messages listlengths 1 1 | ground_truth stringclasses 4
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0, 0],\n [-2, 8, 12, -10, 8],\n [1, -4, -6, 5, -4],\n [-3, 12, 18, -15, 12],\n [-5, 20, 30, -25, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-37, -10, -20, 25, -12],\n [-30, -17, -16, 2, -57],\n [11, 18, 24, 1, -10],\n [-3, -29, -37, -12, 29],\n [1, 1, -7, 10, 43]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[2, 39, -8, -22, -46],\n [-27, -53, 44, -23, 14],\n [35, -34, 3, 3, 25],\n [24, -36, -2, 32, 40],\n [42, -19, 8, -14, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-20, -4, 32, -10, 20],\n [63, 70, 12, -7, 9],\n [-26, -40, -24, 32, -22],\n [-50, -54, -40, 18, -34],\n [19, 17, -32, 8, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-12, 10, -10, -10, 2],\n [-24, 20, -20, -20, 4],\n [36, -30, 30, 30, -6],\n [-6, 5, -5, -5, 1],\n [30, -25, 25, 25, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-7, -9, -18, 31, -19],\n [1, 16, 19, 22, -19],\n [56, 14, -4, -20, -39],\n [-5, 4, 12, 11, -1],\n [41, -21, -32, -11, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-22, 36, -10, 44, -6],\n [10, -40, 1, -42, 11],\n [24, -21, 6, -24, -27],\n [59, -3, 41, -16, -27],\n [4, -20, -14, -4, -46]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[34, -53, -2, 16, 31],\n [22, 22, 0, 18, -2],\n [9, 36, 30, -24, -9],\n [-38, -25, -2, -12, -1],\n [0, -1, 46, -40, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-16, 0, 24, -8, 4],\n [-14, -15, -24, -22, -24],\n [18, 3, -18, 12, 1],\n [14, 3, -12, 10, 2],\n [-16, 6, 42, -2, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[56, -84, -12, -32, 28],\n [19, -28, -23, 16, -21],\n [-21, 24, 5, -10, 13],\n [-5, 20, -15, 60, -65],\n [2, -16, -2, -36, 38]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[18, 12, 24, 18, -36],\n [-19, -11, -2, 21, -32],\n [-16, -10, -12, 0, 4],\n [28, 17, 14, -12, 14],\n [7, 5, 14, 15, -28]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-10, -25, 15, 0, 30],\n [18, -9, -29, -20, -42],\n [1, 43, 0, 15, -12],\n [15, -30, -25, -25, -30],\n [-13, 35, 22, 25, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[10, 30, -27, 19, 0],\n [10, 20, -34, 8, 13],\n [-25, -16, -4, -39, 22],\n [25, 16, -52, 11, 27],\n [-5, -6, -37, -28, 38]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[30, -5, -10, -25, -10],\n [36, -6, -12, -30, -12],\n [36, -6, -12, -30, -12],\n [36, -6, -12, -30, -12],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[10, -10, 25, 10, -20],\n [16, 12, 6, 20, -12],\n [7, -42, 60, 2, -39],\n [-4, 32, -44, 0, 28],\n [16, 12, 6, 20, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[10, -12, 4, 10, 8],\n [25, -30, 10, 25, 20],\n [30, -36, 12, 30, 24],\n [-5, 6, -2, -5, -4],\n [-30, 36, -12, -30, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[30, -36, 24, 12, -30],\n [15, -18, 12, 6, -15],\n [-20, 24, -16, -8, 20],\n [-25, 30, -20, -10, 25],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-9, 12, -7, 5, 9],\n [-4, 18, -20, 31, 28],\n [-20, 28, 6, -28, -16],\n [-39, 8, -17, 53, 15],\n [-5, -30, -14, 45, 27]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[21, -3, 6, 2, 20],\n [18, -30, 36, -12, 24],\n [6, -18, 21, -8, 10],\n [-18, -2, 0, -4, -16],\n [6, 22, -24, 12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[5, -11, 10, 33, -31],\n [29, -3, 6, -7, -7],\n [36, 11, 14, -7, 0],\n [-21, 6, -14, -24, 27],\n [-19, 7, -21, -45, 41]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[6, 0, -1, 4, -1],\n [24, 0, -4, 16, -4],\n [-18, 0, 3, -12, 3],\n [-24, 0, 4, -16, 4],\n [18, 0, -3, 12, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[24, 24, 8, 9, -21],\n [0, 24, -24, -9, -3],\n [-15, 10, -30, -15, 10],\n [-36, -32, -16, -15, 31],\n [-3, -6, 2, 0, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[13, -1, -4, 7, -8],\n [-27, 23, 20, -33, 32],\n [7, 23, 11, -17, 13],\n [3, 39, 21, -33, 27],\n [-7, -23, -11, 17, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[5, -11, 1, 51, 26],\n [65, -8, 43, -12, 23],\n [-49, 5, -32, -10, -11],\n [31, 3, 13, 52, 28],\n [9, -13, 12, -30, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[3, 6, 5, 5, 1],\n [-9, -18, -15, -15, -3],\n [0, 0, 0, 0, 0],\n [18, 36, 30, 30, 6],\n [15, 30, 25, 25, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-25, -20, -25, -15, 25],\n [25, 20, 13, 11, -27],\n [-15, -12, 21, 3, 21],\n [-20, -16, -26, -14, 19],\n [15, 12, -39, -9, -24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[37, -7, 17, -11, 15],\n [-22, 61, -74, -22, 0],\n [30, 1, -33, 18, -25],\n [1, 33, -12, -27, 24],\n [-13, 7, 33, 39, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[8, -4, -12, 4, -8],\n [10, -5, -15, 5, -10],\n [-12, 6, 18, -6, 12],\n [-4, 2, 6, -2, 4],\n [-4, 2, 6, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-16, 4, 24, 0, -8],\n [-24, 6, 36, 0, -12],\n [16, -4, -24, 0, 8],\n [8, -2, -12, 0, 4],\n [20, -5, -30, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-3, 0, 43, 29, -16],\n [7, -3, -21, -24, -7],\n [36, -6, -66, 0, 42],\n [-5, -1, 1, -24, -21],\n [29, -10, -33, -29, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-14, 23, 6, 32, 34],\n [10, 5, 0, 20, -20],\n [0, -10, -2, -20, -2],\n [4, 7, 1, 18, -7],\n [-12, 14, 4, 16, 28]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-50, -36, 3, 5, -22],\n [-33, -1, 1, -17, -39],\n [0, -14, -40, 2, 0],\n [-30, -54, -39, 21, 6],\n [-63, -51, -5, 9, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[14, 10, 16, -20, 27],\n [0, 0, 0, 0, 0],\n [2, 3, -15, 16, -15],\n [-20, -18, 18, -16, 6],\n [-6, -7, 23, -24, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-36, -24, -12, -6, 18],\n [-36, -24, -12, -6, 18],\n [-24, -16, -8, -4, 12],\n [24, 16, 8, 4, -12],\n [30, 20, 10, 5, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-16, 1, -30, -56, 20],\n [-4, 10, 12, 25, -21],\n [-30, -18, 36, 30, 8],\n [-22, -8, 0, -17, 15],\n [38, 31, -18, 13, -39]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-10, -4, -24, 6, 20],\n [24, 20, -36, -56, 30],\n [-8, -8, 24, 24, -20],\n [-10, -10, 30, 30, -25],\n [-12, -8, 0, 20, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-1, 5, 6, 3, 3],\n [2, -10, -12, -6, -6],\n [-6, 30, 36, 18, 18],\n [-2, 10, 12, 6, 6],\n [3, -15, -18, -9, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-10, 33, 9, 11, -3],\n [-2, -15, -19, -33, -7],\n [-18, -24, -21, -12, -14],\n [-24, 51, -2, -47, 17],\n [-28, 39, -2, -21, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[0, 10, -10, 12, -2],\n [0, -10, 10, -12, 2],\n [0, -20, 20, -24, 4],\n [0, -20, 20, -24, 4],\n [0, 0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-11, 14, -13, -23, 4],\n [-11, -28, 9, 1, 44],\n [-1, 16, -7, -7, -15],\n [-10, 57, -23, -24, -47],\n [-23, 36, -1, 3, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-36, -18, 12, 12, 24],\n [12, 6, -4, -4, -8],\n [-36, -18, 12, 12, 24],\n [-36, -18, 12, 12, 24],\n [-30, -15, 10, 10, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-6, -2, 10, -6, 2],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [-15, -5, 25, -15, 5],\n [-9, -3, 15, -9, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[8, -6, 53, 6, -4],\n [-10, -24, -4, -24, -28],\n [-6, -24, -5, -38, -32],\n [4, -6, 43, 7, -4],\n [-6, -9, 9, -39, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-8, -18, -18, 28, -20],\n [-30, -26, 44, -22, 2],\n [65, 61, -56, 41, -2],\n [-9, -2, 38, -16, 9],\n [-64, -63, 58, -29, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-18, 36, -30, -3, -24],\n [-6, 20, -2, 3, -4],\n [14, -42, -14, 7, 5],\n [-12, 24, -20, -2, -16],\n [4, 6, -54, 45, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[40, -32, -30, 24, 14],\n [-15, 12, 18, 0, 15],\n [-25, 20, 30, 0, 25],\n [-10, 8, -3, -20, -35],\n [-15, 12, 21, 4, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-32, -22, 6, 20, 16],\n [-14, -7, -3, 26, 4],\n [23, 18, -9, 0, -14],\n [-7, 0, -9, 36, -2],\n [-10, -6, 0, 12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[40, 14, -18, 34, -11],\n [-12, 3, -6, 6, -4],\n [40, 0, 12, 26, -19],\n [-32, -6, 6, -16, 4],\n [-56, 4, -18, -12, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-59, 8, -10, 17, 2],\n [-11, 28, 62, -29, -58],\n [-13, 6, -6, 1, 8],\n [-4, 8, -8, -24, 0],\n [-22, 2, -8, 9, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[8, -8, -10, -6, 12],\n [10, 44, 7, 45, -6],\n [31, -4, -29, 3, 36],\n [14, -32, -24, -28, 28],\n [-49, 4, 45, -7, -56]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[6, 2, -18, 4, -12],\n [-3, 25, -4, -15, 6],\n [-18, 18, 42, -24, 36],\n [15, -9, -38, 17, -30],\n [0, 20, -10, -10, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[3, 8, 8, -4, -22],\n [15, -6, -6, 3, 5],\n [-36, 12, 12, -6, -6],\n [24, -6, -6, 3, -1],\n [-3, -10, -10, 5, 27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[0, -18, -10, 2, 18],\n [18, 18, 24, 12, -18],\n [-3, 24, 11, -5, -24],\n [3, -15, -6, 4, 15],\n [24, -3, 17, 19, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-36, 6, 30, 30, -24],\n [6, -1, -5, -5, 4],\n [40, 4, -8, -28, 20],\n [28, 6, 2, -18, 12],\n [-32, 0, 14, 24, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-3, -1, 15, -27, -30],\n [12, -11, 9, -27, -18],\n [-24, -4, 51, -42, 13],\n [-9, 4, 15, -24, -35],\n [12, -5, -1, -21, -38]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-4, -18, -16, 42, -34],\n [6, 33, 0, -9, 9],\n [1, 9, -14, 30, -23],\n [-2, -13, 8, -15, 11],\n [-8, -42, -8, 30, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[57, 50, -33, 17, 47],\n [20, 11, -23, 27, 3],\n [19, 7, -6, 2, 20],\n [-53, -33, 45, -23, -29],\n [58, 35, -24, 35, 53]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[19, -4, -4, -29, -25],\n [5, 0, -2, -7, -5],\n [31, 4, -16, -41, -25],\n [35, 20, -32, -37, -5],\n [-24, 4, 6, 36, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-5, -15, -25, 20, -30],\n [0, 0, 0, 0, 0],\n [4, 12, 20, -16, 24],\n [1, 3, 5, -4, 6],\n [-1, -3, -5, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[22, -14, -31, -24, 12],\n [32, -12, -46, -28, 2],\n [2, 34, 21, 4, -22],\n [-4, -2, 35, 33, 67],\n [8, -4, -19, 16, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-12, 0, -10, 8, -6],\n [6, -3, 8, -19, 3],\n [-30, -1, -24, 15, -15],\n [0, 6, -6, 30, 0],\n [-24, 2, -22, 26, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[6, 74, 28, 50, 4],\n [-6, -39, 27, -48, -57],\n [-1, -21, -22, -4, 21],\n [3, 8, -29, 20, 40],\n [-4, -43, -1, -43, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-12, -36, -34, 58, -14],\n [17, 29, 10, -45, -25],\n [-11, -5, 1, -14, 14],\n [-8, -24, -29, 31, -21],\n [-6, -14, -2, 32, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-54, 3, 24, 69, 6],\n [9, -1, 1, -41, 41],\n [18, 21, 33, -30, 6],\n [-45, 12, 42, 33, 39],\n [-18, -21, -24, -15, 58]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[25, 0, -30, 29, 31],\n [17, 2, -22, 21, 19],\n [13, 3, -18, 17, 13],\n [9, -21, 6, -3, 33],\n [18, 8, -28, 26, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[0, 0, 8, -12, 10],\n [0, 0, 8, -12, 10],\n [0, 0, 0, 0, 0],\n [0, 0, 4, -6, 5],\n [0, 0, 24, -36, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[12, -12, 4, 14, 12],\n [17, -23, 1, 19, 21],\n [-20, 8, 24, 5, -2],\n [1, 5, -19, -16, -9],\n [-28, 4, 12, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-8, -2, 40, 30, -8],\n [28, 7, -5, -24, -26],\n [24, 6, 30, 0, -36],\n [16, 4, -40, -36, 0],\n [-8, -2, 30, 24, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[15, 9, 6, -18, 3],\n [10, 6, 4, -12, 2],\n [-20, -12, -8, 24, -4],\n [20, 12, 8, -24, 4],\n [-5, -3, -2, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-19, 23, 11, -3, -24],\n [7, 10, 2, 12, -1],\n [68, -13, -36, -27, 29],\n [-18, 0, 16, 36, 2],\n [16, -28, -9, 10, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[12, 8, 20, -16, -16],\n [-9, -6, -15, 12, 12],\n [-6, -4, -10, 8, 8],\n [-9, -6, -15, 12, 12],\n [12, 8, 20, -16, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[34, 49, 14, -17, -6],\n [-2, 13, -22, 1, -12],\n [-24, -29, -14, 13, 8],\n [-3, 7, -8, 4, 12],\n [1, 13, -10, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[2, -17, 44, 20, -2],\n [-18, 25, -34, -16, 3],\n [10, -15, -32, 16, 11],\n [-32, 16, 20, 8, 2],\n [-10, 14, 9, -12, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-46, -18, 56, -2, -10],\n [-29, -30, 22, 0, 24],\n [7, -5, -40, 15, 59],\n [18, 48, 0, 2, -50],\n [-1, 11, 28, -11, -51]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-31, -3, -25, -20, 19],\n [50, -2, -2, 16, -18],\n [-5, 11, 29, 8, -3],\n [-18, 6, -30, -20, 22],\n [18, -24, -18, 4, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[0, 30, -25, -15, 15],\n [0, 6, -5, -3, 3],\n [0, 36, -30, -18, 18],\n [0, 36, -30, -18, 18],\n [0, -18, 15, 9, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[2, 6, -34, -19, 48],\n [5, -39, 13, -17, 10],\n [1, -33, 5, -10, 12],\n [-8, 24, -34, -8, 39],\n [-11, 54, -5, 32, -32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-36, 30, -12, -12, 0],\n [0, 0, 0, 0, 0],\n [-36, 30, -12, -12, 0],\n [30, -25, 10, 10, 0],\n [24, -20, 8, 8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[52, 2, -20, -6, 14],\n [-46, 3, 45, 6, 15],\n [-32, -24, -18, -36, -12],\n [44, 10, -2, 8, 18],\n [14, -3, -15, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[0, -3, 5, 7, 7],\n [10, 6, 5, -4, 16],\n [8, 12, -8, -20, -4],\n [10, 6, 5, -4, 16],\n [-28, -12, -22, 0, -56]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-18, 0, -54, 12, 18],\n [6, 34, -26, -26, 24],\n [-12, 12, 12, -8, -18],\n [-23, 0, 3, 6, -23],\n [-41, -19, -1, 27, -38]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[10, 20, -5, -15, -20],\n [12, 24, -6, -18, -24],\n [-6, -12, 3, 9, 12],\n [-2, -4, 1, 3, 4],\n [-12, -24, 6, 18, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[15, 12, 15, 15, -6],\n [10, 0, 22, 10, -4],\n [15, 14, 12, 15, -6],\n [-10, -12, -4, -10, 4],\n [15, 22, 0, 15, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[2, -6, 4, -8, -12],\n [-5, -13, 14, 0, 30],\n [-2, -36, 32, -22, 12],\n [7, 14, -16, -3, -42],\n [-4, -9, 10, 1, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-19, -43, -7, 10, -11],\n [1, -23, 13, -10, 5],\n [13, 21, 9, -10, 9],\n [-12, 36, -36, 30, -18],\n [-8, -16, -4, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[25, -25, 7, 46, -36],\n [-8, 9, -5, -18, 16],\n [-8, 34, -22, -44, 32],\n [-10, 38, -26, -52, 40],\n [28, -12, -2, 36, -32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-18, 30, 24, 30, -12],\n [18, -30, -24, -30, 12],\n [18, -30, -24, -30, 12],\n [-9, 15, 12, 15, -6],\n [-3, 5, 4, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[43, 13, -14, -3, -17],\n [-12, 22, 27, -12, 27],\n [23, 21, -3, -41, -44],\n [26, -64, -6, 89, -34],\n [45, 15, -13, -13, -32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-7, 18, -17, 7, 34],\n [-29, 14, -38, 4, -24],\n [-15, -49, 55, -25, -29],\n [33, 12, 9, 6, 36],\n [-29, -44, 39, -21, -32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[13, 33, 3, 16, 24],\n [-15, -27, -3, -12, -12],\n [-2, 6, 0, 4, 12],\n [-31, -27, -5, -8, 16],\n [13, 9, 2, 2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[18, -10, -2, -14, 0],\n [9, -5, -1, -7, 0],\n [-6, 2, 6, 10, 4],\n [6, 0, -14, -18, -10],\n [3, 2, -15, -17, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-10, 22, 36, 12, -16],\n [-30, -39, -18, 15, -27],\n [-10, -13, -6, 5, -9],\n [-25, 10, 36, 21, -31],\n [25, 0, -24, -19, 29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[12, -36, 16, -24, 8],\n [36, -4, 0, -16, -24],\n [24, -7, 2, -13, -14],\n [18, -28, 12, -22, 0],\n [9, -27, 12, -18, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-28, 5, 3, 16, -31],\n [12, 10, 16, -11, -3],\n [6, 20, 8, 2, 24],\n [53, -5, 23, -45, 5],\n [-19, 20, 26, 5, -44]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[6, -18, -9, -18, -3],\n [-2, 6, 3, 6, 1],\n [6, -18, -9, -18, -3],\n [-10, 30, 15, 30, 5],\n [-6, 18, 9, 18, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[24, -9, 10, -32, -27],\n [41, -39, -16, -22, 16],\n [-16, -9, -16, 36, 40],\n [22, 8, 2, -4, 1],\n [-49, 54, 40, -8, -68]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-12, -9, 3, 12, -9],\n [8, 6, -2, -8, 6],\n [-8, -6, 2, 8, -6],\n [-8, -6, 2, 8, -6],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-25, -2, -20, 12, -16],\n [22, -1, 20, -8, 10],\n [-47, -51, 19, 43, -2],\n [-24, -70, 72, 44, 32],\n [21, 21, -27, -33, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[12, -24, 0, -8, -4],\n [-18, 36, 0, 12, 6],\n [-15, 30, 0, 10, 5],\n [-3, 6, 0, 2, 1],\n [-12, 24, 0, 8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[7, 1, -7, -78, -18],\n [12, 25, -26, 10, 36],\n [-7, -31, 23, 12, -33],\n [7, -25, 5, -26, -30],\n [39, 7, -47, -8, 27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
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