messages listlengths 1 1 | ground_truth stringclasses 4
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Calculate the rank of matrix A where A =\n[[-55, -30, 40, -70, -170, 50],\n [88, 6, -13, 49, 62, 1],\n [24, 106, -56, -6, 140, -72],\n [56, 42, -8, -22, -20, 8],\n [-70, -14, 25, -61, -114, 23],\n [-8, 86, -2, -116, -120, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-24, -31, 53, -8, 35, -43],\n [-7, -63, 9, 16, -90, -14],\n [28, 104, -104, -64, -28, 52],\n [-9, -81, 67, 76, 9, -18],\n [-33, -38, 50, -36, 4, -59],\n [-30, -85, 95, 40, 35, -55]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[36, -58, -86, 41, 30, -164],\n [-31, 146, -49, -24, 17, 14],\n [-155, 12, 147, -78, 0, 19],\n [-41, -126, 44, -192, -118, -160],\n [10, 128, -54, 29, 8, -66],\n [35, 179, -103, 25, 23, 54]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-18, -118, 30, -19, 28, -13],\n [13, -4, 133, -49, 9, -42],\n [18, -29, 72, 6, 67, -95],\n [66, -40, -44, 99, 195, 54],\n [3, -103, -49, 20, 63, 121],\n [22, 122, -36, 36, -9, -31]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-101, -57, -70, 64, 4, -93],\n [69, 1, -50, -2, 16, 21],\n [47, -33, -8, -58, 56, 51],\n [92, 76, 36, -16, -32, 64],\n [78, 30, 33, -45, 6, 63],\n [-3, 51, -65, 107, -74, -71]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[126, -44, 18, -71, 81, 17],\n [3, 85, -52, 31, 30, 63],\n [-3, 7, 64, 43, 24, -5],\n [-42, -66, 132, 44, -22, -76],\n [-96, 26, -20, 45, -68, -17],\n [24, 162, -160, 17, 50, 135]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[80, 63, 108, 6, -46, -96],\n [51, 11, 38, 25, 2, -6],\n [-30, -14, -23, -4, -2, 15],\n [-61, -47, -78, -3, 30, 70],\n [-51, -9, -59, -43, 24, 11],\n [-27, -39, -150, -57, 150, 102]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 3 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-5, -63, -38, -19, -1, -9],\n [-72, 111, 39, 45, 90, 75],\n [24, -7, 22, 14, -25, -26],\n [-53, 73, 113, 89, 161, -38],\n [55, 60, 14, 57, 60, 73],\n [102, -16, -89, -73, -67, 43]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 5 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-72, -132, -18, -140, -78, 40],\n [-9, -49, 75, -30, -11, -71],\n [12, 31, -15, 27, 14, 11],\n [-8, 58, -82, 18, 12, 82],\n [-75, -104, 0, -127, -61, 22],\n [-59, 100, 14, -3, 45, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 3 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-21, -29, -32, -50, 28, 47],\n [104, -58, -10, -12, 16, 2],\n [61, 46, 61, 96, -52, -92],\n [-1, -57, -48, -74, 44, 67],\n [-121, 38, -13, -24, 4, 32],\n [71, -41, -8, -10, 12, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 2 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-4, -4, 44, -67, -42, 49],\n [25, 2, 38, -127, -65, 113],\n [62, 48, -48, -55, -48, 53],\n [-49, -34, 74, -17, -7, -1],\n [-50, -57, 42, 32, 55, -18],\n [54, 129, 6, -98, -191, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 3 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[8, 24, 38, 29, -8, 8],\n [-3, -6, -8, -4, 2, -1],\n [2, 36, 72, 76, -12, 22],\n [-13, -42, -68, -54, 14, -15],\n [-72, -96, -92, 14, 32, 8],\n [100, 120, 100, -50, -40, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 2 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[20, -8, -66, 83, -37, 31],\n [55, 47, -9, -65, 88, -70],\n [25, 5, -45, 40, -5, 5],\n [35, 31, -3, -46, 59, -47],\n [45, 13, -71, 55, 2, 0],\n [55, 23, -69, 37, 22, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-30, 23, 4, 40, -20, -35],\n [-53, 52, -13, 64, 4, 11],\n [95, -93, 96, -71, 52, -33],\n [-98, 92, -43, 105, -28, -1],\n [61, -64, 51, -54, 4, -45],\n [-88, 88, -45, 93, -4, 33]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-12, -88, -84, 81, -128, 153],\n [128, 20, 28, 22, 32, -14],\n [-58, -47, -74, 37, -51, 66],\n [177, 15, 91, -32, 5, -24],\n [7, -8, -13, 12, -4, 9],\n [89, -67, -44, -84, 10, -56]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 5 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-48, -16, 8, 48, 12, -56],\n [44, -18, -33, -9, -67, 56],\n [76, 2, -31, -51, -59, 92],\n [40, -38, -47, 15, -98, 54],\n [-12, -4, 2, 12, 3, -14],\n [116, 34, -23, -111, -37, 136]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[12, 110, 15, -48, 84, 176],\n [40, 6, -55, 52, -14, -50],\n [6, 84, 21, -30, 87, 135],\n [-50, -54, 34, -84, -110, -2],\n [-106, -30, 146, -120, 44, 104],\n [93, 55, -141, 42, -105, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-76, -24, 119, -36, -29, -16],\n [68, -223, 7, 11, 193, -65],\n [36, 48, -33, 3, -95, 111],\n [34, -47, 11, -11, 75, -7],\n [68, -75, 13, -15, 51, 61],\n [9, 87, -93, 33, -44, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 4 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-15, -77, 46, -110, -81, 33],\n [0, -33, 14, -52, -35, 23],\n [-20, 84, -39, 148, 93, -84],\n [-75, -95, -15, -90, -80, -25],\n [30, -55, -57, -108, -52, 85],\n [-130, -111, 135, -76, -108, -99]]\n\nPresent the answer in LaTex format: \\boxed{Your answe... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[15, 120, -107, -71, -24, -66],\n [10, 80, -78, -34, -46, -64],\n [7, 56, -23, -87, 110, 50],\n [0, 0, 8, -16, 36, 24],\n [6, 48, -58, 2, -78, -72],\n [-9, -72, 85, 1, 108, 102]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-73, -8, -84, -113, -27, -90],\n [0, 24, 82, -162, 34, 76],\n [44, 56, -29, 55, -90, 55],\n [103, 100, 31, 94, -52, -14],\n [56, 92, 64, -34, -55, 15],\n [-47, -68, -6, 64, 53, -119]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 5 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-74, 99, 55, -79, 91, -169],\n [54, 117, -24, 73, -95, 91],\n [32, -28, 2, 74, -42, 28],\n [-22, 40, 27, -134, 74, -26],\n [-11, -177, -7, -6, 35, -1],\n [17, -110, -87, 94, -79, 106]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-60, 0, -68, 54, -40, 0],\n [37, -154, -106, -67, 171, -14],\n [-87, 144, 19, 108, -231, -21],\n [-15, 88, 119, 27, -13, 17],\n [9, -62, -38, -36, 71, -100],\n [58, 46, 107, -40, -8, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-14, -6, -22, 0, 12, -14],\n [-86, -74, -124, -130, -60, -8],\n [36, 24, 54, 30, 0, 18],\n [19, 21, 26, 45, 30, -8],\n [66, 54, 96, 90, 36, 12],\n [-40, -20, -62, -10, 24, -34]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[42, 12, -54, -20, 0, -16],\n [30, -120, 30, 148, -54, 8],\n [-97, 130, 36, -117, 69, 49],\n [24, 102, -75, -183, 36, -75],\n [69, -78, -30, 39, -45, -63],\n [88, 14, -100, -84, -9, -88]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[15, -61, 38, -4, -43, 20],\n [-61, -83, 92, 19, -99, -37],\n [101, -73, -30, -10, 30, 89],\n [19, 119, -104, -1, 128, 6],\n [88, -118, -14, -13, -108, 19],\n [114, -29, -83, -17, 27, 60]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[30, 57, 226, 26, -109, 85],\n [46, 50, 182, 8, -86, 62],\n [127, 101, 2, 7, 65, -73],\n [-143, -132, -190, 58, 82, -55],\n [-18, 11, -60, -38, 9, 9],\n [2, -12, 120, -41, -100, 81]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-18, -220, -116, 150, -106, -96],\n [-11, 53, 6, -104, -69, 79],\n [-13, -14, -66, 95, 63, -124],\n [-50, -166, -172, 76, -78, -102],\n [18, 29, 80, -77, 60, 89],\n [15, -112, -6, 121, 24, -63]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[21, -66, -77, -252, 61, -124],\n [-14, 85, -126, -129, 39, -40],\n [44, 123, -141, -25, -17, -69],\n [65, -147, 149, 28, 78, 6],\n [-120, -21, -32, -167, 43, 12],\n [27, 43, -97, -34, -42, -102]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 5 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-13, 120, -88, -15, 30, 29],\n [-41, 23, -55, 63, 33, 57],\n [-27, -16, 74, 28, 16, -53],\n [30, -128, 56, -30, -84, -46],\n [-49, -84, 30, 67, -26, -19],\n [53, 8, 12, -51, 6, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-72, 40, 16, 40, 8, 56],\n [148, -130, -45, -55, 104, -62],\n [-95, 155, 20, 31, -92, -71],\n [45, -85, -5, -25, -12, 102],\n [108, -50, -87, -11, 133, 58],\n [51, 45, -41, -19, 1, -82]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[21, 105, 35, 21, -105, -14],\n [-18, 24, 32, 54, -12, 16],\n [-6, -87, -41, -42, 81, 2],\n [12, 117, 51, 48, -111, -6],\n [59, -9, -67, -133, -23, -50],\n [-6, -87, -41, -42, 81, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[3, -40, -38, 17, 43, -57],\n [68, -101, 162, -15, -100, 143],\n [59, 45, 7, 14, 134, -32],\n [1, -89, 46, 16, -57, 36],\n [30, 33, 36, -9, 21, 30],\n [42, -2, 11, -36, 2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[36, -83, 6, 89, -75, -72],\n [-17, 28, -80, 5, -87, -55],\n [-61, 111, -31, -108, 78, 64],\n [-121, 80, -45, -63, 95, -36],\n [-14, 61, -34, -53, -1, 34],\n [104, -46, 80, 10, -6, 100]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[63, -42, -56, 0, -42, -56],\n [-67, 70, 58, 14, 48, 86],\n [35, -74, -28, -28, -30, -84],\n [27, -18, -24, 0, -18, -24],\n [3, 36, -5, 21, 3, 37],\n [119, 22, -112, 56, -66, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[13, -33, -9, 20, -12, 21],\n [38, 11, -17, 28, 14, 14],\n [41, 62, -14, 16, 38, -7],\n [-135, -9, 63, -108, -36, -63],\n [12, -50, -10, 24, -20, 28],\n [-142, -1, 67, -116, -34, -70]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 2 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-24, 34, 104, -125, -22, 11],\n [8, -16, -48, 58, 8, -6],\n [-42, -7, -8, 14, -29, -14],\n [46, -43, -136, 162, 39, -10],\n [-54, -11, -16, 25, -37, -19],\n [18, -1, -8, 8, 13, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-90, -32, 60, 74, -25, -36],\n [-116, 78, 48, 25, -72, -55],\n [39, -202, 62, 64, -28, 33],\n [102, 48, -34, -96, 101, 6],\n [-76, 158, -102, 15, 18, -5],\n [-41, 54, 44, -14, 18, -49]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[84, -64, -124, -56, 100, 34],\n [4, 37, 23, 11, 35, 55],\n [-14, -40, 27, -20, 64, 54],\n [-16, 39, 53, 17, 29, 59],\n [-48, 71, 77, 49, -83, -29],\n [42, 42, -54, 10, -20, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[41, 17, 35, 75, -45, -71],\n [-58, -52, 190, 131, -247, -48],\n [68, -107, -6, 64, 174, 18],\n [-46, -24, 158, 92, -264, -19],\n [103, -66, 3, 59, 58, 41],\n [-8, 49, -26, -90, 62, 52]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 5 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[13, 3, 67, -23, -28, 26],\n [53, -14, -38, 116, -49, 19],\n [-86, 43, 59, -102, 78, 25],\n [63, -58, -78, 46, -65, -81],\n [-59, 64, 64, -28, 75, 93],\n [185, -113, 77, 30, -247, -73]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[55, 97, -34, -24, 69, 34],\n [10, 16, -166, -18, -96, 50],\n [-51, -94, 147, 25, 5, -63],\n [-27, -39, -60, 18, -69, 4],\n [-16, -19, 115, 27, 66, -39],\n [49, 44, -115, -85, -71, 55]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 3 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-88, -12, -59, -17, 83, 70],\n [-20, -7, -25, -25, 120, 155],\n [-88, 24, 65, 11, -53, -48],\n [20, 57, -111, -123, 22, 73],\n [-66, 29, 84, 18, -91, -87],\n [77, 39, -42, -78, 20, 81]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 4 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[16, 62, -29, 42, -76, 47],\n [-77, -60, -61, 9, 144, -108],\n [-18, -102, 33, -12, -24, -9],\n [-72, -34, -26, -60, 15, 17],\n [105, 113, 34, -132, -174, 180],\n [20, 47, -46, -8, 31, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[23, -46, -1, 7, -78, 33],\n [-77, 20, -119, 66, 68, -68],\n [55, 22, 115, -70, 0, 36],\n [-2, -10, 12, -2, 16, 10],\n [13, -47, -6, 12, -58, 30],\n [10, 37, 1, -13, -12, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[51, -20, -31, 42, 49, -55],\n [93, -28, -11, 17, 19, 40],\n [9, -70, -39, 18, -7, -146],\n [-62, -70, 12, -54, -152, -19],\n [69, 2, -27, 55, 101, -98],\n [-222, -140, 2, -161, -246, -124]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 5 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[201, -34, -89, 106, 26, -81],\n [-41, 50, 38, -81, -126, -48],\n [100, 61, 10, 52, 42, 10],\n [37, -36, -35, 32, 22, -15],\n [36, -207, -144, 90, 90, -36],\n [112, -72, -82, 86, 56, -38]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 3 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[78, 150, 33, -7, -29, -84],\n [-51, -25, -72, 36, -11, -5],\n [-6, 30, -11, 9, 13, -12],\n [9, -9, 26, -14, 13, 15],\n [27, -15, 98, -50, 73, 57],\n [24, -112, 91, -57, 17, 82]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[141, -18, 56, 245, -85, -28],\n [-7, 74, 118, 109, -9, -24],\n [-18, 150, 75, 48, -32, -60],\n [177, -12, 153, 143, -143, -120],\n [19, -110, 53, -89, 2, -9],\n [50, 32, 69, 212, -26, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[76, 20, -16, 48, -60, -100],\n [4, -47, -2, -38, 9, 26],\n [-62, 106, 16, 64, 18, 2],\n [-76, -20, 16, -48, 60, 100],\n [76, -63, -18, -22, -39, -46],\n [3, -56, -2, -46, 12, 33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[2, -27, 102, 0, 75, 39],\n [30, -36, 90, -18, 72, 18],\n [26, -160, -10, -14, -60, -102],\n [-4, -44, 80, 4, 48, 20],\n [-13, -61, -60, 9, -78, -61],\n [46, -83, 25, -28, 6, -48]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[60, -87, -25, 108, -63, -89],\n [78, -57, 0, -35, -106, 6],\n [-148, 121, 11, 8, 137, -68],\n [-112, 5, -145, -136, 89, 28],\n [16, 109, -45, -44, -15, 3],\n [-102, -67, -40, -73, 142, 133]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[58, -21, 78, -11, -2, 125],\n [21, 2, -68, 65, 0, -67],\n [50, 5, 8, 19, 40, 80],\n [-33, -87, 4, -72, -5, 113],\n [44, 66, 4, 56, 23, -42],\n [118, 36, 24, 70, 64, 110]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[3, 72, -4, 38, -9, 74],\n [-37, -6, 94, -92, -13, -1],\n [-32, -40, 54, -124, 38, -14],\n [1, 78, -26, 4, 37, 105],\n [-46, 24, 102, -120, 8, 46],\n [-5, 22, 30, 16, -33, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[35, 38, -35, 72, -45, -21],\n [64, -72, 81, -51, 63, 78],\n [91, -11, 54, 34, 12, 68],\n [-83, 131, -65, 87, -81, -54],\n [-57, 105, 34, 46, -24, 44],\n [-112, 105, 39, 6, -9, 39]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-117, 21, -82, 60, 69, 1],\n [2, 42, -41, 3, -53, -8],\n [224, -80, 10, 20, 66, 24],\n [77, -27, -31, -56, -116, 17],\n [-57, 164, 16, 59, 160, 32],\n [-141, -48, -100, 48, 10, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 5 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[39, -103, 103, -161, 103, 45],\n [-71, 5, -36, -94, 29, 9],\n [-31, 13, 8, 58, 39, 59],\n [-131, -63, -41, 220, 27, 152],\n [-76, -13, 38, -109, 121, 53],\n [7, 161, -100, -88, -116, -202]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-58, -4, 66, -8, -22, 56],\n [-5, -12, 81, -11, -79, 12],\n [-36, -21, 142, -18, -121, 46],\n [12, -29, 86, -8, -117, 6],\n [-68, 18, -32, 4, 94, 52],\n [9, -5, -67, 13, 42, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[38, -136, -125, -21, 72, -82],\n [27, -48, -26, 56, -38, -38],\n [-20, -8, -37, -105, 108, 10],\n [7, -32, -32, -14, 26, -18],\n [42, -96, -68, 56, -20, -68],\n [-14, -32, -60, -112, 124, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 2 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[88, -42, 58, 40, 26, -92],\n [-20, -214, -64, 55, -78, 28],\n [13, -5, 208, -17, -73, -69],\n [43, 87, 200, -116, 105, -233],\n [-70, 22, 150, -71, -88, -6],\n [-8, 32, -166, 1, -15, 106]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-51, 129, 9, 89, -3, -59],\n [-135, -63, 96, 30, 93, -90],\n [91, -65, -44, 32, 31, 42],\n [-102, 42, 56, 110, 72, -98],\n [-62, 22, 30, 128, 74, -86],\n [170, -10, -100, -120, -108, 146]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-39, 51, 1, 141, 123, 66],\n [-18, -51, 69, 6, 17, -2],\n [-111, -36, 34, 45, -9, 63],\n [0, -15, 75, -102, -28, 7],\n [38, 36, -126, 4, -55, -37],\n [142, -6, -59, 53, 48, -115]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[10, -49, -129, -99, 116, 55],\n [92, 54, -86, -112, 132, -118],\n [-58, 14, -151, -64, 102, 2],\n [-80, -43, -32, 25, -22, 89],\n [-10, -7, 25, 19, -60, -47],\n [6, 54, 97, 68, -74, -62]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[133, -98, -42, -47, 22, 108],\n [-89, 161, 58, -91, -50, -7],\n [-18, 10, 102, 18, 84, 80],\n [43, 57, 35, -27, 22, 88],\n [111, -96, -123, 123, -6, -45],\n [-127, 22, 127, 9, 62, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[38, -86, 5, -65, 64, 30],\n [-30, 66, -85, -33, 36, -108],\n [-49, 70, -40, -32, 10, -48],\n [-58, 14, 35, -95, 24, 74],\n [62, -60, -20, 28, 20, -32],\n [49, -44, -40, 5, 36, -53]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[51, -70, -45, 9, -8, -39],\n [75, 20, -39, 21, 7, -36],\n [82, 70, -32, 26, 15, -31],\n [118, -80, -86, 26, -6, -76],\n [57, 0, -33, 15, 3, -30],\n [-30, -160, -18, -18, -26, -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[[78, 18, -133, 42, -67, -80],\n [2, -18, -36, -26, -82, -110],\n [130, -73, 3, 27, 37, 88],\n [125, -88, 53, 32, 82, 123],\n [58, -66, 26, 8, 3, -36],\n [56, 112, -225, 72, -73, -46]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[43, -2, 44, 34, -48, -49],\n [-73, -52, -68, -58, 12, 109],\n [-39, 88, -37, -12, 119, 5],\n [-85, 89, -46, 4, 76, 60],\n [18, 64, -13, -18, 119, -52],\n [24, 86, 13, 18, 85, -68]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-134, 36, 48, 173, -30, 27],\n [52, -114, -55, -107, 84, -113],\n [61, 39, 18, -99, -26, 22],\n [50, -30, -98, -40, 84, -58],\n [111, 48, 12, -97, -28, 56],\n [-9, 1, 22, -53, -2, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-5, -29, -1, 90, -40, 47],\n [68, 116, -51, -37, -88, -28],\n [-28, 60, -37, -9, -76, 56],\n [56, 110, -38, -65, -51, -46],\n [89, 119, -51, -79, -67, -61],\n [75, -79, 25, 34, 49, -61]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-30, 99, 100, 35, 51, -100],\n [-130, -56, -12, -187, -113, 56],\n [-36, 58, 20, -46, 86, -40],\n [2, -58, -10, 7, -105, 40],\n [10, -97, -116, -81, -25, 108],\n [8, -21, 38, 56, -100, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[22, 124, 88, -106, -65, -86],\n [153, 137, 44, -37, 43, -78],\n [36, -76, 72, 126, 87, 76],\n [-39, -37, -73, 1, 7, 19],\n [57, 127, -11, -111, -91, -107],\n [-124, -138, -124, 40, -37, 70]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[12, -60, -144, -21, 165, 42],\n [-72, -18, -66, 52, 106, -36],\n [127, -13, -46, 81, -135, -52],\n [-29, 73, -48, 87, -45, -60],\n [8, 94, -95, 62, -37, -26],\n [50, -50, 73, 11, -31, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 5 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[71, -140, -8, 93, -62, -95],\n [11, -56, 52, -27, 46, -23],\n [36, -91, 27, 23, 1, -53],\n [21, -12, -48, 63, -66, -21],\n [36, -91, 27, 23, 1, -53],\n [-28, 16, 64, -84, 88, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[97, 108, 76, -13, 90, -26],\n [30, -6, -124, 96, 44, -4],\n [4, 33, 110, -73, -8, -4],\n [-83, -51, 90, -94, -94, 18],\n [39, 39, 14, 6, 38, -10],\n [80, 75, 10, 25, 80, -20]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-1, -47, -21, -22, -9, -59],\n [-96, 76, -97, -77, 31, 12],\n [91, -25, -4, -66, 52, 75],\n [131, -127, 11, -16, -75, 16],\n [10, 52, 51, 18, 85, 39],\n [16, -72, -100, -96, -58, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[55, 68, 12, -105, -38, 49],\n [80, -8, -139, 123, -135, -52],\n [21, 33, 26, -115, -17, 55],\n [-18, -101, -69, 33, -51, -14],\n [17, 59, 75, 60, 164, -81],\n [48, 49, -63, 141, -54, -56]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-29, -85, -56, -65, -24, -176],\n [2, -30, -80, -62, -1, -99],\n [-1, 36, 72, 71, 7, 123],\n [-7, -37, 24, -51, -29, -131],\n [10, 15, 80, -10, -20, -30],\n [-22, -69, -48, -58, -20, -150]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[59, -82, -96, 48, -63, 59],\n [-43, 32, 39, -30, 21, -43],\n [-39, 78, 90, -36, 63, -39],\n [74, -46, -57, 50, -28, 74],\n [-89, 10, 18, -52, -7, -89],\n [52, -26, -33, 34, -14, 52]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 2 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-133, -138, -131, -109, 33, 45],\n [170, 162, -7, -47, -144, -42],\n [65, 47, -52, -51, -38, -65],\n [-39, -73, 4, 64, 51, -24],\n [-20, -30, -37, -110, -28, 50],\n [166, 97, 76, 32, -148, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"... | 5 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-45, 15, 103, -45, 71, 42],\n [24, -54, -130, -17, -26, -37],\n [7, 15, 94, 40, -10, 10],\n [-52, -18, 59, -84, 91, 37],\n [-48, -42, 79, -86, 95, 35],\n [-18, 24, -74, -33, 14, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-66, 27, 153, 14, 100, 134],\n [1, -77, 35, -42, -56, -51],\n [35, 29, -21, 63, 3, 77],\n [8, -102, 42, -42, -62, -86],\n [20, -42, 0, -7, -49, -12],\n [98, -68, -50, 91, -33, -103]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 4 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[2, -7, 16, 30, -82, -52],\n [-26, -50, 74, 80, -62, 18],\n [12, 24, -36, -40, 36, -4],\n [8, 14, -20, -20, 8, -12],\n [42, 72, -102, -100, 30, -70],\n [-52, -76, 100, 80, 68, 148]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[2, -31, 58, -44, -13, -46],\n [-172, 151, -161, -54, -11, 116],\n [-186, 143, -44, 66, -171, -24],\n [-105, 66, -88, -173, 102, 127],\n [64, -38, 6, 7, 58, 21],\n [56, -58, 90, 11, 14, -39]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 4 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[96, 58, 104, 145, 48, 121],\n [-200, -27, 30, 47, -169, 75],\n [90, -31, 148, 126, 68, 39],\n [120, 35, 20, 49, 67, 21],\n [-84, -8, -35, -42, -53, -8],\n [8, 26, -105, -151, 71, -79]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-38, 64, -19, 67, 64, 56],\n [54, -60, 12, -68, -56, -64],\n [79, -60, -52, -44, -8, -110],\n [-5, -15, -7, -3, -6, -13],\n [42, -9, 24, -38, -26, -13],\n [60, -41, -93, -1, 38, -109]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-47, 108, 22, 45, 17, 51],\n [-19, 56, 25, 20, -2, 61],\n [-27, -24, 21, 30, 18, -21],\n [132, 8, -154, -150, -50, -80],\n [58, 124, -103, -75, -23, -10],\n [11, 116, -38, -20, -9, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-2, 17, -29, 10, 29, -24],\n [46, 34, 82, 44, -56, 66],\n [39, -80, 72, 53, -167, 12],\n [99, 4, -4, 118, -59, -59],\n [-24, 72, 20, -58, 96, 70],\n [77, 32, 28, 72, -25, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[39, 176, -27, -128, 7, 40],\n [38, -86, 88, -11, 70, -49],\n [-40, 63, -99, 56, -112, 35],\n [19, 55, 18, -140, 153, 73],\n [-24, -14, 5, -36, 54, 31],\n [-14, 91, -52, -133, -6, 91]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-60, -45, 26, -92, -23, 28],\n [0, -45, -36, 72, -27, -18],\n [-72, -93, 0, -48, -51, 18],\n [-6, 1, 7, -18, 1, 5],\n [30, 35, -3, 26, 19, -9],\n [84, 76, -26, 108, 40, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-86, 5, 24, -59, -34, 10],\n [-115, 0, 40, -80, -50, 20],\n [123, -9, -96, 71, 8, -30],\n [92, -54, -32, 42, -36, 20],\n [35, -34, 44, 22, 2, 32],\n [155, -71, 54, 101, 34, 50]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[94, 57, 117, 40, 111, -68],\n [66, 45, 78, 48, 63, -66],\n [-34, -21, -42, -16, -39, 26],\n [-22, -3, -36, 32, -57, -22],\n [-4, -12, 3, -40, 24, 38],\n [-52, -36, -61, -40, -48, 54]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-104, -48, -96, 32, 60, 68],\n [99, -27, 81, 48, -75, -3],\n [64, -48, 48, 64, -56, 24],\n [-30, 54, -18, -64, 34, -38],\n [9, -117, -9, 128, -35, 97],\n [-56, -84, -60, 80, 18, 86]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[18, 15, 15, -6, -18, -42],\n [41, -76, 34, -80, 6, 58],\n [63, -35, -55, 78, 52, -88],\n [-46, 12, 62, -96, -48, 96],\n [78, -87, -17, -2, 46, -18],\n [0, -41, 49, -94, -18, 86]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-16, -136, -5, 31, -7, -5],\n [-73, 19, -49, -66, -70, -78],\n [-60, 30, -27, -47, -65, -49],\n [-43, -12, -68, -201, -137, -83],\n [50, 0, 29, 63, 71, 46],\n [-27, 83, -16, -147, -121, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[4, 45, -85, 37, 47, 57],\n [28, -21, 29, -13, -39, -1],\n [26, -12, 13, -6, -28, 8],\n [54, -54, 81, -36, -90, -18],\n [-92, 36, -34, 16, 92, -36],\n [44, -30, 40, -18, -58, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-47, -64, 75, 22, 15, 51],\n [62, 46, -57, 55, -88, -6],\n [-36, -24, 30, -36, 54, 0],\n [-103, -8, 9, -94, 117, -33],\n [-51, 120, -147, -102, 57, -117],\n [-41, 80, -99, -62, 33, -75]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 3 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[39, 10, 19, 23, -35, -27],\n [16, -40, 31, -88, 21, -14],\n [-1, -45, 45, -42, 85, 72],\n [195, -103, 122, 18, -137, 90],\n [19, -51, 49, -56, 53, 50],\n [-51, 23, -78, -60, -60, -100]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 4 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[181, -73, -97, 6, 128, -83],\n [-143, 48, 172, 16, -107, 135],\n [81, 28, 78, -82, 2, -15],\n [4, 13, -194, -86, -83, -140],\n [-15, 44, -48, 60, -52, 30],\n [-55, -57, -152, -6, 10, -89]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 5 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[63, 9, 81, -45, 0, -45],\n [-19, 23, 135, -25, 0, -25],\n [-63, 11, 43, 15, 0, 15],\n [20, 20, 132, -40, 0, -40],\n [8, 4, 28, -10, 0, -10],\n [-80, 0, -32, 40, 0, 40]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 2 | MATH |
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