messages listlengths 1 1 | ground_truth stringclasses 11
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Calculate the rank of matrix A where A =\n[[-966, 885, 331, 393, -437, -372, 1394, 731, -955, 601, -206, 1305],\n [-997, -234, 170, 457, -308, -1, 599, -328, 200, -715, 290, -472],\n [598, -574, 1480, 288, -479, -817, -17, -1211, 507, -2057, -882, -956],\n [-529, -276, 271, 27, 12, 278, 114, -502,... | 10 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-34, -1317, -244, 201, 325, 1971, -348, 6, 536, -782, 1640, -1249],\n [-126, -257, 573, -1005, -94, -574, -571, 503, -1352, 152, -1078, 232],\n [-10, -721, -197, -343, 1737, 1224, 920, 650, 101, -1171, 1976, 444],\n [-832, 225, 433, -1263, -604, -1656... | 11 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[255, -823, -380, 1333, -508, 711, -792, -1128, 113, -1092, 1168, 643],\n [-575, -379, 10, -5, 159, -168, 310, -1023, 217, -1076, 299, -595],\n [869, 358, -886, 587, -58, -282, -410, 1450, -1169, 287, 1268, 641],\n [472, 566, 1089, -1827, 440, -1437, 610, 439, 969, 4... | 11 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[1527, -230, -1123, 643, 1026, -536, -8, 874, -692, 1951, -1193, -392],\n [651, -290, -637, -718, 314, 691, 222, -666, -378, 1731, -242, -626],\n [584, 629, 453, -288, 592, -104, 382, 311, -708, 223, 640, 455],\n [-168, -393, -158, -542, -115, 990, -356, -656, 372, 5... | 11 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-80, -35, 158, 244, -552, 863, 205, 369, -450, -272, -583, -426],\n [-64, -281, -371, 919, -263, 89, 12, 456, -513, -656, -632, -86],\n [-283, -351, -122, 467, 149, -370, 108, 184, -171, -390, 821, -123],\n [246, 106, 68, -454, -276, 447, 548, -50, 296, 332, -40,... | 5 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[483, 483, 336, -399, -294, 147, 273, -168, -378, 273, -462, 504],\n [575, 575, 400, -475, -350, 175, 325, -200, -450, 325, -550, 600],\n [-414, -414, -288, 342, 252, -126, -234, 144, 324, -234, 396, -432],\n [-115, -115, -80, 95, 70, -35, -65, 40, 90,... | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-491, 312, -61, -844, -81, -347, -1064, 443, 627, -193, -957, 870],\n [741, -139, 232, 1611, 337, 49, 963, -1067, -1100, 371, 1703, -391],\n [136, -670, -111, -358, -554, -13, -32, 102, 535, -98, -85, -148],\n [176, 185, -122, -341, -763, -74, -410, -... | 6 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[76, -440, 602, -54, 548, -504, -448, 342, -90, -290, 712, 8],\n [33, -300, 411, -57, 369, -357, -339, 261, -75, -195, 486, 24],\n [-27, 396, -543, 93, -483, 483, 477, -369, 111, 255, -642, -48],\n [83, 224, -310, 158, -249, 343, 445, -354, 134, 130, -366... | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[635, 556, -204, 573, 161, 351, 935, 103, 415, 289, 1085, 1141],\n [243, 807, -532, 86, -468, 283, -152, 307, 354, 911, 981, -202],\n [923, -182, -185, -826, -342, -1290, -412, 686, 303, -112, -700, 230],\n [-164, -148, 447, 511, 245, 545, -117, 71, -624, 171, 25,... | 6 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[116, -120, -936, 618, -150, -135, -357, -383, 113, 625, -12, -144],\n [-315, -418, 383, -130, -118, 398, 412, -64, -205, -549, -223, 242],\n [-755, -210, 513, -558, 108, 525, 243, -151, -92, -496, 219, 606],\n [-309, 130, 729, -622, 190, 190, 208, 212... | 3 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[426, -269, 190, -79, -560, 930, 79, -107, -343, -422, -251, 383],\n [-353, 645, -152, 227, 650, -527, 310, -309, 338, 208, 313, -504],\n [-202, -868, 392, -259, -944, 49, 9, 214, 68, -464, -647, 500],\n [167, -525, 160, -176, -546, 318, -171, 211, -18... | 3 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-471, 37, 251, -439, -6, -101, 822, -166, -578, 152, 11, -263],\n [298, -63, -449, 226, -599, -473, 799, -139, -119, 239, 281, 218],\n [238, -140, 137, 85, 297, -213, 100, 640, -50, 50, 624, -550],\n [560, 162, -909, 439, -952, -563, 655, 257, 181, 35... | 6 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[1147, -338, -188, -26, -615, -246, 886, -103, -435, -718, 626, -723],\n [-212, -435, 89, 374, 345, -669, -447, 858, 713, 242, 139, 131],\n [237, -906, -155, 1853, 814, -109, 1437, -18, -756, -563, 379, -285],\n [-400, 341, -589, -611, -717, 1476, 358, -3... | 9 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[267, -31, 94, 382, 43, 274, 290, -46, 410, -357, 391, 139],\n [-168, 147, -124, -354, -427, -570, -233, -492, -917, 724, -521, 112],\n [335, 92, 98, 476, -440, -96, 413, -754, -263, 139, 182, 447],\n [-722, -238, 330, 276, 142, -22, 254, -16, -354, 374, ... | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[223, -207, -40, -342, -240, 75, -243, 196, -295, 644, -551, 163],\n [770, 554, -310, -470, -377, 67, 960, 319, 434, -433, -531, 504],\n [1051, -1134, 1517, -994, 13, -479, 48, 619, -249, 1031, -633, -99],\n [-1226, 241, -847, 223, 614, 235, -1096, -858, ... | 8 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[46, 143, 305, -513, 106, -260, -80, 278, -259, -207, -284, -858],\n [142, -8, -273, 380, -88, 247, -50, -54, 4, -109, -3, 430],\n [-1049, -409, -382, -124, 325, -338, -634, -1545, 105, 882, 301, 650],\n [-638, -1322, -313, -351, -450, -1147, -301, -121, 436, 1086, 6... | 6 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[54, -77, -462, 271, 810, 79, -976, 67, -517, -430, 796, -161],\n [659, -354, -19, 409, 1001, -36, -991, -1008, 947, 661, 1494, -1283],\n [142, -725, -24, 619, -725, 226, 259, -238, -208, -159, 292, 869],\n [476, 78, -426, 884, 537, -747, -361, 272, 256, 387, -103, -... | 8 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-96, -287, 176, -299, 145, -481, 132, -159, 40, 157, 459, 168],\n [279, 136, -53, 250, 60, -295, 329, 157, -165, 208, 93, 740],\n [-132, -252, 193, -264, -95, -393, -89, -118, -173, -111, 294, 22],\n [-33, -228, 127, -226, 220, -447, 229, -127, 103, 2... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-601, 419, 98, 61, -113, 538, -1070, 919, -1537, -252, 1998, 2425],\n [-415, -565, 72, 187, 338, -469, 698, -707, 270, 359, -285, -411],\n [536, 769, -105, 532, 460, -94, -1024, 1456, -58, -286, -638, -928],\n [481, 958, 465, 1060, 253, -8, -2336, 2283, -1045, 31... | 11 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-861, -62, 2081, -1350, -1148, -1182, 492, 453, 199, 203, 574, 508],\n [-452, 323, 849, 365, 451, -174, -558, 444, -651, 331, -519, 507],\n [230, -808, 436, -899, -1263, -1014, -16, 32, 228, -196, 711, -635],\n [-764, -53, 328, -1017, 291, 720, 208, -246... | 9 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[25, 76, 316, 342, 29, -143, 37, 45, 223, 62, 124, 208],\n [329, 320, 470, 568, -159, -430, 64, -40, 371, 284, -86, 457],\n [-64, -76, -166, -190, 20, 113, -21, -5, -124, -66, -18, -135],\n [313, 340, 640, 746, -123, -485, 83, -5, 487, 298, 8, 554],\n [-434, -296,... | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-21, 20, -8, -12, 12, -22, -12, 25, 18, -1, 12, 18],\n [84, -80, 32, 48, -48, 88, 48, -100, -72, 4, -48, -72],\n [189, -180, 72, 108, -108, 198, 108, -225, -162, 9, -108, -162],\n [-399, 380, -152, -228, 228, -418, -228, 475, 342, -19, 228, 342],\n [-378... | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-201, -122, -230, 152, 264, -267, 660, 116, -119, 120, -544, 194],\n [73, -436, 650, 1125, -434, 173, -429, -360, 455, 342, 188, -654],\n [-765, -292, -789, 132, -641, 72, 582, 1166, -858, 387, 547, 606],\n [-556, -45, 52, -843, -188, 415, 1358, 1013, -1043, 257, -3... | 9 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-481, 455, 12, -500, 1338, 968, -1331, 583, 985, 41, 1391, 83],\n [179, -993, -384, 392, 358, 497, -231, 891, 992, 441, 608, -686],\n [-131, 309, -45, 16, -571, 52, 438, 1129, -203, 1132, 1284, -692],\n [-1054, 256, 814, -1255, 1004, 333, 553, 360, -370,... | 8 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-629, 1021, -323, 204, 422, 809, -128, 42, -14, 6, -331, 789],\n [-837, 1128, -456, 731, 1060, 2480, -349, 107, -1858, 491, 501, -51],\n [-372, -331, 1402, -384, -84, -823, -126, 1403, 821, -429, 696, -1470],\n [-1012, 2041, -1006, -452, 190, -180, 1233,... | 11 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-284, -457, -23, 152, -677, -135, -721, -600, 1337, 927, 1214, -62],\n [645, 258, 602, -269, 921, 1072, 288, -761, -345, 533, -88, 511],\n [365, 1119, 934, -162, 730, 1013, -489, 262, 617, 733, 500, 911],\n [455, -8, 1204, -1291, 809, -408, 793, -323, -11, 831, -... | 10 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-568, 1087, -825, 743, 994, 1065, -1339, -381, 212, 777, 263, -330],\n [328, 1375, -530, 1004, 295, 524, -207, 766, -902, -932, 1233, 2488],\n [-506, -920, 1122, 661, 475, -562, -682, 485, 646, 1141, -16, -310],\n [491, -164, -117, -157, 72, -1005, 308, ... | 11 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[88, -416, -12, 624, 88, -372, -664, -204, 472, 176, 104, -672],\n [169, -636, -52, 940, 155, -541, -992, -338, 706, 247, 152, -1008],\n [-254, -56, 258, 192, -146, -264, -268, 174, 184, 194, 68, -240],\n [276, -560, -170, 776, 212, -374, -788, -394, 5... | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-493, -50, -1095, -304, -807, 512, -1136, 12, -533, -2150, 461, -511],\n [357, 871, -655, 1166, 772, -44, -98, 721, -1130, 223, 904, 744],\n [-453, -672, 100, -399, 1226, 886, 384, 352, 1165, 567, -822, 268],\n [-194, 125, -259, -144, 863, -528, 888, 290, -386, -41,... | 8 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[534, -486, -134, -228, 135, 403, 711, -1441, -1265, -445, 703, 87],\n [-287, 218, 35, 675, -770, 15, -521, -73, -1446, -1089, 667, -570],\n [506, -1349, 183, 80, -862, 109, 656, -518, 379, -672, 580, -478],\n [269, -167, -432, 715, -292, -831, -351, -... | 10 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[198, -892, 158, 76, 147, 421, -142, 407, 292, -417, -151, -134],\n [-347, 292, 272, 273, 545, 546, 373, -398, 235, -31, -802, -511],\n [89, -776, 617, -420, 412, 341, -20, 640, 839, 324, 46, 370],\n [-263, 768, -234, 241, -551, -697, 470, -379, 327, 4... | 6 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[226, 390, 760, 340, -270, 268, -356, -204, -328, -1258, -808, 198],\n [487, 686, 278, 651, 205, 540, -611, 397, -420, -345, -100, 300],\n [-211, -145, -30, 356, -219, 423, 155, 213, 452, 14, 65, 242],\n [527, 626, 492, 457, -131, 313, -406, 64, -652, -886, -467, 63]... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-617, 1465, 618, 272, -899, 632, -289, -254, 1319, 1338, -1076, -1437],\n [272, 279, -375, -1029, -220, -355, -329, 39, 1094, -596, 273, -49],\n [-449, 1061, 1562, -1674, -1160, -710, -94, 237, 486, 431, -1390, 266],\n [614, -264, -161, -1206, -150, -1330, 100, 7... | 11 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-175, 113, -1043, -554, -632, -574, 554, 243, 749, 305, 1181, 90],\n [-41, 1043, -97, -873, -346, 517, 107, -477, -729, -320, -371, -443],\n [270, -352, -21, 413, 168, -276, -73, 492, 4, -168, -81, 347],\n [-159, 534, 221, -576, 62, -4, 88, -338, -1105, -150, 348... | 5 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[218, -20, -62, 89, -2, -500, -84, 290, 158, -526, 197, 237],\n [-138, 306, -234, 237, 162, 204, 15, -276, -315, 339, 30, -363],\n [-20, -400, 380, -410, -220, 200, 60, 100, 280, 40, -230, 270],\n [36, 428, -412, 446, 236, -248, -70, -88, -290, -78, 26... | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-96, 6, 78, 42, 126, 42, -36, 54, 6, 42, 84, 12],\n [144, -9, -117, -63, -189, -63, 54, -81, -9, -63, -126, -18],\n [-112, 7, 91, 49, 147, 49, -42, 63, 7, 49, 98, 14],\n [-48, 3, 39, 21, 63, 21, -18, 27, 3, 21, 42, 6],\n [-256, 16, 208, 112, 336, 112, -96, 144, 16, ... | 1 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[699, -115, 55, 226, -185, 254, 434, 129, 171, -675, 138, -136],\n [827, -229, -92, 501, 417, -38, 240, 346, -219, 434, 515, 98],\n [-10, 244, -55, 130, 205, -84, -253, 34, -252, 296, 101, 241],\n [521, -410, 19, 43, -61, 299, 651, 139, 281, -329, 16, -156],\n [-6... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[229, 279, 72, -28, 365, 260, 42, 155, -86, -131, 221, 22],\n [61, -369, 558, 68, -115, -400, -102, 125, 16, 241, -421, -92],\n [-219, -697, 454, 100, -555, -704, -150, -67, 120, 393, -677, -116],\n [-10, -334, 388, 56, -170, -352, -84, 54, 32, 206, -358, -72],\n [-2... | 2 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[486, 115, 67, 536, 296, 188, -446, 495, 190, 497, 93, 187],\n [-366, -775, 955, 399, 244, -233, -94, 239, 479, 127, 307, -20],\n [-684, -268, -12, -724, -437, -149, 602, -665, -163, -623, -169, -357],\n [-256, -705, 499, 289, -141, 262, 306, 22, 522, ... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[384, -232, -286, -356, 230, 442, 614, -266, -98, 244, -52, 316],\n [407, -223, -304, -362, 237, 427, 620, -240, -105, 262, -26, 296],\n [-176, -44, 199, -46, -123, 155, -203, -243, 9, -490, -694, 514],\n [-67, 114, -57, 293, 42, -353, 1, 331, 86, 564, 984, -855],... | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[770, -700, 653, 193, 280, -1002, 985, 14, 317, 385, 911, 481],\n [248, -671, -1075, 942, -472, 93, -577, 162, -348, 4, -144, -382],\n [-1366, -48, 727, -1336, 233, 455, 576, 503, 99, -637, 608, -839],\n [-441, 1273, 200, -119, -246, -764, 856, 432, 1191,... | 8 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-755, -611, -603, -2143, -614, -881, -428, 305, 1015, 1098, -1007, 515],\n [-82, -491, -570, -1240, -378, -1437, 278, -431, -119, 89, -1020, 740],\n [-247, -53, 201, 596, -337, -672, -1119, 540, 243, -210, -1066, 442],\n [35, -592, -95, -1266, -650, 5... | 11 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-201, 478, -225, 198, 1059, -172, 297, 418, -359, -331, 651, -211],\n [614, -272, -583, -190, 410, -256, -345, 326, 430, -644, 361, 189],\n [-286, 848, -226, 212, 260, -306, 600, 826, -172, -236, 354, -458],\n [-473, 185, -220, -192, 217, -378, 636, 1... | 7 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[197, 155, 226, 166, -53, 32, -65, -450, 291, 26, 254, 106],\n [-583, 56, -659, -341, 7, 377, 439, 705, 219, 35, -172, -74],\n [331, 232, 384, 277, -95, 22, -141, -729, 388, 33, 396, 178],\n [164, 451, 302, 375, -456, 194, -306, -935, -5, -9, 602, 532],\n [451, -5... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-2117, -83, -603, -1051, -113, -526, -1681, -52, -435, -1445, 707, 621],\n [206, 1204, -109, 1742, -712, 1708, 1131, -180, 540, 1538, -454, -1565],\n [-1146, 699, -29, 848, -733, 275, 611, -82, -950, 122, -1393, -928],\n [-315, 303, 340, 885, 73, 210, 396, 286, -433... | 11 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[613, 1013, -351, 16, 843, -199, 260, -28, 257, -259, -180, -144],\n [-419, 24, 777, 847, -179, 1379, 67, -591, -434, -234, -412, -581],\n [-1005, 89, -897, 1165, 453, 300, -212, -58, -2082, 422, -350, 253],\n [-48, -730, 382, -248, -193, -209, -216, -... | 8 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-513, -197, 519, -1070, -76, -16, 62, 829, -124, 20, 567, 205],\n [750, 749, -1058, 779, 616, 621, -46, -717, -108, -94, -1114, 9],\n [718, -340, -600, 889, -78, 218, -35, -144, 371, -481, -864, -476],\n [-241, 499, 668, -365, 263, 338, -33, -18, 84, 437... | 7 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-17, 391, -34, 17, 221, -68, -323, -238, 289, 340, -289, 238],\n [23, -529, 46, -23, -299, 92, 437, 322, -391, -460, 391, -322],\n [-26, 598, -52, 26, 338, -104, -494, -364, 442, 520, -442, 364],\n [11, -253, 22, -11, -143, 44, 209, 154, -187, -220, 187,... | 1 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-310, 742, 271, -68, -342, -758, 507, -1080, 196, -251, 750, -277],\n [182, 376, 514, 325, -594, -494, 774, -765, -281, -221, 615, -703],\n [-106, -656, 300, 237, -122, 522, 272, 375, 121, 369, 139, -479],\n [-282, -394, 298, 496, -382, 562, 446, 370, 217, 694, 2... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[828, -1043, -1055, -563, 490, -554, 286, 322, 621, -1127, -97, -1455],\n [-150, 63, -234, -775, -1111, -1152, -67, -590, 365, -131, -271, 77],\n [594, 274, 664, 1006, 746, -390, -285, 688, 984, 103, -173, -159],\n [-91, 681, 1240, 1009, 1083, 548, 174... | 8 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[40, -594, 443, 428, 269, 22, 540, 199, -278, -405, 1340, 797],\n [-218, -654, -357, -219, -205, -119, -857, 162, 401, -38, -347, -825],\n [264, 606, 111, -684, -349, -329, -273, -70, -1, 187, -910, -479],\n [-886, 368, -106, 608, 462, 460, 465, -1162, 270, 175, -326... | 6 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-599, 743, 750, 421, 1476, 456, 960, -1232, 361, -301, 1274, -735],\n [-385, 119, 49, -1035, 494, 45, -57, -102, -2299, -2455, 190, 621],\n [-645, -137, 490, 798, 2079, -1032, 469, -998, -320, 1337, 616, 958],\n [-620, 319, 415, -799, 495, 141, 134, -381... | 11 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[1035, 15, -366, -537, -135, 963, 411, 199, -83, 1619, -1040, 44],\n [328, -27, 411, -706, -196, 658, 1, -911, 579, 49, 937, 580],\n [641, -648, 297, 145, 969, 148, 466, 26, 842, -91, 918, 64],\n [-1319, 189, 463, 472, 831, 262, 816, -1167, 395, -660, 119... | 9 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-9, 180, 144, -18, -63, -225, -225, -27, 0, 18, -189, -99],\n [7, -140, -112, 14, 49, 175, 175, 21, 0, -14, 147, 77],\n [-6, 120, 96, -12, -42, -150, -150, -18, 0, 12, -126, -66],\n [-15, 300, 240, -30, -105, -375, -375, -45, 0, 30, -315, -165],\n [4, -80, -64, 8... | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-80, 19, 154, -131, 198, -159, 23, -61, -244, -58, 674, 393],\n [594, 100, -992, -121, -498, 734, 135, 63, -562, -165, 250, -350],\n [-378, 359, 413, 142, 27, -29, -93, 192, -257, -135, 569, 698],\n [720, -702, -357, -530, 504, -477, 350, -506, -125, ... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[201, 313, -332, 199, -204, -188, 204, -173, -131, 358, 188, -273],\n [-309, 161, 230, -220, 291, 791, -291, 275, -79, 128, -185, 180],\n [42, 502, -260, 100, -58, 302, 58, -30, -218, 536, 110, -220],\n [-234, -890, 616, -302, 256, -192, -256, 194, 382, -972, -304... | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[370, -256, -1248, -930, 652, -70, 274, -218, 1030, -558, 492, -506],\n [355, -268, -1014, -750, 556, -145, 232, -134, 835, -459, 456, -458],\n [298, -332, 26, 51, 134, -494, 47, 247, -32, -20, 306, -253],\n [-289, 376, -468, -393, 38, 667, 29, -421, 4... | 2 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[805, -654, -414, 294, 73, -863, -687, -945, 704, 456, 415, 612],\n [-134, -512, 943, -402, -313, -261, -1577, -1892, -609, 150, 164, 666],\n [738, -317, 193, 931, 159, 218, -1404, -2099, 153, 60, 220, 1024],\n [258, 618, -981, 849, 492, 298, 888, 1199... | 11 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-350, 75, 525, -50, 525, -275, -525, 300, 475, -50, 625, 400],\n [-112, 24, 168, -16, 168, -88, -168, 96, 152, -16, 200, 128],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n [-70, 15, 105, -10, 105, -55, -105, 60, 95, -10, 125, 80],\n [-238, 51, 357, -34, 357, -187, -357... | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-3, 526, -330, -296, 285, 79, 793, -541, -622, -318, -730, -628],\n [72, -375, -137, -1109, 279, -276, -447, 291, 639, 460, 226, 204],\n [-281, -442, 578, 588, -328, -604, -890, 421, 200, -94, 671, 881],\n [428, -340, 111, 840, -816, -206, -566, 484, ... | 6 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-48, 234, -72, -42, 282, 446, -66, 220, -278, 598, -64, 124],\n [257, -663, -300, -61, -587, -257, -576, -397, 407, -25, 215, -504],\n [646, -441, -1008, 345, -425, 295, -427, -644, 247, 813, -34, -218],\n [555, -807, -768, 131, -739, -103, -700, -687... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[73, -1046, 53, -359, 381, -416, 41, -101, -586, 280, -718, 299],\n [331, 31, -391, 286, -749, 45, 26, 123, -333, -328, 456, 360],\n [322, -301, -271, -88, -286, -266, -339, -15, -519, -7, 418, 125],\n [126, -403, -54, 53, -240, -2, 350, 83, -311, -59, -396, 377],\n ... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[420, -482, -178, 462, 360, -243, 670, 564, -363, 502, 1118, 258],\n [1781, -310, 346, 416, 107, 640, 822, 7, 232, 594, 749, 513],\n [-1411, 822, 559, -538, -78, 554, -198, 232, -11, -655, -507, -991],\n [-459, 322, 590, -594, -317, 303, -605, -879, 11... | 9 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[336, 74, -27, 83, -50, -1616, -548, -394, -5, -640, -636, 255],\n [818, 128, 40, -771, -168, 53, 113, 116, 598, -433, 856, -592],\n [-15, 589, 786, -316, -203, 562, -224, -1288, 240, 1007, -1417, 760],\n [891, 710, -142, -676, 374, -1361, -67, 223, 16... | 10 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-190, 66, 713, 31, 154, -433, 536, 44, 210, 934, 229, -612],\n [-217, -77, 20, 12, -243, 581, -303, 390, 685, 260, 121, -9],\n [-372, 155, -497, -163, 637, 232, 315, -544, -961, 634, 787, 853],\n [838, -268, -230, -741, 615, -233, 234, 75, -355, -494, -1... | 4 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[480, 498, 344, 568, 800, -372, -342, 944, 98, 372, -420, 72],\n [225, -118, 452, 396, 672, -599, 164, 884, -603, 424, -201, -35],\n [78, -245, -1136, 144, -420, 566, -173, -692, 519, -520, -582, -292],\n [-206, 488, 1036, -420, 60, -224, 4, 228, -80, ... | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-60, 400, -280, 180, -220, 340, -340, -140, -120, -100, -80, -20],\n [12, -80, 56, -36, 44, -68, 68, 28, 24, 20, 16, 4],\n [51, -340, 238, -153, 187, -289, 289, 119, 102, 85, 68, 17],\n [9, -60, 42, -27, 33, -51, 51, 21, 18, 15, 12, 3],\n [-39, 260, -182... | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[724, 272, -978, 298, -308, 124, -265, 370, 442, 391, -981, 189],\n [-88, 268, -24, 104, 240, 184, -184, -180, 60, -276, 116, 396],\n [-345, 333, 294, 105, 511, 287, -212, -392, -71, -584, 554, 594],\n [-566, 434, 126, -152, 306, 50, -215, -522, 144, -... | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[56, 501, -503, -695, 184, 222, 204, -56, 84, -438, 40, -29],\n [565, 343, 618, 27, 51, -617, -513, 378, 289, -966, -653, -663],\n [-715, -117, -228, -253, -87, 307, 1257, 378, -635, 1002, 1109, 213],\n [812, -213, 1549, 842, -92, -363, -1567, -177, 149, ... | 9 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-494, 30, 444, -135, 431, 127, -89, -251, 520, 185, 408, -246],\n [-741, 181, 666, -296, 536, -22, -125, -419, 508, 541, 544, -505],\n [38, -18, 312, 38, -18, -454, 340, -358, -374, 602, -312, -350],\n [95, -47, 258, 71, -47, -425, 346, -318, -380, 526, -344, -293],... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[1237, -485, 1143, -351, 95, -742, 1163, -97, -1533, -105, 116, 69],\n [-323, 833, 403, -479, 454, -1045, -278, -166, 389, 153, -429, 1654],\n [270, 443, 214, -758, -1121, -731, 482, 1201, -740, -438, 491, -581],\n [-675, -858, -285, 14, 1343, 538, 95, -407, 573, 125... | 11 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-469, -61, -279, 169, -160, -584, -820, 521, 775, 272, -567, -20],\n [18, 37, 637, -780, -257, -159, 248, 287, 345, -82, -245, 85],\n [94, -45, -247, 344, 177, 209, 62, -259, -343, -16, 269, -71],\n [280, -276, -157, 326, 360, 473, 395, -514, -703, -97, 668, -281],\... | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-159, 144, -211, -1092, 10, 591, 27, 30, 13, -574, 14, 905],\n [-681, 619, 64, -453, 221, 235, 138, 589, 355, -345, 117, 374],\n [484, 835, 740, 514, 595, 264, 1083, 945, 371, 845, -1049, -1461],\n [38, -588, 41, 379, -456, 341, 161, -423, 231, 334, -... | 6 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-1537, -1470, -741, 246, -70, 90, 166, 853, -1009, 644, 846, -350],\n [-806, 984, 1475, 339, -374, -1403, 323, 357, 119, 1911, -2, 436],\n [630, 1032, 469, -534, 752, -1311, -1064, 765, -210, 1640, -129, -454],\n [-254, -289, 101, 409, 918, 825, 147, -14... | 10 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[72, 15, 9, -33, 51, -24, 21, -42, -51, 45, -63, -48],\n [24, 5, 3, -11, 17, -8, 7, -14, -17, 15, -21, -16],\n [528, 110, 66, -242, 374, -176, 154, -308, -374, 330, -462, -352],\n [336, 70, 42, -154, 238, -112, 98, -196, -238, 210, -294, -224],\n [-240... | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-334, 632, 167, 262, 110, 216, -364, -323, 548, -369, 212, 882],\n [-450, 654, -271, -134, -228, 222, -462, 119, 672, -751, 198, 626],\n [1134, 53, -321, -454, 315, -1116, -399, -789, -338, 238, -13, 293],\n [-230, 155, -233, 48, -1268, -576, -674, 1327, -685, -521,... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[668, -284, -502, -40, -181, 429, 382, 741, -182, 95, -312, -102],\n [139, 131, 283, -122, -431, -45, -175, -48, 122, 259, -129, -384],\n [-274, 582, 474, -160, -123, -185, -288, -505, 334, -131, -84, -72],\n [508, -108, 32, -124, -579, 159, 6, 365, -10, 401, -258... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-77, 552, -83, -334, -368, 194, -106, -701, 296, -575, -1837, 1635],\n [-200, -128, 199, -76, 1139, 73, -596, -936, 815, 1303, 877, -120],\n [611, 1167, 567, -1193, 1579, 86, 469, -423, 282, 317, -182, -332],\n [284, 1764, 139, -675, 623, 570, -349, -449, -152, 216,... | 9 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[8, 119, 56, 150, -102, -120, 53, 195, -274, -43, 110, 74],\n [430, -864, 298, -808, -228, 104, -174, 170, 132, 542, 206, -260],\n [-35, -360, -185, -460, 330, 380, -165, -625, 870, 125, -355, -230],\n [-230, 241, -242, 162, 282, 144, 1, -405, 382, -203, -284, 10]... | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[0, 297, 936, 984, -269, 599, -256, -386, 698, 218, 317, 155],\n [350, 42, -78, 151, -639, -455, -266, 56, 502, -298, -654, 309],\n [-866, -617, -171, -462, 1019, 1114, -627, -197, 516, -46, 775, 430],\n [-359, -835, -1052, -608, -291, -772, -141, 409, -2... | 8 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[584, -645, 683, 1067, 783, -40, -6, 1019, 100, -1418, -650, 390],\n [-1128, -236, 356, -411, -1029, -288, -121, 90, 556, -1156, -963, 1268],\n [1167, -497, 1147, -50, 695, 41, 649, -33, 649, -213, -610, -343],\n [-1290, -27, -1260, 412, -313, 131, -10... | 9 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-228, 435, -249, 324, 318, -531, -114, 261, -147, 165, 441, -102],\n [-352, -290, -476, -498, 88, 96, -2, 174, 2, -716, 168, 566],\n [-472, -365, -636, -643, 128, 106, -7, 239, -3, -936, 238, 741],\n [-180, 45, -225, -54, 126, -135, -36, 135, -45, -171, 189, 144]... | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-99, -379, -929, 1477, -410, -785, -546, 195, 177, -264, 569, -1361],\n [-636, 379, -405, -173, -217, 567, 337, -622, -708, -800, 151, 975],\n [-292, 732, -1590, 1334, 342, -353, -940, 271, 202, -628, -564, -980],\n [488, 278, -203, 113, -406, 991, 29... | 9 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-306, -621, -606, -354, -150, -383, 349, -436, -1380, 532, 894, 936],\n [574, -143, -257, -121, 176, 736, 135, -12, -1758, 118, -40, 945],\n [-1365, -508, -269, -1594, -764, -737, 601, 79, 506, -193, 84, -4],\n [-197, 944, -464, 316, 580, -782, -156, 632, -672, 174,... | 10 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[595, -678, 209, -1064, 744, -1576, 449, -792, -709, -235, 691, -227],\n [-748, -967, -558, 472, 155, 879, -327, 841, 752, 517, -27, -43],\n [136, -874, 721, -789, -550, -106, -965, -783, -579, 348, 1624, 145],\n [694, -102, -860, -414, -181, -259, -14... | 11 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-625, 400, 389, 324, 489, -298, 393, 411, -481, 628, -459, 272],\n [848, -3, 45, 481, 509, 276, -534, 190, -254, 212, 462, -1051],\n [323, 479, 245, -440, 490, 6, -621, 368, -850, 172, -644, -311],\n [893, 151, 128, 109, 538, 69, -700, 202, -12, -92, 235, -982],\... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-121, -341, -86, -1261, -384, 806, 1314, -516, 1573, -992, -978, 732],\n [34, 97, -495, 1012, -106, 582, -191, -425, 387, 1559, 431, -1391],\n [-502, -49, -1017, -580, -220, 43, -406, 400, -1280, -814, 1260, 1203],\n [660, 398, 957, 135, 1026, -439, -86, 434, 75, 33... | 11 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-52, -14, 16, -34, -4, 40, 2, 16, 12, 36, -24, -12],\n [390, 105, -120, 255, 30, -300, -15, -120, -90, -270, 180, 90],\n [598, 161, -184, 391, 46, -460, -23, -184, -138, -414, 276, 138],\n [-416, -112, 128, -272, -32, 320, 16, 128, 96, 288, -192, -96],\n [-182, -... | 1 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[495, 530, 159, -374, -38, -912, 216, 143, 1788, 199, 737, 1216],\n [454, 624, -694, -956, 494, -420, 1428, -195, 475, -117, -321, 510],\n [494, -1124, 559, 386, -169, 189, -1114, 801, -388, 746, 328, -197],\n [-1421, 182, -17, 691, -1504, -550, -405, -123, 411, -... | 7 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[674, 42, -50, 135, 196, 345, 4, -682, 1185, -625, -737, 696],\n [1853, -554, 974, -410, 425, -761, 1495, -246, -730, -1066, 67, 744],\n [-1004, -1175, -184, 336, 81, 1337, -632, -1584, -69, 347, -17, -1218],\n [997, 1626, 593, -401, -520, -1310, 1698, 829, -761, -81... | 11 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-378, -1257, -299, -130, -1521, -792, 620, -208, -222, 582, 157, -495],\n [-476, -351, -717, -220, 90, -94, 253, 241, 576, -528, 728, -195],\n [-945, -1682, 74, 657, -329, 665, 701, 890, 521, -325, 879, -1276],\n [-445, -1024, 89, 287, 24, 504, 937, 114, -328, -5... | 8 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-543, 730, -258, 624, 11, 8, -357, -108, -572, -453, 164, -50],\n [-528, 480, -118, 429, 131, 243, -322, 132, -312, -313, 269, 25],\n [24, -144, 76, -114, 58, 114, 28, 120, 144, 82, 46, 38],\n [-87, -86, 76, -57, 108, 209, -35, 192, 124, 40, 123, 57],\n [429, 18, -1... | 2 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[144, 481, -866, -362, 544, 2168, -8, -10, -301, -365, 487, -136],\n [-746, -737, -573, 858, 225, -469, 1091, 667, -720, 577, 364, -1064],\n [541, 735, 620, 43, 1159, 663, 10, 46, 179, -1056, -281, 577],\n [-602, -581, -296, 123, -177, 359, -291, -158,... | 6 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-39, 357, -377, 331, -776, -394, 438, -324, -1043, -144, 24, -374],\n [-219, -168, 571, 239, 116, 62, -439, -106, 483, 376, -37, -54],\n [-178, 225, -13, 394, -395, -450, 225, -345, -627, 109, 55, -320],\n [232, 216, -655, -232, -175, -118, 526, 85, -619, -419, 48, ... | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-310, -233, 99, 302, 431, 458, -877, 363, 176, -372, 687, 863],\n [-265, 106, 561, 281, 143, -454, -25, -126, 878, 210, 204, -259],\n [-213, 72, 519, 213, 189, -498, -3, -120, 846, 138, 90, -309],\n [-10, -34, -25, 6, 43, 63, -84, 44, -32, -59, 42, 93],\... | 3 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[747, 726, -2, 656, 349, 393, -225, 1134, 542, 487, 1644, 390],\n [-1046, -1153, -647, -1548, -947, -285, 1069, -1003, 254, -396, -968, -448],\n [-413, -124, 22, -1509, -587, -82, -54, -511, 1, -412, -1034, -282],\n [-315, -61, 141, -702, -741, -379, 1... | 10 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-181, 947, -562, -678, -826, 44, -960, -1095, 1510, 628, 967, -573],\n [-653, 198, 987, 381, -674, -383, 391, -1307, 492, -1355, -487, -73],\n [13, 1911, 713, 347, 51, 1009, -1314, -545, 75, -105, -369, -391],\n [196, -360, -1151, 103, 285, -891, 481, 92... | 9 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[41, -335, -360, 301, 491, 548, -1496, -202, 650, -444, 209, -17],\n [1323, 750, 996, -751, -304, 159, 329, 1041, -281, -81, 221, 32],\n [147, 229, -382, 298, 601, 26, 462, 839, -304, -123, -52, -349],\n [-155, 6, -478, 199, -816, 705, 707, -329, 627, ... | 7 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[498, 546, 1111, 787, -122, 790, -826, 1024, -1182, 873, 590, -569],\n [606, -47, -11, -769, -117, -446, 81, -119, 761, -711, 375, 466],\n [343, 763, 241, 677, -355, -216, -438, 1316, -573, -191, -118, -544],\n [-16, -135, -416, -618, -409, 368, 547, -719... | 9 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-829, 183, -651, -583, -268, 316, -754, 33, 248, 268, 899, 505],\n [266, -376, 758, -585, -261, -436, -381, -381, 320, 327, -434, 50],\n [1212, 580, 423, 268, 422, 557, -485, 973, -34, 57, 630, 79],\n [162, 291, -1019, 292, -325, -184, 809, -35, -839,... | 8 | MATH |
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