messages listlengths 1 1 | ground_truth stringclasses 11
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Determine the rank of the following matrix:\n[[-719, 12, -285, 31, -54, -71, 206, -484, -465, 247, 543, 410],\n [-817, 415, -461, -65, -263, 407, -251, -935, -432, -600, 257, 38],\n [-233, -15, -236, 183, 24, -101, 379, 19, -302, 432, 371, 221],\n [-48, -169, 680, -674, -55, 24, -1017, -543, 555, ... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[372, 449, -350, -78, -59, -109, -78, -16, -339, 5, 319, -88],\n [-464, -481, -523, -20, -521, -707, 330, 589, -687, -231, 596, -337],\n [840, 586, 489, 568, 174, 312, -258, -575, 362, 670, -313, 557],\n [1021, 814, -10, 495, -137, 64, -114, -396, -188, 689, 282, ... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-173, 359, -548, 222, -734, -46, 386, -545, -332, -978, -128, 1018],\n [323, -701, 176, -156, -289, -236, 358, -187, 290, 123, -271, 92],\n [465, -701, 114, -292, 331, -331, -133, 204, 124, 435, 108, -530],\n [510, -260, -986, -174, -25, -677, -179, -... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-237, 246, 426, 474, 459, 309, 612, -261, 582, -621, -72, -63],\n [416, -572, -416, -520, -624, -338, -546, 156, -520, 624, -78, 78],\n [-145, 84, 418, 438, 367, 286, 625, -303, 594, -601, -141, -54],\n [-154, 194, 196, 232, 254, 151, 269, -96, 256, -290, 3, -33]... | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-1107, 314, -610, -864, -1568, -585, 1708, 44, 221, -34, 190, 744],\n [-576, 207, 47, -126, 718, -805, 1013, -708, -105, 374, 1004, 64],\n [854, -568, 106, -94, -64, 6, -78, 590, 756, -427, -1183, -629],\n [1156, -774, -76, -911, 311, -182, -55, -575, 38... | 7 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[802, -511, 391, -298, -539, 348, -1238, 594, -83, -145, -331, -30],\n [238, 779, 122, 566, -578, 680, -362, 1014, -1084, 1326, 970, -432],\n [-117, -20, 1243, 271, 96, -570, -1046, 705, -2443, 234, -32, -1185],\n [-911, 1269, 827, -830, 624, -805, 1444, -696, -14... | 9 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-1038, -1, -241, -472, 234, -581, -712, 358, 378, -73, 339, -748],\n [-841, -37, -281, -682, 456, -397, -647, 444, 424, -233, 647, -606],\n [-323, -608, 237, 773, -2, -654, 481, -31, -354, -203, 1260, -515],\n [-337, -769, -424, -706, -150, 307, -1180, 925, 1116, 87... | 7 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[637, 92, -372, -555, -178, -289, 166, -424, -543, -623, 535, 558],\n [720, -512, -64, -12, 148, -968, -644, 364, 340, -412, 940, 412],\n [-297, 252, -930, 49, -153, 520, 1107, -1209, -217, -53, -265, -72],\n [182, 384, -236, 502, -602, -228, 414, -330, -78, 26, 6... | 4 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-198, -391, 414, 1089, 945, -64, -277, -720, 143, -420, 249, 236],\n [-1048, -514, 530, 684, 380, -986, 469, -256, -372, 486, 323, 1275],\n [-718, -473, 40, -144, -226, -1207, -509, -156, 145, -83, -632, 940],\n [433, 222, -495, 410, 592, 63, -693, -3... | 7 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[289, 85, 408, 34, 306, 442, 391, 0, -17, -408, -17, 204],\n [323, 95, 456, 38, 342, 494, 437, 0, -19, -456, -19, 228],\n [102, 30, 144, 12, 108, 156, 138, 0, -6, -144, -6, 72],\n [-51, -15, -72, -6, -54, -78, -69, 0, 3, 72, 3, -36],\n [-289, -85, -408... | 1 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-1784, 305, -297, 614, -2026, 311, 249, 830, 844, -302, 71, -1013],\n [193, -1160, -412, 1394, -128, 1010, 348, 406, -800, 730, -798, 1312],\n [-904, -101, 374, 723, -547, 249, 599, 474, 255, -68, -108, -500],\n [-403, -949, 133, 132, 1528, -261, 95, -918, -1052,... | 7 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-24, 0, -7, -9, 11, 6, 11, 10, 12, 14, -6, 22],\n [-480, 0, -140, -180, 220, 120, 220, 200, 240, 280, -120, 440],\n [-336, 0, -98, -126, 154, 84, 154, 140, 168, 196, -84, 308],\n [-336, 0, -98, -126, 154, 84, 154, 140, 168, 196, -84, 308],\n [600, 0, 175... | 1 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-339, -515, 469, 739, -554, 132, 381, 219, 431, 257, 506, -521],\n [87, 402, -189, -261, 234, -203, -263, -138, -30, -128, -68, 317],\n [-113, 326, 372, -11, -446, -27, 357, 412, -348, 89, -247, 182],\n [750, -301, -368, 73, 1383, 700, -474, -1094, -375, -539, 10... | 5 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[548, 415, 79, 213, -685, 213, 123, 400, -565, 58, 239, 261],\n [485, -39, 20, 363, -81, 421, 7, -287, -990, 204, -624, 246],\n [1019, 465, 855, 612, -1365, 126, 185, 35, -616, -118, 395, 1309],\n [-1078, 418, -1040, -210, 1060, -1744, -1230, -966, 116... | 7 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[826, 822, -858, -1347, -205, -41, -1205, 527, -1089, 579, 742, -278],\n [-321, -85, -392, 441, -509, -154, -257, -835, 802, 152, -85, 351],\n [-235, 312, 400, -436, -530, -290, 390, 132, 92, -418, -11, -168],\n [122, -175, -94, 542, -72, 714, 20, 33, ... | 9 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-251, 182, 498, -147, 159, 350, -102, -147, -221, 195, -415, 233],\n [348, -398, -593, 536, 360, -493, 7, -257, 585, 152, 486, -9],\n [270, -300, -654, 250, -394, -351, -21, 467, 513, -92, 492, -470],\n [200, 48, -388, -236, -644, -251, 87, 541, -139, -532, 402, ... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[104, 282, 317, 306, -203, 9, 526, -261, -468, 310, -158, 158],\n [888, -196, 679, -276, 619, 392, 242, 213, -49, 310, 402, -597],\n [-176, 910, 428, 462, 272, 155, -122, -132, -803, 290, -302, -47],\n [-24, 382, -6, -110, -614, 84, 359, -668, -560, 283, ... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-502, 581, -277, -183, 287, 121, 410, -221, 246, -549, -420, 155],\n [-536, -33, -271, 474, 295, 471, -349, -915, 739, 290, -316, 103],\n [617, 372, -833, 61, 995, 79, 257, -202, -13, -396, -127, 951],\n [452, 326, -1631, -755, 21, 146, 197, -899, 470, -643, -321... | 7 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[437, 207, -230, 322, 69, 575, -276, -161, 207, -575, 414, -529],\n [228, 108, -120, 168, 36, 300, -144, -84, 108, -300, 216, -276],\n [-475, -225, 250, -350, -75, -625, 300, 175, -225, 625, -450, 575],\n [342, 162, -180, 252, 54, 450, -216, -126, 162, -450, 324, ... | 1 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-1162, 662, 488, -574, -227, -1522, 183, -852, 231, -667, 21, 226],\n [230, 352, -396, -637, -991, 446, -1007, 634, 270, -416, -288, -603],\n [-864, 654, 593, -737, -44, -457, -417, 404, 928, -1440, -836, 816],\n [525, -114, 220, 414, 17, 411, 246, 1510, 858, -45... | 6 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[119, 276, -250, 540, 102, -104, -653, 402, -413, 236, -326, -156],\n [-152, -29, -155, 281, 231, 157, -323, 221, -253, -151, -354, -107],\n [-194, -237, 665, -759, -265, -561, -159, -555, -109, 471, 314, -559],\n [-413, -183, -383, 555, 579, 569, -412, 441, -382,... | 3 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-382, 102, 16, 200, -191, -117, 197, -236, -328, -490, 155, 268],\n [110, -217, 114, 31, 262, 118, 223, 412, 168, -258, -310, -215],\n [-403, 577, 120, 338, -190, -79, 124, -298, -694, 165, 745, -6],\n [297, -224, 54, -109, 275, 140, 24, 398, 322, 93,... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[980, 198, 744, 1792, -732, 1759, -189, -767, 84, -19, 687, -299],\n [499, -828, 729, 1154, -103, 741, -40, -292, 788, 954, 670, -360],\n [496, 544, -297, 24, 251, 528, -1145, -47, 201, 493, -20, -679],\n [-724, 250, -949, 29, -1193, -55, 1776, 947, -1052, 137, 552, ... | 9 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[1180, 404, 1250, -404, 663, -454, 678, 321, 366, -620, 1155, -1068],\n [63, -261, 1419, 1012, -318, -131, -804, 972, 45, -183, 604, -410],\n [-161, -397, 31, 756, -43, -413, 572, 41, 269, -139, -1541, 88],\n [1458, -96, 461, -224, 624, -1450, 379, 668... | 7 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[162, -588, -445, 544, 525, -1187, 1012, -709, 548, -479, 419, 1183],\n [-593, -535, -230, 296, -118, 422, 1278, -1, 1020, -1677, 768, 420],\n [-432, -736, 2213, 724, 797, -570, -171, 779, 1830, -750, 588, -996],\n [606, -153, 935, -196, -714, -249, -258, -347, 710, ... | 10 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[386, -136, 395, 353, 21, 162, -26, -8, -2, -95, 290, -466],\n [60, 76, 71, -53, -265, -20, -56, -34, 46, 5, -130, 36],\n [-207, -30, -222, -75, 273, -39, 69, 39, -48, 30, 30, 135],\n [-429, 222, -432, -471, -219, -213, -9, -15, 36, 120, -450, 597],\n [585, 10, 62... | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[874, 674, -92, 212, -104, 340, 164, 116, -782, 180, 854, -528],\n [-184, 85, 449, -452, -340, 215, -584, -212, -112, 450, -1094, 942],\n [-538, -513, 1, 44, 176, -305, -48, 24, 526, -222, -348, 174],\n [607, 570, 545, -41, -377, 455, -723, 42, -907, 663, -513, 67... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[290, 480, 837, -258, -19, 214, -445, 274, 274, 122, 512, -493],\n [9, -282, 325, 149, 683, -20, 263, 555, -116, 518, -211, -206],\n [-42, 64, -243, -66, -283, 26, -29, -210, -42, -218, 60, 123],\n [242, 736, 458, -644, -622, 554, -446, 190, -78, -242, 930, -458],\n ... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[222, 9, 270, 263, 550, 557, 80, -45, 554, 444, -739, 278],\n [-472, -471, -37, -215, -1185, -553, 83, 246, -494, -295, 352, -655],\n [516, -298, -265, 182, 425, 578, -137, -203, 102, -65, -539, 229],\n [485, -80, -669, 100, -407, -934, -35, 697, -173, 46, 835, -1... | 5 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[686, -503, -347, -218, -1018, -79, -182, -202, 737, -838, 931, 414],\n [643, -516, -492, -441, 12, -427, 306, 488, -517, 786, 395, -731],\n [-260, -36, 633, -168, 485, -625, -359, -380, -30, 833, -152, -763],\n [678, -15, -40, 203, -546, -373, -875, -... | 6 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-401, 559, -1228, 345, -759, 1178, 521, -117, 13, -699, -15, -106],\n [216, 1161, -27, 837, -1264, -447, -172, 348, -104, -596, 225, 1182],\n [743, 353, 948, 166, 710, 976, 773, -233, -489, 319, 126, 503],\n [610, -56, 405, 864, -117, 234, 477, -365, -25... | 8 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[126, -1042, -1029, 1185, -123, 269, 215, -80, 459, -277, -709, -709],\n [-202, -604, -824, 658, -183, -106, 72, -145, 499, -105, -559, -507],\n [481, -852, -605, 976, 216, 186, -298, 252, 626, -692, -163, 277],\n [-361, 420, -27, -292, 544, -432, 1166, 34, -738, ... | 6 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-388, -292, -422, 123, -1325, 133, 211, 756, -279, 108, 441, -120],\n [-350, -260, -194, -64, -924, 295, -194, 902, -89, -459, 348, -584],\n [-161, 137, -305, -381, -462, 151, -285, 1067, 237, -934, 252, -620],\n [-574, -499, 740, 280, 111, 734, -253, -110, -1036... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[175, -626, -268, 18, 967, -168, 767, -620, 749, -631, 1058, 112],\n [-201, -423, 386, -202, 368, 746, 331, -458, -59, -60, -329, -343],\n [-112, -260, 192, -474, 56, -79, 206, -67, 60, 143, 8, -50],\n [28, -956, 126, -552, 366, -19, 488, 37, -116, -43, 396, 370],\n ... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-339, 331, 491, -687, -277, 154, 530, -362, -322, -329, 81, -620],\n [324, 336, 79, 925, -369, -27, -463, 276, 580, -244, 564, 20],\n [111, 196, -708, -448, -298, 1060, 478, -529, 128, -495, 237, -498],\n [-618, 209, 405, 123, 304, -120, 689, 1275, 295, 978, -18, 15... | 8 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[29, -1196, -1053, 37, -1276, 939, -497, 1706, -793, 497, 121, -696],\n [489, 228, -264, -421, -906, -333, 127, 877, -701, -35, -793, -605],\n [-707, -268, 808, -310, 91, 1114, 1592, 168, 95, -364, -882, -139],\n [411, 39, -236, -396, 773, 155, -217, -300, 215, -378,... | 9 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-135, -85, 282, 105, 1007, -221, -992, 100, 251, -345, -102, 386],\n [481, -201, 91, -193, -547, 246, 461, 128, 190, -142, 173, 93],\n [-491, 174, 597, 638, -1274, -497, 64, 195, -190, 216, 454, -29],\n [259, -407, 112, -723, -370, 284, -110, 1053, 53... | 6 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-849, -144, -791, -785, 467, -1047, 141, -480, 1898, -1459, -1387, -382],\n [565, -439, 716, 36, -1421, 1068, 536, 732, -442, -356, -228, -1694],\n [394, -436, -647, 384, -238, 370, -654, -1092, -343, 909, -69, 140],\n [1586, 1187, 477, -1072, 562, 466, -1593, 27, -... | 11 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[1200, 928, -1192, 284, -70, -218, 42, -429, 37, 409, 451, 1653],\n [159, -417, -386, 156, 727, 705, 343, 468, -310, 453, -174, 424],\n [1712, 100, -1732, -440, -351, 486, 1375, -1032, 320, 365, -121, 673],\n [723, -682, 185, -676, 459, 319, -561, -754, -461, -448, 8... | 11 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[108, 9, -9, 144, -54, -36, -54, -144, 135, 108, -99, 54],\n [132, 11, -11, 176, -66, -44, -66, -176, 165, 132, -121, 66],\n [-228, -19, 19, -304, 114, 76, 114, 304, -285, -228, 209, -114],\n [144, 12, -12, 192, -72, -48, -72, -192, 180, 144, -132, 72]... | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-58, -557, 212, 502, 998, -648, -449, 498, 273, 93, -289, 204],\n [700, 552, -277, -803, -1005, 1084, 129, -313, 51, 213, -51, 204],\n [86, 161, 277, -508, -519, 544, 281, -513, -471, 75, 309, -185],\n [-38, 629, 342, 351, -178, 12, 611, -769, 489, 423, -868, -136],... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-1213, 315, -126, 846, -342, 870, 1207, -2122, -371, -941, 1454, -163],\n [1001, 1324, 246, -128, 1408, 301, -714, -1320, 984, -893, 640, -982],\n [-280, 59, 904, -31, -1575, 565, 645, -598, 794, -52, 179, -37],\n [-436, 56, 1239, -810, -655, -410, 35... | 10 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[878, -847, -1169, 501, 425, -430, 591, -1241, -452, 276, 674, -139],\n [-202, -384, -323, -40, -329, -773, 266, 131, -94, -582, -36, -68],\n [185, -150, -280, -450, 215, -405, 495, -585, 15, 70, -355, 25],\n [-432, -353, -246, -436, -457, -1138, 449, ... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[582, -601, 587, 1092, -587, -2, 1431, 681, -216, -2229, -1287, 698],\n [-669, -528, -860, 100, -338, -545, -1063, -825, 433, 166, 1013, -373],\n [-110, -427, -331, -372, -515, 49, 365, 576, 422, -77, -670, 148],\n [-388, -417, 264, -290, -482, -28, 1451, 1049, 102, ... | 8 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[741, 219, -1036, -365, -605, 200, -691, 906, -296, -549, -309, 40],\n [-1223, 140, 286, -627, -274, 152, 273, -471, 276, 212, -478, 869],\n [-371, 76, 93, -659, 225, -186, 156, -964, 162, 188, 587, -370],\n [182, -478, 132, 453, 1146, 653, 1136, -997,... | 10 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[569, -179, -588, -493, -538, -864, 68, 277, 1252, 388, -1164, -883],\n [-518, -11, -618, 249, -165, 525, -941, 419, -281, 564, -111, -232],\n [-143, -153, -201, 319, -93, 380, -17, -146, -348, 57, 451, 617],\n [475, 1592, 938, 732, 424, -707, 97, 125, 35... | 8 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[882, -331, -300, 713, 216, -569, -197, 489, -361, 410, 207, -69],\n [1047, -365, -488, 1017, 346, -729, -690, 1154, -38, -215, 307, -173],\n [499, 142, 659, 191, 25, -906, 222, -143, -988, 1305, 683, -451],\n [-259, 944, 200, 359, 54, -171, -883, -283... | 6 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-105, 999, 312, 129, 246, -706, 310, 1318, 283, 370, -646, 1253],\n [2, -879, 452, -254, 894, -1, -1339, -149, -738, -553, -1371, -751],\n [678, 1244, 383, 172, 225, 805, -838, 504, -938, -698, -1016, 418],\n [-151, -1281, -463, -382, 468, -358, -285,... | 10 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-448, 317, -188, 633, -107, -272, -175, -186, 500, 225, 683, 59],\n [440, -319, 232, -621, 142, 295, 206, 198, -505, -237, -691, -106],\n [360, -163, -416, -517, -356, -115, -268, -34, -235, 11, -307, 528],\n [-216, 78, 372, 312, 309, 141, 249, 60, 10... | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[629, -168, -751, 130, 415, -622, 77, -504, 881, 424, -630, -26],\n [283, -307, 327, 946, -386, 1121, -220, 691, -129, -1348, -71, -25],\n [-253, 259, -359, -667, -749, -944, -437, -340, 505, 286, 351, 483],\n [-453, 211, 971, -169, -332, 116, 515, 660, -1060, 715, -... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-482, -294, 799, -893, 295, -1001, 1031, 533, 700, 1133, 319, -29],\n [-46, -1255, 992, 3, -276, -668, -5, 124, -69, 897, 828, 541],\n [741, -166, 598, 535, -342, -659, -734, -406, -772, -797, -449, 839],\n [135, 111, -326, -8, -808, -904, -42, 981, 346, 2, 208, -74... | 10 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-379, 491, 136, 857, -230, 789, -1043, -325, -70, 156, -1400, 219],\n [-1369, 125, 307, 347, -479, 318, -845, 80, 245, 675, -488, 411],\n [796, -216, -469, 72, 223, -521, 576, 15, -145, -571, 498, -326],\n [503, -1007, -1459, -109, -449, -496, 19, -17... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-994, -368, 457, 1144, -2061, 483, -538, 411, 126, -150, -720, 273],\n [958, 570, 780, -340, 1988, -51, 136, -142, -605, -247, 1290, 223],\n [904, 72, -928, -1455, 678, -632, -91, -1, 793, -464, -159, -488],\n [-23, -1248, -528, 379, -1719, 67, -122, -573, 1105, ... | 11 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-532, 669, 391, 12, -132, 372, -436, 85, 97, 267, 1630, -508],\n [570, 370, 80, 386, -937, 840, 1281, 1186, -1315, 775, -378, -551],\n [-549, 1309, 48, 414, -683, 395, -341, -10, -1119, 683, 1361, -740],\n [-565, 541, 14, -723, 12, -165, -502, 124, 44... | 7 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-96, -48, -240, -240, -312, -108, -228, -24, 180, 24, -48, 24],\n [-636, -296, -424, -138, -10, 258, 134, 94, 538, -292, -164, 500],\n [-208, -100, -308, -256, -302, -57, -195, -6, 271, -30, -76, 114],\n [178, 84, 180, 115, 111, -21, 49, -13, -185, 58... | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-711, 1079, 126, 294, -761, 207, 674, 425, 200, 366, 26, 1483],\n [2023, -613, 415, -1524, -745, 1120, 1061, -706, -1261, 1062, -1185, -820],\n [1100, 309, 235, -691, -871, -39, -236, 1192, -1334, 1119, 255, -871],\n [-318, 438, 687, 367, 152, -690, 2... | 11 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[108, 566, -154, -124, -220, -164, -544, 236, 234, -198, -516, 184],\n [476, 345, -373, 366, -424, 312, -582, 598, 227, -153, -722, 604],\n [-504, -204, 372, -456, 408, -408, 480, -600, -180, 108, 648, -624],\n [446, 594, -388, 228, -466, 162, -774, 616, ... | 2 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[243, -309, 375, -473, 1304, 763, 76, -49, 575, 424, -459, -873],\n [-449, 1554, 225, 126, 213, 241, -66, 542, -219, 571, 321, -2160],\n [-1003, 422, -1250, 147, 2, -279, -190, 566, 460, 1128, -937, -346],\n [797, -539, 410, -48, -46, -98, -738, 229, -... | 11 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-74, 230, -44, 90, 152, -308, -236, -44, 332, -138, -164, 22],\n [520, -500, 680, -80, -300, 140, 860, -20, -320, 160, 320, -60],\n [-632, 585, -834, 86, 349, -129, -1029, 31, 348, -178, -372, 71],\n [43, -325, -38, -147, -220, 526, 274, 82, -538, 219... | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-56, -112, -161, -28, -154, 182, 154, 161, -154, -63, -70, -168],\n [152, 304, 437, 76, 418, -494, -418, -437, 418, 171, 190, 456],\n [56, 112, 161, 28, 154, -182, -154, -161, 154, 63, 70, 168],\n [-24, -48, -69, -12, -66, 78, 66, 69, -66, -27, -30, -72]... | 1 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[784, -576, -1125, -120, 970, 463, -1089, 153, 191, -220, -365, 437],\n [-1423, -236, -193, -145, 1445, 1619, 882, 492, -566, 368, 206, -60],\n [2038, -661, -1288, -216, 507, 263, -469, 964, 806, -323, -168, -670],\n [-557, 1109, 24, 526, -761, -855, -389, 20, -12... | 9 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-50, -763, 671, 658, -663, 1182, 1157, 510, -475, 1187, -1470, 241],\n [1342, 325, 449, 350, 1061, -588, 1223, 69, -321, 651, 107, 539],\n [182, 127, 340, -839, -544, -1137, 643, 977, 933, -1464, 809, -973],\n [-339, 558, 856, -592, 1697, -402, -1034, -1... | 11 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[398, -446, 248, -128, -420, -212, -24, 416, 300, 424, -202, -132],\n [-425, 395, -20, 410, 105, 200, -15, -545, 30, -505, 460, -135],\n [-114, -10, 344, 500, -462, 16, -62, -290, 508, -210, 472, -430],\n [-133, 245, -372, -280, 546, 102, 56, -20, -514... | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[996, -80, 1102, -768, -854, -324, 178, -855, -239, 582, 691, -91],\n [736, -1261, -941, -112, 1002, 286, -1385, 409, 790, -1087, 354, 76],\n [-333, -1011, 1024, 215, -756, -172, -159, -1047, -2013, 1607, 602, -108],\n [780, -989, 162, -637, -1281, 122, -... | 11 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[266, -98, 126, -224, -70, -308, 238, -98, 56, 112, 98, -350],\n [57, -21, 27, -48, -15, -66, 51, -21, 12, 24, 21, -75],\n [266, -98, 126, -224, -70, -308, 238, -98, 56, 112, 98, -350],\n [-399, 147, -189, 336, 105, 462, -357, 147, -84, -168, -147, 525],\n [-342, ... | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-598, 1223, -59, -43, 768, 1448, -1006, -1176, -119, -258, -702, 1231],\n [-527, -337, -790, -966, -515, 1046, -1484, 702, 487, 606, -220, 1177],\n [972, 912, -489, -111, 978, 1151, -532, 1499, 643, 163, 27, -259],\n [-784, -746, 349, -480, -556, 122, -911, -855, -1... | 8 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[857, 442, -67, -535, 207, -627, 577, 946, 815, 239, -658, -216],\n [-75, 307, -84, 135, 223, 216, 419, 561, 460, 685, -878, 642],\n [-937, 98, 1097, -30, 253, -167, -40, -51, -619, -191, 209, 343],\n [-903, -680, 156, 275, -72, -1171, 526, 35, 880, 301, ... | 7 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-4, -237, -475, 437, -920, -19, 420, 135, -526, -82, 565, 1521],\n [129, -21, 582, 1007, -204, -204, -530, -1169, -543, 88, 1001, 627],\n [896, -9, 725, 388, -309, -1063, 567, -300, -1452, 302, 1349, 754],\n [798, 379, 740, 235, -625, -20, 346, 538, -1078, 703, 8... | 11 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[15, 64, 354, 1, 474, -114, -240, -399, 686, 118, 34, -402],\n [168, 277, 162, -158, 24, 66, -153, 120, 521, 199, 178, -156],\n [246, 407, 162, -244, -24, 114, -171, 222, 679, 269, 254, -156],\n [75, 54, 472, 54, 45, -6, -368, 82, 322, 209, 131, -371],\n [-435, -9... | 3 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[613, -1008, -216, 969, -716, 97, 1026, 1046, -219, -132, 401, -954],\n [-80, 333, 159, -252, 256, 82, -258, -262, 18, -15, 29, 99],\n [341, -285, 131, 277, -169, 306, 295, 183, -299, 210, 33, -390],\n [-604, -111, -647, -88, -199, -857, -121, 107, 596... | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-1220, -864, 232, -1308, 264, -120, -666, 1253, 200, -679, 1165, -1218],\n [325, 1810, 187, 1676, -505, -668, 73, -517, 34, 83, -355, 762],\n [674, 525, -278, 1049, -417, -585, 857, 110, 505, -612, -192, 236],\n [693, 206, 371, 194, -626, -1204, -477, -6... | 11 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[772, -342, -980, 663, -334, -563, -203, 260, 462, -96, 17, -78],\n [-387, 307, 265, -623, -26, -970, 9, -380, -1306, 748, -1103, -1353],\n [-860, 488, 1485, -1641, 44, 212, 350, 1074, -552, 901, -1002, -451],\n [923, 482, -864, -1181, 327, -608, 297, ... | 10 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-498, 216, 281, 253, -327, 45, -517, 246, 128, 274, 135, -57],\n [-285, 426, 484, 418, -65, -45, 149, 16, 98, 893, 409, -885],\n [311, -524, 365, 239, -47, -22, -106, -861, 274, 377, 364, 730],\n [-794, 165, -13, -1125, -376, 492, -526, 167, -1105, 130, -106, -12... | 8 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[914, 661, 140, -137, -127, 560, 136, 473, 418, 503, -270, -578],\n [-750, -428, 1289, -238, -670, -1133, 752, -1499, -1163, -686, 115, 114],\n [175, 217, 357, 357, 877, -430, 373, 306, -105, 168, 722, 447],\n [-363, -163, 527, 140, -514, -696, 1196, 4... | 7 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-284, 654, -583, 154, 249, 530, -1095, -129, 293, 832, -465, -407],\n [0, 72, 950, 462, -531, -1012, 650, -303, -573, -1413, -113, 325],\n [128, -396, -949, -316, 369, 881, -263, 288, 637, 1151, 326, -239],\n [104, 312, -355, 208, -1, -67, 298, -70, 564,... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[692, 488, 72, 772, 5, 207, 195, -327, 158, 18, -221, 408],\n [-678, -554, -875, -571, 787, -1337, 625, 1068, -445, -896, 784, 47],\n [329, 343, -88, 374, 35, -302, 58, -75, -229, -266, 181, 476],\n [-704, 4, 509, -495, -22, 174, -588, -9, -429, 190, 321, 103],\n [21... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-176, -643, -166, 512, -71, 148, -239, 172, -122, -226, -503, 426],\n [-772, 427, 268, -240, 578, -788, 246, 317, -547, -1339, -661, -328],\n [-1301, 308, -1032, 1161, 113, -585, 193, -110, -1023, 213, -985, -857],\n [-287, 675, 348, 484, -1111, 99, -373, -43, 20... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[188, 99, -57, -412, -271, 371, 422, 573, 284, -360, 374, -385],\n [451, 434, -378, -374, -259, 564, 539, 18, 102, -192, 171, -20],\n [-71, 676, -77, -600, -835, 360, 568, 164, 27, -960, 735, -756],\n [127, -468, 15, 201, 445, -112, -242, 267, 137, 516, -348, 300]... | 4 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[1301, 419, -409, 105, -1298, -234, -599, 81, 453, -975, -206, -465],\n [916, 878, -473, -698, -644, 1477, -550, -782, -580, -755, 1008, -579],\n [-1164, 282, 1008, 926, 502, -225, 299, 694, -49, -441, -586, 813],\n [1577, 2444, 654, 1257, 1076, -1217,... | 10 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[1056, -878, -1185, 159, 13, -1619, 555, 379, -1177, 266, 951, -363],\n [470, 1259, -406, 148, 338, 276, -608, 162, 119, 1305, 1378, 107],\n [254, 161, -1330, 762, 153, -1387, -623, 24, -502, -18, 400, -459],\n [-619, -333, 1366, 587, 994, 1367, 900, 545, 482, -75... | 11 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[262, -61, -163, 270, -235, -200, 527, -296, 509, -131, 278, 485],\n [-1186, 406, 154, 565, 290, 610, 568, -193, 690, -588, -745, -122],\n [-813, -348, -221, 393, -605, 470, 384, 378, -698, -600, 173, 192],\n [74, 495, -611, -596, 505, 127, 61, 83, -482, -281, 80, 40... | 6 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[291, 509, -191, -34, -63, 523, -12, -1116, 932, -1206, -770, -788],\n [-1368, 542, -56, -359, 449, 337, -541, 668, 317, 727, 619, 333],\n [-535, -697, -842, -809, -75, 799, 262, -913, 200, 37, 31, -450],\n [3, -472, -505, 755, -647, 752, -396, -413, 712,... | 8 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-710, 165, -174, 230, -359, 237, 112, 630, 293, -1, -56, 902],\n [762, -349, 253, -128, -3, -591, 0, -555, -435, -115, -510, -538],\n [450, 32, -368, 838, -312, 210, -300, -66, -666, -166, 120, -496],\n [-394, 98, 342, -994, 694, 48, 196, -100, 764, 272, 372, 52]... | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-422, -370, 191, 75, -284, 90, 206, -83, -35, -445, 50, 165],\n [554, -89, -27, -370, 780, -845, 177, 715, 530, -413, 582, -202],\n [76, 447, -28, -15, -224, 475, -275, -338, -345, 764, -466, 11],\n [174, -90, -456, 519, 123, 177, 225, -162, 333, 393, 66... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-790, -374, -605, 739, -654, -494, -108, 237, 1075, 18, 564, -315],\n [147, -251, -958, 268, 173, 368, 2, 410, -280, 367, 879, -538],\n [547, 266, 515, -479, 728, 732, 594, -25, -834, 359, -446, 658],\n [-587, -28, 423, 239, -487, -730, -87, -190, 1105, ... | 5 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-651, -112, 69, -41, 447, -159, 480, -288, 830, 1148, 639, 498],\n [-664, 44, 236, 503, -472, 698, 929, -122, 747, -42, 1146, -352],\n [739, -810, -1212, 245, -702, -778, -2070, 412, -251, 154, -810, 210],\n [-425, -169, -143, 385, -360, 332, 130, 41,... | 5 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-551, 110, 423, 200, 148, -356, 43, 443, 60, 310, -135, -48],\n [121, 499, 268, -26, -508, 713, 26, -682, -34, 641, -137, 301],\n [580, -34, 63, -199, 230, 571, 421, -957, -414, 629, 580, 746],\n [-234, 930, 22, 192, -1132, 778, -748, -182, -118, -126... | 5 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[180, 36, -18, -36, 144, -54, -99, -207, 144, 171, -171, -189],\n [-460, -92, 46, 92, -368, 138, 253, 529, -368, -437, 437, 483],\n [-340, -68, 34, 68, -272, 102, 187, 391, -272, -323, 323, 357],\n [-200, -40, 20, 40, -160, 60, 110, 230, -160, -190, 19... | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[85, -195, 767, -1242, 619, -216, 480, 240, -466, -1176, 974, -500],\n [-452, 150, 299, -201, -80, -741, -349, -361, -690, 300, 503, 767],\n [835, -110, 612, -542, 749, 104, 560, -495, 399, -191, 244, 185],\n [987, -225, 579, -471, 1008, 423, 799, -452, 623, -618, 54... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-1172, -115, 84, 849, -280, -757, 70, 742, 1031, 585, 115, 753],\n [-135, -251, 343, 339, -215, -286, -235, -56, 421, 100, 345, 493],\n [278, -305, 819, 239, -202, 133, -475, -269, 552, -228, 1032, 669],\n [67, -180, -294, -64, -207, -363, 20, -283, -375, 82, -58... | 4 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-37, 217, -105, 489, 137, 388, -578, 187, 452, 231, -469, 179],\n [15, 119, -57, 245, 1425, 375, 683, -205, 400, 1382, 63, -98],\n [-685, 95, -205, -955, 1, 436, 733, -1097, -293, 311, 1017, -367],\n [-288, -241, 323, 136, -18, 319, -13, -442, 1126, 6... | 8 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[227, 200, -397, -919, 88, -3, -536, -484, 542, 364, -249, -501],\n [100, 345, 48, 738, 314, 356, -4, 551, -587, -174, 262, 711],\n [322, -217, -325, 497, 244, 469, -378, 487, -361, -197, -364, 268],\n [-246, -443, -91, 47, 1340, 1227, -686, 373, -803, -495, -560,... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[672, -238, -1824, -45, -590, 248, 646, -434, -184, -766, -609, 1024],\n [-8, -708, 871, -481, -327, 135, -1237, 360, 118, 1044, -82, -1320],\n [-75, 1439, -47, -1285, -2078, 625, 1109, -758, 1230, -1141, 456, -1227],\n [198, 350, -1024, -109, 1080, -732, 94, -182... | 11 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-65, 10, 495, 734, 498, 47, 821, 560, -499, 155, 413, 670],\n [393, 718, -1007, -407, -349, 43, -213, -1169, 187, 401, -202, -463],\n [334, 112, -475, -693, -110, 26, 212, 686, -271, -191, -258, -62],\n [372, 434, -83, 1213, 356, -194, 155, -754, 417, 373, 111, 770]... | 8 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[303, 629, -60, 74, 558, 479, 158, 265, 194, -583, 627, 911],\n [406, 306, -312, -540, 236, 342, 332, -390, 84, -230, 350, 86],\n [83, -179, -168, -398, -182, -65, 122, -415, -62, 201, -149, -493],\n [615, 356, -519, -946, 255, 458, 527, -740, 92, -238, 4... | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[123, 1003, 506, -327, 15, -710, -187, 77, 591, -337, 1148, 525],\n [413, -315, 85, -368, 152, 168, -44, 905, -148, 273, 230, 707],\n [458, -1073, -24, 115, 67, 788, -269, 1181, -306, 673, -211, 579],\n [52, 598, -485, 299, -311, -494, 139, -816, 19, -706, -48, -4... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[319, 621, -1071, 576, 221, 80, 407, 566, -598, -783, -244, 293],\n [-267, -138, -542, -355, 428, 598, 169, 677, -533, -621, -791, 883],\n [230, -186, 595, 91, -204, -295, -202, -500, 334, 405, 479, -516],\n [-250, 261, -14, 460, -663, -753, -356, -477, 6... | 4 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[531, -97, -610, 478, 1143, -82, 671, 14, -542, -990, 1019, -475],\n [-552, -468, 691, 814, -289, 1625, 283, 159, 194, -334, -178, 444],\n [381, 1187, 525, -83, 806, 84, 1263, 410, -644, 767, -409, 702],\n [2080, -758, -293, 430, 204, 365, 107, 559, -2... | 11 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[757, 498, 454, -330, -939, -948, -181, -195, -555, 213, 403, -640],\n [-167, -634, 83, 568, 1145, 985, 979, -661, -832, 1085, -886, -104],\n [336, 754, -307, -220, -763, -446, -317, 271, 222, -263, 331, 411],\n [-284, -500, 273, -745, 707, 436, 595, 199, 260, -30... | 6 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-1016, -97, -25, -833, -129, 151, 157, 1029, -206, -126, 422, 393],\n [-688, -322, 452, -262, 295, 29, -1617, 196, -197, -443, -1408, -982],\n [-235, 583, 91, -1366, -757, 424, -45, 154, -522, -768, 189, 772],\n [-14, -400, 128, 256, 25, 45, 292, 208,... | 9 | MATH |
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