messages listlengths 1 1 | ground_truth stringclasses 4
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Determine the rank of the following matrix:\n[[42, -21, 16, 49, -111, 18],\n [-87, 3, 42, -57, 78, -66],\n [-83, -3, 53, -40, 46, -66],\n [119, -18, -58, 36, -85, 56],\n [68, 42, -109, 21, 86, 86],\n [58, 19, -53, 80, -19, 64]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[54, -73, -78, -135, -93, 3],\n [-32, -116, -86, 20, -148, 10],\n [14, 52, -28, -20, 64, -106],\n [-48, -49, -94, 65, -65, -99],\n [35, -68, -49, -92, -86, 32],\n [1, -19, -38, -13, -25, -32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[60, 25, -75, 20, 35, -30],\n [-33, 11, 21, 52, -35, -6],\n [-81, 2, 72, 64, -70, 8],\n [63, 18, -72, 0, 42, -24],\n [102, 48, -132, 48, 56, -56],\n [-39, 25, 15, 92, -49, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[92, 88, -22, -50, -4, -30],\n [-8, 36, 36, -78, 42, 26],\n [1, -22, 20, 113, 98, 107],\n [36, 72, 34, -66, 76, 50],\n [-139, -94, 62, -1, 38, 61],\n [105, 72, -21, 45, 51, 33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[106, -50, 99, -3, 10, 44],\n [-88, 67, -18, -75, 38, -54],\n [-98, -58, -63, 3, 46, -60],\n [10, -96, 3, 34, 23, -3],\n [-2, -51, 75, -68, 80, -30],\n [-6, 21, -27, 18, -24, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-40, -6, 42, -12, 38, 40],\n [-30, -17, 29, -4, 21, 5],\n [20, -17, -25, 14, -31, -60],\n [30, 12, -30, 6, -24, -15],\n [40, -34, -50, 28, -62, -120],\n [60, 59, -53, -2, -27, 40]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 2 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-155, -17, 90, 4, 101, -127],\n [130, 47, -90, 16, -56, 92],\n [47, 76, -137, -17, 70, 41],\n [4, -10, 76, 48, -48, -24],\n [-4, -2, 34, 22, -14, -16],\n [0, 48, -15, 33, 39, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 3 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[30, 70, -160, -10, 40, -10],\n [3, -29, 20, -25, 28, 5],\n [24, 38, -110, -20, 44, -5],\n [21, -29, -34, -59, 80, 6],\n [-30, -40, 130, 30, -60, 5],\n [24, 68, -140, 0, 24, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[112, -145, -166, 131, 141, 15],\n [202, -120, -84, 104, -20, 66],\n [-84, 148, 188, -94, -160, 88],\n [-33, 13, 42, -86, -36, -31],\n [30, -29, -52, 14, 44, -86],\n [65, 13, -34, 91, 26, -37]]\n\nPresent the answer in LaTex format: \\boxed{Your answer... | 5 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-17, -20, -6, -18, -29, 28],\n [-80, -34, -62, -88, -92, 84],\n [-1, 16, -10, -2, 11, -12],\n [4, -64, 40, 8, -44, 48],\n [-50, -3, -49, -56, -44, 38],\n [-8, 55, -39, -12, 34, -38]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[26, -155, 76, -101, 63, 29],\n [-94, -82, 107, -185, -20, -94],\n [75, -23, -56, 81, 73, 96],\n [65, -113, 10, 67, -111, 44],\n [-56, 213, -54, 23, 53, -57],\n [-124, 32, -94, -38, 40, -136]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}... | 5 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-14, 23, 47, 25, -44, 31],\n [-88, 28, 52, 44, -64, 116],\n [-80, 44, 86, 58, -92, 118],\n [6, 29, 61, 27, -52, 13],\n [-84, 36, 69, 51, -78, 117],\n [-70, 47, 93, 59, -96, 109]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-70, 57, -102, -26, -57, 8],\n [12, 59, -14, -6, -55, -68],\n [35, -26, 26, 3, 16, -4],\n [28, 62, 28, 8, -46, -88],\n [-137, -46, -26, 14, 80, 158],\n [107, 2, 70, 8, -16, -94]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-106, -4, 59, -138, -6, 84],\n [44, 21, 32, -54, 8, 30],\n [-180, 21, -79, -13, 70, 117],\n [69, -74, -117, 78, -16, -24],\n [-56, 15, 87, -16, -79, 37],\n [17, 55, -97, 190, 72, -68]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 5 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[31, -25, 26, -7, 9, -16],\n [54, -18, 48, -54, 18, -60],\n [-110, 110, -90, -10, -30, 30],\n [5, -53, -1, 79, -3, 59],\n [-33, -33, -34, 105, -15, 92],\n [-84, 72, -70, 12, -24, 38]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 2 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[5, -78, -22, 19, -143, 68],\n [155, 21, 29, -155, 172, 60],\n [-78, -82, -130, 68, -183, -30],\n [5, -32, 48, 11, -50, 64],\n [-83, 62, 66, 67, 59, -72],\n [84, -66, 72, -104, 101, 70]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-36, 54, -24, -24, 42, 18],\n [4, 10, -20, 2, -6, -8],\n [28, -98, 98, 21, -28, 7],\n [-16, 80, -90, -13, 14, -13],\n [-42, 135, -130, -31, 43, -6],\n [26, -55, 40, 18, -29, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[24, 29, 24, 34, -25, 47],\n [-104, -3, 80, 6, 47, -81],\n [-40, -3, 28, 0, 19, -33],\n [56, 33, 4, 36, -41, 75],\n [-104, -7, 74, 1, 49, -85],\n [112, 10, -76, 2, -54, 94]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-63, 26, 48, 69, 15, 137],\n [111, 34, -54, 168, 108, -77],\n [-57, 28, 23, 59, -110, -43],\n [43, -4, 25, 56, 108, 70],\n [-193, 41, 81, -13, -175, 8],\n [8, -5, 31, 14, 31, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-28, -35, 17, 38, 127, 110],\n [104, -20, 4, 239, -36, -31],\n [28, -161, 17, 26, 17, 1],\n [25, -78, 82, 154, 43, 24],\n [-56, 100, 65, 23, 102, 79],\n [35, 87, 14, 3, -98, -103]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[77, 10, 17, -2, -106, 126],\n [-77, -37, -44, -43, 10, -63],\n [-39, -16, -25, -31, 9, -33],\n [78, 54, -24, -144, -42, 108],\n [-10, -2, 56, 148, 74, -72],\n [22, 26, 28, 38, 52, -18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-64, 57, -65, 10, -66, 39],\n [-17, -53, 62, -78, 52, 34],\n [-20, 76, -88, 72, -80, -8],\n [-21, 70, -81, 64, -74, -5],\n [29, 27, -32, 58, -24, -36],\n [30, -65, 75, -50, 70, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 2 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-58, -44, 38, 60, -4, -12],\n [21, 78, -99, -30, -78, -66],\n [-17, 44, -67, 10, -74, -68],\n [-67, -56, 51, 70, 2, -8],\n [-65, 5, -32, 60, -74, -75],\n [2, -14, 20, 0, 20, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[49, 0, 29, -29, 21, 41],\n [42, -42, 36, -78, -42, 90],\n [-42, -56, -10, -46, -98, 38],\n [0, 0, 0, 0, 0, 0],\n [35, -35, 30, -65, -35, 75],\n [15, -57, 24, -81, -75, 87]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 2 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[34, -93, -101, 190, 146, -93],\n [-113, 37, -59, -129, 23, -42],\n [143, -28, 129, 29, -155, 60],\n [-116, 8, -120, -62, 10, -101],\n [180, -37, 139, 60, -90, 111],\n [23, -78, -156, 85, 142, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your ans... | 5 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-58, 8, 54, 72, -14, 56],\n [-77, 22, -9, 18, -31, 34],\n [84, -26, 24, -6, 36, -30],\n [-66, 11, 48, 69, -18, 57],\n [-88, 22, 12, 42, -32, 50],\n [-72, 5, 102, 123, -12, 87]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[40, -43, 1, 23, -140, 122],\n [41, -21, 72, 71, 73, -85],\n [2, -30, 47, 60, 56, -113],\n [15, 4, 40, 19, 99, -76],\n [-92, 104, -117, -180, 86, 37],\n [-61, 53, -83, -65, -59, 52]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 4 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-4, 44, -5, -68, -4, -41],\n [-89, 68, 126, -55, 33, -84],\n [-84, 5, 145, 31, 36, -49],\n [105, -67, -135, 59, -46, 67],\n [27, 38, -136, -87, 7, 102],\n [157, -82, -112, 96, -100, -52]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[102, -1, 21, -86, -41, 50],\n [-32, 128, 28, -90, -92, -72],\n [-12, 14, 0, 37, 4, -28],\n [-58, 56, 5, -61, -38, -29],\n [-70, -65, -25, -102, 23, 84],\n [84, -12, 12, 9, -6, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-59, -89, -48, -70, -29, -75],\n [-71, -61, 67, 110, -153, -68],\n [-32, -11, -51, 38, -17, -48],\n [-49, -53, 91, 41, -117, -26],\n [-32, 132, 119, 227, -100, 61],\n [19, -83, 7, 73, -71, -72]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[26, 64, -48, 6, -29, 31],\n [-105, 81, 76, -141, 38, -60],\n [-213, -115, 31, -5, -153, 115],\n [165, 97, -77, 15, 113, -73],\n [118, 22, -107, 149, 11, 2],\n [-35, 41, 137, -86, -15, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 5 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[35, 9, 89, -41, -113, -105],\n [18, -82, -111, -148, 87, 75],\n [-35, -53, -89, -67, 130, 97],\n [22, 86, -33, 103, 167, 103],\n [-46, 30, 66, 97, -33, -14],\n [6, 10, -155, 140, 19, 100]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[176, 58, 57, -70, 55, -7],\n [14, -199, -82, 9, -88, 142],\n [-29, -51, -100, 89, 21, 105],\n [-10, 41, -25, 25, 35, -9],\n [-190, -27, -100, 85, -30, -12],\n [125, -37, -72, -21, 26, 64]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[38, 95, -67, -118, 27, -107],\n [-17, 29, 27, -55, 73, -52],\n [-20, 22, -28, -45, 84, -121],\n [-7, -104, -74, 65, 72, -83],\n [-62, 69, 78, 28, -74, 45],\n [10, 36, 3, -77, 85, -51]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 5 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-21, -93, 39, -33, -102, 72],\n [-49, 19, -4, 24, -42, -27],\n [-1, -7, -26, -2, 14, -3],\n [60, 11, 46, -16, 40, 21],\n [22, 65, -127, 23, 152, -78],\n [84, -19, 116, -38, 0, 69]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[65, -10, -82, 92, 67, -37],\n [17, -40, -58, 152, 25, -67],\n [22, -20, -44, 88, 26, -38],\n [6, 15, 8, -46, 3, 21],\n [104, 20, -96, 24, 100, -4],\n [7, -35, -42, 126, 14, -56]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-37, -85, 55, -4, 116, 60],\n [-180, -130, -22, -36, 89, 131],\n [-46, -64, -271, 58, -114, 242],\n [-131, -96, -28, -69, 39, 88],\n [43, -24, 9, 83, -16, -3],\n [147, 97, 46, 112, -15, -87]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 5 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[15, -40, -5, -19, -67, 15],\n [6, 36, -2, 21, 46, -33],\n [18, 8, -6, 8, -2, -24],\n [21, 36, -7, 24, 35, -48],\n [-6, 4, 2, 1, 10, 3],\n [6, -104, -2, -56, -150, 72]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 2 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-8, -12, 4, 16, 40, 4],\n [18, -1, 7, 8, -54, 27],\n [-2, 60, -35, -95, -71, -80],\n [6, 51, -27, -78, -84, -57],\n [-2, 4, -3, -7, 1, -8],\n [-16, 32, -24, -56, 8, -64]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[38, -22, 8, -48, -54, 7],\n [76, -27, -26, 0, 2, 61],\n [-84, 53, 6, 0, 2, -67],\n [116, -102, 20, 0, -8, 92],\n [110, -67, -6, -16, -20, 80],\n [62, -98, 46, 28, 19, 62]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-7, 8, 12, -9, -32, 37],\n [-7, 8, 4, -5, -8, 5],\n [23, -52, -50, -32, -86, 59],\n [19, 4, 52, 49, 56, 15],\n [-13, 32, 28, 25, 72, -57],\n [-15, 30, 34, 10, 18, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[84, 37, -22, 33, 47, -54],\n [118, 54, -60, -94, 32, 32],\n [154, 39, -45, 2, 85, -81],\n [-80, -112, 55, 41, 6, -73],\n [-76, 36, 24, 76, -48, 32],\n [70, 143, -56, -19, -21, 92]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[26, -157, 87, 81, 17, -63],\n [-77, -73, 4, 0, -100, -36],\n [16, -141, 19, 25, 11, -62],\n [-10, -52, -106, -72, -8, -61],\n [-89, -29, 13, 30, -129, -79],\n [40, -41, 42, -3, 18, 128]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-45, 32, 67, 18, 35, -113],\n [-143, 64, -21, -57, 88, 3],\n [141, -101, 31, 67, -130, 25],\n [-18, 35, -26, -123, -8, 55],\n [-116, 23, -37, -51, 58, 47],\n [-31, 50, 26, 4, 49, -75]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 5 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-43, -28, -35, -5, -27, -18],\n [-18, -16, 3, -16, 1, 16],\n [16, 8, 23, -6, 17, 20],\n [-3, 12, -60, 45, -42, -78],\n [-20, -32, 62, -64, 42, 96],\n [22, 24, -22, 34, -14, -44]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-26, -34, -22, -114, 186, -113],\n [-17, 39, -39, -146, 149, -66],\n [-124, -27, -142, -69, -88, 97],\n [-3, -33, -57, -32, 109, 26],\n [42, 62, 154, 172, 26, 10],\n [-28, -94, -96, -160, 136, -101]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[32, 36, 44, 8, -28, 12],\n [-116, 37, -41, -88, 23, 65],\n [68, 64, -4, -18, 138, 178],\n [170, -20, 71, 111, -21, -49],\n [-62, -31, -80, -39, 84, 42],\n [-48, -54, -66, -12, 42, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-68, -42, 84, 48, 32, -26],\n [16, 56, -80, 0, -32, -8],\n [47, 42, -75, -30, -29, 14],\n [41, 70, -109, -18, -43, 2],\n [-21, -49, 73, 6, 29, 3],\n [-26, 56, -62, 36, -26, -32]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 2 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[26, 18, 21, 4, -12, 4],\n [-30, -24, -49, -38, 2, -45],\n [-48, -54, -18, -86, 18, 5],\n [22, 30, 41, 88, 8, 52],\n [90, 84, 14, 68, -52, -55],\n [-104, -90, 3, -32, 72, 99]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-6, -68, -35, 39, 35, -84],\n [-14, -20, -122, -64, 83, 63],\n [19, 96, 181, 34, -129, 19],\n [11, 68, 50, -29, -50, 69],\n [60, 56, -31, -75, -86, 57],\n [-54, -84, 17, 91, 87, -100]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[12, 92, 34, 62, -108, 86],\n [40, 104, 34, 42, -168, 14],\n [75, 89, 49, 17, -123, 59],\n [-122, -8, -82, -41, 90, 56],\n [83, 59, 79, 80, -123, 19],\n [33, 38, 49, 73, -75, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[88, -88, -104, -32, 104, 128],\n [59, -41, -43, -28, 37, 64],\n [89, -68, -74, -40, 67, 104],\n [-38, 32, 36, 16, -34, -48],\n [-16, 10, 10, 8, -8, -16],\n [37, 14, 32, -32, -49, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[28, 95, 25, -59, -71, -121],\n [22, -40, -90, 4, 36, -84],\n [-1, -98, -11, 96, 68, 120],\n [-8, -70, -20, 54, 51, 76],\n [-4, -26, 40, 50, 13, 92],\n [13, 89, 24, -67, -65, -101]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-134, -29, -39, -62, -56, -50],\n [18, 110, 55, 81, -23, 28],\n [116, 9, 50, 34, 27, 45],\n [82, -54, -68, 13, 126, -1],\n [70, 17, -10, 45, 63, 20],\n [40, -17, -18, 8, 45, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-14, -4, -14, -4, 10, -8],\n [-43, -2, 101, 86, -39, 44],\n [27, 9, 45, 20, -28, 24],\n [45, 9, -9, -24, -6, 0],\n [-24, 6, 156, 116, -70, 72],\n [-1, 1, 17, 12, -8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-24, 195, 111, -33, 62, 90],\n [-14, 15, 85, -29, 66, 102],\n [-12, 35, 11, -37, 26, 62],\n [-21, 105, 168, -21, 98, 126],\n [19, -90, -143, 22, -86, -114],\n [12, -85, -133, -1, -66, -70]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",... | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-2, -19, 30, -23, -20, -7],\n [86, 127, 40, 129, -60, 11],\n [54, 169, -132, 140, -56, 131],\n [-68, -124, 6, -104, 88, -64],\n [8, 20, -8, 8, -32, 28],\n [70, 55, 120, 65, -60, -45]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-138, -2, 140, -71, 67, 39],\n [-136, 6, 52, 15, 95, 90],\n [74, -84, 144, -43, 2, 6],\n [65, -62, 218, -141, -19, -67],\n [89, -56, 14, 3, -56, -14],\n [-80, 52, 36, -75, 6, -44]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-83, 86, -227, 159, -27, -86],\n [-148, 76, -243, 62, -30, 0],\n [32, 59, 109, 38, -40, 100],\n [-44, 58, -190, 88, -16, -20],\n [-52, 159, -31, 188, -93, 57],\n [4, -76, -72, -80, 48, -54]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-93, -38, -55, -11, -57, 49],\n [7, -73, -66, 37, -71, 102],\n [-90, 58, 68, -10, 122, -148],\n [24, -164, 35, 23, -50, 37],\n [-54, 99, 78, -16, 138, -161],\n [-181, 74, -103, 43, 55, -13]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[8, 74, -20, -101, -118, -19],\n [44, -28, -23, 10, -40, -61],\n [8, -6, -4, 3, -6, -11],\n [8, 4, -6, -10, -20, -12],\n [0, 90, -18, -117, -126, -9],\n [-36, 32, 17, -20, 20, 49]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-44, 24, -113, -1, 6, 33],\n [-5, -96, 62, -36, -7, 1],\n [-28, 94, -26, -95, 134, -101],\n [70, 106, -108, -37, -28, 67],\n [5, 16, -36, -24, 3, 15],\n [133, 146, -44, 19, -67, 64]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 4 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[127, 175, -34, 92, 71, -70],\n [-39, -57, 52, -63, -31, 7],\n [25, 39, -30, -52, -25, 40],\n [-93, -68, 110, -160, -24, 89],\n [55, 51, -43, -42, -36, 16],\n [-19, -71, 4, -144, -121, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[11, -38, 99, -17, -9, 27],\n [3, 118, -135, -82, 70, 45],\n [-73, 26, 74, -144, -81, -19],\n [-26, -155, 101, 12, 30, -85],\n [-24, -21, 34, -52, 3, -17],\n [-95, -27, -2, -107, 32, 28]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 5 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-143, -17, -140, -93, -57, -108],\n [-147, 81, -97, -86, -46, 46],\n [-101, -24, 7, -106, -90, 150],\n [-125, 82, -58, -84, -34, 104],\n [25, -76, 27, 8, 16, -56],\n [-121, -141, -11, -93, -139, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your ... | 5 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[49, 28, 0, 86, 30, -24],\n [8, 72, 93, 26, -111, 31],\n [-104, -118, -24, -187, -92, -49],\n [-101, -84, 59, -40, 113, -83],\n [-24, -70, -29, 45, 213, -62],\n [-1, -54, -9, 25, 23, 59]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[23, 159, 202, -118, 161, 40],\n [141, 11, -27, 3, -43, -39],\n [106, 16, 34, -40, 70, 1],\n [144, 6, 40, 17, -11, 13],\n [-70, 24, 31, -23, 36, 13],\n [-103, 39, 48, -11, 12, 21]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 4 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-39, -161, -26, 34, 36, -93],\n [-117, -59, -87, 139, -63, -66],\n [-206, -183, 54, 25, 68, -5],\n [-11, -64, 73, -6, -7, 30],\n [148, 54, -115, -122, -19, -42],\n [-82, -107, 145, 21, 97, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}... | 5 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[90, 79, -93, 26, -117, 61],\n [100, 52, -88, -12, -84, 78],\n [50, -65, -5, -110, 75, 65],\n [50, 19, -41, -14, -33, 41],\n [-30, 46, 0, 74, -54, -41],\n [-90, 19, 51, 86, -9, -89]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[71, -88, 115, 7, 3, 91],\n [-121, -120, -85, 59, -97, 29],\n [4, -32, -21, -29, 3, 80],\n [196, 51, 65, -31, 100, 14],\n [-143, -30, -66, 50, -80, -59],\n [144, 91, 103, -57, 98, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-40, -25, 40, 20, 30, 25],\n [34, 15, -104, -47, -58, -10],\n [54, 40, 16, 3, -8, -45],\n [14, 10, 0, -1, -4, -11],\n [114, 80, -16, -15, -40, -87],\n [-34, -30, -64, -25, -20, 37]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[82, 12, 140, -96, -18, 16],\n [57, 67, 43, 12, -86, 16],\n [56, 72, 50, -54, -16, 15],\n [-141, -91, -82, -37, 135, 36],\n [44, -33, 41, -2, 1, -43],\n [-86, -34, -60, 10, 38, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 4 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[20, 80, 95, 65, -45, -5],\n [-68, -110, 1, 49, 99, -91],\n [48, 66, -24, -54, -66, 72],\n [-8, 4, 34, 34, 6, -22],\n [-64, -106, -4, 42, 94, -84],\n [-8, -56, -86, -66, 26, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-179, -6, 1, -91, 2, 28],\n [69, 1, -84, -9, -181, 37],\n [-23, 8, 7, 68, 30, -51],\n [95, 16, -107, -9, -196, 70],\n [47, -31, -47, -1, -177, -31],\n [-182, -22, 32, -132, 34, 32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-12, -84, 90, -18, -40, 6],\n [-25, -35, -56, -62, -33, -6],\n [20, 12, -79, -81, -2, -37],\n [42, 54, 24, 36, 42, -12],\n [44, 109, 22, 106, 76, 6],\n [-3, -4, 106, 92, 13, 32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 3 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[10, 29, -87, 50, 8, -54],\n [17, 36, 32, -70, 72, 121],\n [-50, -95, -51, 180, -49, -200],\n [-88, -24, 26, 35, -57, 31],\n [50, 36, -100, 20, -72, -134],\n [111, -26, 24, -25, 123, -40]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[18, -50, -48, 32, -18, 44],\n [56, -82, 151, -28, 6, -66],\n [-90, 144, 43, -12, -68, -50],\n [6, 10, 122, -40, 8, -74],\n [-92, 142, -25, 4, -60, -12],\n [-26, 4, 2, 40, -93, 15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[29, 28, 68, 10, -7, 42],\n [104, 60, -88, 126, 30, -28],\n [121, 130, 22, 23, -70, -4],\n [100, 76, -62, 84, -4, -28],\n [-170, -184, 52, -32, 106, 60],\n [-55, -84, 32, 38, 81, 50]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[24, -32, 160, -195, 127, 138],\n [-39, -133, -36, -217, 158, 239],\n [42, 42, -21, -54, 30, -39],\n [-89, 41, 111, 31, 94, -2],\n [7, 7, 210, 68, -89, -74],\n [60, -43, 46, -129, 20, 76]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-46, -54, 82, -34, 8, 64],\n [62, -58, -58, 78, -72, -16],\n [-64, -35, 80, -63, 33, 59],\n [15, -69, 13, 34, -44, 28],\n [-2, -70, 58, 24, -36, 52],\n [-14, -21, 46, -3, -3, 31]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[119, 184, 71, 29, 108, 147],\n [152, -34, -6, 86, -26, 10],\n [-122, 101, 76, 12, 26, 39],\n [4, 106, 112, 76, 89, 36],\n [-216, 25, -55, -238, 36, 11],\n [-37, 32, 44, -99, 164, -27]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 5 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[68, 37, -12, -16, 33, 6],\n [-14, 20, 40, -24, -26, 18],\n [18, -51, -136, -2, 83, -41],\n [16, 98, 152, 152, -40, 118],\n [-16, 106, 45, -215, -68, -30],\n [-15, 28, 0, -26, 4, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 5 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-69, 31, -65, -86, 106, 26],\n [-66, 26, 38, -22, 44, 52],\n [-17, 14, -115, -55, 68, -6],\n [49, -21, -103, -70, 34, -82],\n [-20, -2, 72, -42, 20, -8],\n [-7, 10, -77, -11, 28, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-30, 85, -28, 8, 12, 65],\n [38, 61, -78, 88, -6, 71],\n [76, -43, -45, 80, -21, -8],\n [26, 7, -30, 40, -6, 17],\n [12, 54, -48, 48, 0, 54],\n [40, 70, -86, 96, -6, 80]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-71, -30, 3, 11, 2, -24],\n [-4, 52, 18, 64, 126, 107],\n [22, -22, -22, -52, -107, -30],\n [31, -40, -13, -61, -107, -111],\n [6, 12, 32, 42, 112, -49],\n [-52, -4, -4, 16, 6, 48]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[11, 96, 89, -17, 15, -35],\n [-6, -54, -54, 12, -12, 24],\n [-9, -75, -61, 8, -4, 18],\n [3, 48, 97, -41, 55, -75],\n [7, 69, 83, -24, 28, -46],\n [-12, -84, -28, -16, 32, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[26, 59, 101, 65, -93, 42],\n [-106, 15, -16, -79, -71, -32],\n [-105, -13, -67, -84, -39, -40],\n [3, 11, 26, 0, -9, 2],\n [-41, 62, -5, 47, -50, 40],\n [6, -44, 13, -4, -117, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[6, -70, 4, -128, 82, -26],\n [48, -4, 136, 54, 3, -38],\n [-61, -25, -112, -78, 66, -7],\n [-30, 16, 50, 90, 51, -64],\n [-25, -70, 35, -80, 145, -85],\n [-41, 5, -90, -24, 9, 15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[33, 38, 93, 4, -50, -48],\n [-29, -72, -77, 12, 24, -12],\n [144, 78, 90, 147, 111, -42],\n [-73, -23, -26, 4, -149, -61],\n [56, -73, 73, 48, -3, -143],\n [67, 5, 42, -57, 156, 71]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 4 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[13, 40, 25, -31, 41, -15],\n [13, 125, -9, -57, 13, 110],\n [-67, 39, -20, -55, 35, 54],\n [6, 8, -85, -74, -3, -9],\n [56, 50, -4, 167, -236, 175],\n [-32, -129, 26, 104, -48, -67]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 5 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[51, -62, -54, 22, -10, 31],\n [-66, 16, 11, -82, -62, -99],\n [87, -62, -52, 74, 34, 93],\n [-54, 48, 41, -38, -10, -49],\n [6, -44, -40, -28, -44, -30],\n [-105, 38, 29, -120, -84, -146]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[18, 44, 33, -100, 132, 107],\n [-44, 5, -116, -26, -4, 121],\n [51, 22, 80, -44, 123, 9],\n [62, -73, 13, 60, -119, -85],\n [27, 47, 32, 22, 65, 8],\n [98, 13, 132, -18, 78, -41]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 5 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-52, -8, -74, 44, 99, 162],\n [-56, 54, -14, 36, 66, 111],\n [120, -76, -8, 56, -42, 14],\n [-92, 66, 22, -58, 15, -47],\n [-112, 62, 0, -54, 42, -11],\n [0, -140, -112, -36, 36, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-87, 87, -86, -36, 4, 105],\n [52, 21, 76, -12, -74, -33],\n [28, 94, -28, -162, -41, 53],\n [17, -56, 18, 106, 26, -76],\n [-56, -104, 128, 80, -38, 50],\n [-37, -44, 112, -85, -66, 116]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 4 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[5, 77, 14, -82, -19, -97],\n [-49, 50, 96, -52, 41, -113],\n [16, -21, 14, 74, -9, 14],\n [10, -12, 18, -60, 58, 14],\n [-55, 48, 24, 24, -49, -83],\n [60, -62, -87, -30, 23, 134]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[103, -121, -93, 8, -156, -36],\n [-9, 79, 65, -19, 86, 67],\n [108, -49, 53, -30, -15, 178],\n [-50, 57, 27, 0, 61, -12],\n [19, -26, 26, -7, 3, 67],\n [-35, 57, 1, 2, 36, -46]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 3 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[0, -77, 56, 49, 21, -7],\n [-14, 10, -20, -49, -46, -22],\n [0, 77, -56, -49, -21, 7],\n [18, 39, -12, 30, 45, 33],\n [6, -20, 20, 31, 24, 8],\n [8, -23, 24, 39, 31, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 2 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[27, 44, -30, -23, -134, -40],\n [104, -44, 95, 169, 88, -137],\n [-19, 17, -113, -74, -138, 48],\n [37, 9, 112, 82, 10, -127],\n [-94, 37, -26, -106, -116, 29],\n [194, 13, -79, 88, -32, -32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-1, -24, 1, 24, 18, -12],\n [20, 24, -36, -40, -24, -16],\n [-22, -129, 36, 143, 102, -40],\n [27, -36, -51, 12, 18, -60],\n [-7, -54, 11, 58, 42, -20],\n [-27, -135, 45, 153, 108, -36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[6, -55, -15, 33, -35, 131],\n [28, 101, 27, 17, 1, -109],\n [-72, -16, -83, -23, 4, 101],\n [237, 181, 217, 104, -39, 50],\n [-12, 74, -32, 32, -22, -36],\n [182, 38, 188, 46, -10, 66]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 4 | MATH |
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