messages listlengths 1 1 | ground_truth stringclasses 11
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-636, -901, 296, -977, 44, 132, 853, 331, 2, -1058, -58, 828],\n [1044, 1247, 873, 434, 638, 430, 43, -53, 500, -142, -300, -954],\n [-1281, -1237, 280, 124, -677, -431, 486, -310, -570, 1360, -331, -399],\n [196, -219, -704, 56, -233, 378, 950, -468,... | 9 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[139, 350, 315, -862, -287, 963, -142, -311, -536, -657, 361, -268],\n [-331, 148, 232, 400, -332, 112, -513, 46, 65, 449, 99, 232],\n [195, 14, -239, 17, 56, -169, 521, -199, 131, -46, -185, -202],\n [-4, 280, 226, -589, -39, 702, 431, -516, -443, -477, ... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[1114, -964, 541, 518, -320, 30, 103, 272, 725, -400, 686, 226],\n [904, -570, 474, -48, -243, -116, 132, 175, 326, -821, 842, -152],\n [233, 137, 587, -383, 160, 40, 514, 1113, 230, 506, -240, -299],\n [-826, 356, 307, -144, 377, -78, -136, -10, -476,... | 6 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[1346, 98, 257, 53, 533, 133, -642, -863, -543, -217, -90, 977],\n [-87, -415, -299, 476, 354, 238, -204, 247, -268, -144, 479, 281],\n [568, -319, -138, 16, 584, -152, -353, -331, -210, -314, -134, 354],\n [-556, -596, 30, 86, 106, -484, 26, 154, -72, -424, 560, -40... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[687, -336, -62, 175, 131, -114, -624, -393, -569, 850, 912, -3],\n [385, -302, 83, -212, 590, -603, -603, 71, 66, 440, 5, -159],\n [-45, -3, -544, 197, -503, 600, 570, -366, -412, -115, 561, -96],\n [-242, 483, 403, 567, -899, 829, 259, -193, -328, -115,... | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[259, 275, 500, -374, -301, -458, -418, 5, 93, -229, 849, 221],\n [1008, 454, 677, 207, -110, -317, 415, -679, 11, -974, 1354, -6],\n [-168, -916, -360, 714, 426, 812, -166, 128, -388, 172, -934, -208],\n [449, -908, 1027, -393, -268, 265, -851, -205, ... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[342, -523, -1482, -233, 566, 392, 83, 410, 477, 792, -487, 763],\n [-458, 664, -1053, -1598, -447, -591, 42, 320, 608, -1041, -882, -631],\n [1271, -1469, -872, -903, 1375, -632, -545, 1160, -441, 1051, -1220, 72],\n [362, -315, -158, -686, 378, -568,... | 10 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[1624, 591, -1125, -52, -16, -317, 413, 1053, 135, 620, -806, 855],\n [-400, -991, 4, -603, -657, -357, -401, -1066, -733, -1166, 216, -49],\n [-238, -749, 1532, 1062, -782, 309, 234, -42, 187, 910, 167, -1108],\n [-877, 1309, -1711, -273, -114, -161, -633, 464, -182... | 11 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-266, -397, -1021, -34, -181, -61, -425, 494, -301, 46, -459, -657],\n [-286, -33, -677, 50, -121, 115, -79, 84, -47, -300, -147, -823],\n [463, 511, -662, -908, -647, 513, -20, 23, 498, -408, 542, -664],\n [28, 241, 535, 136, 145, 51, 292, -343, 162, -135, 233, ... | 3 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[844, 218, -336, 187, 293, -437, 208, -906, -590, -234, -640, -1157],\n [813, 450, -862, 91, -352, -1409, 753, -904, 196, -60, -1165, -848],\n [279, 18, 353, 663, 250, -1340, -759, 548, 591, 256, -279, 325],\n [-52, -853, -829, 850, -162, -525, 77, 331... | 8 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[347, -149, 509, -1003, -316, -800, -482, -96, 307, 648, -1764, -269],\n [-313, -287, -196, -287, 66, 315, -107, -1219, 223, 62, -518, -991],\n [95, 167, 973, 694, 246, -1364, -106, -804, 1278, 268, 105, 328],\n [186, 680, -1298, -51, 55, 354, 656, -991, 231, 1215... | 10 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-365, -189, -854, -1521, 299, -19, -265, -145, -227, 12, 340, -1635],\n [-712, -547, -819, -135, -97, 533, 335, 508, 203, 199, -213, 225],\n [545, 681, 675, -578, 1041, 444, 55, 1023, -160, 171, -655, 450],\n [387, -281, -939, 847, -131, 774, 1553, 48... | 11 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[104, -259, 390, 1040, 428, 12, 1049, 115, 710, -288, -483, 190],\n [-363, 931, 904, -147, -292, 221, -280, -106, -398, -137, 655, -1411],\n [-612, -745, 284, 215, 1032, -116, 849, 252, 1072, -1308, -1110, 345],\n [-3, 332, 1266, -308, -974, 270, -782,... | 11 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[146, -779, -448, 135, 1215, 615, 306, -1721, -176, 189, -1056, -350],\n [522, 507, -381, 414, -1164, 9, -676, 278, -949, -157, 547, 290],\n [-512, -49, 64, -1146, 903, 681, 1353, -166, 587, -330, -459, -235],\n [-780, 108, -964, 994, -48, 132, 44, -41, -... | 6 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[84, 270, -505, 332, -651, -490, 34, -581, -620, -24, -570, -426],\n [525, -279, -142, -985, 1041, 101, -332, 571, 217, -291, 24, 78],\n [-447, -124, 879, 185, 23, 384, 21, 201, 712, -209, 1178, 317],\n [-315, -229, 682, -21, 407, 583, 98, 509, 687, 169, 680, 512]... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-302, -142, -166, -198, -299, 79, -173, -313, 16, 203, 124, -25],\n [308, 252, 196, 252, 322, 14, 182, 350, -56, -322, -336, 14],\n [-156, -548, -204, -324, -230, -378, -114, -298, 184, 614, 992, 38],\n [886, 252, 446, 504, 851, -377, 499, 871, 14, -419, -42, 91]... | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[1293, 456, 548, 433, 988, 682, -266, 973, -669, -849, -141, 423],\n [-460, -806, 366, 193, 676, 259, -897, 957, -265, 800, 468, -583],\n [-118, -349, 252, -814, 696, 267, -1273, 1286, -942, 199, -280, -929],\n [1046, -220, 410, 772, 311, 547, 201, 891, -... | 8 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-32, -241, 83, -575, -349, 199, 461, 137, 401, 173, 153, -913],\n [276, -126, 131, -146, -267, 283, -304, -310, -280, 175, -169, -612],\n [-1071, -529, 838, 28, 808, -765, 1072, 975, 644, -1054, -357, -391],\n [672, 397, -553, -179, -642, 336, -806, -... | 5 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-115, 90, -10, -55, 65, 95, 0, 10, -75, 125, -100, -15],\n [460, -360, 40, 220, -260, -380, 0, -40, 300, -500, 400, 60],\n [368, -288, 32, 176, -208, -304, 0, -32, 240, -400, 320, 48],\n [-506, 396, -44, -242, 286, 418, 0, 44, -330, 550, -440, -66],\n [-... | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-16, -453, -374, -435, 134, -308, -1876, -532, -227, -434, 1459, 38],\n [-72, 886, -1372, 1101, -633, 1221, -1877, -1008, -205, 338, 631, 299],\n [513, -665, -908, -264, -28, 561, 767, 1231, 761, -274, 357, 645],\n [1840, 824, -1436, 1304, 241, 760, -1165, -511, -55... | 9 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[273, 294, -20, 117, -20, -1223, 530, 294, -223, -668, -210, 169],\n [-287, 525, -516, 978, 202, -607, -136, 682, -306, 243, 826, -546],\n [-335, -182, 2, -225, -362, 117, 785, 438, 779, 447, -510, 488],\n [-252, 183, -162, -343, 97, 295, 3, -106, 101, 64, -204, 1... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[500, 64, 1035, -1722, 448, -185, 1255, 286, -405, -1821, 1570, 208],\n [-12, 467, 279, -423, 399, 590, 307, 211, -188, 53, 558, -388],\n [381, 268, 360, -432, 472, 726, 436, 399, -115, -199, 579, -100],\n [489, 1346, 861, -385, -685, 323, 565, 535, 94, 839, 137, -16... | 8 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[45, 135, -345, -180, 315, -300, 75, 90, -210, -150, 390, 195],\n [21, 63, -161, -84, 147, -140, 35, 42, -98, -70, 182, 91],\n [12, 36, -92, -48, 84, -80, 20, 24, -56, -40, 104, 52],\n [-27, -81, 207, 108, -189, 180, -45, -54, 126, 90, -234, -117],\n [-72... | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-737, 435, 1114, -174, -936, 252, -914, 459, 268, 902, -45, 260],\n [-275, -621, -58, -611, -315, -605, -188, 405, -831, 441, -460, -753],\n [-433, -244, 1140, -698, -159, -438, -234, -387, -496, 16, -376, -722],\n [828, 17, -520, -183, 263, -58, 1, -795, 84, -277, ... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-587, -864, -1087, -384, -374, -1082, 554, -513, 280, 1082, 451, 164],\n [-503, -928, -529, 1225, -8, 103, -1117, -1151, 449, -90, -2306, -708],\n [-205, -712, -690, 22, -784, -1077, 178, -455, 349, 1023, 752, 31],\n [-813, -344, 90, -645, -922, -597, 35, 112, 321, ... | 11 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-829, -304, 627, -299, 778, -24, 117, -1075, -906, -117, 1898, -422],\n [1856, 1390, 1009, 1243, -281, -743, -593, 2762, 242, -1261, -1618, 1278],\n [-1333, -563, 96, -479, 531, -845, 11, -666, 5, 424, 205, -904],\n [863, -407, -1174, -461, 583, 180, ... | 10 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[8, 816, -140, 265, -625, -194, 1054, -331, 757, -1197, 34, -5],\n [-1057, 46, -1355, 837, 765, -1127, -280, -57, -15, 463, -217, -983],\n [-148, 409, 5, 81, -1401, -121, 368, 1187, -50, -544, -969, 919],\n [-212, 596, -475, 612, -380, -188, 346, -474, -2, -611, 3... | 9 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-536, 1534, 59, 752, -115, -247, 690, -159, -643, -91, -353, -927],\n [572, 1053, -8, -321, 1239, -505, -796, -603, 1302, 894, 1304, -307],\n [-261, 308, -319, -77, 216, -920, -465, -238, -32, -617, 1095, 475],\n [-122, -291, -1232, 1020, -110, -56, -... | 8 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[211, 13, 137, -38, 495, -734, -512, -122, -551, -443, 20, -728],\n [-1158, -61, 592, 1022, -82, 1708, 498, -1533, -275, -1079, -878, 247],\n [174, 1005, -1030, -591, -296, -1272, -591, 262, -762, -84, 279, -389],\n [231, -714, 1337, -472, 518, -1303, -339, 388, -303... | 9 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[71, -827, 457, -896, -214, -874, 751, 469, 107, 1233, 503, 426],\n [-520, 536, -1251, 468, -342, 87, -878, -598, -348, -49, -96, -588],\n [-1002, -103, 157, -83, -465, 120, 673, -565, -843, -1336, -17, -282],\n [774, -1026, 1080, -1292, 908, -1257, 87... | 8 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-1127, 255, -75, -315, 899, -653, -363, 999, -57, -368, -618, -250],\n [1283, 178, 1514, -341, -567, 632, -291, 353, 349, 305, 1077, -1216],\n [-683, -1024, -489, -112, 285, 782, 391, 1514, -932, -284, -680, 866],\n [610, -226, 116, -1297, -1772, -691... | 11 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[100, -310, -729, 44, 249, 83, 371, 230, 459, 80, -10, -481],\n [447, 117, 411, -799, -1248, 1574, 130, -412, 670, -513, 356, -758],\n [247, -868, -784, 743, 597, -586, 494, 242, 47, 1376, -691, 27],\n [-280, -82, -661, 275, 282, -371, 256, 491, -94, 1... | 6 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[634, 270, -600, 596, -177, -614, -323, -709, -28, -39, 1165, 24],\n [-471, -980, 1708, 540, 66, 747, 894, -484, 442, -826, -880, -468],\n [23, 89, 565, -416, -219, -541, 1553, -766, 791, 303, -236, -560],\n [396, 543, -1618, 253, -23, -496, -740, 169,... | 8 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[202, -202, 821, 227, 413, -688, 184, 714, 294, 775, 433, -114],\n [40, 696, 168, -396, 326, 102, -478, -270, 122, 66, 70, -576],\n [-358, 16, -341, -119, -557, -248, 236, 150, -582, 455, 455, 114],\n [-228, 136, 256, -118, -191, -691, 199, 543, -373, 1031, 801, -168... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-344, 153, -192, -656, -50, 713, -76, 21, -943, 619, -193, 70],\n [1032, 378, 167, 977, 24, 337, 328, -828, 219, -101, 886, -117],\n [-230, -146, 303, -464, 221, 492, -333, 344, -743, 104, 239, -104],\n [-1114, -339, 580, -1935, 355, 128, -98, 932, 184, 343, -522, -... | 8 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[100, 254, -124, -690, -1211, 786, -355, 1032, 353, 34, -626, 888],\n [-701, -1087, -248, -317, 654, 114, -552, 663, 346, 2028, 511, -1020],\n [-261, -374, -72, 1, 762, -288, 358, -262, -133, -406, 470, -75],\n [-597, -380, -1301, -1393, -268, 770, -1125, 35, -824, -... | 6 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-1104, 365, 378, 1294, 512, 382, -716, -718, 876, -106, 738, 475],\n [117, -577, -475, -802, 181, -22, 591, 314, 303, 1063, 159, 613],\n [-978, -432, 53, -230, 419, 328, 95, 762, 159, 844, 1085, -20],\n [-116, 116, -355, -378, -1445, 851, -35, 243, 11... | 9 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-81, 153, -162, -225, 216, 99, 45, -126, 180, -27, -225, 189],\n [-180, 340, -360, -500, 480, 220, 100, -280, 400, -60, -500, 420],\n [-81, 153, -162, -225, 216, 99, 45, -126, 180, -27, -225, 189],\n [198, -374, 396, 550, -528, -242, -110, 308, -440, ... | 1 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-721, -677, 501, 371, 50, 239, 866, 366, -501, 555, -798, -873],\n [322, 745, -212, -880, 1913, 449, 301, 269, 169, -1754, -575, -147],\n [-706, 793, -280, -1465, 142, 275, 1000, 859, 888, 686, 993, -64],\n [-32, -60, 590, 194, 250, -192, 824, -70, -954, -38, -11... | 8 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-268, 132, -308, -661, 607, 1057, 547, 936, 347, -1363, -494, -892],\n [-1352, -592, -179, 1337, 744, -693, -1359, 341, 284, 199, 301, 555],\n [1089, -837, 286, 786, 138, -243, 39, 660, -1048, 190, 379, 367],\n [-273, 210, 950, 40, -1245, -629, -953, ... | 9 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[114, -77, -304, 694, 196, 344, -796, -363, 712, 761, 789, -552],\n [-487, -896, 37, 1177, -657, -1084, 644, -734, 78, 40, -135, -948],\n [-595, -230, -1188, 1188, -836, 61, -419, -78, 330, -684, 832, -102],\n [-413, 990, 2261, -631, -150, -682, 334, 1... | 10 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[110, 122, 575, 218, 1247, -677, -395, 116, -52, 1227, -380, 317],\n [121, -131, -461, 328, 519, 143, 443, -116, 84, -311, 646, 53],\n [-507, -1483, -19, 770, 115, 218, 153, -663, -427, 143, 583, 770],\n [-347, -553, 1227, 176, 297, -139, -839, -462, -747... | 6 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-282, -596, 326, -21, -51, -48, -117, -197, -170, -656, 938, 330],\n [-709, 278, 340, -494, 238, -44, -722, 17, 195, -1332, 541, 374],\n [-217, 105, -67, 571, -58, 103, -345, 806, -513, -534, -714, -446],\n [331, 423, -793, 290, -393, -209, -752, 475, 197, 416, -... | 5 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[726, -467, 835, -198, -885, 242, -741, -1271, -4, -507, -924, -320],\n [-286, -116, -912, 970, 95, 274, 903, 1585, 259, 295, 1300, 1000],\n [470, -995, 799, 116, -733, 672, -787, -681, 310, -9, -654, -172],\n [1272, -598, 444, -113, -890, -423, 25, -1195... | 7 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[77, 423, 339, 143, 936, -74, -128, -196, 415, -1035, -42, 130],\n [-947, -1136, -257, 814, -7, -203, -676, 1131, -252, -298, -335, -479],\n [-764, 810, 365, 501, -571, -306, -464, 417, 635, -824, 257, 1016],\n [-456, 580, 259, 522, -76, 511, -694, 696... | 11 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[24, -288, 240, -600, -216, -168, 192, -120, -552, 120, -552, -432],\n [-5, 60, -50, 125, 45, 35, -40, 25, 115, -25, 115, 90],\n [-19, 228, -190, 475, 171, 133, -152, 95, 437, -95, 437, 342],\n [9, -108, 90, -225, -81, -63, 72, -45, -207, 45, -207, -162],... | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-93, 126, -126, -309, -144, -150, 240, 84, -276, -159, 180, -306],\n [-231, 402, 78, -423, -408, 90, 420, 348, -492, -273, 60, -342],\n [218, -328, 152, 598, 356, 182, -498, -248, 576, 328, -280, 564],\n [211, -320, 136, 569, 346, 163, -477, -244, 552, 3... | 2 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-345, 713, -598, 207, -575, 552, -460, 23, -322, 391, -276, -230],\n [605, -149, -111, 29, 390, 19, 585, -864, -84, -618, 8, -40],\n [-441, 345, -168, 63, -417, 198, -474, 453, -78, 465, -108, -66],\n [423, -119, -62, 15, 281, 0, 412, -593, -50, -433,... | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[359, 839, 1097, -114, 522, -1471, 365, 797, -306, 268, 1342, -911],\n [-305, 288, -499, -315, 18, -40, -161, 772, 270, -103, -180, 21],\n [-1136, 809, -1512, -769, -184, -476, -382, 199, -322, -1168, -1380, -477],\n [954, -486, 602, 704, -599, 1260, 689, -1299, 7... | 11 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-393, 9, -826, -498, -850, 705, -650, 302, 862, -371, -34, 167],\n [-33, -63, -1016, -400, -414, 910, -856, -121, 328, 417, -75, -851],\n [-546, -366, -264, -838, -348, 683, -664, 575, 746, -72, 445, -1122],\n [1423, -190, -182, 702, -785, 523, -133, 49,... | 5 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[868, 1002, -950, 189, -221, 1072, -561, -923, 835, 869, -1126, -488],\n [731, -1687, -272, 847, 162, -1052, -1260, 1957, 112, 862, 378, -301],\n [-999, -1120, 775, 542, 1922, -1266, -708, 1031, -670, -471, 658, 646],\n [-488, 1015, -918, -560, -890, 1... | 11 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-804, -79, -592, 572, 745, 69, 167, -333, 418, 344, -79, 447],\n [636, -277, 712, -1012, -829, 391, -31, 73, -10, -360, 239, -495],\n [286, -84, 1004, -937, -523, 333, 83, 2, 169, -745, 563, -357],\n [-196, 241, -254, 509, 346, -302, -25, 59, -121, 87, -... | 3 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-430, 307, 64, 101, 221, 14, -177, -33, -148, -346, -182, 193],\n [-520, 354, 70, 132, 356, 12, -235, -104, -248, -395, -262, 226],\n [-100, 116, 34, -2, -178, 16, 13, 158, 144, -141, 66, 64],\n [360, -132, 0, -156, -828, 24, 300, 492, 624, 120, 456, ... | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-964, -939, -1425, -255, -1391, -1801, 2108, -205, 500, 1794, 573, 251],\n [-810, 303, 5, -1612, 963, -447, 564, -209, -1696, 376, 137, -1751],\n [728, -8, -257, -1455, -627, 935, -586, -852, -101, 1388, -1153, -416],\n [-37, 339, -167, -843, 777, 627... | 11 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[10, 118, 1164, -33, -444, -69, 298, -491, 526, -271, -18, -1073],\n [-663, -724, -904, -405, 720, -818, 542, 475, 259, 358, -1394, 110],\n [-393, -780, 511, 699, 477, -701, 570, -253, 37, 897, -527, -336],\n [-309, 20, -259, 50, -63, 467, -346, -426, -10... | 6 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-693, 87, -288, -382, -19, 488, -747, -259, 223, -1292, -333, 1427],\n [1056, 792, -585, -620, -1635, -1655, 180, 217, 1534, 799, 1356, 1102],\n [73, -1042, 63, -74, 680, 1196, 8, -824, 455, -398, -88, 995],\n [832, 324, -654, -6, -225, 552, -438, 893, -563, 308,... | 11 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[568, 191, -83, -34, 21, 418, -11, -415, -69, 262, 435, -324],\n [186, -240, -426, -6, 63, -426, -48, -384, 252, -723, 423, 216],\n [-419, -854, -323, 503, -70, -339, -324, 438, -571, -522, -177, -184],\n [325, 345, 154, -115, 5, 423, 73, -185, -4, 470... | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[466, -364, -376, 280, -190, -182, -390, 178, 484, 170, -184, 8],\n [571, -442, -526, -146, -277, -104, -390, -158, 580, 371, -1, -61],\n [-146, 108, 216, 648, 126, -122, -10, 510, -132, -298, -280, 104],\n [152, -112, -232, -728, -136, 140, 20, -572, 136... | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-79, -50, 302, -453, 300, -216, -334, -898, -873, 477, -445, 12],\n [-83, -1230, -787, 391, -975, 182, 11, 650, 660, -354, 722, -215],\n [-629, 725, 111, 21, -232, -142, -164, -728, -177, 979, -669, -624],\n [-376, 169, 467, -70, -968, 133, 555, 371, -149, -433, ... | 9 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[986, -1454, -1523, -203, -460, 361, 550, 623, 180, 893, 745, 425],\n [-279, 136, -988, -545, -666, 1605, 295, -52, 1227, -569, 854, 6],\n [-752, 376, 858, 1043, 1692, -1199, -511, -447, -91, 715, -2026, -223],\n [-1010, 468, -941, -75, 397, 149, 198, -9,... | 11 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-26, -77, -91, -32, 47, 122, 78, -38, -123, 14, 5, -202],\n [-300, 145, -329, 440, 240, 93, 106, 10, -393, -377, 395, -242],\n [-828, -320, -360, 928, 94, -290, 760, -840, -408, -606, 488, 168],\n [210, -162, 216, -348, -171, -27, -30, -48, 252, 297, ... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[270, 76, 257, -523, -59, 754, 224, -496, 430, -523, 332, 344],\n [92, 88, 98, -182, 42, 292, 128, -224, 156, -182, 152, 112],\n [-60, -46, -62, 118, -16, -184, -74, 136, -100, 118, -92, -74],\n [-214, 456, -117, 383, 563, -306, 252, -64, -262, 383, 60, -316],\n [... | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[204, -1001, 410, -879, 377, 391, -945, -171, -322, -46, -953, 477],\n [-163, 183, -172, 1001, 262, 68, -791, -290, 189, 255, 919, -258],\n [64, 714, -144, 1288, -798, -692, -200, -858, -32, 989, 1765, -402],\n [-22, -810, -253, 100, 696, -753, 877, 384, ... | 9 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-171, -209, -475, -19, 133, -285, 399, -323, 38, -475, -209, 171],\n [-72, -88, -200, -8, 56, -120, 168, -136, 16, -200, -88, 72],\n [54, 66, 150, 6, -42, 90, -126, 102, -12, 150, 66, -54],\n [-45, -55, -125, -5, 35, -75, 105, -85, 10, -125, -55, 45],\n ... | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[1005, -521, 434, 288, -1080, 1053, -334, 229, -606, 270, -83, -30],\n [-174, -682, -324, 696, -174, 452, 14, -468, -172, 374, -840, 342],\n [-179, 217, -13, -37, 141, 459, 495, 448, -49, 339, 5, -833],\n [335, -507, 21, 205, -165, -57, -409, -420, 187... | 5 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[35, -66, 427, -658, 66, 75, 671, 715, -135, 411, -139, 96],\n [38, 486, -70, 72, -343, -454, 268, 130, 332, 439, 166, -4],\n [-96, -411, 118, -104, 434, 351, -343, 272, 97, -362, 22, -264],\n [85, 312, -155, 330, -180, -277, -221, -135, 409, 31, 179, -10... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[29, 666, -696, 441, -561, -652, 592, 338, 951, -674, 497, 480],\n [-213, 1390, 514, 784, -883, -365, -169, 695, 1138, -35, 1117, -713],\n [-235, -1, 478, 844, 604, -1457, 942, 39, 1197, -263, -321, 618],\n [-213, -357, 899, -667, -79, 197, -1888, 658,... | 8 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[878, -357, 263, -1085, 601, 8, 165, 130, -222, 148, -125, 167],\n [466, -134, 556, -879, 510, -57, 264, 183, 165, -2, -147, -239],\n [-216, -763, 1056, 311, 221, -5, -21, 899, -141, 1, 164, -501],\n [556, -89, -140, -219, 89, 193, 295, -200, -390, 563... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[103, -74, -1, -70, -236, 137, -68, 35, 287, -196, 142, -84],\n [29, 273, 338, -88, -605, -25, -166, -358, 799, -443, -198, -523],\n [359, 384, 437, 326, -686, 425, 128, -475, 811, -278, -330, -394],\n [257, 505, 410, 584, -175, 303, 362, -512, 155, 201, -594, -117],... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-629, -147, 276, 716, -491, 21, 66, -354, -466, 455, 86, -387],\n [-856, -4, 686, 1248, -573, -502, -387, -1146, -885, 887, -398, -1167],\n [-856, -17, 376, 1002, -688, 61, -92, -392, -538, 544, 205, -382],\n [-263, 58, 184, 494, -901, 64, 224, 2, -501, -54, 539, 12... | 5 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[743, -257, -881, -235, 1749, -298, 696, 84, -69, 1048, -379, -830],\n [-281, 814, 234, 303, -220, 299, -1041, 371, 468, 2, 830, -754],\n [558, -754, -1008, 763, 1224, -747, 832, 74, -379, 1153, 94, -603],\n [-57, 975, -377, -299, -663, -210, -446, 196... | 9 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[493, 200, 160, 39, -352, 280, -198, 462, 70, 382, -1138, -274],\n [1130, 186, 152, -66, -798, -879, 400, -1024, 779, 1327, -949, 960],\n [-775, 682, -127, 495, -91, 1051, 70, 1512, -689, -1706, 675, -797],\n [325, 595, 22, 388, 487, -11, 741, -912, 1335, 180, 319, -... | 9 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[680, 355, -1073, 190, 1589, 845, 190, -1277, 416, 39, -22, -346],\n [-620, 79, -450, -1375, 487, -377, -484, 432, -465, 948, 186, 277],\n [-1448, -588, -1881, 980, -434, 1078, 642, -755, 555, 1088, -458, -80],\n [681, 1400, 741, 321, 1168, 1545, -1326, 9... | 11 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[504, -1127, 1612, -863, -1503, 511, -1387, -387, -1162, 827, 373, -907],\n [-1059, 158, -753, -566, -812, -400, -740, 332, 386, -255, -621, 476],\n [1072, -373, 220, -823, 300, -212, 410, 154, -545, -472, -593, -1010],\n [1781, 26, 1336, -1517, -542, ... | 10 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-392, 47, -418, 0, -24, -757, -215, 717, -534, 980, 373, -1048],\n [71, 696, 951, 60, 191, -125, -1502, -741, -1348, 949, 860, -819],\n [1362, 551, -137, 464, 746, 489, -236, -251, 550, -450, -807, 349],\n [401, 188, 87, 753, 430, 236, 1328, 454, 1532, -1098, -84... | 10 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-464, -78, 258, 184, 34, -109, 451, 554, -44, 56, 474, 96],\n [-228, 254, 502, 408, -364, 534, -460, -74, 287, -467, -259, -407],\n [352, 388, -60, 288, -426, 271, -539, -536, 387, -395, -581, -531],\n [-534, 822, 402, 1464, -1044, -51, 513, 576, 936,... | 3 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[130, 304, 61, 689, -226, -416, -1131, 311, -84, -147, 457, 298],\n [130, 335, -543, 207, -473, -159, -567, 422, 145, 155, 337, 73],\n [-10, 7, -22, -306, -371, 263, 86, 367, 419, -142, -414, 279],\n [-85, -138, 8, -925, -650, 731, 658, 619, 907, -275,... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[44, 201, -257, -246, 151, 213, 332, -86, -211, -377, -308, 154],\n [530, 528, 49, -348, -326, 531, 434, 319, -466, -368, -254, 289],\n [292, 714, -416, 8, 104, 396, 400, 328, -118, -400, -554, 218],\n [-278, -683, 370, -98, -79, -338, -310, -365, 43, 299, 490, -1... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-126, -56, 0, 161, 77, -14, -56, 42, -98, -28, 56, -119],\n [-126, -56, 0, 161, 77, -14, -56, 42, -98, -28, 56, -119],\n [-18, -8, 0, 23, 11, -2, -8, 6, -14, -4, 8, -17],\n [144, 64, 0, -184, -88, 16, 64, -48, 112, 32, -64, 136],\n [234, 104, 0, -299, -143, 26, 1... | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[308, -456, -66, -484, 723, -205, -386, 481, 1035, -27, 505, 91],\n [103, -301, -433, 155, 1396, -405, -971, 376, 1430, 1145, -152, -1016],\n [98, 457, 472, 344, -719, -140, 1135, -987, -584, -213, -77, -17],\n [-950, -183, 688, -346, -371, -159, -112,... | 6 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-121, 196, -89, -312, -493, -307, -655, -248, 358, -228, 619, 477],\n [-252, 772, 755, -74, -355, -751, 139, 263, -210, 1020, -87, -1112],\n [-6, -397, 318, -419, 364, -200, 487, -1315, -1272, -389, -120, -1526],\n [108, -401, 395, 91, -285, 110, 401,... | 8 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-344, -322, 370, 413, 147, -152, -157, 596, 658, 341, 66, -294],\n [-339, -31, 579, 734, 461, -827, -274, 634, 668, 522, 575, -196],\n [233, -415, 135, 592, 787, 31, 634, -556, -726, -286, 801, 492],\n [-470, -606, 246, 1233, 916, -159, -544, -354, 649, 525, -24,... | 5 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-396, 153, 21, -813, -32, -572, 957, -52, 766, 400, 368, 415],\n [-76, 315, 443, 35, 53, 389, -76, -232, -270, -46, -638, 260],\n [-495, 529, 361, -372, 288, 230, -222, 129, 753, 1148, 145, -64],\n [50, -224, -110, 294, 746, 158, -384, -78, -25, 360, ... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[631, 805, 166, -238, 230, -379, -374, 826, -129, -450, -570, 216],\n [430, -474, 332, -348, -354, -586, 622, 508, -542, 1258, 1208, 134],\n [668, 639, -95, -278, -25, -317, 280, 338, -507, -65, 506, 546],\n [494, 880, 53, -163, 368, -103, -539, 530, -4, ... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[58, 286, 208, 574, -25, 1418, 442, -236, -43, 555, -53, -1565],\n [890, 519, -895, 133, 1575, -19, -485, 340, 1387, 57, 892, 1090],\n [-559, -207, 762, 519, -510, 372, 559, 743, -456, -220, -69, -743],\n [-793, 127, -780, -250, 451, -81, -364, -310, 6... | 8 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[371, -823, -151, -171, 1114, 360, -914, 1524, 172, -332, -302, 295],\n [-812, -1011, -157, 681, 85, 432, 206, 907, -628, -1021, -759, 300],\n [-726, 313, -288, 635, -854, -630, 658, 18, -238, -461, 267, -667],\n [23, -155, -1035, -279, -602, 384, -300... | 6 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-571, -71, 638, -849, -498, -527, 69, -402, -448, 148, -897, 175],\n [436, -347, 764, 266, 156, -439, -162, -747, 895, -1386, -133, -625],\n [981, 355, -174, 25, -634, -51, 119, 200, -860, 376, 627, -597],\n [-982, -140, 716, 189, 378, -391, 473, -534, 363, -904,... | 8 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[805, -1591, 730, -455, 1032, 308, -943, -541, 125, -605, -47, 756],\n [159, -601, 104, -351, 497, 303, -107, -52, 278, 361, 744, 536],\n [694, -638, 376, -522, 518, 3, -361, -542, -32, -144, 78, 291],\n [1020, 382, 54, -794, 185, -684, -40, -1055, -376, 495, 83, ... | 5 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[1534, -1420, -245, 281, -1180, 468, 12, 1018, -72, 250, 1002, 771],\n [-332, -173, 595, 463, 1274, 723, 234, -398, -229, -894, 735, -118],\n [-38, 243, -205, 343, 689, 91, 946, -440, -184, 784, -120, 387],\n [-811, 1026, -1285, -1310, -478, -461, 61, ... | 9 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-206, 1124, -370, 318, 158, -244, -278, -343, -617, 938, -1502, 536],\n [647, -1150, 515, -904, 194, -270, 637, 550, 805, -645, 852, -194],\n [-1632, 476, 127, 1371, -721, 598, -880, -686, 252, -641, 268, 694],\n [627, 114, -358, 25, 512, 49, 1248, 83... | 7 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[256, -134, 60, 175, 158, -286, -91, 24, 128, -144, -296, 261],\n [-733, 88, -183, 134, -20, -414, 250, 98, 168, 520, 555, 92],\n [-269, 704, -786, 499, 943, -963, -159, 535, 481, -22, -62, -76],\n [718, -372, 520, -445, -506, 982, -103, -358, -426, -4... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[344, 440, 308, 572, -800, 160, -520, -576, 436, 540, -164, 400],\n [246, -110, -215, -949, 833, -94, -238, -356, -69, -369, 42, 281],\n [638, -446, 1005, 459, -794, 464, 226, -4, -7, 155, 681, 18],\n [-350, 388, -707, -395, 572, -322, -308, -174, 77, -75... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[64, -76, -56, -24, -8, 84, 80, -72, 68, 28, 72, 40],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n [416, -494, -364, -156, -52, 546, 520, -468, 442, 182, 468, 260],\n [320, -380, -280, -120, -40, 420, 400, -360, 340, 140, 360, 200],\n [400, -475, -350, -150, -50, 525... | 1 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-271, -445, -708, -425, -831, -217, -217, 1337, -206, -48, 653, -319],\n [-547, 493, 822, -564, -428, -10, -804, 738, -372, -276, 554, -488],\n [767, 520, -234, -508, 12, -125, 1009, -630, 878, -26, -216, -207],\n [-471, 270, 236, 447, 112, 145, 70, -... | 6 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-572, -376, 672, -332, 640, -8, -68, -184, -124, 348, -568, -456],\n [595, 368, -667, 388, -609, -52, 166, 210, 144, -455, 526, 513],\n [812, 580, -1018, 386, -1022, 132, -94, 224, 146, -308, 936, 570],\n [-542, -220, 448, -566, 272, 348, -626, -284, ... | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[596, -362, 1018, 220, -616, 416, -64, 46, -372, -468, -234, 178],\n [-461, 325, -916, -247, 575, -283, 68, -29, 276, 484, 295, -103],\n [-766, 90, -236, 358, -30, -858, -72, -114, 576, -416, -650, -518],\n [688, -63, 161, -352, 66, 786, 72, 105, -522, 42... | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-203, 108, 298, 346, -335, 145, -243, -196, 302, 313, -629, 42],\n [212, -32, -228, -224, 160, -128, 236, 216, -132, -196, 484, 24],\n [-270, -80, 166, 80, 80, 128, -274, -292, -106, 54, -358, -132],\n [15, -140, -158, -250, 335, -49, 47, -4, -322, -2... | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[407, 225, -808, -210, -568, -166, -164, -649, 154, 439, -470, -579],\n [305, -293, 530, -631, -154, -246, 30, 645, -152, -990, 782, 1072],\n [439, 149, 89, -1031, -1655, -1349, -174, -349, 431, -998, 755, 805],\n [998, -461, 371, 332, 118, 211, -616, 527, -95, -1... | 5 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[74, 174, 431, -503, -1017, -262, -63, -40, -527, -1089, 1106, 471],\n [1007, 1, -85, -1108, -286, -714, 328, 124, -652, -998, -599, 202],\n [-197, 386, -1049, -256, -349, -895, 653, -342, -726, 228, -174, 344],\n [-225, 69, 114, 80, -118, 199, 499, 52... | 9 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-434, -125, -403, -1010, -871, 301, 376, 35, -789, 59, 497, -381],\n [-726, -26, -195, 485, 7, -363, -597, 34, -524, 15, 723, -1070],\n [-223, -72, 360, -271, 239, 455, -260, 83, -852, -471, 1038, -729],\n [-1032, 678, -315, 705, 58, -1052, -671, 380, 283, 443, -354... | 7 | MATH |
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