messages listlengths 1 1 | ground_truth stringclasses 9 values | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Find the rank of the matrix:\n[[226, 270, -378, -80, 286, -296, 68, 240, 20, -20],\n [324, -20, 28, -144, 340, -312, 288, -488, -56, -312],\n [-143, -235, 329, 46, -192, 205, -13, -283, -26, -32],\n [36, 220, -308, 0, 76, -96, -72, 400, 40, 120],\n [-228, -60, 84, 96, -252, 240, -168, 192, 24, 168... | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[569, -60, 14, -363, -532, 391, -239, -286, -512, -630],\n [80, 593, 406, -171, 130, -343, 155, -267, 6, -244],\n [229, 694, 770, 29, -476, 333, 801, 116, -150, -990],\n [-390, -47, 166, -253, 402, 187, 217, 805, 658, 204],\n [139, 764, 744, -44, -310,... | 5 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[104, -78, 130, 149, 66, 17, -327, -796, 187, -301],\n [92, 54, 1, 392, -147, 48, -368, -847, 23, -184],\n [514, 186, 226, -168, 50, 60, -478, -48, 656, -72],\n [414, 264, 68, -3, -118, 7, -367, 32, 363, 93],\n [-283, 63, -229, 563, -332, 268, 19, -300... | 4 | MATH |
[
{
"content": "Compute the rank of the given 10x10 matrix:\n[[310, -324, -92, -229, -79, 222, -482, 319, 249, -321],\n [270, -306, -178, -296, -291, 73, -273, 381, 201, -64],\n [178, -216, -176, -253, -325, -24, -92, 313, 123, 87],\n [-188, 180, -12, 72, -106, -218, 394, -122, -162, 344],\n [258, -306, -226, -33... | 2 | MATH |
[
{
"content": "Compute the rank of the given 10x10 matrix:\n[[143, -462, -187, -374, 165, -242, 209, 132, 495, -99],\n [-44, 36, 146, -76, -302, 32, -36, 62, 336, -426],\n [71, -144, -164, -32, 284, -86, 81, -17, -147, 318],\n [-138, 432, 192, 336, -192, 228, -198, -114, -414, 36],\n [61, -174, -99, -118, 125, -... | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[118, 274, -478, -610, 657, 205, 206, 318, -26, -48],\n [-419, 36, -592, -275, 446, 517, 80, -106, 526, 84],\n [49, 214, -539, 78, 137, -90, 450, 173, 400, 319],\n [-228, 628, -33, -611, 276, 44, 148, -209, 548, 481],\n [-668, 766, -370, -643, 863, 36, 115, -11, 701,... | 7 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[42, 42, -28, 224, 182, 140, 98, 196, 0, -182],\n [-3, -3, 2, -16, -13, -10, -7, -14, 0, 13],\n [18, 18, -12, 96, 78, 60, 42, 84, 0, -78],\n [-27, -27, 18, -144, -117, -90, -63, -126, 0, 117],\n [15, 15, -10, 80, 65, 50, 35, 70, 0, -65],\n [-54, -54, 36, -288, -234, ... | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-54, -221, 355, 158, 22, 258, 221, 192, 214, -426],\n [190, -170, -426, 593, 226, 26, 72, -151, -510, -327],\n [-618, -107, 313, -145, -134, -15, 359, -486, -209, -678],\n [-182, 466, -102, -238, -338, -361, 88, -259, -179, 123],\n [-106, -79, 126, -2... | 4 | MATH |
[
{
"content": "Compute the rank of the given 10x10 matrix:\n[[-500, -241, -498, 257, -703, -387, -278, -574, 320, -672],\n [184, 233, 1, 542, -72, 79, 306, 98, -229, -19],\n [-333, -635, -61, 797, -445, -522, -267, -743, 329, -473],\n [-509, 307, 41, -50, 641, 263, 206, 42, 383, -428],\n [-329, 208, -178, -6, -3... | 9 | MATH |
[
{
"content": "Compute the rank of the given 10x10 matrix:\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n [-308, 308, -140, -266, -308, 238, 126, 154, 70, 112],\n [-308, 308, -140, -266, -308, 238, 126, 154, 70, 112],\n [286, -286, 130, 247, 286, -221, -117, -143, -65, -104],\n [286, -286, 130, 247, 286, -221, -117, -143, ... | 1 | MATH |
[
{
"content": "Compute the rank of the given 10x10 matrix:\n[[439, 260, -151, 40, 109, 327, -367, -26, -140, -364],\n [-516, 80, 103, 605, 258, 691, -218, -72, -75, 119],\n [379, 349, 68, -116, -118, 246, -242, 401, 468, 127],\n [82, -390, 134, -290, 144, -342, 156, 174, 290, 132],\n [-602, -363, 202, 347, 334, ... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[735, -948, 182, -230, 448, -572, 95, -268, 523, -548],\n [171, 294, -25, 38, 31, 272, 61, -219, 308, 298],\n [-135, 11, -8, -130, -336, -427, 495, 686, -100, 70],\n [-587, 398, -435, 509, 188, 580, -2, 105, -449, 324],\n [717, -1114, -209, 438, 407, -... | 7 | MATH |
[
{
"content": "Compute the rank of the given 10x10 matrix:\n[[-1121, 589, 643, 229, 195, -65, 392, 1025, -102, -971],\n [352, -353, -85, -341, 673, -112, 84, 148, -22, 220],\n [-1127, -283, 267, -363, 99, 32, 808, 1169, 263, -1108],\n [536, 30, -877, -791, -185, 192, -536, -676, -172, -101],\n [96, 758, -212, 57... | 8 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[315, 98, 780, 226, 119, -129, 431, 388, -465, -520],\n [-650, 103, -715, -533, -334, 262, -105, -191, 359, 296],\n [5, 199, 366, 25, 9, 207, 449, 627, -450, -23],\n [-415, -21, -203, -299, -171, 30, -69, -46, 106, 73],\n [-261, -380, 742, 34, 219, -670, -128, -281, ... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-278, 450, -154, 322, -444, -47, 310, -88, 161, -246],\n [-142, 263, -61, 156, -215, 4, 190, -69, 108, -107],\n [299, -153, -173, -138, -17, 4, -224, 396, 80, -355],\n [-284, -370, -42, 224, -86, -396, -252, -74, -476, 154],\n [80, -66, -50, -36, -2, -14, -80, 11... | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[1129, -333, -414, 18, 517, -80, 416, -471, 228, 30],\n [-469, 275, 686, 356, -314, 199, -55, -498, -138, -2],\n [-122, 121, 654, 133, -203, -368, 238, -425, -84, -133],\n [213, -92, -213, 187, 343, 318, 262, 3, 172, 126],\n [-491, 316, -6, 465, 188, 935,... | 6 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-32, -52, -29, 50, -1, 76, 39, 45, -87, 4],\n [-223, 44, 14, -70, 181, -323, -377, -398, 222, -335],\n [-458, -130, -42, -20, 84, -410, -366, -310, 120, -408],\n [-186, -189, -3, -60, -375, -270, 174, 339, -18, 111],\n [49, -88, -6, 10, -231, 61, 255,... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-556, 276, -828, 14, -5, -1, 638, 535, -314, -952],\n [-255, -124, -320, 390, 269, -799, -413, 285, -493, 41],\n [-310, -214, -979, 440, -301, 192, 141, 369, -38, -187],\n [-492, -3, 314, -481, 682, -419, -228, 354, 150, -301],\n [-22, 10, 454, -694, 129, 756, 177, ... | 6 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-79, 39, -327, 223, -469, 97, -135, -23, 453, -39],\n [-165, 105, -10, 195, -130, 130, -125, 105, 75, -105],\n [-134, 102, 470, -34, 498, 54, 10, 194, -558, -102],\n [-480, 312, 158, 492, -142, 358, -320, 348, -24, -312],\n [-216, 132, -169, 318, -367, 187, -200,... | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-427, -227, 145, 245, -363, -4, -54, -275, 87, -6],\n [-222, -55, 98, 146, -214, 35, -60, -132, 2, -54],\n [-574, -330, 186, 322, -478, -20, -60, -374, 134, 12],\n [375, 139, -149, -233, 343, -32, 78, 231, -35, 54],\n [75, 331, 79, 43, -53, 172, -138, 99... | 2 | MATH |
[
{
"content": "Compute the rank of the given 10x10 matrix:\n[[-131, 729, 265, -355, 25, 247, -310, -82, -612, -365],\n [222, -175, 71, 227, 54, 160, 155, 52, 206, 523],\n [356, -208, 187, 345, -491, -103, 116, 965, -267, -91],\n [112, -362, 130, 244, -524, -376, 48, 986, -90, -194],\n [131, -6, -60, 120, -36, 28... | 6 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[32, -247, -97, 119, 665, 759, -604, 157, 174, -245],\n [265, -90, 281, -36, 44, -296, 59, -111, -459, 172],\n [-150, 678, 650, 426, -395, 190, -513, -292, 1029, 553],\n [271, -141, 384, 159, 448, 711, -870, 84, 408, -22],\n [-752, 200, -927, -49, -105, -106, 757, 60... | 5 | MATH |
[
{
"content": "Compute the rank of the given 10x10 matrix:\n[[80, 988, 212, 225, -563, 533, 162, 691, -183, 9],\n [558, 149, -60, -85, -1, -58, 685, -418, 133, -286],\n [103, -523, 399, 46, 1198, 816, 542, -547, 568, 865],\n [-820, -20, -98, 411, 1191, 534, -201, 110, 15, 1293],\n [466, -586, 340, -410, 116, -22... | 8 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-62, 194, 49, -43, -202, 136, -159, -113, -85, -216],\n [598, 524, 529, 197, -142, 256, -339, -173, -385, -486],\n [-116, -313, -191, -19, 212, -188, 231, 145, 181, 321],\n [-302, -226, -251, -103, 38, -104, 141, 67, 175, 204],\n [436, 488, 430, 134, -196, 256, -... | 2 | MATH |
[
{
"content": "Compute the rank of the given 10x10 matrix:\n[[-40, -22, -54, -120, 72, 68, 200, -260, 178, -108],\n [6, 73, -78, -64, -101, -2, -30, -43, 2, 49],\n [-42, -18, -63, -132, 69, 72, 210, -279, 189, -111],\n [10, 354, -417, -380, -469, 24, -50, -345, 99, 191],\n [6, -63, 90, 96, 75, -18, -30, 117, -54... | 2 | MATH |
[
{
"content": "Compute the rank of the given 10x10 matrix:\n[[326, -32, -118, 27, -351, 504, -279, 380, -248, -723],\n [275, -477, -382, 131, 17, -87, -200, -53, 182, -367],\n [-211, -54, 598, -47, -160, -604, 333, -284, -213, 579],\n [-22, 277, 461, -174, -87, -153, 135, 32, -62, 234],\n [-244, -286, -63, -388,... | 5 | MATH |
[
{
"content": "Compute the rank of the given 10x10 matrix:\n[[449, 5, 152, 1220, 149, -222, -368, -96, 123, -384],\n [-339, -708, 214, 476, -287, 45, 440, -53, 187, 288],\n [1411, 727, -96, 443, 379, 172, 160, 166, -281, 82],\n [759, -195, -192, -977, 992, -218, 1031, 969, -112, 1155],\n [-1021, -267, -176, -449... | 6 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-73, -368, -187, -20, -195, -375, -281, 226, -506, 386],\n [-328, 21, 764, -365, 323, 115, 218, 248, 169, -37],\n [-121, 48, 440, -107, 278, 228, 375, -158, 446, -258],\n [132, 687, -68, -32, 122, 460, -54, -152, 548, -498],\n [-187, 232, 62, -284, 189, 197, -187, -... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-34, 12, -28, -32, -12, -26, -30, -32, -28, -24],\n [-238, 84, -196, -224, -84, -182, -210, -224, -196, -168],\n [85, -30, 70, 80, 30, 65, 75, 80, 70, 60],\n [-272, 96, -224, -256, -96, -208, -240, -256, -224, -192],\n [-119, 42, -98, -112, -42, -91, ... | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[174, -507, 287, 298, -159, -132, 289, -197, -41, -244],\n [102, -833, 361, -368, -50, -320, 176, 187, 275, -123],\n [-88, -414, 237, 31, -260, -24, 170, -77, -26, -265],\n [162, -1256, 650, -73, -184, -170, 463, -1, 80, -691],\n [156, 150, -223, 733, -50, 196, 214, ... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[130, 369, -413, -311, 11, 166, -609, 110, -229, -216],\n [53, 480, -412, -237, -66, 146, -618, 264, -316, -139],\n [-485, -3, 237, -152, -189, -294, -137, 52, -235, -191],\n [-409, -549, 607, 6, -59, -362, 481, -352, 167, -111],\n [-618, 171, 67, -387, -179, -382, -... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-35, 621, -130, -239, 99, 218, -113, -203, -94, 181],\n [-52, 165, -126, 873, 317, 332, 373, 96, 580, -87],\n [-202, -758, 252, 124, 224, -108, -332, -34, -76, 222],\n [-696, -367, 28, 686, 558, -546, -93, -391, 111, 480],\n [-155, 108, 162, -313, 82, 71... | 7 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-438, -278, 105, -879, 592, -111, -770, 943, 734, 346],\n [73, 151, -185, 829, -495, -554, 217, -1030, -456, 183],\n [-634, 875, 514, 6, 507, -757, 115, -384, 1046, 577],\n [-626, -356, -22, -429, 25, -461, -798, -512, -245, 291],\n [37, 1, -89, -600, -2... | 8 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-344, 50, 276, 316, 236, 174, 60, -330, -278, 234],\n [-220, 126, 740, 20, 308, 142, 296, -674, 98, 234],\n [297, -177, -108, -281, -231, -24, 114, 22, 581, -112],\n [249, -75, -396, -164, -228, -132, -129, 394, 116, -196],\n [-411, 234, 234, 367, 333, 5... | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[58, 489, -539, 252, 85, -610, 367, -988, 203, -20],\n [377, 458, 30, 29, -42, -241, -199, 166, -467, 158],\n [-420, -688, 187, -256, -118, 467, -4, 530, 77, -191],\n [-145, -282, -162, -701, -96, 216, -48, 623, -442, -124],\n [449, 582, 119, 308, -209... | 6 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-151, 68, -682, -290, 398, 127, -672, 541, -327, -200],\n [131, -471, 362, 117, -269, -539, 765, 85, -220, 279],\n [221, -123, -386, -547, 317, -148, -321, 718, -423, -117],\n [-509, -32, 376, 828, -358, 96, 482, -796, 406, 160],\n [602, 101, -33, -1015, 406, 176, -... | 5 | MATH |
[
{
"content": "Compute the rank of the given 10x10 matrix:\n[[-699, -234, 68, -352, 723, 154, 410, 603, -113, -543],\n [-402, -100, 460, -42, 76, 946, -117, -63, -14, -227],\n [-39, 192, -124, 140, -61, 176, -81, -268, -113, 138],\n [-75, -246, 608, -70, -151, 704, -195, 14, 175, -180],\n [-405, -53, 10, -133, 3... | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-60, 55, -396, 557, -430, -154, 226, -240, 163, -290],\n [-333, 194, 342, 71, -8, 393, -263, 487, 108, 29],\n [-52, -303, 240, 123, 22, 252, 124, 302, -227, 418],\n [-291, -4, 34, 837, -512, 330, 248, 368, 110, 113],\n [695, 608, -179, 366, -400, -378... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-124, 197, 383, -435, 591, -519, -492, -412, 322, 822],\n [-525, -112, -925, 272, -467, 808, 666, 316, -603, -457],\n [-211, 235, 2, 495, -16, -219, -89, 83, 469, 13],\n [-1156, -137, 423, -375, -954, 421, -165, -684, 177, 600],\n [578, -126, 1218, -1656, 619, -1... | 8 | MATH |
[
{
"content": "Compute the rank of the given 10x10 matrix:\n[[796, 87, -113, -1131, -73, 232, -565, 352, 186, -231],\n [-137, -143, 67, 422, -125, -47, 88, 17, 100, 79],\n [171, 299, 351, -647, -703, -268, -315, -54, 297, -77],\n [595, -175, 475, -58, -889, -293, -672, 405, 260, 223],\n [-639, 220, 0, 219, -32, ... | 5 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-76, -102, -122, -70, -8, -126, 77, -15, -89, 81],\n [-121, -224, 258, -10, 264, 179, -57, 293, -431, 208],\n [171, 444, -221, -105, 378, -248, -459, -42, 543, -229],\n [-59, -198, 49, 95, -145, 162, 247, -74, -309, 103],\n [-43, -102, 289, 43, 337, 254,... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-28, -42, -56, -56, -154, 196, 266, -84, 196, 224],\n [-20, -30, -40, -40, -110, 140, 190, -60, 140, 160],\n [-2, -3, -4, -4, -11, 14, 19, -6, 14, 16],\n [-42, -63, -84, -84, -231, 294, 399, -126, 294, 336],\n [24, 36, 48, 48, 132, -168, -228, 72, -16... | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-50, -25, 70, -50, 65, 40, -105, -35, -70, -70],\n [-180, -90, 252, -180, 234, 144, -378, -126, -252, -252],\n [-120, -60, 168, -120, 156, 96, -252, -84, -168, -168],\n [50, 25, -70, 50, -65, -40, 105, 35, 70, 70],\n [90, 45, -126, 90, -117, -72, 189, 63... | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-418, 329, 66, 187, 354, -134, -103, 171, 260, -654],\n [-352, -387, -73, 115, 393, -220, 40, -1201, -561, 922],\n [99, -253, 382, -59, -96, 612, -389, 789, -127, -1206],\n [483, -6, -975, -274, 39, 96, -208, -790, 188, 639],\n [1, -574, 708, 151, -840, ... | 7 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[674, -152, 230, -642, -744, -640, -302, -80, -268, 404],\n [208, -9, -90, -114, -173, -130, 141, 115, -306, 93],\n [-186, 100, -310, 306, 292, 280, 442, 236, -268, -160],\n [351, -111, 255, -405, -435, -390, -354, -159, 48, 237],\n [-351, 111, -255, 4... | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-29, -1111, -143, -315, 281, 234, 14, -476, -670, -34],\n [-34, -50, 430, -160, 204, 55, 271, -79, -506, -20],\n [-334, 126, -259, 661, -24, 65, -288, -128, 197, -328],\n [343, 857, 312, -364, -301, -368, -40, 571, 717, 522],\n [-174, -93, -298, -254,... | 6 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-120, 397, -78, 690, -93, 44, -195, -779, 523, 27],\n [-336, 406, -295, 867, -1024, -500, 19, -12, -140, 692],\n [339, -337, 456, -461, 528, 97, 164, 567, 866, -1107],\n [-411, 768, 123, -220, -500, 384, -335, 291, -671, 390],\n [109, -330, -129, 281, -151, -228,... | 8 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[365, -504, 964, 127, 108, 666, -714, -539, 55, -198],\n [1138, 244, -206, 166, -871, -502, -753, -247, 5, -766],\n [-763, -94, 637, 80, 1235, 854, 37, 207, 98, 113],\n [-139, -486, 880, -356, 59, 111, -503, -63, -281, 375],\n [375, -192, 432, 63, -202... | 8 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[148, 271, -212, -92, -210, -227, -124, -314, 404, 61],\n [-45, -180, 163, 168, -56, 256, 223, 410, -604, 48],\n [-125, -186, 212, 69, 25, 102, 275, 172, -217, 84],\n [-398, -392, 369, -138, 606, -44, 144, -146, 395, -102],\n [-461, -520, 408, -54, 414... | 5 | MATH |
[
{
"content": "Compute the rank of the given 10x10 matrix:\n[[-38, -267, 56, -440, 103, -853, 535, 295, -253, -327],\n [-206, -302, 432, -1, -709, 178, -96, 8, -256, -582],\n [181, -43, -288, 178, 302, 6, -200, 161, 16, 438],\n [89, 358, -105, 296, 159, 528, -202, -359, 345, 271],\n [35, 137, -73, 464, -180, 857... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-123, 662, 67, -266, -456, 881, -780, 67, 191, 478],\n [-294, -223, -855, 83, -345, -256, 516, 225, -476, -364],\n [-59, 215, -415, 66, -462, 798, -187, 203, 63, 199],\n [776, -476, -132, 510, 246, -430, 588, 196, 190, -704],\n [30, -233, -142, 487, -75,... | 9 | MATH |
[
{
"content": "Compute the rank of the given 10x10 matrix:\n[[189, 311, 802, 663, 174, -77, 589, -220, 15, -156],\n [65, 76, -172, -19, 45, 283, 241, -335, 35, -244],\n [553, -286, 265, 111, 652, 195, -416, 705, -158, 147],\n [-645, 736, 288, -312, 16, 527, 803, -680, 10, -247],\n [-85, 118, 313, -339, -709, -37... | 7 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-522, 152, 201, 189, 369, -585, -632, 226, -115, 406],\n [241, -21, -26, 173, -329, 562, -310, -418, -363, 324],\n [1004, -705, 664, -709, 324, 343, 380, 584, -293, -61],\n [458, -32, 496, -473, 305, 9, 249, 302, 36, -340],\n [-508, -60, 455, -40, 643, -... | 7 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[537, 321, -360, -176, -79, -11, -97, -471, 19, 472],\n [151, -71, -69, 401, -209, -577, -555, -339, 311, 548],\n [-169, 211, 434, -283, 63, 667, 356, 156, -337, -560],\n [-312, -10, 122, -141, -46, 242, 297, 243, -120, -316],\n [-339, 152, 624, 152, -... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[250, -472, -932, 157, 111, -432, -206, -75, 469, -247],\n [-269, -356, -663, -532, 153, -271, -113, -470, 646, 132],\n [404, -727, -581, 117, 126, -80, -412, 449, 577, 373],\n [-322, -274, -45, -245, 187, -222, 319, -678, 134, -521],\n [12, 550, -1098, -391, 53, ... | 9 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-399, 209, -304, -57, 190, 285, -95, -133, 266, -304],\n [-45, 79, -152, -71, -34, -13, 43, -7, 22, -60],\n [75, -67, 116, 43, -8, -31, -9, 21, -46, 70],\n [159, 83, -232, -171, -242, -249, 199, 77, -130, 44],\n [255, 102, -306, -238, -357, -374, 289, 119, -204, 85]... | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[194, -100, -86, -72, -30, 54, -64, -56, 140, -64],\n [170, 99, -301, 30, -138, -87, -174, -34, 85, -2],\n [143, -256, 157, -144, 87, 171, 68, -56, 140, -100],\n [-475, 132, 347, 120, 141, -51, 228, 128, -320, 124],\n [248, 189, -493, 66, -228, -159, -... | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[78, -99, 13, 764, 97, 111, -400, -218, 167, -175],\n [-27, -2, -23, -59, 27, 5, 16, 34, 24, -20],\n [305, 69, 264, 543, -260, -70, -114, -362, -233, 187],\n [122, -76, 107, 416, -272, -21, -145, -177, -257, 240],\n [-148, -344, -85, 54, -622, -29, -63, 141, -663,... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-20, 300, -564, 428, 8, 88, 500, -4, -380, -44],\n [-218, 58, 291, -109, -234, -165, -317, -321, 19, 265],\n [20, -300, 564, -428, -8, -88, -500, 4, 380, 44],\n [22, 198, -438, 314, 44, 88, 398, 50, -266, -74],\n [394, -454, 174, -322, 388, 176, -54, 550, 418, -3... | 2 | MATH |
[
{
"content": "Compute the rank of the given 10x10 matrix:\n[[-251, 764, 340, 320, -68, 64, -710, -321, -124, 128],\n [643, 60, -645, -631, 337, 297, -43, -1097, 982, 84],\n [580, 297, -595, -833, 426, 302, 97, -57, -91, 47],\n [582, -556, -585, -505, 178, 627, 433, -68, 70, -437],\n [706, -238, -550, -258, 452,... | 7 | MATH |
[
{
"content": "Compute the rank of the given 10x10 matrix:\n[[473, -18, 308, 275, 115, -712, 779, -132, 210, -134],\n [-543, 149, 318, 491, -496, 370, -135, -599, -351, 830],\n [-151, -805, -38, -163, -104, 542, -269, 815, 263, -167],\n [530, 634, -714, -112, 841, -347, -73, -24, -23, -30],\n [-38, -1414, 1096, ... | 8 | MATH |
[
{
"content": "Compute the rank of the given 10x10 matrix:\n[[297, 164, -300, -126, -59, 81, 99, 398, -141, 552],\n [-319, -214, -263, -598, -148, 578, -333, -185, -223, -380],\n [90, 132, -274, -125, -84, 169, -144, 294, -337, 174],\n [-389, -108, 5, -709, 179, 422, 85, -205, 454, 70],\n [639, -28, -11, 307, -1... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[108, -24, -126, 66, 18, -132, 18, 84, -96, 114],\n [378, -84, -441, 231, 63, -462, 63, 294, -336, 399],\n [-108, 24, 126, -66, -18, 132, -18, -84, 96, -114],\n [54, -12, -63, 33, 9, -66, 9, 42, -48, 57],\n [306, -68, -357, 187, 51, -374, 51, 238, -272, 323],\n [270,... | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-23, -398, -349, 355, -763, -135, -43, 699, 269, 533],\n [-293, 510, 236, -307, 228, 374, 189, -528, -125, -836],\n [-58, -198, 89, 38, -814, 237, -1091, 425, 557, 325],\n [245, -7, -133, 812, 699, -434, 251, -193, -131, 67],\n [666, -263, -345, 1353, 11... | 9 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-203, -303, -501, -247, -202, -390, -545, -490, 205, -184],\n [-348, -91, 237, -772, -647, 32, -426, -597, -225, 46],\n [777, -633, -231, 238, 193, 471, -436, -272, 957, 308],\n [160, -330, -338, -153, -1058, 223, -738, -168, -698, 416],\n [611, -130, 101, -159, 271... | 6 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[19, 10, -185, -42, 136, 32, -152, -7, -42, -91],\n [-151, -586, 500, -113, 220, 282, 381, 172, 123, 81],\n [-995, 393, -444, 379, -62, 228, -583, 82, 69, -717],\n [-413, 129, -237, -186, 42, -178, -216, 85, -118, -361],\n [252, 129, 493, 387, -558, -18, 303, -135... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[330, -326, 489, -264, -288, -495, 463, -485, 238, 102],\n [-46, -541, 247, -73, 89, -225, -65, -93, 306, 556],\n [-381, -152, -120, 159, -72, 9, -71, 112, 40, 24],\n [486, 230, 202, -216, -102, -120, 288, -262, -68, -224],\n [178, -95, 192, -119, -83, -174, 168, ... | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[35, -77, -14, -154, 119, 14, 119, -63, -126, -140],\n [70, -154, -28, -308, 238, 28, 238, -126, -252, -280],\n [110, -242, -44, -484, 374, 44, 374, -198, -396, -440],\n [-95, 209, 38, 418, -323, -38, -323, 171, 342, 380],\n [20, -44, -8, -88, 68, 8, 68, ... | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[769, -313, 44, -244, -378, 312, 248, -126, -113, -531],\n [918, -1302, -529, 550, 176, -607, 298, 391, -719, -316],\n [353, -75, 315, -514, 688, -404, 520, -187, -722, 133],\n [-474, -133, 78, 997, 251, -309, 301, 98, 657, 677],\n [474, -940, -360, 56... | 9 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[389, -26, -34, -63, -321, 67, 456, 24, 84, -490],\n [-619, 55, -189, 249, 466, -323, 96, -344, 541, 337],\n [599, 70, -121, 211, 241, -412, 543, 174, 65, -441],\n [45, -172, 361, 290, -28, -469, 440, -177, 52, 136],\n [73, -218, 138, -108, -459, -111, 448, -531, 1, ... | 9 | MATH |
[
{
"content": "Compute the rank of the given 10x10 matrix:\n[[56, -359, 124, 144, 390, 89, -394, -137, -630, 214],\n [80, 206, 28, 165, -396, -331, 138, -13, 455, 36],\n [263, 477, 141, -567, 88, 252, 210, -10, -16, -550],\n [12, -822, -413, 233, -71, 552, -279, -196, -147, 369],\n [939, 80, 22, -196, -843, 485,... | 5 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[27, -222, -136, -24, -123, 310, -65, 86, 171, -127],\n [415, 273, -544, -163, -47, -429, 218, 475, -783, -230],\n [51, -59, -7, 209, -238, 421, -135, -73, 215, -197],\n [5, -573, -437, 259, 205, 308, -122, 163, 56, -287],\n [33, -287, -396, -91, 350, ... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[22, 29, -56, -119, -60, 13, -73, -204, 24, -119],\n [-25, 506, -231, -606, -66, -661, -96, 353, 11, 32],\n [184, -654, 172, 757, 343, 531, -304, -41, 350, 422],\n [381, 419, -375, -760, 347, -216, 96, -432, 32, -533],\n [160, 411, -134, -434, 421, -28... | 6 | MATH |
[
{
"content": "Compute the rank of the given 10x10 matrix:\n[[-125, -726, 366, -65, -160, 209, 287, -809, -153, 24],\n [588, 234, -271, 35, -453, -583, -369, 405, 575, -1],\n [379, 484, 324, 828, -455, -217, 215, 727, 251, -675],\n [254, -130, -338, -206, -369, -908, -262, -98, -78, -271],\n [-22, 94, -103, -358... | 9 | MATH |
[
{
"content": "Compute the rank of the given 10x10 matrix:\n[[-30, -54, -36, -39, -30, 54, -24, 57, -48, 51],\n [-10, -18, -12, -13, -10, 18, -8, 19, -16, 17],\n [110, 198, 132, 143, 110, -198, 88, -209, 176, -187],\n [70, 126, 84, 91, 70, -126, 56, -133, 112, -119],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n [-170, -3... | 1 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[507, -761, -154, 234, 268, 0, 248, 191, 268, -47],\n [-407, -43, 282, 142, -360, -785, -15, 217, 536, 665],\n [1122, -686, 764, 72, -98, -432, -196, -448, -260, 16],\n [274, -653, -615, 235, 433, 203, 339, 321, 271, -301],\n [640, -546, 259, -336, -63, -334, -26,... | 6 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[147, 210, 168, -84, 399, 147, -147, -441, -147, -273],\n [-7, -10, -8, 4, -19, -7, 7, 21, 7, 13],\n [-119, -170, -136, 68, -323, -119, 119, 357, 119, 221],\n [-56, -80, -64, 32, -152, -56, 56, 168, 56, 104],\n [-56, -80, -64, 32, -152, -56, 56, 168, 56, 104],\n [-11... | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-27, -551, -423, -368, -337, 305, 105, -457, 659, 125],\n [-64, -38, 454, 302, 661, -199, 406, -306, -456, -495],\n [-170, -226, -297, 180, 89, 228, -337, 179, -357, 366],\n [664, 644, 564, 213, 50, -528, -94, -301, -372, -219],\n [-52, -309, -519, -248,... | 6 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[191, 193, 50, -91, -113, 240, -468, -40, 154, 78],\n [-413, 179, -497, -9, 50, -205, 298, -64, 5, -836],\n [-441, 232, 160, 440, 121, -451, 646, 347, -202, 53],\n [-320, 84, 306, 480, 82, -434, 532, 336, -242, 160],\n [35, -133, 416, 289, 7, -168, 136, 190, -168, 41... | 4 | MATH |
[
{
"content": "Compute the rank of the given 10x10 matrix:\n[[111, -196, 62, 269, -19, -144, 693, 638, -76, 131],\n [512, 456, 787, 97, 137, -444, -59, 135, -179, 10],\n [-340, -39, 392, 398, -547, -284, 252, 205, 177, -458],\n [-464, -240, -85, 162, -572, -25, 262, 68, 127, -508],\n [-131, -492, -678, -63, -11,... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[627, 478, -136, -375, -7, -74, -568, -259, -479, 268],\n [-339, -313, 214, 276, 175, 122, 349, 49, 284, -166],\n [443, 267, 86, -170, 217, 54, -347, -301, -306, 162],\n [422, 238, 124, -140, 258, 76, -318, -314, -284, 148],\n [67, -54, 256, 101, 329, 150, 20, -203, ... | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[326, 869, 368, -92, -106, -321, 241, 512, -445, -166],\n [-254, 508, -406, -205, 49, 399, -61, -529, 0, 339],\n [-538, 20, 131, 374, -31, 504, 144, -383, 68, -161],\n [-783, 484, 836, 611, -365, 1237, -13, -396, 1230, 118],\n [-602, 34, 192, 868, -461, 945, 216, -83... | 8 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-863, 349, -712, 243, 145, 1077, 382, -823, -404, -603],\n [249, 90, -355, -359, -83, -230, 503, 337, 638, -570],\n [-690, 164, 287, 649, 576, 283, -309, -663, 3, -783],\n [-110, -1012, -130, 2, -489, -462, -782, -914, 181, -26],\n [-433, 419, 350, -4... | 9 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[342, 84, -428, -336, -210, -206, 494, -608, 322, -664],\n [-241, -110, 78, 92, 171, -15, -389, 268, -91, 244],\n [152, 169, 392, 236, -147, 308, 380, 114, -185, 242],\n [-92, -52, 7, 85, 116, -157, 264, -173, 178, -284],\n [-412, -236, -86, -10, 296, -130, -868, ... | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[117, -310, -696, 71, 340, 373, 1456, 136, 116, 848],\n [-229, -127, -409, -324, 72, 372, 260, 0, -247, 420],\n [623, 379, 395, -534, -10, 630, 966, 175, 305, 16],\n [1071, -193, 796, 592, -558, -1257, -293, 654, 244, -1085],\n [-133, -257, -115, -832,... | 9 | MATH |
[
{
"content": "Compute the rank of the given 10x10 matrix:\n[[-196, -371, -11, -861, 5, -846, -1623, 166, -227, -513],\n [-168, -237, 452, -302, 122, 210, -178, 340, 291, 542],\n [-112, -215, 536, -208, 78, 150, -230, 36, 37, 94],\n [211, 27, 29, -390, 23, -68, -343, -259, -408, -579],\n [154, -16, 111, 106, -15... | 5 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[558, -69, -292, -16, -176, 530, 228, 272, -906, 106],\n [226, -203, -69, 635, -307, -146, -719, 475, 231, -43],\n [-504, 979, 159, 862, -34, 454, 72, 795, -191, 533],\n [398, -161, -301, -214, 179, 41, 214, 16, -10, -131],\n [-60, 280, -15, -739, -399... | 7 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[154, 332, 379, -825, -160, 227, -996, 636, 9, 14],\n [-646, 81, -361, 382, 33, 770, 49, -9, -570, 211],\n [291, -434, 293, -236, -286, -349, 110, -341, 29, -65],\n [-68, -491, 495, -117, -287, -136, 129, -262, -13, 96],\n [-583, 502, -580, 274, 235, 7... | 9 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-149, -133, 247, -129, -698, 267, 413, -28, -97, 110],\n [-34, -27, -213, 651, -211, -34, -423, 177, 334, -473],\n [231, 62, -516, 649, 466, -292, 2, 391, 175, -735],\n [-159, -54, -128, 249, -196, 78, -438, -163, 181, -189],\n [109, -115, 491, 41, -9, -474, -306... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-88, -229, -478, 730, -963, 81, -869, -577, -653, 235],\n [-645, 364, 278, 581, 25, -285, 201, -149, 178, 529],\n [170, 570, 220, 254, 606, 767, 208, 330, 149, 323],\n [206, -192, 118, -410, 138, -74, -63, 18, -79, -240],\n [-347, -750, -232, -85, -469, -663, -37... | 6 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-383, -1358, -912, 203, 240, 637, 414, 143, 378, -221],\n [-266, -1019, -239, -1144, 242, 378, -112, -817, 505, -419],\n [141, 87, 231, -450, -220, -436, -299, -591, 419, -538],\n [219, 380, -102, 154, 155, 354, 1148, -240, 777, 1376],\n [-494, 265, -311, 530, -1... | 9 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-332, -157, -148, -445, -95, -323, -49, 424, 344, -295],\n [-260, -65, -52, -221, -91, -195, -65, 260, 208, -143],\n [-466, 124, 172, 133, -232, -109, -227, 167, 118, 109],\n [570, -135, -192, -126, 279, 150, 270, -225, -162, -108],\n [736, -149, -220... | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[200, -718, -66, 438, -341, 561, -298, 56, 503, -30],\n [-308, 723, -311, -278, 577, -747, 164, -422, -580, 240],\n [71, -10, -86, 160, 171, -10, -438, -196, -418, 637],\n [-267, 704, 188, -594, 237, -509, 538, 122, -326, -350],\n [65, -630, 126, 160, -309, 562, -182... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[227, -359, 21, -43, 497, -166, -523, -238, 116, 298],\n [867, -341, -990, 1089, -110, 132, -463, 543, -729, -459],\n [105, -120, 459, -469, 267, -31, -253, -638, 557, 98],\n [340, -69, -82, 262, -186, 253, 244, 66, 265, -640],\n [220, -159, -640, 415, -35, 125, -36,... | 6 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[499, -219, -402, -319, 348, -197, 115, 178, 273, 56],\n [-191, 853, -761, -124, 1099, -450, 712, -203, 340, -158],\n [-143, 395, 580, -208, 79, 124, 368, 448, -78, -400],\n [183, -422, 422, 141, 146, -312, 640, 245, -294, -620],\n [-181, 725, 121, -47... | 9 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[640, 198, -284, 416, -116, -524, -144, -694, -374, -138],\n [446, -321, -630, 108, 90, -56, -32, -101, 117, -425],\n [146, 435, 503, -170, 135, 628, 83, 102, -391, 135],\n [-327, 83, 373, -328, 283, 871, 53, 589, -9, -33],\n [629, 50, -384, 264, 50, -125, -105, -402... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[417, 287, -91, 427, 65, -401, -189, 325, 188, 209],\n [244, 57, -14, 207, 177, -203, -286, 217, -61, 45],\n [446, 388, -126, 488, -32, -452, -74, 328, 326, 280],\n [119, -130, 49, 40, 284, -54, -389, 144, -273, -88],\n [-10, 118, -42, 38, -158, -26, 202, -38, 188, 8... | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-104, 127, 537, -503, 343, -256, -91, 240, 717, 156],\n [570, 664, -352, 543, -604, -255, -265, -555, 62, -325],\n [-480, -453, -203, -325, -143, -296, 3, 372, -95, 148],\n [281, 194, -366, 457, -440, 78, -149, -350, -283, -208],\n [-1, -141, -355, 265, -264, 126, 9... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[90, -75, -45, -135, 165, 120, 255, 285, -75, 105],\n [-66, 55, 33, 99, -121, -88, -187, -209, 55, -77],\n [132, -110, -66, -198, 242, 176, 374, 418, -110, 154],\n [-36, 30, 18, 54, -66, -48, -102, -114, 30, -42],\n [-42, 35, 21, 63, -77, -56, -119, -133,... | 1 | MATH |
[
{
"content": "Compute the rank of the given 10x10 matrix:\n[[-52, -90, 8, -16, -18, 38, 56, 82, 90, 106],\n [215, 150, -160, 170, 210, 190, -120, -365, -325, -320],\n [236, 213, -148, 164, 201, 133, -156, -395, -367, -377],\n [100, -360, -320, 280, 360, 760, 160, -220, -60, 80],\n [-259, -84, 248, -250, -312, -... | 2 | MATH |
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