messages listlengths 1 1 | ground_truth stringclasses 3 values | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Find the rank of the matrix:\n[[5, -14, 6, -1],\n [-2, -1, 5, -4],\n [10, -10, -6, 10],\n [-19, 1, 3, -31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[4, 6, -2, 0],\n [-6, 9, 3, -6],\n [-10, -6, 5, -3],\n [-20, 6, 10, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-7, -2, 1, 2],\n [-12, 0, 1, 6],\n [-4, -20, -6, 8],\n [-1, -2, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-6, -2, -3, -6],\n [-1, 4, -4, -3],\n [18, -6, 15, 10],\n [15, -8, 15, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 4x4 matrix:\n[[-11, 4, 7, 12],\n [7, -3, -4, -8],\n [15, -5, -10, -16],\n [12, -8, -4, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-4, 4, -2, -16],\n [9, -12, 11, 4],\n [13, -14, 7, 18],\n [16, -16, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-10, 16, 6, 10],\n [-4, 10, 6, 8],\n [-2, 10, 12, 8],\n [4, -1, 3, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-13, -1, 7, -15],\n [8, -4, 13, 0],\n [2, 2, -8, 6],\n [-13, -1, 7, -15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Compute the rank of the given 4x4 matrix:\n[[-4, -2, 1, 0],\n [2, 8, -8, 0],\n [8, 4, -2, 0],\n [-12, -20, 18, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[9, 9, -8, 15],\n [-9, 0, 7, -10],\n [-18, 18, 15, -13],\n [-5, 15, 3, 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[[-1, 5, 12, -3],\n [7, 7, 6, 3],\n [16, 11, 3, 9],\n [14, 0, -18, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[0, 0, -4, 4],\n [-1, 1, 1, 5],\n [0, 0, -1, 1],\n [3, -3, -6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-6, 14, -3, -28],\n [11, -18, 1, 25],\n [-18, 30, -19, -16],\n [12, -14, 13, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-1, -2, 6, -9],\n [-12, 11, -15, 1],\n [12, -5, 0, 18],\n [4, -8, 12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-2, 0, -8, 4],\n [-10, 0, 0, 4],\n [-1, 0, -4, 2],\n [-13, 0, 28, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[0, 1, 8, -6],\n [-16, 15, -24, 26],\n [14, -11, 5, -8],\n [-10, 7, 5, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 4x4 matrix:\n[[-2, -2, -10, -6],\n [-4, 4, -3, 1],\n [16, -7, 24, 5],\n [2, -13, -10, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[21, -11, -3, 10],\n [19, 5, 2, -1],\n [4, 6, -3, -5],\n [0, -12, -4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 4x4 matrix:\n[[4, -6, 12, -18],\n [3, -18, 9, -9],\n [1, 0, 3, -5],\n [3, -6, 9, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[0, 3, -1, -1],\n [7, 6, -20, 4],\n [1, -12, 16, 0],\n [-10, -9, 30, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-4, 1, -8, -1],\n [-11, 2, -20, -2],\n [7, -1, 12, 1],\n [-7, -2, -4, 2]]\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, -4, 9, -7],\n [1, -4, 3, -1],\n [5, 12, -13, 6],\n [-2, 3, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[9, -3, 9, 0],\n [-12, 14, -17, -15],\n [6, -10, 10, 12],\n [9, -7, 11, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-18, -5, 8, -13],\n [-22, 0, 2, -12],\n [11, -2, 1, 5],\n [-4, 9, -10, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[0, 4, -16, 0],\n [-4, 2, 0, -4],\n [6, 2, -20, 6],\n [7, -1, -10, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-16, 8, -12, 4],\n [-10, 12, -6, 10],\n [-15, 18, -9, 15],\n [-11, 2, -9, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[10, -6, -8, -10],\n [0, 12, 11, 0],\n [13, -3, -6, -13],\n [9, -3, -5, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[6, -6, 3, -6],\n [-12, 8, -4, 16],\n [-3, 4, -2, 2],\n [-8, 6, -3, 10]]?\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, -1, 0],\n [-8, -24, 10, 0],\n [1, -2, -1, 18],\n [8, 22, -12, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[2, 4, 0, -4],\n [-3, 4, 4, 0],\n [9, -22, -16, 6],\n [-10, 10, 12, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-2, 0, -8, 4],\n [3, 4, 5, -3],\n [2, 0, 8, -4],\n [2, -4, 15, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[2, -2, -3, 2],\n [-2, -8, 3, 8],\n [2, 2, -3, -2],\n [2, -2, -3, 2]]\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, 5, -2, 23],\n [-12, 28, 28, 4],\n [3, -19, -19, 5],\n [2, 9, 8, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [-9, 13, 5, 9],\n [0, 1, 17, 0],\n [4, -5, 11, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[0, 8, -20, 0],\n [0, 8, -20, 0],\n [0, 0, 12, 8],\n [0, -16, 19, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-11, -13, 6, 15],\n [14, 9, 13, -6],\n [-4, 9, -7, 10],\n [2, -2, -4, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-22, 6, -5, -6],\n [6, 3, 4, -3],\n [-11, 16, 20, -16],\n [-25, 7, -4, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[4, 3, -9, -18],\n [16, 15, 2, -21],\n [8, 0, -7, -22],\n [-12, 0, 0, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[9, 4, 0, 17],\n [5, 8, -2, 9],\n [1, -12, 12, -7],\n [-2, 1, 8, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[8, 12, 5, 0],\n [-5, -4, -11, 7],\n [-16, -16, -28, 16],\n [1, 4, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-1, 6, 26, 9, 14],\n [-9, -28, -20, -27, -16],\n [-13, -36, -10, -33, -12],\n [22, 25, 27, 12, 39],\n [8, 1, -5, -6, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-3, -35, 38, 36, -23],\n [5, -6, -4, 3, -31],\n [-7, -44, -2, -1, -65],\n [-1, 29, -20, -16, -3],\n [-21, 2, 36, 33, -38]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-20, -35, -15, -5, 40],\n [-33, 0, 5, 8, -10],\n [-2, 4, -27, -47, 4],\n [-3, 25, 2, -11, -30],\n [1, -3, 5, 10, 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[[-66, -48, 20, 10, -48],\n [36, -9, -43, 45, 20],\n [-37, -31, 23, 16, -45],\n [-27, -18, -6, 29, -25],\n [-85, -29, 55, -43, -49]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[24, -2, 4, -28, -30],\n [28, 9, -10, -34, -33],\n [-19, 3, -5, 22, 24],\n [-35, -24, 29, 44, 39],\n [-20, -4, 4, 24, 24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-3, 0, 9, -15, 6],\n [31, 15, 12, 15, 23],\n [29, 15, 18, 5, 27],\n [-25, -12, -9, -13, -18],\n [40, 18, 6, 32, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[54, 20, 43, 36, 11],\n [-12, 42, -12, -30, 0],\n [56, 13, 45, 41, 11],\n [52, 8, 42, 40, 10],\n [-28, 22, -24, -34, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[11, -21, -26, -55, 20],\n [0, 29, 43, 60, -33],\n [44, 25, -5, -20, -9],\n [-33, -44, -23, -11, 51],\n [-2, 24, 5, 1, -48]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[26, -33, -5, 28, 9],\n [34, 7, 46, -3, -22],\n [-14, 16, -9, 12, -21],\n [22, 2, 42, -53, -12],\n [-32, 14, -18, -14, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-7, 4, 4, -34, -33],\n [-30, 9, 28, 9, -22],\n [23, 2, -31, 27, 45],\n [30, -1, -37, -16, 18],\n [7, -3, -6, -43, -27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[52, -36, 46, -15, -17],\n [30, -24, 18, -27, -21],\n [-46, 27, -22, 33, 35],\n [-23, 24, -20, 21, 11],\n [20, -30, 32, -12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-40, -28, 30, 34, 22],\n [15, 14, -20, -25, -17],\n [20, 4, 10, 18, 14],\n [-5, -8, 15, 20, 14],\n [25, 12, -5, -2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[4, 24, 20, -12, -24],\n [-6, -18, -15, 9, 18],\n [10, 24, 20, -12, -24],\n [0, -12, -10, 6, 12],\n [8, 24, 20, -12, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[0, -21, 0, -30, -36],\n [-16, 10, -42, 24, -6],\n [-16, 24, 0, 28, 24],\n [-16, -10, -54, 0, -42],\n [-20, 8, -51, 23, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-2, -22, 14, 0, -14],\n [-38, -26, 32, 0, -8],\n [-6, -5, 8, 0, 1],\n [-24, -12, 16, 0, -4],\n [17, -46, 17, 0, -38]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[24, 12, -22, -8, -12],\n [-14, 38, -3, -17, 22],\n [6, 18, -13, -19, -14],\n [-34, 19, 16, -17, 11],\n [-40, -26, 36, 4, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-31, 28, 9, -23, 29],\n [47, -29, 23, 38, -16],\n [4, 38, 43, -9, -13],\n [-8, 21, -50, -35, -7],\n [-18, -23, -30, -1, 53]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[24, -44, 36, -12, -16],\n [18, -15, 12, -6, 0],\n [36, -48, 39, -15, -12],\n [18, -27, 22, -8, -8],\n [18, 21, -18, 0, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-9, -26, -8, 15, -49],\n [-62, -23, 29, 52, -36],\n [11, -12, 8, 1, -19],\n [57, 9, -9, -41, -15],\n [13, -18, 6, 3, -20]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-8, 10, -2, -4, -12],\n [11, 10, -26, -7, 29],\n [3, -18, 18, 9, -3],\n [26, -61, 41, 28, 24],\n [4, -5, 1, 2, 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[[6, 9, -12, 3, -37],\n [-3, 27, 2, 16, 33],\n [5, -30, -16, -25, -60],\n [-5, 27, 1, 25, 21],\n [-4, 15, -9, 13, -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[[-50, 39, -98, 13, 0],\n [-7, 26, 2, 20, 20],\n [-14, 40, -32, -10, 23],\n [-21, -25, -8, 37, -7],\n [-15, 77, -44, -3, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-6, 22, 3, -39, 31],\n [-42, 20, 37, 5, -7],\n [-34, 45, -19, -12, 1],\n [7, 38, -21, -7, 32],\n [8, 21, -44, -25, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-49, 26, 16, 11, -4],\n [-9, -1, -13, 12, 8],\n [51, 14, 10, -21, -4],\n [2, 15, 8, -3, -2],\n [4, 10, -15, 18, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-2, 30, 18, -2, 32],\n [-6, 25, 15, -32, 18],\n [-3, 0, 0, -21, -6],\n [3, -30, -18, 9, -30],\n [3, 15, 9, 27, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-18, 25, -26, -1, -18],\n [-34, -26, -2, -62, -12],\n [16, -31, 24, -5, 18],\n [17, 12, -23, 37, 3],\n [-35, -25, -19, -58, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[17, -18, -38, 22, 15],\n [-13, 40, 31, -39, -12],\n [6, -48, -21, 63, -27],\n [-20, 34, 18, -40, 4],\n [33, -27, -54, 9, 66]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[26, -20, -24, 32, 7],\n [2, 7, 7, -5, 22],\n [-12, 21, 23, -25, 26],\n [10, 8, -30, 6, -6],\n [-21, 12, 39, -27, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[56, 22, -45, -11, -34],\n [-14, 2, 10, -10, 10],\n [-10, -18, 14, -38, 32],\n [6, 16, 1, -37, 2],\n [-8, 6, 8, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-47, -2, -4, 9, 13],\n [-17, 1, 30, 1, -5],\n [-8, 22, -4, -16, 10],\n [-45, 4, -8, 5, 16],\n [32, 7, 36, -16, -20]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[0, -2, -2, 18, 4],\n [30, -6, -36, 9, 12],\n [0, 3, 3, -27, -6],\n [-20, 5, 25, -15, -10],\n [-20, 6, 26, -24, -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[[4, -48, -11, -13, 11],\n [-19, 30, -22, -29, 22],\n [10, -60, -5, -5, 5],\n [-16, 48, -10, -14, 10],\n [-10, -12, -22, -28, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[2, 54, 48, 20, -39],\n [-52, 16, 0, -44, -28],\n [-50, 30, -12, -24, -27],\n [-21, -40, 3, -57, 4],\n [49, -18, 15, 31, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-6, -6, -1, -3, 10],\n [20, 20, 36, -18, 4],\n [16, 16, 33, -18, 8],\n [-20, -20, -8, -6, 28],\n [-22, -22, -34, 15, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-8, 9, 10, -23, 12],\n [-25, -49, -38, 39, -54],\n [15, 27, 24, -45, 30],\n [-19, 6, 8, -18, 10],\n [5, 3, -4, 43, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-4, -44, 6, 4, 64],\n [-10, 6, 4, 20, 22],\n [-11, -27, -10, 6, 5],\n [16, -7, 5, -8, -18],\n [1, 8, 18, 46, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[29, -1, -12, 24, -4],\n [-6, -36, -12, -18, -18],\n [-11, 9, 8, -6, 6],\n [-19, 11, 12, -12, 8],\n [18, 8, -4, 18, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[7, -48, 48, 22, -19],\n [21, 30, 0, -6, -3],\n [45, 55, 8, -7, 8],\n [1, -46, 38, 18, -17],\n [-19, -64, 28, 18, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-49, 24, 50, 34, 0],\n [37, 20, -43, 11, -8],\n [-33, -4, 33, 20, 3],\n [-9, -16, 14, -23, 5],\n [-26, 32, 24, 36, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[18, 26, 16, 1, -30],\n [18, 27, -42, -62, 77],\n [-44, -11, 19, 31, -16],\n [8, 0, -14, -16, 18],\n [-12, -12, -26, -20, 54]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[1, -17, -62, -25, 17],\n [-55, -68, 8, -40, -33],\n [5, -6, -28, -4, -7],\n [-11, -3, 50, 18, -40],\n [47, 45, -12, 26, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[12, 8, 8, 15, 16],\n [-72, 19, -78, -34, -5],\n [24, -23, 34, -3, -21],\n [6, -23, 4, -6, -28],\n [18, 21, 12, 27, 36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[11, 0, 21, -23, 11],\n [3, -29, 11, 28, 3],\n [-8, -7, -14, 25, -8],\n [-2, -21, 0, 29, -2],\n [4, -35, 14, 33, 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[[46, -100, -20, 4, -48],\n [-18, 52, -22, 17, 2],\n [8, -28, 12, 14, -8],\n [59, -74, -15, -5, -41],\n [26, 0, -15, 24, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-15, -5, 0, -25, 25],\n [-18, -18, -30, -60, 0],\n [-18, -16, -25, -55, 5],\n [-3, 9, 25, 20, 30],\n [12, 0, -10, 10, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-12, -14, 24, 10, 26],\n [12, 21, 18, -3, -33],\n [-6, -4, 30, 8, 10],\n [6, 12, 18, 0, -18],\n [0, -6, -36, -6, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[7, 18, -21, -1, -13],\n [0, 4, 0, 6, 8],\n [8, 28, -24, 10, 0],\n [-6, -16, 18, 0, 10],\n [2, 8, -6, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-25, -12, 2, 9, -7],\n [43, 46, 28, -5, -13],\n [-30, -14, 14, -12, 12],\n [10, -40, 4, -46, 8],\n [51, 1, -33, -8, 7]]\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, -16, -2, -12, -55],\n [-5, -19, 38, 27, 12],\n [-5, -17, 34, 25, 5],\n [-12, -48, 60, 24, 12],\n [8, 28, -12, 12, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[15, 4, 23, -9, 12],\n [-27, -31, 13, -28, -42],\n [27, 10, 35, -11, 24],\n [12, 27, -36, 37, 30],\n [-3, -5, 5, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[28, 18, -46, 16, 23],\n [-30, -26, 14, -28, -29],\n [23, 0, -42, 0, 10],\n [-44, 6, 32, -2, -16],\n [-7, -33, -8, -31, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[9, -21, -29, 36, 46],\n [-14, 22, 34, -40, -52],\n [-9, -27, -21, 36, 42],\n [-15, -21, -10, 24, 26],\n [29, -1, -24, 16, 26]]\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, -6, -30, 9, 19],\n [-18, -20, -30, -49, -20],\n [0, -6, 12, 0, 37],\n [16, 4, -36, 10, 1],\n [6, 6, -8, 9, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[27, 23, 30, 3, 34],\n [23, -27, -3, 29, -8],\n [-32, -4, -30, -26, -30],\n [-25, -23, -45, -19, -48],\n [-1, 19, -30, -55, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[28, 0, -24, 2, 2],\n [4, -4, -12, -6, 2],\n [-18, 4, 24, 5, -3],\n [-28, -7, 9, -13, 1],\n [-36, -6, 18, -12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-4, 27, 13, 10, 13],\n [13, -16, 10, 12, 5],\n [3, -14, 4, -10, -21],\n [10, -49, -27, -8, -7],\n [17, -14, 8, 27, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-23, 10, 28, 8, 36],\n [0, 9, -11, -13, 6],\n [40, -8, -36, -33, -60],\n [-8, 2, 6, 6, -12],\n [45, -21, -37, -17, -42]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-13, -37, -2, -5, 34],\n [3, 21, -12, 15, 6],\n [2, -7, 37, -4, 38],\n [-12, -24, -24, 2, 14],\n [-6, -16, 6, 2, 36]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[3, -3, 3, -18, -5],\n [2, 2, -10, 12, 2],\n [-7, 8, -10, 48, 13],\n [-6, 3, 3, 18, 6],\n [-18, 0, 36, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-25, 5, -10, 10, -5],\n [-15, 3, -6, 6, -3],\n [-4, -44, -40, 24, -28],\n [-9, -15, -18, 12, -12],\n [12, 48, 48, -30, 33]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
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