messages listlengths 1 1 | ground_truth stringclasses 11
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "What is the rank of the matrix:\n[[-357, -348, -121, 462, -635, -226, 813, -156, -461, 834, -184, -1012],\n [-1196, -597, 55, 663, 54, -53, 781, -890, -714, -925, -414, -622],\n [-1707, -1250, 134, -785, -954, -473, -92, -461, 1045, -660, -635, -1237],\n [-90, 10, 642, -314, -732, -571, 680, -323,... | 10 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-1247, -1391, 507, 951, -247, 362, -374, 1068, 27, -885, 1369, -291],\n [-132, 24, 333, -170, -2015, 841, -265, 163, -1323, -1607, 893, -618],\n [567, -287, 531, -607, 222, -309, 1557, 801, -652, 260, -1777, 502],\n [-638, 1324, 177, 144, -1222, 935, -313, -159, ... | 11 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[8, -18, -12, -24, 8, -34, -42, -6, 12, 2, 2, -34],\n [-72, 162, 108, 216, -72, 306, 378, 54, -108, -18, -18, 306],\n [-28, 63, 42, 84, -28, 119, 147, 21, -42, -7, -7, 119],\n [92, -207, -138, -276, 92, -391, -483, -69, 138, 23, 23, -391],\n [-64, 144,... | 1 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[406, -915, 709, -284, 557, -489, 303, 243, 66, -194, 966, 214],\n [-193, 1403, -857, 401, -297, 423, -99, -744, 498, -575, -455, -818],\n [527, 83, 252, -859, 1099, -186, 1395, -63, -738, 202, 445, 159],\n [880, 635, 463, -164, 251, 249, 587, 321, -43... | 5 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[34, 1, 291, 188, -307, 287, -272, -272, 239, 329, -277, 183],\n [161, 69, 469, -74, 541, -217, -168, -720, 399, -251, -700, -445],\n [233, -418, -484, 18, 186, -392, 124, -174, 54, -312, -419, -154],\n [-200, 355, 221, -182, 175, 56, 102, 275, -191, -50,... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[1244, 535, 54, 781, -461, 44, 983, 864, 572, 243, -749, -75],\n [-232, 458, -978, 801, 209, 93, -524, 750, 64, 1863, -202, -109],\n [829, 708, -645, 481, 252, 499, 222, 387, 178, 584, -180, -450],\n [221, -145, -613, 553, 906, 255, -101, 989, 324, 560, -170, -329... | 8 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[100, 69, 26, 35, 19, -208, 90, -7, -21, 2, 82, 215],\n [-520, -159, 109, -293, -454, 571, -357, 325, 420, -77, -271, -563],\n [240, 162, 58, 86, 52, -490, 214, -22, -56, 6, 194, 506],\n [480, 261, 39, 207, 216, -819, 393, -135, -210, 33, 339, 837],\n [80, 192, 188, ... | 2 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[284, 193, 797, -23, 526, -388, 452, -109, 745, 271, 335, 982],\n [52, -616, 427, 552, -222, 267, -580, -526, 796, -495, 870, -349],\n [-666, -278, 1282, -1240, 1398, -432, 304, 647, -660, 680, -1077, 889],\n [626, 1078, -718, -45, -131, 158, 83, -507,... | 11 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-392, -211, -352, -863, -507, 44, -814, 564, -108, -31, 565, 630],\n [-579, -662, 167, -933, -1231, -345, -346, 182, -68, 611, 435, 668],\n [216, 131, -88, 545, 313, 241, 362, -167, 102, -15, -174, -324],\n [184, 238, 282, -29, 166, -700, 585, -284, 1... | 4 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-315, -332, -165, -137, -187, -222, -788, 463, 280, 320, -232, 580],\n [-207, 180, 463, -527, 603, -140, 462, -417, -376, -478, -82, 398],\n [216, 436, 371, -440, -83, 414, -107, 699, -81, -88, -325, -617],\n [-30, 88, 121, -203, 46, 6, -50, 89, -5, -... | 5 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-16, -34, -36, -28, 36, -2, -42, 26, 34, -50, 4, 42],\n [176, 374, 396, 308, -396, 22, 462, -286, -374, 550, -44, -462],\n [-152, -323, -342, -266, 342, -19, -399, 247, 323, -475, 38, 399],\n [-96, -204, -216, -168, 216, -12, -252, 156, 204, -300, 24,... | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-660, -203, -520, 129, -271, 178, -1384, 830, -1458, 236, 1899, 1522],\n [782, 1298, -562, 1227, 640, 983, 675, -905, 952, 799, -585, -343],\n [-792, -178, -592, -352, -212, -96, -299, -295, -888, 217, 944, 1001],\n [-242, 406, -1132, 821, -383, 494, 507, -727, 312,... | 7 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-347, 883, -125, -597, 649, -1388, -692, 658, -194, -561, -953, -116],\n [-500, 393, 77, -302, 127, -450, -153, -310, -534, 291, -743, -54],\n [-571, 409, 27, -369, 201, -548, -152, -250, -544, 289, -897, 50],\n [512, 199, -90, 38, -146, -488, -668, 730, 303, -439, ... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[63, -1541, 300, -390, -1098, 187, -286, 198, -34, -1235, 446, -988],\n [743, -7, -114, -509, -5, -7, 466, 487, -434, 257, -115, 480],\n [-707, 443, -38, 131, 21, 150, 816, -292, 569, -124, -324, -194],\n [-606, 758, 413, 83, 523, -343, 292, 241, 93, 475, -694, -58],... | 8 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-540, 805, 26, 287, -1071, 2271, 1265, -513, -28, -1127, -2334, -1018],\n [1021, -358, 281, -374, 490, -566, -599, 1073, -761, 1570, 1532, 310],\n [707, 176, -327, -761, -723, 1111, -1129, 491, -1271, 1638, 161, 283],\n [205, -569, 662, -166, 834, -23... | 11 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[1417, -1025, -1238, 1017, 132, 1501, 759, -753, 1254, -612, 1226, 391],\n [110, 648, -472, 775, -439, 345, -229, -572, -386, 184, 243, 296],\n [-576, 461, 675, 60, -326, -662, 66, 264, 37, -701, 346, -1132],\n [859, 581, 517, 350, -330, 502, 265, -253, -... | 8 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[5, -435, 370, -388, 1125, 399, 1279, -521, -469, -1746, -542, 676],\n [-146, -470, -503, 128, 978, -142, -101, -319, -614, -390, -316, 358],\n [715, -89, -604, 449, 527, -434, -382, 199, 601, 481, 629, 1317],\n [8, 449, -67, 127, -662, -117, -567, -132, ... | 9 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-174, -317, -370, -171, -621, 3, -101, 88, 501, 1062, 106, -503],\n [573, -399, 607, -125, -572, -764, 686, -56, -99, -870, 286, 871],\n [35, -839, -142, 459, -503, -1365, -471, -237, 1019, 546, 800, 848],\n [533, 735, 1622, -615, 417, -181, -147, 506, -1777, -11... | 7 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[480, -396, 669, 1112, -436, -437, 80, 672, -309, 884, 915, 509],\n [-552, 1215, -606, -1791, 1856, -31, -290, -323, -832, -1229, -1871, 232],\n [481, 44, 676, 241, -491, 115, -614, -245, -238, -393, 68, -719],\n [77, 251, 1239, 533, 807, -208, -602, 7... | 8 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-448, -372, -1701, 450, 965, -457, -496, 635, 485, 760, 295, -997],\n [-230, -820, -148, 166, 682, -385, 85, -235, -1248, 384, 346, 93],\n [620, -233, -950, 282, 1288, -157, 642, -192, 455, 484, 787, 171],\n [656, 167, 457, 793, 385, 31, 831, -455, -3... | 8 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-92, 370, -164, 171, -137, -334, -82, 4, 109, 73, -93, -60],\n [-24, -102, -11, -36, 47, 107, 54, 13, 25, 46, 56, -61],\n [-889, 548, -239, 6, 528, -31, 574, 643, 16, 748, -215, -1112],\n [14, -612, -806, 194, -378, 342, -8, -418, 1026, 458, 816, -288],\n [410, -... | 3 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-536, 344, -374, 56, 780, -682, 58, -772, 46, 228, -548, -286],\n [96, 369, 711, 544, 427, -528, 714, 311, -491, 364, 642, 232],\n [176, -72, 581, 149, 98, -133, 234, 223, -113, 233, 307, 296],\n [22, 335, -1083, -267, -348, 154, -102, -112, 92, -150,... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-176, -464, -224, 810, -319, 685, 597, -438, 195, 1003, -355, -726],\n [-307, 693, 559, -1, 945, -749, 271, 1213, -372, -707, -409, -182],\n [-1342, -75, -101, 134, -427, -176, 394, 211, -256, 39, 369, 1321],\n [-180, -1047, -950, -684, -1502, 239, -5... | 9 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-275, -506, -442, 105, -341, 587, 224, -119, 299, -198, 275, -114],\n [-364, -136, -210, 48, -140, 316, 158, -110, 510, 116, 86, -68],\n [613, -122, 107, -21, 31, -229, -175, 154, -934, -444, 38, 60],\n [-155, -26, -67, 15, -41, 107, 59, -44, 224, 72, 20... | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[322, -483, -200, 906, 659, -624, -957, 156, 1253, 247, 428, -982],\n [395, 66, 220, -600, -66, -195, 649, 263, -196, -44, -895, 549],\n [-54, 1008, 77, 447, -1001, -93, 1044, -97, -2091, -344, 540, 306],\n [2, 744, -353, 71, -399, 1222, -733, 482, 687, -... | 7 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[11, -2274, 136, 277, -483, -160, -678, 1007, -306, 812, 285, -2334],\n [774, 0, -906, 192, -213, 44, 813, -757, 397, 44, -1510, 109],\n [-393, 899, -1161, 891, 746, -201, 437, -404, -161, 519, -1705, 1363],\n [418, -642, -1011, 403, 467, -86, 514, -154, ... | 9 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-399, -171, 152, 418, -133, 190, -19, -171, -209, -57, 171, 399],\n [-189, -81, 72, 198, -63, 90, -9, -81, -99, -27, 81, 189],\n [-294, -126, 112, 308, -98, 140, -14, -126, -154, -42, 126, 294],\n [-378, -162, 144, 396, -126, 180, -18, -162, -198, -54, 1... | 1 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[24, -117, 416, 285, -48, 240, -526, 102, -88, -285, 704, -123],\n [-46, -316, -344, 550, 84, 127, -480, -655, 300, 573, 326, 486],\n [399, -715, 374, 1485, 27, 908, -505, -1025, 507, 377, 1131, 65],\n [288, -59, -441, 726, 282, 253, -180, -877, 581, 7... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[275, -700, -680, 640, -830, -549, 264, -862, -322, -821, 15, 1071],\n [693, -431, -1180, -1787, 348, -893, -631, -204, 83, -497, 224, -612],\n [-1020, 417, 630, 697, 105, 668, -672, 256, -799, 7, 614, 622],\n [949, -537, -703, 996, -837, -658, 1285, -992, -203, 1... | 10 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[324, -707, 465, -875, 246, -832, -845, -233, 449, -466, -732, -1055],\n [50, -527, -533, -368, 241, -335, -714, -594, 180, 71, -208, -331],\n [41, -171, 468, -512, -97, -568, -261, 257, 441, -185, -545, -594],\n [394, -661, -91, -316, 503, -157, -678, -726, -156,... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[555, -172, -1296, -1232, 1198, 697, 1130, 495, 1259, -241, 1553, -472],\n [-918, 388, 734, -168, -614, -152, -388, 296, -738, 113, -247, 92],\n [-19, -988, -162, 182, 57, -3, -21, 125, 425, -611, -32, -486],\n [151, 509, 103, 671, -815, -672, -909, -114, -155, -1... | 9 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-289, 1031, 126, -555, -143, 95, -838, -255, 47, 373, 263, 473],\n [1002, -416, 1389, -1147, 187, 583, 289, -980, -483, -1, 80, 1765],\n [-890, 662, -1133, 732, -260, -413, -521, 771, 406, 134, -38, -1309],\n [356, -246, 574, -160, 174, 755, -290, -6, -1... | 6 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[533, -1291, 1037, 376, -763, -390, -416, -273, 619, 1070, 319, -171],\n [-753, -257, -343, 426, -203, -408, 274, -199, 252, -475, 790, 202],\n [-486, -193, -37, 158, -848, -622, 142, -710, -381, -198, 918, 185],\n [515, -406, 244, 351, -740, -877, 258... | 9 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[546, 267, -255, 416, -1154, -674, -219, 135, 748, 366, -244, -868],\n [988, 471, -402, -74, -897, 342, 457, 309, 917, 810, -99, -556],\n [-569, -584, 717, -857, 472, -240, 461, -559, -901, -442, 379, -466],\n [-30, -34, -820, 976, -401, -295, -279, 681, 282, 104,... | 7 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-341, 134, 34, 143, -37, 579, 145, 146, 667, 34, 750, 480],\n [-80, -243, -827, -617, -35, -253, 118, 292, -1017, 440, -148, 284],\n [-855, -743, -166, -1363, 46, -506, -199, 424, -1004, -60, 677, -65],\n [-199, 501, 235, 410, -752, 548, 1181, -670, 1... | 6 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[286, 38, -123, 103, 82, -488, 94, -278, -49, 260, -107, -279],\n [-606, 147, 593, 290, 213, 209, -66, -25, 670, -882, 193, 537],\n [-304, -705, -486, -125, 27, -21, 1008, -143, 41, -134, 98, -666],\n [-195, -382, -61, 511, 457, -912, 745, -764, 464, -... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[330, 862, -193, 630, -68, -318, -406, -373, 810, -861, -581, -1557],\n [509, 334, 331, -665, -38, -58, 71, 362, -602, 370, -872, 370],\n [-665, 340, -102, -390, -806, 420, 146, 50, 455, 32, 34, -402],\n [502, 1035, 16, 912, 508, -175, 860, -471, 321, ... | 7 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[566, 768, 662, 263, 628, -506, 891, 138, 273, -778, -239, -371],\n [444, 165, -251, 45, 727, -745, 82, 63, -843, -589, -1421, 565],\n [-937, -535, 142, -370, -326, 1241, 86, 87, 949, 1161, 532, -838],\n [-431, 756, 319, 124, 1711, -791, 832, -722, 375, 831, -315, -2... | 7 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[722, 342, -282, 43, 16, -186, 72, 704, 1103, 40, 613, 536],\n [71, -108, 653, -254, -182, -942, -290, 643, -925, -566, -671, 88],\n [370, -26, -880, -176, -320, 589, -129, -376, 586, 564, -321, 72],\n [-32, -21, 746, 1286, -250, -352, -306, -510, 16, -176, 159, -... | 6 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-68, -285, -226, -231, -708, 375, 27, -266, -639, 314, 140, 537],\n [-380, 606, 112, 452, 682, -1483, -854, -977, 233, -648, 131, -929],\n [462, -330, 7, 71, 246, -460, -603, -476, -74, -1000, 152, 272],\n [141, 1073, 688, 167, 926, 298, -90, 465, 622, -60, -318,... | 7 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-69, 1496, -771, -306, 608, 97, 388, 489, 94, 576, -580, 684],\n [-1987, -1824, 825, 442, -274, -257, 2578, 635, 2109, -233, 1099, -1487],\n [511, 1204, 237, 1103, 636, 587, -1159, 367, 1291, -2111, 72, -45],\n [436, -481, 21, -39, 1018, 85, -578, -15... | 11 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[613, 905, 472, 215, -476, 737, 105, -164, 730, 1059, 456, 287],\n [-213, -1197, -1017, -1392, -474, 10, -379, -350, -88, 1436, -921, 256],\n [848, 1023, -188, 1095, 260, -1085, -20, 994, 305, -889, 160, 555],\n [-342, 447, 659, 1635, 15, 935, -386, -221, 286, -1135,... | 8 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[173, -84, 321, -260, -578, 93, 49, -512, -120, 705, 739, -471],\n [29, 1030, 142, -423, -594, -950, -433, 164, 669, 740, 531, 29],\n [288, -1014, 261, 165, -48, 933, 414, -732, -675, 75, 384, -636],\n [435, -409, 225, 212, 52, 331, 102, -401, -144, 17... | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[352, 1140, 684, 206, -260, -602, -336, -1133, -1004, -1148, 255, 113],\n [862, 29, -14, -1343, -273, 221, -464, -972, -21, 798, 698, -33],\n [3, -495, 313, -416, 284, 497, -258, -974, -271, -1063, 1036, 937],\n [1235, 1218, -727, 383, -1063, 250, 1309, -... | 10 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[16, -240, -232, -168, 544, -744, -16, 464, 8, 360, -584, -40],\n [384, -558, -213, -207, 255, -159, -333, 171, -216, 276, 60, -348],\n [154, -270, -133, -117, 216, -221, -134, 166, -83, 185, -101, -145],\n [-492, 750, 309, 291, -413, 323, 427, -293, 274, -410, 18... | 2 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[162, -540, 99, -225, 551, 79, 126, 3, 200, -448, -104, 140],\n [-207, -144, -57, 357, 323, 262, 117, -444, -271, -277, -593, -148],\n [45, 36, 12, -78, -76, -59, -27, 99, 59, 65, 133, 32],\n [264, -876, 161, -367, 893, 127, 204, 7, 326, -726, -166, 22... | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-571, 756, -661, 37, -64, 51, 316, -335, 458, -277, 982, -167],\n [-650, -963, -370, 467, -1855, 81, -104, -937, -734, 1047, -790, -191],\n [175, -1137, 318, -202, -1392, -332, -597, -737, 201, 1426, -242, -158],\n [-847, 124, -1141, -57, 545, -151, -216, 1247, -110... | 8 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-57, 160, -114, 108, 35, -320, 418, -74, 121, 381, 107, -75],\n [38, -186, 117, -166, -71, 375, -503, 99, -131, -446, -119, 16],\n [-224, 316, -577, -121, 73, -558, 394, -106, 327, 526, 225, -686],\n [-99, 272, -437, 35, 160, -492, 406, -134, 248, 469, 176, -347]... | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[0, -743, 745, -106, -698, -1864, -495, 330, -331, -417, -574, 1558],\n [408, 820, -1131, -302, -766, 420, -462, -239, -135, 302, 909, -209],\n [1492, -1065, 330, 177, -527, 113, -72, 425, -647, -86, 130, -162],\n [-1547, -148, 914, -277, 82, -1211, -6... | 11 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[537, -218, -322, -289, 155, 370, 175, 67, 194, 26, 28, -164],\n [51, 70, 302, 77, 203, 64, -239, -17, 116, 188, -176, -164],\n [-741, 202, 82, 285, -419, -542, 37, -67, -374, -238, 156, 388],\n [-102, 58, 122, 74, 5, -65, -80, -17, -19, 29, -38, 4],\n [582, -32, ... | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-334, 426, 267, 471, -160, 768, -611, 724, 72, -627, -340, 305],\n [-314, 858, -255, -425, 920, -834, -165, 142, 431, -307, -733, -131],\n [112, -157, -228, 33, 45, -88, -151, -209, 210, 138, -585, -4],\n [404, 637, 42, -835, 1461, -854, -561, 450, 561, ... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[1355, -111, -292, -444, -352, -1268, 1490, 346, 1356, -2125, -848, 606],\n [390, -158, 375, -909, -38, 214, 349, 915, -205, 1041, 533, 347],\n [-976, 694, 80, -462, 633, 173, -1019, 667, -1424, 2131, 1037, -649],\n [355, -218, -311, -430, -1501, 193, -632, -370, ... | 10 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-1756, -355, -245, -255, -197, 746, 321, 1072, 774, -428, -158, -8],\n [-219, -966, 350, 287, 708, -494, 534, 819, -475, 1323, 118, 767],\n [206, 748, 976, 852, -1661, -789, -1351, 1530, 556, 459, -270, 363],\n [463, 98, -195, -475, 604, -229, 404, -294, -1361, 423,... | 11 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-154, 327, -212, 105, 659, 163, 526, -884, 346, 619, 943, 701],\n [-414, 455, -500, 1807, 178, -793, 599, -1694, 418, 538, 284, 21],\n [552, 399, -789, -960, -579, -5, 407, 1081, -1117, 226, -209, -48],\n [333, -270, 359, 412, -850, -140, -520, 641, -... | 6 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[373, -1332, -157, 749, -446, 634, 214, 188, 409, 208, 684, -941],\n [783, -305, -383, 916, 179, 385, -340, 136, 775, 450, 766, 206],\n [56, -1147, -545, -122, -436, 457, 1235, -16, 4, -140, 220, -719],\n [226, 88, 405, 504, 228, -374, -594, 624, 134, 835... | 7 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[278, 487, 1093, -878, -1013, 973, 288, 1320, 638, 589, 375, 625],\n [-598, -585, 577, -197, -261, 1520, -385, 1639, 574, 417, 179, 1113],\n [58, -144, 669, -1201, 441, 242, -776, 265, 709, 329, -83, -203],\n [-60, 1382, 1108, -642, 1423, -234, 493, 51, 1176, 1490... | 11 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[5, -316, -88, 319, 1726, -38, 1781, 18, 270, -672, 1948, -314],\n [778, -74, -879, -224, 1273, 437, 394, 254, -49, -678, -390, -255],\n [-907, -666, 217, -681, -550, 1401, -185, 1643, -437, -131, 390, 513],\n [-620, -996, -136, -1783, 1638, 227, 459, 194, 157, -640,... | 9 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-200, -559, 531, -500, 261, -1078, 999, 714, -1323, 3, -944, 762],\n [1133, 55, -109, -221, -563, 94, 787, -1187, 1243, -740, -1055, -237],\n [-508, 372, -1471, 582, 235, 133, -148, -170, -8, 1197, 237, -1623],\n [943, 411, 627, 444, -306, -234, -1753, 952, 990, -96... | 10 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-80, 746, 21, -223, 820, -87, 1059, 415, -118, 877, 619, -941],\n [819, 590, 721, 264, 215, -137, 379, 12, -579, 304, 245, -338],\n [33, -26, -32, 187, -111, -91, -354, -147, -73, -210, -2, 362],\n [-314, -567, 175, 341, -589, -40, -534, -196, 383, -472,... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-813, -90, -431, 57, -677, -994, 135, -121, -629, 220, -497, -85],\n [-104, 84, 355, 689, -330, -411, -265, 330, -92, -656, -136, -328],\n [98, 664, 30, -216, -794, -810, -412, -266, -634, 272, -130, -744],\n [219, -182, 286, 308, 419, 299, -82, 213, 301, -446, 137,... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[859, -632, -202, 1170, -966, -1282, 611, 720, 277, 417, -26, 31],\n [731, -696, 878, -74, -627, 26, -511, -301, -237, -12, 898, 91],\n [-84, 102, -312, -548, 240, 676, 114, 262, 356, -344, -1016, 678],\n [-408, 218, -208, -323, 351, 1176, 261, 455, 405, -3, -1583, 8... | 7 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[15, -1390, -168, 1254, 422, 1660, 821, 554, 609, -691, -1026, -1569],\n [6, -1097, 248, 758, -1307, 524, -2, 1914, 209, -1342, 1219, -953],\n [37, 519, -747, 851, -1557, 795, -848, 308, 706, -1550, 831, -372],\n [1025, -286, -735, -513, 153, 89, -132, -18, -136, 587... | 11 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[265, -615, -143, 283, -79, 914, -1092, -479, 733, -2419, 104, 196],\n [-301, 212, 660, 157, -900, 45, 206, -351, -49, 86, 884, -1184],\n [330, 366, -485, 313, -915, 762, -484, -532, -54, -321, -533, -233],\n [-689, 1237, 1654, 221, -1839, -676, -99, -... | 8 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[588, 660, -285, 660, 96, 48, 99, -81, -273, -510, -438, -354],\n [-1010, -1110, 77, -264, 169, -337, 420, 173, -532, 105, 654, -499],\n [-57, 913, 13, 1150, -333, 0, -491, -525, -379, -764, -924, -849],\n [-232, -804, -445, -404, 574, -532, 1097, 764, -648, 120, 109... | 5 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[120, 75, -90, 30, 120, 10, 20, 85, -40, 90, 100, -125],\n [-480, -300, 360, -120, -480, -40, -80, -340, 160, -360, -400, 500],\n [72, 45, -54, 18, 72, 6, 12, 51, -24, 54, 60, -75],\n [264, 165, -198, 66, 264, 22, 44, 187, -88, 198, 220, -275],\n [-24, -1... | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-182, 63, 147, -42, 119, 63, -168, -49, 84, 168, 133, -168],\n [-390, 135, 315, -90, 255, 135, -360, -105, 180, 360, 285, -360],\n [598, -207, -483, 138, -391, -207, 552, 161, -276, -552, -437, 552],\n [-156, 54, 126, -36, 102, 54, -144, -42, 72, 144, 11... | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-303, 832, 370, 268, -793, 904, -502, 741, -281, -954, -91, 141],\n [-590, 362, 674, 212, -762, -1247, 98, 275, -371, -37, -481, -1142],\n [-84, -60, -86, 266, 15, -149, 544, -182, 44, 218, 240, 730],\n [130, -805, -4, 12, 657, -777, 857, -836, 91, 953, ... | 6 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[514, 259, 213, 250, 143, -131, 141, -961, -66, -490, 1028, -768],\n [871, 1041, -977, -430, 1353, 373, -222, -340, -1569, -817, 112, -981],\n [-513, 208, 602, 729, 193, -187, 182, 46, -130, 7, -505, -398],\n [443, 337, -652, -457, 130, 1025, -250, -12... | 7 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-545, 549, -154, -348, 454, 409, -289, 195, -98, 68, -673, 153],\n [269, 89, 228, -112, 139, -301, -261, 174, 406, -177, -132, -317],\n [228, 194, 245, -249, 66, -122, 169, 165, -437, 460, -299, -222],\n [-343, 535, 161, -269, 663, 101, -308, 605, 289... | 4 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[1079, 375, 463, -378, -10, 897, -1189, 981, 1501, -239, -295, 1574],\n [-61, 778, 195, -1025, -380, 198, 582, -913, 106, -1645, 251, -60],\n [-75, -5, -228, 1794, -315, 540, -806, 1481, 476, 1071, -69, 947],\n [-180, 99, 824, -373, 1067, 720, 827, 242... | 7 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-1299, 88, -175, -302, -182, -530, -1079, -549, 1277, 203, -625, 749],\n [743, 6, -97, 1207, 936, -1103, 27, 315, 388, 552, 739, -345],\n [-49, -1354, 521, -79, 875, 28, -422, 869, -649, -87, -110, -533],\n [-1432, 961, 259, -487, 380, -539, -76, -37,... | 11 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-560, 8, 82, 158, 470, -337, -171, -23, 141, -394, 851, 245],\n [21, 37, -123, -62, 58, 950, -20, -410, -782, 339, 8, 539],\n [139, 43, 155, 54, -242, -930, 120, 446, 770, -179, -260, -743],\n [-414, -106, 108, 128, 332, -968, -154, 302, 734, -612, 60... | 3 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[41, 143, -186, -371, 52, 759, 7, 114, -124, -221, -227, 399],\n [-394, -364, 255, 235, 91, 120, -170, -111, 53, 52, 298, 138],\n [13, -41, 72, 167, -34, -393, 11, -48, 58, 107, 89, -213],\n [516, 542, -433, -523, -81, 322, 216, 209, -143, -202, -512, ... | 2 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[542, -199, 534, 77, -463, 275, 236, -730, -558, 69, 378, 450],\n [560, 2, 1010, -378, -988, 1154, -956, 238, -333, -304, 345, -772],\n [650, -1434, 28, 577, -750, 660, 695, -522, -483, -96, -610, 110],\n [515, -506, -545, 530, -204, -181, 1127, -396, ... | 7 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[374, -410, 360, 1269, -1357, 378, -293, 112, 89, -5, 595, 327],\n [-1720, -652, 420, -960, 1552, -1000, -150, -64, -144, 355, 850, -172],\n [40, -28, -205, -742, 557, -917, 262, 35, 315, -1356, -1392, -703],\n [-329, 518, 226, -914, 851, -140, 1821, -... | 11 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-875, -328, -551, -190, 1181, 461, 341, 688, -51, 1116, 381, 103],\n [365, 675, 719, 466, 758, 80, 603, 982, -824, -115, -1039, 169],\n [-603, -1366, -176, 96, -113, 295, -1337, 246, 907, -566, 1312, 844],\n [-1046, -320, -223, -322, 136, 543, -772, 2... | 8 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-159, 182, -93, -290, -466, 490, -107, -277, 274, -405, -503, -70],\n [364, -175, -340, -272, 102, -285, -269, 183, -332, 411, 479, 25],\n [-149, -151, 681, 988, 700, -511, 586, 270, 38, 210, 166, 115],\n [4, -198, 444, 756, 788, -686, 414, 370, -248,... | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[656, 72, 52, 1266, 76, 953, -32, -408, -479, -518, 99, 1128],\n [-589, 95, 476, -968, 226, 239, -514, 383, -273, 849, 479, -275],\n [-358, 613, 267, -428, 324, -1, -64, -251, -393, 948, 489, -263],\n [59, 427, -199, -1212, 1069, 442, -99, -666, -1036, 27... | 8 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[904, 102, -473, -392, 1230, 793, -704, 185, 30, 307, -989, 1604],\n [427, -50, -44, 415, -709, 111, -869, -719, -680, 1063, -661, 471],\n [-438, -921, -439, -235, -49, 350, -467, -74, -122, -678, 517, -141],\n [-1632, -114, 134, -347, -1392, -59, -439, 5... | 8 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-1646, -175, 1752, 292, 1002, 474, 23, -820, 135, 102, -669, -202],\n [-474, 372, -55, 356, 429, 990, -540, -199, -164, -443, 584, -1150],\n [-1118, 915, 799, 2380, 499, -261, 1950, 71, 193, 447, -542, -1114],\n [-427, 1676, 334, 696, 230, 65, 742, -222, 592, 367, 3... | 11 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[540, 373, 625, 352, -313, 232, -156, -351, 660, 127, 5, 1020],\n [309, -331, 124, -64, -421, 86, -135, 284, 668, 305, 249, -514],\n [-551, -897, -353, 151, 405, -214, -183, 1219, -552, -227, 154, -428],\n [1052, -36, 800, 292, 19, -307, 216, 907, -502, -... | 8 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-1256, 340, -358, -683, -228, -1183, -243, 1118, 1875, -541, 1327, -1003],\n [1050, -664, -326, 337, -233, 111, 503, 362, 343, -947, 1480, 158],\n [134, 1083, 795, 373, 550, -420, -799, -725, 503, -586, -865, -196],\n [897, 799, 549, -126, 433, 82, -1... | 11 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[108, 59, -27, 12, 26, -736, 354, -109, -28, -571, -135, -321],\n [334, -743, 506, -813, -162, 338, 729, -33, -1112, -227, 258, 634],\n [-244, 162, -276, 494, -36, -236, -198, -66, 432, 26, -36, -4],\n [-296, -19, -279, 538, -130, -260, -60, -127, 308, -33, 45, 259],... | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-587, 927, 208, -156, -260, 301, -477, -623, 859, 456, -88, 1129],\n [1080, -444, 459, -1172, 961, 342, 405, -353, -596, 171, -281, -665],\n [-276, 392, 54, 662, -1429, -752, -933, -817, 62, -46, 1024, -597],\n [-381, -196, 646, -333, -444, 1737, -31, 12... | 8 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-161, -389, 746, -835, 1105, 411, 759, -490, 228, 139, 756, 960],\n [267, 875, 1037, 28, -530, -286, 886, 37, -1856, -976, 677, -735],\n [-1891, -12, -731, 1080, -602, -624, 590, 725, -236, 861, 341, 933],\n [562, -324, 114, -990, 111, 1006, 149, 369, 14... | 10 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-240, 513, 644, -66, 222, 340, -326, -872, -102, -571, -897, 185],\n [1356, -185, 6, -845, -1555, 533, 24, 360, -740, 998, -557, -1314],\n [812, -833, -36, -19, 89, 1355, 558, 760, -130, 478, 689, -1134],\n [-687, -390, -467, 853, 977, -490, -250, -1010, 203, -14... | 11 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[87, -164, -814, -361, -189, 1001, 527, -433, -422, -379, 402, -204],\n [-384, 514, 872, -522, 374, -240, 32, 799, 358, 212, -421, 361],\n [373, -394, -324, 1046, -531, -662, -252, -947, -264, 355, -254, -624],\n [393, 23, -1118, -81, 127, 1122, 502, -448, -514, -... | 5 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-371, -721, -756, 475, 60, -472, 553, -965, 143, -225, 569, 368],\n [-394, -332, -454, -366, -247, -281, 329, 336, -236, -291, 297, 376],\n [773, -89, 91, 527, 311, 477, -323, 139, -252, 579, -86, -232],\n [-251, 43, -192, -493, 102, -50, 31, 495, -38... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-82, -387, 523, 688, 306, 994, -1468, -190, 531, 183, 344, 867],\n [-1029, 98, -403, -239, -57, 204, 305, 513, -481, -789, 543, 1],\n [468, 94, 309, -725, -222, -318, 1139, -49, -184, -312, -694, -356],\n [-373, -735, -54, -59, -439, 738, -533, 380, 22, -854, 256... | 7 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[595, 484, -163, -538, -64, -312, -511, -150, 280, -551, 911, -178],\n [-460, -450, 196, 136, -732, 422, 640, -718, 600, 356, -576, 610],\n [620, 524, -188, -488, 136, -372, -596, 60, 80, -556, 916, -308],\n [-410, -344, 122, 332, -64, 240, 386, -12, -... | 2 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-511, 231, -314, 10, -260, 682, 1219, 551, -468, 274, 259, -969],\n [-863, -1029, 114, 133, 573, 37, 91, 433, -149, 362, -203, 201],\n [925, 985, 523, 166, -800, 240, -177, -1074, -53, -622, 285, -303],\n [-855, -421, 108, 487, 480, 1075, 469, 454, 41... | 7 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-108, -1010, -1400, -473, 398, 196, -1883, -66, 45, -419, 1122, 147],\n [-542, 541, 467, -279, -101, 31, 145, 51, -661, -105, -48, -88],\n [962, -177, 676, -1031, -537, -235, 145, -647, -858, -196, -291, -49],\n [-118, -51, 1141, -253, -74, -1234, 102... | 6 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-493, -171, 360, -428, 1177, -230, -147, -104, -20, -784, 160, 526],\n [-85, 603, 759, -236, -31, -744, 107, 512, -212, -109, -1000, -375],\n [617, -276, -426, 595, -1120, 266, 207, 366, 492, 746, -83, -495],\n [555, -1265, -147, 144, 69, -480, 497, -756... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[63, -54, 78, 42, -30, -24, -51, 3, -45, 54, 30, -33],\n [-84, 72, -104, -56, 40, 32, 68, -4, 60, -72, -40, 44],\n [-546, 468, -676, -364, 260, 208, 442, -26, 390, -468, -260, 286],\n [336, -288, 416, 224, -160, -128, -272, 16, -240, 288, 160, -176],\n [-315, 270,... | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-475, -596, -54, -681, 839, -448, -868, 465, -532, 486, 453, 320],\n [909, 442, 292, 242, -283, 668, -274, -614, 178, -846, 1345, 499],\n [-1025, 143, 586, -8, 135, -638, -633, 504, -112, 451, 291, 28],\n [378, 218, 0, 380, -432, 234, 238, -486, -58, -646, -168, -24... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-858, 910, 977, 357, -1257, 484, 307, 129, 695, -130, -899, -564],\n [46, -201, -1598, 1036, 531, -1154, 707, 866, 313, -978, 842, -22],\n [508, -904, 370, 627, -374, 629, 1033, -17, -414, -884, -656, -642],\n [381, 129, 1704, -615, -87, 595, 202, -1525, 969, 884, -... | 10 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[106, -526, -1050, -1661, 1908, 842, -1706, -196, 294, -193, 1088, -1622],\n [-450, 1021, -851, 921, -723, 72, 306, 1434, -1579, -524, -812, 199],\n [-123, -1109, 434, 120, -543, 1297, 514, -176, 1278, 87, -449, 73],\n [15, -1718, 124, -1179, -1014, 1553, 8, -221,... | 10 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-573, 417, 193, 422, -199, 500, -197, -213, 196, -627, 227, -336],\n [167, 520, 632, -113, 247, -772, -887, -23, 135, -324, 342, 271],\n [-904, 5, 814, 287, 557, -107, -848, -85, 329, -704, -62, -171],\n [905, -613, -126, -846, 423, -540, 57, 679, -10... | 5 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-578, -680, -431, 860, -770, 1792, -244, 547, -81, -585, -1284, 1016],\n [16, -115, 766, 431, 665, -88, -811, 605, 750, 111, 812, 881],\n [1374, -558, -275, 650, -377, 202, 584, 300, 518, 514, 101, -1592],\n [345, -432, 418, 905, 672, 838, 52, 1539, 1088... | 10 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-960, 860, 564, 182, -902, 560, -108, -570, -408, -282, -704, 116],\n [-224, 379, 495, 135, 111, 200, -577, 499, -171, -214, -272, 602],\n [589, -925, -815, -756, -230, 385, 647, -226, 1119, 397, -187, -613],\n [-667, 673, 499, 493, 25, -205, -419, 27... | 4 | MATH |
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