messages listlengths 1 1 | ground_truth stringclasses 11 values | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Find the rank of the matrix:\n[[-39, 1004, -540, -702, -250, 518, 777, 55, -535, 814, -916, -78],\n [214, 951, 1991, -1144, 1097, -524, -1084, 683, -151, 710, 580, 1051],\n [516, 389, 171, -350, 1225, -1387, -475, -891, 1039, -461, 152, -543],\n [1805, 4, 431, -1178, -5, -890, -570, 1086, 942, 770... | 11 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[420, -525, -294, -126, -273, -252, 189, -273, 546, 336, -21, 42],\n [220, -275, -154, -66, -143, -132, 99, -143, 286, 176, -11, 22],\n [-40, 50, 28, 12, 26, 24, -18, 26, -52, -32, 2, -4],\n [480, -600, -336, -144, -312, -288, 216, -312, 624, 384, -24, 48... | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[326, -151, 521, 83, -15, -445, 136, -333, -55, 434, -160, -395],\n [-326, -475, -581, 651, 511, -553, -100, -5, -377, 336, -134, -619],\n [-21, -527, 838, -534, -71, -116, 1157, -462, 350, 550, 161, 794],\n [461, 1607, 99, -660, -351, 845, -957, 479, ... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-36, 852, 73, -335, -166, -610, 517, 720, 571, -743, -125, 580],\n [-198, 184, -258, 302, -188, -544, 264, 490, -252, -298, -186, 208],\n [-151, -237, -304, 483, -134, -250, -8, 127, -600, 52, -171, -69],\n [-311, 527, -302, 265, -266, -910, 542, 895, -54, -618, -22... | 3 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-581, 1183, -368, 549, 1540, -1887, 472, -917, -251, -1011, -1, -96],\n [323, -334, -317, 961, -295, -1093, 1036, -223, 864, -840, 1769, -99],\n [-949, 1335, -184, 598, 240, -24, -963, -1075, -535, -432, 116, 453],\n [861, -239, 449, -818, -108, 1315,... | 11 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[502, -77, -605, -8, -282, -163, -517, 555, -463, -477, -196, -234],\n [374, -45, -506, 18, -190, -191, -510, 473, -389, -406, -141, -298],\n [452, -110, -363, -86, -320, 82, -55, 304, -272, -263, -193, 196],\n [-168, 12, 264, -24, 72, 132, 312, -252, ... | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-595, -1465, -350, -763, -310, 395, 11, -416, -2227, 209, 306, 1353],\n [45, 128, -1587, 216, -1180, -1302, -226, 778, 212, -312, 654, 925],\n [657, -91, -1101, 197, -1206, -1235, 30, 444, 254, -208, -748, 1187],\n [721, 126, -112, -77, -91, -793, -857, 29, 988, 547... | 7 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[275, 475, 575, -325, 575, 50, 600, -125, 600, 0, -50, -125],\n [154, 266, 322, -182, 322, 28, 336, -70, 336, 0, -28, -70],\n [-176, -304, -368, 208, -368, -32, -384, 80, -384, 0, 32, 80],\n [-176, -304, -368, 208, -368, -32, -384, 80, -384, 0, 32, 80],\n [-231, -399... | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-323, 130, 303, -363, 1090, -788, -458, 714, -172, 327, 714, 280],\n [610, -50, -213, 531, -611, 838, 457, -432, 377, -573, -282, -44],\n [-599, -399, 194, -860, -456, -138, 556, -195, -464, 984, -133, -108],\n [608, -465, 200, 123, -171, 402, 715, -2... | 4 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[87, -132, -633, -506, -1842, -76, -130, -699, -419, 821, 467, 91],\n [944, -726, 801, -190, -1948, 18, -606, 920, -616, 839, 430, 37],\n [707, -766, 302, 483, -1195, 386, -808, 987, -40, -107, -438, 12],\n [382, -1007, 520, 96, -1854, -228, -693, -128... | 9 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-352, 330, 22, 308, -286, 198, 44, -132, -440, -286, -352, 330],\n [-112, 105, 7, 98, -91, 63, 14, -42, -140, -91, -112, 105],\n [-256, 240, 16, 224, -208, 144, 32, -96, -320, -208, -256, 240],\n [-272, 255, 17, 238, -221, 153, 34, -102, -340, -221, -... | 1 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-628, 219, 718, -301, 204, -162, 414, 200, 470, 143, -108, 202],\n [243, 504, -820, 715, -204, 238, 114, -390, -201, -408, 82, -163],\n [-874, -79, 337, -144, 363, -76, -70, 10, 506, 413, -117, -27],\n [-653, -612, -882, 377, 110, 142, -430, 414, 427,... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[490, -196, -686, 65, 910, -376, -94, 657, -537, -253, -609, 103],\n [-410, 663, 65, 60, -1698, -929, -79, 675, 333, -542, 1028, 690],\n [116, 363, -209, 9, 402, -505, 689, 2140, -54, -339, -145, 339],\n [-924, 883, 67, 739, -406, 137, 542, -40, 237, -... | 7 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-357, 494, -1015, 808, 1108, -694, 455, -17, -544, 1164, -1692, 318],\n [-745, -31, 831, 1029, -331, 900, -226, 313, -856, -676, 179, 622],\n [-176, -196, 493, 1061, -37, 201, -117, 886, -431, 122, 410, 1207],\n [523, -218, -677, -544, 585, -491, -243... | 8 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[10, -1650, 1085, 121, 482, 351, -603, -522, 365, -1171, -283, -937],\n [1001, -782, 924, 446, 448, -551, 87, 526, -53, -820, 146, -254],\n [614, 206, 239, 683, 190, -397, 429, 365, 268, 309, -186, 373],\n [9, 13, 477, 434, -847, -649, -269, -36, 971, 389, -53, -532]... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[263, -170, 497, 52, 437, -480, -109, -226, -421, -106, 48, 44],\n [155, 23, 60, 240, 497, -299, -238, -127, -434, -347, 498, 451],\n [448, -198, 422, 112, 712, -566, -218, -674, -642, -42, 204, 438],\n [317, -87, 338, 243, 724, -554, -283, -311, -653, -347, 473, ... | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[354, -69, -901, 121, -166, 970, 82, -294, -351, 118, -355, 892],\n [-354, 340, 43, -383, -115, 1012, 681, 422, -423, -783, -1230, 638],\n [546, -73, -811, -31, 472, -150, -308, -114, 349, -24, 159, 336],\n [402, 540, 680, -486, -119, 646, 249, -428, 406,... | 6 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-604, -68, 247, 212, 137, 63, -397, -533, -909, -239, -273, -674],\n [-440, -434, -358, -589, -1002, -304, 350, 506, -591, 431, 600, -367],\n [16, 163, 92, 38, 87, 476, 203, 119, -117, -256, -186, -187],\n [212, 81, -21, 6, 74, 67, 96, 108, 296, -7, -... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[885, 812, 154, 26, 195, -335, -87, 517, -315, 104, -514, 167],\n [-1051, -715, -560, -625, -455, 474, -106, -815, 639, 43, 264, -738],\n [-246, -567, 780, 689, 531, 515, 36, -824, -547, 4, 268, 339],\n [311, 592, 125, 365, 353, -772, 92, 1151, -138, 97, 488, 987],\n... | 6 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[65, 415, 313, 486, -57, 337, 236, -133, -82, 383, 502, -208],\n [96, -600, -252, -795, -192, -321, -423, 63, 108, -654, -549, 87],\n [-283, 115, -231, 281, 419, -170, 195, 168, -6, 265, -141, 281],\n [-397, 85, -369, 299, 581, -290, 225, 252, 6, 295, -279, 419],\... | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-557, 520, 134, 311, 45, 315, -767, 164, 422, -514, -237, -253],\n [177, -288, -500, -717, 883, 483, -145, 360, -384, 460, -689, 1023],\n [322, -224, 208, 206, -586, -546, 686, -352, -88, 112, 614, -442],\n [345, -372, -269, -444, 337, 42, 317, 66, -363,... | 2 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[125, -664, -147, -128, -343, 424, -725, -13, -214, 310, -418, -299],\n [190, 16, -480, -1130, -428, -666, -836, -238, -1136, 134, -772, 258],\n [655, 393, -268, -887, 135, -848, 445, -430, -31, -552, -1147, -982],\n [487, -368, -286, 348, -28, 166, 71... | 6 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-316, 378, -1251, -197, -447, 401, -1173, 862, 470, 684, 771, 471],\n [206, -28, 571, 265, -465, -228, 830, -558, -751, 103, -130, 396],\n [102, 267, -341, 425, -544, 496, -488, 525, 191, 566, 594, 7],\n [-343, 36, -870, -73, 0, 233, -895, 589, 701, 89, 117, -130],\... | 5 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-388, 1085, -105, 725, -1166, -414, 231, 638, 241, 377, -523, 800],\n [952, 207, -231, -353, 76, 146, -475, 889, -707, -156, 125, -143],\n [929, -660, 117, -949, 302, 354, -498, 339, -639, -461, 707, -1103],\n [279, -442, 267, 626, 865, 373, 377, -311... | 8 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[10, -308, -37, -96, -338, -131, -152, -24, -336, -428, -82, -158],\n [-12, 216, 326, -192, 252, -278, 80, 336, -160, -152, -260, 36],\n [-2, -104, 311, -312, -98, -443, -80, 336, -540, -632, -370, -134],\n [-9, 57, 437, -354, 84, -506, -10, 462, -505, -569, -440,... | 2 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-236, -140, 196, -268, -470, 766, -308, 324, -214, 570, 334, -420],\n [85, -292, 91, -319, 25, -601, 538, -336, -148, -238, -153, 486],\n [-261, -452, 357, -657, -645, 565, 30, 168, -432, 602, 341, -174],\n [237, 302, -273, 465, 540, -616, 108, -222, ... | 2 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-804, -747, 560, 602, 699, -18, 519, 38, 212, -115, 1279, -355],\n [-129, -114, -79, -601, 323, 310, -154, -436, -934, -758, 205, 586],\n [1236, 1062, 340, -408, 546, -96, -834, 480, -556, 350, 38, 54],\n [-285, -438, 2, -254, 218, 256, 298, -536, -52... | 5 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-110, -165, 137, 118, -419, 279, 53, 422, -125, 125, -257, 792],\n [-23, 9, 45, -135, 35, -97, -158, -441, 46, 63, -31, -506],\n [-132, 232, 446, -32, 463, 489, 467, -375, -41, 107, 384, -74],\n [18, -740, -854, -344, -875, -718, 137, 539, -743, 489, ... | 6 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-175, -175, -158, -176, -500, 570, 633, -266, -592, -611, 9, -97],\n [520, -225, -708, -312, 13, -642, 319, 275, 167, -337, 498, -500],\n [-151, -12, 909, 184, 124, -371, -746, -333, 251, 284, 171, 348],\n [373, 397, -820, 39, 248, 53, 531, 606, 264, 265, -631, 13],... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-378, -216, -162, 90, -288, -126, -54, -216, 378, -360, -108, 270],\n [-189, -108, -81, 45, -144, -63, -27, -108, 189, -180, -54, 135],\n [-336, -192, -144, 80, -256, -112, -48, -192, 336, -320, -96, 240],\n [147, 84, 63, -35, 112, 49, 21, 84, -147, 1... | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[474, 415, -189, 35, 179, 155, -287, 423, 778, -241, -404, 176],\n [-955, -978, 340, 187, -1127, 549, 261, 765, -114, -329, 258, -231],\n [-203, -103, -373, -458, 413, -256, 394, -681, -441, 221, -119, -524],\n [-96, -345, -347, 125, -124, 317, 148, 806, 431, -395, -... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-472, -285, 16, 385, 744, -221, -183, -925, 39, -703, 259, -73],\n [-2, -225, -55, 287, 99, -7, -141, -620, -108, -359, 32, -554],\n [253, 374, 664, -684, -860, 127, 742, 299, -336, 83, 322, 367],\n [751, -299, -115, 148, -222, 644, 106, -420, -528, -29, 244, -763],... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[580, -220, -886, -144, 1131, 812, 735, -117, -283, 837, -701, 130],\n [-417, 936, -649, 903, -183, -257, -747, 3, 659, -1166, -283, -260],\n [-237, -414, -168, -19, 546, 440, 33, 311, -264, 482, 71, 448],\n [90, -631, 682, -929, 616, 676, 534, -860, -405... | 7 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-132, -974, -493, 566, -231, -183, 380, -272, 577, 205, 356, 1006],\n [-258, -635, 465, -1729, -381, 897, -471, 699, -277, -921, 898, 33],\n [-105, 142, 375, -1929, -466, 870, -1391, 896, -1088, -319, 21, -279],\n [-230, -915, 232, -916, -129, 640, -25, ... | 8 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-946, -18, 80, 496, 1010, 178, -94, -54, -38, -238, 230, 124],\n [-615, -509, 112, 430, 619, 307, 279, -355, -375, 319, 871, 532],\n [-328, -396, 81, 268, 327, 155, 235, -297, -249, 213, 623, 393],\n [959, 650, -189, -699, -1008, -136, -342, 601, 287, 24... | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[247, 569, 313, -273, -483, -749, -344, 852, -612, -173, -141, -222],\n [82, -90, 471, 509, 123, -64, -729, -455, -173, 521, 522, 31],\n [-159, -714, -354, 425, -669, -964, 727, -319, -151, 99, -196, -694],\n [-24, 257, -108, 14, 1028, 1631, -854, -247... | 6 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[744, -595, 814, 1087, -951, -97, 146, -27, 258, -188, 171, -341],\n [-645, 344, -41, -439, -505, 94, -538, 115, -1354, 230, 766, 956],\n [702, -292, 164, 349, -436, -288, 193, 671, 733, 85, -152, -67],\n [-208, -898, 449, -873, 479, -416, -837, -707, -4,... | 11 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-460, -1161, -915, -152, -522, -662, 313, 883, -1177, 827, 102, 659],\n [-798, -536, 165, -205, -99, 378, -645, 986, -655, 809, 241, -579],\n [238, 1555, 691, 827, 357, 821, 229, -292, 871, -1341, 1037, -17],\n [-1031, 350, 410, 1572, -99, 1431, -490, -279, 234, 297... | 11 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[294, 379, 471, 30, -793, 443, 1011, -1339, -211, -940, -1000, 43],\n [1040, -363, 1376, -1320, -776, -229, -717, 387, 151, -52, 406, 132],\n [980, -294, 1476, -960, -1289, -349, -650, 1780, 621, 591, -72, 732],\n [-71, 689, 347, 914, -48, -829, 79, 12... | 10 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[401, 593, 146, 379, 716, 584, -149, -160, -241, 781, -726, 440],\n [460, -754, 274, 310, 731, -199, 246, -93, -42, 808, 386, 645],\n [-1196, -113, 1088, 481, 608, 632, 604, 549, -65, -115, 521, -315],\n [383, -128, -623, 1813, -968, 301, 444, 1059, 11... | 9 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-239, -359, 445, -32, 327, -402, 293, -720, -263, 237, -502, 176],\n [589, 267, 211, -390, 491, -496, 72, -214, -205, -287, 207, 481],\n [-547, 55, -55, -404, 23, -184, 602, -244, -543, 235, -661, -243],\n [-859, 163, -709, 10, -781, 704, 224, 698, -69, 265, -337... | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-702, -112, 535, 29, -496, -364, -567, -117, 164, -172, 710, -806],\n [1079, 698, -264, -155, 313, 594, 285, -641, -80, -429, -223, 304],\n [-815, -524, 562, -293, -255, -144, -433, 539, 616, 469, 79, -64],\n [-721, -642, 315, -419, 100, -54, -261, 739, ... | 7 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-351, -41, -262, 191, 221, 48, -925, -645, 18, -479, -144, -504],\n [-995, 225, 460, 678, 541, 506, -505, -175, 827, 409, -86, 41],\n [573, -177, -200, -1596, -778, 223, 320, -499, -403, 400, 277, -853],\n [515, 372, -374, -1196, 796, -152, 1855, 861,... | 11 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[282, 199, 137, -160, -340, 397, 155, 208, 567, -215, 112, -277],\n [-312, 85, -247, -136, 80, -263, -235, -266, -309, 331, -602, 179],\n [-208, -276, -8, 308, 440, -412, -184, -48, -664, 140, -8, 464],\n [-399, -83, -374, 539, 245, 114, 723, 451, 463, 65... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[51, 39, 48, -15, -21, -57, 6, 39, -3, 9, -30, -21],\n [-238, -182, -224, 70, 98, 266, -28, -182, 14, -42, 140, 98],\n [-238, -182, -224, 70, 98, 266, -28, -182, 14, -42, 140, 98],\n [-425, -325, -400, 125, 175, 475, -50, -325, 25, -75, 250, 175],\n [1... | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-75, -450, 200, 600, -175, 250, 375, -250, 500, 100, -475, -300],\n [33, 198, -88, -264, 77, -110, -165, 110, -220, -44, 209, 132],\n [-57, -342, 152, 456, -133, 190, 285, -190, 380, 76, -361, -228],\n [-48, -288, 128, 384, -112, 160, 240, -160, 320, 64,... | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[51, 638, -146, -530, -389, -883, -780, 695, -769, 503, -906, -48],\n [-259, 69, -159, 243, 440, 7, -242, 163, -1152, 976, -99, 434],\n [1019, 286, -42, 439, -735, 178, -10, 679, -93, 432, -20, 376],\n [-791, 794, 250, -663, -6, -789, -1070, 847, -543, 25... | 7 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-648, -268, -228, -276, -18, -378, 594, 4, 388, -132, 318, -454],\n [366, -2, -468, 288, -270, -258, -438, -22, 80, 234, 588, 160],\n [-612, -298, -390, -222, -99, -495, 531, -2, 454, -78, 525, -457],\n [-440, -172, -116, -196, 6, -226, 410, 4, 244, -... | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-338, 288, -832, 197, -342, -81, 200, 220, -955, 312, -329, -297],\n [87, 409, 143, -18, 243, -219, 224, -86, 231, -187, 224, 296],\n [466, 296, -1189, 1111, 188, 807, -1044, 207, -593, -539, -2622, -344],\n [-596, -1613, -62, -608, 185, -184, 1677, 1271... | 10 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[236, 32, 543, -380, 457, 742, -675, 707, -92, -144, 237, -139],\n [281, -525, -113, -549, 207, 385, 110, -115, -547, -284, -269, -371],\n [-734, 24, -696, 99, 242, 179, 360, -656, 343, 166, -122, 178],\n [50, 314, -118, 518, -432, -786, 146, -234, 154, 212, -16, ... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[189, 117, 197, 426, 433, -312, -758, -226, -119, -257, 288, 786],\n [-10, 556, 405, -662, 88, 337, 377, -307, 1373, 826, 768, 317],\n [-901, 850, -471, -179, -146, -357, 769, -152, -1129, -847, 248, -164],\n [-255, 210, 392, -1354, 912, 588, -164, 570, 639, -874,... | 7 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-425, 453, 35, 322, -164, 593, -134, -137, 144, -295, 551, -561],\n [525, -522, -150, -322, -42, -246, 80, 45, -174, 243, -451, 630],\n [-787, 741, 297, 394, 372, -139, 18, 55, 212, -303, 359, -917],\n [-850, 783, 455, 400, 442, -429, -22, 144, 310, -136... | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[66, -246, -75, 110, -290, 377, 280, 210, 38, 150, -110, 171],\n [-231, 182, 629, 191, 446, -276, -309, -466, -266, 168, -178, 239],\n [217, -148, -448, -184, -359, 337, 260, 323, 189, -70, 77, -110],\n [77, -320, -146, 149, -386, 435, 363, 310, 70, 15... | 3 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[325, 406, 968, 699, 121, 422, -440, -1655, 1004, 140, -26, 1139],\n [-829, 690, -724, 988, -864, 928, 78, -571, 266, 1158, 1083, 890],\n [-1046, 1027, 163, -578, 29, 196, -968, 823, -894, -759, -46, -752],\n [261, 1476, -81, -88, -895, 803, -715, 177,... | 9 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[247, 49, 459, 58, -406, 264, 614, 160, 214, 1125, 85, 1226],\n [1240, 702, -562, -366, -614, 32, 426, -508, -906, 608, 258, -378],\n [474, 692, 637, -752, -1251, 317, 152, -481, -886, 657, -422, -12],\n [699, 184, -646, 579, -3, 390, 882, 39, -445, 65... | 5 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[1249, -454, -351, 73, 275, 857, 229, -352, -655, -250, 529, -31],\n [269, 293, 645, -314, 166, -462, -189, -562, -219, 678, 11, 199],\n [-431, -382, -291, 75, 35, 194, 219, 405, 547, -26, 573, 242],\n [-124, 328, -619, 485, -203, 479, -935, -230, -587... | 7 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-4, 229, -361, -304, -1139, 1152, -790, 206, 811, 709, -317, -1079],\n [83, 223, -2, -167, 538, -140, 64, 507, -689, -12, 432, 483],\n [48, -251, 389, 871, 1073, -741, 979, -405, -582, -133, 231, 1090],\n [349, 1378, 101, -338, -697, 673, 18, 984, 457, 4... | 7 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[20, 111, -528, -608, -267, 108, 106, -495, 18, -148, -287, -204],\n [45, -37, 92, -99, 46, 53, -22, -15, 347, 135, -251, -10],\n [-99, 125, 1168, 969, 704, 137, -500, 997, 737, 219, -61, 90],\n [-72, 19, 426, 450, 222, 4, -171, 391, 115, 36, 69, 107],... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[1559, -642, 241, 519, 668, 851, 239, -384, 965, 651, 863, -461],\n [561, 402, -186, -496, -1073, -1, 88, 4, 678, 1267, -520, 74],\n [1576, -364, 240, -357, 113, 189, -527, 689, 30, 148, 175, -78],\n [-521, 232, -526, 33, 69, -98, -166, 130, -230, -6, -152, 326],\... | 9 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[130, -101, -411, 460, -447, -50, 534, -457, -311, -125, -445, 289],\n [-410, 352, -243, 490, -531, 325, 792, -31, 412, 160, 65, 427],\n [-470, 397, 21, 184, -231, 340, 426, 251, 583, 229, 335, 229],\n [300, -245, -400, 370, -340, -175, 350, -530, -515, -205, -550, 1... | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[215, -115, 281, 133, 69, -17, 533, 478, -302, -502, 95, -328],\n [-142, 118, 32, -50, 110, 212, 80, 48, -36, -214, 158, 142],\n [404, -316, 11, 160, -240, -509, -25, 34, -8, 353, -346, -439],\n [-181, 129, -70, -83, 61, 168, -118, -124, 74, 5, 89, 219... | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[1144, 292, 342, -321, -162, -209, -851, 720, 49, -67, 1055, -1100],\n [-870, -53, -387, 833, 206, -344, 27, -1348, 334, 1366, -1045, 733],\n [13, 220, -789, 762, -91, 426, 547, -392, 289, 286, 519, 143],\n [1064, -2130, 68, 7, 594, 768, 714, -1554, 65... | 11 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-401, -1285, -874, 2221, -844, 539, 446, -156, 402, -170, -49, -250],\n [-58, 56, -135, -74, -917, -665, -361, -314, 1493, 701, -265, -708],\n [-389, 1468, 714, -932, 721, 317, -192, 66, -1133, 659, 625, 870],\n [659, 330, 690, 889, 1322, 1208, 637, 1003, 383, 13... | 11 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-283, 106, 424, -640, 846, 1527, 382, 714, -87, -800, 296, 870],\n [184, 584, -1459, 373, -428, 180, -970, 1006, 732, -800, 1080, 405],\n [944, 167, -157, 350, -1257, -1255, -756, -1440, 693, 110, 62, -1703],\n [348, 397, 340, 560, 133, -684, -1259, -602, -223, -237... | 10 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[305, 679, 802, 738, 703, -323, -586, 232, -33, 91, -94, -14],\n [97, -291, -775, -801, 107, 457, 623, 209, 439, 12, -61, 88],\n [938, 177, -565, 363, 748, 193, 430, -2, 389, 224, -151, -543],\n [-118, -270, -399, 251, -1658, -217, -327, -396, 130, 331, 204, 15],\... | 7 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-327, -687, -115, 361, 490, -1580, 185, 864, -67, 300, -781, -812],\n [134, 1871, 117, -1576, -160, 1255, 1168, -303, -480, 309, 323, -352],\n [-742, 205, -474, -886, 133, 190, 494, 230, -1028, 116, -844, -102],\n [103, -168, 748, 472, 646, 65, -244, 1076, -375, ... | 10 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-1450, -990, 1638, 344, 2316, -1441, -257, 1488, -786, -608, 1022, 199],\n [482, -258, -766, 1208, -26, -149, -209, 381, -370, -1071, 495, -213],\n [-1386, -17, 1399, -539, 340, 312, 21, -54, -219, 863, 940, 1090],\n [890, -22, -1178, 79, -2079, 1321, 47... | 9 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[23, 878, -1219, -705, 59, -582, 722, 530, 230, 19, 732, 1175],\n [678, -1218, 1380, 615, -716, -502, -512, 282, 709, 525, -691, -160],\n [-1082, -141, 1311, 271, -209, -335, -746, -782, 399, -465, -189, -1745],\n [-527, -69, -999, -1341, 697, -423, 1308, 106, 170, -... | 9 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-121, 1355, 1237, -672, -825, 669, 1129, -103, -330, -259, 1370, 803],\n [1014, 210, 1661, 775, -1089, 576, 833, -730, 729, -94, -359, -1158],\n [392, 376, -323, -1026, 224, -1187, -607, 229, -148, 1111, 710, -814],\n [291, -46, -1021, -447, 75, -350, 467, 1435, -94... | 11 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[1096, -408, 500, 840, -500, 709, 317, 1380, 1042, 27, -204, 1455],\n [-649, -379, 1686, -16, 1430, 223, -1077, -242, 186, 1191, -1202, -285],\n [548, -246, -221, -873, 632, -746, 74, 0, 439, -524, -1004, 289],\n [578, -223, 140, 767, -711, -178, 275, ... | 11 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-428, 287, 312, 109, 572, 17, 139, 392, -339, 466, 287, -462],\n [113, -155, 243, -650, 46, 284, 434, -212, -517, -406, -814, -698],\n [29, 516, -259, -35, 344, 531, -73, 98, 84, 1010, -511, 108],\n [786, -566, -152, -482, -622, 322, -306, -358, 198, -12... | 5 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-104, 120, -64, -176, 48, -184, -128, -72, -168, 80, -40, -112],\n [-441, 291, -168, -518, 110, -683, -480, -181, -233, 298, -297, -350],\n [-17, -171, 80, 171, -74, 55, 34, 97, 392, -23, -118, 91],\n [-49, 111, -56, -140, 46, -111, -76, -65, -199, 48, 1... | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[910, 625, 122, 1045, 1302, 175, 307, -571, 338, 359, -228, -321],\n [-499, -125, -1074, 379, 404, -299, -274, -84, 71, -542, 526, -200],\n [-327, -320, 27, -201, -577, 184, -173, -523, 185, -409, -349, -291],\n [-429, 127, 1091, -363, -71, -91, 1159, ... | 7 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-299, 113, -113, 23, -546, 0, 373, -59, -240, 634, -238, -26],\n [-460, -162, 479, 127, -875, -343, 567, -589, -85, -1371, 1447, -747],\n [-609, 205, 1299, 318, -229, -50, -728, 123, -90, 377, 745, -893],\n [409, -439, -319, -889, 464, -404, 89, 556, 326, -549, -372... | 8 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-686, -95, -341, 104, 841, 451, -245, 161, 39, -234, 666, -136],\n [-373, 416, -323, 238, -626, -107, -336, -401, 153, 401, -337, 399],\n [-422, -674, 500, -412, 692, -121, 495, -325, -246, 286, -158, 270],\n [-949, -458, 11, -198, 1176, 475, 249, -38... | 5 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-132, -396, -124, 206, -96, 58, -382, -286, 68, 346, -124, 28],\n [-290, -358, -344, 346, 635, 549, -167, 287, -80, 248, -59, -446],\n [316, 922, -294, -474, -542, 14, -66, 100, -62, -432, -408, 322],\n [-108, -259, 193, 148, 401, 12, 256, 157, -19, 2... | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-287, -320, -503, -237, 346, -328, -31, -109, -452, -182, -363, 355],\n [73, -214, 300, -194, -222, 21, 419, -21, -51, -7, 776, -541],\n [-79, -470, 84, -394, -78, -171, 523, -93, -339, -119, 784, -485],\n [83, -44, 225, -49, -162, 66, 199, 9, 54, 28, 42... | 2 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-165, -1426, 567, -422, -309, -231, 44, 395, 446, -1276, -8, -1511],\n [-458, -733, -402, -204, -1368, 1475, 469, 401, 210, 57, -571, -309],\n [-436, -518, -70, 238, -816, 1758, 837, 1086, 130, -539, 216, -281],\n [1052, -926, -338, 625, -106, -369, -... | 11 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[274, -772, 1448, -434, 725, -198, 538, -1389, -750, -889, 1635, -321],\n [-1072, 778, -1100, -634, -220, 575, -599, 1, -737, -754, 939, 19],\n [1001, -435, 250, -198, 202, 155, -652, -971, 2001, -506, 389, -1878],\n [-401, 353, -1308, 402, 659, -328, ... | 10 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[508, 1062, -78, 286, 708, -32, 368, -350, -62, -368, -694, -452],\n [-735, -845, 172, -251, -916, 279, -225, 538, -214, 670, 868, 259],\n [-71, 351, 104, 81, -76, 127, 111, 14, -306, 110, 0, -245],\n [-373, -127, -45, -67, -244, 386, 207, 468, 58, 528, 3... | 3 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[68, 51, 615, -432, 361, -43, -656, 533, 179, -75, -344, 102],\n [-86, 317, -561, 359, -234, -50, 548, -573, 193, -117, 104, 74],\n [-202, 594, -248, 212, 10, 106, 82, -280, 652, -40, -290, 110],\n [384, -394, 1166, -933, 565, -359, -1014, 992, -344, -... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[1034, 828, 491, 689, 575, 590, -183, 513, -845, 82, 144, -1054],\n [1880, -162, 469, 735, -27, 889, 935, 794, 128, -403, -781, -536],\n [-312, 26, -104, -657, -167, -288, 2441, -952, -574, -732, 466, -853],\n [176, -217, 222, 192, -147, 436, -1334, 184, 682, -270, -... | 9 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[35, 295, -817, -542, -1223, -695, 653, 729, -1185, -422, -1096, 356],\n [-663, 540, 129, 513, 235, -755, -167, 879, 634, 1124, -730, -269],\n [1087, -496, 1036, 1146, 989, 172, -1334, -846, 1388, -942, -155, 434],\n [277, 953, 543, 1546, 975, 1066, -975,... | 10 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[183, -194, 606, 3, 163, 350, 1644, 361, 566, 220, 509, -535],\n [-191, 36, -247, 27, -1210, 110, 814, -1164, 1414, -676, -526, 191],\n [525, -596, 631, 480, 19, 570, 59, -171, -247, -520, 282, 1095],\n [-177, 265, -1316, -323, -427, -10, 5, -753, 352, -642, -263, 93... | 8 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-96, -234, 72, 65, 406, 247, 104, 250, -260, -361, -305, -41],\n [-192, -180, -144, 106, 188, -58, 256, -124, -136, -170, -154, -202],\n [288, 102, 384, -145, 82, 409, -412, 550, -20, -67, -35, 373],\n [-16, 31, -58, 5, -84, -93, 29, -110, 50, 74, 60, -3... | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-633, 1203, -707, -296, 1000, 844, -1172, -1022, 222, -849, 833, 343],\n [-261, -332, -258, -145, 33, -340, 51, 536, -395, -117, -370, -158],\n [986, -316, 402, -271, -1040, -687, 725, 450, 407, 248, -1364, 435],\n [282, -139, 723, 67, -243, 98, 457, ... | 5 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[170, -306, 272, -51, -136, -238, -187, 85, -442, -272, -357, -408],\n [110, -198, 176, -33, -88, -154, -121, 55, -286, -176, -231, -264],\n [200, -360, 320, -60, -160, -280, -220, 100, -520, -320, -420, -480],\n [230, -414, 368, -69, -184, -322, -253,... | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-918, -89, 388, -1013, -281, -776, 1111, 436, 5, -90, -144, 627],\n [-187, -785, -51, 402, -876, 174, 174, 1073, 59, -624, 120, 1241],\n [-283, -416, -343, 887, -721, 460, -1094, 258, -916, 921, -477, 116],\n [-624, 440, 943, -474, 176, 413, 54, -1415, -169, 443, -1... | 10 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[112, -24, -216, 14, -28, 270, 64, -566, -318, 438, 442, -444],\n [-154, -396, 132, 0, -308, 528, 440, -792, -396, 836, 286, -858],\n [331, 450, -438, 18, 338, -294, -452, 234, 72, -452, 221, 471],\n [-318, -528, 384, -13, -402, 483, 552, -575, -255, 755, -13, -78... | 2 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-74, -26, 108, -313, -38, 91, -193, 81, 242, 51, 8, -93],\n [-16, -40, 105, -506, -193, 458, -89, 357, 250, 372, 49, -510],\n [176, 64, -262, 772, 102, -244, 462, -214, -588, -144, -22, 252],\n [250, 90, -370, 1085, 140, -335, 655, -295, -830, -195, -... | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[236, -107, -248, 3, -567, 40, -393, 210, -22, 259, 484, 464],\n [-240, -122, -86, 142, 706, -336, -144, -290, -66, -662, -462, -690],\n [-646, 506, 73, 513, -182, -135, 400, 22, 545, 84, -224, 128],\n [88, -115, -125, -7, -33, -56, -224, 9, -71, -69, ... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-641, -127, 689, 1154, -786, 85, -326, 335, -458, 178, -495, -1047],\n [-1898, 1228, -402, -354, 507, -310, -74, 1483, -845, -250, -172, -143],\n [-395, -259, 809, -1471, -944, -9, -670, -98, -390, 28, -421, -210],\n [-1175, -138, 1222, 1656, 295, 153, -979, -700... | 11 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-435, 518, 183, -121, -507, -162, 516, 723, -571, 1415, 588, -377],\n [-159, 262, 1157, 680, 542, -139, 248, -554, -273, 1038, 1164, -262],\n [-1435, -368, -73, 846, -736, 179, -19, 79, 30, 655, 171, -522],\n [1025, 431, -535, -1076, -258, -332, 159, ... | 9 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-294, 137, 49, -470, 643, 37, -9, 678, -1016, -763, -415, 90],\n [-10, -130, -141, 190, 430, 301, -1032, -181, -1, -903, 556, 425],\n [-46, 184, -10, 400, 137, 308, -504, -386, 84, -405, 274, 437],\n [-239, -836, 356, -501, 659, 377, -174, 323, -257, ... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[1809, -360, 743, -228, 156, -373, -654, -10, 534, -674, -1096, 782],\n [-895, -356, -607, 156, 225, 176, 376, 47, -388, 699, 740, -56],\n [-706, -381, 377, -1728, -566, -1008, 168, 1215, 70, -163, -458, -443],\n [114, 638, 784, -398, -583, -739, 1450, -408, -935,... | 10 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[609, 6, 315, 737, 418, -582, -129, 396, 729, -1225, 117, 1137],\n [167, 16, -79, 191, 542, -454, -247, 158, 151, -983, -83, 827],\n [73, 147, 271, 398, -958, 60, 213, 121, 585, 863, 881, -246],\n [-628, 338, -1076, -349, 467, -649, -261, -229, -384, -... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[182, 135, 266, -616, 430, 341, -83, -240, -158, 225, -23, 182],\n [685, -785, -290, 521, 56, -170, 416, 253, -767, 443, -305, 681],\n [-512, 325, 29, 261, -472, -327, -70, 368, 624, -599, 149, -888],\n [-186, 460, 322, -858, 204, 624, -280, -290, 364, -3... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-821, -1167, -734, -446, 1241, 769, -670, 1172, 84, 466, 502, -112],\n [134, 213, 319, 269, -213, -775, 938, -1447, -1264, -268, -1715, 1514],\n [545, 1419, 742, 1246, -715, -348, -733, 384, -242, -225, 597, -511],\n [-387, -820, 276, -235, -265, -145, 5... | 7 | MATH |
[
{
"content": "Compute the rank of the given 12x12 matrix:\n[[-236, -345, 839, 1095, 385, 702, -311, 971, 70, 224, -615, 244],\n [1815, 452, -1042, -667, -266, 526, -885, -926, 140, -89, -98, -506],\n [493, -409, 193, 481, -267, -619, 1344, -43, 11, -1107, 711, 403],\n [-805, -892, 1220, 1312, 154, 85, 935, 271,... | 8 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[118, 394, -127, -163, 60, 507, -391, -138, 916, 753, 226, -211],\n [-324, -774, 379, 200, -85, -313, 277, 573, -657, -257, -311, -246],\n [331, 762, 1168, -502, -776, -93, 1617, -357, -88, -621, 435, 361],\n [38, -197, -303, 256, 625, 170, -94, -338, -592, 70, -161,... | 8 | MATH |
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