messages listlengths 1 1 | ground_truth stringclasses 11
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Determine the rank of the following matrix:\n[[-612, 120, -194, 362, 664, 626, 652, 990, 46, -318, -38, 180],\n [222, 308, -73, 489, 612, -483, -432, -33, -27, -493, 439, -156],\n [-99, 848, -429, 1805, 927, -1313, 797, 141, -431, -112, -540, 14],\n [110, -764, 328, -1234, -542, 630, -477, -98, 82... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-330, 647, -165, -257, -455, 83, 138, -456, -182, -331, 669, 84],\n [-60, 142, -45, -67, -100, 13, 18, -81, -22, -56, 144, 9],\n [22, -61, 22, 32, 43, -4, -4, 29, 4, 19, -61, -1],\n [-382, -159, 368, 458, 117, 174, 424, -599, -624, -539, -59, 331],\n [32... | 2 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-147, -56, 182, 175, 168, -133, -91, -119, -168, 77, 14, -84],\n [-147, -56, 182, 175, 168, -133, -91, -119, -168, 77, 14, -84],\n [42, 16, -52, -50, -48, 38, 26, 34, 48, -22, -4, 24],\n [483, 184, -598, -575, -552, 437, 299, 391, 552, -253, -46, 276]... | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[591, 565, -636, -529, 460, -235, -225, -760, 128, -478, 434, 457],\n [78, 454, 602, -185, 118, 431, 1609, 1129, 67, -867, 964, 542],\n [517, 873, -235, -418, 441, -263, 444, 72, -217, -428, 656, 299],\n [-209, 495, -434, 122, -872, -640, 346, 1518, 10... | 9 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-760, 128, -1104, -161, 471, 1128, 1290, 492, 306, -94, 1001, -613],\n [-284, -61, -255, 615, 1068, -783, -799, 862, 1047, 896, 1496, -1509],\n [195, -865, -309, 523, 307, -880, -883, -422, -766, -98, -1185, 180],\n [536, 364, 706, 386, 80, -763, -765... | 10 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[114, -209, 38, -76, -57, 133, -380, 209, 190, -437, 133, 285],\n [-30, 55, -10, 20, 15, -35, 100, -55, -50, 115, -35, -75],\n [-24, 44, -8, 16, 12, -28, 80, -44, -40, 92, -28, -60],\n [78, -143, 26, -52, -39, 91, -260, 143, 130, -299, 91, 195],\n [108, -198, 36, -72... | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-1350, -154, -51, 1082, 269, 386, -605, -440, -67, -3, 667, 1093],\n [957, -735, -1762, -663, -961, 1435, -1201, -953, -547, 495, 1052, -37],\n [437, -553, -924, -559, 444, -402, -434, 172, -542, 716, 31, -66],\n [825, -1189, 278, 359, -10, 472, 1097, -58, -849, -29... | 11 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[677, 294, -467, 856, 389, 122, -17, 500, 83, 319, -688, -306],\n [-150, 467, -55, 372, 302, -217, -293, 475, 463, 301, -366, -579],\n [-153, -962, -161, -599, 13, 271, 533, -473, -34, -551, 814, 82],\n [-629, -180, 478, -729, -399, -95, -48, -441, -96, -233, 556, 31... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[126, -28, -98, 7, 70, -49, 126, -168, 98, 154, -98, 98],\n [432, -96, -336, 24, 240, -168, 432, -576, 336, 528, -336, 336],\n [-180, 40, 140, -10, -100, 70, -180, 240, -140, -220, 140, -140],\n [18, -4, -14, 1, 10, -7, 18, -24, 14, 22, -14, 14],\n [216, ... | 1 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[596, -584, -648, -510, -646, 614, 162, 166, -230, 396, 556, 458],\n [-802, 302, 842, 196, -92, -595, 268, -643, -93, -231, -624, -156],\n [134, 348, -116, 371, 807, -91, -445, 453, 347, -210, 2, -353],\n [422, -368, -456, -315, -367, 413, 69, 157, -12... | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[416, 291, -270, -545, 277, -336, -447, -405, -642, -640, -307, -33],\n [318, -826, 180, 185, 756, 448, 26, 202, 69, 359, 30, 592],\n [-78, 720, 236, -103, -300, -301, -1, 111, -88, -254, 14, -275],\n [-613, -112, 290, 500, -491, 324, 568, 457, 716, 599, ... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[751, -561, 730, 1166, -425, -199, 787, -200, -142, 780, -45, 323],\n [-203, 87, 1218, 521, 1865, 788, 958, -421, 346, 684, 369, 203],\n [496, 436, 1279, 531, 1029, 677, 1107, 320, 853, 299, -311, 696],\n [-530, 405, -1103, 8, -626, -46, -519, -368, -2031, -1359, ... | 11 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[326, -603, 136, -881, 995, 361, -341, -23, 72, -678, -800, -677],\n [792, -353, -762, 584, -159, 807, -761, 530, -363, 123, 152, -5],\n [-1049, 486, 57, 430, -427, -110, 1077, 920, -790, -341, 638, -107],\n [-175, -44, 609, -789, 673, -126, 155, -61, ... | 4 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[363, -172, -395, 219, 150, -4, 549, 401, 29, 10, -327, 535],\n [401, -213, 471, 316, 433, 652, -371, 464, -104, -612, -70, -491],\n [-190, -287, -251, -164, -296, -368, 543, -193, 68, 175, -37, 782],\n [-318, 392, 363, -183, -75, 40, -709, -368, -37, ... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-1635, 1791, 389, 715, 1093, 210, 507, -110, -1519, -875, 511, 1695],\n [-69, -898, -1040, -293, 222, -541, 632, 697, -167, 687, 907, 302],\n [53, -358, -1685, 896, -1007, -625, 166, 98, -134, 1162, 1075, -276],\n [-1491, 842, 275, 466, -395, 392, 815, 949, 224, ... | 10 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[1056, -1398, -718, 226, 307, -497, 175, -175, 214, 113, -129, 153],\n [-404, 96, 631, -65, -389, -197, 734, -292, -177, -80, 348, -1069],\n [-316, 636, -34, -522, 66, 490, -296, 268, 166, -344, 188, -46],\n [115, 8, -816, -1284, 730, 471, 204, 567, 264, -907, 632... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[789, -11, 350, -249, -490, 72, 379, 266, -211, 886, -88, 1246],\n [541, -487, 231, 153, -500, -609, 158, 93, 16, 454, 355, 1132],\n [596, -1607, 1057, -232, -477, -407, 361, 1266, -233, 1239, 250, 970],\n [-568, 561, -884, 302, -119, 167, 339, -847, -... | 7 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[290, 45, -235, -145, 20, -105, 495, -275, -350, 255, 230, -75],\n [697, -28, -637, -693, -301, 136, 487, -300, -430, 548, 646, -501],\n [283, 103, -198, 8, 171, -271, 788, -425, -520, 277, 184, 66],\n [-719, 40, 663, 743, 339, -172, -445, 280, 410, -560, -674, 543],... | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-58, 742, 377, 1842, 232, 146, -71, 534, -1361, 416, 314, 17],\n [-257, 197, -1273, 363, -99, 1035, -50, -36, -627, -236, 543, 614],\n [-121, 769, 873, 566, 190, -73, -237, 59, 25, -30, -267, -729],\n [-353, -931, 1721, -57, 512, -1619, -974, -782, 681, 114, -24,... | 11 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[585, -77, -644, 279, -141, 489, -50, 334, 781, 687, -530, -344],\n [115, 489, 224, 508, -400, -158, 840, 157, 639, -183, -758, -303],\n [826, -97, -626, -454, -943, -154, 534, 3, 723, -207, -664, -483],\n [-695, -213, 686, 536, 601, -300, -201, -162, -738, -4, 83... | 6 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-34, 1061, -402, -682, -469, -786, -454, -595, -1163, -876, 149, -1224],\n [71, -522, 23, -771, -1214, -211, 270, -583, 1173, -430, -147, -274],\n [-237, -340, 368, -65, -401, -164, 707, -486, -55, 450, -305, -71],\n [613, -823, -263, -261, -1513, -421, 604, -860... | 7 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-40, 28, -24, -8, -92, 48, 16, -60, 96, -40, -8, -72],\n [220, -154, 132, 44, 506, -264, -88, 330, -528, 220, 44, 396],\n [110, -77, 66, 22, 253, -132, -44, 165, -264, 110, 22, 198],\n [200, -140, 120, 40, 460, -240, -80, 300, -480, 200, 40, 360],\n [-190, 133, -114... | 1 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-475, 114, -190, 361, 0, -380, -152, 399, -342, -323, 152, 171],\n [-125, 30, -50, 95, 0, -100, -40, 105, -90, -85, 40, 45],\n [650, -156, 260, -494, 0, 520, 208, -546, 468, 442, -208, -234],\n [50, -12, 20, -38, 0, 40, 16, -42, 36, 34, -16, -18],\n [-625, 150, -... | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[338, -540, 1136, -346, 574, 774, 808, -86, 213, 368, 954, 548],\n [-1017, 435, -75, 210, -777, -783, -109, 105, 272, -34, 32, 266],\n [35, -217, 428, 614, 159, 293, 56, 124, 213, -1034, -483, 570],\n [854, -240, -832, -246, 452, 614, -628, 184, -1067, 644, 72, -858]... | 6 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[327, 157, 147, -312, 411, 444, -205, -209, -242, -174, -708, 572],\n [-22, -486, 487, -250, -556, -235, 49, 384, 66, 574, 197, -493],\n [85, -286, 344, -392, 59, 313, -461, -206, -88, 211, -526, 417],\n [149, 181, 115, 26, -159, -184, 445, 381, -80, 1... | 4 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-444, -451, -924, 59, -219, 172, 194, -198, 39, -499, 492, -299],\n [76, 116, -222, -1218, -420, 209, 276, -782, 548, -617, -399, 167],\n [106, 318, -164, 186, 206, -70, -368, 104, -618, 272, -670, -272],\n [75, 162, 276, 648, 486, -213, -534, 432, -6... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-586, -276, 448, 548, 722, 127, -101, -153, -336, 266, 98, -662],\n [-21, 624, -26, -64, -668, -484, 158, -286, 1278, -668, 153, 750],\n [304, -352, -213, 28, 562, -215, -440, 243, 738, 189, 479, -280],\n [-244, -268, 240, 488, 1060, 177, -490, 352, -... | 8 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[82, 337, -105, 702, -676, 702, 312, 914, 479, 267, 108, -332],\n [-465, -248, -50, 101, 229, 44, 114, -408, -314, 131, -135, -337],\n [-319, 267, 513, -437, 409, 1310, -1330, 382, 227, 154, -1057, 1551],\n [661, 126, -80, 370, -543, -804, 401, 33, 536... | 7 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[345, 826, -453, 379, 764, 686, 248, -75, 218, 211, 215, 882],\n [-303, -329, -101, -927, -441, -1137, 92, 140, -1059, 489, 573, -428],\n [-671, -1090, 409, -485, -301, -747, -473, 593, -897, 70, 81, -766],\n [-291, -204, -203, 153, 712, 523, -431, 331, -349, -189... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-214, 574, -38, 352, -572, 1413, 551, 1259, 477, -229, 984, -708],\n [232, -27, 326, 675, -290, 268, 76, 244, -277, -646, 208, -403],\n [40, 442, -246, -596, 540, -809, -527, -519, -23, 657, -310, 908],\n [447, 411, 86, 345, -582, -383, -171, -497, -435, -183, -87, ... | 4 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[724, 529, 519, -13, -1103, -362, 314, 44, -141, -189, 637, 385],\n [181, 109, -1710, -523, -455, 1048, -392, -208, 868, 1382, -1093, -111],\n [744, -879, 855, -1306, -309, 272, 188, 142, 1058, 36, 321, -12],\n [368, -148, -301, -1019, 13, -628, 48, 62... | 8 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[128, 380, -504, -364, -268, 148, 204, 232, -348, -284, 84, 56],\n [138, 327, -108, -87, 57, -21, -153, -192, 99, 33, -225, -240],\n [-193, -501, 381, 283, 103, -66, 17, 35, 112, 133, 148, 177],\n [-267, -589, -21, 7, -293, 136, 493, 605, -442, -243, 602, 623],\n [20... | 2 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[1131, -1077, -632, 750, 154, 336, -927, -78, 477, 12, 320, -549],\n [-1121, 1185, -437, 323, -1397, -321, -31, 429, -982, -383, -569, 158],\n [745, -344, 793, 632, -78, -431, 1242, -177, 603, -534, 29, 396],\n [40, -530, 494, 199, 1191, -296, 1634, -1... | 11 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-169, 247, -156, -312, -156, 312, -39, 325, 247, -247, -286, 312],\n [312, -456, 288, 576, 288, -576, 72, -600, -456, 456, 528, -576],\n [-91, 133, -84, -168, -84, 168, -21, 175, 133, -133, -154, 168],\n [104, -152, 96, 192, 96, -192, 24, -200, -152, 152, 176, -192]... | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[292, 809, 463, 540, -226, -422, 295, 256, -280, 443, 391, 179],\n [-111, 638, 355, 161, -212, -455, 41, -259, 660, -314, -47, -269],\n [-378, 314, 128, -78, -368, -398, -376, -662, 612, -634, -292, -72],\n [149, 897, 557, 444, -146, -514, 338, 106, 42... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-582, 906, -634, -884, -659, 481, 458, -799, -427, 52, -240, 521],\n [110, -468, 413, 104, 512, 107, 254, 646, -191, 246, -460, 47],\n [126, 666, -44, -393, -29, 146, 156, -745, 521, 344, -18, -28],\n [-1236, 1490, -595, -437, -1404, 712, -1738, 1304, -192, 370, ... | 7 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-1231, -1434, 678, 466, -1425, -1144, 685, -225, 275, 466, -701, -254],\n [-904, -206, 277, 281, 68, -54, -287, -342, -480, 1159, -800, -199],\n [42, 59, 1077, -254, 727, -768, 322, 992, -968, 324, 81, -1199],\n [-267, 139, 407, -227, -335, -234, -343... | 8 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[286, 346, -1118, 597, -23, 503, -253, -243, -521, 839, -226, 5],\n [-556, -112, -348, -60, 97, 269, 68, 248, -86, 340, -667, -38],\n [-262, 464, -636, 411, 777, 40, 63, 54, 159, 369, -344, 511],\n [-56, -209, -501, 789, -1165, -1095, -1190, 280, 661, 418, 573, 24],\... | 7 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-487, 372, 15, 664, 117, -3, 16, -88, -239, 25, 367, 46],\n [-384, 6, 878, -446, -595, 368, 564, -109, 826, 942, -440, 594],\n [398, 148, -786, 502, 350, -256, -248, 118, -712, -804, 330, -488],\n [-433, 314, -65, 639, 203, -52, -92, -77, -304, -70, 397, -20],\n ... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-460, 520, 180, -260, -320, 240, -420, -440, 200, -340, 340, 140],\n [207, -234, -81, 117, 144, -108, 189, 198, -90, 153, -153, -63],\n [46, -52, -18, 26, 32, -24, 42, 44, -20, 34, -34, -14],\n [230, -260, -90, 130, 160, -120, 210, 220, -100, 170, -170, -70],\n [... | 1 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-764, 263, -681, 57, 397, -524, 803, -98, 101, 334, 417, 413],\n [1409, -803, -510, 165, -193, 601, 52, -1000, -42, -303, -187, -414],\n [157, -155, 88, -297, 189, 77, -362, -54, -48, 265, -423, -122],\n [232, -273, -390, 561, -1249, 1098, -296, 78, 659, -171, -1... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-15, 346, -389, -795, -315, -70, 712, -1038, 63, -101, -586, 485],\n [-259, 125, 578, 219, -686, -543, 56, -310, -115, 308, -210, -683],\n [765, 281, -599, -432, 502, 875, 664, -4, 81, -905, -270, 286],\n [258, 118, 285, 176, -49, 377, -5, 458, -246, 24, 145, 144... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-251, -88, -968, 134, -619, -330, 107, 314, -618, 771, 86, -42],\n [670, 695, -54, -510, -262, -255, -690, -839, -118, 723, 623, -277],\n [-636, -1124, -260, -28, 320, -457, 106, 342, -812, 490, -104, 378],\n [-82, -281, 359, -92, 37, -11, -121, -468, 110, 567, 6... | 9 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[207, 244, 87, -372, 521, 340, -153, 205, -329, 244, 215, -418],\n [212, 314, 43, 5, -44, 351, 90, -15, 4, 8, 77, -229],\n [-51, -144, 20, 83, -147, -147, 43, -130, 59, -152, -160, 227],\n [644, 229, 509, -594, 539, 584, -34, -330, -635, -330, -374, -3... | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[421, 95, -438, -644, 216, -798, 323, 490, -705, -247, -564, -784],\n [991, 1219, 665, 188, -585, 482, 305, 553, -212, 150, 868, 564],\n [-1203, -462, -319, 134, 255, 12, -378, -805, 709, -231, -296, -280],\n [-152, 71, 666, 346, -158, 910, -307, -446,... | 5 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[315, 462, -273, 420, -399, -63, -189, 168, -42, -210, 105, -63],\n [-225, -330, 195, -300, 285, 45, 135, -120, 30, 150, -75, 45],\n [-60, -88, 52, -80, 76, 12, 36, -32, 8, 40, -20, 12],\n [105, 154, -91, 140, -133, -21, -63, 56, -14, -70, 35, -21],\n ... | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[111, 1534, 581, 21, -471, 389, -75, 533, -175, 109, 1832, -475],\n [904, -152, 596, 469, -633, -221, -755, -270, 93, -754, 52, -295],\n [38, -474, 382, -189, -422, 131, 570, 886, -589, 820, -549, -138],\n [-22, -983, -103, -740, -341, -300, -294, 903, -399, 1478, -6... | 9 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-102, 268, -36, -39, 496, -322, 364, -216, -35, -468, -198, -444],\n [-979, -468, -135, -20, -563, 406, -955, -240, 787, 831, 365, 1087],\n [-229, 1422, 554, -6, -1304, -651, 889, 431, 201, -813, 29, 353],\n [68, -552, 216, -190, -949, 696, -923, 171, 376, 1384, 344... | 6 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[306, -85, 357, -374, -221, 102, 340, 340, -340, -204, 0, 323],\n [270, -75, 315, -330, -195, 90, 300, 300, -300, -180, 0, 285],\n [162, -45, 189, -198, -117, 54, 180, 180, -180, -108, 0, 171],\n [108, -30, 126, -132, -78, 36, 120, 120, -120, -72, 0, 1... | 1 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[436, -471, -113, 1506, -316, 26, 1053, 692, 452, 305, 1203, 189],\n [1608, 1362, -54, 745, -1659, -1328, -570, 422, 935, -507, -205, -838],\n [-49, 908, -122, -587, -339, 945, 1065, 901, -155, -1962, -288, -485],\n [-32, 586, 989, -617, 415, 261, -195... | 8 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[1459, -619, -405, 728, -676, -876, 1047, -589, -780, 342, 127, -166],\n [-1073, -417, 1584, 414, 833, 42, 234, -809, 878, -1534, -62, 39],\n [259, -1310, -563, 1087, 1028, -734, -325, 522, -1196, 64, 1377, -239],\n [136, 1320, 941, -1940, -461, 549, 1... | 9 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-240, 180, -108, 180, 108, -264, -288, -252, -192, -84, -252, -72],\n [-160, 120, -72, 120, 72, -176, -192, -168, -128, -56, -168, -48],\n [480, -360, 216, -360, -216, 528, 576, 504, 384, 168, 504, 144],\n [300, -225, 135, -225, -135, 330, 360, 315, 2... | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[575, 405, 498, 566, -174, 338, 385, 160, 515, -471, 454, -730],\n [-230, -396, -30, -212, -204, 106, -172, 278, 28, -24, -448, 310],\n [-410, -152, -454, -412, 284, -382, -264, -314, -504, 460, -168, 510],\n [-90, -73, -71, -88, 16, -43, -61, -11, -71... | 2 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[55, -90, 320, 355, -75, 530, 40, 70, -395, 365, -15, -130],\n [-101, 163, -474, -511, 40, -696, -128, -299, 389, -443, -77, 41],\n [107, -173, 518, 561, -56, 776, 128, 293, -459, 501, 67, -71],\n [38, -63, 262, 296, -87, 466, 8, -13, -394, 334, -48, -... | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[288, 384, 156, -348, -84, -432, -336, -408, -480, -324, 216, -540],\n [-310, -461, -178, 634, -59, 652, 523, 584, 656, 456, -381, 771],\n [208, 260, 109, -157, -115, -244, -184, -242, -296, -195, 102, -321],\n [572, 702, 297, -361, -357, -620, -462, -... | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[792, 158, 553, -1015, -236, 340, 689, -969, 1308, 69, -226, -920],\n [449, 1839, -536, -1159, 66, -220, 479, -1436, 294, 860, -444, -960],\n [-862, -755, -584, 845, 213, 139, -1119, 1247, -293, -684, 530, 745],\n [-352, 488, 178, -119, 871, -781, 468, -23, -978, 822... | 7 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-1044, 653, -872, -975, 403, 1154, 719, -1084, 400, 16, -581, 312],\n [-132, -161, -363, 290, 1286, 909, 889, 240, -25, 51, -1416, 1283],\n [418, -240, -667, -573, -52, -282, -482, 804, 593, -200, 743, -322],\n [-143, 433, 857, 396, -257, -226, -521, ... | 10 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[845, -195, 989, 1091, 1031, -1303, 1140, 278, -10, 466, 844, 1774],\n [1191, 205, 1345, -1082, 650, 658, 172, -1133, -83, 1043, -67, 894],\n [-362, 450, -1464, 981, -501, -67, -225, 34, 1096, -788, -268, 408],\n [165, 899, 250, -46, -100, -836, -1042,... | 10 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[24, -252, 180, 216, 204, -252, 204, 216, 12, -96, 0, -48],\n [34, -357, 255, 306, 289, -357, 289, 306, 17, -136, 0, -68],\n [36, -378, 270, 324, 306, -378, 306, 324, 18, -144, 0, -72],\n [-34, 357, -255, -306, -289, 357, -289, -306, -17, 136, 0, 68],\... | 1 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[32, 168, -272, -40, -8, 264, -152, 448, 88, 264, 568, 24],\n [-43, -211, 359, 53, 22, -346, 197, -599, -107, -339, -755, -26],\n [26, -188, -78, -16, -254, 22, 36, 298, -176, -132, 280, -118],\n [-22, 740, -190, -16, 658, 326, -316, -134, 592, 732, 88, 346],\n [3... | 2 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[535, 675, 721, 1233, -831, -98, -193, 1442, 73, 506, 265, -1027],\n [-617, 181, -635, -20, -879, -357, -916, 26, -645, 778, 480, -384],\n [-95, -1313, -1024, -807, -128, -256, 1735, -2282, 1110, -751, 854, -1164],\n [245, -471, -340, -905, -49, -872, ... | 11 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[1182, -1008, 1405, -620, -869, -769, 85, 740, -199, 218, 126, -551],\n [352, -990, -258, 1021, -563, 426, -153, 975, 174, -271, -234, -384],\n [575, -173, 1005, -1226, -1236, -678, 1033, 1484, 171, -487, -398, -1230],\n [-294, 572, -59, -344, 583, -28... | 10 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[640, 137, 200, -140, -601, -329, 227, 79, 899, -154, 402, 668],\n [-498, -501, -35, -291, 530, 877, -711, 725, 1198, 816, 180, -523],\n [-600, -160, 470, -1284, -496, 654, 321, 489, 1050, 27, 232, -164],\n [931, -153, -331, 821, 178, -632, 159, -654, -49... | 6 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[1041, -382, -360, -321, -133, -80, 438, 72, -435, 1009, 525, -961],\n [558, -701, -148, -960, 663, -48, 31, 209, 102, 750, 533, -383],\n [-194, -10, 367, -184, -171, 103, -141, 353, 682, -340, -632, 590],\n [-162, 164, -5, 239, 638, 184, -468, -390, -545... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[86, 293, 317, -152, 345, -8, 268, 269, 286, 236, -165, -144],\n [631, 842, 746, -108, 764, 123, 777, 594, 400, 318, -509, -72],\n [785, 445, 235, 445, 648, -160, 214, -343, 280, 94, -473, 587],\n [-61, 221, -529, 556, -81, 143, -151, -701, -156, -290, 98... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-555, -454, 768, 214, -515, -315, -664, -582, 125, 222, 533, -415],\n [431, -270, 279, -838, -204, 817, -755, 505, 1018, -392, 230, 842],\n [215, -236, 32, -613, 556, 529, -72, 68, 68, -109, -121, 543],\n [-21, 243, 1204, -440, -216, 656, -1013, -8, 1... | 7 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[699, -471, -354, 105, 585, -1139, -341, 212, 901, -147, 213, 325],\n [-377, 648, 620, 517, -1710, 309, 201, -44, -1489, -1268, 902, -1068],\n [28, -378, 556, 1441, 404, 1077, -194, 287, -466, 39, 7, -1226],\n [1262, 6, -664, -1819, -303, -170, -414, -959... | 11 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-453, 53, 407, 749, 580, 1563, 350, 1167, -67, -676, 235, -531],\n [362, 296, 1333, -1052, -795, -1447, 292, -917, 915, -138, 403, 727],\n [-75, -446, 833, -516, -995, 877, -470, 1132, 1193, -1106, 187, -752],\n [212, -241, 49, -564, 593, 479, -638, 263,... | 8 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[46, 258, 186, -67, 156, 130, -273, -45, 216, 72, 203, 236],\n [278, 24, 510, 372, 552, 460, -538, 170, 40, -272, -220, 12],\n [322, 486, 774, 199, 756, 630, -955, 65, 424, -104, 177, 436],\n [-11, -198, -99, 85, -72, -60, 164, 50, -164, -80, -177, -182],\n [25, -240... | 2 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[319, 83, 31, 405, 82, 151, 29, -81, -255, -267, 240, -354],\n [-979, 192, -696, -374, 587, -82, -598, -186, 474, 288, 1031, 1341],\n [-991, 874, -116, 443, -456, 540, 447, -727, -668, 313, 337, 377],\n [152, -1259, 205, -633, -712, 227, 592, -520, 156... | 8 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[690, 573, -1082, -73, 318, -734, -1406, -1261, -899, -446, -646, 279],\n [633, -574, -984, -25, 495, 794, -905, -329, -151, 850, 402, 638],\n [-406, 458, 1507, 180, 307, -515, 601, -248, 362, -680, 378, -761],\n [-991, 505, -182, 369, -366, -1765, 99, -1427, -645, -... | 10 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[85, -95, -270, 215, 75, 155, 35, 155, 75, 145, 55, 150],\n [222, -98, 180, 238, -50, -118, 94, -118, 302, 50, 242, 296],\n [92, -154, -594, 343, 165, 346, 37, 346, 45, 269, 26, 195],\n [-307, 135, -252, -328, 70, 165, -130, 165, -418, -68, -335, -409]... | 2 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[447, -847, 115, -1115, -251, -407, -986, 146, -141, 388, 390, -558],\n [31, 237, -78, 463, -142, 402, 225, -99, 126, -33, -138, 206],\n [501, 51, -444, 4, -833, 237, -391, 334, -65, -138, 229, -126],\n [79, 713, -561, 846, -366, 4, 386, 369, -384, -68... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[43, 345, 198, -809, -353, -807, -519, 507, 333, -426, -472, -199],\n [-184, -63, 53, 184, -357, 388, 155, 389, -410, 54, 212, 1],\n [-757, 694, -508, 579, 529, 1353, 1193, 501, 613, -524, -309, -4],\n [-149, -839, -66, -459, -1545, -755, -551, 873, -1... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[1025, -578, 531, 214, 759, -573, -268, 948, -862, 1205, -321, 874],\n [121, -823, 219, 190, 34, 1432, 564, 620, -157, -329, 191, -1648],\n [59, -1, 438, 6, 515, 169, -685, -94, -815, -85, -524, -208],\n [-95, 503, -492, -251, -609, -1057, 491, -162, 1087, 537, 593, ... | 6 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[94, 394, 350, 267, -301, 549, -236, 842, 484, 115, -647, -170],\n [138, 453, 418, 297, -338, 613, -219, 920, 501, 107, -733, -150],\n [276, 271, 410, 88, -449, 656, -139, 948, 261, -190, -568, 30],\n [-440, -583, -34, -722, -359, 126, 453, -359, 496, 383... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[675, -138, -276, -456, 300, 1397, 242, -40, -542, 592, 405, -5],\n [-199, 146, -58, -140, 244, 313, 370, 166, 286, -52, 253, 239],\n [565, -1030, -605, -832, 88, 293, -508, -412, -682, 465, -625, -957],\n [204, -864, -433, -1050, 422, 160, -124, -50, ... | 5 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[478, -390, 295, 143, -108, 431, 898, -1148, 131, 449, -265, -649],\n [-338, 121, -446, -747, 768, 368, -272, 426, -13, 381, -336, 411],\n [403, 55, 1128, 543, -151, -276, -169, -82, -334, -635, 507, 247],\n [125, -1184, 713, 995, 278, 1169, 475, -1052... | 8 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[118, -241, 1319, -4, 254, 265, -812, -341, 1362, -743, 295, -1474],\n [-962, -231, 29, 666, -322, -519, 110, -875, 280, 99, 89, -386],\n [-174, -113, -219, -588, 84, 361, -876, -31, -228, 240, -616, 58],\n [-7, 90, 351, 536, -70, -302, 495, -99, 358, ... | 5 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-691, 928, 401, 1104, -552, 515, -90, -252, -119, 875, 339, 344],\n [-1286, -63, 1015, 252, -782, 410, -100, 617, -90, 341, 360, 765],\n [937, 75, -251, 1070, -108, -336, -449, -323, 994, 940, -1128, -57],\n [-878, -60, 157, 1919, -718, -538, 597, 144... | 11 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[400, 600, 575, -150, 350, -475, -125, 600, -550, -250, 250, -325],\n [-320, -480, -460, 120, -280, 380, 100, -480, 440, 200, -200, 260],\n [336, 504, 483, -126, 294, -399, -105, 504, -462, -210, 210, -273],\n [-352, -528, -506, 132, -308, 418, 110, -5... | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-255, 163, 154, 11, -371, 347, -99, -240, 24, 416, 29, -138],\n [-72, -347, -696, -396, -718, 92, -332, 352, -530, 590, -52, 202],\n [29, -478, -463, -617, -923, -709, -565, 199, -20, 241, -406, 50],\n [215, 465, 930, 105, 860, 406, -691, -1040, -743, -183, 286, 866... | 5 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-374, 276, 178, 389, 52, -298, -570, 208, 490, 205, 324, 532],\n [-184, -60, -196, 52, 83, 352, -132, -208, 158, 38, 225, 35],\n [-663, 369, 154, 557, 112, -221, -856, 218, 794, 354, 561, 783],\n [75, 45, -36, 534, 138, -207, -690, -342, 216, -345, 519, ... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[57, 163, 6, 75, 30, -143, -92, -118, 65, -15, 26, -61],\n [-134, -345, -6, -152, -86, 262, 197, 237, -114, 36, -33, 96],\n [-230, -63, 102, 76, -362, -578, 71, -153, 342, 72, 333, -492],\n [401, 552, -84, 149, 452, 149, -347, -201, -147, -117, -255, 309],\n [260, 55... | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[19, -550, -525, -148, -162, -345, -243, 477, 353, -299, -483, 258],\n [-513, -203, 451, -725, 395, 497, -497, 63, -865, 809, 1396, 325],\n [-522, 239, -468, -314, 45, 96, 581, 156, 204, 904, 852, -818],\n [-781, -1466, 318, 309, -23, -666, -129, 1252,... | 9 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-145, 214, -541, -455, 684, -265, 420, 44, -324, -652, -70, -27],\n [-590, 1071, 612, 337, -363, 287, -5, 316, 598, -129, -1125, 1385],\n [584, 23, -425, -393, 172, -59, 555, -1226, -467, -235, -282, 84],\n [439, -262, -238, -48, -471, -53, 56, -621, -51... | 5 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[264, -318, -1000, -642, -2, -7, 206, -955, 876, 677, 155, 777],\n [337, 412, 1039, 61, 24, -34, 409, -964, -571, -543, -516, 514],\n [40, -311, -705, 389, -1, -863, -618, -452, 1037, 239, 660, -691],\n [43, -125, -148, 918, -387, -310, -372, -533, 595... | 10 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-1123, 347, 263, 439, 1335, 132, 551, 487, 176, -429, -455, -1117],\n [-447, 909, 238, 583, 295, -268, 316, 1375, 599, 204, 567, 31],\n [904, -484, -948, 1038, -288, -667, -1875, 649, 936, 635, 645, 312],\n [608, 360, -314, -156, -337, 361, -370, -635... | 6 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-477, 104, -527, 589, 210, -802, 1285, 295, 1067, 565, -593, -1305],\n [31, -52, 376, -499, 773, 228, -232, 436, 796, 647, 91, 645],\n [1137, -741, -661, 286, 63, -277, -1250, -1545, -850, -4, -455, 33],\n [-212, 2, 2005, 1188, -281, -112, 510, 1116, -10... | 11 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[1405, 294, 362, -1041, -18, 90, 733, 19, -947, -335, -49, 460],\n [-703, 727, 1397, -474, -1553, -596, 1215, 367, 831, 218, 35, -1708],\n [-826, -385, -537, -487, -185, 1056, 1127, -1935, 1373, -502, 326, 960],\n [-532, -902, -268, 1093, 1381, -1096, -1746, 910, ... | 9 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[886, -66, 572, -464, 727, -358, -318, -218, -268, -25, -162, -362],\n [-982, -225, -1192, -191, -1008, -32, -645, 560, -113, -1189, -52, 425],\n [701, -459, 232, -220, 739, 716, 273, -812, -790, 246, 96, 860],\n [-724, -94, -749, 50, -685, 123, -35, 344, -123, -392,... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-10, -33, -33, 142, -45, 120, 84, -13, -141, -79, 124, 24],\n [95, 243, -39, -738, 216, -717, -328, -135, 799, 398, -661, -87],\n [-20, 39, 459, -626, 225, -390, -532, 359, 523, 367, -522, -162],\n [-110, -270, 102, 756, -216, 762, 304, 198, -838, -404, 682, 78],... | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-188, -62, 86, 518, 849, 17, -180, 211, 651, -179, -776, -23],\n [-108, 13, 93, 208, 233, -196, -418, -14, -317, -620, -387, -506],\n [-3, 617, -508, 326, -544, 671, -518, 117, -105, 740, 624, -899],\n [-493, -216, -809, 344, 1229, -117, -136, 807, 1036, 846, -283, ... | 5 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-10, -90, 90, -190, -90, -70, 50, 20, 220, 210, -90, -200],\n [22, 198, -198, 418, 198, 154, -110, -44, -484, -462, 198, 440],\n [-26, -234, 234, -494, -234, -182, 130, 52, 572, 546, -234, -520],\n [3, 27, -27, 57, 27, 21, -15, -6, -66, -63, 27, 60],\n [... | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-93, -406, -14, 413, 750, -317, -76, 763, 347, 542, -147, 784],\n [305, 36, -588, -219, -1012, 107, -428, -736, -790, -675, 397, -593],\n [-351, 890, 915, -520, -41, 664, 385, -392, 364, -169, -349, -655],\n [-113, 234, 321, -132, 85, 148, 239, -62, 202,... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[30, 48, -16, -258, -416, 432, 868, -42, 664, 548, 22, -562],\n [-734, -385, -75, -425, -625, 354, -371, -268, -136, -364, -1178, -230],\n [280, -137, 109, 393, -1, 242, 617, 278, 364, 632, 340, -584],\n [-93, 103, -51, -140, 119, -230, -437, -123, -288, -398, -85... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-222, 82, -212, -534, 177, 417, -1252, -787, -135, 779, 579, -760],\n [-1396, -1895, 136, 610, 678, -998, -558, -608, -849, 1717, -735, -417],\n [527, 94, -50, -616, 307, 58, 595, -724, -333, -531, -139, 748],\n [17, 804, -406, -90, -580, 332, 1037, -805, 362, -7... | 9 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-539, -408, -2028, 116, 1207, -732, -339, -1008, -1045, -592, -135, 837],\n [-486, 86, 589, -527, 1245, 86, -222, -11, 667, 69, -230, 236],\n [-528, 142, 613, 591, 125, 289, 1436, -975, 1189, 97, 436, 299],\n [1379, 465, 803, -816, -322, 155, 145, 948, 557, -404, -4... | 9 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-165, -671, -303, -88, -76, 166, 489, -37, -272, 17, -645, 128],\n [-283, -513, 335, 376, 268, 378, 279, 229, -464, -49, -539, -320],\n [-82, -542, -430, -216, -168, 52, 426, -114, -136, 34, -506, 240],\n [173, 403, -85, -156, -108, -218, -249, -99, 284, 19, 409, 12... | 2 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[158, -126, 378, 403, 298, -8, 447, 306, -88, 386, 242, 300],\n [-478, 25, -216, -368, 432, 472, -20, 295, 27, 144, 866, -400],\n [364, -154, 534, 629, -372, -508, -175, -454, -18, 282, -284, 748],\n [149, 91, -200, -136, -199, -94, 24, -45, 6, -350, -... | 3 | MATH |
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