messages listlengths 1 1 | ground_truth stringclasses 4 values | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[28, 4, 6, -1, -11],\n [20, 1, 26, 48, 11],\n [-38, -16, -15, -37, -6],\n [-32, 7, -31, -32, 6],\n [-32, 17, -33, -14, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-13, 24, 4, 13, -19],\n [-31, 36, 5, 14, -21],\n [33, -33, 17, -8, 5],\n [18, -32, -10, -19, 28],\n [11, 39, 6, 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[[20, 44, 3, -49, 5],\n [7, -3, 6, -12, 10],\n [11, -7, 30, -28, 50],\n [-12, -37, 5, 35, 0],\n [22, -13, 39, -5, -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[[-4, 7, 6, -1, -24],\n [8, 21, 7, -12, -6],\n [28, -21, -18, 21, 25],\n [10, -20, 8, 12, 2],\n [-30, -38, -42, 34, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[16, -12, 20, -4, -4],\n [8, -8, 18, -4, -2],\n [0, 1, -4, 1, 0],\n [-28, 18, -23, 4, 7],\n [24, -13, 10, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-12, 1, 17, -9, 3],\n [-5, -50, 15, -5, -20],\n [-2, -13, -1, 1, -8],\n [-20, -44, 6, -2, -29],\n [23, 15, 10, -4, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-35, 5, -11, -20, -31],\n [-80, -15, -56, -30, -31],\n [-75, -20, -57, -22, -15],\n [6, -1, -2, 6, 10],\n [11, 29, 12, 14, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-11, 0, 0, -4, -10],\n [-52, -26, -6, -16, -14],\n [19, 6, 15, 12, 25],\n [-1, 20, 13, -12, -13],\n [-7, 42, 54, -40, 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[[-16, -13, 16, 22, 13],\n [-3, 4, 15, -31, 9],\n [1, -9, 2, 18, 8],\n [47, 4, -36, 2, -7],\n [34, -1, -31, 19, -7]]\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, 28, -2, 12, 14],\n [9, 15, -13, -6, 4],\n [8, -8, -4, -4, 36],\n [-30, -24, -4, -16, -26],\n [3, 15, 7, 23, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[0, -24, 2, -3, -8],\n [9, 7, -48, -14, 33],\n [-15, -19, 14, 5, -11],\n [-7, -30, 32, 11, -29],\n [-4, -42, 13, 6, -20]]?\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, -20, -14, 4, -16],\n [9, 10, 7, -2, 8],\n [1, 19, -7, 6, 11],\n [8, 14, 4, 0, 10],\n [3, 11, -1, 2, 7]]\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, -3, -3, -4, 0],\n [-6, 9, 1, 20, -8],\n [-9, 0, 12, -12, 12],\n [-16, 3, 19, -12, 16],\n [-7, 12, 0, 28, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-13, 5, 9, -6, 4],\n [30, 4, 14, -17, 41],\n [18, 10, 16, -14, 36],\n [-25, 1, -9, 14, -30],\n [-15, -9, -19, 18, -38]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[1, 27, -20, -25, 20],\n [-7, -19, 21, 22, -4],\n [2, 14, -12, -14, 8],\n [2, 14, -12, -14, 8],\n [3, 31, -25, -30, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[14, 16, 18, -2, -6],\n [3, 6, 6, -1, -1],\n [15, 30, 30, -5, -5],\n [-17, 14, 6, -5, 11],\n [-20, 8, 0, -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[[-50, 22, -19, -12, -8],\n [-5, 4, -15, 15, -23],\n [43, 10, 18, 29, -11],\n [19, -34, -18, 7, -1],\n [-37, 30, -15, 5, -24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[16, 16, -4, 12, 22],\n [16, -8, 20, -12, 10],\n [-4, -5, 2, -4, -6],\n [12, -5, 14, -8, 8],\n [8, -2, 8, -4, 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[[-11, -22, 2, -18, 5],\n [10, 13, -30, 10, 16],\n [22, -4, 18, -13, -34],\n [-32, 1, 18, 21, 8],\n [8, 9, 14, -16, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[8, -1, -8, -13, 1],\n [-47, 30, -22, -26, -4],\n [-10, 3, 10, 18, -6],\n [29, -27, 10, 1, 29],\n [-16, 9, -26, -44, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-13, -31, -25, 2, -2],\n [-4, -4, -16, 20, -20],\n [-7, -11, -22, 21, -21],\n [5, 7, 17, -18, 18],\n [0, 0, 0, 0, 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[[-10, 16, 10, -22, 4],\n [-33, 31, 49, -16, -29],\n [-18, 3, 36, -1, -20],\n [5, -14, 27, 2, -30],\n [-33, 22, 3, 25, 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[[15, -1, 11, 15, -8],\n [1, 17, -6, -24, 1],\n [12, 10, -6, -25, -26],\n [-13, 32, 15, 4, -5],\n [32, -22, 7, 19, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[25, -11, -23, -17, -6],\n [0, 9, 2, 3, 4],\n [-25, 2, 21, 14, 2],\n [-10, -10, 6, 2, -4],\n [5, 41, 5, 11, 18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[12, -25, -8, 40, 28],\n [2, -16, -2, 46, 8],\n [14, 8, -8, 28, -1],\n [-21, 11, 21, -4, -37],\n [2, -13, 2, -3, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-37, -12, 20, -20, -13],\n [34, 8, -27, 15, 7],\n [8, 0, 11, 5, 7],\n [-4, 16, 0, -1, 7],\n [-10, 8, 28, 1, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-6, 13, 13, -5, 0],\n [6, -13, -13, 5, 0],\n [6, -13, -13, 5, 0],\n [14, -7, -3, -1, 8],\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[[15, -6, -19, -3, 4],\n [42, -7, 6, 32, 17],\n [-30, 26, -11, -7, 16],\n [-19, 23, -10, 0, 19],\n [-22, 6, -2, -14, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[14, 8, 15, -29, -4],\n [9, 7, -1, 3, 3],\n [24, -14, -16, -2, -11],\n [-29, -1, -1, 21, 8],\n [-11, 5, 20, -24, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[9, -9, -9, -4, 8],\n [-10, 6, 10, -2, -8],\n [-1, 1, -6, -5, 3],\n [7, 3, -43, -15, 24],\n [-12, 12, 9, 3, -9]]\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, -15, 11, -10, 1],\n [-5, 5, -4, 15, 1],\n [-10, -35, 25, 0, 5],\n [-5, -10, 7, 5, 2],\n [-10, 10, -8, 30, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[1, -25, 12, 4, 19],\n [-4, 20, -10, -2, -14],\n [-6, -10, 4, 4, 10],\n [3, -35, 17, 5, 26],\n [11, -35, 18, 2, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[18, -4, 7, -9, -9],\n [-24, -5, -5, -46, 8],\n [36, 1, 17, 21, -24],\n [0, -1, 3, -10, -4],\n [-28, 0, -10, -18, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-6, -2, 1, 4, 0],\n [8, -4, 18, 4, 16],\n [-19, -8, 8, 15, 4],\n [-9, -8, 16, 13, 12],\n [-1, -2, 5, 3, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[15, -16, 16, -11, 25],\n [-40, 35, -12, -12, -35],\n [-20, 25, -36, 9, -40],\n [10, -7, -4, -4, 7],\n [-65, 52, 0, -36, -40]]?\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, 2, 4, -1, -8],\n [3, -4, -2, -3, 2],\n [0, 0, 0, 0, 0],\n [12, -28, -20, -16, 28],\n [-6, 14, 10, 8, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-14, -16, -8, -4, -12],\n [3, 10, 6, -4, -14],\n [8, 1, 5, 10, 21],\n [3, 17, 1, -12, -21],\n [2, 6, -6, -5, 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[[4, 2, -10, -6, -18],\n [2, 1, 16, -3, 5],\n [0, 0, 0, 0, 0],\n [0, 0, 15, 0, 10],\n [2, 1, 10, -3, 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[[27, 2, 5, 33, 8],\n [6, 16, -2, -2, 8],\n [12, -13, 5, 23, -2],\n [12, 17, -1, 5, 10],\n [0, 5, -1, -3, 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[[0, -1, 16, 9, -20],\n [6, 3, -12, -3, 18],\n [-16, -21, 0, 0, 12],\n [3, 1, 2, 3, -1],\n [16, 4, -16, 3, 32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-133, 12, -14, -30, 26, -110],\n [-6, 6, 82, 70, 36, 156],\n [73, 25, -53, -31, -14, 2],\n [-57, 27, 39, 29, 46, 76],\n [112, -63, 7, 17, -44, 26],\n [-5, -11, -72, -40, 102, 79]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[52, -16, 36, 84, 84, -24],\n [49, -28, 35, -63, -7, 0],\n [21, 0, 14, 105, 77, -21],\n [135, -60, 95, 15, 95, -30],\n [72, -24, 50, 96, 104, -30],\n [-112, 52, -79, 12, -64, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-41, 7, 13, 15, 12, -12],\n [139, -25, -42, -53, -42, 39],\n [135, -37, -20, -73, -54, 21],\n [30, -14, 5, -26, -18, -3],\n [-27, 49, -64, 85, 54, 51],\n [-5, 11, -15, 19, 12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 2 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[18, 2, -32, -14, -2, -16],\n [38, -18, -40, -18, -22, 16],\n [18, -48, 30, 12, -42, 96],\n [-27, 47, -14, -5, 43, -88],\n [15, -65, 56, 23, -55, 136],\n [62, -32, -62, -28, -38, 32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-46, -1, 68, -30, -14, -65],\n [-105, -42, 130, -71, -37, -149],\n [-65, -11, 90, -43, -21, -92],\n [-24, -6, 32, -16, -8, -34],\n [-3, -48, -26, -5, -7, -5],\n [-63, 0, 94, -41, -19, -89]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[29, 47, -47, 21, 16, -93],\n [36, -27, 27, 108, -45, -54],\n [-14, -77, 77, 42, -49, 84],\n [-18, -99, 99, 54, -63, 108],\n [15, 45, -45, -9, 24, -63],\n [11, -27, 27, 51, -28, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[22, -80, -37, 10, -46, 47],\n [8, 112, 4, 2, 2, -66],\n [8, -20, -68, -10, -34, 18],\n [10, 37, 47, 17, 7, -28],\n [-98, 61, -151, -109, 73, -4],\n [-66, 76, 87, -29, 115, -44]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-60, -104, -44, -92, -20, 12],\n [-42, -96, -6, -96, -30, 0],\n [-10, 2, -28, 11, 10, 9],\n [-26, 40, -110, 76, 50, 36],\n [24, -28, 92, -58, -40, -30],\n [-68, -114, -54, -99, -20, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[20, -67, -115, -9, 85, 113],\n [-36, -141, 206, 28, -131, -158],\n [-63, 1, 104, 43, -55, -76],\n [22, 56, -37, -19, -18, 89],\n [-201, -116, 17, 79, 68, -121],\n [-18, 49, 35, 31, 1, -29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 5 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-10, -70, 82, 20, -74, -12],\n [-35, 69, 8, -16, 9, 36],\n [125, 43, 195, -11, -52, 24],\n [-145, -45, 56, 17, -93, 6],\n [-149, 57, -179, -18, 78, -114],\n [-125, 100, 81, 9, -97, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-21, 29, -23, 144, 117, 47],\n [12, -17, 14, -93, -75, -32],\n [18, -24, 18, -102, -84, -30],\n [27, -35, 25, -128, -107, -33],\n [-18, 16, -2, -98, -68, -66],\n [-39, 49, -33, 146, 125, 29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-44, 4, 76, 22, 80, -154],\n [-132, -92, -74, -85, -1, -148],\n [103, 22, 4, 34, 6, 116],\n [-24, 51, 96, 18, -1, -50],\n [-80, 122, 32, 108, -22, -36],\n [-58, -33, -96, -14, -17, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[18, -121, -15, -16, 160, -166],\n [-99, -113, 20, 78, 66, -51],\n [115, -78, 71, -92, -26, -5],\n [67, 103, -44, -60, -79, 35],\n [-220, -66, 59, 31, 18, -55],\n [-131, -14, -46, 31, 64, -102]]\n\nPresent the answer in LaTex format: \\boxed{Your answe... | 5 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-120, 160, 0, -150, 190, 70],\n [-66, 48, -20, -30, 62, 46],\n [45, -56, 2, 51, -67, -27],\n [66, -112, -12, 114, -130, -34],\n [9, -24, -6, 27, -27, -3],\n [-60, 80, 0, -75, 95, 35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-6, -211, 119, -71, 127, -74],\n [19, -217, 111, -85, 124, -107],\n [-77, -103, 167, 65, -3, 147],\n [15, -86, 62, -89, 117, 2],\n [-79, 148, -44, 146, -141, 132],\n [-60, 21, 91, 97, -83, 184]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 5 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-119, 109, 72, 129, 23, -13],\n [68, -65, -42, -96, -29, 19],\n [59, -59, -36, -29, 11, -21],\n [5, 7, 0, -68, -64, -27],\n [143, -27, -62, 96, 150, -110],\n [25, 58, 2, -145, -118, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[131, 19, 94, 0, 32, 56],\n [7, 53, 74, -65, -2, 5],\n [-16, -38, -56, 18, -10, -34],\n [85, 111, 106, 58, 94, -34],\n [123, 19, 36, 101, 77, -9],\n [-115, -29, -100, 8, -29, -64]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 4 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[56, 28, -95, -42, -45, -58],\n [-85, 0, 59, 8, 29, -52],\n [-6, 83, 133, -37, -111, -165],\n [143, -264, -29, 132, -189, 225],\n [-59, 23, 126, 118, 100, 79],\n [22, -41, 70, 235, 40, 147]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 5 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-100, 24, 95, -53, -27, 14],\n [-59, -64, 27, -115, -61, 97],\n [-10, -34, 16, 13, -55, -4],\n [99, 46, -60, 156, 61, -94],\n [-81, -80, 40, -122, -46, 213],\n [52, -60, -83, -76, 3, 61]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-7, -46, -86, -62, 59, 4],\n [-113, -90, -30, 18, 136, 104],\n [-53, -10, -101, -100, 69, 12],\n [104, 87, 129, 88, -159, -71],\n [141, 39, 36, -52, -88, -129],\n [-10, 36, -51, -110, 16, -40]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-109, 62, -17, -119, 78, -38],\n [-128, 31, 56, -102, 91, -62],\n [97, -33, -27, 77, -71, 10],\n [-40, 55, 100, -47, 55, -45],\n [36, -134, 26, 180, -46, 32],\n [1, -55, -85, 63, -24, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 5 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[86, -44, 30, -28, 10, 102],\n [19, -120, -19, 71, 75, 23],\n [96, -116, -100, 36, 89, -122],\n [60, -53, -25, -105, -36, 121],\n [39, 6, -9, -65, -37, 33],\n [65, 6, -11, -60, -16, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 5 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-21, -12, -56, 8, -70, 86],\n [18, -100, -17, -48, -23, 44],\n [-25, 55, -25, 50, -40, 65],\n [-20, 87, 5, 50, 4, -9],\n [24, 5, 59, -10, 72, -83],\n [-4, -22, -24, -36, -10, -38]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 3 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-149, 158, -64, 87, 78, 24],\n [23, 24, -25, 61, -168, 7],\n [72, -37, 39, -119, 90, -28],\n [1, 23, 81, -108, 78, -121],\n [15, 31, 93, -130, 70, -143],\n [49, -126, 16, 5, -24, 35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[98, -18, 20, 22, -56, -8],\n [-106, -4, -57, -19, 97, 7],\n [32, 68, 54, -10, -110, -2],\n [60, 55, -10, -4, -93, -9],\n [-43, 48, 47, -18, -36, 6],\n [65, -95, 85, 38, 21, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-31, 9, -52, 0, 114, 63],\n [50, -100, -91, -7, -7, 111],\n [-17, -17, -94, -11, 99, 113],\n [-42, -11, -14, 18, 115, 57],\n [-59, 40, 80, 10, -17, -28],\n [94, 8, -214, -116, -83, 84]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[46, 66, -65, 63, -105, -37],\n [-99, 58, 35, -8, -55, -196],\n [108, 90, 1, 193, -19, -53],\n [-77, -122, 25, -81, -22, 64],\n [86, 105, 14, 96, 36, -62],\n [-80, 22, 83, -11, -32, -163]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-4, -9, 0, 8, 2, 4],\n [40, -170, -60, -10, 70, 120],\n [-72, 20, 42, 95, -27, -40],\n [60, -125, -60, -50, 60, 100],\n [-4, -113, -24, 36, 38, 68],\n [-4, 43, 12, -6, -16, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-109, 65, -134, 64, -31, -88],\n [66, -73, 81, 23, 27, 8],\n [69, -99, 84, -12, 15, 36],\n [-26, -7, -33, -68, -32, 42],\n [-17, -22, -21, 73, 4, -60],\n [-4, -37, -5, 85, 11, -64]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 3 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[37, 146, -67, 44, 47, -24],\n [-33, -50, -83, -74, -55, -85],\n [-134, -14, -35, -26, -66, -143],\n [-71, -270, 59, -86, -13, 10],\n [106, 159, 21, 114, 93, 102],\n [22, -27, 56, 12, 65, 63]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[9, 40, 0, -63, 2, -48],\n [7, 99, 62, 18, -26, -77],\n [-14, -112, -55, -36, -1, 85],\n [23, 59, -24, -66, 52, -67],\n [-27, -53, 46, 120, -62, 75],\n [20, -52, -100, -24, 116, 32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 3 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[57, -117, -86, -44, 35, -87],\n [-48, 124, 104, 4, -16, 60],\n [102, -19, 62, -171, 60, -156],\n [-40, 15, 34, -121, 112, -54],\n [-98, 79, 30, -66, 73, 21],\n [-138, 145, 26, 84, -41, 150]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-3, -48, 33, -27, -9, 54],\n [68, -69, 32, 27, -30, 50],\n [41, -56, 29, 9, -21, 46],\n [42, -40, 18, 18, -18, 28],\n [23, 101, -73, 72, 15, -120],\n [11, -2, -1, 9, -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[[-116, 9, -64, 122, 60, -49],\n [-72, -99, -132, -54, -6, -6],\n [-250, 155, -46, 12, 128, -164],\n [20, -146, -208, 33, -25, 117],\n [-73, -154, -185, 91, 3, 30],\n [183, -25, 123, 1, -73, 83]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-10, -45, -30, 7, 6, 47],\n [40, 80, 80, -32, 24, -72],\n [-68, -46, -100, 58, -84, 18],\n [48, 106, 100, -38, 24, -98],\n [-60, -70, -100, 50, -60, 50],\n [30, -40, 20, -28, 66, 62]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[91, 91, 88, 54, 10, 104],\n [27, 34, 28, 28, -33, 34],\n [-54, -60, -54, -54, 6, -54],\n [69, 97, 75, 141, -52, 45],\n [7, -5, 3, -55, 0, 37],\n [61, 46, 55, 15, 91, 59]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[137, -22, 115, 12, -129, 57],\n [15, -90, 20, 113, -143, 112],\n [30, -58, 105, 23, 32, -31],\n [27, -108, 45, 126, -153, 117],\n [57, 52, 30, -65, 13, -32],\n [61, 96, -65, -62, -99, 51]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-8, 47, 26, -23, 50, 14],\n [-67, -34, -66, 1, -53, 15],\n [-17, -48, 60, 65, -130, -52],\n [19, -17, 128, 12, -52, -73],\n [109, -34, -70, -5, -22, 41],\n [-60, -102, 116, 88, -201, -124]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 5 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-85, -67, -18, 136, -27, 88],\n [-26, -9, -32, -32, -63, 63],\n [32, 76, -39, -34, 34, 60],\n [-84, -76, -29, 34, -106, 88],\n [41, 98, -40, 57, 85, 47],\n [34, 42, 30, 20, 150, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[8, 127, -30, -32, 14, -16],\n [24, -5, -5, 8, -90, 66],\n [78, 36, 75, 36, 12, -126],\n [59, 118, 1, -18, -30, -44],\n [-42, -62, 1, 24, 10, 48],\n [-30, -123, -23, -20, -18, 50]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-16, 64, -72, 40, 40, -112],\n [-26, -14, 37, 21, 69, 0],\n [-36, -27, 41, 2, 38, 47],\n [-30, -35, 33, -24, -18, 89],\n [32, -75, 95, -36, -24, 107],\n [26, -31, 54, 1, 25, 13]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[45, -6, 2, 26, -80, 73],\n [-75, -41, -198, -117, -35, 36],\n [63, -42, 16, 112, -1, -52],\n [-4, 61, 176, 17, 80, -85],\n [103, -25, 80, 171, 53, -8],\n [57, 13, 40, 181, -5, -58]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-50, -44, 0, -68, -60, -22],\n [82, 60, -136, 28, 68, -18],\n [-55, 4, -38, -128, -102, 77],\n [-73, -74, 130, -8, -48, -25],\n [-56, 38, -44, -152, -122, 148],\n [-63, -16, -26, -124, -102, 49]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-23, -84, 191, -177, 145, 65],\n [-75, 68, -16, -44, -15, -35],\n [96, -156, 66, -30, 70, -16],\n [-77, 119, -44, 34, -36, 58],\n [-72, 106, 41, -39, -28, 22],\n [28, -56, 16, 40, 44, 70]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 5 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[21, -1, 35, 5, 22, 15],\n [-54, 23, 20, 50, -44, 84],\n [43, -20, -25, -45, 34, -77],\n [107, -28, 55, -45, 98, -61],\n [44, 1, 90, 20, 48, 50],\n [55, -15, 25, -25, 50, -35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[45, -13, 40, -6, -18, 59],\n [34, -25, 37, -61, 42, 112],\n [98, -32, 58, -14, -40, 66],\n [-56, 20, -33, 14, 17, -43],\n [-90, 32, -29, 12, 39, -7],\n [57, -32, 23, -51, 18, 55]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-14, 56, -12, 2, 0, 16],\n [-17, 124, -18, -9, 24, 24],\n [-16, 36, -12, 8, -12, 16],\n [26, -83, 21, -8, 9, -28],\n [22, -25, 15, -16, 27, -20],\n [-25, -54, -12, 35, -66, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 2 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-46, 56, 74, 66, -74, -96],\n [66, -36, -16, 28, 84, -16],\n [88, -38, -1, 65, 107, -56],\n [44, -4, 30, 74, 46, -80],\n [82, -32, 6, 70, 98, -64],\n [-54, 54, 63, 45, -81, -72]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-112, -30, 18, -102, 140, -5],\n [-72, -81, 25, 76, 3, 82],\n [68, -87, 36, -31, 70, -74],\n [-152, -15, -61, -86, 79, 117],\n [50, -9, 101, -117, 63, -138],\n [78, -20, -37, 47, -33, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[65, 127, 17, -63, 67, 78],\n [-34, -79, -27, 53, 90, -120],\n [20, -31, -44, 42, 109, -63],\n [13, -28, -16, 7, 10, -3],\n [-74, -151, 79, 107, -22, -34],\n [16, 70, -2, -91, 61, -15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 5 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-118, -65, 26, -19, -92, 6],\n [43, 35, -8, -50, 59, -6],\n [81, -31, 68, -38, 69, -48],\n [137, -2, 22, 131, 47, -26],\n [63, -28, 22, 127, -11, -14],\n [-9, -144, 154, -69, -7, -76]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-30, -10, -26, -36, 7, -71],\n [-27, -6, -6, 9, -24, 9],\n [-3, -56, 92, 121, -130, -37],\n [96, 56, -24, -80, 144, 32],\n [-18, -10, 14, 36, -43, 27],\n [-87, -47, 27, 89, -141, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 3 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[47, -30, -93, 21, -83, -33],\n [57, 29, 10, -29, -86, 80],\n [29, -13, 55, -54, -110, 97],\n [160, -2, -55, 7, -79, -7],\n [19, 136, -118, 50, 20, 14],\n [-50, 49, 86, 7, 175, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-60, 29, -20, -107, -41, -114],\n [37, -1, -8, 7, -17, 26],\n [-49, -12, 28, 44, 58, 8],\n [39, -5, -12, -20, -21, -8],\n [-97, 55, 0, 7, -21, 26],\n [149, -58, -28, -84, -28, -88]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-35, -38, -95, -58, -41, -46],\n [-35, 24, -45, -26, -57, -52],\n [8, -48, -24, -16, 24, 16],\n [-26, -61, -97, -60, -22, -31],\n [55, -20, 85, 50, 85, 80],\n [-38, -51, -111, -68, -42, -49]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-31, -18, 32, -54, 25, -160],\n [-26, -78, 49, 91, -59, 116],\n [-26, -48, 80, -15, -1, -64],\n [-30, -10, -1, -86, 110, 32],\n [-24, -32, 58, -44, 38, -36],\n [-35, -100, 43, 199, -212, -80]]\n\nPresent the answer in LaTex format: \\boxed{Your answer... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-99, 139, 56, -67, -12, 91],\n [-44, -17, 27, 226, 209, 121],\n [16, 22, -82, -140, -162, -139],\n [35, -135, 151, 39, -47, 33],\n [87, -8, -42, -74, 4, -30],\n [-120, 141, -92, -93, -94, -59]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-86, 111, 17, -96, 67, -42],\n [-54, 5, 53, -102, 7, -4],\n [84, -80, -47, 105, -43, 55],\n [-45, 103, -50, -39, 77, 22],\n [-14, 21, 52, 17, -18, -111],\n [-65, 36, -5, -133, 54, 84]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[11, -36, 16, -184, -103, -16],\n [9, 27, -148, 66, 118, 100],\n [-72, -75, 124, 46, -63, -92],\n [50, 51, 34, -42, -27, -14],\n [-69, -69, 93, 56, -40, -71],\n [20, 15, -120, -30, 55, 80]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-36, -32, -32, -28, 52, -32],\n [-29, -20, -33, -102, 78, -33],\n [10, 8, 10, 20, -20, 10],\n [-59, -60, -43, 58, 38, -43],\n [1, -4, 7, 68, -32, 7],\n [53, 52, 41, -26, -46, 41]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 2 | MATH |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.