messages listlengths 1 1 | ground_truth stringclasses 4
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Find the rank of the matrix:\n[[9, 15, 9, -7, 8, 0],\n [-77, -70, -27, 71, -74, -25],\n [-76, 25, 54, 88, -82, -65],\n [-36, -60, -36, 28, -32, 0],\n [12, 90, 72, 4, 4, -30],\n [-63, 0, 27, 69, -66, -45]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[41, 37, 4, 28, -75, -19],\n [79, 96, -30, 72, -107, -54],\n [27, -88, 56, -94, 122, -2],\n [23, 146, -41, 120, -182, -31],\n [-67, 116, -10, 80, -101, 10],\n [83, 46, -67, 78, -135, -35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[32, -48, 14, -14, 3, -18],\n [10, -107, 21, 20, -54, 59],\n [42, -165, 15, 17, -60, 62],\n [-38, 3, 31, 40, -36, -61],\n [-14, 110, -26, -19, 52, -40],\n [12, -15, 17, -34, 10, 78]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[19, 45, 112, -35, -103, -16],\n [-149, 31, -75, 10, 16, 30],\n [-34, 56, 16, 128, 62, -42],\n [-75, 47, 6, 41, -55, -52],\n [0, 36, 81, -53, 17, 96],\n [-40, 20, 40, -100, -16, 108]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-30, 52, -74, 19, -73, -68],\n [-66, 26, -10, 5, -17, -34],\n [154, 27, -34, 52, -46, -44],\n [52, 46, -58, 6, -8, -180],\n [70, -30, -41, -25, -7, 35],\n [-16, 37, -48, 17, -51, -46]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-46, 72, -110, 26, 112, -2],\n [-27, 15, -99, -45, 60, -27],\n [-96, -112, -154, -76, 28, 10],\n [43, 110, 42, 53, 38, -14],\n [72, 157, 106, 106, 32, -4],\n [-22, 27, -62, -4, 52, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[1, -38, -24, 16, 56, 160],\n [231, -133, 25, -30, -119, -6],\n [-84, 93, -57, 70, 5, -44],\n [-47, 103, 0, -34, -55, -46],\n [-123, 40, -46, 100, 94, -56],\n [36, -74, -22, 56, 42, 38]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[32, 40, -125, -86, 27, -20],\n [-120, -175, -48, 19, 78, 24],\n [28, 53, -56, -64, 56, -62],\n [158, 233, 96, 10, -55, -28],\n [36, 93, 151, -46, -122, -142],\n [12, -17, -28, 29, 33, 72]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 5 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[113, -77, -13, -2, 44, -45],\n [60, -28, 4, -8, -20, 30],\n [-34, 56, 15, 33, -144, 192],\n [113, -81, -11, -16, 64, -75],\n [-49, 29, 17, -42, 14, -36],\n [30, -28, 9, -53, 60, -90]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-28, -2, 23, 27, -33, 42],\n [-12, 42, 57, 63, -117, 108],\n [56, 24, -24, -30, 18, -42],\n [36, 44, 16, 15, -57, 33],\n [12, 48, 42, 45, -99, 81],\n [24, 56, 40, 42, -102, 78]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 2 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[44, -70, 8, 44, -14, 16],\n [-82, -36, -94, 30, 54, 80],\n [22, -31, 76, 22, -27, -24],\n [19, 55, 79, -37, -30, -64],\n [35, -64, 65, 43, -27, -8],\n [60, 8, 102, -8, -48, -64]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-50, 53, -18, 100, -81, -110],\n [8, -2, 9, -7, 9, 5],\n [-4, -26, -30, -34, 12, 50],\n [-38, 5, -47, 27, -40, -15],\n [4, -10, -4, -16, 10, 20],\n [-28, 16, -23, 37, -37, -35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-50, -78, -22, 42, -79, 59],\n [32, 75, -49, -31, 76, -49],\n [-4, 99, -45, -113, 115, -159],\n [26, -6, -6, 46, -15, 61],\n [8, 45, -27, -35, 49, -51],\n [-18, -57, 31, 35, -60, 52]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[86, 62, 51, 121, -32, -17],\n [-46, 27, 70, 33, 12, 128],\n [-74, -91, -22, -114, -70, 4],\n [24, -59, 13, -22, -4, -53],\n [6, 38, 58, 59, 76, 70],\n [-54, -45, -27, -81, 88, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-92, -52, 48, -52, 100, -24],\n [42, 51, -53, 18, -60, 54],\n [-18, 27, -33, -18, 0, 54],\n [1, 8, -9, -1, -5, 12],\n [16, -43, 51, 20, 10, -78],\n [71, 55, -54, 37, -85, 42]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 2 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-6, -2, -18, -10, 5, 71],\n [31, 43, -44, 115, 112, -68],\n [-74, 22, -128, -20, 16, -56],\n [54, -43, 126, -23, -65, 103],\n [40, -11, 128, -77, -22, 92],\n [-16, -41, -84, 106, -62, -56]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[7, 3, -61, 50, 58, 49],\n [-44, -27, 55, -32, -66, -42],\n [135, 87, -1, -46, 50, -7],\n [106, 69, 27, -60, 14, -28],\n [-45, -27, 81, -54, -90, -63],\n [14, 12, 120, -108, -104, -98]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[60, 97, 3, -61, 1, -86],\n [-56, -77, 7, 63, -7, 70],\n [56, 48, -28, -76, 20, -48],\n [52, -30, -80, -104, 52, 12],\n [-24, -91, -39, 1, 23, 74],\n [-52, 1, 59, 91, -39, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[42, 62, 80, 28, -17, 22],\n [11, -115, 172, -129, 23, 30],\n [20, -26, -3, -67, -21, 65],\n [-12, -88, 118, -56, 38, 6],\n [4, 70, 25, 61, -4, -105],\n [27, 33, -134, 9, -40, 178]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[28, -44, 19, -14, 16, 2],\n [92, -2, -42, -75, 7, -69],\n [-64, -52, 26, 26, -46, -2],\n [32, -88, 60, 1, 45, 42],\n [-8, 70, -41, -2, -14, -19],\n [60, 14, -18, -34, 28, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[24, -32, 48, -16, -40, -64],\n [53, 44, -78, 26, 61, 128],\n [81, -22, 24, -8, -23, -14],\n [-40, -4, 12, -4, -8, -28],\n [-91, 21, -21, 7, 21, 7],\n [-66, 2, 6, -2, -2, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[46, 32, -26, 50, 40, 70],\n [-43, -24, 9, -69, -52, -95],\n [-26, -24, 30, -6, -8, -10],\n [73, 70, -91, 7, 16, 15],\n [48, 26, -8, 80, 60, 110],\n [74, 67, -82, 22, 26, 35]]\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, 46, 38, 63, 36, 46],\n [34, 4, -28, -38, -16, -16],\n [-31, -102, 30, 19, -10, -29],\n [10, 84, -12, 2, 16, 32],\n [79, 30, -66, -85, -32, -28],\n [54, -4, -44, -62, -28, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 2 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-50, -41, -67, -8, 43, 87],\n [-57, 7, -84, -78, 32, 22],\n [-71, -49, -66, -22, 52, 96],\n [15, -14, 21, 36, -4, 13],\n [-43, 1, 24, -50, 8, -18],\n [14, -30, 40, 56, -2, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[33, -15, -55, 52, -122, 134],\n [73, -81, 15, 18, -38, 66],\n [-40, 85, 55, 18, 52, -64],\n [42, -25, 125, 0, 100, -80],\n [91, -61, -5, 76, -126, 162],\n [78, -80, -70, 53, -158, 186]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 3 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-61, 70, -23, -83, -9, -27],\n [26, 101, -14, 52, -28, 125],\n [14, -9, 65, -4, 100, -161],\n [-32, -62, 53, 29, 85, 31],\n [-54, -7, 43, -46, 114, -61],\n [-34, 49, -14, -8, -8, 89]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-66, -8, -76, 85, -38, 65],\n [44, -25, 19, -104, 12, -5],\n [-66, 34, -39, 135, -18, 32],\n [-36, -130, -119, -28, -88, 37],\n [-58, 106, 8, 153, 26, 41],\n [0, -41, -34, -44, -20, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 3 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[109, 38, 95, 63, -62, -130],\n [58, 101, 161, 147, 22, -112],\n [-84, 39, -12, -19, 86, 45],\n [-107, -6, -20, 45, 90, 129],\n [-103, -10, -63, -41, 74, 104],\n [80, -28, -24, -68, -88, -76]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",... | 3 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-19, 4, -36, 17, -8, 12],\n [-32, 74, -41, 105, -49, -74],\n [-39, 58, -47, 80, -43, -58],\n [-19, -34, -44, -29, 12, 62],\n [0, 19, 4, 23, -10, -25],\n [25, 62, 67, 54, -25, -110]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 3 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[14, -19, 75, -45, -98, -94],\n [-54, -84, 2, -21, 53, 106],\n [66, 114, 6, 66, -42, -36],\n [-97, -68, -70, -3, 104, -10],\n [-68, -100, -17, -34, 71, 94],\n [-68, 58, 41, 177, 46, 92]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[10, -31, 7, 45, 23, 15],\n [-22, 51, -18, -44, -35, -30],\n [-12, -77, -1, 56, 33, 51],\n [-154, 20, -110, 77, -56, -18],\n [-98, 111, -86, 54, -71, -90],\n [-82, -26, -61, 126, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 3 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[76, 28, -104, -37, 8, 53],\n [-25, -135, 6, -27, 35, 95],\n [27, 169, -22, 5, -20, -54],\n [100, -64, -47, -72, -6, 120],\n [77, -111, -66, 39, 44, 68],\n [-17, 114, -57, 101, 13, -140]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-11, 97, 3, 30, 11, -18],\n [74, -34, -30, 24, 34, 18],\n [-41, -5, 17, -22, -23, -6],\n [95, -13, -39, 42, 49, 18],\n [-46, -64, 20, -46, -36, 3],\n [58, 4, -24, 30, 32, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-117, 147, -96, 3, -155, 42],\n [-58, -30, -44, 136, 69, 68],\n [20, 55, -31, -43, -51, 128],\n [-108, 7, -31, 183, 11, -24],\n [20, 63, 41, 39, -88, 32],\n [115, -150, 85, 30, 170, 10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-71, -104, -121, 32, 142, 78],\n [52, 50, 4, 46, 0, 40],\n [5, -13, -53, 45, 64, 66],\n [27, 63, 87, -19, -91, -84],\n [24, 41, 64, -33, -78, -52],\n [105, 113, 13, 115, 7, 68]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 3 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-106, -33, -92, -87, 61, 12],\n [2, -51, -80, -112, -88, -60],\n [-46, 66, -35, -88, 112, 29],\n [56, -143, -108, 34, -57, 37],\n [70, -18, -33, 72, 158, 81],\n [-88, 22, 88, 69, -47, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 5 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-69, -52, 53, -149, 2, -24],\n [-26, 71, -155, -130, -35, 62],\n [-11, -143, 89, -25, -53, -94],\n [15, 115, 6, -89, 87, 112],\n [146, -67, 61, -94, 79, -4],\n [28, -70, -114, -20, -18, -84]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-78, -135, 18, -24, 78, -143],\n [-48, -108, -156, -66, 54, -194],\n [-30, -34, 70, 86, 96, -92],\n [49, 87, 20, -21, -131, 198],\n [-34, -67, -94, -25, -25, -62],\n [-32, -47, 88, 13, 79, -60]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[33, 36, 18, 93, 90, -111],\n [171, -184, -33, -61, -70, -66],\n [-72, 54, -14, 84, 39, 5],\n [37, 24, 68, -45, -36, -23],\n [44, -58, -30, 29, 5, -39],\n [40, -48, 47, -183, -144, 91]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[71, -144, -59, 41, -88, 53],\n [-56, 18, -4, -62, -2, 34],\n [24, -45, -18, 15, -27, 15],\n [-47, 99, 41, -26, 61, -38],\n [-54, 36, 6, -54, 12, 18],\n [82, -132, -50, 58, -76, 34]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[72, -10, -162, -89, 86, 32],\n [-12, 18, 58, 4, -6, 10],\n [-47, -38, 17, 91, -81, -65],\n [-35, 47, 100, 62, -50, -8],\n [13, 37, 22, -24, 24, 30],\n [-21, 25, 160, -45, 22, 50]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[56, 187, 71, -5, 79, -142],\n [-80, -88, 4, 20, -40, 40],\n [-31, 0, -46, 142, 77, -101],\n [-94, -60, 48, -8, -50, 30],\n [112, 49, -52, -28, 29, 8],\n [34, 62, 36, -52, 0, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-40, 60, -100, 50, 90, -40],\n [47, -63, 62, -49, -57, 26],\n [11, -9, -28, -4, 24, -10],\n [47, -53, -12, -36, 8, -2],\n [40, -50, 26, -37, -25, 12],\n [30, -20, -110, -5, 95, -40]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-25, 26, 66, -28, 51, 22],\n [130, -92, 40, 4, 78, -168],\n [39, 158, 61, -16, 10, 110],\n [-115, -56, -32, -29, 127, -25],\n [21, -114, -12, 24, -81, -82],\n [-55, 78, -24, 12, -121, 130]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-14, -6, -3, -4, -17, 17],\n [-26, 0, 18, -10, -8, 14],\n [-56, -24, -12, -16, -68, 68],\n [-69, -24, -3, -21, -72, 75],\n [11, -38, -88, 13, -77, 54],\n [-15, -38, -70, 3, -85, 68]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-80, -132, 48, 62, -20, 50],\n [15, 27, -3, -27, -30, -30],\n [-22, -30, 30, -26, -100, -44],\n [54, 90, -30, -48, 0, -42],\n [9, 9, -21, 33, 90, 48],\n [18, 24, -26, 25, 90, 41]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 2 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-168, -78, -123, -53, -68, 107],\n [5, -59, 166, -15, 6, 19],\n [5, 56, -87, 32, 43, -37],\n [-172, -63, 64, -180, -73, -43],\n [-81, -95, -36, -68, 21, 46],\n [-136, -19, -31, -102, -70, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[75, -18, 47, 78, -92, -127],\n [-53, -11, 45, -7, -36, 87],\n [-76, -1, -3, -17, 63, 168],\n [85, 28, -34, 36, -17, -131],\n [13, 31, -25, 87, 54, 105],\n [32, -43, -40, 11, 111, -54]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-39, 42, 9, -84, 274, -75],\n [-31, 8, 37, -24, 198, -57],\n [-47, -24, 77, 80, 22, -46],\n [-84, 4, 108, 64, 96, -101],\n [-65, 20, -85, 40, -110, 10],\n [-15, 0, -19, 54, -188, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[18, -135, 144, 18, 36, 27],\n [-6, 3, 0, 0, -48, 9],\n [-10, 110, -120, -15, 10, -30],\n [-8, 67, -72, -9, -10, -15],\n [16, -1, -8, -1, 134, -27],\n [-2, -20, 24, 3, -34, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 2 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[36, -24, 0, -32, 40, -32],\n [-72, -6, -24, 10, 40, -32],\n [-45, 66, 16, 76, -130, 104],\n [27, -63, -20, -69, 130, -104],\n [-180, 30, -40, 70, 0, 0],\n [99, -48, 8, -70, 70, -56]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 2 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-22, 2, -104, 17, -22, -70],\n [-90, 163, 31, 60, 48, 10],\n [-9, 76, -4, -49, 18, -86],\n [-1, 7, 99, 57, -7, 142],\n [-35, 35, 87, 63, 34, 116],\n [-109, -60, -114, 40, 161, -78]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[44, -17, 75, -58, -65, 37],\n [-9, 21, 85, -51, -31, 63],\n [-8, -40, 78, 58, -88, 80],\n [-57, 83, 118, -10, -37, 153],\n [143, -72, 119, -114, -154, 34],\n [0, -87, -82, 45, 37, -117]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-77, -38, 31, 129, 108, -93],\n [-9, -20, -89, 92, 32, -60],\n [60, -46, -28, -7, -6, 85],\n [-3, 110, -41, -82, -151, -83],\n [48, -106, 32, 21, 110, 149],\n [-74, 92, 24, -46, 9, -87]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[14, 42, -60, -2, -3, -75],\n [-110, -10, -100, -30, 115, -5],\n [-4, -8, 10, 0, 2, 14],\n [20, -44, 100, 12, -34, 86],\n [-42, 14, -70, -14, 49, -35],\n [32, 64, -80, 0, -16, -112]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-80, 60, -64, -32, 40, 76],\n [50, 0, 34, -10, -22, -28],\n [-10, 45, -14, -34, 8, 29],\n [110, 30, 70, -46, -46, -46],\n [-15, 30, -15, -21, 9, 24],\n [-20, 115, -32, -88, 18, 71]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-26, 71, -57, 27, -69, 14],\n [-9, 3, 58, 44, 29, -39],\n [-54, 88, -24, 18, -84, 32],\n [-6, -47, 51, -75, 21, 44],\n [11, -45, 38, -32, 37, 5],\n [-4, -26, 44, -26, 22, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 3 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[44, 127, -7, -90, 13, 14],\n [50, 156, 30, -96, -40, 16],\n [24, 82, -17, -18, 28, -100],\n [-18, 155, 18, -100, 46, 44],\n [28, 76, 6, 32, 8, -140],\n [-74, 39, -51, -193, -10, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[39, -25, 62, 88, 91, -67],\n [-43, -22, 26, 41, -50, -104],\n [39, -73, -20, -83, 18, 17],\n [12, 107, -24, 19, 11, 71],\n [-15, 82, -60, -54, -57, 84],\n [-3, 73, -22, 6, -19, 27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-2, -28, 78, -26, 116, -28],\n [108, 20, -20, 6, 10, 38],\n [108, 35, -85, 73, -136, 84],\n [-17, 61, -38, 73, 82, 39],\n [37, -77, 58, -44, -100, -22],\n [-127, -61, 70, -56, 0, -78]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[74, 65, -56, -81, -95, 39],\n [-11, 37, 48, 15, -20, -43],\n [84, 28, -64, -8, -60, -32],\n [76, 122, -16, -92, -140, 12],\n [-68, 26, 112, 52, 20, -68],\n [13, 141, 64, -88, -125, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[39, 19, -10, 37, 0, -48],\n [-22, -12, 5, -22, -1, 28],\n [-60, 40, 50, 4, 54, 24],\n [34, -86, -60, -58, -80, 32],\n [36, -44, -40, -20, -48, 0],\n [-31, -51, -10, -61, -28, 64]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 2 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-42, -28, -84, -27, 24, -25],\n [2, 34, 177, 45, -12, 44],\n [48, -69, -106, -37, 44, -40],\n [136, -106, -20, -24, 72, -34],\n [68, -32, 137, 13, 76, 58],\n [-37, 64, 93, 34, -44, 35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[52, 115, -24, 64, 113, 18],\n [49, 115, -77, 124, 9, 77],\n [50, 136, -22, 46, 127, 31],\n [110, 218, -2, 50, 143, 77],\n [117, 98, 99, -52, 16, 45],\n [-48, -57, -32, 29, 38, -61]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-90, 36, 90, -18, 54, 54],\n [100, -132, -170, 66, -98, 2],\n [6, -30, -27, 15, -15, 15],\n [58, -60, -86, 30, -50, -10],\n [-10, 4, 10, -2, 6, 6],\n [-36, -4, 22, 2, 14, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[94, -162, -123, -303, -87, 90],\n [60, 68, 16, 9, 25, 42],\n [-47, 15, 61, -2, 0, 5],\n [-80, 58, 40, 65, -12, -74],\n [-12, -46, -144, 93, 45, -63],\n [48, -128, -167, -176, -77, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 5 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-34, -142, 134, 160, 74, -34],\n [-9, -30, 33, 23, -5, 0],\n [3, 32, -22, -59, -57, 11],\n [8, 48, -45, -64, -36, -9],\n [-52, -151, 152, 115, 2, -97],\n [-3, -3, 15, -18, -45, 33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[117, 60, 51, -184, -8, -30],\n [-18, 8, -44, 62, 10, -40],\n [-11, 86, 102, -40, -67, 15],\n [74, -57, -66, -119, 82, 23],\n [0, 13, 5, 1, -1, -20],\n [64, -46, 92, 18, -94, -40]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[17, -6, 23, -34, -33, 17],\n [-3, -6, -7, 46, 37, -23],\n [44, -24, 56, -40, -48, 20],\n [34, -36, 36, 68, 40, -34],\n [-19, 18, -21, -26, -13, 13],\n [-3, -6, -7, 46, 37, -23]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[39, 135, 26, 55, 92, 21],\n [154, 78, -81, 70, 82, 65],\n [-56, 186, 46, 7, 77, -51],\n [68, 30, -50, 67, 45, -17],\n [-52, 116, 78, -8, 48, 4],\n [75, -25, -14, 25, 14, 69]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-8, -68, 80, -20, -4, -56],\n [5, -45, 30, -20, -25, -25],\n [-18, 57, -12, 33, 57, 18],\n [-41, 89, 10, 60, 117, 13],\n [-33, -53, 122, 2, 55, -75],\n [-27, -2, 62, 17, 58, -33]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[10, -50, 6, -8, 76, -40],\n [52, -44, -36, 40, 16, -40],\n [14, 2, -14, 16, -20, 0],\n [-25, 35, 13, -14, -32, 30],\n [93, -51, -73, 82, -20, -50],\n [-13, 11, 9, -10, -4, 10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[94, 8, -13, -30, -13, -68],\n [2, -54, 44, 88, -50, -177],\n [5, -61, 11, 76, -57, -186],\n [-52, 52, 53, -2, 17, 147],\n [50, 66, -22, -56, -38, 78],\n [-77, 21, 114, 118, -104, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-133, 31, -41, -36, 61, 52],\n [-108, -7, -69, 24, 0, 76],\n [111, 8, 2, -9, 18, 14],\n [153, -81, 15, 82, 2, -11],\n [-141, 65, -52, 24, 84, 80],\n [-94, -57, -82, 158, 137, 120]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-221, 36, 129, 110, -71, -113],\n [-35, 121, 105, -29, 26, 36],\n [-157, 2, 131, 94, -20, -116],\n [117, -5, -153, -79, 13, 62],\n [-48, 84, -36, -12, -11, 0],\n [-5, 83, -4, -57, -59, 92]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-2, -62, -82, -68, -4, 74],\n [36, 11, -84, -56, -53, 98],\n [26, 60, -48, -18, -46, 67],\n [25, 9, -125, -80, -52, 138],\n [-14, -62, -76, -62, 8, 65],\n [-30, 10, 176, 118, 64, -189]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-44, -39, 47, 1, -45, 30],\n [10, 70, 26, -130, -43, -97],\n [67, 48, -74, -22, 26, -119],\n [-14, 66, 48, -125, -53, -67],\n [-42, -135, -17, 152, -47, -94],\n [-81, 58, 36, -29, -100, -19]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 5 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-61, -29, 23, 43, 70, 69],\n [58, 47, 10, -18, -36, -63],\n [47, 31, -13, -49, -112, -60],\n [94, 77, 14, -38, -84, -105],\n [92, 100, 44, -36, -120, -108],\n [56, 82, 72, 32, 40, -54]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[197, 0, 61, 13, 69, 112],\n [-134, 79, -65, -9, -113, -73],\n [-125, 66, -136, -163, -9, -79],\n [-55, -82, 38, 21, 7, -43],\n [-65, 78, -61, -10, -62, -26],\n [50, -9, 26, 62, 24, 44]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-26, 29, -52, -1, 35, 18],\n [-35, -29, -75, -52, 26, 49],\n [-20, 88, -24, 29, 41, -26],\n [31, 19, 87, 5, -37, -71],\n [0, -85, -14, -50, -22, 42],\n [-19, 1, -23, -44, 10, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-40, -81, -96, -10, -202, 33],\n [-33, -2, -77, -37, 11, 158],\n [38, -156, 67, 35, -113, -176],\n [62, -42, -6, 29, 7, 119],\n [42, 42, 0, 4, 91, 138],\n [-83, -42, -20, -79, 18, -27]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 5 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-36, 100, -24, -84, -14, -54],\n [-13, 61, 3, -56, -8, -86],\n [-56, 7, 21, 14, 22, -7],\n [0, 9, -15, -8, -5, 24],\n [-120, 80, 0, -32, 24, 0],\n [-41, 57, -9, -40, 0, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[93, 106, -46, -73, 7, -39],\n [-19, -82, 31, 68, -31, 18],\n [4, -69, 46, 39, -44, -15],\n [92, 34, -114, 88, 8, 84],\n [61, -80, -23, 132, -51, 54],\n [137, -61, 91, -1, -127, -117]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 3 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[50, -24, 38, -106, -29, -37],\n [-67, 101, 18, 142, 47, 78],\n [34, 30, 70, -71, -17, -5],\n [39, 117, 68, 22, -56, 27],\n [-27, -1, -22, 49, 27, 10],\n [91, 49, 20, -36, -108, -33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[128, -120, -16, 16, -64, 24],\n [-7, 44, 32, -97, 1, -21],\n [-26, 28, -7, 27, 3, -18],\n [-39, -25, -5, 30, 54, 60],\n [11, -95, 15, -40, 64, 120],\n [44, -74, 1, -11, 5, 54]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[15, -5, -86, 87, -61, 65],\n [-84, 129, -78, -15, 18, 75],\n [60, -95, 40, 30, -25, -40],\n [55, -145, 50, 75, -45, -35],\n [-14, -83, 76, 16, 7, -38],\n [-85, 164, -94, -35, 26, 81]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-6, 80, -52, -44, -82, 126],\n [-53, 25, -105, -26, -56, 78],\n [136, 64, 112, 0, -72, 24],\n [-88, 0, -162, -22, -62, 70],\n [30, 41, -59, -1, -105, 63],\n [-29, 40, -72, -20, -53, 79]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-27, 16, -101, -44, 158, 24],\n [-58, 11, -105, 2, 37, -9],\n [160, 78, 47, 63, 48, -67],\n [-70, -55, 12, -23, -55, 36],\n [91, -32, 42, 33, 120, -16],\n [149, -5, 100, 107, 7, -94]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 5 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[2, 16, -22, -16, -156, -56],\n [-11, 59, -49, -16, -125, -36],\n [-3, 3, 15, -7, -28, 2],\n [27, -48, -22, 20, -163, -46],\n [30, -105, 41, 52, 130, 58],\n [6, -42, 52, 1, 49, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[57, 86, -43, 30, 21, 58],\n [-26, 92, -72, 155, -31, -4],\n [-45, -110, 75, -39, -22, -24],\n [56, 37, 1, -22, 29, 65],\n [107, -115, 85, -35, -53, 126],\n [-48, 226, -178, 93, 55, -104]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-17, -6, -12, -11, 37, -9],\n [67, 74, 38, 10, 84, 105],\n [16, 57, -6, 140, -29, 19],\n [32, 17, 67, -22, 45, 77],\n [-58, -20, -45, 92, -36, -92],\n [121, 114, 61, 132, 48, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 5 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-96, 41, -122, 8, -59, 90],\n [-23, -78, 89, 36, 37, -123],\n [20, -82, -16, 29, -86, -164],\n [-20, -45, 219, 53, 176, -131],\n [9, 71, -46, 4, -25, 22],\n [-26, -67, -17, 4, 28, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 5 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[87, -96, -60, 0, 3, 16],\n [-41, 90, 14, -39, -36, -96],\n [-37, -70, -51, 43, -88, 27],\n [30, -80, 115, 48, 37, -85],\n [-49, 129, 19, -2, 105, 115],\n [33, -15, 3, -63, -62, -83]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-11, 16, -20, 49, -46, -46],\n [83, -5, 90, -53, 73, 73],\n [-44, 7, -50, 40, -49, -49],\n [52, 9, 50, 0, 17, 17],\n [57, -19, 70, -79, 87, 87],\n [46, -22, 60, -82, 86, 86]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-20, -37, -54, -28, -41, 67],\n [30, -11, -33, 4, -24, 61],\n [0, -28, -48, -16, -36, 68],\n [20, -5, -18, 4, -13, 35],\n [-30, -31, -39, -28, -30, 41],\n [60, 55, 66, 52, 51, -65]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 2 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-39, -51, 132, -60, -24, -45],\n [-16, 1, 38, -5, 34, -15],\n [-26, -72, 116, -74, -92, -36],\n [-14, 8, 28, 2, 44, -12],\n [6, 2, -16, 4, -8, 6],\n [17, 31, -64, 34, 28, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[29, 20, 16, -2, 6, -66],\n [14, 8, 16, -30, 6, -82],\n [91, 76, 41, 74, -6, -53],\n [39, 60, 81, -22, -54, -61],\n [2, 8, 28, -44, -12, -64],\n [50, 56, 43, 46, -30, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[11, 48, -12, -77, -27, 103],\n [-82, 78, 60, 34, -35, 80],\n [125, -71, 15, -103, -56, 58],\n [-145, 74, -2, -5, -57, 140],\n [-135, 68, 95, 37, -46, 102],\n [94, -59, 100, 70, -85, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 5 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[51, 0, 32, -4, -28, 48],\n [-1, -1, -133, 107, 119, -134],\n [-135, 39, -19, -23, 10, 79],\n [12, -35, -53, 136, 50, 19],\n [-203, -1, -23, -1, -24, -91],\n [85, 6, 13, -49, -5, -67]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-60, 4, -124, -6, -11, 46],\n [-11, -29, 97, -7, 50, -56],\n [28, 23, 101, 43, 12, -42],\n [132, 90, 19, 136, -2, 17],\n [46, 68, -71, 61, -67, 65],\n [-2, 79, -16, 82, -51, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
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