messages listlengths 1 1 | ground_truth stringclasses 4
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Find the rank of the matrix:\n[[-54, 32, 14, 82, -104, 18],\n [-12, -4, 2, 136, -62, -36],\n [-32, 16, 8, 80, -72, 0],\n [63, -54, -18, 81, 63, -81],\n [-19, 2, 4, 127, -69, -27],\n [-56, 38, 15, 34, -91, 36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-103, 77, -3, 76, 39, 22],\n [-52, 70, -10, 57, 27, 65],\n [4, 200, 55, 131, -164, 98],\n [-87, 58, -24, 82, 20, -65],\n [-36, -197, -19, -147, 155, -101],\n [30, -136, -68, -130, 134, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 5 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[27, -88, -38, 68, 12, 24],\n [19, 67, 68, 103, -122, -53],\n [59, -36, -73, -17, 43, -67],\n [56, -81, -91, -8, 67, -34],\n [36, 94, 55, 71, -115, -99],\n [11, -44, -13, 43, -1, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[2, -18, -108, 97, 140, 138],\n [-12, -1, -42, 130, 110, 144],\n [-14, -15, 72, 16, -72, 32],\n [3, 6, -110, 116, 161, 123],\n [-81, 125, 127, 72, -169, -46],\n [28, -66, -221, -42, 272, 71]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[61, -79, 57, 88, 10, 84],\n [51, -85, 67, 88, 2, 74],\n [-111, -49, 0, -29, -54, -18],\n [3, -103, -8, 61, 2, 140],\n [68, -66, 75, 87, 8, 54],\n [10, 156, -1, -87, 8, -188]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[25, -100, 40, 32, -52, -85],\n [100, -111, 11, 146, 7, -159],\n [0, 18, 16, -38, 13, 21],\n [6, -51, -80, -56, -49, 15],\n [129, 17, -76, 8, 99, -42],\n [-4, -140, -42, 14, -113, -59]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 5 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-10, -13, -45, 14, -40, -57],\n [-6, 29, -50, -10, -24, -48],\n [-12, -54, -30, 36, -48, -54],\n [-8, -84, 10, 48, -32, -18],\n [-10, -21, -40, 18, -40, -54],\n [14, 135, -10, -78, 56, 36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-52, 93, -52, -111, -35, 90],\n [-87, 71, 35, 0, -80, -33],\n [-31, -21, 135, 180, -100, -197],\n [123, -21, 7, 66, -50, -41],\n [-52, 80, -13, -54, -60, 31],\n [74, -75, 56, 123, -5, -102]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-3, -3, 8, -31, -32, -47],\n [68, 65, 31, 109, 120, 25],\n [41, 62, 47, 62, 29, 45],\n [20, 20, 32, -28, -28, -96],\n [-13, 22, 25, 6, -55, 97],\n [8, 51, 57, 7, -67, 62]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-9, 28, 56, -95, 20, -46],\n [-21, 27, -3, -9, 18, -30],\n [-5, 5, 67, -76, 47, -34],\n [-5, 29, 3, -43, -24, -22],\n [31, -43, -5, 29, -28, 50],\n [1, 24, -28, -9, -52, -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[[-86, 39, 59, -20, 119, -35],\n [-78, -40, 100, -19, 70, -97],\n [46, -13, -27, 15, -79, 16],\n [25, -68, -83, 14, -37, -8],\n [66, -81, -69, 17, -94, 3],\n [-4, -75, 19, -20, 45, -31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[134, 78, 44, 61, 56, 23],\n [-78, -1, -76, -66, -57, -40],\n [-128, -211, 298, -102, 184, 100],\n [-50, -35, 72, -51, 53, -23],\n [-93, -95, 144, -86, 78, 14],\n [3, -21, 158, -29, 110, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-6, 0, 6, -24, -12, 0],\n [41, 49, 1, -25, 26, -28],\n [62, 70, -2, -22, 44, -40],\n [19, 14, -7, 22, 22, -8],\n [-39, -42, 3, 6, -30, 24],\n [2, 0, -2, 8, 4, 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[[0, -1, -9, 16, -12, -27],\n [21, 13, -9, 37, -26, -76],\n [-24, -16, 0, -24, 16, 56],\n [-15, -14, -36, 49, -38, -73],\n [30, 23, 27, -18, 16, 11],\n [-39, -32, -54, 57, -46, -71]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[33, 28, -33, 36, 50, 13],\n [27, 20, -51, 60, 22, -25],\n [41, 36, -31, 32, 70, 31],\n [-28, -24, 26, -28, -44, -14],\n [25, 16, -68, 82, 4, -54],\n [20, 12, -61, 74, -2, -53]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[137, 153, -131, 24, -14, -100],\n [41, 29, -4, 2, -4, -21],\n [-38, -16, -129, -33, 22, -11],\n [-195, -175, 108, -18, 12, 119],\n [77, 141, -68, 5, 72, 3],\n [127, 47, -104, -116, 76, -47]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"... | 5 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[6, 44, -114, -57, -36, -30],\n [-110, -59, -154, -77, -127, -76],\n [-11, 1, 35, 17, 57, -14],\n [10, 10, 114, 0, 54, 64],\n [-177, -118, -90, -98, -155, -46],\n [-55, -7, -31, -76, -45, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-6, -44, -14, 34, -16, 34],\n [18, -33, 9, 30, 48, 63],\n [3, 17, 6, -13, 8, -12],\n [21, -1, 18, 5, 56, 36],\n [6, -16, 2, 14, 16, 26],\n [-6, -44, -14, 34, -16, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-32, 14, 42, -3, 38, 0],\n [96, -36, -44, 10, -84, -16],\n [-100, 28, -84, -12, 40, 42],\n [-92, 38, 90, -9, 98, 6],\n [-128, 44, 4, -14, 92, 32],\n [-118, 40, -4, -13, 82, 31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 2 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-27, 75, 7, 45, 15, -7],\n [75, 25, 120, -4, 105, -82],\n [10, -90, -150, 30, -130, 110],\n [-56, 70, -59, 65, -40, 39],\n [35, 98, 53, 82, 61, -36],\n [-85, 16, -99, 20, -83, 66]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[3, 22, 59, -94, 11, 60],\n [-48, 96, 93, 27, 87, -48],\n [-31, -45, 9, 40, -43, 20],\n [-9, 23, -36, 117, -36, -52],\n [-17, -5, -109, -69, 64, 64],\n [-55, 95, 112, 42, 77, -52]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[130, 36, -56, -12, -36, -58],\n [77, 130, 42, -66, 50, -77],\n [10, 0, -31, -58, -34, -11],\n [35, -74, -24, 144, -6, 32],\n [54, 100, 11, -61, 10, -64],\n [-45, 18, 74, -95, 78, 15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-13, -88, 27, -26, -144, -41],\n [22, -42, 61, -29, -9, 75],\n [-40, 64, -104, 48, 0, -136],\n [-15, -44, -1, -8, -90, -49],\n [-2, 44, -28, 18, 54, -8],\n [-20, 66, -71, 37, 45, -69]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[31, 83, -108, -127, 52, 38],\n [125, 44, 22, -54, 13, -43],\n [31, 8, -86, 6, 75, -14],\n [-89, -15, -56, -9, 22, 144],\n [17, 10, 142, -23, -112, -57],\n [68, 48, 28, -57, -25, -86]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-109, 26, -84, -84, 125, 103],\n [4, -52, -10, -95, -137, 27],\n [-45, 22, 69, 29, 94, -16],\n [-21, 6, -69, -39, 14, 48],\n [9, 34, 120, 35, -90, -34],\n [10, 20, -160, 40, 160, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[85, 30, 25, 5, 75, 105],\n [100, 90, 2, -38, -20, -8],\n [-98, -121, 19, 71, 90, 92],\n [-64, -78, 31, 77, 80, 80],\n [56, 43, 2, -20, 0, 10],\n [-51, -57, -26, -22, -5, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[74, 11, 42, 35, -31, 34],\n [-73, 82, 80, -74, -44, 2],\n [-1, 72, -2, 79, 5, 15],\n [-13, 4, 112, -61, -117, 93],\n [-104, 67, -93, 21, 104, -97],\n [1, -66, -141, 54, 111, -73]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-45, -38, 47, -35, -96, 37],\n [45, -7, 54, 80, 49, 38],\n [23, 63, -8, 48, 83, -100],\n [-30, -12, 38, -19, -78, 42],\n [-17, -56, 72, 11, -88, 32],\n [-12, 15, -110, -90, -64, 63]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 5 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-22, 15, -48, 16, 26, -27],\n [117, -135, -20, -60, -13, -77],\n [-109, 149, -62, 36, 71, 15],\n [-22, -106, 30, 116, -9, 116],\n [-49, 78, -130, 12, 147, 2],\n [120, -38, 0, -128, 44, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-24, -85, -15, 93, -39, 48],\n [-51, -22, 39, 66, -93, 102],\n [-64, 24, 72, 40, -120, 128],\n [34, -48, -54, 8, 66, -68],\n [15, -82, -51, 54, 33, -30],\n [-46, 29, 57, 19, -87, 92]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 2 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-172, -162, 104, -100, -94, -212],\n [-24, 48, 133, 4, -114, -20],\n [98, 174, 31, 64, -7, 132],\n [34, 79, 30, 30, 83, 70],\n [-54, -120, -119, -68, -15, -104],\n [17, -12, -38, 2, -69, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",... | 4 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[40, -14, -2, 20, 70, -46],\n [-14, 28, 37, -40, -41, 15],\n [-46, -28, -67, 40, -49, 55],\n [-18, 0, -9, 0, -27, 21],\n [18, -21, -24, 30, 42, -20],\n [18, 21, 42, -30, 12, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-44, 42, -13, 1, -14, -53],\n [-21, 36, -24, -3, -3, -48],\n [-33, 12, 12, 5, -15, -12],\n [105, -24, -54, -19, 51, 18],\n [-38, 54, -31, -3, -8, -71],\n [-16, 72, -68, -12, 8, -100]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 2 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-6, 6, 0, 18, 4, -12],\n [6, 42, 24, -54, 24, 72],\n [-6, 66, 30, -27, 39, 63],\n [-12, 60, 24, 0, 36, 36],\n [-20, 88, 34, 9, 53, 45],\n [-26, 70, 22, 45, 43, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-17, 71, -61, -60, 81, 66],\n [-118, 95, -7, 10, -56, 41],\n [84, -33, -2, -33, 6, -43],\n [75, -45, 56, -61, 37, 6],\n [-90, 18, 43, 33, -18, 50],\n [-39, 11, 55, -24, 19, 60]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 4 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[38, 139, 92, 8, 35, 40],\n [-43, 51, 22, 13, 72, -95],\n [-109, -7, -95, 17, 133, 58],\n [21, 64, 17, 38, 64, 58],\n [21, -68, -47, -86, 2, -35],\n [56, -87, 9, -85, -90, -149]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 5 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[55, -112, 23, 42, 98, 67],\n [115, -32, -76, 33, 72, 64],\n [-29, 156, -41, -34, 0, -25],\n [-60, 102, -6, -87, -84, -81],\n [-45, -77, 33, -12, -58, 5],\n [124, 5, -29, -80, 31, -90]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-226, 138, 174, 128, 44, 209],\n [-8, -114, -47, 36, -15, 3],\n [114, 0, -51, -123, -78, -105],\n [-7, 63, 28, -42, 105, 14],\n [-78, 26, 42, 60, 156, 78],\n [-126, 20, 67, 135, 54, 115]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[38, -34, -29, 102, -46, 30],\n [22, -36, -9, 90, -14, 3],\n [-25, 14, 18, 12, -14, 17],\n [103, -52, -87, 66, -48, 23],\n [6, -48, 25, -18, 118, -113],\n [-80, 36, 72, -72, 64, -42]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[24, -71, 41, -117, -22, 18],\n [-25, 51, -17, 80, 39, -32],\n [29, -66, -89, -82, 108, -2],\n [-23, 32, -12, 49, 63, -42],\n [16, -12, -40, -8, -4, 24],\n [-18, 50, 37, 69, -63, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-38, 25, 72, -85, -154, 133],\n [-59, 117, 61, -28, -97, 77],\n [-30, 10, 70, -98, -76, 16],\n [-13, -17, 22, -74, -50, -15],\n [53, -77, -72, 73, 99, -46],\n [21, -27, -24, 24, 78, -75]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[127, -118, -38, 97, -46, 84],\n [-50, 44, 9, -90, 155, -108],\n [110, -78, -10, 22, 110, -46],\n [32, -140, 3, 8, 35, 57],\n [-25, 82, -13, -46, 106, -173],\n [71, -21, 19, 1, 67, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 5 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-115, -80, -131, 54, 57, -92],\n [55, 57, 81, -57, -16, 42],\n [23, -46, 24, 149, -8, 63],\n [-110, -44, -70, -64, 78, -64],\n [-102, -26, -21, 49, 117, -57],\n [-7, 66, -92, -55, -30, -143]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-20, 98, 41, 13, 74, 109],\n [-42, -68, 17, 17, 41, 41],\n [88, 72, 34, 174, 22, 78],\n [-66, -54, -1, -71, 22, 1],\n [-76, -42, 27, -25, 70, 71],\n [-19, 82, 16, -37, 34, 47]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[18, 64, 73, 46, -86, -17],\n [90, -23, 47, 93, -96, -12],\n [121, -4, -43, 158, 86, 20],\n [97, 49, 17, 141, 24, 3],\n [97, -77, 9, 59, -28, -7],\n [36, 85, 38, 87, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[24, 40, -62, -16, 62, -86],\n [-36, 42, 27, 99, -90, 24],\n [-96, 40, 78, 92, -50, -54],\n [-27, -45, 36, -81, 90, -63],\n [15, 5, -30, -37, 58, -53],\n [0, -44, 32, -22, -18, 62]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[79, 43, -151, -55, 50, 52],\n [-66, -53, 166, 26, 27, 32],\n [70, -69, -89, -31, 12, 86],\n [20, -175, 2, -6, -23, 100],\n [-71, 88, -42, -20, 2, -90],\n [-30, 40, 42, -6, 42, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-54, -22, 102, -18, 20, -44],\n [-57, 75, 33, -51, -54, -66],\n [53, 60, -65, 23, -43, 54],\n [-56, 31, 80, -32, -19, -52],\n [-10, 80, -28, -26, -59, -20],\n [-121, 11, 143, -71, -5, -122]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-33, -61, -57, 48, 119, -78],\n [30, 56, -51, -50, -134, 104],\n [47, -96, 18, 32, 126, -49],\n [-77, 102, -47, -60, -92, -40],\n [-7, -20, -39, -64, 68, -113],\n [32, 57, -78, -65, -103, -28]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 5 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-32, 17, 52, -39, 95, 57],\n [16, -5, -20, 24, -8, -54],\n [100, 56, -28, -56, 5, 9],\n [-154, -4, 44, 75, -14, -26],\n [196, 22, -76, -71, -26, -6],\n [-127, -20, 40, 68, 17, -37]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-92, -72, -7, 3, -5, 62],\n [160, 93, -7, -19, 56, 3],\n [68, -28, -24, -39, 32, 0],\n [-28, 9, -149, -136, 130, -13],\n [-62, 89, -5, 25, 23, 54],\n [-82, 76, -187, -151, 168, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-69, -52, 81, 2, 36, 16],\n [58, 1, 31, 15, 96, -41],\n [-15, -11, 38, 19, 20, 5],\n [59, 7, -111, -64, -47, -106],\n [-35, 15, 85, 74, 27, 100],\n [-44, -22, 34, -2, 3, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[72, -14, 25, -84, -76, 22],\n [152, -78, 77, -32, -112, 107],\n [-120, 70, -65, 0, 80, -95],\n [-24, -14, 1, 84, 44, 16],\n [-48, 4, -14, 72, 56, -8],\n [-8, 10, -7, -16, 0, -13]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 2 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-19, -37, -56, 47, -17, 45],\n [-29, -72, -42, 53, -20, 66],\n [-39, -42, -60, 51, -39, 69],\n [36, -7, 6, 0, 43, -37],\n [79, 12, 6, -7, 88, -90],\n [30, 0, 46, -26, 37, -41]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 3 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-7, 0, 7, 42, -7, -63],\n [-17, -10, 2, 46, -2, -75],\n [-15, -10, 0, 34, 0, -57],\n [-93, -110, -72, -58, 72, 21],\n [134, 160, 106, 92, -106, -42],\n [58, 70, 47, 44, -47, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-50, 1, -14, -25, -47, 5],\n [-90, 33, -46, -71, -69, -17],\n [0, 24, -16, -20, 12, -20],\n [-40, -22, 4, -1, -49, 23],\n [-60, 84, -72, -99, -15, -63],\n [100, -80, 80, 115, 55, 55]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[87, -39, 48, 24, 75, -51],\n [-85, 59, -38, -22, -89, 61],\n [-23, -116, -5, 63, 9, -79],\n [24, 25, -33, -69, 60, 30],\n [-106, 29, -51, -11, -94, 46],\n [121, 53, 74, -8, 65, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[95, 41, -116, 72, -68, 65],\n [-66, 78, 48, -20, -70, -28],\n [45, 101, -10, 102, -66, 69],\n [-27, 79, -80, -20, -112, -25],\n [9, -101, -44, -58, 65, -32],\n [-84, -10, 137, -117, -44, -66]]\n\nPresent the answer in LaTex format: \\boxed{Your answer... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-11, 85, -25, 20, 19, -25],\n [3, 54, -16, 57, -81, -27],\n [86, 1, -29, -27, 170, -68],\n [-74, 56, 28, -68, 4, 80],\n [121, -26, 3, -11, 16, -46],\n [78, -86, 16, 44, -120, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-22, 10, 11, 33, 42, -49],\n [3, 5, -54, -53, -30, 41],\n [27, 23, 128, 175, 151, -48],\n [-26, -18, 1, -5, -33, -52],\n [-53, 9, 9, -6, 37, -75],\n [9, 9, 11, 32, 31, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-9, 8, -92, 21, 16, -35],\n [-135, -40, 93, -91, -180, -130],\n [23, 47, 48, 71, -1, -21],\n [-106, -100, -19, -143, -110, -56],\n [-36, -34, -14, -78, -14, 16],\n [-51, 44, -1, 13, -40, -72]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[57, 65, 1, 160, -55, -25],\n [-45, -92, -107, 120, -19, -5],\n [29, 94, 30, 75, 13, -35],\n [-31, 18, 43, 70, 33, -45],\n [40, 69, 171, -125, 2, 0],\n [85, 46, 109, -50, -77, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[77, 3, 11, -33, -37, 12],\n [-93, -33, -17, 25, 69, -2],\n [84, 27, 15, -24, -60, 3],\n [20, -6, 2, -12, -4, 6],\n [-30, 96, 8, 62, -66, -46],\n [-96, 81, -3, 84, -24, -51]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-19, -2, 40, -30, -59, 61],\n [-52, -46, 80, -60, 8, 38],\n [-8, 9, 24, -18, -66, 57],\n [-53, -49, 80, -60, 17, 32],\n [21, 19, -32, 24, -5, -14],\n [-10, 3, 24, -18, -48, 45]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-19, 17, 17, 1, 26, 2],\n [44, 8, 8, -8, -28, 56],\n [64, 23, 23, -13, -33, 96],\n [16, -38, -38, 2, -38, -32],\n [9, 13, 13, -3, 2, 26],\n [24, -32, -32, 0, -40, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 2 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[12, -33, -21, -28, -50, 18],\n [-1, 54, -70, -25, -30, 60],\n [26, -114, 14, -38, -80, -12],\n [-9, 36, 0, 15, 30, 0],\n [9, 9, -63, -39, -60, 54],\n [6, 66, -126, -58, -80, 108]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[59, 44, 59, 50, 51, 17],\n [33, -41, 83, 16, 25, 44],\n [70, 40, 106, 5, 139, 101],\n [-122, 51, -82, -97, -2, 46],\n [97, -23, 55, 5, 100, 29],\n [-34, -71, 14, -87, 38, 74]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-55, -52, -27, -48, 103, 56],\n [59, 36, -42, 21, -107, 55],\n [-164, -109, 142, 79, 17, -113],\n [-141, -102, 49, 139, -50, -51],\n [116, 85, -97, -88, 79, 38],\n [-23, -6, 2, 137, -95, -73]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"... | 4 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-9, -9, -3, -14, 20, -27],\n [135, 135, 135, 90, -36, 0],\n [63, 63, 51, 58, -52, 54],\n [36, 36, 12, 56, -80, 108],\n [15, 15, 15, 10, -4, 0],\n [-93, -93, -81, -78, 60, -54]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[41, 95, 25, -96, -28, 46],\n [102, 25, 109, 11, -9, 99],\n [8, 120, 35, -121, 8, 10],\n [-5, -20, -143, -26, -109, 11],\n [64, -60, 90, 98, 20, 56],\n [-27, 90, -35, -112, -13, -21]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-65, 50, -15, -20, -35, 30],\n [33, -10, -25, -16, 19, -26],\n [-117, 90, -27, -36, -63, 54],\n [70, -100, 114, 100, 34, 0],\n [-46, 70, -84, -73, -22, -3],\n [42, -40, 26, 26, 22, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-16, -130, -38, 112, -52, 4],\n [106, -43, 31, 36, 99, 23],\n [60, -22, 46, 8, 82, 18],\n [-40, -63, -51, 62, -77, -8],\n [8, -5, -19, 12, -12, -2],\n [-76, -3, -27, 2, -77, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-21, -21, 77, -120, 11, -75],\n [37, -112, -27, 20, -7, -42],\n [-41, -11, 24, -131, 30, -60],\n [23, -5, -79, 36, 63, 97],\n [23, 52, 218, -73, -6, -19],\n [60, -98, 44, -140, 160, 66]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-24, 33, -69, -77, -133, 6],\n [-47, -12, 36, 74, 12, -149],\n [-59, -47, 77, 112, 116, -89],\n [33, 58, -34, 64, 42, -89],\n [55, -69, 111, 24, 68, 1],\n [-4, 50, -80, -59, -97, 14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[122, 77, -139, 274, 88, 7],\n [116, -105, 23, -28, -87, -86],\n [4, -25, 89, -46, 45, -65],\n [-16, 56, -54, 74, 31, 37],\n [-47, 23, -2, -24, 52, 83],\n [14, -56, 46, -68, -102, -100]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[41, 82, -35, -70, 60, 0],\n [-9, 13, 19, 149, -29, 48],\n [63, 83, -28, 19, 22, 20],\n [7, -36, 15, -112, 11, -13],\n [-21, -120, 14, 85, -57, -55],\n [26, 22, 36, -45, -13, 64]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-15, -9, -66, 3, 85, 80],\n [186, 155, -70, 11, 157, 29],\n [-78, -91, 49, 13, -63, -3],\n [49, 103, -19, -49, -29, -70],\n [98, 56, 9, 105, 12, -15],\n [-3, -43, 54, 0, -19, -11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-18, 15, 0, -9, 3, -6],\n [1, 12, -70, -45, -69, 40],\n [45, -32, -30, 3, -37, 32],\n [-20, 24, -40, -36, -36, 16],\n [-10, 1, 40, 21, 41, -26],\n [-35, 31, -10, -24, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-33, 72, 30, 30, 15, -18],\n [-19, -48, -22, 50, 13, -6],\n [-37, 36, 14, 50, 19, -18],\n [-22, -34, -16, 50, 14, -8],\n [74, 10, 8, -130, -42, 32],\n [40, -132, -56, -20, -16, 24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-111, 18, 71, 49, -20, 25],\n [-116, -16, 93, 155, 2, 34],\n [11, -26, 18, -112, -6, 3],\n [-44, 20, 26, -91, -26, 7],\n [-1, 10, -10, 51, 4, -2],\n [95, -110, 9, -40, 42, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-36, -61, -6, 18, 46, -62],\n [94, 90, 69, -113, 52, -34],\n [-17, -26, 48, 53, 149, -9],\n [76, 116, 117, -130, 103, -30],\n [151, 185, 99, -83, 110, -85],\n [-33, -88, 54, -22, 132, 33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 5 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-53, 20, 93, -17, -31, 102],\n [12, 40, -42, 38, 24, -38],\n [30, -57, -63, -42, -15, -72],\n [-4, -2, -72, -46, -42, -66],\n [0, 58, -57, 29, 8, -47],\n [-26, -7, -42, -71, -67, -33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-21, 12, -47, -12, 8, 14],\n [38, 20, -45, -75, -8, -61],\n [-18, 0, 13, 24, 2, 20],\n [-25, -60, -14, 33, -17, 58],\n [12, -40, 116, 52, -42, -2],\n [53, 4, -89, -87, 17, -50]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[1, -143, 43, 4, 35, 79],\n [-145, 7, -116, 18, -77, 44],\n [-69, -79, 6, -29, 1, -17],\n [35, 195, -78, 37, -53, -13],\n [23, 38, -37, -20, -32, 46],\n [26, -8, -36, 9, -24, 109]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-32, 90, -66, -10, -26, 2],\n [-120, 49, -44, -76, 107, -128],\n [7, -106, -84, 11, 66, -150],\n [-74, 70, -25, 25, 143, -113],\n [36, -49, -86, -44, -46, -17],\n [-99, 53, 118, 85, 48, -33]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 5 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[62, -108, 36, 8, 36, 64],\n [-30, -56, -43, 14, -103, -100],\n [-55, 2, 47, -253, 17, 73],\n [-37, -58, -130, 17, -88, -43],\n [-79, 58, 14, -11, -40, 89],\n [18, 18, 29, -29, 71, 99]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 5 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[139, -100, -24, -79, -48, -53],\n [-97, 90, 3, 48, 53, 3],\n [40, 40, -13, -51, 64, -124],\n [82, -20, 47, -69, 34, -82],\n [-17, 40, 74, -9, 58, -25],\n [22, -20, -52, -6, -26, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 3 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-26, 30, -73, -41, 70, 32],\n [36, 66, -66, 51, 56, 3],\n [-10, -37, 70, 116, 174, -139],\n [49, 50, -47, -77, -82, 69],\n [-25, -39, -78, -94, 48, 1],\n [12, 18, 8, -57, -42, 36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 5 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-14, -28, 168, 21, 7, 7],\n [11, 52, -77, 55, 0, -2],\n [9, 34, -127, -44, -47, -21],\n [-7, -67, 86, 25, 87, 35],\n [-14, -32, 154, 2, 0, 4],\n [-7, 79, 122, 44, -104, -36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[55, 117, 9, -32, 94, -175],\n [-31, -11, -89, 131, 6, 223],\n [29, 17, -77, 107, 3, 109],\n [-8, -84, -29, -12, -32, 41],\n [-14, -86, 61, -104, -61, -79],\n [33, -155, -42, -7, -112, 48]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-20, 105, 28, -122, -2, -18],\n [17, 94, 58, -117, -30, -23],\n [-47, -116, -30, 151, 70, -43],\n [-70, 61, -50, -58, 44, 14],\n [-106, 10, -62, 12, 90, -20],\n [-96, 0, 39, 23, 101, -131]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",... | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-8, -8, -4, -26, 26, -44],\n [-105, -29, 52, -23, -15, -17],\n [52, 4, -40, -32, 56, -68],\n [92, 28, -42, 31, 1, 34],\n [-80, -16, 48, 8, -40, 32],\n [41, -3, -40, -51, 73, -99]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-97, -92, 10, 30, 17, -9],\n [146, 19, 22, -112, -107, 24],\n [-10, 28, 6, 88, 30, 4],\n [74, -11, -108, -52, -119, 64],\n [-32, 74, 0, 72, 88, -22],\n [-44, -133, 12, 0, -65, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[7, 21, 7, -14, 7, 35],\n [17, 11, -55, -42, -39, 21],\n [-6, 7, 39, 17, 29, 10],\n [-13, 11, 77, 36, 57, 15],\n [14, 17, -31, -33, -21, 30],\n [10, 5, -35, -25, -25, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[49, -28, -46, -10, -45, -27],\n [-82, 90, 45, 49, -35, -49],\n [-92, -28, 66, -22, -70, -34],\n [-60, 36, 86, 6, 190, 130],\n [120, -40, -122, -6, -130, -90],\n [-18, 120, -8, 72, -10, -46]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[18, 55, -52, -84, 17, -42],\n [33, 33, 46, -72, 36, -27],\n [56, -48, 38, -10, 40, -34],\n [-27, 115, 41, -93, 2, 12],\n [36, -76, 2, 42, 16, -18],\n [-21, -78, -38, 108, -33, 27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[15, -24, 13, -78, -7, 63],\n [9, -25, 25, -64, 25, 0],\n [47, -103, 1, 32, 106, -29],\n [-8, 9, 26, -66, -2, -7],\n [19, -28, -13, 2, 0, 50],\n [-40, 80, 18, -64, -73, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[110, -19, -96, 46, -56, -27],\n [140, 28, -97, 65, 18, 21],\n [-29, 59, 82, 21, -80, -80],\n [52, 165, -30, 83, 6, -45],\n [91, -9, -50, 59, -172, -120],\n [-152, 21, 109, -29, 38, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 5 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-81, 54, -20, -8, -12, -14],\n [42, 36, 33, -42, 64, 40],\n [-12, -44, 28, 40, 34, 36],\n [68, -58, 36, 44, 99, 35],\n [-58, -23, 50, 30, 37, 80],\n [-17, 55, 28, -70, -13, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 5 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-14, 10, 28, 16, 24, -2],\n [-16, -3, 16, 8, 3, 3],\n [-39, -73, -63, -4, -134, 69],\n [-132, -44, 126, 40, 8, 12],\n [-20, -20, 25, -20, 0, -20],\n [-13, -62, -73, -20, -119, 50]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 3 | MATH |
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