messages listlengths 1 1 | ground_truth stringclasses 4
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Find the rank of the matrix:\n[[29, -9, 46, -58, -57, 39],\n [71, 76, 9, 44, 0, -73],\n [90, 123, -50, 143, -7, -131],\n [30, 154, 77, -65, -96, -35],\n [-134, -97, 107, -180, -68, 53],\n [-109, -181, -30, -13, -9, 50]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 5 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[36, -8, -56, 40, 42, 22],\n [-34, 32, 72, 20, -33, 9],\n [-62, 67, -8, 20, 16, 28],\n [84, -51, -25, 50, 23, 11],\n [36, 2, -23, 70, 32, 34],\n [40, 12, -61, 90, 60, 50]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[81, 38, 23, -57, 113, 0],\n [40, -126, -17, 65, -56, 60],\n [37, -146, 7, 43, -42, -63],\n [-169, 114, 5, 19, -73, -48],\n [78, -122, 57, 40, 55, -59],\n [-10, -74, -43, 18, -92, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[70, 24, 83, 8, 73, 43],\n [63, 12, 111, 6, 33, -54],\n [-35, 59, 8, 28, 3, -47],\n [89, -161, -26, -76, -15, 119],\n [56, 22, 73, 8, 57, 23],\n [-51, 37, -5, 20, -34, -90]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[54, -78, 122, -162, -81, 24],\n [18, 116, -42, 91, 41, -79],\n [80, -111, -55, -33, 99, 99],\n [132, 43, 19, -60, 67, -42],\n [-228, -30, 28, 56, -162, 22],\n [-16, -140, 73, -134, -65, 89]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-49, 88, 21, -135, 12, -3],\n [-94, 119, 132, -102, -68, 39],\n [-61, 62, 54, -142, 24, 62],\n [102, -35, -69, 58, -7, 44],\n [-30, 0, 29, 56, -51, -36],\n [12, 19, 0, -95, 59, 59]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 5 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[1, 81, 79, 50, -6, 11],\n [-12, 24, -35, 27, -96, -89],\n [-134, 4, 67, 9, -124, -115],\n [-20, 14, 34, -146, -59, 38],\n [12, -38, -28, -40, 29, 28],\n [-32, 59, 126, -75, -2, 74]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[14, 41, 101, 61, -34, 9],\n [102, -18, 17, 19, 138, -3],\n [-38, -18, 14, -15, -61, -21],\n [31, 19, -31, -60, 75, 31],\n [135, 61, 10, -54, 140, 75],\n [112, 39, 33, 40, 37, 43]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[28, -47, -45, 13, 2, 72],\n [12, 4, -36, 52, 12, -36],\n [-11, 18, 18, -6, -1, -27],\n [-14, 4, 36, -44, -10, 18],\n [-30, 55, 45, -5, 0, -90],\n [-55, 51, 117, -105, -23, -27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 2 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-93, 70, -78, 51, -16, -36],\n [86, -5, 34, 59, 10, 56],\n [-21, 43, -152, 16, -108, 2],\n [107, -18, 103, -40, -28, 94],\n [37, -12, -47, -48, -78, 28],\n [-73, 11, 32, 30, 82, -56]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[95, 123, -23, 20, -41, -72],\n [-67, -5, 66, -33, 5, -35],\n [37, -14, -18, -55, 86, 40],\n [76, 121, -117, -85, -71, 166],\n [94, 27, -88, -48, 48, 101],\n [98, 54, -126, 80, -136, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 5 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-27, 141, -124, -70, -104, 117],\n [34, 80, 26, -197, 35, -7],\n [-21, 60, -32, -46, -13, 35],\n [9, -87, -36, 176, -52, 11],\n [-42, 63, -4, -66, 35, 16],\n [-12, -27, 68, -34, 115, -54]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[30, 32, -40, 16, 38, -50],\n [-29, -52, 0, -20, -47, 77],\n [-60, -8, 175, -22, -44, 20],\n [50, -12, -75, 42, -36, 60],\n [-31, -68, -15, -22, -61, 103],\n [85, -40, -130, 76, -91, 145]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-8, -4, -19, -2, 2, 5],\n [-73, -26, -120, 15, 69, 78],\n [25, 14, 67, 11, 1, -11],\n [-47, -10, -43, 31, 77, 71],\n [-24, -24, -118, -44, -52, -22],\n [-6, 0, 1, 8, 16, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-190, -6, -18, 37, 16, 11],\n [-140, 12, -16, 4, 20, -22],\n [60, -74, 51, 27, -15, 103],\n [0, -70, 35, 50, -15, 105],\n [40, 54, -19, -53, 11, -85],\n [-50, 48, -27, -31, 17, -74]]\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, 1, -7, 6, 8, 3],\n [28, 12, 24, -24, -64, 0],\n [-35, -11, -58, 54, 112, 12],\n [-49, -37, 70, -54, -16, -48],\n [-7, -5, 8, -6, 0, -6],\n [42, 22, 8, -12, -64, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-36, -20, 48, 12, -8, 56],\n [27, 48, -54, 0, 39, -30],\n [33, 44, -58, -4, 33, -42],\n [15, -10, -10, -10, -15, -30],\n [3, -46, 22, -14, -47, -22],\n [0, -44, 24, -12, -44, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-26, -4, -12, -6, 7, -30],\n [-18, 0, -3, -15, 15, -27],\n [-16, -20, -41, 65, -60, 21],\n [-2, -16, -31, 61, -57, 33],\n [28, -4, -3, 39, -38, 51],\n [76, 32, 74, -62, 54, 42]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 2 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-194, 196, -20, 38, 51, 171],\n [35, -101, -154, -74, -95, 12],\n [-54, 77, -50, 49, 7, 68],\n [49, 20, -37, 126, -22, -29],\n [-192, 194, -106, 142, -95, 234],\n [-72, 62, -50, 124, -164, 144]]\n\nPresent the answer in LaTex format: \\boxed{Your answer... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[16, -111, -65, -20, -138, 17],\n [-12, 80, -18, -40, 108, -6],\n [18, -105, 0, 60, -132, -12],\n [-12, 98, -24, -20, 140, -32],\n [18, -102, 21, 80, -130, -17],\n [-6, 41, -90, -80, 68, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[124, -100, 57, 12, 6, 102],\n [146, -127, 64, 82, 28, 80],\n [72, -37, 20, 8, 56, -5],\n [-180, 148, -80, -52, -24, -122],\n [114, -52, 29, 2, 98, -17],\n [12, 34, -2, -148, 12, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-32, -47, -9, 22, 11, 51],\n [-92, 44, 110, -81, -141, 110],\n [-49, -22, 4, 11, 19, 11],\n [-3, 10, 27, -75, -60, 14],\n [-58, -66, 13, -98, -21, 17],\n [46, -10, -35, 59, 40, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 5 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-25, 44, 54, -109, 75, 165],\n [-4, 83, -28, -49, -94, -22],\n [79, -36, -36, -5, 39, -3],\n [-54, 78, 2, -24, -94, -22],\n [81, -54, 14, -69, 161, 143],\n [7, 70, -36, -35, -93, -39]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-35, 30, 21, -12, 5, 38],\n [27, -15, -18, 6, -6, -21],\n [40, 20, -36, -8, -20, 12],\n [-100, -50, 90, 20, 50, -30],\n [3, 30, -9, -12, -9, 30],\n [-2, -20, 6, 8, 6, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[72, 7, -58, -74, 3, 6],\n [-38, 37, 70, 140, 6, -32],\n [-30, 41, 148, 159, -86, 29],\n [-26, -35, -202, -96, 151, -140],\n [-18, 33, -80, 77, 63, -145],\n [42, 63, 288, 99, -160, 177]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-30, -40, 73, 46, 46, 42],\n [-96, 40, 8, 80, 80, 48],\n [94, -80, 47, -62, -62, -26],\n [-58, -5, 44, 60, 60, 44],\n [-74, 130, -127, 22, 22, -14],\n [-56, 70, -58, 28, 28, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 2 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[32, -20, 4, 20, 20, 60],\n [36, -9, 36, 27, 18, 117],\n [4, -13, -24, -1, 6, -31],\n [52, -31, 10, 33, 32, 103],\n [-108, 135, 144, -45, -90, 45],\n [4, -13, -24, -1, 6, -31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-97, -86, -31, -29, 92, -76],\n [60, 53, -43, 129, -104, -13],\n [-46, -46, 36, -144, 110, 52],\n [65, 55, -40, 110, -95, 10],\n [-20, 6, 86, 2, -33, -97],\n [-10, 5, 39, 23, -30, -67]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[10, -27, -75, 77, -3, -14],\n [124, -9, -34, -61, -116, 122],\n [-20, -78, 22, -150, -66, 100],\n [-66, -5, 47, 13, 83, -82],\n [74, 57, -23, -81, -149, 162],\n [14, 189, 13, 103, 2, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 4 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[110, -11, 120, -88, 10, -1],\n [31, 67, -16, -22, 69, 53],\n [-165, -95, -53, 173, 11, -82],\n [-25, -97, 97, 67, 51, -74],\n [-82, 53, -190, 2, -154, 33],\n [-25, -74, 24, 14, -83, -58]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[0, 27, -63, -63, -9, 9],\n [11, 87, -38, -38, 15, -26],\n [6, 66, -64, -64, 2, -8],\n [14, 96, -14, -14, 24, -38],\n [6, 30, 20, 20, 14, -20],\n [-5, -54, 51, 51, -2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[92, 80, -52, -36, 18, -10],\n [92, 54, 4, -114, 126, 22],\n [-58, -31, -16, 3, -69, -43],\n [-106, -90, 46, -56, 1, -25],\n [68, 62, -40, 34, -14, 6],\n [-156, -123, 54, 21, -60, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[0, -19, 80, 26, -221, -14],\n [41, 100, 20, -21, 113, 24],\n [62, 0, 69, 40, -61, 34],\n [130, 20, 84, 74, -15, 51],\n [-52, 32, 33, -124, 116, 1],\n [42, 10, 40, 52, -85, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[30, -105, -131, 31, -27, 49],\n [109, 4, -30, 92, -26, -50],\n [-19, 139, -65, -30, 43, 43],\n [37, 209, -151, 114, -35, 113],\n [35, 132, -6, 48, 2, 28],\n [23, -55, -149, 16, -11, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 5 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[9, -37, -18, 52, 130, -50],\n [102, -22, -71, 90, 89, 13],\n [39, 14, -51, 13, -114, 97],\n [-111, 5, 61, -72, -53, -23],\n [-150, 16, 137, -120, 11, -115],\n [-75, 35, 50, -88, -150, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 3 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-18, 70, -96, 14, -92, 54],\n [60, 44, 0, 60, 8, 12],\n [-84, -20, -48, -68, -56, 12],\n [39, 104, -87, 68, -76, 60],\n [-24, -2, -18, -18, -20, 6],\n [9, -74, 93, -22, 88, -54]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[64, -86, -46, -35, 36, -16],\n [56, 4, 60, 6, 36, 48],\n [-16, 92, 112, 62, -36, 22],\n [60, -120, -88, -42, 18, -62],\n [-36, 100, 98, 56, -36, 27],\n [76, -106, -90, -99, 126, 78]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-52, -38, 30, -21, 69, 4],\n [49, 11, -30, 12, -18, 17],\n [43, 43, -24, 21, -79, -13],\n [0, -86, -6, -27, 163, 72],\n [16, -28, -12, -6, 54, 32],\n [-32, -30, 18, -15, 55, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[56, 42, 36, 44, 6, -76],\n [114, 91, 78, 22, -31, -106],\n [49, 42, 36, -26, -36, -20],\n [98, 77, 66, 34, -17, -102],\n [39, 28, 24, 46, 14, -64],\n [-41, -35, -30, 20, 29, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[30, 21, 115, -35, -92, -27],\n [-42, -36, -121, 14, -46, 15],\n [-91, 139, -102, 3, 78, 81],\n [74, -150, -59, 60, -118, -55],\n [71, -55, -27, 51, -64, -12],\n [-54, -38, 27, -56, 78, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-104, -132, 72, 106, 4, 32],\n [-38, -46, -54, 22, -148, -24],\n [-4, -6, 36, 11, 62, 16],\n [103, 131, -81, -107, -22, -36],\n [26, 34, -54, -34, -68, -24],\n [-76, -96, 36, 74, -28, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 2 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-12, 6, 63, -28, 25, 25],\n [25, 40, 70, -70, -20, -20],\n [48, 48, 24, -64, -56, -56],\n [-14, -26, -53, 48, 9, 9],\n [-110, -86, 37, 88, 143, 143],\n [24, 6, -57, 12, -39, -39]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[57, 91, 19, -45, -63, 139],\n [13, -91, -43, -39, 25, -55],\n [-56, -63, -16, 51, 56, -128],\n [-17, 14, 35, 24, -5, 23],\n [-26, -133, -60, -3, 66, -152],\n [19, -98, -50, -48, 25, -56]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-76, 122, -10, -88, -186, 202],\n [-90, 38, -35, -74, -77, 139],\n [-18, 27, -28, -6, -24, 28],\n [98, -137, 54, 69, 28, -76],\n [-42, 84, 3, -42, -3, 21],\n [-86, 130, -59, -59, -59, 93]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-29, 196, -34, 104, -154, 78],\n [27, 70, 150, 116, -46, 145],\n [7, 82, 77, 95, -105, 73],\n [-44, 28, 1, -21, 35, -76],\n [1, -64, 66, -8, 126, 46],\n [-49, 74, -48, 17, -118, -96]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[39, -123, -12, 143, 36, -13],\n [-73, 93, -33, -91, -78, -101],\n [91, -24, 156, -43, -63, 15],\n [19, -45, 15, 103, 97, 109],\n [-10, 51, 109, -20, -12, 48],\n [149, 54, 121, -110, 20, 148]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 5 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[3, -84, 3, 5, 109, -133],\n [-8, 62, 49, -51, -59, 26],\n [75, 32, -75, -61, 38, -91],\n [63, 67, -132, -138, 8, -96],\n [-34, -23, 132, 64, -7, 41],\n [-52, -58, 179, -9, 55, -112]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-28, -88, 6, -69, -9, -1],\n [55, 27, 52, -47, -23, -63],\n [-99, -74, 11, -125, 84, -16],\n [38, 1, -125, -63, -71, -5],\n [-66, -159, 93, 25, -92, 130],\n [84, 4, -166, 63, -116, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[71, 56, 28, 15, 81, 41],\n [29, 2, -18, -11, -29, -25],\n [1, -8, -12, -7, -25, -17],\n [94, 28, -28, -18, -30, -38],\n [23, 50, 54, 31, 121, 77],\n [65, 65, 45, 25, 115, 65]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[121, 111, -48, -41, -42, -91],\n [50, 43, -109, 35, -81, 31],\n [-31, 11, 43, 67, 83, 153],\n [24, 18, 16, -100, -29, -165],\n [115, 39, 52, -35, 63, 55],\n [152, 6, -41, 6, -19, 86]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 5 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[60, -146, -8, 68, 12, 100],\n [-6, 27, 12, -6, 6, -18],\n [4, -18, -8, 4, -4, 12],\n [55, -139, -12, 62, 8, 95],\n [-31, 31, -36, -38, -32, -23],\n [-34, 29, -44, -42, -38, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[8, 92, 15, -98, -114, -4],\n [-17, -5, -32, 18, -231, 47],\n [-70, -109, 31, 58, 8, -35],\n [38, -54, -119, 136, 94, -31],\n [71, 48, -78, 28, 103, -8],\n [7, 43, 94, -89, -2, 79]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 5 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-15, 90, 60, -95, -35, -100],\n [42, 9, 39, -13, -19, -26],\n [-42, -67, -85, 75, 45, 94],\n [-114, 17, -73, -9, 33, 22],\n [-39, 60, 18, -61, -13, -56],\n [0, 29, 23, -31, -13, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[50, 125, -48, -134, -35, -3],\n [-3, 7, -2, 1, -12, 7],\n [66, 3, 120, 17, 119, -144],\n [17, 94, -118, -146, -67, 65],\n [39, 117, -6, -80, -44, -12],\n [-18, -117, 48, 89, 83, -36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[67, -108, 20, 14, -82, -80],\n [-110, 27, -67, 36, 113, 101],\n [92, -95, 15, 10, -97, -83],\n [-18, -31, 143, 11, 25, 123],\n [50, -166, 30, 56, -58, -8],\n [37, -50, 250, -25, -42, 72]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-30, 64, -154, -32, -36, -48],\n [45, -96, 81, -42, 9, 147],\n [-79, 35, -48, -64, -73, -47],\n [104, -93, 133, 74, 97, 90],\n [70, -113, 157, 2, 44, 150],\n [39, -21, 154, 108, 75, -41]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-67, 69, -38, -110, 17, -102],\n [-47, 41, -10, -50, 25, -46],\n [6, -42, 48, 96, 42, 102],\n [-115, 81, 75, 19, 126, 2],\n [-59, -15, -3, 5, 72, 52],\n [-44, 60, -42, -106, -6, -104]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 3 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[41, -72, 124, -53, -90, -6],\n [-25, -80, -145, 201, 104, 86],\n [46, -110, 63, 7, -94, 54],\n [18, 30, -63, 66, -9, -59],\n [104, -146, 26, 84, -83, -63],\n [-34, 147, 93, -73, -77, -83]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 5 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-34, -6, 21, 45, 51, -80],\n [-16, 3, -10, 7, 1, -18],\n [-36, -6, 18, 36, 36, -60],\n [47, 11, -24, -18, -3, 9],\n [-58, -3, -1, 16, -8, -18],\n [-9, 9, -9, 63, 90, -153]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-25, 139, -15, -46, -220, 72],\n [51, -128, -38, 7, 129, 34],\n [-59, 106, 65, 77, -113, 0],\n [26, -120, -81, 110, 64, -24],\n [0, -44, -28, 163, 63, -43],\n [28, -113, -104, 176, 51, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"... | 5 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[53, 7, -87, 75, 67, 12],\n [4, 40, 44, -30, 11, 23],\n [-15, 8, -81, 75, 63, -13],\n [20, 78, 14, 6, 26, 104],\n [23, -63, 128, -132, -104, -67],\n [-140, -35, -129, 123, -119, 158]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-18, -3, -3, 15, -9, 24],\n [-52, -118, 56, 142, -20, 102],\n [77, 108, -34, -148, 26, -133],\n [-64, 24, -96, 8, 16, 88],\n [54, 88, 19, -104, -21, -107],\n [-23, 87, -40, -59, -30, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[15, 23, 77, 67, 58, 14],\n [98, 35, 5, 97, -47, -89],\n [-12, -60, 200, 80, 21, 67],\n [-207, -92, 32, -142, -23, 139],\n [161, 8, 165, 133, 166, 21],\n [-73, -55, -72, -116, -74, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[96, 53, -15, -9, -149, -83],\n [-1, 73, -54, -92, -21, -15],\n [21, -13, 38, 32, -3, 4],\n [-70, 0, -141, -17, -53, 55],\n [5, 3, -45, -17, -30, 103],\n [120, 26, 54, 24, -108, 7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[11, -71, 138, -31, 73, -5],\n [-5, -98, -36, 19, -17, 168],\n [-24, -31, 73, -131, 21, 94],\n [-35, -40, 66, -63, 67, 124],\n [11, -106, -32, 206, -60, -73],\n [-69, -136, 29, 49, -16, 135]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 5 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-1, 45, 11, -13, 26, 27],\n [40, 157, 59, -45, 120, 71],\n [79, -15, -45, -89, -34, -81],\n [-65, 98, 30, 14, 50, 106],\n [-120, -127, -43, 91, -110, 7],\n [74, -62, -28, -38, -34, -94]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[78, -37, 146, 100, -41, -95],\n [-35, 86, -92, -19, 70, 62],\n [-4, -36, 121, 46, -38, -78],\n [-46, 90, -30, 7, 16, -7],\n [24, -100, 33, -19, 0, 19],\n [-38, -67, -10, -60, -15, 23]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[66, 3, -8, 144, 1, -116],\n [-111, 69, 41, -84, -79, 86],\n [-65, 64, 42, 45, -78, -95],\n [-131, 70, 64, -37, -96, -93],\n [-62, 121, 35, 55, -117, 101],\n [103, -47, -38, 128, 57, -180]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 4 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-79, -40, 12, -136, 64, 153],\n [-115, -94, -162, 5, -78, 80],\n [2, 27, -35, -3, 19, -142],\n [31, 0, -55, 27, -51, -76],\n [-139, -63, -76, 1, 6, 93],\n [60, -9, 45, -138, 7, 109]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[84, 0, 117, -61, -42, -62],\n [89, 18, 151, -59, -132, -65],\n [-36, -30, -30, -26, 56, 83],\n [24, 3, 117, -17, -173, -7],\n [-49, 14, -42, -10, -38, 95],\n [-110, -20, -111, 127, 2, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[63, -12, 18, 60, -36, -141],\n [55, -51, 58, -78, -5, 2],\n [36, -20, 24, -8, -12, -40],\n [-74, 36, -44, 0, 28, 98],\n [72, -40, 48, -16, -24, -80],\n [73, -61, 70, -82, -11, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[13, 28, -11, 51, -7, -58],\n [46, -7, -210, -102, -169, 126],\n [-109, -23, 49, 65, 36, -10],\n [-24, 30, 21, -2, 6, -11],\n [-183, 64, 55, 37, 7, -7],\n [16, -80, -40, 74, -2, -11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[126, 75, -22, -234, 52, -55],\n [-28, -33, 5, 14, -8, 26],\n [119, 159, 75, -70, 15, -159],\n [31, 161, -76, -9, -28, -125],\n [99, 105, -31, -29, 15, -224],\n [-77, -23, -134, -113, -38, 53]]\n\nPresent the answer in LaTex format: \\boxed{Your answer... | 5 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[69, -35, -35, -101, 17, 74],\n [-145, -38, -1, 135, 11, 8],\n [-1, -8, -13, 55, -9, -124],\n [-8, -31, -23, 15, 7, -20],\n [-74, -9, 5, 87, -1, -36],\n [-124, -88, -39, 85, 31, 70]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-51, -41, -11, 38, -59, -37],\n [15, -27, 15, -6, -9, 9],\n [-57, 86, -52, 25, 23, -35],\n [100, -14, 50, -62, 52, 68],\n [-7, -87, 23, 16, -63, -9],\n [-22, 23, -17, 11, 2, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[41, 15, -74, 44, 14, 55],\n [-30, -40, 84, -72, -26, -90],\n [28, 35, -76, 64, 23, 80],\n [-50, 15, 56, -8, 1, -10],\n [27, -20, -18, -12, -7, -15],\n [-25, -10, 46, -28, -9, -35]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[72, -14, -5, 29, -92, -5],\n [-35, -5, -18, 3, 20, -26],\n [94, -2, 12, 0, -91, 30],\n [107, -13, 73, -28, -19, -37],\n [-97, 8, -80, 107, -31, 59],\n [-9, -12, 51, 12, 69, -60]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[72, 111, -75, -60, -16, -45],\n [-19, -62, 10, -66, -145, -205],\n [2, -6, -4, 20, -46, -70],\n [-19, -45, 8, -72, -12, -17],\n [50, 35, -81, 2, -61, -137],\n [10, 42, 16, -62, -39, -26]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[30, -60, -144, -172, -16, 78],\n [9, -7, 100, 102, 56, -55],\n [-4, -21, 92, 85, 67, -60],\n [7, -60, 44, 21, 81, -35],\n [22, -58, 38, -21, 59, -103],\n [34, -71, 48, -1, 81, -80]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[15, 85, 0, 40, -35, -30],\n [-30, -34, -51, -12, 53, 60],\n [-15, -61, -9, -28, 32, 30],\n [-45, -71, -69, -28, 82, 90],\n [21, 87, 12, 40, -45, -42],\n [6, 18, 6, 8, -12, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-37, 30, -6, -19, -13, 34],\n [27, 36, 18, -27, -171, -18],\n [-14, 38, 4, -26, -88, 16],\n [8, -46, -8, 32, 126, -12],\n [25, -46, -2, 31, 89, -26],\n [16, -24, 0, 16, 40, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[116, -144, -59, -20, -22, -64],\n [-76, 54, -17, 94, -7, 88],\n [69, -112, 149, -166, 36, -88],\n [21, -54, -84, 19, -20, -4],\n [-104, 244, 0, 124, -178, -72],\n [-1, -22, 84, -73, -59, -90]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-17, -41, 135, 37, -141, 32],\n [-23, 84, 20, -25, -38, -13],\n [90, -88, 44, 145, -28, -80],\n [83, -19, -125, -81, 173, -25],\n [104, -259, -99, 11, 97, 161],\n [90, 31, 111, -79, -46, -63]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[19, 23, 76, 35, -46, 4],\n [23, 25, -53, 92, 48, 78],\n [19, 37, -79, 32, 54, 34],\n [-27, -129, -77, 87, -8, 118],\n [-58, -156, 39, 5, -58, 34],\n [2, 40, 51, -21, 14, -38]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-71, -34, 58, -133, -56, 0],\n [-24, -33, 54, -101, -19, 28],\n [4, -17, 30, -41, 5, 28],\n [-58, -5, 50, -39, -21, 14],\n [-64, -20, 104, -74, -7, 63],\n [-11, -6, -22, -31, -29, -35]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[28, 105, -42, 63, -21, -14],\n [108, -55, 54, 79, -133, -94],\n [42, -15, 18, 33, -51, -36],\n [-102, 20, -36, -86, 122, 86],\n [1, 90, -42, 33, 9, 7],\n [121, -35, 48, 98, -146, -103]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[85, -197, 69, -86, 35, -1],\n [77, -39, 24, -29, -68, -8],\n [-39, -67, -111, -43, 137, -59],\n [78, 44, -2, 67, -157, -153],\n [-25, -246, 106, -73, 139, 9],\n [-113, 45, -56, 7, 109, 41]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 5 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-61, 134, 12, 73, 60, -27],\n [169, -1, -178, 60, -134, 13],\n [-69, -112, 118, -82, 70, 29],\n [81, 101, -134, 77, -59, -40],\n [-65, -7, 68, -36, 51, -14],\n [18, 121, -76, 74, 2, -46]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[50, 60, 48, -111, -70, 170],\n [-108, -99, -18, -54, -63, 0],\n [-6, 2, 20, -75, -56, 90],\n [4, -3, -18, 66, 49, -80],\n [-62, -61, -22, 9, -7, -50],\n [12, 6, -12, 54, 42, -60]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[136, 150, -20, 128, 216, 26],\n [104, 104, -100, 66, 35, -22],\n [-106, -114, 29, -101, -108, 74],\n [-124, -163, 46, -136, -242, -33],\n [20, 101, 40, 6, 51, -109],\n [-212, -116, -74, -98, -24, 140]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"... | 5 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[31, 10, 29, -34, -25, -18],\n [2, -2, -14, 56, -36, -21],\n [45, 14, 39, -38, -43, -30],\n [-51, -16, -45, 46, 47, 33],\n [70, 20, 50, -20, -90, -60],\n [-90, -28, -78, 76, 86, 60]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[2, -74, 108, 54, 14, -96],\n [-17, 2, 33, 3, -11, -57],\n [-15, -2, -9, -3, -17, 17],\n [-37, -13, -18, -3, -42, 44],\n [-54, -32, 60, 18, -47, -64],\n [-124, -1, -3, -18, -126, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 3 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[56, -24, -32, -2, -12, -84],\n [-56, 24, -16, -28, -24, 48],\n [-21, 9, 78, 42, 54, 81],\n [63, -27, -18, 9, 0, -81],\n [42, -18, -76, -34, -48, -102],\n [-56, 24, -24, -33, -30, 42]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[19, -35, -67, 9, -15, -11],\n [-15, 56, 61, -76, 24, -44],\n [-8, -7, 22, 49, -3, 45],\n [-7, 21, 27, -23, 9, -11],\n [-24, 56, 88, -40, 24, -8],\n [-17, 28, 59, 0, 12, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-13, -104, -75, 65, 39, -25],\n [9, 59, 16, 1, -29, 96],\n [-13, -71, -50, 34, 21, -2],\n [-11, 5, -76, -31, 69, -94],\n [24, 28, 22, 48, -6, 0],\n [-51, -18, 23, -170, -19, -19]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-98, -63, -58, -16, 18, -114],\n [62, -51, -54, -70, 6, -10],\n [24, 0, 64, -120, 72, -216],\n [-79, 37, -62, 137, -35, 25],\n [-43, -104, -44, -70, 4, 4],\n [54, 125, 16, 101, -10, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 4 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[80, 30, -25, -85, 120, -80],\n [-61, -15, -82, 53, 24, 82],\n [2, 0, 9, -1, -8, -4],\n [-70, -24, -7, 71, -72, 76],\n [25, 15, -80, -35, 120, -10],\n [0, -6, 77, 9, -88, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[21, 158, 44, 14, 50, -152],\n [-58, 65, 5, -51, -27, -50],\n [46, 73, 27, 41, 49, -82],\n [49, -68, -4, 16, 20, 92],\n [-19, 52, 11, -30, -2, -28],\n [-5, 57, 11, 13, 9, -78]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[61, -1, -45, -141, 32, -97],\n [12, -9, 96, -46, -102, -57],\n [-19, 25, -62, 24, -7, 51],\n [-32, -30, 121, 87, 28, 32],\n [56, 84, -69, -85, -24, 69],\n [-16, -19, -50, 40, 60, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-17, -36, -22, 43, -1, -56],\n [-57, -95, 30, -113, 89, 37],\n [-150, 21, -52, -42, -125, -34],\n [-268, -23, -70, -80, -21, 70],\n [6, 53, -103, 100, -138, 32],\n [-10, 36, 39, -113, -39, 38]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 5 | MATH |
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