messages listlengths 1 1 | ground_truth stringclasses 4
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Find the rank of the matrix:\n[[-11, -9, 4, 15, -13],\n [40, -10, -38, -4, -36],\n [19, -9, -23, 0, -49],\n [38, 18, -37, -11, -48],\n [-59, -17, 52, 15, 35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[18, 12, -5, -13, -3],\n [9, 7, 2, -2, -1],\n [-31, -23, -8, 7, 4],\n [-11, -5, -2, 6, 3],\n [17, 9, -3, -13, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[12, -12, -30, -15, -26],\n [-39, 54, -48, 19, 54],\n [-9, -52, -30, -20, -25],\n [-26, -60, -36, -12, 20],\n [18, 16, -42, -15, -42]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-18, 0, 0, 6, -3],\n [-36, 0, 0, 12, -6],\n [12, 0, 0, -4, 2],\n [-36, 0, 0, 12, -6],\n [6, 0, 0, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[6, 5, 4, 2, 0],\n [-36, -30, -24, -12, 0],\n [-6, -5, -4, -2, 0],\n [18, 15, 12, 6, 0],\n [6, 5, 4, 2, 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[[36, -18, 24, -24, -16],\n [-19, 6, -8, 22, 10],\n [-13, 6, -8, 10, 6],\n [3, 0, 0, -6, -2],\n [-13, -3, 4, 34, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-2, 16, 2, 20, -7],\n [-14, -18, 14, -55, 3],\n [-34, 42, 34, -5, -27],\n [14, 8, -14, 40, 1],\n [-34, 42, 34, -5, -27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-2, -38, 6, -42, -10],\n [6, 9, -23, 11, -12],\n [-6, -9, 43, -6, 5],\n [-7, 26, 16, 24, 33],\n [0, 0, 0, 0, 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[[-20, -20, 0, 0, 15],\n [21, 0, 9, 0, -3],\n [-6, -48, 18, 0, 30],\n [-13, 8, -9, 0, -3],\n [11, 32, -9, 0, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[12, -18, 9, 12, 6],\n [-12, 18, -9, -12, -6],\n [-24, 36, -18, -24, -12],\n [-20, 30, -15, -20, -10],\n [4, -6, 3, 4, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[25, -9, 20, -13, 20],\n [10, -12, 8, 20, -34],\n [15, -13, 12, 15, -26],\n [20, -15, 16, 13, -23],\n [20, -11, 16, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[12, -30, 18, 6, -36],\n [13, 59, 17, 24, 13],\n [9, -54, 14, -10, -33],\n [-3, 30, -4, 29, -15],\n [-11, 2, -16, -15, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[4, -4, 40, -50, -9],\n [-14, -2, -10, 10, 17],\n [-60, -30, 21, -39, 60],\n [1, 7, 29, -36, 0],\n [1, 1, 20, -25, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[46, 32, 50, 50, 15],\n [16, -12, -12, 88, -69],\n [-13, 44, 40, -57, 54],\n [-25, 10, 8, -29, -12],\n [13, -40, -32, -7, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[10, -30, 15, -25, -15],\n [6, -18, 9, -15, -9],\n [6, -18, 9, -15, -9],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[0, -7, -33, 24, 21],\n [8, -39, 31, -8, 29],\n [-2, -25, 33, -16, 9],\n [-18, 5, 26, -24, -26],\n [54, 44, -30, 24, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-18, 32, -32, -2, 4],\n [4, -29, 10, -13, 3],\n [-29, 35, 12, -32, -31],\n [28, -19, -7, 38, 23],\n [3, 9, -6, 12, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[15, 30, -30, 25, 15],\n [-6, -12, 12, -10, -6],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [12, 24, -24, 20, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[12, 0, -10, 10, 6],\n [18, 0, -15, 15, 9],\n [-30, 0, 25, -25, -15],\n [-18, 0, 15, -15, -9],\n [6, 0, -5, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[31, -5, 26, -34, -8],\n [-5, -2, 17, 30, -13],\n [-7, -26, -47, -28, 35],\n [40, -40, -5, -37, 41],\n [6, 39, 72, 35, -64]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[29, 18, 31, 42, -22],\n [24, -2, 0, 15, 5],\n [-7, 11, -20, -30, 30],\n [-9, -3, 18, 15, -27],\n [18, 31, 15, 13, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[18, -27, 5, 4, -2],\n [20, -14, 6, 8, -24],\n [36, -26, 18, 20, 20],\n [-20, 21, -9, -9, -13],\n [-54, 34, -22, -27, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[18, -34, -7, 10, -7],\n [-2, 6, 2, -1, 2],\n [10, -10, 1, 6, 1],\n [4, -12, -4, 2, -4],\n [18, 46, 37, 14, 37]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-12, -6, 0, 12, -4],\n [-12, -6, 0, 12, -4],\n [18, 9, 0, -18, 6],\n [-24, -12, 0, 24, -8],\n [6, 3, 0, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-61, 18, -15, 25, -2],\n [-20, 15, 6, -10, 23],\n [9, 3, 9, -15, 15],\n [1, 12, 15, -25, 32],\n [-24, 12, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-40, -42, 26, -68, 8],\n [-30, 33, 14, 30, 10],\n [30, 39, -23, 60, -10],\n [-12, -45, 18, -60, 12],\n [-2, -27, 8, -34, 6]]\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, 24, -40, -4],\n [-16, -6, 23, -29, 9],\n [-20, 60, -5, -25, -45],\n [-8, 18, 1, -11, -13],\n [0, 18, -9, 3, -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[[1, 24, -3, 2, 19],\n [18, -5, -13, 13, 62],\n [-17, 6, 11, 4, -1],\n [10, -17, -18, 19, 0],\n [-6, -25, 5, 9, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[30, -12, -9, -24, -6],\n [-4, -8, 50, 8, 8],\n [20, 14, -37, -17, -18],\n [-26, 4, 8, 20, 9],\n [2, 36, -26, 0, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-7, 20, -4, 13, -15],\n [30, -2, 15, 9, -53],\n [10, 28, -29, -62, 54],\n [42, 12, 12, -46, 22],\n [-3, 20, -27, -13, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-4, 6, 2, 0, 4],\n [8, -12, -4, 0, -8],\n [12, -18, -6, 0, -12],\n [-4, 6, 2, 0, 4],\n [6, -9, -3, 0, -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[[-53, 14, 19, -4, -60],\n [18, -5, -37, 29, 7],\n [16, -33, -21, 38, 33],\n [6, 1, 0, -39, 30],\n [26, -23, 49, 13, 33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-43, -48, -5, -12, 39],\n [-26, -72, -68, 28, 4],\n [17, -12, -5, 6, -9],\n [16, 30, 26, -9, -6],\n [33, -6, -29, 25, -33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-19, 12, -2, -5, 15],\n [-19, 5, -3, -8, 9],\n [16, -36, 4, -2, -39],\n [24, 12, 4, 16, 6],\n [-29, -7, 21, 4, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[23, -15, 24, 21, 29],\n [17, 30, -21, 12, 5],\n [3, -5, 6, 3, 5],\n [19, 15, -6, 15, 13],\n [-3, 5, -6, -3, -5]]\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, -17, 0, 3, -6],\n [18, 3, 0, 3, -36],\n [27, -12, 0, 6, -45],\n [-18, 30, 0, -6, 18],\n [-25, 16, 0, -6, 39]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[10, -30, -5, 20, 30],\n [12, -36, -6, 24, 36],\n [8, -24, -4, 16, 24],\n [-4, 12, 2, -8, -12],\n [-4, 12, 2, -8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[11, 4, 2, 6, -13],\n [-15, 10, -16, -31, 13],\n [3, -21, 10, 28, 9],\n [30, 33, -34, -15, -8],\n [10, -38, 38, 60, -10]]\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, 16, 25, -4, -18],\n [-36, 6, -26, 13, 44],\n [-4, 4, 7, 21, -16],\n [22, -1, 22, -13, -31],\n [40, -12, 16, -12, -36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-17, 17, 16, 7, -5],\n [-9, 11, 8, 3, -5],\n [4, -20, 0, 4, 20],\n [33, -12, -36, -21, -15],\n [12, 8, -16, -12, -20]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-50, 37, -25, -10, -37],\n [-64, 56, -10, -18, -28],\n [48, -51, -15, 18, 3],\n [22, -35, -25, -10, 35],\n [-66, 48, -30, -24, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-68, 54, 25, -5, 29],\n [9, -2, -9, -44, 29],\n [-2, 23, -9, -32, -12],\n [29, -42, -3, 14, 15],\n [-43, 41, 3, -9, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[33, 33, -66, -12, 45],\n [14, 34, -58, -1, 50],\n [42, -2, 0, -33, -20],\n [21, 25, -27, -17, 24],\n [-22, -34, 59, 7, -47]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-12, 12, -8, -8, 24],\n [3, 12, -11, 4, 21],\n [-12, -3, 5, -10, -3],\n [15, 0, -3, 12, -3],\n [-5, -15, 14, -6, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[68, -34, -2, -20, -10],\n [-6, 2, 0, -7, 22],\n [-52, 32, 0, 20, -11],\n [-42, 27, -1, 4, 17],\n [-12, -28, 12, 32, -17]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-5, -10, 0, -20, 20],\n [0, 0, 0, 0, 0],\n [5, 10, 0, 20, -20],\n [-3, -6, 0, -12, 12],\n [-6, -12, 0, -24, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[21, -9, 30, -21, -6],\n [66, -18, 48, 6, -60],\n [-42, 10, -24, -14, 44],\n [9, -1, 0, 11, -14],\n [-45, 13, -36, 1, 38]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-8, -2, -6, 54, 48],\n [4, 4, 6, -22, -20],\n [10, 22, 27, -35, -34],\n [12, 27, 33, -41, -40],\n [-4, 2, 0, 32, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[2, -54, -26, 26, -8],\n [37, 0, 14, -46, -2],\n [-2, 24, -20, -10, -3],\n [-8, -18, 30, -16, 59],\n [-34, -17, -23, 27, 35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[0, 0, 0, 0, 0],\n [-36, -18, 30, -24, 18],\n [-36, -18, 30, -24, 18],\n [18, 9, -15, 12, -9],\n [24, 12, -20, 16, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-15, -24, 6, 3, 12],\n [-25, -46, 0, 5, 18],\n [-31, -53, 9, 5, 25],\n [32, -19, -55, -46, -5],\n [-29, 6, 40, 37, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[3, 0, -9, 12, -12],\n [0, 0, 0, 0, 0],\n [2, 0, -6, 8, -8],\n [-6, 0, 18, -24, 24],\n [-1, 0, 3, -4, 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[[19, 26, -10, -4, 12],\n [4, 44, -4, 8, 12],\n [-12, 51, 3, 18, 9],\n [11, -1, -5, -6, 3],\n [11, 60, -8, 8, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-25, -25, 10, -15, 15],\n [-1, -5, -2, -13, 15],\n [21, 25, -6, 25, -27],\n [15, 15, -6, 9, -9],\n [1, 5, 2, 13, -15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-13, -7, 6, -6, -8],\n [-3, 33, -8, -51, 54],\n [6, 6, 34, 39, -24],\n [10, -14, 32, 66, -52],\n [-2, 34, -14, -57, 60]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-11, 19, -12, 29, 39],\n [52, -6, -10, 48, 38],\n [21, -10, -21, -17, -20],\n [-14, 17, -25, 4, 7],\n [50, -29, -17, -22, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[22, -11, -4, 2, 2],\n [6, 1, 4, 2, -14],\n [24, -7, 2, 4, -16],\n [21, -13, -7, 1, 11],\n [-9, 4, 1, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-32, -20, 16, -26, 15],\n [4, -20, -2, -8, -30],\n [-16, -20, 8, -18, -5],\n [8, 24, -4, 16, 20],\n [32, 12, -16, 22, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[56, -14, 12, 35, 22],\n [34, 7, 18, 26, 36],\n [23, 1, 27, 51, 48],\n [-31, -8, -7, -24, -27],\n [-15, 12, -39, -36, -39]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[20, 4, -12, 0, -4],\n [5, 1, -3, 0, -1],\n [-20, -4, 12, 0, 4],\n [-25, -5, 15, 0, 5],\n [10, 2, -6, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[6, 5, 6, 4, -3],\n [-6, -5, -6, -4, 3],\n [-30, -25, -30, -20, 15],\n [6, 5, 6, 4, -3],\n [-36, -30, -36, -24, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-9, 3, 12, 0, 18],\n [-3, 1, 4, 0, 6],\n [-6, 2, 8, 0, 12],\n [-15, 5, 20, 0, 30],\n [-6, 2, 8, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[12, 2, -6, -6, -8],\n [0, 0, 0, 0, 0],\n [-12, -2, 6, 6, 8],\n [-6, -1, 3, 3, 4],\n [18, 3, -9, -9, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-27, -15, -24, -9, 30],\n [5, -5, -2, -5, 0],\n [-18, -10, -16, -6, 20],\n [-12, 5, -1, 6, 5],\n [22, 20, 26, 14, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-47, -28, -47, 39, -45],\n [47, 50, 31, -47, 15],\n [-13, 7, -7, -14, -24],\n [-18, -3, -1, 27, 21],\n [46, 26, 35, -81, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[36, 9, -26, -18, 37],\n [-1, 4, -1, -19, 11],\n [-36, -27, 13, -9, -23],\n [29, 28, -7, 11, 17],\n [-51, -30, 20, -24, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-28, -50, 12, 45, -43],\n [-12, 9, 0, 2, 12],\n [12, 54, 12, -51, 51],\n [32, 43, -12, -43, 35],\n [0, -30, 0, 20, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-29, 31, -22, -6, 13],\n [12, 13, 27, -22, 2],\n [13, -21, 36, 10, -18],\n [-17, -15, 32, 34, -10],\n [13, -12, 25, 10, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[10, 10, -5, 15, 20],\n [18, 10, 33, -39, -12],\n [0, 12, 15, -39, -12],\n [-17, 11, -41, 33, 29],\n [16, 24, 15, -25, 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[[6, 8, 43, 35, 61],\n [1, 15, 10, 16, -35],\n [2, -6, 34, 24, -2],\n [1, 33, -29, -8, 7],\n [-2, -10, -10, -12, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[22, -24, -28, 26, 12],\n [-1, 12, -6, 1, -2],\n [2, 6, -8, 4, 0],\n [4, -3, -6, 5, 2],\n [18, -21, -22, 21, 10]]\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, 12, 6, -36, -24],\n [4, -8, -4, 24, 16],\n [0, 0, 0, 0, 0],\n [4, -8, -4, 24, 16],\n [3, -6, -3, 18, 12]]\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, 43, -9, 15, -37],\n [5, -17, 7, -7, 14],\n [-1, -18, -23, -6, 20],\n [-9, 2, -31, -30, 2],\n [12, -11, 40, 15, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[5, -26, 24, -7, -22],\n [-18, 41, 22, 7, 53],\n [-66, 25, 28, 5, -5],\n [-10, 18, 3, -9, 10],\n [-5, -3, 5, -11, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0, 0],\n [0, -10, -10, 12, -6],\n [0, -15, -15, 18, -9],\n [0, 0, 0, 0, 0],\n [0, -10, -10, 12, -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[[12, 6, -27, 39, 17],\n [7, -14, -28, -39, -29],\n [24, 12, -12, -6, 6],\n [10, 26, 34, 23, 33],\n [6, -18, -57, 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[[2, -22, -2, -12, 4],\n [30, 4, 9, 40, 38],\n [3, 6, -39, -3, -6],\n [-18, -27, -72, -57, -36],\n [32, -22, -29, 16, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-30, 7, 21, 13, 31],\n [-7, -14, 10, -29, -5],\n [-30, -13, 24, -1, 32],\n [-13, 13, 15, -44, -22],\n [-1, 22, -3, 19, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[10, 0, 0, -5, -15],\n [10, 0, 0, -5, -15],\n [-10, 0, 0, 5, 15],\n [10, 0, 0, -5, -15],\n [-4, 0, 0, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[0, 0, 0, 0, 0],\n [-2, 0, -3, 5, 0],\n [10, 0, 15, -25, 0],\n [2, 0, 3, -5, 0],\n [6, 0, 9, -15, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[18, 24, 7, 33, -37],\n [16, 3, 16, 11, -6],\n [-2, 9, -7, 8, -13],\n [30, -15, 41, 0, 19],\n [2, 21, -9, 22, -31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[6, -10, 12, 37, 30],\n [36, 28, -12, 2, 24],\n [-8, -16, 12, 24, 12],\n [-14, 21, 9, -21, 6],\n [12, -65, -21, 36, -42]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[5, -27, 30, 29, -14],\n [7, -31, 52, 47, -22],\n [25, 48, 1, -32, 43],\n [1, 29, -29, -44, 39],\n [12, -48, 36, 30, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[31, -22, -49, 1, -35],\n [-4, -19, 37, -7, -9],\n [0, 8, -29, -14, 19],\n [-15, 26, 27, 0, 46],\n [-24, 13, -34, -7, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[2, -23, 5, -1, -7],\n [-19, 18, 25, 9, -11],\n [-14, -28, 4, -17, -8],\n [-7, -19, -18, -26, 6],\n [-18, -43, 15, -16, -17]]\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, 36, -42, 10, 8],\n [-34, 26, 43, -2, -29],\n [-26, -4, 61, -4, -24],\n [-16, 32, -5, -31, -39],\n [-6, 8, 4, 7, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[6, -2, 12, 4, -12],\n [-12, 4, -24, -8, 24],\n [-6, 2, -12, -4, 12],\n [-9, 3, -18, -6, 18],\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[[-9, -28, -9, -23, -24],\n [-17, 0, -17, -3, -36],\n [3, 15, 3, 12, 9],\n [-16, -12, -16, -12, -36],\n [3, -36, 3, -27, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[0, 6, 6, 30, 30],\n [0, -2, -2, -10, -10],\n [0, 6, 6, 30, 30],\n [0, 2, 2, 10, 10],\n [0, 6, 6, 30, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-3, -6, 4, -1, -4],\n [-15, -30, 20, -5, -20],\n [9, 18, -12, 3, 12],\n [18, 36, -24, 6, 24],\n [-18, -36, 24, -6, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-18, -36, 36, 12, 6],\n [-15, -30, 30, 10, 5],\n [-15, -30, 30, 10, 5],\n [0, 0, 0, 0, 0],\n [-18, -36, 36, 12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[26, 30, -18, 10, -13],\n [-5, 25, -10, 25, -10],\n [-13, 1, 2, 9, 0],\n [0, 0, 0, 0, 0],\n [-27, -25, 16, -5, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[23, 14, -5, -35, 28],\n [-34, -10, -44, 18, 11],\n [20, 18, 26, 0, -21],\n [10, 54, -15, -12, 16],\n [53, 12, 3, -37, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[20, -8, -20, -20, -4],\n [-25, 10, 25, 25, 5],\n [25, -10, -25, -25, -5],\n [-10, 4, 10, 10, 2],\n [-15, 6, 15, 15, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-31, -30, 20, -42, -2],\n [41, 4, -30, 33, 30],\n [3, 28, -46, 21, -22],\n [-21, 30, -36, -19, -22],\n [5, -42, 41, 4, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[59, -1, 43, 59, 57],\n [-15, 21, -16, -20, -23],\n [-16, -28, -10, -10, -14],\n [-20, 10, -14, -26, -10],\n [35, 5, 3, 15, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-30, -12, 30, 12, 18],\n [20, 8, -20, -8, -12],\n [15, 6, -15, -6, -9],\n [-25, -10, 25, 10, 15],\n [-25, -10, 25, 10, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[2, -10, -14, -13, 17],\n [-6, 7, 27, 32, 26],\n [20, -11, -20, -36, -9],\n [28, 8, 44, 18, 18],\n [-14, 3, -12, -1, -22]]\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, 0, 0, 0, 0],\n [5, -1, 2, -6, 5],\n [-10, 2, -4, 12, -10],\n [0, 0, 0, 0, 0],\n [-5, 1, -2, 6, -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[[-12, -18, -36, 12, 6],\n [0, 0, 0, 0, 0],\n [-6, -9, -18, 6, 3],\n [6, 9, 18, -6, -3],\n [8, 12, 24, -8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
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