -25, -5, 45]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[-32, -40, 50, 60, -4],
 [16, 8, -7, -40, -8],
 [-11, -32, 24, 25, 3],
 [9, -22, -11, 0, 18],
 [-6, -24, 0, 30, 18]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-15, 34, 36, -39, 29],
 [2, -32, 21, -19, 32],
 [-14, 56, -1, -1, -12],
 [-9, 18, -17, 23, -5],
 [3, -54, 23, -17, 47]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[-57, -21, -33, -30, 27],
 [41, 9, 27, 24, -25],
 [-52, -22, -42, -14, 23],
 [25, -12, 20, 47, -9],
 [-48, -26, -35, -3, 25]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[-4, -8, 12, -6, -4],
 [0, -36, 32, 0, 12],
 [-10, -2, 14, -15, -16],
 [14, -17, -2, 21, 29],
 [6, -6, -2, 9, 12]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[10, 0, 12, -2, 2],
 [5, 0, 6, -1, 1],
 [30, 0, 36, -6, 6],
 [-10, 0, -12, 2, -2],
 [-25, 0, -30, 5, -5]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[4, -22, 3, -1, -12],
 [-1, 2, 15, 16, 17],
 [5, -36, 42, 37, 19],
 [-2, 6, -6, -12, -4],
 [-1, 26, -39, -22, -19]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[20, -20, 25, 15, 0],
 [0, 0, 0, 0, 0],
 [20, -20, 25, 15, 0],
 [16, -16, 20, 12, 0],
 [4, -4, 5, 3, 0]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[-38, -2, -41, 13, 15],
 [16, 26, 19, -20, 24],
 [32, 24, 40, -14, 6],
 [24, 12, 34, 4, -12],
 [24, -54, 3, -24, -36]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[7, -12, -6, -11, 10],
 [8, -12, -6, -13, 11],
 [4, -16, -8, -4, 8],
 [11, -28, -14, -15, 18],
 [-4, 16, 8, 4, -8]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[5, -24, 11, 0, -11],
 [10, 22, 8, 14, -8],
 [20, -26, 30, 14, -30],
 [-15, -13, -16, -17, 16],
 [-30, -11, -35, -31, 35]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[14, 19, -28, -7, 3],
 [-17, 4, 0, -11, 12],
 [40, 33, -32, 13, -7],
 [-12, 30, 6, 6, 18],
 [21, 27, -36, -6, 3]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-26, -7, -38, -41, -10],
 [22, 17, 34, 31, 2],
 [16, -16, 20, 32, 18],
 [8, -32, 6, 24, 23],
 [4, 38, 12, -6, -20]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[3, -7, 2, -6, 6],
 [3, -3, 33, 21, 27],
 [29, 19, 47, -5, 9],
 [-19, -25, 2, 26, 30],
 [-9, -11, -1, 11, 12]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[36, -1, 55, 28, 11],
 [-27, 11, -56, -18, -12],
 [32, 43, 59, 16, 15],
 [43, -30, 62, 20, 22],
 [23, -15, 42, 15, 10]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[5, 18, -19, -63, 25],
 [-31, -56, 16, 80, -60],
 [-38, 0, 20, 28, -30],
 [1, -27, -20, 9, -4],
 [24, -7, -14, 7, 16]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-18, 0, 3, 9, 15],
 [0, -18, 28, 6, -4],
 [16, 6, -12, -10, -12],
 [10, -12, 17, -1, -11],
 [32, 3, -10, -17, -26]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-24, 10, -21, 14, 15],
 [-2, 45, 24, 32, -15],
 [29, -5, 10, -9, -10],
 [13, -12, -17, -24, -13],
 [20, -6, 18, -7, -9]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-31, 9, -1, 16, 12],
 [9, 2, 12, -14, 8],
 [-15, 11, -87, 26, 29],
 [50, 2, -6, -6, -15],
 [-20, -41, 48, -43, -18]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[4, 0, 28, -16, -28],
 [17, 6, 17, -14, -23],
 [20, 8, 4, -8, -12],
 [-11, -6, 25, -10, -19],
 [-44, -20, 32, -4, -12]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[4, -4, 1, -4, 4],
 [-24, 24, -6, 24, -24],
 [-20, 20, -5, 20, -20],
 [-20, 20, -5, 20, -20],
 [-20, 20, -5, 20, -20]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[-37, 12, 40, -6, 35],
 [-7, 10, 21, -14, -18],
 [7, 8, 21, -35, 18],
 [20, 4, 5, -25, 1],
 [16, 26, 37, 6, -1]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-38, 19, 21, -19, -27],
 [-14, 29, 7, -15, -17],
 [40, -25, 19, -39, 5],
 [-32, -8, -16, 14, 4],
 [3, 23, -14, 5, 1]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-19, 11, -14, 7, -6],
 [14, -16, 9, 8, -14],
 [-6, 6, -4, -2, 4],
 [7, -5, 5, -1, 0],
 [-2, -2, -2, 6, -8]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[-8, -5, -6, -7, -14],
 [-34, -25, 0, -17, -40],
 [22, 20, -26, -2, 6],
 [22, 20, -26, -2, 6],
 [10, 5, 16, 13, 24]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[3, 3, -9, 15, -12],
 [5, 5, -15, 25, -20],
 [1, 1, -3, 5, -4],
 [-2, -2, 6, -10, 8],
 [5, 5, -15, 25, -20]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[5, -5, -10, -30, -10],
 [5, -5, -10, -30, -10],
 [-3, 3, 6, 18, 6],
 [0, 0, 0, 0, 0],
 [-2, 2, 4, 12, 4]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[0, 3, -21, -3, -18],
 [-30, -23, 6, -27, -2],
 [6, 8, -25, 2, -20],
 [30, 19, 22, 31, 26],
 [-12, -7, -13, -13, -14]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[-15, 3, -45, 33, 72],
 [13, -22, 16, -16, -33],
 [-7, -13, 19, -31, 0],
 [-15, 40, 6, 2, 9],
 [27, 3, 0, 24, -54]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[21, 15, 25, 17, 27],
 [-16, -20, 0, 8, -52],
 [15, 13, 15, 8, 27],
 [-39, -1, -35, -51, 27],
 [16, 16, 20, 9, 34]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-43, 12, 27, 49, 4],
 [7, -4, 36, -12, 6],
 [-17, 17, -3, 0, 0],
 [46, -8, -7, -48, -1],
 [26, -3, -18, 3, -4]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-24, -33, -21, 54, -18],
 [0, -15, -25, 30, -20],
 [0, -3, -5, 6, -4],
 [-24, -9, 19, 6, 14],
 [4, 1, -4, 0, -3]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-17, -7, 18, 12, 6],
 [17, 33, 5, 26, -38],
 [31, 25, -22, -4, -26],
 [7, 9, -2, 4, -10],
 [28, 36, -8, 16, -40]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-24, 6, 24, -6, -12],
 [0, 0, 0, 0, 0],
 [-4, 1, 4, -1, -2],
 [20, -5, -20, 5, 10],
 [-16, 4, 16, -4, -8]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[0, 0, 0, 0, 0],
 [-6, 18, 0, -24, 6],
 [-5, 15, 0, -20, 5],
 [4, -12, 0, 16, -4],
 [-6, 18, 0, -24, 6]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-4, -8, 16, -4, -16],
 [0, 0, 0, 0, 0],
 [6, 12, -24, 6, 24],
 [0, 0, 0, 0, 0],
 [-4, -8, 16, -4, -16]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-18, 18, -36, 24, -12],
 [6, -6, 12, -8, 4],
 [-9, 9, -18, 12, -6],
 [-18, 18, -36, 24, -12],
 [0, 0, 0, 0, 0]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[19, -22, -23, -8, -21],
 [-15, 10, 15, -20, 25],
 [9, -6, -9, 12, -15],
 [-21, 21, 24, -3, 27],
 [15, -10, -15, 20, -25]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-24, -23, -51, 54, 30],
 [28, -21, -3, 20, -34],
 [-44, -44, -68, 84, 30],
 [4, 13, -19, 8, 23],
 [63, 34, 10, 0, -36]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[27, -30, -5, 2, -11],
 [-30, 15, 30, 21, 0],
 [10, 10, -30, -26, 10],
 [-3, -15, 25, 23, -11],
 [-12, 0, 20, 16, -4]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-42, -24, 30, -21, 15],
 [-21, -28, 15, -21, 17],
 [12, 39, -5, 31, -15],
 [27, -21, -18, -9, 15],
 [48, 27, -45, 12, -42]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-2, 5, 6, 0, 5],
 [14, -44, -54, 30, -32],
 [19, -10, -46, 28, -3],
 [15, 9, -22, -2, 4],
 [-20, -13, 28, 6, -5]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[19, -3, 27, 9, 17],
 [0, -2, -25, 15, 13],
 [20, 14, -71, 67, 61],
 [31, 1, -30, 59, 51],
 [-5, 1, 46, -36, -4]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-19, -18, 14, 4, -19],
 [35, 18, -22, -23, 26],
 [-19, -18, 14, 4, -19],
 [4, 24, -8, 20, 16],
 [-9, 10, 2, 21, 2]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-7, -9, -17, 25, -27],
 [-11, -8, -18, 0, 25],
 [-31, 10, -2, 10, 1],
 [-26, -13, -28, 27, -8],
 [32, 21, 21, -32, 20]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-21, -25, 25, -48, -4],
 [-22, 39, 74, 9, 29],
 [-2, 29, 62, -3, 39],
 [40, -6, -32, -8, 2],
 [21, 28, -13, 52, 23]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[19, -18, 0, 14, 6],
 [54, -29, 25, 21, -28],
 [11, -3, -7, 1, -1],
 [-43, 1, 6, -2, 16],
 [4, -41, 4, 14, -10]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[12, -6, -3, 12, 12],
 [-4, 2, 1, -4, -4],
 [-20, 10, 5, -20, -20],
 [-4, 2, 1, -4, -4],
 [16, -8, -4, 16, 16]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[13, 17, -43, -21, 32],
 [15, 21, -15, -9, 6],
 [28, -13, -5, -5, 1],
 [33, -54, 46, -4, 23],
 [-1, 37, -51, -8, -4]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[0, 37, -19, 48, 31],
 [10, 33, -11, 42, 29],
 [-40, -21, -13, -24, -23],
 [-35, -23, -9, -27, -24],
 [14, -13, 15, -18, -9]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[-20, 30, -10, -5, 0],
 [24, -36, 12, 6, 0],
 [20, -30, 10, 5, 0],
 [12, -18, 6, 3, 0],
 [-8, 12, -4, -2, 0]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-54, 18, 52, 51, -2],
 [-69, -17, 24, 18, 9],
 [6, -6, -8, -8, 6],
 [-69, -16, 30, 25, 20],
 [-18, 1, 6, 4, -13]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[10, -2, -4, -12, -10],
 [5, -1, -2, -6, -5],
 [5, -1, -2, -6, -5],
 [-25, 5, 10, 30, 25],
 [-20, 4, 8, 24, 20]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[24, 22, -24, -9, 17],
 [-8, 20, 10, -2, -10],
 [-1, 21, 11, -1, -19],
 [56, 2, -31, -3, -3],
 [15, 35, -15, -10, 10]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-14, 20, -26, -16, -45],
 [24, -48, 48, 18, 66],
 [8, -20, 22, 12, 34],
 [-12, 44, -34, -4, -32],
 [26, -8, 16, 6, 31]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[0, 25, 33, 40, -9],
 [16, 9, -29, 42, -1],
 [11, -1, 54, 20, 20],
 [18, -50, -8, -42, 38],
 [10, -2, 30, 28, -2]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[13, 9, 11, -12, 0],
 [12, 6, -22, -6, -1],
 [-18, -14, 27, 51, -17],
 [7, -28, -30, -35, -16],
 [3, 33, 0, -27, 36]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-4, 16, 4, -24, -16],
 [0, 0, 0, 0, 0],
 [-4, 16, 4, -24, -16],
 [2, -8, -2, 12, 8],
 [-4, 16, 4, -24, -16]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[12, 6, -18, -9, 12],
 [-8, -4, 12, 6, -8],
 [8, 4, -12, -6, 8],
 [4, 2, -6, -3, 4],
 [24, 12, -36, -18, 24]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[0, 6, 6, 47, -10],
 [37, 32, -31, 16, -10],
 [-65, -10, 21, -21, -16],
 [3, -36, 35, 38, 22],
 [12, 36, -32, -6, -20]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-20, 24, -20, -4, 8],
 [-15, 18, -15, -3, 6],
 [15, -18, 15, 3, -6],
 [-15, 18, -15, -3, 6],
 [15, -18, 15, 3, -6]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[-50, -21, 13, -54, -31],
 [-13, 3, 32, -75, -19],
 [42, 23, 3, 74, 13],
 [74, 45, 11, 57, 29],
 [14, -7, -43, 59, 29]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[-38, -11, -42, -35, -20],
 [-3, 19, 12, 50, 38],
 [35, -50, 90, 23, 44],
 [19, -51, 69, -15, -11],
 [8, -5, 33, 37, 40]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[24, -24, 16, 4, -12],
 [16, -60, 4, 6, -22],
 [-40, 18, -30, -5, 13],
 [10, -54, 0, 5, -19],
 [-43, -12, -37, -3, 4]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[-6, 2, -6, 4, -1],
 [0, 0, 0, 0, 0],
 [24, -8, 24, -16, 4],
 [-6, 2, -6, 4, -1],
 [6, -2, 6, -4, 1]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[5, -4, 4, 6, -5],
 [30, -24, 24, 36, -30],
 [25, -20, 20, 30, -25],
 [-20, 16, -16, -24, 20],
 [-20, 16, -16, -24, 20]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-30, 20, -24, 30, 31],
 [4, 2, 6, 10, 8],
 [-30, 15, -27, 15, 18],
 [-40, 20, -36, 20, 24],
 [-8, 11, -3, 25, 23]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-36, -30, 36, -6, 12],
 [42, -10, -30, -2, 10],
 [-33, -20, 31, -4, 7],
 [18, 0, -14, 0, 2],
 [18, -30, -6, -6, 18]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-2, -31, 53, -28, 2],
 [40, 15, 23, 9, -39],
 [-8, -42, 34, -48, 8],
 [44, 12, -16, 36, 16],
 [-48, 12, -24, -6, -6]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[20, -44, -2, 21, -12],
 [-27, -2, 20, 5, 34],
 [20, -16, 12, 14, 16],
 [20, -16, 12, 14, 16],
 [-8, 34, -19, -23, -25]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[19, -46, -34, -14, 87],
 [-9, -11, 64, -2, -30],
 [29, -31, 14, 42, 32],
 [49, 21, -5, -18, -20],
 [32, -20, 5, -48, 28]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[6, -26, 10, -4, -1],
 [15, 24, -31, 27, -12],
 [4, -28, 16, -48, 28],
 [-15, -13, 22, 10, -11],
 [-25, 23, 8, 44, -29]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[21, -36, 24, -18, 36],
 [-31, 28, -4, -19, -6],
 [20, -16, 0, 16, 0],
 [18, -24, 12, -3, 18],
 [12, -16, 8, -2, 12]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-1, -39, -13, -13, -30],
 [0, -30, 24, -38, 32],
 [2, 11, 8, 3, 15],
 [9, 48, -6, 41, -2],
 [-14, -8, 34, -36, 60]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[22, -9, -5, -13, -12],
 [-2, -12, 9, 15, -8],
 [16, -10, 1, -31, 2],
 [31, -10, -16, -21, -19],
 [-4, 34, 36, 14, 34]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[6, -18, 12, -36, -11],
 [15, -12, 18, -14, 44],
 [-35, 6, -27, -24, -26],
 [16, 5, 14, 23, -15],
 [-15, 2, -13, -10, -29]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-18, -30, -36, -18, 18],
 [-3, -5, -6, -3, 3],
 [-6, -10, -12, -6, 6],
 [9, 15, 18, 9, -9],
 [-3, -5, -6, -3, 3]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[-12, 0, 35, 7, -29],
 [9, 0, 26, 9, -40],
 [15, 0, -30, -5, 20],
 [27, 0, 12, 9, -42],
 [-3, 0, 17, 4, -17]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-6, 9, 9, -15, 15],
 [-8, 12, 12, -20, 20],
 [-6, 9, 9, -15, 15],
 [12, -18, -18, 30, -30],
 [2, -3, -3, 5, -5]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[0, 0, 0, 0, 0],
 [6, -36, 12, 18, 30],
 [3, -18, 6, 9, 15],
 [-3, 18, -6, -9, -15],
 [1, -6, 2, 3, 5]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[2, 39, 1, 8, -4],
 [24, -18, -6, 24, -12],
 [16, 15, -3, 20, -10],
 [-5, -30, 0, -10, 5],
 [-30, -18, 6, -36, 18]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-18, 14, -20, 16, -6],
 [18, 16, 44, -10, 24],
 [0, -25, -20, -5, -15],
 [-12, 11, -12, 11, -3],
 [12, -6, 16, -10, 6]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[6, -4, 4, -2, -8],
 [-3, 2, -2, 1, 4],
 [-15, 10, -10, 5, 20],
 [0, 0, 0, 0, 0],
 [6, -4, 4, -2, -8]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[3, 34, -9, 47, -54],
 [-8, -19, 49, -16, 44],
 [19, 30, -11, 45, -38],
 [-20, -18, 4, -30, 16],
 [43, -11, 1, -4, 46]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[-10, -24, -10, -4, -23],
 [-12, 12, 10, -8, 2],
 [-32, -17, -10, -52, 14],
 [8, -24, -22, -16, 16],
 [28, -15, -18, 12, 12]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[8, 2, 13, 11, 6],
 [-2, -4, -19, 13, 30],
 [5, 3, 16, -1, -12],
 [-14, -2, -16, -26, -24],
 [6, 2, 12, 6, 0]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[-6, 18, 12, -6, 0],
 [-5, -3, 4, -5, -3],
 [6, -18, -12, 6, 0],
 [-2, -30, -8, -2, -6],
 [1, 27, 8, 1, 5]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[-28, 63, -16, -19, -13],
 [-13, 9, -15, 32, 1],
 [-3, -21, -20, 57, 11],
 [4, 13, 14, -43, -7],
 [-1, -3, -13, 14, 5]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[15, -30, 10, -20, 15],
 [-15, 30, -10, 20, -15],
 [0, 0, 0, 0, 0],
 [15, -30, 10, -20, 15],
 [-6, 12, -4, 8, -6]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-5, 16, -3, 4, -27],
 [-4, -8, 4, 14, 7],
 [-13, -22, 0, 14, 30],
 [2, 22, -5, -10, -31],
 [33, 14, 4, -36, -9]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[14, 7, 25, -5, 0],
 [-26, -1, -55, 3, -8],
 [-3, -9, 0, 5, 5],
 [15, 45, 0, -25, -25],
 [0, -21, 15, 11, 14]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[8, -5, -25, -15, -6],
 [-32, -33, 4, -8, 28],
 [28, 14, -6, -21, -25],
 [-48, -13, 26, 26, 16],
 [0, -12, 29, -12, 20]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[14, -18, -36, -19, 51],
 [-11, 69, -11, 8, -52],
 [28, -10, -43, 7, -18],
 [-43, 24, 58, -23, 17],
 [1, 42, -47, -25, 20]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[27, -65, 30, -17, 11],
 [2, -70, 20, -38, 34],
 [-17, 10, 1, 27, -2],
 [-14, 55, -23, 16, -15],
 [-4, -35, 11, -13, 18]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[-6, 0, 0, 0, -12],
 [-12, 0, 0, 0, -24],
 [-6, 0, 0, 0, -12],
 [-2, 0, 0, 0, -4],
 [10, 0, 0, 0, 20]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-6, -6, 3, 3, -9],
 [-4, -4, 2, 2, -6],
 [-10, -10, 5, 5, -15],
 [-8, -8, 4, 4, -12],
 [-6, -6, 3, 3, -9]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[-1, 10, 5, 7, 5],
 [-6, -36, 6, 6, -6],
 [3, -14, -11, -15, -9],
 [-7, -2, 17, 22, 8],
 [8, 0, -20, -26, -10]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-12, 3, 6, 12, 18],
 [-8, 2, 4, 8, 12],
 [16, -4, -8, -16, -24],
 [24, -6, -12, -24, -36],
 [-4, 1, 2, 4, 6]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-6, 9, -1, 29, -22],
 [2, -8, 12, -33, 34],
 [-17, -13, 3, -6, 5],
 [-13, -22, -8, -19, 5],
 [31, 44, 46, -2, 45]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[-4, 34, 21, 9, 15],
 [3, -28, -26, -14, -6],
 [-15, 4, 33, 27, -19],
 [9, 17, 40, 25, -15],
 [3, 35, 2, -7, 29]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-4, 12, 8, -12, -8],
 [-6, 18, 12, -18, -12],
 [8, -24, -16, 24, 16],
 [6, -18, -12, 18, 12],
 [12, -36, -24, 36, 24]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[8, 2, 38, 31, 28],
 [22, 16, -12, 22, -36],
 [12, 0, -2, 16, -1],
 [-8, -22, 12, -1, 47],
 [-22, -8, 30, -14, 37]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[4, 21, 24, 21, -14],
 [-10, 8, 46, 12, -2],
 [-4, -4, -5, -3, 1],
 [-5, -7, -20, -6, 0],
 [-5, -36, 9, -36, 37]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[-34, -28, 31, 38, 24],
 [15, 13, -16, -16, -10],
 [9, 8, -12, -10, -5],
 [-40, -31, 48, 54, 21],
 [-4, 3, 13, 24, -7]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[6, 27, -16, 8, 24],
 [-24, 17, 2, 7, 12],
 [5, 20, -22, 22, 19],
 [24, 8, -28, 22, 12],
 [22, 14, -1, -17, 8]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[33, 9, 0, -15, 6],
 [-9, -1, 2, 2, 14],
 [-27, -23, -16, 33, 22],
 [13, -41, -48, 46, 46],
 [-15, -57, -66, 30, 6]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-4, -9, -28, -30, -36],
 [12, 11, 4, 10, 12],
 [-16, -15, -7, -15, -18],
 [32, 30, 14, 30, 36],
 [8, 3, -19, -15, -18]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[-33, 18, -39, -15, -6],
 [18, 19, -18, 25, -18],
 [19, -23, 35, 2, -6],
 [12, -3, 0, 9, -38],
 [-43, 7, -23, -30, 26]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[23, -28, 39, -27, -30],
 [-18, 0, 24, -34, -2],
 [14, -32, 48, -61, -34],
 [41, -19, -39, 10, -13],
 [2, 16, -29, 9, 25]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[19, -20, 3, 43, -29],
 [3, -12, 7, -33, -5],
 [-10, -52, 6, 35, -25],
 [20, -16, 8, -55, 4],
 [26, 42, 1, -24, -5]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[1, 2, -1, 7, 5],
 [13, -27, -10, -39, -36],
 [6, -19, 1, 1, -2],
 [-7, 18, 1, -15, -6],
 [-19, -30, 15, 24, 3]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[10, 12, 2, -6, 12],
 [5, 6, 1, -3, 6],
 [5, 6, 1, -3, 6],
 [-30, -36, -6, 18, -36],
 [10, 12, 2, -6, 12]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[21, -3, -9, -6, 1],
 [0, 48, 39, -30, -30],
 [-18, -34, -22, 28, 22],
 [-27, -3, 6, 12, 3],
 [6, -26, -23, 14, 16]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[45, -37, -7, -60, 90],
 [17, -15, -19, -44, 52],
 [-15, 11, 15, 32, -38],
 [-28, 29, -53, -8, -26],
 [30, -16, -19, -34, 46]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[30, 0, 6, -36, -6],
 [25, 0, 5, -30, -5],
 [0, 0, 0, 0, 0],
 [-25, 0, -5, 30, 5],
 [5, 0, 1, -6, -1]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[-16, -16, -8, 24, -9],
 [-20, -34, -26, -52, -70],
 [-47, -1, 4, 26, 1],
 [-38, 13, -9, -25, -33],
 [-18, -35, 5, -34, -19]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[10, -50, -28, -14, 4],
 [-20, 50, -25, 20, 20],
 [3, -25, 7, -9, -10],
 [32, 15, 28, 0, 3],
 [-55, -40, 15, -11, -43]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-18, 33, 42, 31, -9],
 [-22, 41, -19, -41, 29],
 [-39, 75, 0, -18, 33],
 [14, -5, -22, -51, 17],
 [9, -27, 24, 22, -27]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[-17, -19, -8, -31, 14],
 [-22, -26, -28, -31, 19],
 [0, 8, 12, 1, -3],
 [25, -29, 4, -8, -1],
 [9, 32, 9, 36, -15]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[10, -2, -4, -6, 0],
 [-20, 4, 8, 12, 0],
 [-15, 3, 6, 9, 0],
 [-15, 3, 6, 9, 0],
 [30, -6, -12, -18, 0]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-52, 4, 5, -4, 11],
 [-21, -17, -15, 23, 10],
 [18, 5, 19, -13, -27],
 [-50, -6, 7, -6, -40],
 [-10, -12, -25, 24, 34]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-39, 19, 19, 6, 35],
 [61, -31, -31, -12, -55],
 [-2, 17, 17, 33, 5],
 [11, 19, 19, 48, -5],
 [-4, -16, -16, -36, 0]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[30, -3, 14, -3, -18],
 [0, 50, 45, 5, -15],
 [54, 11, -3, 44, -15],
 [-2, -32, -2, -28, 12],
 [-10, 16, 51, -33, 9]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-58, 29, -42, 8, 8],
 [-59, -5, -53, -2, 23],
 [2, 4, 10, 2, 12],
 [-12, 42, 0, 12, -18],
 [-43, -21, -45, -7, 23]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[21, 0, -35, -8, -40],
 [-12, -30, 0, -34, -6],
 [-12, 33, -14, 27, 5],
 [5, -3, -11, -6, -13],
 [2, 12, 14, 18, 16]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[-44, -4, 26, -56, -26],
 [8, -4, -2, 16, 14],
 [-21, -18, 12, -22, -11],
 [16, 24, -10, 12, 4],
 [9, 2, -6, 10, 3]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-2, 5, 1, 6, 6],
 [-6, 15, 3, 18, 18],
 [8, -20, -4, -24, -24],
 [-6, 15, 3, 18, 18],
 [4, -10, -2, -12, -12]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[3, -18, 15, -3, -18],
 [6, -36, 30, -6, -36],
 [-5, 30, -25, 5, 30],
 [4, -24, 20, -4, -24],
 [3, -18, 15, -3, -18]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[32, 6, 14, 29, -20],
 [14, 1, 11, 7, -12],
 [-6, -3, 3, -12, 0],
 [2, -5, 17, -17, -12],
 [-2, 3, -11, 10, 8]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[40, 34, 3, -8, -4],
 [-28, -34, 3, 8, 4],
 [30, 46, -16, -8, -12],
 [-33, -33, -12, 12, -6],
 [-1, 7, -20, 4, -14]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[16, 27, 32, -18, -6],
 [36, -21, 18, 2, -22],
 [0, -54, -26, 44, 16],
 [24, 36, 43, -28, -14],
 [-14, -18, -26, 10, 2]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[25, 50, 3, -29, -1],
 [-22, -36, 1, 29, 5],
 [30, 2, -25, -50, -36],
 [13, 26, 0, -8, -4],
 [-33, -22, 21, 35, 35]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[0, -4, 4, -20, 12],
 [0, -6, 6, -30, 18],
 [0, -1, 1, -5, 3],
 [0, 1, -1, 5, -3],
 [0, -4, 4, -20, 12]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-13, -5, -10, 5, 19],
 [30, 4, 17, -3, -36],
 [17, 7, 14, -10, -29],
 [25, 7, 17, -6, -33],
 [15, 17, 19, -10, -23]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-36, -6, 18, -12, 12],
 [36, 6, -18, 12, -12],
 [-24, -4, 12, -8, 8],
 [-24, -4, 12, -8, 8],
 [6, 1, -3, 2, -2]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[16, 3, 21, 3, -12],
 [-4, -12, -3, -12, -6],
 [12, -9, 18, -9, -18],
 [-16, -8, -20, -8, 8],
 [8, -1, 11, -1, -8]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-14, 24, 17, -9, 14],
 [16, -12, 13, -8, -27],
 [-11, -33, -56, -53, -9],
 [11, 5, 19, -9, -34],
 [29, -13, 76, 21, 17]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[6, -36, 16, -12, 16],
 [6, -18, 9, -3, 9],
 [3, 12, -12, 9, 0],
 [-20, -4, 6, -22, -10],
 [-4, 36, -7, 14, -19]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[12, -17, 16, 42, 7],
 [20, 4, -32, 19, -30],
 [0, -15, 56, 6, 41],
 [-40, -10, 0, -29, 10],
 [5, 7, 18, 4, 14]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-16, 8, -16, 0, -16],
 [8, -4, 8, 0, 8],
 [24, -12, 24, 0, 24],
 [-12, 6, -12, 0, -12],
 [24, -12, 24, 0, 24]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[45, -5, -20, 20, 20],
 [-18, -40, 20, -2, -11],
 [-24, -16, 16, -8, -12],
 [21, -21, -4, 12, 8],
 [15, 45, -20, 0, 10]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-3, 0, -4, -2, -5],
 [3, 0, 4, 2, 5],
 [-18, 0, -24, -12, -30],
 [-9, 0, -12, -6, -15],
 [-15, 0, -20, -10, -25]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[0, 18, 36, 24, -20],
 [-18, -9, -45, -6, 5],
 [12, -15, -12, -24, 20],
 [18, -9, 9, -18, 15],
 [2, -13, -23, -18, 15]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[3, -8, -11, -15, 15],
 [-1, 28, -17, -51, -5],
 [-18, 30, -24, -18, 27],
 [-1, 26, -10, -39, -11],
 [-1, 14, -2, -15, -9]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-12, 36, -18, -6, 12],
 [-6, 18, -9, -3, 6],
 [-8, 24, -12, -4, 8],
 [6, -18, 9, 3, -6],
 [-8, 24, -12, -4, 8]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[-16, 12, 17, 0, -6],
 [23, -16, -21, -15, -12],
 [16, -12, -17, 0, 6],
 [-16, 8, 6, 48, 60],
 [11, -8, -11, -3, 0]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[18, 42, 8, 22, -46],
 [13, -66, -22, -29, 33],
 [-23, -30, -4, -17, 42],
 [-21, -12, 20, -11, 44],
 [-46, 6, 2, -2, 31]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[-12, 12, 27, 18, -9],
 [8, 40, 22, 36, -10],
 [4, -4, -9, -6, 3],
 [24, 18, -19, 6, 4],
 [16, 14, -11, 6, 2]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-5, -4, -6, -4, 1],
 [-15, -12, -18, -12, 3],
 [10, 8, 12, 8, -2],
 [-10, -8, -12, -8, 2],
 [-15, -12, -18, -12, 3]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-2, 34, -37, 36, 11],
 [19, -27, -17, -8, -6],
 [5, -40, 10, -36, -13],
 [-40, 22, 37, -8, 13],
 [-28, 59, 12, 12, -12]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-54, -22, 18, -40, 27],
 [-23, 28, -2, 4, -24],
 [6, 12, 12, 9, -28],
 [-34, 36, -4, 3, -28],
 [28, -8, -8, 10, 8]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[11, -31, -7, 23, -10],
 [16, -25, -9, 15, -8],
 [-40, -7, -14, 6, -26],
 [25, 11, 28, 2, 32],
 [22, -32, -48, -4, -36]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-56, -3, 28, -34, 1],
 [24, -8, -12, 16, -4],
 [-2, -21, 1, 2, -8],
 [48, 10, -24, 28, 2],
 [-40, 9, 20, -26, 5]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[30, -27, 41, 20, -46],
 [26, 28, 7, -27, 1],
 [-10, -21, 3, 20, -8],
 [-14, 30, -29, -37, 27],
 [12, 16, 2, 14, 22]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[42, 8, 5, -19, 2],
 [-37, -14, -17, 18, -30],
 [28, -18, 6, 15, 16],
 [-41, 12, -18, -7, -8],
 [30, 30, 12, -38, 0]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-12, -10, -10, 10, 2],
 [-18, -15, -15, 15, 3],
 [-12, -10, -10, 10, 2],
 [6, 5, 5, -5, -1],
 [-18, -15, -15, 15, 3]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[24, -12, -4, 16, 16],
 [-6, 3, 1, -4, -4],
 [24, -12, -4, 16, 16],
 [36, -18, -6, 24, 24],
 [24, -12, -4, 16, 16]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[14, 0, -23, -15, 12],
 [24, -4, -41, -29, 18],
 [9, -26, -25, -31, -9],
 [-7, -14, 6, -4, -15],
 [18, 60, -6, 30, 54]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[12, 24, 4, -12, 12],
 [-18, -36, -6, 18, -18],
 [0, 0, 0, 0, 0],
 [-9, -18, -3, 9, -9],
 [-3, -6, -1, 3, -3]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[0, 0, 0, 0, 0],
 [-9, -6, 12, -3, -3],
 [3, 2, -4, 1, 1],
 [9, 6, -12, 3, 3],
 [0, 0, 0, 0, 0]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[29, 38, 39, 45, 27],
 [-28, -35, 8, -11, -44],
 [-37, -47, -35, -34, -35],
 [-24, -29, 20, 7, -40],
 [34, 41, 2, -5, 38]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[0, -40, -24, 0, 16],
 [3, 6, -23, 29, 27],
 [-16, 4, -14, 21, 15],
 [-18, -31, -54, 57, 22],
 [-40, -15, -20, 9, 34]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-19, 33, -29, 10, 13],
 [26, -6, -32, -15, -6],
 [28, -12, -25, -18, -7],
 [21, -3, -24, -9, -7],
 [42, -38, 12, -21, -22]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[36, -30, -24, 6, 18],
 [13, -10, -7, -7, 14],
 [1, 0, 1, -9, 8],
 [-11, 9, 7, 0, -7],
 [-6, 6, 6, -12, 6]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[0, -18, 36, 0, -6],
 [0, 12, -24, 0, 4],
 [0, -6, 12, 0, -2],
 [0, -6, 12, 0, -2],
 [0, -12, 24, 0, -4]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[8, -10, 2, 4, -12],
 [-24, 30, -6, -12, 36],
 [-16, 20, -4, -8, 24],
 [8, -10, 2, 4, -12],
 [20, -25, 5, 10, -30]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[-20, 24, 60, -8, -4],
 [-15, 21, 48, -5, -2],
 [0, -36, -36, -12, -12],
 [20, 18, -18, 22, 18],
 [-10, 30, 48, 2, 4]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[6, -36, -18, -18, 18],
 [4, -24, -12, -12, 12],
 [-2, 12, 6, 6, -6],
 [-2, 12, 6, 6, -6],
 [-5, 30, 15, 15, -15]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[8, 0, 24, -12, 4],
 [2, 8, -12, -1, -11],
 [-26, -28, -15, 32, 29],
 [-16, -12, -21, 21, 10],
 [8, 8, 6, -10, -8]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-8, -12, 0, 8, 4],
 [2, 3, 0, -2, -1],
 [6, 9, 0, -6, -3],
 [8, 12, 0, -8, -4],
 [-6, -9, 0, 6, 3]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[38, -2, 9, -57, 20],
 [-28, -10, -9, 57, -30],
 [-8, -33, -4, -13, 5],
 [22, 2, 18, -24, -8],
 [6, -5, 16, -23, -2]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[0, -8, -16, -8, 20],
 [0, -8, -16, -8, 20],
 [-30, -24, -30, 36, 18],
 [-30, -26, -34, 34, 23],
 [-15, -2, 5, 28, -16]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[8, 4, -16, -4, -16],
 [-10, -5, 20, 5, 20],
 [12, 6, -24, -6, -24],
 [-2, -1, 4, 1, 4],
 [2, 1, -4, -1, -4]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-24, 14, -10, -2, -39],
 [-25, -44, 26, -9, -16],
 [-26, 11, -7, -4, -36],
 [-30, 0, -4, -2, -50],
 [-32, 26, -14, -6, -41]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[-4, 12, -16, 24, -16],
 [1, -3, 4, -6, 4],
 [-1, 3, -4, 6, -4],
 [3, -9, 12, -18, 12],
 [-5, 15, -20, 30, -20]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[-12, 6, 3, 9, 6],
 [-4, 2, 1, 3, 2],
 [-12, 6, 3, 9, 6],
 [20, -10, -5, -15, -10],
 [8, -4, -2, -6, -4]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[13, 0, 5, -22, 44],
 [0, 89, 6, -59, -50],
 [35, -29, -14, 51, 26],
 [4, -13, 6, 5, 16],
 [17, -6, -30, 26, 4]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-19, -2, -16, 22, 7],
 [-17, -18, -4, 2, -7],
 [0, 11, -7, 12, 9],
 [8, 13, -1, 4, 7],
 [34, 25, 15, -16, 5]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[-48, 9, -28, 18, -19],
 [-54, 9, -33, 21, -21],
 [12, -18, -14, 6, 10],
 [-12, 0, -10, 6, -4],
 [-18, 18, 9, -3, -12]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[2, -10, 2, -4, 4],
 [-5, 25, -5, 10, -10],
 [5, -25, 5, -10, 10],
 [6, -30, 6, -12, 12],
 [-4, 20, -4, 8, -8]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[0, 0, 0, 0, 0],
 [-12, 4, 2, 10, -6],
 [-30, 10, 5, 25, -15],
 [12, -4, -2, -10, 6],
 [-12, 4, 2, 10, -6]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[-10, -2, 10, -2, -10],
 [-30, -6, 30, -6, -30],
 [10, 2, -10, 2, 10],
 [-5, -1, 5, -1, -5],
 [-20, -4, 20, -4, -20]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[-48, -18, 13, -23, -63],
 [-25, -43, 26, -13, -35],
 [-18, 18, -12, -26, -46],
 [49, -20, 7, 0, 33],
 [-30, -3, -17, -5, -36]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[36, -42, 6, -25, -63],
 [18, -30, -30, -23, -15],
 [27, 6, 51, 16, -15],
 [12, 36, -64, 16, -22],
 [44, -36, -59, -29, -53]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[12, 12, -2, -4, -10],
 [-24, -24, 4, 8, 20],
 [6, 6, -1, -2, -5],
 [-30, -30, 5, 10, 25],
 [-6, -6, 1, 2, 5]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[9, -36, 12, -18, 0],
 [0, -18, 7, -8, -5],
 [-15, -12, 8, -2, -20],
 [39, -30, 3, -22, 35],
 [18, 18, -11, 4, 25]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-9, -16, 45, -7, 1],
 [10, 16, -50, 6, 2],
 [1, 4, -5, 3, -4],
 [-5, -24, 25, -19, 27],
 [10, 20, -50, 10, -5]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-21, 20, -51, 8, -25],
 [21, -24, 30, -8, -6],
 [-8, 8, -10, 12, -10],
 [28, -30, 26, 1, -3],
 [-6, 7, -6, -22, 16]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[12, 10, -6, -12, 10],
 [0, 0, 0, 0, 0],
 [-6, -5, 3, 6, -5],
 [6, 5, -3, -6, 5],
 [-30, -25, 15, 30, -25]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[-15, -8, -25, 4, -7],
 [-1, 20, -9, 38, -27],
 [-11, 10, -4, 3, 6],
 [11, 40, 39, 12, 13],
 [30, 4, 35, -2, -1]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[14, 32, 15, 42, 18],
 [48, -12, -32, 40, -26],
 [-8, 14, 14, 40, 14],
 [4, -35, -29, -8, -26],
 [19, -1, -11, 3, -8]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[26, -20, 13, 1, -38],
 [-42, -40, 10, -10, -10],
 [-10, -16, 6, 2, -10],
 [34, 27, -8, -6, 6],
 [6, 14, -8, -16, 14]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[32, -9, 2, 1, -4],
 [42, 27, -16, -4, 26],
 [-40, -78, -6, 52, -2],
 [24, -39, 7, 14, -15],
 [-36, -66, 3, 37, -13]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[30, 24, 15, 45, -4],
 [-45, -3, 18, -23, 2],
 [41, -21, -44, 1, -2],
 [38, 9, -5, 46, -7],
 [-4, 39, 46, 21, 3]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-10, 0, -2, 0, -8],
 [30, 0, 6, 0, 24],
 [0, 0, 0, 0, 0],
 [-20, 0, -4, 0, -16],
 [-25, 0, -5, 0, -20]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[-20, -20, -20, -16, 4],
 [15, 29, 35, 12, -17],
 [-5, 37, 55, -4, -41],
 [10, -4, -10, 8, 12],
 [30, 30, 30, 24, -6]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[13, 5, 23, 15, -22],
 [-26, -2, -4, -32, -12],
 [-41, -5, -16, -50, -6],
 [13, 1, 2, 16, 6],
 [7, -1, -7, 9, 14]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[12, 6, 3, -18, 12],
 [36, 18, -1, -34, 36],
 [-30, -15, -2, 34, -30],
 [6, 3, -2, -2, 6],
 [6, 3, 3, -12, 6]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-5, 4, 11, -12, -3],
 [1, 0, 1, 0, -1],
 [30, -10, -10, 30, -10],
 [-23, 10, 17, -30, 3],
 [-35, 12, 13, -36, 11]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[0, 36, 30, 6, 24],
 [0, 6, 5, 1, 4],
 [0, 24, 20, 4, 16],
 [0, 6, 5, 1, 4],
 [0, -6, -5, -1, -4]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-5, -7, -45, -57, 13],
 [19, 20, 6, 4, 13],
 [14, 19, 39, 35, -16],
 [13, 21, -15, -49, -11],
 [-7, -13, -33, -25, 23]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[3, -6, -16, 6, -23],
 [25, 28, 32, -15, 20],
 [-16, -16, 2, 27, 20],
 [45, 30, 18, 1, 1],
 [44, 41, 43, -21, 7]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-20, 8, 4, -16, 24],
 [30, -12, -6, 24, -36],
 [0, 0, 0, 0, 0],
 [0, 0, 0, 0, 0],
 [-30, 12, 6, -24, 36]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[-30, -2, -4, -12, -4],
 [-2, -18, -40, -38, -32],
 [20, -18, -35, -15, -37],
 [31, -1, -3, 5, -1],
 [14, 4, 9, 13, 7]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-10, -20, 0, 0, 15],
 [-12, -6, 2, 3, 8],
 [-2, 14, 2, 3, -7],
 [8, -2, -2, -3, -2],
 [20, -50, -10, -15, 20]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[16, 9, -8, -6, 1],
 [-6, 3, 8, -10, 57],
 [-22, 45, 9, 37, 17],
 [-49, 48, -9, 33, 31],
 [43, -34, -5, -39, -7]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-7, -17, -8, 4, -9],
 [23, 15, 42, -10, 39],
 [-9, -33, -6, 6, -9],
 [-13, -39, -12, 8, -15],
 [-14, -34, -16, 8, -18]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-4, 19, -6, -3, -30],
 [20, -23, 14, 7, 6],
 [-44, 38, -28, -14, 12],
 [12, -30, 12, 6, 36],
 [-24, 24, -16, -8, 0]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[12, -12, 20, 0, 4],
 [-9, 9, -15, 0, -3],
 [-18, 18, -30, 0, -6],
 [15, -15, 25, 0, 5],
 [-12, 12, -20, 0, -4]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[39, 6, -30, -35, 4],
 [7, -10, -15, -8, 11],
 [-18, 21, 1, 2, -9],
 [20, -8, 9, -7, 13],
 [-11, -7, 34, 28, -18]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[20, 16, 16, 28, 6],
 [-26, 11, -38, -13, -36],
 [-31, 25, -37, -28, -34],
 [13, -40, 45, -3, 47],
 [6, -12, -6, 14, -5]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[20, -30, -10, 0, -30],
 [-24, 30, 10, -4, 35],
 [-24, 30, 10, -4, 35],
 [-16, 36, 12, 8, 26],
 [8, 18, 6, 20, -7]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[6, 0, 30, -24, -6],
 [3, 0, 15, -12, -3],
 [3, 0, 15, -12, -3],
 [3, 0, 15, -12, -3],
 [3, 0, 15, -12, -3]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-27, -8, 26, 19, 17],
 [33, 17, 4, 4, -37],
 [-18, 16, 35, 38, 49],
 [14, 20, 30, 22, -16],
 [50, 20, -27, -23, -43]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[15, -14, 12, 11, 7],
 [-24, 24, -18, -19, -10],
 [0, -8, -6, 7, -6],
 [24, 0, 36, -2, 28],
 [-15, -10, -30, 10, -25]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[24, -11, -24, 29, -28],
 [2, 7, -3, -26, 9],
 [-40, -34, 36, 48, -13],
 [32, -19, -36, 15, -37],
 [22, 43, -9, 6, 22]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[21, 9, 15, -48, -40],
 [14, 5, 16, -13, -20],
 [20, -19, -6, 3, -14],
 [21, -6, -11, -44, -13],
 [-16, -31, -38, 39, 14]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-4, 4, -4, 8, 0],
 [10, -10, 10, -20, 0],
 [10, -10, 10, -20, 0],
 [-12, 12, -12, 24, 0],
 [-2, 2, -2, 4, 0]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[-2, -21, -39, -10, -11],
 [-21, -16, -26, -39, -6],
 [-20, 19, -2, 1, 27],
 [-3, 15, 33, -2, 2],
 [-8, -13, -9, -23, -30]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[9, -11, -19, 16, -4],
 [17, -1, -14, 12, 6],
 [21, 41, 34, 25, -31],
 [30, 40, 24, 22, -6],
 [15, -5, -15, 19, -15]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[0, 6, -54, -36, 18],
 [-17, 12, 6, 7, -40],
 [1, -16, 42, 19, -10],
 [7, -6, -12, -11, 20],
 [-6, 41, -27, 11, -10]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[-20, 4, -10, 18, -10],
 [10, 22, -1, 33, 11],
 [-15, -11, -4, -11, -11],
 [0, 16, -4, 28, 4],
 [-40, -16, -14, -6, -26]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[33, 38, -41, -12, 14],
 [-12, -48, 30, 27, -24],
 [-14, -44, 64, 13, 7],
 [45, 22, -35, 1, 9],
 [-2, 28, -12, -19, 15]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-8, -4, 2, -8, -12],
 [8, 4, -2, 8, 12],
 [12, 6, -3, 12, 18],
 [16, 8, -4, 16, 24],
 [-12, -6, 3, -12, -18]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-12, -20, 12, 8, 4],
 [-3, -5, 3, 2, 1],
 [9, 15, -9, -6, -3],
 [-9, -15, 9, 6, 3],
 [15, 25, -15, -10, -5]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-48, -10, -51, -62, 0],
 [28, 8, 38, 38, -6],
 [13, 23, -7, -2, 19],
 [27, 21, 3, 17, 22],
 [7, 7, 2, 4, 5]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 5x5 matrix:
[[-9, -30, -6, 9, 45],
 [-13, -18, -4, 23, 7],
 [-20, -10, -7, 31, -19],
 [-53, -30, -35, 37, -1],
 [-26, -16, -18, 16, 4]]

Present the answer in LaTex format: \boxed{Your answer}