messages listlengths 1 1 | ground_truth stringclasses 4
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-2, -31, -17, 3, 9],\n [20, -10, -14, -6, 14],\n [-10, -20, -13, 3, 18],\n [18, 14, 4, -6, -5],\n [-16, -3, 6, 6, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-16, -23, 9, 21, -14],\n [-34, -35, 25, 36, -13],\n [-20, -31, 21, 11, 0],\n [-4, 28, 18, -18, 40],\n [6, 36, -2, -9, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[19, -30, 9, 73, 74],\n [19, -26, 2, 46, 55],\n [-41, 54, -24, -30, -29],\n [11, -22, 19, 50, 41],\n [-8, 12, -24, 43, 53]]?\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, -41, 0, -10, -45],\n [-65, -64, -66, -17, -21],\n [-18, -23, 18, -26, 0],\n [11, 23, -12, 35, -21],\n [-21, -12, -72, 27, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[10, -39, -3, 6, 8],\n [5, 21, 3, -6, -2],\n [21, -30, 22, -5, 12],\n [1, 48, 28, -17, -4],\n [-5, 27, 11, -7, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[18, 36, 30, 24, -36],\n [6, 12, 10, 8, -12],\n [9, 18, 15, 12, -18],\n [-12, -24, -20, -16, 24],\n [6, 12, 10, 8, -12]]\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, 1, 3, 5, 5],\n [-15, 0, -19, -28, -29],\n [-21, 12, -21, -24, -27],\n [19, -13, 18, 19, 22],\n [20, -5, 23, 31, 33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-5, 1, 18, -12, -2],\n [7, -47, -27, 4, 4],\n [36, -40, 6, -21, -10],\n [5, 43, 21, -10, -12],\n [33, -55, -15, -14, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-49, -14, -40, -5, -40],\n [-21, -19, -41, 18, 17],\n [61, -7, 24, 18, 52],\n [-46, -5, -48, -1, -4],\n [-25, 10, -10, -21, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-3, 3, -12, -15, 0],\n [4, -4, 16, 20, 0],\n [-2, 2, -8, -10, 0],\n [0, 0, 0, 0, 0],\n [3, -3, 12, 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[[-9, 27, -45, 30, 18],\n [10, -6, 6, 0, -8],\n [-23, 21, -27, 10, 22],\n [36, 0, -18, 30, -18],\n [-4, 6, -9, 5, 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[[32, 7, -39, 44, -7],\n [-39, -6, 6, -42, -33],\n [6, -6, 46, -11, 52],\n [-28, 34, -2, 12, -30],\n [5, 38, 18, 41, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-10, 10, 2, 14, 1],\n [10, -10, 0, -30, 0],\n [18, -18, -10, 26, -5],\n [28, -28, -8, -20, -4],\n [-2, 2, 4, -26, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-12, -15, 9, 0, 3],\n [-20, -25, 15, 0, 5],\n [-20, -25, 15, 0, 5],\n [16, 20, -12, 0, -4],\n [-24, -30, 18, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-25, -10, 25, -20, 20],\n [-25, -10, 25, -20, 20],\n [25, 10, -25, 20, -20],\n [0, 0, 0, 0, 0],\n [-30, -12, 30, -24, 24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-34, 4, 0, 27, -15],\n [16, -11, -6, -28, 7],\n [40, -35, 29, -40, 50],\n [9, -18, 23, -9, 10],\n [-49, 27, -24, 46, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-20, 12, -19, -1, -18],\n [-16, 18, 16, -16, 12],\n [20, 3, 29, -17, -8],\n [44, -33, 8, 16, 4],\n [16, 3, 27, -15, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-12, -16, -26, -20, 26],\n [36, -24, 24, 24, -24],\n [-36, 24, -24, -24, 24],\n [-9, 10, -3, -4, 3],\n [15, 2, 19, 16, -19]]?\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, -30, 30, 30, -30],\n [-6, -30, 30, 30, -30],\n [-3, -15, 15, 15, -15],\n [3, 15, -15, -15, 15],\n [1, 5, -5, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-1, 27, 6, -2, -17],\n [-11, 42, -18, -20, 21],\n [11, 15, 4, -10, -64],\n [-15, 21, 16, 27, 26],\n [18, -30, 18, 7, -49]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[16, -18, 8, -37, 15],\n [-15, 9, -3, 33, -9],\n [-5, 17, -9, 14, -12],\n [19, -3, -1, -40, 6],\n [-7, 7, -3, 16, -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[[-53, -18, -30, -34, -24],\n [-22, -29, 13, -19, -30],\n [-18, -29, 48, -23, -22],\n [27, -6, 49, 14, -8],\n [4, -8, 9, 4, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[0, 20, 22, 13, 14],\n [-32, -4, -86, -31, -28],\n [-28, 16, -72, -6, -18],\n [-60, 0, -48, -102, -6],\n [42, 0, 28, 74, 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[[6, -8, 4, 6, 23],\n [-13, -17, 17, 24, -1],\n [-4, -6, 1, -58, 23],\n [34, 34, -25, 16, -38],\n [-8, -16, 15, -52, 4]]\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 [-8, -10, 10, 12, 2],\n [-24, -30, 30, 36, 6],\n [8, 10, -10, -12, -2],\n [12, 15, -15, -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[[21, -22, -14, 8, -32],\n [6, -32, -4, 10, -4],\n [-12, -36, 8, 10, 28],\n [24, 2, -16, 1, -42],\n [9, 32, -6, -9, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[15, 6, -15, 12, -15],\n [10, 4, -10, 8, -10],\n [30, 12, -30, 24, -30],\n [5, 2, -5, 4, -5],\n [-20, -8, 20, -16, 20]]\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, -74, 36, 15, -16],\n [-4, -36, -36, -62, 38],\n [-9, 72, -2, -16, 25],\n [-19, 40, -12, 14, 14],\n [9, 40, -32, -66, 40]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-20, -30, -30, 0, 5],\n [20, 30, 30, 0, -5],\n [-16, -24, -24, 0, 4],\n [4, 6, 6, 0, -1],\n [24, 36, 36, 0, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[20, 10, -25, -15, -25],\n [-8, -4, 10, 6, 10],\n [20, 10, -25, -15, -25],\n [-12, -6, 15, 9, 15],\n [12, 6, -15, -9, -15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[2, 16, 24, -6, 30],\n [-13, 6, 16, 2, 13],\n [35, 4, 14, -17, 62],\n [12, -27, -18, 27, 0],\n [0, -13, -8, 16, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-17, 22, 26, 31, 4],\n [15, 2, 14, 34, -8],\n [51, -24, 0, 33, -16],\n [53, -22, 4, 39, -10],\n [-3, 2, 23, 25, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[15, 15, -12, -6, -3],\n [-20, -20, 16, 8, 4],\n [-25, -25, 20, 10, 5],\n [5, 5, -4, -2, -1],\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[[2, -42, 8, -18, 16],\n [4, 27, 35, 17, -11],\n [-16, 45, -23, 31, -10],\n [15, 17, 24, -3, -14],\n [-34, 60, -30, 56, -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[[-30, -46, 23, 41, 42],\n [2, 7, -21, -28, -24],\n [66, 6, -18, -54, -22],\n [-27, -58, 14, 23, 43],\n [-52, 5, -5, 5, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-6, 0, 10, -22, 6],\n [-11, -19, -68, 29, -15],\n [10, -4, -30, 42, -12],\n [-30, 6, 24, -30, 0],\n [-24, 13, 45, -32, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-26, 10, 22, 11, 0],\n [-34, 10, 28, 24, 0],\n [0, 0, 0, 0, 0],\n [17, -13, -16, 13, 0],\n [27, -7, -22, -22, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[18, 18, -20, 12, -3],\n [0, 0, 0, 0, 0],\n [-36, -15, 5, -3, -15],\n [0, 15, -25, 15, -15],\n [6, 5, -5, 3, 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[[12, 30, 12, -18, 24],\n [-4, -10, -4, 6, -8],\n [-4, -10, -4, 6, -8],\n [12, 30, 12, -18, 24],\n [6, 15, 6, -9, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[8, -16, -5, 22, -29],\n [24, -20, -28, -10, -52],\n [48, 58, 70, 57, -6],\n [27, 30, 22, 2, -4],\n [24, 36, 30, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[11, 52, -32, 64, 38],\n [-20, -4, 41, 5, 29],\n [58, 28, -8, -1, 0],\n [38, 46, 26, 18, 44],\n [-33, -48, 11, -26, -27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[49, 54, -44, -25, 12],\n [-42, -10, 3, -35, 39],\n [66, 72, -60, -30, 12],\n [-22, 8, -16, -46, 14],\n [-19, -8, 4, 3, 22]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-16, -4, -12, -16, -20],\n [-20, -5, -15, -20, -25],\n [-8, -2, -6, -8, -10],\n [-24, -6, -18, -24, -30],\n [20, 5, 15, 20, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-17, 64, 64, -14, 47],\n [8, -12, -33, -9, -16],\n [-26, 6, 36, 3, 19],\n [-7, -6, 23, 16, 6],\n [4, 16, -4, -12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[27, 1, -33, -13, 21],\n [-45, -27, -13, 7, -15],\n [54, 15, 12, -27, 27],\n [-33, -27, -15, 3, -9],\n [-2, -10, 22, 2, -6]]\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, 5, -26, -2, 40],\n [21, -30, 39, -22, -53],\n [24, -25, -1, 3, -39],\n [-29, 0, -13, 36, 28],\n [20, 25, 2, 16, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[12, 20, -4, 8, 24],\n [6, -18, 36, -12, -66],\n [-7, 7, -23, 6, 38],\n [-8, -18, 9, -8, -29],\n [-22, -32, 1, -12, -31]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[2, -16, -2, -31, 14],\n [6, 32, 6, -12, 36],\n [-1, 21, 38, 55, 17],\n [0, -26, 54, 26, 34],\n [19, 35, -20, -30, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-2, 34, -6, 34, -33],\n [-4, 20, 3, 10, -17],\n [14, -19, 0, -12, 23],\n [-2, 16, -9, -36, -8],\n [-16, -20, -18, -64, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-5, -1, -6, 4, 4],\n [20, 4, 24, -16, -16],\n [-20, -4, -24, 16, 16],\n [0, 0, 0, 0, 0],\n [-5, -1, -6, 4, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[30, 25, -15, -25, -5],\n [-24, -20, 12, 20, 4],\n [-12, -10, 6, 10, 2],\n [-30, -25, 15, 25, 5],\n [-12, -10, 6, 10, 2]]\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 [-12, 20, 12, 0, 24],\n [-9, 15, 9, 0, 18],\n [15, -25, -15, 0, -30],\n [-12, 20, 12, 0, 24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[0, -30, 47, 2, -50],\n [-26, -40, 27, 14, -48],\n [22, -13, -38, -20, 69],\n [-26, -43, 14, 12, -45],\n [-61, -32, 27, 36, 24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-9, 38, 11, 32, -8],\n [-24, -5, 1, -9, 6],\n [29, -2, 4, -2, 14],\n [1, 9, -9, 17, -32],\n [0, -19, -10, -13, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-27, 12, -6, 8, 2],\n [21, -9, 6, -6, -2],\n [-3, -3, -18, -2, 6],\n [-15, 15, 30, 10, -10],\n [-54, 36, 36, 24, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-12, 0, -8, 4, -8],\n [15, 0, 10, -5, 10],\n [15, 0, 10, -5, 10],\n [-12, 0, -8, 4, -8],\n [12, 0, 8, -4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[1, -7, 59, -34, 36],\n [-16, 0, -10, -30, 20],\n [-5, -2, 22, -15, 28],\n [-2, -4, 52, -8, 54],\n [-10, 0, -37, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[28, -27, -20, 27, 33],\n [0, -55, 1, -15, 12],\n [-54, -40, 34, -28, -31],\n [8, 3, -2, 17, 9],\n [10, -20, 16, 28, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[20, -30, 30, 20, 5],\n [-16, 24, -24, -16, -4],\n [24, -36, 36, 24, 6],\n [-16, 24, -24, -16, -4],\n [-4, 6, -6, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[3, 16, -27, 35, -6],\n [-18, 0, 2, -50, 4],\n [-12, 14, -22, -10, -2],\n [-12, 5, -7, -25, 1],\n [6, -13, 21, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[2, 2, -8, 2, 10],\n [6, 6, -24, 6, 30],\n [-2, -2, 8, -2, -10],\n [-4, -4, 16, -4, -20],\n [4, 4, -16, 4, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-14, 16, 42, 62, -44],\n [2, -5, 6, 23, -6],\n [-4, -23, -2, 17, 18],\n [7, -31, -8, 25, 15],\n [-40, 42, 33, -5, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[15, -12, 6, -15, 9],\n [20, -16, 8, -20, 12],\n [5, -4, 2, -5, 3],\n [15, -12, 6, -15, 9],\n [25, -20, 10, -25, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[30, 0, 5, 20, 15],\n [36, 0, 6, 24, 18],\n [-24, 0, -4, -16, -12],\n [-18, 0, -3, -12, -9],\n [24, 0, 4, 16, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[14, -24, -6, -24, 8],\n [23, 15, -18, -34, 18],\n [-41, -15, 16, 48, -36],\n [-13, -6, 1, 11, -13],\n [-13, 42, -7, 15, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-6, -18, -12, 0, -36],\n [-4, -12, -8, 0, -24],\n [6, 18, 12, 0, 36],\n [1, 3, 2, 0, 6],\n [2, 6, 4, 0, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-51, -9, -18, 5, -30],\n [-41, 20, -33, -3, -9],\n [27, -45, 54, 15, -36],\n [-5, 35, -3, -2, -36],\n [10, -28, 6, 20, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[12, 7, 10, -2, -6],\n [6, -40, 11, 18, 24],\n [4, 20, -6, -8, -44],\n [24, -26, 16, 14, -30],\n [-26, 85, -25, -40, -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[[-20, 26, -24, -8, -2],\n [-1, 9, 36, -5, -30],\n [17, 0, 45, 1, -36],\n [-30, 7, -45, -6, 36],\n [13, -17, 18, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-18, 0, 24, 36, 36],\n [27, -36, 16, 6, 0],\n [6, 0, -8, -12, -12],\n [-16, 12, 4, 12, 14],\n [-19, 12, 8, 18, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-18, -18, 33, -39, -8],\n [0, -26, 30, 10, -32],\n [16, 16, 2, 22, -24],\n [-24, -38, 24, -32, 8],\n [-18, -37, -21, -1, 44]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-2, -3, 4, -5, -2],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [-8, -12, 16, -20, -8],\n [-12, -18, 24, -30, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-14, -2, 4, 29, 38],\n [-22, -18, 8, 21, 62],\n [12, -2, -3, -31, -32],\n [1, -2, -6, -1, -2],\n [-11, -18, -20, 15, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-20, -6, 0, 0, 4],\n [27, 9, 2, 2, -7],\n [27, 9, 2, 2, -7],\n [13, 3, -2, -2, -1],\n [-4, -3, -4, -4, 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[[2, -33, -15, -14, 22],\n [0, -28, -46, -26, 18],\n [28, 4, -36, -47, -14],\n [16, 34, -1, -26, -17],\n [42, 9, 23, -21, -32]]\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, -15, 9, 9, -18],\n [6, -5, 3, 3, -6],\n [-6, 5, -3, -3, 6],\n [18, -15, 9, 9, -18],\n [-24, 20, -12, -12, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[8, 16, 2, 8, -4],\n [-8, -8, -24, -12, 8],\n [-4, -24, 43, 4, -6],\n [-2, -26, 60, 9, -10],\n [-4, 12, -56, -14, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[20, 13, -10, 20, -28],\n [-10, 24, 58, 96, -24],\n [12, 5, -24, -24, 44],\n [-13, 11, 42, 58, -62],\n [-5, 6, 24, 38, -92]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-2, -18, 5, 24, -1],\n [-2, 10, -3, -12, 3],\n [-42, -14, 1, 36, 31],\n [48, 12, 0, -36, -36],\n [-22, -16, 3, 30, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[15, -24, 60, 9, 12],\n [11, -20, 15, -14, -20],\n [-10, -16, 15, 11, 8],\n [16, 30, -15, -9, 0],\n [-20, 14, -6, 26, 32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[25, -28, 8, 0, 42],\n [46, -40, 32, 0, 59],\n [-21, 34, -47, -24, -1],\n [-59, 16, -38, 24, -64],\n [6, -64, 0, 36, 34]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-15, -9, 3, -18, 9],\n [-5, -3, 1, -6, 3],\n [-30, -18, 6, -36, 18],\n [25, 15, -5, 30, -15],\n [10, 6, -2, 12, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[6, 2, -2, -17, 18],\n [-18, -18, 2, 61, -66],\n [9, 0, -4, -23, 24],\n [9, 12, 0, -33, 36],\n [6, 26, 6, -37, 42]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-26, 36, 6, 32, -18],\n [38, -36, 30, -26, 18],\n [18, -24, -2, -21, 12],\n [18, -24, -2, -21, 12],\n [0, 0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-20, 20, -15, 0, -5],\n [-10, 8, 3, -2, 1],\n [11, -10, 3, 1, 1],\n [-6, 8, -15, 2, -5],\n [-9, 10, -12, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-20, 2, -14, 18, 4],\n [36, -7, 24, -31, -5],\n [-14, -19, -17, 21, 16],\n [-4, 14, 2, -2, -8],\n [-14, 15, -5, 7, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[30, -24, 12, -4, 16],\n [-2, -24, 52, -72, -12],\n [-14, 36, -44, 48, -12],\n [-5, -22, 24, -21, 19],\n [24, -17, 4, 5, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[6, 5, 3, -6, -1],\n [24, 20, 12, -24, -4],\n [24, 20, 12, -24, -4],\n [6, 5, 3, -6, -1],\n [-30, -25, -15, 30, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-6, 36, 46, 28, 22],\n [12, -6, 28, 90, 54],\n [16, -16, -12, 20, 16],\n [-10, -2, -5, -17, -16],\n [5, -26, -41, -38, -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[[0, 0, 0, 0, 0],\n [-15, 6, -9, 18, 3],\n [-30, 12, -18, 36, 6],\n [15, -6, 9, -18, -3],\n [25, -10, 15, -30, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[5, -30, 10, 20, -15],\n [6, -36, 12, 24, -18],\n [5, -30, 10, 20, -15],\n [1, -6, 2, 4, -3],\n [-2, 12, -4, -8, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[73, -6, -13, 46, 5],\n [-14, -50, -14, -32, 1],\n [-15, -66, -14, -31, -4],\n [9, 20, -71, 24, 22],\n [-10, 24, 0, -20, 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[[-5, 1, 1, 6, -6],\n [-36, 18, 24, 33, -45],\n [15, -21, -31, -1, 21],\n [-28, 2, 0, 37, -33],\n [22, -8, -10, -23, 27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-50, -1, -32, 30, 4],\n [15, -33, 46, -26, -13],\n [-46, 19, -56, 38, 24],\n [-13, -6, 16, 4, -51],\n [8, -11, 7, -10, 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[[-23, -17, -22, 17, 35],\n [1, 7, 8, -7, -25],\n [-29, -19, -25, 19, 35],\n [-20, -12, -16, 12, 20],\n [15, 1, 3, -1, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-21, 28, -18, 72, -58],\n [-8, 36, -25, 59, -11],\n [-21, -32, 13, -25, -35],\n [-4, -26, 2, -32, 23],\n [-30, 11, -16, -2, -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[[5, -6, 2, -5, 6],\n [-30, 36, -12, 30, -36],\n [2, -4, 0, 18, -12],\n [26, -32, 10, -16, 24],\n [21, -24, 9, -36, 36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[5, -5, 0, 3, 5],\n [5, -5, 0, 3, 5],\n [-5, 5, 0, -3, -5],\n [-10, 10, 0, -6, -10],\n [-20, 20, 0, -12, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[17, 1, -16, 18, -11],\n [-32, 5, 2, -30, 14],\n [-9, 17, -18, -24, -21],\n [6, -13, -20, 36, 24],\n [31, -4, 16, 18, -19]]\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, -4, -2, -2, 6],\n [20, 10, 5, 5, -15],\n [4, 2, 1, 1, -3],\n [-12, -6, -3, -3, 9],\n [-12, -6, -3, -3, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.