[User]
Determine the rank of the following matrix:
[[-36, -18, -30, 12, 30],
 [30, 42, 28, 20, -34],
 [42, 39, 37, 6, -41],
 [27, 36, 25, 16, -30],
 [6, 30, 8, 28, -14]]

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


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

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


[User]
What is the rank of the matrix:
[[-3, -18, -15, -12, 3],
 [-28, -3, -30, 18, -27],
 [15, 24, 31, 8, 7],
 [-18, 24, -2, 32, -26],
 [-23, -6, -27, 12, -21]]?

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


[User]
Calculate the rank of matrix A where A =
[[-24, 20, -20, 40, -12],
 [-18, 5, -20, 0, 21],
 [-18, 11, -17, 18, 3],
 [6, 7, 11, 26, -33],
 [-24, 0, -30, -20, 48]]

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


[User]
What is the rank of the matrix:
[[-36, -8, -4, 22, 54],
 [10, 10, 38, 20, -14],
 [-14, 4, 26, 18, 18],
 [6, 13, 20, 40, -21],
 [0, 5, -10, -36, -18]]?

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


[User]
Find the rank of the matrix:
[[-3, -13, -6, 17, -27],
 [0, 9, 8, -24, 27],
 [15, 20, 1, 2, 18],
 [-24, 21, -9, 19, 41],
 [3, 6, -10, 31, -10]]

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


[User]
Determine the rank of the following matrix:
[[-13, -6, 9, 19, -6],
 [-32, 30, 45, -22, 14],
 [-23, 18, 27, 2, 16],
 [18, 12, -18, -6, 28],
 [27, 18, -21, -30, 28]]

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


[User]
What is the rank of the matrix:
[[-14, 1, -22, 4, 16],
 [-2, 1, 27, 17, 19],
 [38, -8, -27, -13, -19],
 [-18, 4, 3, -7, -9],
 [4, 2, 40, -4, -20]]?

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


[User]
Compute the rank of the given 5x5 matrix:
[[30, -30, 12, -36, 6],
 [10, -10, 4, -12, 2],
 [-5, 5, -2, 6, -1],
 [-20, 20, -8, 24, -4],
 [30, -30, 12, -36, 6]]

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


[User]
Find the rank of the matrix:
[[-6, 0, -2, 2, -2],
 [9, -9, 2, -17, 17],
 [3, 0, 1, -1, 1],
 [0, -18, -2, -28, 28],
 [-10, -24, -6, -34, 34]]

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


[User]
Calculate the rank of matrix A where A =
[[24, -12, 0, -8, -20],
 [-18, 9, 0, 6, 15],
 [18, -9, 0, -6, -15],
 [-12, 6, 0, 4, 10],
 [-18, 9, 0, 6, 15]]

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


[User]
Determine the rank of the following matrix:
[[50, 15, -25, -8, 12],
 [-50, 28, 24, 15, 32],
 [-9, -9, -51, -32, -17],
 [-4, -73, -49, -40, -18],
 [1, -55, -45, -34, 5]]

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[User]
Calculate the rank of matrix A where A =
[[16, 12, 9, -5, -3],
 [42, 45, 0, -21, -9],
 [6, 15, -15, -8, -2],
 [-50, -45, -15, 20, 10],
 [2, 21, -33, -12, -2]]

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


[User]
What is the rank of the matrix:
[[-28, 10, 49, -27, 25],
 [4, 22, -3, -23, 5],
 [-37, -6, 9, 5, -32],
 [33, -28, 32, -23, -48],
 [40, -20, 29, -27, -31]]?

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


[User]
Find the rank of the matrix:
[[-15, 30, -25, 15, -5],
 [12, -24, 20, -12, 4],
 [-3, 6, -5, 3, -1],
 [3, -6, 5, -3, 1],
 [15, -30, 25, -15, 5]]

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


[User]
What is the rank of the matrix:
[[8, 16, -12, -4, 16],
 [12, 24, -18, -6, 24],
 [-8, -16, 12, 4, -16],
 [-4, -8, 6, 2, -8],
 [10, 20, -15, -5, 20]]?

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


[User]
Find the rank of the matrix:
[[-12, -12, -4, -16, 8],
 [15, 15, 5, 20, -10],
 [-18, -18, -6, -24, 12],
 [18, 18, 6, 24, -12],
 [9, 9, 3, 12, -6]]

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


[User]
Determine the rank of the following matrix:
[[-6, -36, -26, -34, -20],
 [51, 40, 23, -19, 20],
 [20, 45, 73, 29, -23],
 [19, -9, -53, -55, 1],
 [-6, -24, -61, -37, 2]]

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[User]
Calculate the rank of matrix A where A =
[[41, 7, -26, 40, 4],
 [30, -14, -22, 36, -26],
 [-3, -13, -7, 4, -35],
 [-28, -24, 16, -21, -29],
 [-21, -23, 14, -15, -23]]

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


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

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


[User]
What is the rank of the matrix:
[[-11, 5, -17, 26, 12],
 [-10, 9, -7, 2, -8],
 [-9, 9, 10, -34, -20],
 [-43, 29, -31, 18, -4],
 [-14, 11, -7, -2, -8]]?

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[User]
Calculate the rank of matrix A where A =
[[1, 1, -6, 11, 13],
 [-16, -23, -6, -26, 10],
 [-7, -12, -6, -3, -14],
 [-12, -19, -18, 2, 24],
 [11, 22, 24, -21, 23]]

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


[User]
Find the rank of the matrix:
[[-12, -24, -18, 18, 6],
 [-24, -8, 0, -24, -4],
 [10, 0, -3, 15, 3],
 [30, 20, 9, 15, 1],
 [-40, -20, -6, -30, -4]]

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


[User]
Determine the rank of the following matrix:
[[5, -10, 10, 0, -5],
 [-6, 12, -12, 0, 6],
 [0, 0, 0, 0, 0],
 [-6, 12, -12, 0, 6],
 [2, -4, 4, 0, -2]]

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


[User]
Calculate the rank of matrix A where A =
[[0, 0, 0, 0, 0],
 [8, -16, -4, -20, 24],
 [-4, 8, 2, 10, -12],
 [10, -20, -5, -25, 30],
 [-8, 16, 4, 20, -24]]

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


[User]
Calculate the rank of matrix A where A =
[[-20, 5, -25, 25, -10],
 [8, -2, 10, -10, 4],
 [8, -2, 10, -10, 4],
 [12, -3, 15, -15, 6],
 [8, -2, 10, -10, 4]]

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


[User]
Determine the rank of the following matrix:
[[6, -15, -9, 18, 3],
 [12, -30, -18, 36, 6],
 [2, -5, -3, 6, 1],
 [4, -10, -6, 12, 2],
 [0, 0, 0, 0, 0]]

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


[User]
Determine the rank of the following matrix:
[[-24, -15, -42, 13, 2],
 [-18, -15, -47, 10, 0],
 [12, 11, 56, -3, 6],
 [-30, -16, -3, 23, 14],
 [-6, 13, 25, -4, -2]]

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[User]
Calculate the rank of matrix A where A =
[[-23, -14, -14, -2, 10],
 [-19, -2, 18, -10, 6],
 [16, -7, -12, -5, -9],
 [20, 38, 18, 31, 0],
 [1, 3, -2, 5, 1]]

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


[User]
Find the rank of the matrix:
[[-5, -12, -6, -42, -34],
 [10, -3, -24, -33, -31],
 [5, -6, -18, -36, -32],
 [13, 6, -18, 0, -4],
 [27, 18, -30, 24, 12]]

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


[User]
What is the rank of the matrix:
[[30, 25, -10, -10, 10],
 [18, 15, -6, -6, 6],
 [-30, -25, 10, 10, -10],
 [12, 10, -4, -4, 4],
 [36, 30, -12, -12, 12]]?

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


[User]
Compute the rank of the given 5x5 matrix:
[[-21, -32, -6, -2, 21],
 [40, 65, 22, -9, -14],
 [64, -24, 64, -20, 88],
 [-7, -43, -8, 0, 16],
 [1, -33, 12, 0, 32]]

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


[User]
Find the rank of the matrix:
[[5, 0, -6, 2, -4],
 [21, -12, -6, 10, -32],
 [34, 12, -60, 12, -12],
 [13, -6, -6, 6, -18],
 [-21, -18, 54, -6, -6]]

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


[User]
Compute the rank of the given 5x5 matrix:
[[3, 5, -23, -30, 10],
 [-22, -10, 22, -20, -20],
 [8, 2, 1, 22, 4],
 [15, 9, -27, -6, 18],
 [-18, -10, 28, 0, -20]]

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


[User]
What is the rank of the matrix:
[[-12, 36, -27, -21, -21],
 [-24, -54, 4, 0, -12],
 [-27, -12, -32, -7, 35],
 [19, 6, 31, 24, 18],
 [-1, -9, 21, 4, -32]]?

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


[User]
Calculate the rank of matrix A where A =
[[-8, 19, -13, 11, -1],
 [12, -6, 6, -62, 6],
 [4, -5, -17, -16, 4],
 [26, -34, -8, -22, 13],
 [9, -6, 23, 41, 2]]

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


[User]
Find the rank of the matrix:
[[23, -17, 14, -18, 20],
 [-10, -18, -9, 35, 25],
 [8, -30, -24, 50, 31],
 [28, 18, 7, -31, 34],
 [-22, -20, 6, 16, -17]]

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


[User]
Compute the rank of the given 5x5 matrix:
[[-30, -8, -34, 10, 6],
 [-29, -28, 19, -50, -25],
 [3, 0, 0, 13, 6],
 [-14, -8, 0, 9, 0],
 [13, -12, 36, -69, -25]]

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


[User]
What is the rank of the matrix:
[[-3, 4, 33, 16, 31],
 [2, -5, -32, -5, -28],
 [17, -1, -10, -6, -19],
 [-6, 2, -14, -42, -14],
 [0, -5, -16, 21, -10]]?

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


[User]
Compute the rank of the given 5x5 matrix:
[[-24, 10, -22, -12, 0],
 [3, -2, -52, -37, 2],
 [-12, 23, 15, 22, 8],
 [-3, 23, -25, -5, 12],
 [-18, 6, -34, -22, 0]]

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


[User]
Calculate the rank of matrix A where A =
[[-12, 10, -5, 22, 12],
 [20, 6, 30, 16, -21],
 [-8, 4, 0, -8, -6],
 [24, -24, -10, -8, 15],
 [-40, 8, -30, -16, 15]]

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


[User]
What is the rank of the matrix:
[[10, -3, -1, -3, 3],
 [-22, 8, 5, 36, -1],
 [4, -2, -2, -18, -2],
 [16, -6, -4, -30, 0],
 [-38, 12, 5, 24, -9]]?

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


[User]
Determine the rank of the following matrix:
[[-21, 42, 0, -42, 24],
 [-1, -34, 9, 16, -31],
 [-13, 34, -2, -30, 22],
 [-18, 32, 1, -34, 17],
 [-27, 6, 12, -30, -12]]

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


[User]
Calculate the rank of matrix A where A =
[[-15, 20, -9, -14, 13],
 [-6, -24, -22, 34, 16],
 [2, 24, 16, -31, -13],
 [-22, 32, -15, -23, 4],
 [7, 36, 36, -51, 3]]

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


[User]
Determine the rank of the following matrix:
[[-28, -37, -37, -13, -13],
 [35, 9, 2, -53, -86],
 [-6, -47, -38, 5, 6],
 [-29, -45, -30, 29, 50],
 [23, 0, -7, -50, -79]]

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


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

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


[User]
Determine the rank of the following matrix:
[[24, -2, 22, 25, -14],
 [-35, 15, 76, 18, 9],
 [-3, -25, 27, 16, 17],
 [11, 5, -30, -28, -45],
 [12, 42, -21, 15, 18]]

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


[User]
What is the rank of the matrix:
[[-7, 31, -7, 30, -42],
 [78, -18, 61, 40, 30],
 [28, -1, 29, 22, 12],
 [35, 14, 22, 40, -33],
 [-25, 34, -23, 20, -45]]?

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


[User]
Determine the rank of the following matrix:
[[5, -3, -4, 0, -1],
 [10, -6, -8, 0, -2],
 [-25, 15, 20, 0, 5],
 [25, -15, -20, 0, -5],
 [30, -18, -24, 0, -6]]

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


[User]
Calculate the rank of matrix A where A =
[[12, -14, 1, 1, -10],
 [-12, 10, 1, -2, 2],
 [-12, 2, 5, -4, -14],
 [20, -18, -1, 3, -6],
 [36, -38, 1, 4, -22]]

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


[User]
What is the rank of the matrix:
[[3, 17, 4, 33, -30],
 [12, -6, 33, 39, -2],
 [42, 31, -22, -3, 23],
 [15, -18, 8, 30, -3],
 [13, -20, -20, -16, 21]]?

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


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

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


[User]
Calculate the rank of matrix A where A =
[[-24, -2, -10, -4, 24],
 [-6, 5, -8, -23, 6],
 [-42, -6, -15, 3, 42],
 [6, 6, -3, -21, -6],
 [42, 1, 20, 17, -42]]

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


[User]
Calculate the rank of matrix A where A =
[[15, 3, -3, 0, 3],
 [25, 5, -5, 0, 5],
 [25, 5, -5, 0, 5],
 [20, 4, -4, 0, 4],
 [0, 0, 0, 0, 0]]

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


[User]
Find the rank of the matrix:
[[23, 38, 4, -38, 21],
 [23, 24, -12, -24, 6],
 [18, 20, -8, -20, 6],
 [-22, -26, 8, 26, -9],
 [-1, 2, 4, -2, 3]]

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


[User]
What is the rank of the matrix:
[[-22, 10, -6, -20, 24],
 [-13, 11, -15, -8, 18],
 [-21, 11, -9, -18, 24],
 [1, 5, -12, 5, 3],
 [6, -2, 0, 6, -6]]?

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


[User]
Compute the rank of the given 5x5 matrix:
[[34, -26, -20, 0, -20],
 [4, -6, 10, 0, -10],
 [-18, 22, -24, 0, 32],
 [-20, 15, 13, 0, 11],
 [-36, 24, 36, 0, 12]]

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


[User]
Find the rank of the matrix:
[[-7, 39, 39, -22, -3],
 [-22, 34, 32, 22, -23],
 [4, -61, -35, -12, 23],
 [11, 22, 8, -25, 2],
 [-37, 30, 30, 59, -39]]

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


[User]
Calculate the rank of matrix A where A =
[[0, 16, 12, -16, -8],
 [0, 16, 12, -16, -8],
 [0, 20, 15, -20, -10],
 [0, -4, -3, 4, 2],
 [0, -4, -3, 4, 2]]

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


[User]
What is the rank of the matrix:
[[13, -32, 18, -38, 37],
 [4, 4, 4, 6, -4],
 [44, 8, 48, 20, -4],
 [-54, 0, -60, -12, -6],
 [-39, -12, -42, -24, 9]]?

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


[User]
Determine the rank of the following matrix:
[[14, -4, 28, 11, 22],
 [-6, -20, 4, -9, 6],
 [21, 30, -14, 12, 10],
 [15, 33, -8, 15, -2],
 [-28, -33, 10, -16, -18]]

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


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

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


[User]
Determine the rank of the following matrix:
[[-3, 12, -15, -12, 6],
 [15, 45, -15, -45, 10],
 [27, 18, 27, -18, -6],
 [-2, -34, 26, 34, -12],
 [15, 24, 3, -24, 2]]

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


[User]
Find the rank of the matrix:
[[7, -1, 32, -42, -13],
 [-40, 41, 51, -16, -25],
 [-9, 5, 4, -14, -4],
 [18, -9, 3, 12, 3],
 [9, -6, 15, -30, -6]]

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


[User]
What is the rank of the matrix:
[[-21, 15, -15, 48, -21],
 [-21, 25, 3, 3, 0],
 [-26, 30, 2, 8, -2],
 [4, 0, 8, -22, 10],
 [24, -30, -6, 3, -3]]?

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


[User]
Calculate the rank of matrix A where A =
[[23, -17, -10, 5, 34],
 [-11, 11, 19, -44, -42],
 [21, -6, -11, -9, 6],
 [-22, 1, 35, -40, -20],
 [-29, -1, 48, -53, -22]]

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


[User]
Calculate the rank of matrix A where A =
[[48, 6, 9, 9, -27],
 [32, 15, 34, 16, -25],
 [-52, -3, -10, 2, 35],
 [-4, 6, 1, 19, 11],
 [16, 0, -19, 17, 7]]

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


[User]
Calculate the rank of matrix A where A =
[[-23, -25, -31, -22, 5],
 [-9, 36, 30, 24, 18],
 [31, -7, 27, 10, -37],
 [-32, -16, -18, -14, 8],
 [18, 51, 25, 28, 27]]

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


[User]
Determine the rank of the following matrix:
[[28, -6, -50, 34, 4],
 [-4, 18, 34, 0, 6],
 [10, -3, 39, -6, -17],
 [24, 12, 8, 38, 6],
 [30, 36, -18, -5, 11]]

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


[User]
Compute the rank of the given 5x5 matrix:
[[-34, -3, -26, 40, -22],
 [12, 13, 8, 18, -21],
 [0, 18, 39, 30, -21],
 [10, 0, 3, -12, 6],
 [-8, -9, 6, -18, 21]]

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


[User]
What is the rank of the matrix:
[[10, 0, -2, 12, 6],
 [-51, 24, -27, -36, 3],
 [11, -24, 35, -12, -27],
 [49, -16, 15, 42, 7],
 [20, 0, -4, 24, 12]]?

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


[User]
Find the rank of the matrix:
[[-13, 26, -19, 32, 9],
 [13, 2, -6, -5, -9],
 [43, 18, -28, -25, -11],
 [72, 24, -42, -42, -24],
 [-21, -18, 24, -17, 25]]

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


[User]
Determine the rank of the following matrix:
[[-4, -6, -15, 5, -12],
 [-27, 12, -40, -3, -18],
 [-41, 66, -5, -38, 30],
 [-24, 24, -20, -12, 0],
 [-19, 24, -10, -13, 6]]

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


[User]
Determine the rank of the following matrix:
[[8, -2, -3, 10, -21],
 [-24, 8, -23, -15, 14],
 [-28, 2, -33, 1, 38],
 [22, 7, 29, 35, -33],
 [20, 4, 24, 43, -21]]

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


[User]
Find the rank of the matrix:
[[15, 32, -51, 27, 16],
 [20, 17, -45, 11, -4],
 [-10, 32, -8, 24, 16],
 [-13, -8, 5, 4, -26],
 [27, 7, -37, -4, -6]]

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


[User]
Calculate the rank of matrix A where A =
[[30, -15, 20, 30, -15],
 [-24, 12, -16, -24, 12],
 [6, -3, 4, 6, -3],
 [30, -15, 20, 30, -15],
 [36, -18, 24, 36, -18]]

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


[User]
What is the rank of the matrix:
[[-4, 26, 2, 28, -40],
 [13, -23, -20, -39, 24],
 [6, -21, 12, -15, 30],
 [12, -9, 33, 8, 4],
 [3, 12, -3, 9, -24]]?

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


[User]
Compute the rank of the given 5x5 matrix:
[[-26, -6, -9, -18, 10],
 [35, 3, 53, 26, 15],
 [-18, -18, 72, 24, 54],
 [-21, 15, -12, 8, -19],
 [19, -57, 45, 22, 65]]

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


[User]
Compute the rank of the given 5x5 matrix:
[[29, -10, -21, -11, 16],
 [-37, -43, 0, 8, 17],
 [-18, -33, -9, 0, 15],
 [13, 0, -3, -1, 6],
 [31, 3, -18, -12, 7]]

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


[User]
Determine the rank of the following matrix:
[[-4, 1, 3, -6, 3],
 [2, -14, 3, -18, -15],
 [-2, 5, 0, 4, 6],
 [26, -20, -15, 18, -33],
 [16, -13, -9, 10, -21]]

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


[User]
Calculate the rank of matrix A where A =
[[24, -12, 42, 12, 2],
 [-20, 14, 24, -18, -22],
 [2, 27, 0, -21, -9],
 [-24, 26, 42, -30, -34],
 [4, -16, 21, 12, 1]]

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


[User]
What is the rank of the matrix:
[[-5, -35, -18, -19, -18],
 [-12, -7, 15, -3, -11],
 [16, -34, -18, -22, 24],
 [-2, 9, -61, -11, -22],
 [27, -55, -12, -9, 11]]?

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


[User]
Determine the rank of the following matrix:
[[-36, 18, 24, 36, 12],
 [-18, 9, 12, 18, 6],
 [6, -3, -4, -6, -2],
 [18, -9, -12, -18, -6],
 [-36, 18, 24, 36, 12]]

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


[User]
Calculate the rank of matrix A where A =
[[-6, 42, -6, -2, -30],
 [-15, -23, 33, 11, 37],
 [-9, 39, 0, 0, -24],
 [-18, 22, 21, 7, 1],
 [-12, -4, 21, 7, 17]]

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


[User]
Calculate the rank of matrix A where A =
[[36, -12, -24, -30, 12],
 [30, -10, -20, -25, 10],
 [18, -6, -12, -15, 6],
 [36, -12, -24, -30, 12],
 [-6, 2, 4, 5, -2]]

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


[User]
Determine the rank of the following matrix:
[[-28, -2, 44, -8, 0],
 [-8, -1, 10, -4, 0],
 [26, 4, -28, 16, 0],
 [-2, -1, -2, -4, 0],
 [-4, 1, 14, 4, 0]]

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[User]
Calculate the rank of matrix A where A =
[[13, -4, 26, -17, -7],
 [-15, 19, -8, -21, -19],
 [18, 52, -8, 8, 0],
 [9, -28, 26, -9, 1],
 [32, 11, 26, 2, 6]]

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


[User]
Determine the rank of the following matrix:
[[-11, -10, 3, -19, -54],
 [21, -2, 21, 3, -48],
 [21, -2, -6, -6, -9],
 [-5, -6, -21, -19, 0],
 [-8, -8, -9, -19, -27]]

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


[User]
Determine the rank of the following matrix:
[[32, -15, 10, 41, -16],
 [-6, 20, -7, -6, 2],
 [-25, 36, -1, -31, 29],
 [-26, 4, 11, -6, -22],
 [-13, -7, -11, -35, 28]]

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


[User]
Determine the rank of the following matrix:
[[32, 36, -18, 21, -22],
 [18, -20, 10, 0, -22],
 [26, 24, -5, 21, -17],
 [-44, 12, 27, 15, 55],
 [-24, 0, 33, 18, 33]]

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


[User]
Compute the rank of the given 5x5 matrix:
[[-18, -36, -3, 50, 35],
 [-8, 20, -38, -44, -22],
 [-5, 15, -42, -24, -13],
 [-6, -4, -14, -3, 2],
 [-23, -19, -26, 7, 14]]

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


[User]
Find the rank of the matrix:
[[-11, -18, -43, -41, -30],
 [1, -18, 1, -7, 2],
 [37, -11, -8, -3, -23],
 [16, 28, 53, 15, 47],
 [36, 37, 46, 41, 24]]

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


[User]
Compute the rank of the given 5x5 matrix:
[[-6, -18, -17, 8, 23],
 [-6, -14, -4, 33, 5],
 [-20, 38, 12, -5, -31],
 [-50, 58, 17, 0, -43],
 [9, -6, 20, 33, -18]]

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


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

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


[User]
Compute the rank of the given 5x5 matrix:
[[-30, -30, 36, -12, 6],
 [-30, -30, 36, -12, 6],
 [0, 0, 0, 0, 0],
 [5, 5, -6, 2, -1],
 [10, 10, -12, 4, -2]]

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


[User]
Determine the rank of the following matrix:
[[25, -10, -25, -25, -10],
 [-18, 2, 26, 40, 16],
 [-61, 40, 37, -5, -2],
 [-43, 25, 31, 10, 4],
 [6, 8, -22, -50, -20]]

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


[User]
Find the rank of the matrix:
[[5, 27, 22, 13, 16],
 [2, -42, -33, -19, -20],
 [14, -30, -22, -12, -8],
 [-12, 12, 8, 4, 0],
 [3, -27, -21, -12, -12]]

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


[User]
What is the rank of the matrix:
[[13, -6, 57, 43, -16],
 [18, 85, -34, 42, -30],
 [-33, -46, 18, -33, 16],
 [-4, 15, -63, 4, -30],
 [-26, 4, -55, -22, -12]]?

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[User]
Calculate the rank of matrix A where A =
[[-25, -25, 0, 5, 25],
 [15, 15, 0, -3, -15],
 [-20, -20, 0, 4, 20],
 [-30, -30, 0, 6, 30],
 [-15, -15, 0, 3, 15]]

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[User]
Calculate the rank of matrix A where A =
[[-41, -61, -3, -37, -58],
 [43, 4, -1, 7, 12],
 [6, -2, 12, 9, 0],
 [-70, -38, 17, -15, -34],
 [-14, -11, 19, 6, 40]]

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


[User]
Determine the rank of the following matrix:
[[-18, -18, -32, -13, 19],
 [-28, -25, -43, -21, 24],
 [-32, -17, -6, -26, -10],
 [-16, -31, 0, -4, -14],
 [-42, -9, -36, -41, 17]]

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


[User]
Determine the rank of the following matrix:
[[-6, -23, -30, -16, -9],
 [9, -16, -9, 20, -44],
 [-15, -20, -20, -20, 7],
 [-33, -31, 4, -4, 0],
 [-3, 2, 23, 20, -10]]

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


[User]
Find the rank of the matrix:
[[-17, 20, 30, 4, 0],
 [-18, 21, 39, 3, 0],
 [45, -55, 5, -25, 0],
 [10, -12, -8, -4, 0],
 [0, 1, -41, 7, 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, 0, 0, 0],
 [0, 0, 0, 0, 0],
 [6, -1, -6, 0, 3],
 [-36, 6, 36, 0, -18]]

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


[User]
Determine the rank of the following matrix:
[[-1, -1, 12, -18, -3],
 [-24, 4, -6, -12, 12],
 [16, -6, 39, -42, -18],
 [-2, 2, -18, 24, 6],
 [6, 2, -30, 48, 6]]

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


[User]
What is the rank of the matrix:
[[-3, 29, -40, 63, -4],
 [-21, 20, -7, 66, 18],
 [10, 0, 1, 27, 14],
 [-48, 11, 76, 57, 42],
 [-33, 12, 33, 45, 24]]?

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


[User]
Compute the rank of the given 5x5 matrix:
[[34, -17, 34, 38, 30],
 [-2, 6, 8, 8, -6],
 [28, -27, 2, 8, 36],
 [-7, 9, 4, 25, -9],
 [5, -4, 2, -29, 3]]

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


[User]
Calculate the rank of matrix A where A =
[[-23, -5, 22, 40, -29],
 [-10, -22, -21, 14, 29],
 [1, 9, 19, 18, -4],
 [-29, -23, -7, 22, -20],
 [20, 3, -11, -6, 49]]

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


[User]
Find the rank of the matrix:
[[61, -10, -18, -43, -28],
 [-12, 26, 24, -4, 14],
 [-5, -10, -15, -25, -7],
 [8, -48, -17, -60, -47],
 [31, -8, 16, 4, -19]]

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


[User]
What is the rank of the matrix:
[[-10, 4, -18, 8, 10],
 [-6, -6, 20, -26, -8],
 [30, 0, 10, 20, -10],
 [30, -3, 21, 9, -15],
 [8, -5, 21, -13, -11]]?

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


[User]
What is the rank of the matrix:
[[3, -51, 23, 7, 13],
 [40, -30, -15, -33, -2],
 [17, -11, -17, -23, 10],
 [-44, -34, -4, 31, 38],
 [-61, 13, -27, 49, 11]]?

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[User]
What is the rank of the matrix:
[[25, -8, -37, -34, 42],
 [12, -42, -25, -22, 39],
 [25, -22, -25, -37, -3],
 [-41, 46, 45, 33, 3],
 [38, 6, -40, -15, -3]]?

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


[User]
What is the rank of the matrix:
[[13, -10, 1, -9, 13],
 [-4, -50, 68, 32, 28],
 [15, -25, 39, 9, 12],
 [24, -55, 84, 24, 27],
 [2, 5, -10, -6, -1]]?

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


[User]
Find the rank of the matrix:
[[10, 10, -10, -2, -4],
 [-25, -25, 25, 5, 10],
 [-5, -5, 5, 1, 2],
 [-20, -20, 20, 4, 8],
 [25, 25, -25, -5, -10]]

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


[User]
What is the rank of the matrix:
[[30, 3, 13, 31, 15],
 [-24, 16, -23, -19, -12],
 [6, -13, 17, 7, 3],
 [-36, -6, -9, -33, -18],
 [18, -9, 24, 24, 9]]?

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


[User]
Calculate the rank of matrix A where A =
[[40, 26, -35, 0, 25],
 [42, 24, -36, 0, 30],
 [-31, -24, 28, 0, -15],
 [-29, -26, 27, 0, -10],
 [-2, 2, 1, 0, -5]]

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


[User]
Compute the rank of the given 5x5 matrix:
[[-24, 0, 6, 18, -12],
 [-24, 0, 6, 18, -12],
 [-8, 0, 2, 6, -4],
 [-8, 0, 2, 6, -4],
 [20, 0, -5, -15, 10]]

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


[User]
Compute the rank of the given 5x5 matrix:
[[-6, -15, -52, 24, 23],
 [-1, -38, -46, 57, 8],
 [40, -16, -38, 6, 34],
 [-44, -23, -5, 42, -5],
 [-13, -1, 33, 6, -24]]

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


[User]
Find the rank of the matrix:
[[-14, 5, 19, 24, -28],
 [-29, 7, -34, -28, -76],
 [-9, 28, -21, -28, -20],
 [54, -2, -37, 51, 0],
 [16, 44, -24, -18, 13]]

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


[User]
Find the rank of the matrix:
[[7, -35, 15, 7, -31],
 [22, 18, -26, -10, -6],
 [11, 37, -29, -12, 17],
 [0, 0, 0, 0, 0],
 [-1, -11, 7, 3, -7]]

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


[User]
What is the rank of the matrix:
[[26, 37, -15, -6, 31],
 [-11, -43, 9, -9, -28],
 [-39, -13, 30, 16, 15],
 [14, -48, -9, -13, -65],
 [30, 55, -16, 10, 27]]?

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


[User]
Find the rank of the matrix:
[[-42, -52, 32, 22, 30],
 [10, 6, -24, 12, -26],
 [-20, -30, -18, 45, 25],
 [6, 6, 8, -16, -30],
 [22, 23, -18, -10, -41]]

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


[User]
Compute the rank of the given 5x5 matrix:
[[0, 18, -6, -30, 0],
 [0, 12, -4, -20, 0],
 [0, 3, -1, -5, 0],
 [0, 15, -5, -25, 0],
 [0, 18, -6, -30, 0]]

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


[User]
Find the rank of the matrix:
[[-30, -10, 10, 20, -5],
 [-14, 6, -8, -6, -1],
 [30, 10, -10, -20, 5],
 [-34, -6, 5, 15, -5],
 [-22, -18, 20, 30, -5]]

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


[User]
Calculate the rank of matrix A where A =
[[12, 2, -10, 4, -2],
 [-12, -2, 10, -4, 2],
 [-24, -4, 20, -8, 4],
 [36, 6, -30, 12, -6],
 [36, 6, -30, 12, -6]]

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


[User]
Compute the rank of the given 5x5 matrix:
[[2, 0, 10, 4, 12],
 [0, 0, 0, 0, 0],
 [2, 0, 10, 4, 12],
 [1, 0, 5, 2, 6],
 [2, 0, 10, 4, 12]]

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


[User]
Determine the rank of the following matrix:
[[27, -6, -25, -4, 44],
 [19, -13, -17, -24, 34],
 [-2, 1, -10, 4, 6],
 [23, -9, -5, -16, 26],
 [-2, 16, -5, 39, -4]]

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


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

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


[User]
What is the rank of the matrix:
[[12, 6, 36, 30, -18],
 [-6, -3, -18, -15, 9],
 [10, 5, 30, 25, -15],
 [0, 0, 0, 0, 0],
 [10, 5, 30, 25, -15]]?

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


[User]
Compute the rank of the given 5x5 matrix:
[[48, 16, 4, 11, -15],
 [-12, -4, 20, -8, -54],
 [-12, -4, 16, -7, -43],
 [-48, -16, -8, -10, 26],
 [-6, -2, 22, -7, -60]]

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


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

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


[User]
What is the rank of the matrix:
[[0, 0, 0, 0, 0],
 [5, 1, 4, -1, -6],
 [-15, -3, -12, 3, 18],
 [-15, -3, -12, 3, 18],
 [-10, -2, -8, 2, 12]]?

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


[User]
Find the rank of the matrix:
[[-8, 20, 16, 16, -36],
 [-22, -40, -36, -11, 1],
 [20, 27, 23, 7, 7],
 [-24, 12, 26, -4, -38],
 [-36, 8, 14, 10, -64]]

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


[User]
Compute the rank of the given 5x5 matrix:
[[-5, -63, -32, 59, 26],
 [44, 18, 29, -26, -41],
 [1, 48, 49, -8, -42],
 [16, -25, 20, 31, -26],
 [-14, -19, -25, 27, 26]]

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


[User]
Determine the rank of the following matrix:
[[-47, -26, 48, -49, 25],
 [14, 11, -30, 8, 13],
 [4, -31, 6, -18, -3],
 [-1, -28, 15, -16, -8],
 [-22, -23, 21, -33, 18]]

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


[User]
Calculate the rank of matrix A where A =
[[-2, 8, 10, -10, 8],
 [-6, 24, 30, -30, 24],
 [-4, 16, 20, -20, 16],
 [4, -16, -20, 20, -16],
 [1, -4, -5, 5, -4]]

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


[User]
Calculate the rank of matrix A where A =
[[-34, -24, 15, -13, -2],
 [22, -8, 3, -9, 6],
 [-5, -55, 30, -40, 10],
 [26, -14, 6, -14, 8],
 [-12, -32, 18, -22, 4]]

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


[User]
Compute the rank of the given 5x5 matrix:
[[-18, 6, 12, 0, -30],
 [-3, 1, 2, 0, -5],
 [15, -5, -10, 0, 25],
 [3, -1, -2, 0, 5],
 [18, -6, -12, 0, 30]]

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


[User]
Determine the rank of the following matrix:
[[-47, 30, -11, -2, -7],
 [-47, 18, -26, 4, -37],
 [-28, 16, -6, -12, 13],
 [-30, 26, 12, 24, -37],
 [17, 8, -6, -4, 34]]

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


[User]
What is the rank of the matrix:
[[-8, -11, -39, 12, -7],
 [-30, -18, -69, 4, 11],
 [6, 27, -14, 22, 21],
 [-33, -30, 37, -38, 27],
 [-14, -5, -41, 16, 11]]?

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


[User]
What is the rank of the matrix:
[[-2, -12, 10, 4, -10],
 [3, 18, -15, -6, 15],
 [1, 6, -5, -2, 5],
 [-6, -36, 30, 12, -30],
 [1, 6, -5, -2, 5]]?

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


[User]
Calculate the rank of matrix A where A =
[[-51, 13, 33, -13, 12],
 [-27, 4, 29, -38, 21],
 [-12, 7, -8, -31, -14],
 [39, -13, -13, 7, 5],
 [-42, 6, 46, 0, 31]]

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


[User]
What is the rank of the matrix:
[[-9, -6, 6, -16, 6],
 [-4, 30, -9, 10, -16],
 [5, 36, -15, 26, -22],
 [-23, 36, -3, -14, -14],
 [-20, 24, 0, -16, -8]]?

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


[User]
Calculate the rank of matrix A where A =
[[-12, -10, 13, 0, -18],
 [0, 10, 5, 0, -30],
 [38, 50, -32, 0, 2],
 [-34, -40, 31, 0, -16],
 [40, 50, -35, 0, 10]]

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


[User]
Calculate the rank of matrix A where A =
[[-7, -17, -24, -18, -8],
 [8, 2, -36, -2, 2],
 [-15, -8, 44, -13, 17],
 [11, 10, -10, 25, -31],
 [-11, -14, 12, -7, -17]]

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


[User]
Find the rank of the matrix:
[[-1, 30, -14, 29, 0],
 [16, 11, -16, 5, 4],
 [12, -19, 0, -17, -8],
 [-3, 10, -6, 23, -26],
 [-19, 29, -2, 36, -8]]

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


[User]
Calculate the rank of matrix A where A =
[[-16, 12, 4, 24, 8],
 [16, -12, -4, -24, -8],
 [-20, 15, 5, 30, 10],
 [-12, 9, 3, 18, 6],
 [-4, 3, 1, 6, 2]]

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


[User]
Compute the rank of the given 5x5 matrix:
[[11, -8, -19, -12, -5],
 [-46, -27, -36, -28, -35],
 [21, 35, 25, 28, 34],
 [14, 0, 15, 37, 41],
 [50, 19, 17, -15, -8]]

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


[User]
Calculate the rank of matrix A where A =
[[-2, 18, 4, 16, 10],
 [12, 31, 0, 13, 15],
 [-16, 1, 9, 5, -5],
 [-48, 48, 51, -54, -66],
 [8, 2, -11, 44, 36]]

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


[User]
Compute the rank of the given 5x5 matrix:
[[30, -4, 5, -7, 57],
 [-11, -25, 23, -22, -9],
 [-14, 15, -4, 19, -6],
 [28, 28, 29, 9, 33],
 [6, -13, -31, -16, -42]]

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


[User]
Find the rank of the matrix:
[[-8, -14, 5, 6, 5],
 [3, 16, 36, 5, -6],
 [10, 34, 29, -4, -4],
 [-14, -22, -7, 4, 17],
 [9, 2, -15, -3, -15]]

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


[User]
Compute the rank of the given 5x5 matrix:
[[0, 14, 22, -10, -21],
 [-39, 33, 6, 6, -13],
 [38, -27, -38, -6, -23],
 [-51, 57, 5, -8, -5],
 [-41, 17, 33, 26, -22]]

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


[User]
Find the rank of the matrix:
[[-13, 31, 8, 61, -15],
 [-17, 7, 4, 37, 13],
 [19, -6, -8, -42, -22],
 [-26, -17, -10, 13, 31],
 [2, 33, 22, 51, -11]]

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


[User]
Compute the rank of the given 5x5 matrix:
[[22, 6, -42, -9, 31],
 [10, -30, -4, 30, -9],
 [30, -18, -50, 3, 19],
 [-41, 24, 62, -20, -33],
 [17, -42, -14, 34, -12]]

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


[User]
Find the rank of the matrix:
[[4, -36, 31, 20, 32],
 [7, 2, 45, 14, 20],
 [7, 42, -7, -32, -22],
 [2, 32, -4, -15, -17],
 [24, 24, 35, -41, 9]]

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


[User]
Calculate the rank of matrix A where A =
[[10, 10, 12, -10, 10],
 [15, 15, 18, -15, 15],
 [0, 0, 0, 0, 0],
 [-20, -20, -24, 20, -20],
 [10, 10, 12, -10, 10]]

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


[User]
What is the rank of the matrix:
[[2, 13, -28, -25, 11],
 [-9, 42, -26, -31, -3],
 [11, 16, -2, 3, 11],
 [-1, 46, -26, -27, 5],
 [16, 14, 16, 22, 10]]?

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


[User]
Calculate the rank of matrix A where A =
[[-11, -19, -16, -9, 19],
 [18, 54, 60, -12, -54],
 [-7, -12, -31, 35, 17],
 [-24, -17, -3, -40, 18],
 [-28, -33, -39, 0, 38]]

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


[User]
Find the rank of the matrix:
[[-17, -25, 66, -6, 30],
 [-18, 22, -5, 6, 11],
 [27, 19, -1, -47, 3],
 [17, -28, 50, -32, -6],
 [59, -70, 37, -36, -3]]

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


[User]
Compute the rank of the given 5x5 matrix:
[[-2, -8, 6, 6, -6],
 [6, 24, -18, -18, 18],
 [1, 4, -3, -3, 3],
 [-6, -24, 18, 18, -18],
 [1, 4, -3, -3, 3]]

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


[User]
Determine the rank of the following matrix:
[[8, -2, -10, -12, 0],
 [-4, 1, 5, 6, 0],
 [-4, 1, 5, 6, 0],
 [12, -3, -15, -18, 0],
 [20, -5, -25, -30, 0]]

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


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

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


[User]
Compute the rank of the given 5x5 matrix:
[[24, -39, 12, -28, 9],
 [-50, 46, 19, 4, 35],
 [26, 11, -12, 38, -21],
 [20, 11, -23, 30, -34],
 [-2, -15, 11, -22, 14]]

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


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

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


[User]
What is the rank of the matrix:
[[-21, 5, -38, 22, 17],
 [7, 31, 1, 16, -6],
 [5, 13, -22, 26, 17],
 [5, 31, -16, 38, 17],
 [42, 12, 55, -10, -15]]?

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


[User]
What is the rank of the matrix:
[[25, 68, 17, -31, 49],
 [22, -9, -22, 0, -23],
 [17, -1, -27, -14, -14],
 [-23, -17, -19, -8, 2],
 [30, 32, -34, -38, 12]]?

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


[User]
Find the rank of the matrix:
[[58, -7, 69, -19, -5],
 [2, -4, -28, 72, -64],
 [-22, 15, -41, -44, 46],
 [-22, -3, 51, -33, 35],
 [30, -14, -62, -30, 30]]

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


[User]
Find the rank of the matrix:
[[-14, 44, 30, -7, 7],
 [-4, 25, 24, -8, -4],
 [6, 40, 24, -23, -8],
 [-12, 5, 42, 6, -15],
 [-8, 46, 12, -12, 14]]

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


[User]
Calculate the rank of matrix A where A =
[[6, -14, 23, 12, 7],
 [23, 60, -7, -43, 47],
 [34, 8, 4, -14, 8],
 [-18, 36, -12, -18, 24],
 [-21, 68, -50, -45, 20]]

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


[User]
Find the rank of the matrix:
[[67, 25, 4, -25, -19],
 [-21, 6, -9, 17, 32],
 [-6, 35, -12, 23, 11],
 [-30, 5, 3, 23, 23],
 [50, 55, -7, 5, 29]]

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


[User]
Determine the rank of the following matrix:
[[-9, -12, 12, -6, -13],
 [-36, -42, 24, 6, -23],
 [-66, -72, 24, 36, -18],
 [1, 0, 4, -6, -5],
 [0, 0, 0, 0, 0]]

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


[User]
What is the rank of the matrix:
[[-12, 0, -38, 18, 8],
 [-20, 24, 10, 5, 36],
 [-5, -19, -5, 2, 25],
 [30, -30, -6, -7, -22],
 [7, -39, 43, -24, 13]]?

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


[User]
Compute the rank of the given 5x5 matrix:
[[-24, -16, 4, 12, 24],
 [0, 0, 0, 0, 0],
 [0, 0, 0, 0, 0],
 [36, 24, -6, -18, -36],
 [-12, -8, 2, 6, 12]]

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


[User]
Calculate the rank of matrix A where A =
[[-24, 45, -8, -31, -2],
 [-12, -42, 30, -16, -2],
 [8, -27, 8, 9, -2],
 [-12, -3, 10, -15, 0],
 [-8, 27, -8, -9, 2]]

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


[User]
Compute the rank of the given 5x5 matrix:
[[21, 23, 14, 13, -15],
 [-3, -33, 24, 39, 30],
 [-8, -8, -6, -6, 5],
 [-30, -42, -12, -6, 30],
 [-13, 1, -22, -29, -5]]

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


[User]
Find the rank of the matrix:
[[-10, 2, 6, 10, -8],
 [4, -20, 4, -24, 24],
 [7, 13, -9, 8, -10],
 [23, 5, -17, -13, 8],
 [-6, -18, 10, -14, 16]]

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


[User]
Calculate the rank of matrix A where A =
[[31, -22, -29, 28, 27],
 [8, -12, -12, 6, -6],
 [-30, 33, 42, -30, -24],
 [5, 17, 17, 2, 19],
 [6, -5, -8, 7, 11]]

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


[User]
Find the rank of the matrix:
[[3, 18, 18, 15, 6],
 [-5, -30, -30, -25, -10],
 [-3, -18, -18, -15, -6],
 [0, 0, 0, 0, 0],
 [-3, -18, -18, -15, -6]]

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


[User]
Compute the rank of the given 5x5 matrix:
[[-27, -4, -10, 6, 9],
 [-34, -39, -1, -14, 32],
 [-20, -12, -14, -4, 22],
 [-46, 14, -33, 20, 9],
 [-30, 12, -20, 20, 14]]

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


[User]
What is the rank of the matrix:
[[0, 0, 0, 0, 0],
 [-36, 36, -12, 6, -6],
 [-24, 24, -8, 4, -4],
 [6, -6, 2, -1, 1],
 [30, -30, 10, -5, 5]]?

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


[User]
Calculate the rank of matrix A where A =
[[23, 5, 29, 9, -8],
 [14, 3, 14, 2, -4],
 [-26, 7, -20, -3, 11],
 [10, -7, 12, 7, -7],
 [8, -21, -10, -7, -7]]

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


[User]
What is the rank of the matrix:
[[1, 2, 0, 3, -5],
 [-18, 7, -19, -25, -15],
 [-14, 10, -8, -26, -14],
 [-3, 10, -10, 5, -27],
 [-22, -24, -44, -14, 26]]?

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


[User]
Find the rank of the matrix:
[[0, 24, 0, -18, 24],
 [0, -24, 0, 18, -24],
 [0, -16, 0, 12, -16],
 [0, 12, 0, -9, 12],
 [0, -16, 0, 12, -16]]

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


[User]
Calculate the rank of matrix A where A =
[[13, -16, 37, -4, 3],
 [-22, 17, -61, 2, -9],
 [-8, 29, -6, 11, 10],
 [11, 8, -17, 8, 1],
 [-2, 15, 13, 6, 9]]

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


[User]
Determine the rank of the following matrix:
[[-5, -10, 18, 12, -64],
 [7, 42, 15, -30, -9],
 [13, -54, 20, -10, 27],
 [-3, 26, -8, -2, -1],
 [9, -14, 4, -14, 37]]

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


[User]
What is the rank of the matrix:
[[-26, -5, 54, -34, -10],
 [22, 1, -22, 18, 2],
 [8, -4, 24, -8, -8],
 [24, 3, -38, 26, 6],
 [16, 4, -40, 24, 8]]?

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


[User]
What is the rank of the matrix:
[[51, -30, -17, -16, -49],
 [-44, 26, 7, 10, 26],
 [-20, -28, -22, 8, 8],
 [-18, 18, -2, 0, -11],
 [-40, -44, -57, -33, 46]]?

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


[User]
Find the rank of the matrix:
[[18, 4, 14, 16, 16],
 [-20, 24, 4, 0, 0],
 [30, -36, -6, 0, 0],
 [35, -10, 15, 20, 20],
 [-18, 60, 30, 24, 24]]

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


[User]
Determine the rank of the following matrix:
[[57, -21, -47, 15, -29],
 [0, -11, -3, -4, -7],
 [5, -27, -37, -31, -13],
 [25, 30, -13, 20, 20],
 [49, 18, -36, 23, 6]]

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


[User]
Compute the rank of the given 5x5 matrix:
[[-12, 50, -44, 36, 30],
 [-22, 25, -33, 15, -1],
 [-19, 6, -5, 39, 8],
 [-36, 13, -25, 31, -9],
 [7, 8, -3, 1, 10]]

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


[User]
Determine the rank of the following matrix:
[[30, -26, 14, -24, 9],
 [-24, -5, -13, 12, -6],
 [66, -61, 27, -30, -3],
 [6, -50, -2, -6, -7],
 [12, 7, 11, -33, 30]]

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


[User]
Compute the rank of the given 5x5 matrix:
[[-10, -20, -34, -4, -1],
 [14, 3, -3, 7, 9],
 [22, -23, -44, -7, 15],
 [-4, 18, 67, -34, -20],
 [5, 28, 28, -20, -22]]

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


[User]
Compute the rank of the given 5x5 matrix:
[[24, 12, 8, 24, -12],
 [-30, -15, -10, -30, 15],
 [-12, -6, -4, -12, 6],
 [-6, -3, -2, -6, 3],
 [-12, -6, -4, -12, 6]]

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


[User]
Compute the rank of the given 5x5 matrix:
[[26, 22, -6, 22, 30],
 [-43, -2, -9, -11, -45],
 [21, 23, -14, 23, 19],
 [14, -44, 12, -26, -6],
 [23, 44, -7, 35, 41]]

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


[User]
Determine the rank of the following matrix:
[[-9, -1, 8, 3, -12],
 [9, 1, -8, -3, 12],
 [3, -13, -16, 23, 12],
 [-15, -5, 10, 11, -18],
 [-3, -2, 1, 4, -3]]

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


[User]
Find the rank of the matrix:
[[-4, -20, -4, 12, -8],
 [10, 26, 1, -16, 10],
 [-21, 15, 24, -7, 8],
 [21, -39, -33, 21, -18],
 [-3, -15, -3, 9, -6]]

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


[User]
Calculate the rank of matrix A where A =
[[-3, -3, 0, -18, -27],
 [9, 12, 3, -18, -18],
 [16, 20, 4, 0, 12],
 [2, 2, 0, 12, 18],
 [19, 24, 5, -6, 6]]

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


[User]
What is the rank of the matrix:
[[9, 30, 15, -15, 18],
 [5, 14, -4, -11, 31],
 [22, 20, -15, -10, 19],
 [42, 26, -38, -12, 25],
 [-16, -6, 7, -2, 18]]?

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


[User]
Find the rank of the matrix:
[[50, -40, 6, 32, -4],
 [-15, 12, 7, -8, -6],
 [-10, 8, -54, -16, 44],
 [0, 0, 22, 4, -18],
 [-25, 20, 19, -12, -16]]

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


[User]
What is the rank of the matrix:
[[10, 17, 32, 34, -21],
 [0, 3, 21, 25, -23],
 [10, -23, -10, 18, 15],
 [-22, -6, 10, 1, -36],
 [14, 1, -23, -20, 41]]?

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


[User]
Calculate the rank of matrix A where A =
[[-33, 42, -27, 15, 39],
 [-6, 14, -12, -8, 23],
 [-27, 14, -23, 31, -5],
 [-3, -20, -13, 17, -34],
 [8, -20, 4, 4, -26]]

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


[User]
Compute the rank of the given 5x5 matrix:
[[-18, 7, 0, 2, -20],
 [-16, -9, 36, 6, -14],
 [-2, 22, -18, 2, 6],
 [-5, 33, -6, 8, 15],
 [23, -38, 12, -8, 9]]

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


[User]
Compute the rank of the given 5x5 matrix:
[[8, -16, -4, 16, 12],
 [-10, 20, 5, -20, -15],
 [-12, 24, 6, -24, -18],
 [12, -24, -6, 24, 18],
 [10, -20, -5, 20, 15]]

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


[User]
Compute the rank of the given 5x5 matrix:
[[-16, 10, -6, -4, 26],
 [0, 2, 2, 28, 2],
 [9, -4, 5, 25, -13],
 [-9, 3, -6, -39, 12],
 [1, 0, 1, 9, -1]]

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


[User]
Compute the rank of the given 5x5 matrix:
[[-20, 36, 16, 24, 38],
 [-17, 24, 6, 3, 55],
 [12, -37, -21, -35, -19],
 [-4, -8, -12, -28, 42],
 [19, -27, -19, -42, 33]]

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


[User]
Compute the rank of the given 5x5 matrix:
[[46, 6, -44, 28, 20],
 [48, -27, -12, 12, 33],
 [-68, 12, 44, -32, -40],
 [12, -13, 4, -4, 3],
 [-8, -13, 19, -6, 11]]

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


[User]
Find the rank of the matrix:
[[0, 0, 0, 0, 0],
 [30, -25, 30, 15, -25],
 [18, -15, 18, 9, -15],
 [-36, 30, -36, -18, 30],
 [-36, 30, -36, -18, 30]]

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


[User]
Calculate the rank of matrix A where A =
[[6, 24, 0, 24, -24],
 [-4, -16, 0, -16, 16],
 [-1, -4, 0, -4, 4],
 [-4, -16, 0, -16, 16],
 [2, 8, 0, 8, -8]]

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


[User]
Determine the rank of the following matrix:
[[-12, 24, 16, -24, 8],
 [12, -24, -16, 24, -8],
 [-12, 24, 16, -24, 8],
 [18, -36, -24, 36, -12],
 [15, -30, -20, 30, -10]]

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


[User]
What is the rank of the matrix:
[[1, 4, 6, 1, -1],
 [11, 8, -6, 11, 10],
 [18, 12, -12, 18, 17],
 [-9, 24, 66, -9, -26],
 [7, 16, 18, 7, 0]]?

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


[User]
Compute the rank of the given 5x5 matrix:
[[-64, 4, 2, -6, -20],
 [-40, 6, 19, -13, -6],
 [-7, -4, 12, -12, -3],
 [-77, 6, -11, 4, -24],
 [-6, 2, -51, 30, -20]]

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


[User]
What is the rank of the matrix:
[[0, -54, 6, 0, 0],
 [-1, 4, -3, -2, -6],
 [-11, -10, -27, -22, -66],
 [-5, -34, -9, -10, -30],
 [-4, -11, -9, -8, -24]]?

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


[User]
Find the rank of the matrix:
[[-49, -18, -13, -20, 19],
 [-18, -16, 18, -51, -13],
 [31, 22, 12, -35, 19],
 [-11, -10, -1, 9, -12],
 [37, 26, 11, -30, 21]]

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, 0, 0, 0],
 [2, -5, 2, 1, -2],
 [0, 0, 0, 0, 0],
 [-6, 15, -6, -3, 6]]

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


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

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


[User]
Calculate the rank of matrix A where A =
[[20, 32, -14, -30, 56],
 [14, 22, -12, -36, 20],
 [-14, 16, -7, 21, 6],
 [18, -23, 19, 12, 57],
 [19, -11, 8, -54, 22]]

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


[User]
Compute the rank of the given 5x5 matrix:
[[-10, -24, 16, -15, 30],
 [-43, 24, -4, -9, -5],
 [30, 19, -53, -42, 21],
 [28, -10, 43, 17, 5],
 [15, 10, 62, 3, 19]]

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


[User]
Find the rank of the matrix:
[[-41, 42, -16, -23, 6],
 [7, -12, 14, 5, -30],
 [-8, 15, -19, -6, 42],
 [-5, 15, -25, -5, 60],
 [-34, 30, -2, -18, -24]]

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


[User]
Determine the rank of the following matrix:
[[12, -25, -7, 22, -22],
 [0, 11, 8, -20, 38],
 [-5, -3, -9, 17, -41],
 [16, -30, 19, 2, 28],
 [-39, 43, 23, -25, -11]]

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


[User]
What is the rank of the matrix:
[[29, 11, -21, 29, -17],
 [40, 2, -12, 14, -43],
 [13, 58, 53, 0, -28],
 [48, -8, -53, 20, -27],
 [62, -6, -54, 30, -44]]?

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


[User]
Determine the rank of the following matrix:
[[11, -6, 13, 8, -14],
 [4, -36, 5, -11, -8],
 [-18, 51, -1, 13, 0],
 [-33, 45, -69, -21, 78],
 [3, 9, 7, 2, -2]]

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


[User]
Calculate the rank of matrix A where A =
[[25, -4, 32, 9, -35],
 [-36, -4, 7, -24, -25],
 [57, 6, 21, 45, 12],
 [-19, 1, -22, 33, 48],
 [24, 20, -15, -42, 15]]

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


[User]
What is the rank of the matrix:
[[-8, 37, 4, 29, 20],
 [27, 39, -26, 43, 31],
 [59, -1, -42, 3, 15],
 [-21, 3, 8, 15, -3],
 [1, -17, -8, 3, -9]]?

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


[User]
What is the rank of the matrix:
[[-13, -2, -13, -14, -2],
 [-11, 2, -3, -2, -6],
 [-7, -2, -9, -10, 0],
 [-2, 8, 16, 20, -10],
 [-17, 2, -7, -6, -8]]?

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


[User]
Find the rank of the matrix:
[[-8, 16, 24, 12, 16],
 [2, -4, -6, -3, -4],
 [2, -4, -6, -3, -4],
 [2, -4, -6, -3, -4],
 [-4, 8, 12, 6, 8]]

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


[User]
Find the rank of the matrix:
[[0, -6, 2, -4, -6],
 [0, -36, 12, -24, -36],
 [0, -24, 8, -16, -24],
 [0, 18, -6, 12, 18],
 [0, -30, 10, -20, -30]]

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


[User]
Determine the rank of the following matrix:
[[40, 20, -16, 22, -20],
 [-8, -55, -26, -31, -4],
 [-10, 25, -42, 47, -64],
 [32, 10, -36, 26, -40],
 [28, 20, 12, 7, 10]]

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


[User]
Determine the rank of the following matrix:
[[12, -9, -12, -15, 15],
 [8, -6, -8, -10, 10],
 [16, -12, -16, -20, 20],
 [-12, 9, 12, 15, -15],
 [4, -3, -4, -5, 5]]

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


[User]
Find the rank of the matrix:
[[20, -10, -13, -9, -10],
 [28, -25, -12, -3, 26],
 [-38, 23, 15, -17, -70],
 [-62, 69, 26, 24, -36],
 [-18, -2, 8, -23, -50]]

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


[User]
What is the rank of the matrix:
[[-23, 22, -4, -7, 33],
 [7, -8, -4, 3, -17],
 [-4, 5, 4, -2, 12],
 [8, -4, 16, 0, 8],
 [10, -11, -4, 4, -22]]?

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


[User]
What is the rank of the matrix:
[[11, 19, 28, 35, -10],
 [-24, -57, -30, -33, 45],
 [14, -9, -51, -67, 38],
 [-22, -3, -11, -14, -35],
 [62, 61, -13, -26, 23]]?

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


[User]
Find the rank of the matrix:
[[-24, -36, 36, 0, -6],
 [20, 30, -30, 0, 5],
 [20, 30, -30, 0, 5],
 [-16, -24, 24, 0, -4],
 [-12, -18, 18, 0, -3]]

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


[User]
Find the rank of the matrix:
[[1, -10, -8, -5, -6],
 [5, -18, -22, -5, -8],
 [-11, 14, 34, -5, 0],
 [6, -12, -21, 0, -3],
 [-8, 0, 19, -10, -7]]

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


[User]
Compute the rank of the given 5x5 matrix:
[[-7, -6, -23, -38, 19],
 [-14, 4, 25, 41, -26],
 [-33, -16, -7, -1, 2],
 [28, 18, -9, -33, 12],
 [-24, -15, 8, 38, -37]]

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


[User]
What is the rank of the matrix:
[[2, 35, 33, -13, -24],
 [38, -52, -30, 11, 12],
 [8, -34, -34, 16, 0],
 [16, -38, -22, 6, 30],
 [10, 23, 29, -13, -12]]?

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


[User]
Determine the rank of the following matrix:
[[-20, -18, -12, -6, 3],
 [12, 10, 4, 0, 0],
 [-6, -5, -2, 0, 0],
 [-2, 5, 26, 30, -15],
 [0, -8, -32, -36, 18]]

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


[User]
Determine the rank of the following matrix:
[[13, -16, -21, 9, 34],
 [17, -17, -27, 15, 38],
 [-24, 6, 36, -36, -24],
 [-5, -20, 5, -25, 30],
 [22, -14, -34, 26, 36]]

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


[User]
Find the rank of the matrix:
[[-23, 3, 18, 28, 42],
 [32, 4, -18, -29, -36],
 [5, 9, 18, 23, 0],
 [-14, -16, -24, -31, -6],
 [-13, 13, 18, 16, -6]]

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


[User]
Find the rank of the matrix:
[[4, -20, -8, 16, -4],
 [6, -30, -12, 24, -6],
 [0, 0, 0, 0, 0],
 [-1, 5, 2, -4, 1],
 [3, -15, -6, 12, -3]]

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


[User]
What is the rank of the matrix:
[[-35, 12, -5, 23, -12],
 [24, 4, -22, 36, 16],
 [-14, 10, -6, 38, 13],
 [-11, -1, -16, 11, -10],
 [18, -30, -6, -42, -3]]?

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


[User]
Determine the rank of the following matrix:
[[-52, -56, -13, -35, -12],
 [19, 0, -40, -5, 2],
 [-35, -34, 9, -45, 11],
 [65, 60, 2, 17, 26],
 [-41, -28, 35, -38, 10]]

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


[User]
What is the rank of the matrix:
[[-10, -3, 11, 18, -7],
 [11, -25, 19, -8, -23],
 [36, 11, 19, -26, -29],
 [-72, -9, 21, 82, -11],
 [-13, -19, 1, 20, 14]]?

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


[User]
Compute the rank of the given 5x5 matrix:
[[34, 32, 31, 12, 30],
 [-44, 0, -26, 24, -20],
 [25, -14, 10, -27, 5],
 [41, 14, 29, -9, 25],
 [-9, 42, 9, 45, 15]]

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


[User]
Calculate the rank of matrix A where A =
[[9, 15, 6, 18, 18],
 [12, 20, 8, 24, 24],
 [3, 5, 2, 6, 6],
 [0, 0, 0, 0, 0],
 [-15, -25, -10, -30, -30]]

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


[User]
Calculate the rank of matrix A where A =
[[73, 58, 36, 46, -17],
 [2, -21, -22, -14, 77],
 [-7, 18, 22, 10, -39],
 [-7, 32, -17, 20, -20],
 [-4, 16, -17, 9, 29]]

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


[User]
Find the rank of the matrix:
[[-16, 20, -1, 3, -8],
 [-4, -12, -23, -37, -4],
 [28, -52, -9, -13, -6],
 [4, -8, 6, 17, -13],
 [-12, 36, 19, 28, 9]]

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


[User]
Compute the rank of the given 5x5 matrix:
[[30, 0, 0, -24, -6],
 [10, 0, 0, -8, -2],
 [-30, 0, 0, 24, 6],
 [25, 0, 0, -20, -5],
 [0, 0, 0, 0, 0]]

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


[User]
What is the rank of the matrix:
[[4, 2, -4, 46, 17],
 [-1, -6, -25, -1, 4],
 [31, -34, -16, -11, -31],
 [6, -11, 4, -59, -30],
 [72, -50, -31, -16, -44]]?

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


[User]
What is the rank of the matrix:
[[4, -27, 40, 34, 4],
 [4, 33, -50, -46, -6],
 [-4, 3, -4, -2, 0],
 [4, -27, 40, 34, 4],
 [-28, -15, 26, 34, 6]]?

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


[User]
Calculate the rank of matrix A where A =
[[11, -10, -15, -9, 48],
 [20, -30, -6, -14, -12],
 [-27, 40, 9, 19, 12],
 [0, 0, 0, 0, 0],
 [-14, 15, 15, 11, -42]]

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


[User]
Find the rank of the matrix:
[[0, 0, 0, 0, 0],
 [-24, -16, -4, -24, 8],
 [-18, -12, -3, -18, 6],
 [-30, -20, -5, -30, 10],
 [-6, -4, -1, -6, 2]]

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


[User]
Compute the rank of the given 5x5 matrix:
[[10, -5, -20, -10, 25],
 [-8, 4, 16, 8, -20],
 [4, -2, -8, -4, 10],
 [-6, 3, 12, 6, -15],
 [-2, 1, 4, 2, -5]]

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


[User]
Determine the rank of the following matrix:
[[12, 40, -12, 7, -26],
 [24, 27, -4, 7, -16],
 [40, -7, 11, 7, 24],
 [4, 37, -6, -1, -38],
 [-8, 41, -32, 17, -24]]

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


[User]
Determine the rank of the following matrix:
[[13, -3, 28, 18, -23],
 [-40, -40, 19, 13, 23],
 [-6, -2, -32, -20, 10],
 [40, 24, 10, 6, -38],
 [-1, -9, -73, -45, 2]]

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


[User]
Calculate the rank of matrix A where A =
[[-14, 10, -12, -6, -6],
 [9, -19, -30, -26, -15],
 [-1, 3, 6, 5, 3],
 [3, -9, -18, -15, -9],
 [-10, 14, 12, 12, 6]]

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


[User]
Find the rank of the matrix:
[[6, 6, -10, 10, -12],
 [-18, -18, 30, -30, 36],
 [-18, -18, 30, -30, 36],
 [15, 15, -25, 25, -30],
 [12, 12, -20, 20, -24]]

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


[User]
Find the rank of the matrix:
[[8, -2, -2, -8, -8],
 [8, -2, -2, -8, -8],
 [-8, 2, 2, 8, 8],
 [8, -2, -2, -8, -8],
 [0, 0, 0, 0, 0]]

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


[User]
Calculate the rank of matrix A where A =
[[9, 12, 15, -1, -26],
 [-3, 29, 45, -5, -60],
 [-42, -1, 24, -38, -18],
 [-25, 7, 17, 4, -6],
 [-20, 10, 10, 35, 10]]

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


[User]
Find the rank of the matrix:
[[-36, -28, 25, -12, 8],
 [1, -9, 19, 14, 49],
 [5, -23, -1, 22, 56],
 [-5, 5, -13, -2, -15],
 [-12, 8, -10, -8, -26]]

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


[User]
Find the rank of the matrix:
[[4, -14, 12, -12, -12],
 [36, -18, -36, 36, -12],
 [22, -5, -30, 30, -2],
 [14, -22, 6, -6, -18],
 [0, -9, 12, -12, -8]]

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


[User]
Calculate the rank of matrix A where A =
[[0, 0, 0, 0, 0],
 [10, -8, 0, 0, -12],
 [15, -12, 0, 0, -18],
 [-20, 16, 0, 0, 24],
 [-25, 20, 0, 0, 30]]

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


[User]
Determine the rank of the following matrix:
[[24, -43, 12, 38, 12],
 [62, 28, 27, 9, -8],
 [4, 3, -30, -27, 17],
 [-18, -47, -34, 8, 17],
 [-30, -39, 24, 31, 6]]

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


[User]
Determine the rank of the following matrix:
[[5, -35, 21, 4, 4],
 [34, 11, -9, 38, -85],
 [-13, 49, -27, -14, 19],
 [-29, 0, -16, -16, -26],
 [-44, 6, -10, -40, 52]]

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


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

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


[User]
Determine the rank of the following matrix:
[[-35, -15, 0, -38, -10],
 [5, -19, 16, -9, 3],
 [6, -11, 22, 13, 9],
 [9, -14, 18, -39, 1],
 [25, 34, -51, 34, -8]]

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


[User]
Determine the rank of the following matrix:
[[-17, 9, 24, -18, 14],
 [-15, -9, 24, -6, 18],
 [14, 6, -22, 7, -16],
 [18, -18, -24, 24, -12],
 [5, 3, -8, 2, -6]]

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


[User]
Find the rank of the matrix:
[[-30, 6, 0, 6, -18],
 [10, -2, 0, -2, 6],
 [-10, 2, 0, 2, -6],
 [-20, 4, 0, 4, -12],
 [0, 0, 0, 0, 0]]

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


[User]
Calculate the rank of matrix A where A =
[[30, 39, -23, 47, 56],
 [-6, 21, -7, 10, 1],
 [-25, -10, 39, -5, -9],
 [-17, 25, 0, 9, -6],
 [-46, 2, 46, -7, -25]]

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


[User]
Compute the rank of the given 5x5 matrix:
[[0, 12, -30, 18, 0],
 [0, 8, -20, 12, 0],
 [0, -6, 15, -9, 0],
 [0, 2, -5, 3, 0],
 [0, 10, -25, 15, 0]]

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


[User]
Compute the rank of the given 5x5 matrix:
[[12, 21, -18, -8, -10],
 [-6, 24, 4, -5, -33],
 [-24, 26, -19, 6, -42],
 [-24, 8, 11, 6, -30],
 [-24, -16, 16, 12, -4]]

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


[User]
Calculate the rank of matrix A where A =
[[-38, -32, 32, -18, -18],
 [15, 20, -9, 0, -17],
 [16, 14, -7, 5, 25],
 [-30, -22, -30, 40, -43],
 [3, -12, 6, -17, -14]]

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


[User]
Compute the rank of the given 5x5 matrix:
[[-27, 22, -28, -15, 30],
 [-28, 24, -16, -12, 24],
 [-11, 8, -22, -9, 18],
 [15, -12, 18, 9, -18],
 [18, -12, 48, 18, -36]]

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


[User]
Determine the rank of the following matrix:
[[26, 7, 14, -24, 4],
 [22, 2, -30, -2, -28],
 [-32, -10, -32, 36, -16],
 [-30, -9, -26, 32, -12],
 [24, 6, 8, -20, 0]]

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


[User]
Determine the rank of the following matrix:
[[6, 43, -21, -38, 4],
 [-17, 52, 21, -11, 26],
 [-32, 22, 6, -64, 22],
 [-4, 23, -4, -27, 15],
 [21, -12, 0, 40, 2]]

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


[User]
Determine the rank of the following matrix:
[[-26, 59, -7, 38, -24],
 [14, 45, -54, -12, 29],
 [5, -9, 1, -16, 7],
 [7, 5, 14, 21, 4],
 [-13, -12, 4, 9, -19]]

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


[User]
Calculate the rank of matrix A where A =
[[36, 30, -12, 6, -42],
 [-30, -18, -8, 20, 36],
 [-24, -6, -22, 12, 18],
 [39, 14, 32, -45, -43],
 [0, -2, -6, 56, 22]]

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


[User]
Calculate the rank of matrix A where A =
[[-29, -45, 12, 21, 17],
 [-2, -2, -2, 18, 6],
 [12, 75, -3, 12, -12],
 [-57, -9, 33, 33, 15],
 [15, 28, -5, -15, -11]]

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


[User]
Calculate the rank of matrix A where A =
[[16, -10, 4, 14, -20],
 [31, -18, 5, 23, -14],
 [27, -16, 5, 21, -18],
 [-13, 9, -5, -14, 32],
 [29, -17, 5, 22, -16]]

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


[User]
Calculate the rank of matrix A where A =
[[-4, -16, 14, -28, 8],
 [11, 6, 23, 7, 5],
 [-1, 22, 23, 3, -7],
 [13, -14, -3, 9, 11],
 [5, -18, 31, -27, 15]]

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


[User]
What is the rank of the matrix:
[[-37, 23, -21, -4, 4],
 [7, -2, -9, 7, -21],
 [37, -5, -10, -7, -41],
 [-36, -7, -28, -7, -15],
 [24, 6, 48, 30, 46]]?

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


[User]
Find the rank of the matrix:
[[0, 0, 0, 0, 0],
 [-5, 4, -4, 1, 0],
 [20, -16, 16, -4, 0],
 [10, -8, 8, -2, 0],
 [25, -20, 20, -5, 0]]

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


[User]
Calculate the rank of matrix A where A =
[[20, -30, -24, 6, -4],
 [-40, -10, -32, 18, 8],
 [-35, -14, -34, 18, 7],
 [-50, -2, -28, 18, 10],
 [25, -20, -10, 0, -5]]

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


[User]
Determine the rank of the following matrix:
[[30, 0, 19, -29, -2],
 [-24, -1, -10, 11, 17],
 [-1, -15, -50, -4, -20],
 [32, -4, 43, -10, -29],
 [23, 6, 64, -6, -6]]

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


[User]
Calculate the rank of matrix A where A =
[[-4, 8, -8, 10, 8],
 [6, -12, 12, -15, -12],
 [8, -16, 16, -20, -16],
 [-4, 8, -8, 10, 8],
 [-2, 4, -4, 5, 4]]

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


[User]
What is the rank of the matrix:
[[0, 0, 0, 0, 0],
 [-18, -30, -12, 0, -30],
 [-12, -20, -8, 0, -20],
 [6, 10, 4, 0, 10],
 [-15, -25, -10, 0, -25]]?

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


[User]
Compute the rank of the given 5x5 matrix:
[[-6, -6, -18, 0, -27],
 [5, 12, 12, -10, 2],
 [11, 10, 18, -8, 19],
 [-30, 14, 12, 11, -2],
 [-8, 14, 18, 0, 11]]

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


[User]
Calculate the rank of matrix A where A =
[[3, -6, -15, -15, 6],
 [5, -10, -25, -25, 10],
 [0, 0, 0, 0, 0],
 [1, -2, -5, -5, 2],
 [-1, 2, 5, 5, -2]]

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


[User]
What is the rank of the matrix:
[[40, -26, 44, 9, -26],
 [-3, -4, -28, 22, -8],
 [20, -29, 20, 12, -28],
 [32, -26, 30, 5, -24],
 [15, -15, 10, 25, -20]]?

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


[User]
Determine the rank of the following matrix:
[[15, 5, -20, 30, -10],
 [0, 0, 0, 0, 0],
 [6, 2, -8, 12, -4],
 [12, 4, -16, 24, -8],
 [-15, -5, 20, -30, 10]]

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


[User]
Compute the rank of the given 5x5 matrix:
[[20, -15, -30, -10, -20],
 [-16, 12, 24, 8, 16],
 [-12, 9, 18, 6, 12],
 [-16, 12, 24, 8, 16],
 [16, -12, -24, -8, -16]]

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


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

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


[User]
Find the rank of the matrix:
[[15, 9, -7, -27, 7],
 [-10, 24, 18, -22, -8],
 [-8, 15, 10, -38, 13],
 [45, 13, -23, -19, -9],
 [-15, -18, 3, 39, -6]]

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


[User]
Determine the rank of the following matrix:
[[23, -7, -35, -19, 27],
 [25, -26, 6, -21, 0],
 [47, -1, -29, -34, -9],
 [19, 10, -36, -3, -12],
 [-52, 0, 30, 25, 42]]

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


[User]
Find the rank of the matrix:
[[12, -18, 0, 0, -15],
 [8, -12, 0, 0, -10],
 [16, -24, 0, 0, -20],
 [12, -18, 0, 0, -15],
 [0, 0, 0, 0, 0]]

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


[User]
Find the rank of the matrix:
[[-60, -2, -1, 12, -3],
 [14, -35, 7, 17, 60],
 [-19, 29, -17, -17, -42],
 [43, 6, -30, -16, 18],
 [-9, -22, 3, 46, 39]]

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


[User]
Calculate the rank of matrix A where A =
[[0, 6, -9, -12, -6],
 [0, -4, 6, 8, 4],
 [0, 0, 0, 0, 0],
 [0, 10, -15, -20, -10],
 [0, -4, 6, 8, 4]]

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


[User]
What is the rank of the matrix:
[[3, 19, -24, 25, 38],
 [18, 13, -6, 12, 20],
 [-12, -1, -14, 10, 16],
 [6, 1, -2, 4, 8],
 [15, 21, -18, 23, 36]]?

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


[User]
Find the rank of the matrix:
[[72, -34, -38, -56, -22],
 [6, -16, -14, -17, 9],
 [-30, 14, 10, 41, -9],
 [30, -56, -55, -36, -5],
 [30, 5, 10, -21, -13]]

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


[User]
Determine the rank of the following matrix:
[[5, 18, 0, -19, -10],
 [2, 6, 1, -5, -5],
 [-15, -30, -20, 5, 50],
 [-5, -6, -10, -7, 20],
 [10, 36, 0, -38, -20]]

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


[User]
Determine the rank of the following matrix:
[[-67, 32, -2, -40, -30],
 [31, -14, 4, 18, 16],
 [-45, 12, -4, -22, -32],
 [-13, 8, 40, -10, 12],
 [-56, 42, -5, -41, -9]]

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


[User]
Compute the rank of the given 5x5 matrix:
[[12, -32, -27, 12, -17],
 [6, -34, -24, 12, -14],
 [30, -11, -54, -6, -38],
 [24, 13, -18, -6, -16],
 [-80, 29, 16, -46, 22]]

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


[User]
Calculate the rank of matrix A where A =
[[18, 54, -6, -54, 66],
 [5, 2, 37, 30, -34],
 [-14, -30, 26, 54, -66],
 [-29, 28, -33, -30, 26],
 [30, 30, -24, -63, 81]]

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


[User]
Calculate the rank of matrix A where A =
[[27, -36, -24, -9, 3],
 [-23, 9, -10, 33, 25],
 [-37, 33, 22, 27, 11],
 [2, 10, 12, -14, -14],
 [-22, 35, 24, 2, -8]]

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


[User]
What is the rank of the matrix:
[[16, 16, -8, -16, 16],
 [4, 14, 23, 21, -6],
 [0, -12, -30, -30, 12],
 [-16, -24, -12, -4, -8],
 [-24, -14, 37, 49, -34]]?

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


[User]
Compute the rank of the given 5x5 matrix:
[[-2, -36, -21, -10, -23],
 [-39, 79, 54, 32, 65],
 [-25, 25, -2, 50, 25],
 [-9, 46, 36, -5, 36],
 [14, 0, 16, -26, -8]]

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


[User]
Determine the rank of the following matrix:
[[0, 2, -6, 6, 0],
 [0, -3, 9, -9, 0],
 [0, 6, -18, 18, 0],
 [0, -3, 9, -9, 0],
 [0, -4, 12, -12, 0]]

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


[User]
What is the rank of the matrix:
[[36, -12, -30, -6, -34],
 [-8, -2, 23, -29, -1],
 [-38, 10, 41, -11, 31],
 [42, -12, -42, 6, -36],
 [18, -6, -15, -3, -17]]?

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[User]
Compute the rank of the given 5x5 matrix:
[[-42, 20, -38, -32, 18],
 [28, 44, -1, 47, 32],
 [43, -9, 28, 37, -10],
 [3, -68, 24, -29, -53],
 [14, 0, -7, 11, -2]]

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[User]
Determine the rank of the following matrix:
[[-15, -24, 6, 18, 2],
 [25, 39, -11, -30, -5],
 [-30, -21, 39, 36, 49],
 [15, 15, -15, -18, -17],
 [10, 18, -2, -12, 2]]

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


[User]
Determine the rank of the following matrix:
[[-34, -33, -26, -16, 30],
 [7, 41, 17, -67, -21],
 [35, 2, 36, 22, -28],
 [-3, -11, 10, -2, 2],
 [-59, 8, -18, -47, 40]]

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[User]
Calculate the rank of matrix A where A =
[[-3, -3, -27, -12, 9],
 [27, 21, 35, 19, -32],
 [-16, -32, -2, 47, -23],
 [-11, -3, 1, -14, 19],
 [33, 27, 13, 5, -28]]

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


[User]
What is the rank of the matrix:
[[0, -12, -7, 11, 10],
 [22, 43, 42, 3, -3],
 [16, -8, -3, 3, 6],
 [23, -22, -8, 22, 23],
 [-36, -6, -17, -17, -16]]?

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


[User]
What is the rank of the matrix:
[[21, 19, 2, -30, -11],
 [-21, -10, -32, 39, -13],
 [-27, -21, -14, 42, 5],
 [30, 28, 0, -42, -18],
 [-3, -1, -6, 6, -3]]?

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[User]
Calculate the rank of matrix A where A =
[[-16, 12, 4, 8, -12],
 [-24, 18, 6, 12, -18],
 [24, -18, -6, -12, 18],
 [20, -15, -5, -10, 15],
 [12, -9, -3, -6, 9]]

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[User]
Calculate the rank of matrix A where A =
[[22, 16, -12, 14, -30],
 [-30, -18, 0, -24, 30],
 [-3, 1, -12, -6, -5],
 [-1, -2, 6, 1, 5],
 [4, -6, 36, 14, 20]]

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[User]
Calculate the rank of matrix A where A =
[[30, -9, -10, 18, 27],
 [42, 0, -8, 36, 45],
 [0, 21, 10, 18, 12],
 [-18, 60, 32, 36, 15],
 [42, -21, -18, 18, 33]]

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[User]
Compute the rank of the given 5x5 matrix:
[[-18, 21, -51, 30, 27],
 [-30, -37, -13, 14, -15],
 [-18, 15, -45, 27, 22],
 [6, 5, 5, -4, 1],
 [-6, -35, 25, -11, -26]]

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[User]
Compute the rank of the given 5x5 matrix:
[[10, -42, -58, 2, 5],
 [19, -2, -8, -4, 20],
 [-11, 12, 38, -10, -19],
 [34, 18, 22, -14, 35],
 [24, -74, -51, -29, -9]]

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[User]
Compute the rank of the given 5x5 matrix:
[[-12, -20, -20, 8, -20],
 [-18, -30, -30, 12, -30],
 [-12, -20, -20, 8, -20],
 [-18, -30, -30, 12, -30],
 [18, 30, 30, -12, 30]]

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


[User]
Find the rank of the matrix:
[[-15, 42, -78, -40, 4],
 [21, -2, 2, 0, 12],
 [21, -22, -14, 13, 17],
 [-21, 28, -22, -22, -10],
 [48, -56, 56, 45, 21]]

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[User]
What is the rank of the matrix:
[[3, 14, 19, -19, 9],
 [-13, 7, 40, -3, 31],
 [2, 21, 23, -23, 15],
 [5, 5, 3, 5, -2],
 [5, 29, -9, -48, 5]]?

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

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[User]
Compute the rank of the given 5x5 matrix:
[[35, -50, -14, -28, -64],
 [27, 27, -24, -10, 15],
 [13, -3, -9, -8, -14],
 [-18, 0, 9, 66, -1],
 [-4, 5, -1, 44, -2]]

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[User]
Calculate the rank of matrix A where A =
[[4, 24, 10, -12, 44],
 [-4, 30, -4, -13, 6],
 [-4, 10, -3, 3, 5],
 [-1, -16, 1, 12, 18],
 [12, -66, 18, 15, 72]]

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

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


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

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


[User]
Determine the rank of the following matrix:
[[-6, -3, -2, -4, -1],
 [12, 6, 4, 8, 2],
 [12, 6, 4, 8, 2],
 [-30, -15, -10, -20, -5],
 [36, 18, 12, 24, 6]]

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[User]
What is the rank of the matrix:
[[-5, 27, 2, 8, 17],
 [3, -8, 22, -24, -30],
 [-7, -10, -4, 12, -22],
 [-21, 82, 24, 12, 10],
 [6, -38, -16, 6, -4]]?

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[User]
Determine the rank of the following matrix:
[[-18, 15, 0, -6, 33],
 [-18, 16, -27, -4, 16],
 [-9, -4, 36, 41, -16],
 [-11, -1, 32, 23, 13],
 [-5, 20, -29, 5, -56]]

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[User]
Compute the rank of the given 5x5 matrix:
[[7, 27, -42, 24, 13],
 [-28, -27, 42, -27, -40],
 [58, -6, 30, -48, 54],
 [21, -18, 21, 5, 31],
 [1, 3, -6, 6, 3]]

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[User]
What is the rank of the matrix:
[[26, 8, -16, 32, -16],
 [19, 38, 6, 6, 27],
 [-13, -16, 18, -16, 7],
 [14, -11, 2, 30, -19],
 [23, -9, 0, 46, -26]]?

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

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


[User]
Determine the rank of the following matrix:
[[-44, 40, -26, -86, 24],
 [-36, 14, 19, 17, -44],
 [11, -8, 28, 40, 30],
 [62, -40, -7, 21, 14],
 [-5, 15, -24, -58, 40]]

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


[User]
Compute the rank of the given 5x5 matrix:
[[42, -13, 88, -51, 22],
 [-11, 32, -75, 54, 14],
 [50, 2, 64, -29, 36],
 [-8, -15, -10, 16, -34],
 [-23, 22, -58, 26, 12]]

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


[User]
Determine the rank of the following matrix:
[[-15, -9, 6, -6, 9],
 [0, 0, 0, 0, 0],
 [10, 6, -4, 4, -6],
 [-10, -6, 4, -4, 6],
 [30, 18, -12, 12, -18]]

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


[User]
Determine the rank of the following matrix:
[[8, 22, 12, 32, -12],
 [9, -28, -19, 24, -1],
 [-19, 40, 37, 38, -15],
 [-37, -12, 5, 55, -4],
 [-14, -16, -5, 39, -3]]

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


[User]
Calculate the rank of matrix A where A =
[[4, -4, 10, -14, 13],
 [26, 21, 14, 2, 18],
 [-10, 0, -32, 23, -43],
 [-28, -18, -42, 34, -45],
 [-17, -19, -21, 14, -17]]

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


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

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


[User]
Calculate the rank of matrix A where A =
[[-8, 13, 12, 3, 21],
 [-5, -5, 18, -6, 0],
 [-18, 18, 36, 0, 36],
 [-13, -7, 42, -12, 6],
 [15, -30, -18, -9, -45]]

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


[User]
Compute the rank of the given 5x5 matrix:
[[-8, -5, -27, 15, -5],
 [-24, -25, -31, -5, 15],
 [8, 5, 27, -15, 5],
 [-8, -12, 8, -20, 16],
 [-16, -11, -49, 25, -7]]

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


[User]
What is the rank of the matrix:
[[-14, -20, 24, 54, 4],
 [-16, -22, 30, 60, 5],
 [-12, -12, 36, 36, 6],
 [-3, -4, 6, 11, 1],
 [-10, -12, 24, 34, 4]]?

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[User]
Determine the rank of the following matrix:
[[29, 21, 33, 60, 27],
 [-31, -6, -17, -58, -21],
 [10, 6, -10, 64, -6],
 [-6, 17, 30, -26, 12],
 [-7, 25, -46, 12, 0]]

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


[User]
What is the rank of the matrix:
[[20, 28, -60, -12, -6],
 [-6, -18, 18, 42, -11],
 [-10, -20, 30, 30, -5],
 [6, -3, -18, 42, -17],
 [-2, -19, 6, 66, -21]]?

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


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

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


[User]
Compute the rank of the given 5x5 matrix:
[[1, 6, -4, 2, -5],
 [-1, -6, 4, -2, 5],
 [-5, -30, 20, -10, 25],
 [0, 0, 0, 0, 0],
 [-6, -36, 24, -12, 30]]

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


[User]
Determine the rank of the following matrix:
[[8, -1, -4, -30, -18],
 [-6, 11, -38, 0, -6],
 [-41, 9, 5, 28, 39],
 [-26, 10, -14, 58, 36],
 [-13, 9, -23, 32, 15]]

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[User]
Calculate the rank of matrix A where A =
[[20, 15, -23, 7, -44],
 [-18, -12, 18, 5, 21],
 [8, 6, -30, 21, -67],
 [6, 6, 8, -2, 10],
 [-8, 0, 16, 27, -15]]

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


[User]
Compute the rank of the given 5x5 matrix:
[[19, -11, 14, 6, 27],
 [-6, 4, -1, 1, -3],
 [31, -21, 3, -7, 12],
 [7, -5, -1, -3, 0],
 [-13, 9, 0, 4, -3]]

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


[User]
Determine the rank of the following matrix:
[[-12, -24, 4, -4, 16],
 [-7, -18, 6, 4, 13],
 [15, 42, -16, -14, -31],
 [-2, -12, 8, 12, 10],
 [-9, -42, 25, 35, 34]]

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


[User]
What is the rank of the matrix:
[[0, 0, 0, 0, 0],
 [20, -5, 30, -20, 10],
 [16, -4, 24, -16, 8],
 [-20, 5, -30, 20, -10],
 [20, -5, 30, -20, 10]]?

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


[User]
Determine the rank of the following matrix:
[[-18, -18, -67, -13, 5],
 [-15, 12, -9, 6, -9],
 [-22, 28, 6, -19, -10],
 [15, -54, -60, -34, -2],
 [44, -38, 22, 9, 9]]

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


[User]
Determine the rank of the following matrix:
[[14, 5, -3, 40, 32],
 [-53, 8, 3, -2, -50],
 [-37, 17, -2, 58, -6],
 [-35, 8, 9, 70, -8],
 [-40, 10, 6, 56, -16]]

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[User]
Calculate the rank of matrix A where A =
[[48, 7, -43, -12, 26],
 [23, -26, -7, -6, 24],
 [16, -10, -20, 24, 36],
 [-8, 14, 1, 0, -12],
 [40, -14, -34, 8, 44]]

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


[User]
Compute the rank of the given 5x5 matrix:
[[25, 15, 35, 15, -10],
 [25, 9, 32, 12, -10],
 [20, -48, -2, -18, -8],
 [30, 6, 36, 12, -12],
 [30, 12, 39, 15, -12]]

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


[User]
Find the rank of the matrix:
[[14, -13, 26, 9, -24],
 [-10, 19, -2, 28, 3],
 [8, -15, -21, -15, 4],
 [10, -9, -48, 27, 2],
 [-2, 7, -26, 26, 5]]

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


[User]
What is the rank of the matrix:
[[-16, -24, -6, 24, -4],
 [13, 21, 4, -21, 5],
 [9, 21, -1, -21, 11],
 [5, 9, 1, -9, 3],
 [4, 12, -2, -12, 8]]?

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


[User]
Compute the rank of the given 5x5 matrix:
[[-20, 6, -28, 38, 52],
 [-38, -24, -54, -22, -43],
 [17, -12, 25, -20, 5],
 [-39, -6, -48, -15, -57],
 [40, 25, 58, -3, -15]]

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


[User]
Determine the rank of the following matrix:
[[25, -10, 25, 15, 0],
 [-25, 10, -25, -15, 0],
 [-5, 2, -5, -3, 0],
 [30, -12, 30, 18, 0],
 [15, -6, 15, 9, 0]]

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[User]
Calculate the rank of matrix A where A =
[[30, -21, -32, -25, 2],
 [28, -17, -18, -115, -36],
 [-64, -19, -52, -10, 10],
 [14, -34, 4, 20, 4],
 [-22, -40, -27, 10, 9]]

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


[User]
Determine the rank of the following matrix:
[[2, -5, -2, 2, -22],
 [4, -4, 2, 7, -17],
 [2, 9, 12, 9, 41],
 [6, -1, 8, 13, -3],
 [14, 1, 22, 32, 8]]

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


[User]
Calculate the rank of matrix A where A =
[[-27, -1, -34, 17, 11],
 [6, 24, -7, 3, 7],
 [-21, -5, -32, 8, 10],
 [8, 52, -28, 18, -6],
 [-6, -66, 24, -27, -3]]

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


[User]
Compute the rank of the given 5x5 matrix:
[[-2, 0, 12, -24, -8],
 [-6, 6, -6, 10, 2],
 [-19, -17, -33, 25, 23],
 [-32, -4, -27, 12, 15],
 [-13, 12, -6, 8, 0]]

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


[User]
What is the rank of the matrix:
[[8, -28, 22, 42, -4],
 [9, 6, -9, 36, 3],
 [8, 12, -14, 30, 4],
 [-8, 8, -4, -36, 0],
 [0, 50, -45, -15, 10]]?

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


[User]
Calculate the rank of matrix A where A =
[[-23, 7, -27, -6, 29],
 [-7, -1, 45, 42, -35],
 [2, -2, 26, 20, -22],
 [0, 0, 0, 0, 0],
 [-39, 9, 3, 30, 9]]

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


[User]
Calculate the rank of matrix A where A =
[[-25, 3, -23, -5, 21],
 [10, -14, 6, 2, -2],
 [35, 3, 34, 7, -33],
 [-10, -6, -11, -2, 12],
 [-25, 19, -19, -5, 13]]

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


[User]
Calculate the rank of matrix A where A =
[[-36, 15, -6, 20, -9],
 [42, -37, 3, -6, -18],
 [-36, 52, 33, -24, -3],
 [32, -60, -39, 36, -7],
 [-54, 48, 0, 6, 18]]

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


[User]
Find the rank of the matrix:
[[6, 8, 4, 0, 2],
 [6, 8, 4, 0, 2],
 [-9, -12, -6, 0, -3],
 [18, 24, 12, 0, 6],
 [18, 24, 12, 0, 6]]

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


[User]
Determine the rank of the following matrix:
[[-13, 1, 32, 32, -29],
 [-13, 15, -43, 3, 14],
 [-33, 7, -23, 35, -2],
 [16, -2, -14, -28, 18],
 [33, 57, 18, -12, -45]]

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


[User]
Calculate the rank of matrix A where A =
[[-15, -15, 3, 0, -18],
 [-25, -25, 5, 0, -30],
 [-25, -25, 5, 0, -30],
 [-30, -30, 6, 0, -36],
 [-5, -5, 1, 0, -6]]

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


[User]
Find the rank of the matrix:
[[18, 30, 18, 30, -18],
 [-6, -26, -14, -38, 22],
 [21, -13, -3, -49, 27],
 [-33, -7, -9, 29, -15],
 [0, 8, 4, 14, -8]]

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


[User]
Calculate the rank of matrix A where A =
[[26, 17, -12, -26, 1],
 [-2, 3, 4, 10, -5],
 [-30, -25, 10, 20, 5],
 [18, 8, -11, -25, 5],
 [14, 7, -8, -18, 3]]

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


[User]
Determine the rank of the following matrix:
[[-5, 6, -6, 2, -1],
 [-5, 6, -6, 2, -1],
 [-20, 24, -24, 8, -4],
 [-15, 18, -18, 6, -3],
 [0, 0, 0, 0, 0]]

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


[User]
What is the rank of the matrix:
[[-6, -4, -6, 4, 16],
 [-16, -6, -21, 8, 45],
 [-9, -6, -9, 6, 24],
 [11, 12, 6, -10, -27],
 [-4, -54, 51, 32, -15]]?

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


[User]
Find the rank of the matrix:
[[12, -8, -8, 16, 0],
 [12, -8, -8, 16, 0],
 [15, -10, -10, 20, 0],
 [12, -8, -8, 16, 0],
 [-18, 12, 12, -24, 0]]

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


[User]
Determine the rank of the following matrix:
[[-13, -37, -11, -25, 16],
 [-24, 17, -45, -12, 42],
 [42, -19, 27, 30, -30],
 [-27, 11, -25, -19, 26],
 [-51, 11, -32, -41, 37]]

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


[User]
Find the rank of the matrix:
[[-32, 4, -60, -7, -12],
 [26, -24, -54, -7, 17],
 [-20, 1, 7, 2, -1],
 [22, -22, 14, -9, 0],
 [17, -12, -20, -4, 7]]

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


[User]
Calculate the rank of matrix A where A =
[[0, 0, -30, -25, 5],
 [0, 0, -30, -25, 5],
 [0, 0, -18, -15, 3],
 [0, 0, 36, 30, -6],
 [0, 0, -18, -15, 3]]

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


[User]
Calculate the rank of matrix A where A =
[[32, 16, 26, -3, -6],
 [-50, -7, -7, -22, -1],
 [34, 15, 19, 8, -3],
 [4, -18, -6, -18, -2],
 [24, 2, 19, -18, -7]]

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


[User]
Find the rank of the matrix:
[[28, 23, -23, 20, 5],
 [-7, 14, -4, -3, -19],
 [-8, -17, 25, -8, -3],
 [-12, 5, -9, -6, -6],
 [-16, -25, -31, -8, 49]]

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


[User]
Determine the rank of the following matrix:
[[-25, 22, 33, -35, 17],
 [7, 19, 3, 3, 17],
 [-6, -11, 0, -4, -10],
 [-9, -35, -9, -1, -31],
 [3, -13, -9, 7, -11]]

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


[User]
Calculate the rank of matrix A where A =
[[35, -46, -4, 1, 20],
 [41, 1, -28, -14, 24],
 [-21, -13, 16, 26, -2],
 [-21, 42, -12, 21, 12],
 [-49, 37, 0, 24, 22]]

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


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

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


[User]
Compute the rank of the given 5x5 matrix:
[[-16, -20, -20, 11, -9],
 [-16, -24, -24, 26, 2],
 [-18, -24, -24, 18, -6],
 [-22, -24, -24, 2, -22],
 [17, 20, 20, -7, 13]]

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


[User]
Find the rank of the matrix:
[[2, 6, -22, -4, -16],
 [-35, -39, -11, -18, 16],
 [20, 21, 14, 12, -4],
 [3, 3, 3, 2, 0],
 [6, 9, -12, 0, -12]]

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


[User]
Find the rank of the matrix:
[[7, -10, -32, -21, -17],
 [-3, 15, -22, -16, -7],
 [-8, 23, -2, -3, 4],
 [-3, -6, 48, 33, 21],
 [11, -26, -16, -9, -13]]

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


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

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


[User]
Calculate the rank of matrix A where A =
[[10, -10, 4, -4, -6],
 [-25, 25, -10, 10, 15],
 [-15, 15, -6, 6, 9],
 [-10, 10, -4, 4, 6],
 [25, -25, 10, -10, -15]]

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


[User]
Calculate the rank of matrix A where A =
[[5, -23, -3, 6, -7],
 [25, 17, 29, -14, 31],
 [-25, 7, -21, 6, -19],
 [-20, 2, -18, 6, -17],
 [5, -11, 1, 2, -1]]

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


[User]
Calculate the rank of matrix A where A =
[[-11, 7, -4, 9, -11],
 [-2, 7, 19, -6, -9],
 [40, -23, 23, -36, 37],
 [26, -19, 1, -18, 29],
 [-40, 23, -23, 36, -37]]

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


[User]
What is the rank of the matrix:
[[-6, 2, 10, -6, -6],
 [-6, 2, 10, -6, -6],
 [-3, 1, 5, -3, -3],
 [18, -6, -30, 18, 18],
 [-18, 6, 30, -18, -18]]?

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


[User]
Compute the rank of the given 5x5 matrix:
[[-6, -38, -45, -42, 20],
 [14, 32, 23, 12, -36],
 [-2, -37, -44, -30, 15],
 [-48, -29, -9, -18, 77],
 [36, -23, -33, -36, -31]]

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


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

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


[User]
Calculate the rank of matrix A where A =
[[9, 27, -18, -3, 15],
 [-1, 19, -6, -5, 7],
 [1, -19, 6, 5, -7],
 [13, -16, -6, 9, 0],
 [-4, -23, 12, 4, -11]]

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


[User]
Calculate the rank of matrix A where A =
[[5, 19, 11, 10, 27],
 [15, -3, -7, 10, 11],
 [30, 0, -10, 22, 29],
 [0, 12, 8, 4, 14],
 [-45, 27, 33, -24, -12]]

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


[User]
Calculate the rank of matrix A where A =
[[-25, -10, 30, -25, 0],
 [-15, -6, 18, -15, 0],
 [10, 4, -12, 10, 0],
 [-5, -2, 6, -5, 0],
 [10, 4, -12, 10, 0]]

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


[User]
Compute the rank of the given 5x5 matrix:
[[0, 0, 0, 0, 0],
 [20, 24, -4, -12, 16],
 [-15, -18, 3, 9, -12],
 [0, 0, 0, 0, 0],
 [5, 6, -1, -3, 4]]

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


[User]
Calculate the rank of matrix A where A =
[[-8, 10, -10, 0, -4],
 [-2, 28, -45, 34, 16],
 [-2, 10, -15, 10, 4],
 [10, -20, 25, -10, 0],
 [-16, 14, -10, -8, -12]]

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


[User]
What is the rank of the matrix:
[[-8, -10, -5, -41, 10],
 [54, 36, -52, 2, 20],
 [-45, -22, 39, 2, -10],
 [6, -22, 7, -15, -18],
 [17, 4, -5, 16, -8]]?

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


[User]
What is the rank of the matrix:
[[18, 9, -15, 0, 9],
 [-41, -16, 36, 6, -13],
 [24, 12, -20, 0, 12],
 [-26, 5, 29, 24, 17],
 [31, -7, -35, -30, -22]]?

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


[User]
Find the rank of the matrix:
[[20, -14, -32, -10, -72],
 [-19, -2, 25, -24, 6],
 [-17, -4, 27, -20, 18],
 [-1, 7, 1, 11, 18],
 [1, 5, -3, 8, 6]]

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


[User]
Calculate the rank of matrix A where A =
[[-36, -16, -12, 12, -11],
 [-22, -62, 16, -66, -12],
 [-20, -32, -4, -6, 4],
 [27, -3, 18, -36, 3],
 [37, 17, 8, -1, 18]]

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


[User]
What is the rank of the matrix:
[[-6, 6, -6, -14, 53],
 [-24, -4, 3, 9, 33],
 [-24, -44, 28, 34, 8],
 [-48, 48, -21, 23, -35],
 [-30, 30, -12, 20, -41]]?

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


[User]
What is the rank of the matrix:
[[0, -2, 1, 5, -6],
 [0, 10, -5, -25, 30],
 [0, 6, -3, -15, 18],
 [0, 12, -6, -30, 36],
 [0, 0, 0, 0, 0]]?

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


[User]
Find the rank of the matrix:
[[12, -4, 15, 6, 11],
 [-24, -8, -6, 20, -14],
 [12, 4, 3, -10, 7],
 [30, 3, 18, -11, 21],
 [-30, -11, -6, 27, -17]]

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


[User]
Determine the rank of the following matrix:
[[-2, -52, -62, -30, 56],
 [7, -37, -36, -30, 26],
 [-2, -32, -22, -30, -4],
 [28, -41, -41, -39, 44],
 [22, -48, -40, -48, 26]]

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


[User]
Compute the rank of the given 5x5 matrix:
[[-18, 15, -21, 6, -33],
 [-6, -11, 17, -10, 9],
 [0, -12, 18, -9, 15],
 [18, 21, -33, 21, -12],
 [-30, -3, 7, -11, -20]]

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


[User]
Find the rank of the matrix:
[[0, 0, 0, 0, 0],
 [-24, 24, -18, 30, -30],
 [-8, 8, -6, 10, -10],
 [16, -16, 12, -20, 20],
 [-4, 4, -3, 5, -5]]

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


[User]
Determine the rank of the following matrix:
[[-40, -42, -34, 34, 21],
 [37, 12, 32, 30, -24],
 [-1, -6, -16, 16, 9],
 [-1, -30, 51, -1, -13],
 [6, 0, -16, 104, -28]]

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


[User]
Compute the rank of the given 5x5 matrix:
[[4, 37, 16, -11, -12],
 [-40, -2, 12, 10, -58],
 [-2, 9, 38, 3, -8],
 [-1, -26, 11, -9, 14],
 [-12, -61, -12, 7, 14]]

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


[User]
Calculate the rank of matrix A where A =
[[12, 12, 6, -6, -15],
 [12, 12, 6, -6, -15],
 [-16, -16, -8, 8, 20],
 [12, 12, 6, -6, -15],
 [20, 20, 10, -10, -25]]

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


[User]
Calculate the rank of matrix A where A =
[[-18, 10, -12, -81, -45],
 [-4, 10, -14, -37, -23],
 [-22, 6, -12, 41, 29],
 [-10, -10, 14, 32, 24],
 [48, 27, -42, 3, -18]]

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


[User]
Determine the rank of the following matrix:
[[-19, 8, 4, 3, 2],
 [-44, -8, 10, 4, 12],
 [14, 32, -4, 2, -12],
 [-27, 0, 6, 3, 6],
 [-25, 20, 5, 5, 0]]

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


[User]
Calculate the rank of matrix A where A =
[[-40, 6, -29, 7, 7],
 [20, 12, 12, -16, 24],
 [10, -24, 11, 17, -43],
 [40, -6, 29, -7, -7],
 [-5, 21, -7, -16, 38]]

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


[User]
Determine the rank of the following matrix:
[[28, 23, 8, -3, 2],
 [38, 34, -4, -18, -14],
 [7, 8, -10, -12, -13],
 [23, 19, 6, -3, 1],
 [-4, -5, 8, 9, 10]]

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


[User]
What is the rank of the matrix:
[[2, 4, -4, -9, -2],
 [7, 8, -7, -24, -5],
 [-1, -25, 13, 27, 17],
 [27, -18, 11, -39, 7],
 [-2, -9, -6, 9, 12]]?

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


[User]
Determine the rank of the following matrix:
[[18, -3, 0, -31, -2],
 [-7, 2, 0, 14, 8],
 [-1, -4, 0, -8, -36],
 [5, 5, 0, 5, 50],
 [-10, 2, 0, 18, 4]]

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


[User]
Calculate the rank of matrix A where A =
[[-6, -16, -33, 19, 11],
 [27, 23, 5, -13, -1],
 [29, 47, 36, -42, -38],
 [6, 30, 27, -33, -45],
 [29, 33, 28, -26, -10]]

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


[User]
Determine the rank of the following matrix:
[[-13, -4, -12, 8, -1],
 [-43, -16, -10, -1, -26],
 [-48, -63, -21, 22, -82],
 [-13, -66, -16, 41, -39],
 [17, 47, 15, -31, 23]]

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


[User]
Calculate the rank of matrix A where A =
[[34, 20, -2, 20, -38],
 [-48, -7, 8, 0, 24],
 [57, 55, 34, -18, -39],
 [-34, -16, -14, 4, 22],
 [-39, -7, 26, 18, 1]]

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


[User]
Determine the rank of the following matrix:
[[-12, 2, -10, -24, -8],
 [4, -10, 34, -62, 22],
 [12, -6, 36, -42, 24],
 [4, -22, 12, 20, 10],
 [0, 24, -31, 46, -21]]

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


[User]
Calculate the rank of matrix A where A =
[[33, -13, 37, 26, 39],
 [-6, 10, -6, -4, -12],
 [27, 33, -33, -30, 27],
 [-9, -28, 15, 13, 0],
 [11, -4, 3, 1, 16]]

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


[User]
Find the rank of the matrix:
[[55, -14, 0, -18, 48],
 [-16, -10, 36, 22, -6],
 [54, -9, -27, -16, 33],
 [-45, 12, 10, 50, -36],
 [22, -20, 0, -28, 6]]

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


[User]
What is the rank of the matrix:
[[-10, 18, 24, -13, -16],
 [-28, 12, -16, -14, 0],
 [29, -15, 11, 16, 3],
 [-25, 3, -31, -8, 9],
 [-27, 9, -21, -12, 3]]?

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


[User]
What is the rank of the matrix:
[[-6, 6, -4, 5, -1],
 [6, -6, 4, -5, 1],
 [12, -12, 8, -10, 2],
 [-30, 30, -20, 25, -5],
 [-30, 30, -20, 25, -5]]?

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


[User]
Calculate the rank of matrix A where A =
[[3, -15, -18, -15, 12],
 [-43, -1, -14, -9, 12],
 [51, -3, -27, -18, 21],
 [20, -7, -54, -36, 43],
 [-22, -31, -20, -20, 11]]

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


[User]
Compute the rank of the given 5x5 matrix:
[[2, 33, 62, -55, -15],
 [20, -20, -23, 42, 50],
 [14, 4, 17, -4, 20],
 [14, -20, -27, 28, 20],
 [4, 11, 23, -21, -5]]

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


[User]
What is the rank of the matrix:
[[5, -5, -30, 10, 0],
 [-3, 3, 18, -6, 0],
 [3, -3, -18, 6, 0],
 [-4, 4, 24, -8, 0],
 [4, -4, -24, 8, 0]]?

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


[User]
Determine the rank of the following matrix:
[[-26, 18, 6, 10, -16],
 [-54, 36, 11, 22, -37],
 [-15, 12, 9, 12, -18],
 [1, 10, -3, -38, 78],
 [-3, -6, -4, 16, -37]]

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


[User]
Find the rank of the matrix:
[[43, 46, -17, 8, -12],
 [30, 43, 0, -1, -17],
 [8, 19, 18, 15, -5],
 [-21, -49, -31, -9, 21],
 [-62, -55, 38, -16, 9]]

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


[User]
Find the rank of the matrix:
[[-54, -13, 5, -19, -2],
 [-30, -9, 1, -9, 0],
 [6, -27, -29, 27, 18],
 [24, -12, -20, 24, 12],
 [-18, 9, 15, -18, -9]]

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


[User]
Compute the rank of the given 5x5 matrix:
[[4, -28, 0, 4, 26],
 [8, 36, -12, -4, -36],
 [10, 22, -12, -2, -23],
 [-36, -1, 33, -3, 8],
 [-50, 5, 45, -5, 5]]

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


[User]
Find the rank of the matrix:
[[0, 0, 0, 0, 0],
 [-24, 18, 30, -6, 0],
 [-24, 18, 30, -6, 0],
 [0, 0, 0, 0, 0],
 [12, -9, -15, 3, 0]]

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


[User]
Compute the rank of the given 5x5 matrix:
[[-20, -12, 1, 0, -34],
 [38, 19, 3, -29, 32],
 [-23, 19, 15, 10, -8],
 [-1, -39, -6, -6, -18],
 [13, -26, 10, -53, -36]]

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


[User]
Find the rank of the matrix:
[[-29, 22, 64, 8, 2],
 [-18, -42, -14, -82, -22],
 [21, -1, -24, -4, 6],
 [19, -45, -54, -28, 9],
 [-9, -21, -28, -40, -30]]

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


[User]
Find the rank of the matrix:
[[-32, -16, 64, -26, 14],
 [-16, 23, -42, 32, -57],
 [16, -16, 0, -18, 22],
 [-14, -15, 34, -21, 12],
 [39, 0, 4, -2, 52]]

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


[User]
Compute the rank of the given 5x5 matrix:
[[-42, 26, 44, -6, -34],
 [15, 1, 6, -5, -3],
 [-27, 3, 30, 3, -15],
 [0, 12, 10, -7, -11],
 [-3, -37, -38, 23, 37]]

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


[User]
Compute the rank of the given 5x5 matrix:
[[35, 5, 29, -6, -12],
 [13, -29, -17, 24, 21],
 [-48, 24, -12, -18, -9],
 [-60, 20, -24, -14, -3],
 [-28, 4, -16, -2, 3]]

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


[User]
What is the rank of the matrix:
[[-21, -42, 13, -2, 10],
 [-31, -58, 3, -12, 16],
 [-15, -3, -5, -2, 7],
 [51, 21, -43, -28, -19],
 [-7, 4, 31, 22, 0]]?

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


[User]
Find the rank of the matrix:
[[1, 4, 0, -12, 16],
 [-22, 3, -13, 30, -1],
 [-9, 6, -6, 0, 18],
 [-17, 9, -11, 6, 25],
 [15, 4, 8, -36, 24]]

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


[User]
Find the rank of the matrix:
[[6, 3, -9, 9, -18],
 [0, 0, 0, 0, 0],
 [-2, -1, 3, -3, 6],
 [-6, -3, 9, -9, 18],
 [10, 5, -15, 15, -30]]

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


[User]
What is the rank of the matrix:
[[-5, -1, -1, 0, 5],
 [3, 28, 50, 6, -7],
 [4, 26, 42, -22, 30],
 [15, -3, -13, -35, 32],
 [-26, -16, -20, 28, -14]]?

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


[User]
Compute the rank of the given 5x5 matrix:
[[-44, -16, -12, 0, -24],
 [7, 24, -29, -20, -6],
 [33, 39, -30, -25, 6],
 [-12, -23, 31, 5, -24],
 [1, -17, 26, 15, 6]]

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


[User]
What is the rank of the matrix:
[[1, -24, -23, -44, 31],
 [-16, 8, -4, 0, -27],
 [36, -24, 0, 24, 51],
 [-36, 50, 29, -13, -65],
 [40, -48, -24, 20, 67]]?

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


[User]
Compute the rank of the given 5x5 matrix:
[[23, 29, 5, -26, 14],
 [-7, -11, -5, 9, -6],
 [-5, 5, 17, 0, 6],
 [13, 9, -9, -11, 2],
 [-9, 3, 21, 3, 6]]

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


[User]
Determine the rank of the following matrix:
[[24, 4, 4, -24, 16],
 [12, 2, 2, -12, 8],
 [-36, -6, -6, 36, -24],
 [-18, -3, -3, 18, -12],
 [36, 6, 6, -36, 24]]

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


[User]
Calculate the rank of matrix A where A =
[[8, -36, 24, 5, -16],
 [22, 23, -60, -20, -31],
 [6, 36, 10, 8, 14],
 [-50, -32, -30, -24, 30],
 [2, -28, 38, 43, -26]]

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


[User]
Compute the rank of the given 5x5 matrix:
[[-6, -2, -6, 0, -8],
 [12, 4, 12, 0, 16],
 [15, 5, 15, 0, 20],
 [-18, -6, -18, 0, -24],
 [-6, -2, -6, 0, -8]]

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


[User]
Calculate the rank of matrix A where A =
[[14, 43, 25, 45, 47],
 [-8, -5, 9, 17, 35],
 [10, 25, 3, 2, -13],
 [-1, 4, 0, -18, -31],
 [-16, -25, -3, -13, -1]]

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


[User]
Determine the rank of the following matrix:
[[-24, -20, 16, 20, 20],
 [18, 15, -12, -15, -15],
 [-6, -5, 4, 5, 5],
 [24, 20, -16, -20, -20],
 [12, 10, -8, -10, -10]]

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


[User]
Find the rank of the matrix:
[[-13, -13, 15, -1, 5],
 [3, 9, -15, -3, 15],
 [-15, -6, 0, -6, 30],
 [-28, -19, 15, -7, 35],
 [7, 8, -10, 0, 0]]

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


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

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


[User]
Calculate the rank of matrix A where A =
[[8, 3, -11, -20, -33],
 [-33, -24, -3, -36, 30],
 [16, 33, -9, 28, 13],
 [19, -3, 4, 0, -49],
 [-20, -41, 1, -56, -33]]

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