messages listlengths 1 1 | ground_truth stringclasses 4
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Calculate the rank of matrix A where A =\n[[-37, -27, 18, -9, -16],\n [5, -8, -39, 55, -7],\n [-16, -7, 24, 11, -7],\n [-39, 10, -47, 17, -16],\n [-64, 41, 46, -47, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[5, -45, 23, 46, -23],\n [-21, 6, -39, -75, -6],\n [1, -9, 25, 63, 28],\n [10, 2, 0, -14, -22],\n [21, 30, -12, -33, -33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[29, 32, 36, -35, -35],\n [75, -7, -45, 13, 16],\n [-50, -2, -1, 8, -11],\n [22, 0, 45, -28, -9],\n [2, 49, -12, -6, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[15, 25, -15, 15, 15],\n [-15, -25, 15, -15, -15],\n [-6, -10, 6, -6, -6],\n [15, 25, -15, 15, 15],\n [6, 10, -6, 6, 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[[12, 39, -8, 29, 17],\n [24, 39, 12, -28, -39],\n [14, 0, 17, -50, -47],\n [30, -6, -31, 40, 53],\n [-64, 24, -4, 61, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-4, -8, -16, -14, -10],\n [-4, -25, 6, -2, -23],\n [0, 53, 17, -6, 53],\n [1, -12, 14, 2, -9],\n [7, 4, -13, -10, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[19, -22, -21, -34, -27],\n [-41, 11, 5, 4, -8],\n [42, 18, 2, 30, 28],\n [8, 19, 2, 22, 13],\n [-28, -23, 18, -14, 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[[12, -18, -12, 12, -30],\n [16, 2, -12, 24, -30],\n [-3, -2, 2, -5, 5],\n [-21, -1, 16, -31, 40],\n [-3, 11, 4, -1, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-4, 0, -8, -12, 24],\n [-1, 0, -2, -3, 6],\n [-3, 0, -6, -9, 18],\n [-4, 0, -8, -12, 24],\n [5, 0, 10, 15, -30]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-17, 8, 17, -30, -36],\n [-26, 14, 11, -24, 27],\n [31, -18, -23, 40, 6],\n [19, 28, 38, 4, 9],\n [-35, 0, 0, -36, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-9, -11, -43, 57, -44],\n [10, -13, 23, -5, 38],\n [22, -32, -6, 46, 22],\n [40, -15, 15, -1, 40],\n [23, -21, -36, 58, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[25, 10, 20, 20, 30],\n [-20, -8, -16, -16, -24],\n [-20, -8, -16, -16, -24],\n [-10, -4, -8, -8, -12],\n [-15, -6, -12, -12, -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[[-16, 12, 16, 24, 16],\n [-16, 12, 16, 24, 16],\n [24, -18, -24, -36, -24],\n [-8, 6, 8, 12, 8],\n [-24, 18, 24, 36, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[30, 10, -30, 25, 10],\n [-24, -8, 24, -20, -8],\n [6, 2, -6, 5, 2],\n [-6, -2, 6, -5, -2],\n [-6, -2, 6, -5, -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[[-39, -7, 21, 15, 28],\n [-25, -25, 32, 2, 58],\n [33, 26, -21, -18, -14],\n [-9, -21, 18, 0, 30],\n [-3, -40, 18, 3, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[0, 20, -22, -4, 39],\n [18, 11, -17, -3, 45],\n [15, 20, -9, 9, 33],\n [-24, 2, 16, 10, -45],\n [18, -19, 1, -9, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-17, 22, 28, 34, -36],\n [15, -38, 50, 38, 21],\n [-9, -40, 4, 7, 51],\n [-36, 52, -2, 16, -55],\n [16, 20, -12, -18, -24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[2, 0, 4, -2, -1],\n [-12, 0, -24, 12, 6],\n [8, 0, 16, -8, -4],\n [-6, 0, -12, 6, 3],\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[[-19, -14, 26, -3, 4],\n [12, 15, -42, -9, -12],\n [-40, -20, -16, -30, -17],\n [-36, -37, 30, -1, 2],\n [36, 42, 12, 6, 12]]\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, 19, 10, 40, -4],\n [14, 11, 2, -4, 4],\n [15, 22, 10, 35, -2],\n [-15, -9, 0, 15, -6],\n [-16, -7, 2, 26, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[2, -6, 0, -3, 4],\n [-10, 30, 0, 15, -20],\n [-12, 36, 0, 18, -24],\n [-6, 18, 0, 9, -12],\n [6, -18, 0, -9, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-13, 21, -10, -29, 17],\n [37, -45, -6, 11, -33],\n [35, -37, -8, -3, -34],\n [-23, 17, 8, -50, 30],\n [-40, 33, 52, 4, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[32, -4, 26, 12, 40],\n [-21, 9, -50, 7, -22],\n [-23, 7, -40, 1, -26],\n [-34, 2, -16, -18, -44],\n [-27, 9, -51, 3, -30]]\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, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [30, 6, -36, -6, -12],\n [-20, -4, 24, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[5, 3, -1, -6, 2],\n [15, 9, -3, -18, 6],\n [20, 12, -4, -24, 8],\n [-20, -12, 4, 24, -8],\n [-25, -15, 5, 30, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-15, 20, -15, -15, -25],\n [18, -24, 18, 18, 30],\n [3, -4, 3, 3, 5],\n [3, -4, 3, 3, 5],\n [-6, 8, -6, -6, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[10, 14, -6, 48, 8],\n [-12, -10, 26, -38, 24],\n [-11, -10, 19, -38, 14],\n [30, -9, -30, 36, -30],\n [-18, 30, -1, 23, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-45, 34, 30, -25, 42],\n [25, -25, -6, 2, -32],\n [13, 17, -26, -10, 28],\n [-30, -8, 21, -50, 8],\n [34, -13, -23, 13, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-36, 15, 12, 32, -14],\n [-22, 15, 14, 19, -13],\n [18, 3, 6, -17, -1],\n [38, -24, -22, -33, 21],\n [-12, -30, -36, 14, 22]]\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, -20, 26, 2, 16],\n [30, -25, 45, 10, 20],\n [12, 10, 22, 20, -8],\n [9, -25, 10, -11, 20],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[12, -6, -6, -10, 2],\n [-12, 6, 6, 10, -2],\n [30, -15, -15, -25, 5],\n [0, 0, 0, 0, 0],\n [-12, 6, 6, 10, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[16, -21, 36, 14, -47],\n [29, -9, 2, 8, 18],\n [-11, 22, -41, -14, 59],\n [35, -6, 25, 30, 13],\n [-21, -9, -24, -36, -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[[3, -19, -13, -20, -6],\n [0, 15, 12, 12, 3],\n [-3, 29, 21, 28, 8],\n [15, 25, 31, -4, -6],\n [15, 10, 19, -16, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[0, 2, -3, 1, 1],\n [0, 8, -12, 4, 4],\n [0, 10, -15, 5, 5],\n [0, 8, -12, 4, 4],\n [0, 6, -9, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[16, -15, 15, 27, 19],\n [28, -8, 29, 41, 49],\n [3, 23, -9, 20, 25],\n [27, -34, 32, -9, 8],\n [6, -2, 6, -53, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-6, 6, 0, -3, 6],\n [0, 0, 0, 0, 0],\n [4, -4, 0, 2, -4],\n [10, -10, 0, 5, -10],\n [4, -4, 0, 2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-38, -68, 16, -28, -2],\n [24, 47, -17, 18, -1],\n [-3, 9, -10, 3, -5],\n [2, -34, -16, -26, 2],\n [16, -27, -7, -22, 9]]\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, -2, 19, 0, 8],\n [11, -7, -12, 28, -21],\n [-18, -5, 28, -38, 26],\n [16, -27, 23, 18, -11],\n [-36, -37, -28, -48, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[21, -1, -17, 5, -37],\n [-23, 21, 33, -27, 23],\n [-18, 31, -14, -1, 15],\n [-12, -42, 27, -10, 23],\n [-11, 34, -31, 8, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-30, -19, 29, -6, -24],\n [-2, 20, -9, -3, 4],\n [-16, 2, 0, -10, -8],\n [50, -15, -3, 28, 24],\n [-12, 3, -10, -13, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [-36, 36, 6, 30, 12],\n [-24, 24, 4, 20, 8],\n [6, -6, -1, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-11, -30, -7, 21, -1],\n [7, 4, -5, 1, -7],\n [36, 51, -15, 3, 30],\n [7, -3, -7, 0, -25],\n [40, 25, -32, 19, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[12, 0, -4, 16, -16],\n [-18, 0, 6, -24, 24],\n [12, 0, -4, 16, -16],\n [6, 0, -2, 8, -8],\n [-15, 0, 5, -20, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-20, 13, -4, 9, 14],\n [-40, 19, -1, 27, 30],\n [-36, 29, -10, 25, 6],\n [16, 13, -17, -19, -38],\n [24, -32, 18, -8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[8, -12, -6, -2, -8],\n [-12, 18, 9, 3, 12],\n [-20, 30, 15, 5, 20],\n [4, -6, -3, -1, -4],\n [12, -18, -9, -3, -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[[1, 4, -5, 2, -6],\n [5, 20, -25, 10, -30],\n [4, 16, -20, 8, -24],\n [3, 12, -15, 6, -18],\n [-5, -20, 25, -10, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-28, -6, -19, 6, 22],\n [12, 18, 9, 1, 13],\n [-51, -39, 1, 42, -41],\n [44, -56, -12, -33, -3],\n [3, 25, 16, 13, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[15, -13, 18, 18, 33],\n [-41, 2, 10, 54, -33],\n [57, -13, -18, -8, 43],\n [-14, -28, 36, 17, 32],\n [-27, 48, 22, 11, -37]]?\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, 20, -25, 0],\n [-10, -18, 28, 7, 20],\n [8, 24, 16, -20, 0],\n [-21, -48, 18, 30, 25],\n [14, 24, -44, -8, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-10, 26, -7, 21, -1],\n [54, -24, 6, -12, -18],\n [15, -29, 5, -22, 3],\n [-39, -16, 14, -23, 8],\n [-29, 9, -16, 7, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-16, 18, -32, -30, -22],\n [-10, -8, -13, -10, -19],\n [-4, 32, -18, -20, 2],\n [-8, 9, -16, -15, -11],\n [2, 17, -3, -5, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[32, -33, -41, 13, -42],\n [18, -33, -29, -19, -30],\n [-24, 21, 29, -17, 30],\n [25, -25, -31, 13, -33],\n [19, -22, -24, 6, -27]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-18, -1, -26, 1, 17],\n [25, -8, -46, -26, 41],\n [-9, 15, -8, -17, -10],\n [-10, 33, 10, -1, 13],\n [-6, 44, 28, 4, 14]]\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, -24, 5, -12, 8],\n [-20, 22, 35, 40, 20],\n [-32, 32, -15, 12, -16],\n [52, -46, 20, 12, 28],\n [29, -28, -15, -19, -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[[-29, 30, -24, 13, 2],\n [-18, 8, -42, 16, 14],\n [9, 4, 32, -13, -2],\n [-36, 47, -16, 10, 8],\n [24, -26, 18, -10, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[10, -12, -12, -30, 34],\n [10, -3, -12, -12, 19],\n [-30, -9, 36, 0, -27],\n [15, 6, -18, 3, 11],\n [15, 24, -18, 39, -19]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[6, -1, -4, -3, 13],\n [-3, -25, -19, -21, 28],\n [16, 3, -6, -3, 27],\n [19, 45, 27, 33, -24],\n [18, -3, -12, -9, 39]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[24, -16, 20, 10, 17],\n [-27, 33, -33, -19, -10],\n [9, 15, 17, -23, 35],\n [3, -13, 31, -95, 31],\n [-18, 59, -30, 7, 15]]\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, 5, 13, -11, 3],\n [18, -6, -18, 18, 6],\n [6, 5, 29, -7, 11],\n [16, -12, -6, 42, 24],\n [7, 0, -7, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-2, 12, -4, -4, -12],\n [4, -24, 8, 8, 24],\n [-5, 30, -10, -10, -30],\n [1, -6, 2, 2, 6],\n [6, -36, 12, 12, 36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[25, 5, 20, -30, -5],\n [-5, -1, -4, 6, 1],\n [15, 3, 12, -18, -3],\n [10, 2, 8, -12, -2],\n [-30, -6, -24, 36, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[26, -22, 16, 6, 28],\n [-2, 1, -4, 12, 11],\n [-2, 2, 0, -6, -8],\n [-8, 6, -8, 12, 6],\n [-18, 14, -16, 18, 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[[-33, -6, 3, -6, -18],\n [-7, 11, -3, -14, 18],\n [-6, -6, 2, 4, -12],\n [5, -31, 9, 34, -54],\n [22, 4, -2, 4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[30, 12, -18, 24, 30],\n [20, 8, -12, 16, 20],\n [-20, -8, 12, -16, -20],\n [-10, -4, 6, -8, -10],\n [-20, -8, 12, -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[[-15, -48, -15, -37, 21],\n [-54, 4, -10, -22, 15],\n [-21, -24, -13, -15, 17],\n [-15, -20, -3, -37, 7],\n [39, 8, 15, 5, -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[[-18, 15, -21, 42, -15],\n [-3, -7, -1, -1, -5],\n [12, -10, 14, -28, 10],\n [3, -12, 6, -15, 0],\n [7, -9, 9, -19, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[23, -9, 22, 50, 54],\n [-24, 16, 38, 40, 30],\n [21, 37, 6, 3, -32],\n [24, 6, -18, -21, -36],\n [28, -18, -1, 10, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-3, 9, 9, 0, -15],\n [-6, 18, 18, 0, -30],\n [-3, 9, 9, 0, -15],\n [3, -9, -9, 0, 15],\n [5, -15, -15, 0, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-11, -32, 37, 19, -44],\n [-17, -6, 2, -22, 8],\n [42, -26, 29, 17, -4],\n [-21, 6, -11, -26, 16],\n [37, -12, 19, 37, -20]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[15, 2, 22, -6, 18],\n [4, -44, -24, -24, 24],\n [-50, 11, -8, -8, 8],\n [15, 11, -6, 22, -34],\n [0, 15, 21, 0, 9]]\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, -5, 4, -3, 0],\n [-30, -25, 20, -15, 0],\n [0, 0, 0, 0, 0],\n [-24, -20, 16, -12, 0],\n [6, 5, -4, 3, 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[[-5, 20, -11, 48, 12],\n [14, 20, 3, 9, -24],\n [14, -13, 3, -57, -3],\n [-45, -52, 2, -15, 60],\n [17, -7, 1, -36, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-55, 21, 25, 29, -35],\n [14, 37, -37, 22, -26],\n [0, 29, 0, 36, -27],\n [9, -23, 19, -9, 13],\n [1, 20, -31, -1, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[2, 17, -7, -26, 4],\n [8, 11, 29, -9, -22],\n [10, 37, 13, -50, -12],\n [0, -6, 6, 10, -4],\n [-8, -14, -26, 14, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-36, 30, -18, -18, 30],\n [-30, 25, -15, -15, 25],\n [-36, 30, -18, -18, 30],\n [18, -15, 9, 9, -15],\n [24, -20, 12, 12, -20]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-3, -9, 9, -11, -27],\n [-8, 4, 10, -20, -16],\n [8, -22, -1, 14, -20],\n [5, -25, 5, 5, -35],\n [-6, 0, 9, -16, -18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[30, -25, -10, -17, 5],\n [12, -36, 0, -12, -24],\n [8, 18, -7, -1, 26],\n [12, 18, -4, 10, 30],\n [38, -27, -12, -17, 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[[-28, -27, -40, -18, -18],\n [10, 0, 2, 40, 20],\n [-9, 24, 11, -36, -6],\n [44, 54, 65, 19, 10],\n [-43, -18, -50, -29, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[3, -7, -1, 5, 8],\n [-9, 25, -8, -11, -17],\n [2, -10, 14, -2, -4],\n [-2, 18, -36, 10, 18],\n [-13, 37, -14, -15, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[12, -6, 24, -30, 12],\n [-10, 5, -20, 25, -10],\n [12, -6, 24, -30, 12],\n [-2, 1, -4, 5, -2],\n [-10, 5, -20, 25, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[48, 33, 30, -49, -43],\n [-47, 60, -20, -39, -45],\n [23, -15, -49, -41, -48],\n [-32, 3, -65, -24, -38],\n [-13, 15, 5, -11, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[46, 15, 18, 16, -21],\n [-23, -4, -15, 19, 43],\n [7, -9, 5, 9, 28],\n [-44, -25, -12, -26, 25],\n [-8, 0, -9, 25, 39]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[24, 49, -23, 21, -48],\n [-28, -33, 11, -17, 36],\n [-3, -17, 10, -6, 15],\n [-19, -40, 19, -17, 39],\n [-25, -16, 1, -11, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-21, -12, 46, 27, 17],\n [20, -6, -14, -21, 0],\n [15, -13, -20, -33, 5],\n [-19, -26, 14, -15, 23],\n [-24, -25, 56, 21, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-46, 51, -3, 45, -50],\n [10, -10, -8, -10, 16],\n [-23, 19, 20, 13, -6],\n [-7, 7, 0, 5, -2],\n [55, -62, 19, -51, 43]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[2, -14, 40, -28, 18],\n [40, -28, 24, 10, -36],\n [48, -26, 4, 25, -30],\n [31, -9, -21, 35, -39],\n [-13, 1, 19, -16, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[24, 1, -4, 11, -49],\n [32, -1, -26, 22, -26],\n [-1, -32, -76, 41, -25],\n [-12, 38, 72, -48, 38],\n [-44, 16, 28, -34, -30]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[24, -9, 6, -13, -13],\n [0, 0, 0, 0, 0],\n [0, 25, 10, 5, 5],\n [-30, 0, -12, 14, 14],\n [-24, 29, 2, 17, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-39, 57, -9, 9, 16],\n [18, -31, -5, 5, -2],\n [-23, -8, -38, 38, 10],\n [-47, 48, -7, 7, 0],\n [-6, -30, 0, 0, -28]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-3, 19, -18, 28, 1],\n [-18, -30, -12, 24, 6],\n [-15, -19, -14, 26, 5],\n [9, 9, 10, -18, -3],\n [6, 46, -20, 28, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-5, 3, 6, 6, 6],\n [5, -3, -6, -6, -6],\n [10, -6, -12, -12, -12],\n [15, -9, -18, -18, -18],\n [10, -6, -12, -12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-2, 10, 8, -2, 10],\n [3, -15, -12, 3, -15],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [-5, 25, 20, -5, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-3, -7, 10, 10, -28],\n [-18, 0, 10, -10, 24],\n [-33, -62, 10, 45, -38],\n [-42, -29, 25, 9, 4],\n [-18, -51, 5, 43, -48]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[36, 7, -13, 8, 36],\n [-6, -12, 13, -10, -6],\n [-30, 15, -10, 10, -30],\n [-6, -17, 18, -14, -6],\n [18, 21, -24, 18, 18]]\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, 0, -6, -2, -4],\n [6, 0, -36, -12, -24],\n [1, 0, -6, -2, -4],\n [-2, 0, 12, 4, 8],\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[[21, 21, 6, 30, 12],\n [0, 0, 0, 0, 0],\n [-17, -18, -6, -26, -12],\n [0, -14, -16, -24, -32],\n [-12, -23, -16, -36, -32]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[33, 15, 35, -25, -18],\n [11, 16, -3, -13, -3],\n [14, 1, 22, -16, -23],\n [-18, -9, -18, -4, -23],\n [20, 46, -28, 0, 55]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[22, -1, 30, 0, -39],\n [-22, 1, -30, 0, 39],\n [2, -3, -6, 0, -21],\n [4, 2, 12, 0, 6],\n [18, -1, 24, 0, -33]]\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, 10, 0, -24, 13],\n [27, 17, -30, -32, 46],\n [-13, -7, 3, 30, -23],\n [14, -10, 31, -44, -16],\n [-8, -16, 40, -18, -49]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[5, -2, 5, 4, 4],\n [-30, 12, -30, -24, -24],\n [25, -10, 25, 20, 20],\n [5, -2, 5, 4, 4],\n [-5, 2, -5, -4, -4]]?\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.