{"messages": [{"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, 75, -1323],\n [-1259, -49, -449, 928, 1235, 1194, 554, -952, -877, -474, -110, 454],\n [-481, 389, -1564, 713, -179, -219, -105, -1567, 75, -1305, -162, -1676],\n [160, 880, 1631, -353, -68, -494, -792, -46, -972, 579, 805, 2144],\n [208, 466, 2228, -1392, 539, -478, -255, 843, -275, 155, -320, 710],\n [211, 260, 1287, -608, 1578, -618, -532, 727, 225, -81, -5, -684],\n [-223, 535, 900, -1199, -521, -255, 137, -178, 543, -611, -288, -16],\n [-207, 188, 51, -732, -1011, -2083, -1545, -1523, 624, -1494, 1384, -569],\n [-1138, 700, -64, -225, -988, -870, 224, -859, 21, -660, -139, 893]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"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],\n [140, -175, -98, -42, -91, -84, 63, -91, 182, 112, -7, 14],\n [-180, 225, 126, 54, 117, 108, -81, 117, -234, -144, 9, -18],\n [160, -200, -112, -48, -104, -96, 72, -104, 208, 128, -8, 16],\n [20, -25, -14, -6, -13, -12, 9, -13, 26, 16, -1, 2],\n [480, -600, -336, -144, -312, -288, 216, -312, 624, 384, -24, 48],\n [160, -200, -112, -48, -104, -96, 72, -104, 208, 128, -8, 16],\n [140, -175, -98, -42, -91, -84, 63, -91, 182, 112, -7, 14],\n [-100, 125, 70, 30, 65, 60, -45, 65, -130, -80, 5, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"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, 88, -908, 73, 579],\n [-429, 488, -666, -89, 492, 212, -253, 386, -209, -260, 135, 592],\n [-10, -952, 365, 158, -231, -274, 682, -384, 209, 419, -19, -296],\n [297, 637, -145, -86, -501, 589, -757, 335, 114, -732, -11, -201],\n [287, 808, 378, -311, 341, -221, -213, -53, -218, 203, -74, 321],\n [721, 134, 945, -175, -520, -133, -19, -355, 177, 166, -169, -425],\n [458, -293, 885, -245, -552, -26, 428, -392, 338, 209, -41, -122],\n [-186, -250, -114, 52, 110, -58, 210, -22, 0, 100, 42, 90],\n [-701, 31, -1057, 404, 920, -278, -211, 326, -493, 93, 36, 150]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"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, -225, 455],\n [-427, -195, -467, 686, -136, -564, 207, 451, -571, -15, -94, -19],\n [234, 173, 110, -189, -90, 56, -55, -64, -7, -162, -169, 121],\n [-243, -441, 123, -66, 408, 480, -129, -369, 465, 591, 582, -417],\n [126, 295, -70, 25, -238, -312, 107, 256, -229, -374, -331, 267],\n [495, 76, -71, 105, -402, -56, -248, -137, -854, -291, -683, 176],\n [204, 467, -91, 12, -360, -466, 164, 386, -322, -579, -502, 415],\n [-496, -83, -130, 179, 206, -212, 271, 302, 375, 150, 411, -95],\n [460, -170, 25, 35, -210, 270, -385, -420, -675, 25, -435, -50]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"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, 333, -300, -165, 500, -555, -435],\n [771, 488, -231, 346, 1998, -956, 1188, -820, -1532, -2021, 372, -18],\n [-505, -406, -638, -683, -1671, -76, -686, 625, -201, -13, 149, 617],\n [1153, -259, -1308, 1094, 1380, -395, 1200, 623, -880, -344, -535, 1131],\n [-66, 200, 421, -1121, -120, 297, 418, -366, -1339, -197, -494, 128],\n [677, 120, -324, -206, 1323, -862, 845, -348, -72, 111, -766, -85],\n [-685, -134, 65, -1788, -2231, 499, -614, -756, -839, 735, 420, 867],\n [-199, 478, -81, -133, 527, -183, 757, -753, -1010, 25, -857, 549],\n [1201, -1001, 1092, -1162, -184, 860, 1703, -598, 141, 258, -54, -1021]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"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, 204, 216, 60, 216],\n [218, -11, -363, 40, -86, -197, -451, 349, -281, -299, -76, -326],\n [352, -80, -308, -56, -240, 32, -100, 264, -232, -228, -148, 96],\n [696, -132, -726, -60, -432, -84, -462, 648, -552, -558, -282, -72],\n [656, -152, -561, -110, -452, 76, -157, 478, -422, -413, -277, 208],\n [-154, 43, 99, 40, 118, -59, -37, -77, 73, 67, 68, -122],\n [-394, 115, 231, 112, 310, -179, -145, -173, 169, 151, 176, -362],\n [44, -58, 176, -100, -108, 274, 472, -198, 142, 168, -38, 492],\n [-116, 118, -308, 196, 228, -526, -892, 354, -250, -300, 86, -948]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"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, -41, -183],\n [-495, 181, 355, -550, 853, 582, 178, -667, 381, -418, 117, -191],\n [479, -536, 1083, -205, 405, 279, -540, -300, -817, 1234, 378, -85],\n [793, 397, 832, 5, 426, -401, -607, -64, 643, 931, 782, -260],\n [985, -701, 636, 723, -652, -47, -212, 546, -1111, 960, 1, -168],\n [140, 121, -403, 571, -796, -843, -729, 997, -699, 1401, 369, 77],\n [63, -141, -974, -16, -767, -838, -344, 357, -54, 162, -268, 671],\n [-1255, 425, -632, -511, 384, 243, 307, -240, 53, -587, 144, 299],\n [1135, -149, 331, 565, -248, -67, 151, 146, 854, -709, 307, -624]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"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, -483, 273, -483, -42, -504, 105, -504, 0, 42, 105],\n [176, 304, 368, -208, 368, 32, 384, -80, 384, 0, -32, -80],\n [-264, -456, -552, 312, -552, -48, -576, 120, -576, 0, 48, 120],\n [-220, -380, -460, 260, -460, -40, -480, 100, -480, 0, 40, 100],\n [44, 76, 92, -52, 92, 8, 96, -20, 96, 0, -8, -20],\n [121, 209, 253, -143, 253, 22, 264, -55, 264, 0, -22, -55],\n [-44, -76, -92, 52, -92, -8, -96, 20, -96, 0, 8, 20],\n [176, 304, 368, -208, 368, 32, 384, -80, 384, 0, -32, -80]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"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, -202, 112, -292, 58, -242],\n [-267, -65, 153, -77, 463, -944, -713, 205, -373, -17, -155, -504],\n [97, -504, 361, -203, 246, -556, 78, 34, -338, 17, -34, -596],\n [605, 187, 46, 488, 646, 230, -46, 355, 434, -624, 569, 340],\n [325, -375, 242, 246, 324, -662, -348, 3, -238, -508, -247, -824],\n [-391, -311, 297, -737, 73, -208, 465, 119, -315, 787, 287, 96],\n [-274, -17, 149, -37, 562, -1026, -834, 261, -370, -65, -133, -504],\n [-760, 452, -53, -541, 377, -230, -283, 434, -79, 783, 468, 740],\n [-295, 65, -5, -326, -73, 98, 181, 50, -42, 443, 150, 306]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"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, -441, 225, -68, 881],\n [-1023, 587, -1183, -616, 484, -553, -615, -53, 702, -1067, -1073, -494],\n [6, 163, -1111, 418, -172, 850, -100, -133, -23, -526, -139, -590],\n [-606, 804, -1521, -33, 521, 644, 347, 791, 1259, 46, -690, -692],\n [-1298, 293, -721, -30, 786, -271, -219, 75, 910, -875, -1124, 715],\n [-1114, -344, -3, 635, 1289, 451, 404, 300, 843, -853, -1067, 1002],\n [-1517, 534, -254, -1320, 444, -920, -574, 1210, 686, -1302, -816, -32],\n [-435, 510, -648, -188, 1050, -285, -298, 101, 609, -409, -902, -702],\n [-414, -216, 546, -1310, -1280, -1984, -1638, -282, -546, -182, -484, 591]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"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, -272, 255],\n [208, -195, -13, -182, 169, -117, -26, 78, 260, 169, 208, -195],\n [176, -165, -11, -154, 143, -99, -22, 66, 220, 143, 176, -165],\n [-336, 315, 21, 294, -273, 189, 42, -126, -420, -273, -336, 315],\n [-304, 285, 19, 266, -247, 171, 38, -114, -380, -247, -304, 285],\n [-64, 60, 4, 56, -52, 36, 8, -24, -80, -52, -64, 60],\n [320, -300, -20, -280, 260, -180, -40, 120, 400, 260, 320, -300],\n [-16, 15, 1, 14, -13, 9, 2, -6, -20, -13, -16, 15],\n [304, -285, -19, -266, 247, -171, -38, 114, 380, 247, 304, -285]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"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, 696, -48, -189],\n [-706, -229, -269, 170, 329, 70, -458, -234, 302, 421, -65, -249],\n [368, 1055, 211, 264, -255, 26, 842, -302, -160, -799, 51, 189],\n [-236, 521, -88, 294, -98, 39, 570, 124, 256, -184, -19, 130],\n [205, 1282, 328, 304, -216, 17, 1018, -370, -53, -869, 31, 221],\n [-92, 208, -1438, 1010, -286, 324, 144, 172, 136, -24, 58, -150],\n [1937, -735, 393, -812, -689, -199, 52, 852, -961, -342, 174, 396],\n [479, -178, -759, 329, -479, 103, 330, 788, -49, -9, 72, 170],\n [-56, -109, -599, 349, -5, 139, -270, -122, -26, 92, 24, -183]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"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, -851, 523, 41],\n [-865, 469, 691, 91, -575, 44, 779, 467, 1, -145, 126, 308],\n [1274, -249, -1283, 35, 1686, 299, -1550, -82, 331, 72, 216, -617],\n [-475, 77, 152, 80, -814, 535, -137, -854, -403, 896, 330, 73],\n [130, -359, 477, -386, 216, -243, 316, 245, 80, -126, -506, 44],\n [-58, 210, 195, -373, -526, -805, -593, 703, 213, -408, 459, 598],\n [1044, -578, -562, -358, 575, -612, -578, 314, 18, -146, -364, -41],\n [-197, 393, -78, 295, -656, 297, -360, -701, 577, -59, 899, -226],\n [862, -637, -214, -717, 1070, -1048, -1601, -20, 75, -846, -435, 306]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"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, 219, 792, 333, -507, -962],\n [-631, -1480, 133, -569, -860, 680, -621, 149, 201, -278, -234, 552],\n [-599, -568, 1050, -486, -1307, 1323, -319, -511, 655, 478, -741, -350],\n [-431, -1280, -809, -529, -279, -153, -421, -551, 215, 745, -571, 858],\n [152, -310, 726, 837, -239, 389, -574, 904, -147, -355, 1213, 957],\n [-77, -509, -40, 1907, 1474, -583, 458, 417, -317, 168, 322, -579],\n [463, 742, 281, -230, -78, -44, 152, -407, 131, -300, 713, -569],\n [-483, 207, 275, -197, -577, 416, 221, -867, -383, -164, -70, 139],\n [607, 270, 32, 404, 760, -488, 322, 939, 516, 440, -189, -716]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"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],\n [-844, 522, -251, 205, 16, 375, 585, -930, 141, 801, -419, 421],\n [648, -287, 905, 566, 4, -847, 423, 198, 111, -273, 181, -185],\n [-304, 203, -273, -782, -1371, -498, -992, 355, 273, -23, 660, -876],\n [873, -428, 277, -29, -312, -526, -742, 1005, 279, -549, 328, -525],\n [459, -296, 312, 736, 1482, 471, 985, -217, -418, -158, -581, 876],\n [286, 724, -805, -507, -23, -64, 82, 744, -740, 109, 453, 502],\n [95, 293, -213, -468, -1145, -635, -767, 636, 297, 63, 573, -608],\n [657, 431, -280, 225, 468, -125, 469, 642, -407, 142, 38, 696]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"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, 467],\n [-58, 119, -357, 78, -16, 193, -55, -55, 49, -35, 216, 289],\n [258, -158, -88, -228, -22, 114, 96, -874, 48, 654, -424, 178],\n [-74, 148, -66, 294, 292, -154, -212, 376, -256, -568, 606, 284],\n [46, -110, 574, 49, 201, -425, -35, 348, -237, -300, 5, -332],\n [219, 38, -149, 231, 526, -189, -258, -440, -432, -192, 523, 698],\n [67, 4, 93, 123, 250, -187, -116, 10, -226, -214, 243, 164],\n [23, -160, 687, -48, 65, -410, 53, 404, -131, -188, -216, -566],\n [111, -112, 49, -171, -92, 51, 102, -374, 84, 378, -347, -76]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"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, -498, -783, -315],\n [285, -914, -1245, -345, 136, -291, -152, -263, -10, 933, 1306, 590],\n [-608, -317, 262, -75, 102, -568, 178, 539, -217, 400, 591, -340],\n [-257, -142, -672, -56, -265, 305, 105, 140, -397, -711, -516, 1103],\n [171, -356, -897, -238, -222, -103, -226, -324, 35, -562, 35, 1037],\n [608, -277, -1090, 127, 333, 560, -67, -225, -93, 928, 440, 399],\n [-551, -139, 353, -473, -415, 367, 551, 180, -390, -137, -201, 195],\n [339, -308, -342, 130, 353, -31, -83, -95, 45, 1270, 930, -428],\n [541, -149, -1042, -432, -1036, 1397, 80, -1137, -271, -917, -897, 1834]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"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, -7, 201],\n [-536, -234, -86, -279, -558, 60, 162, 166, -829, 57, 188, -617],\n [96, 31, 148, 341, 501, -406, -547, -563, 280, 17, -176, 292],\n [252, -247, -387, -407, -550, -541, 256, 480, 519, 540, 573, 492],\n [-396, -6, 119, 9, -83, 329, 27, -73, -688, -224, -151, -571],\n [-740, -414, -155, -369, -765, -237, 45, 97, -1048, 228, 347, -713],\n [-288, -219, -124, -219, -413, -190, 51, 107, -382, 181, 236, -238],\n [192, -323, -404, -403, -573, -742, 131, 379, 490, 629, 628, 514],\n [-220, -299, -81, -4, -114, -781, -460, -360, -94, 359, 233, 99]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"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 [-110, -54, -147, -883, -331, -969, -98, 547, 473, 218, -144, -244],\n [0, -110, -262, -396, -354, -928, -42, 926, 210, -446, 224, 42],\n [-285, -62, -729, -179, -493, 397, 106, -29, 463, -194, 49, -422],\n [-21, 597, -855, 178, -6, 407, -414, 283, -211, -833, 626, 74],\n [-572, -1261, -184, 325, -664, 1096, 515, -995, 324, -430, -177, -770],\n [413, -722, -18, 530, -882, -309, 1122, 964, 505, -309, -488, -9],\n [-735, 6, -558, 962, 242, 938, 102, -84, -36, -400, 1287, 698],\n [268, 128, 559, 1213, 577, -79, 358, 609, -533, -116, 616, 1220]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"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],\n [303, -735, -113, -1064, -503, -231, -598, -49, 122, -899, -500, -102],\n [-178, 10, -182, 99, 258, -149, 83, 119, 8, 104, -155, 197],\n [23, 25, 39, 20, -31, 37, 6, -21, -6, 13, 48, -34],\n [422, -230, 310, -492, -630, 214, -328, -238, 20, -454, 148, -400],\n [355, -115, 307, -316, -523, 233, -226, -217, 2, -303, 208, -362],\n [-478, -50, -534, 170, 686, -452, 174, 336, 36, 202, -498, 554],\n [-2, 530, 310, 662, 50, 356, 338, -112, -100, 534, 562, -170],\n [-412, 100, -376, 325, 604, -293, 241, 259, 4, 318, -277, 431]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"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, 439, -164, 540],\n [-183, 144, -56, -33, 211, 231, -337, 144, 84, -104, -245, 123],\n [258, -360, -506, -744, 850, 420, -22, 324, -438, 526, -632, 1032],\n [-65, -20, -285, -370, 595, 420, -345, 290, -115, 135, -530, 590],\n [75, 36, 377, 492, -781, -546, 439, -378, 159, -187, 692, -780],\n [-109, 44, -189, -230, 431, 336, -333, 226, -35, 39, -406, 394],\n [299, -328, -254, -413, 333, 63, 257, 76, -326, 394, -177, 511],\n [-365, 424, 398, 623, -579, -189, -239, -172, 446, -538, 363, -805],\n [198, -204, -119, -207, 124, -21, 212, 6, -189, 229, -35, 237]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"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, 716, 341, 661, 77, 103, -769],\n [328, -502, 64, 332, 920, 286, 458, 346, 1128, -230, 64, -996],\n [1115, 168, -837, -1005, 2, -426, 215, 117, 420, -384, -861, -834],\n [923, -48, -863, -609, -870, 74, -63, 125, 52, 86, -621, -424],\n [-795, 169, 657, 40, 395, -491, -204, -440, -754, -49, 18, 409],\n [-50, 705, 23, -155, 173, -726, 688, -105, -138, -286, 156, 254],\n [596, 589, -745, -449, -916, -1424, 1462, -63, -775, 92, -233, -271],\n [914, 1668, -625, -1446, -599, -994, 463, -618, -157, -903, -1185, -18],\n [-1, 408, 135, -825, 523, -3, -955, -339, 7, -518, -641, 221]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"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],\n [-696, -759, -579, -513, 474, -731, -139, -419, 452, -693, -1065, -146],\n [-209, 184, 124, -509, 1150, -75, -23, 103, 487, -1105, -731, -412],\n [174, 121, 6, 808, -676, 456, -111, 286, 104, 380, 247, -208],\n [42, -52, -377, 451, -774, 255, -358, 247, 34, 729, 518, 100],\n [52, -888, 554, -1048, 112, -1313, 1079, -1464, -1313, 329, -45, 865],\n [175, 166, 414, -65, -25, -100, 487, -260, -478, -29, 19, 296],\n [347, 380, 406, 967, -357, 686, 51, 404, 204, 13, 107, -526],\n [-98, -171, -548, -144, -667, -149, -279, -29, -281, 828, 579, 604]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"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, 12, 111, 468, 488],\n [412, -929, 250, -134, 902, -780, 297, -986, 758, 169, -927, 250],\n [403, -85, 809, 143, -99, 709, 1151, -296, 223, 1194, 1292, -260],\n [803, -1344, -269, -713, 1523, -558, -818, -534, -16, -1005, -904, -200],\n [-480, 731, -391, -285, -1014, 324, 17, 158, 621, 135, -183, 280],\n [1588, 52, 187, -950, -443, 1052, 239, 1043, -1073, 603, 1654, -768],\n [565, 459, -400, -711, -673, -167, 223, 593, -918, 698, -2, 57],\n [-461, 303, -223, 789, -270, -363, -959, 689, 90, -1284, -603, 319],\n [-313, 358, -501, -554, -898, -668, -574, 461, -347, -426, -751, -231]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"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, -78],\n [-12, 210, 337, -204, 246, -295, 76, 348, -182, -178, -274, 30],\n [-10, 92, 433, -336, 122, -481, 8, 456, -456, -508, -422, -58],\n [-8, 34, 419, -348, 58, -497, -20, 444, -510, -578, -430, -86],\n [0, 120, -220, 240, 120, 340, 80, -240, 440, 520, 280, 120],\n [5, -121, -79, 18, -136, 28, -54, -78, -47, -71, 36, -46],\n [20, -382, -503, 276, -442, 401, -148, -516, 186, 158, 382, -82],\n [5, -175, 20, -90, -190, -125, -90, 30, -245, -305, -90, -100],\n [25, -443, -692, 414, -518, 599, -162, -714, 359, 347, 558, -68]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"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, 321, -557, -320, 264],\n [-229, -786, 497, -1049, -730, 126, 512, -102, -635, 491, 262, 228],\n [103, -46, -35, -13, 160, -436, 268, -210, 23, -259, -156, 288],\n [-66, -368, 210, -474, -270, -98, 324, -120, -276, 128, 62, 204],\n [5, -436, 203, -527, -175, -433, 554, -288, -284, -54, -49, 438],\n [-9, -212, 105, -261, -105, -167, 246, -120, -144, 2, -7, 186],\n [-156, -174, 168, -276, -345, 429, -102, 162, -195, 369, 213, -198],\n [-164, -46, 112, -124, -305, 581, -278, 258, -115, 401, 237, -342],\n [-206, -620, 406, -838, -620, 196, 352, -36, -514, 450, 244, 120]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"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, -527, -682, 236, 402],\n [-37, 38, -111, 36, -258, -152, -135, 517, 686, 429, -148, -194],\n [-831, -624, -348, 528, -710, -64, 600, -216, 757, 88, -344, -272],\n [967, 262, 566, -351, 751, -2, -101, 335, -103, 47, 461, 162],\n [-1088, -827, 241, -16, 601, 100, 118, 331, 217, -314, 1239, 5],\n [247, -98, -31, -283, -100, -39, 25, 403, 601, 166, -135, 102],\n [-423, 57, -623, -254, -719, -28, -368, 277, 382, 164, -631, 65],\n [-153, 732, -513, -539, -317, -94, -1252, 820, -56, 408, -319, 32],\n [-418, -763, -317, -1036, 77, 452, 208, -399, -387, -1072, 71, 965]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"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, -986, 422],\n [-31, -50, -505, -267, -103, -881, 650, 961, -124, 289, -769, 721],\n [-611, 153, 507, 400, 482, 212, 48, -283, 398, 643, 109, -228],\n [640, -656, -1022, -630, -831, -380, 255, 361, -1109, -307, -410, 314],\n [700, 512, 180, -1267, 148, -11, 1309, -141, -525, -703, -114, 404],\n [-843, 96, 390, -227, 517, -401, 918, -308, 56, 1321, -666, -174],\n [404, -15, -244, 104, -230, -21, -648, 48, 130, -648, 258, -191],\n [-52, -304, -2, 494, -567, 319, -805, 229, 115, -89, 4, 302],\n [-33, -413, -806, -736, -476, -1162, 938, 762, -688, 655, -1284, 621]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"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],\n [-656, 265, 383, 338, 98, 993, -297, -61, -263, 485, -618, 313],\n [151, 59, -539, 17, 445, -210, -261, 512, 324, 419, 67, -354],\n [-683, 347, 469, 394, 101, 1061, -287, -78, -250, 547, -767, 440],\n [-278, -687, 942, -284, -741, -176, -99, -1013, -585, -975, 996, -52],\n [232, 305, 655, 144, -170, -325, 195, -309, 233, -35, -474, 777],\n [292, 92, -1274, -208, -26, 354, 912, 572, -168, -220, -284, -450],\n [268, 1, -937, -182, 38, 73, 543, 439, -43, -147, -38, -419],\n [588, -25, -548, -154, 277, -848, 27, 407, 491, 55, 294, -296]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"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, 140, 42, -105],\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 [126, 72, 54, -30, 96, 42, 18, 72, -126, 120, 36, -90],\n [483, 276, 207, -115, 368, 161, 69, 276, -483, 460, 138, -345],\n [-483, -276, -207, 115, -368, -161, -69, -276, 483, -460, -138, 345],\n [-126, -72, -54, 30, -96, -42, -18, -72, 126, -120, -36, 90],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n [420, 240, 180, -100, 320, 140, 60, 240, -420, 400, 120, -300]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"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, -432, 49],\n [1166, 1024, -519, 455, 819, 845, -461, 127, 989, -526, -449, -154],\n [-278, -164, -11, -271, -358, 123, 27, 304, 392, -147, -200, -233],\n [893, 764, -250, 41, 855, -477, -309, -205, 270, 181, -294, 565],\n [-635, -370, -199, -324, -30, 472, 524, -870, -661, 9, 251, -1247],\n [-833, -440, 755, -316, -1392, 208, -187, 564, 463, -116, 262, -207],\n [94, -389, 478, 856, -363, -318, -192, 943, -312, 26, 330, 1385],\n [-101, -347, -606, -413, -106, -201, 147, 1268, 1062, -373, -1058, 298],\n [-544, -512, -471, -245, -242, 701, 436, 256, 240, -440, -351, -933]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"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],\n [238, -266, -867, 491, 568, 240, -689, 466, 283, 563, -459, -243],\n [196, -37, -114, 138, -523, -57, -174, -94, -27, 48, -361, -799],\n [277, -88, -491, 83, 536, 397, -211, 655, 107, 576, -29, 458],\n [-734, 377, 540, -319, -318, -741, 205, 1, 293, -317, -103, 435],\n [405, 93, -434, -97, -12, 334, -151, 1022, 137, 834, -277, 312],\n [-248, 272, 589, -531, 112, -20, 613, 134, -111, -157, 583, 1105],\n [-13, -247, 79, 82, 826, 340, 192, -520, -250, -375, 686, 503],\n [-184, 222, 239, -287, -88, -142, 217, 296, 81, 67, 75, 529]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"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, 804, -131, -422],\n [-866, -749, 602, -133, -929, 950, -534, 473, -1082, -67, 77, 1727],\n [-203, 1026, 905, -372, 350, 166, -126, 809, 223, -304, -495, -405],\n [754, 1003, -643, -198, 751, 732, 341, -355, 211, -297, -1653, -714],\n [129, 460, -630, 504, -154, -631, -594, 542, 557, -667, -139, -220],\n [36, 184, -463, 561, -234, -1080, -468, 20, 739, -520, 517, -580],\n [1137, -756, -812, -111, -188, -544, 682, -463, -96, 644, 168, -93],\n [316, -584, -474, 302, -250, -800, 257, -484, 196, 298, 821, -171],\n [616, -336, 902, -1047, -294, -17, 394, -273, -317, 391, -207, -399]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"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, 412, 87, -1007, 1186, -84],\n [-72, 868, 782, -58, 274, -138, 359, 152, -303, -41, 720, -498],\n [614, -800, 60, -1479, -1389, 1344, -1001, -365, -473, -631, -202, 439],\n [671, -795, -1117, 1515, -633, -650, 853, -1170, 437, 483, -862, 244],\n [-1137, -266, -121, -607, 696, 82, 816, 836, 960, -305, 33, 679],\n [266, -643, -892, 1105, -144, -273, 264, -814, 811, 405, -1053, 766],\n [471, 540, -170, 282, -634, -480, 99, -466, -420, 910, -997, 220],\n [-627, -683, -450, 820, 381, -590, 1766, -10, 1054, -96, 621, 470],\n [351, 162, 392, -1138, -690, 945, 469, -479, 244, -790, -722, -55]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"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, -1037, -680],\n [297, -233, -25, -158, -364, 296, 188, -10, -334, 650, 376, 195],\n [-586, 141, 39, 289, 645, -19, -161, 30, 132, -387, -106, -66],\n [-260, -482, 83, 246, 245, 201, 301, -337, -325, 347, 743, 465],\n [240, -261, 21, -51, -267, -27, 207, -198, -120, 201, 294, 204],\n [89, -302, 44, 47, -103, -35, 219, -256, -118, 131, 366, 255],\n [1076, 397, -151, -673, -1135, -215, -153, 368, 218, 89, -756, -474],\n [1474, 288, -148, -814, -1546, -450, -30, 216, 292, 26, -764, -434],\n [341, 171, -57, -230, -360, -52, -80, 162, 78, 30, -292, -189]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"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, 299, 608, 300, -156],\n [-43, 1447, 546, -1118, 194, 63, -187, 795, -821, -392, -109, -101],\n [664, 391, -306, -354, 20, 349, -608, 759, 183, -90, -564, -156],\n [-1246, 572, 1521, 202, -240, -912, 17, 690, -1112, -298, 1567, 1128],\n [267, 547, 471, -59, 875, 1034, -1136, -562, -22, 577, 387, 71],\n [-846, 1049, 992, -385, 349, 177, -298, 694, -915, -96, 962, 419],\n [-794, -1419, 248, 1450, -1080, -1515, 574, 351, 50, -129, 955, 868],\n [331, -984, -251, 875, -849, -1002, -48, 259, 332, 10, -80, 174],\n [-613, -306, 636, 569, -253, -690, 159, -235, -359, 71, 844, 474]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"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, -1118, 1803, -1059],\n [332, -35, 720, 1073, -860, -82, -766, -267, -18, -1130, 641, 932],\n [-202, -18, 552, -47, -297, 575, -438, 554, 1460, -1355, 794, 1234],\n [91, 214, -300, 102, -531, 41, -171, -6, 91, -391, 461, 361],\n [-48, 365, -1119, 79, 755, -290, 606, -955, 256, 98, -860, -541],\n [308, -128, 873, 1289, 55, 184, -282, 80, 33, -166, -751, -220],\n [1743, -685, 157, -117, 242, -303, 150, 442, -78, 981, -692, -1221],\n [49, 642, 1262, 331, 278, -254, -599, 1148, -882, -573, 366, -671],\n [-676, -644, 1139, 640, -361, 742, 309, 524, 254, 510, -281, 163]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"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, 160, -821],\n [614, -14, -316, -722, 84, -632, 1102, 271, -146, 512, -867, 1047],\n [-102, 17, -294, 1180, 862, 1188, 63, -1424, -680, 176, 62, -58],\n [1196, 371, -54, 146, 130, 382, 253, -1208, 1605, -265, -468, 929],\n [578, -167, 509, -1029, -102, -1211, 351, 1555, 109, 588, 393, 460],\n [1934, -387, -338, -1557, 164, -1673, 539, -389, 2159, 36, -249, 488],\n [-1152, -127, 74, 1035, -469, 1760, -731, -144, -1694, 59, 940, -813],\n [-492, 346, 1227, 633, -875, 130, 313, 501, 512, 1275, 340, -1109],\n [-732, -56, 45, -485, 359, -15, -1780, 249, 954, -1085, -567, -1070]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"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, 1266, -494, -272, 268, -1130],\n [-792, 343, -703, 1410, 16, 63, 853, -809, -638, -786, -566, -1283],\n [-1136, -611, -163, 1320, -308, -1450, 153, 779, 248, 310, 123, 128],\n [-869, 553, 681, -859, -1225, -599, -432, 2443, 5, 691, -1271, 1224],\n [311, -1082, 310, -571, 396, -277, -498, -1511, 515, -91, 880, -182],\n [-95, 650, -872, -453, 1081, 599, -1115, -363, -176, 936, 102, 797],\n [-1291, 836, -397, 857, 502, -667, -680, 1618, -383, 647, 141, -791],\n [-88, 556, -801, 728, 300, 1454, 1099, -112, -889, -1085, -76, -2228],\n [-884, -242, -17, -351, -175, -264, -359, 2026, 431, 785, -102, 255]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"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, 1143, -650, 191, -1081],\n [999, 158, -598, 241, -662, -85, 553, -92, -197, -176, 573, -484],\n [-227, -60, 536, -185, 1453, -1237, 598, -948, -831, 721, 1200, -98],\n [-1249, -183, -95, -1752, -158, 415, -93, 883, 186, -720, -362, 667],\n [1116, -601, -698, -1305, 433, 35, 929, -489, -907, 542, 839, 225],\n [-158, 171, -415, -264, 88, 765, 359, 1214, 247, -677, 31, 140],\n [-905, 610, 520, 792, -216, 628, -629, 619, 322, -1192, -283, -737],\n [248, -209, 151, 1305, 1262, 574, 1050, -135, -228, 698, 663, -1175],\n [386, 77, -382, -440, -75, 748, 355, -451, -523, 90, -79, -735]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"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, -879],\n [-135, 161, -203, -144, -129, 94, 125, 192, -111, 5, -70, -176],\n [495, -207, 287, 368, 173, -44, -472, -112, 415, -151, 455, 373],\n [476, -474, 899, 93, 802, -776, -45, -1067, -41, -7, -72, 800],\n [-206, -458, 419, 215, 196, -214, 66, -593, -21, 235, -333, 139],\n [372, -608, 1022, 126, 864, -856, 22, -1266, -90, 82, -224, 824],\n [-329, -303, 288, -1, 163, -234, 266, -521, -216, 246, -472, 26],\n [299, -119, 689, -446, 845, -940, 422, -1006, -519, -17, -373, 657],\n [1077, 27, 389, 176, 479, -308, -592, -112, 421, -445, 821, 751]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"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, 606, 1031, -198, 386],\n [-344, -973, 320, 175, -697, -487, -1023, 916, 556, 209, -1164, -941],\n [343, 304, 87, -642, 958, -48, 780, -89, -192, 465, 108, 780],\n [-525, -212, -199, 40, 140, 310, 514, 423, 132, 389, 198, 1032],\n [-702, -600, 1288, -84, -281, -1201, -70, 799, 586, -385, 21, -719],\n [-227, -424, 55, 458, -664, 360, -512, 501, 924, 1, -394, 74],\n [1097, 290, 339, -305, 494, -194, 293, -55, 262, -287, -724, -30],\n [596, 508, -738, 203, -294, 1557, -253, -562, 476, -55, -80, 779],\n [107, 683, -637, 361, 358, 282, 471, -848, -570, 123, 1183, 400]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"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, 45, -116, 180, 1184],\n [-733, -660, 1305, 1068, -623, 1153, 1000, -295, -278, -317, 658, 381],\n [735, 723, 479, -894, -770, 226, -577, -471, -1577, 360, -899, -365],\n [214, -258, -187, -149, 1937, 80, 18, 797, -804, -284, -1170, 1543],\n [-356, -85, 1777, 1351, -49, 715, -752, -325, -298, 605, -587, 52],\n [113, 1153, 795, -695, 380, -970, 584, -708, -93, -279, -9, 1154],\n [-922, 328, -1367, -851, 458, -967, 390, -926, 2317, -825, 1519, -136],\n [863, 1223, 887, -477, 1208, -205, -1181, -145, -1003, 491, -1767, 1055],\n [-616, -692, -147, 494, -1008, -419, 592, -300, 244, -457, 1117, -501]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"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, 655, 531, -363],\n [487, 91, 247, -447, -480, 344, 24, -263, 415, -661, 363, -525],\n [370, -49, 205, -571, -325, -27, -315, -718, -182, -719, 142, -318],\n [262, 245, 87, -523, -445, 215, -173, -286, 272, -341, -258, -272],\n [-219, -113, -169, 263, 200, -74, 242, 103, 3, 283, 229, -73],\n [-683, -56, -563, -3, 315, -523, -102, -491, -530, 692, -531, 60],\n [463, -218, 478, -168, -15, -129, -443, -287, -507, -776, 223, 277],\n [-705, 141, -560, 510, 330, -48, 445, 555, 270, 1135, -369, 100],\n [23, -125, 68, -14, 100, -174, -171, -185, -328, -139, 23, 138]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"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 [170, 130, 160, -50, -70, -190, 20, 130, -10, 30, -100, -70],\n [374, 286, 352, -110, -154, -418, 44, 286, -22, 66, -220, -154],\n [187, 143, 176, -55, -77, -209, 22, 143, -11, 33, -110, -77],\n [-425, -325, -400, 125, 175, 475, -50, -325, 25, -75, 250, 175],\n [153, 117, 144, -45, -63, -171, 18, 117, -9, 27, -90, -63],\n [-17, -13, -16, 5, 7, 19, -2, -13, 1, -3, 10, 7],\n [-272, -208, -256, 80, 112, 304, -32, -208, 16, -48, 160, 112],\n [-323, -247, -304, 95, 133, 361, -38, -247, 19, -57, 190, 133]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"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, -304, -192],\n [60, 360, -160, -480, 140, -200, -300, 200, -400, -80, 380, 240],\n [33, 198, -88, -264, 77, -110, -165, 110, -220, -44, 209, 132],\n [-54, -324, 144, 432, -126, 180, 270, -180, 360, 72, -342, -216],\n [-60, -360, 160, 480, -140, 200, 300, -200, 400, 80, -380, -240],\n [-63, -378, 168, 504, -147, 210, 315, -210, 420, 84, -399, -252],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n [-78, -468, 208, 624, -182, 260, 390, -260, 520, 104, -494, -312],\n [12, 72, -32, -96, 28, -40, -60, 40, -80, -16, 76, 48]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"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, 250, -973, -123],\n [-676, 162, 277, -16, 1606, 366, -392, -585, -553, 301, 681, -472],\n [437, 703, -417, 547, 638, 446, -45, 361, -1020, 1261, 621, 407],\n [343, 319, 282, 173, 319, 100, -314, -92, -805, 585, 161, -286],\n [-134, -316, -299, 450, 235, 257, -14, 337, -543, 703, 22, 841],\n [209, -242, -328, 424, 133, 488, 423, 29, 293, 92, 498, 477],\n [580, -681, -259, 85, -1482, -202, 729, 66, 805, -612, -474, 409],\n [-601, 113, 366, -867, 289, -978, -1436, 440, -535, 15, -1063, -371],\n [140, 98, 680, 226, 231, 286, -113, -406, -450, 149, 235, -516]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"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, -100, 166, -302],\n [289, 79, -56, 158, -66, 44, -292, -7, -94, 101, 61, 177],\n [-217, -139, -268, -50, -96, -278, 166, -5, 226, 7, 353, -183],\n [864, 290, 42, 426, -99, 297, -837, -14, -386, 246, -87, 563],\n [-753, -231, 48, -390, 126, -192, 744, 15, 294, -237, -33, -477],\n [-1016, -298, 118, -538, 195, -217, 1013, 22, 370, -334, -113, -635],\n [-293, 59, 598, -280, 321, 383, 389, 25, -176, -247, -758, -92],\n [554, 178, -4, 280, -78, 166, -542, -10, -232, 166, -16, 356],\n [-348, -114, -6, -174, 45, -111, 339, 6, 150, -102, 21, -225]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"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, 724, -852, 1693, 510],\n [-970, -572, -656, -1073, -172, 794, 355, 39, -520, 1101, 178, 422],\n [-277, 866, -1392, -105, 890, -878, 128, 1569, -369, 467, -613, -66],\n [-35, -593, 583, -195, -535, 1001, 87, -559, -886, 345, 143, 145],\n [1184, 1162, 2431, 1063, -566, -824, -1562, -1093, 1898, -1019, -1138, -176],\n [796, -211, 189, 308, -64, 976, -1575, -562, -129, 421, -2130, -1368],\n [1778, 488, 512, 1427, 1299, -371, -810, 98, 877, -857, -1222, -35],\n [52, -146, 194, -477, 418, -999, 477, 1223, -138, 1290, 486, -573],\n [-599, 953, 610, 169, -1293, 668, -574, -1195, -337, -501, -694, 1017]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"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, 236],\n [304, -820, 963, -692, -271, 542, 297, 943, -300, -544, 197, -539],\n [-822, 638, -485, 164, 885, 758, -597, -221, 656, 364, 193, 421],\n [1257, -49, 32, -21, -318, -809, -279, -142, -955, -116, -398, -244],\n [168, 188, -195, 633, -790, -1235, 488, -427, 41, 192, -138, 202],\n [-726, 6, -284, 75, 131, 273, 311, -228, 471, 104, 83, 155],\n [610, 590, 300, 281, 69, -317, -827, 332, -123, 168, 117, 165],\n [14, -60, 93, -418, 588, 794, -460, 253, -118, -110, 52, -132],\n [-154, 100, -693, 257, -53, -437, 285, -769, -27, 178, -293, 143]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"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, 101, -780],\n [298, -238, 1083, -106, 1761, 94, -783, 104, 365, -511, -228, -223],\n [-333, -226, 218, 486, 260, 538, 783, 136, -248, 14, 194, -552],\n [150, 889, -712, -1016, -965, -1511, 1234, -830, -976, -422, 530, 1062],\n [-280, -331, -258, 1065, -140, 70, -1061, 273, -426, 233, -1172, -574],\n [40, 197, -149, 1624, -423, -862, -144, -858, -748, 845, -133, 982],\n [120, -612, -463, -44, -340, 1, -622, 587, -526, -492, -993, -667],\n [-935, 772, -561, -1013, -481, 440, 140, 411, 270, -288, -119, -842],\n [-244, 176, -381, -333, -749, 460, 214, 177, 579, 458, 208, -172]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"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, 400, -883],\n [767, -732, -227, -400, -328, -14, -28, -10, -174, 382, -362, 942],\n [382, -357, -607, -236, 190, 395, 418, -182, -546, -586, -790, 21],\n [168, -180, 72, -120, 0, -300, -24, 84, 24, 252, -108, 300],\n [329, -231, -639, -38, -420, 1265, 90, -377, -364, -591, -73, -17],\n [-259, 180, 434, 18, 406, -972, 4, 279, 214, 353, -57, -52],\n [-26, 12, 446, 32, -248, -424, -352, 172, 396, 668, 492, 360],\n [14, -18, 251, 10, -182, -216, -220, 93, 232, 407, 301, 248],\n [663, -582, -563, -268, -424, 788, 72, -248, -362, -188, -312, 524]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"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, 154, -102, 170],\n [-46, 178, -251, -111, 129, -491, -187, 55, 101, -326, 293, -403],\n [510, 770, -295, -1250, 450, 65, -560, -610, 90, -330, 150, -385],\n [-77, -512, -590, 443, -622, -19, 517, 826, 266, -154, 246, -234],\n [244, -160, -712, -232, -452, 220, 296, 500, 300, -232, 236, -320],\n [-292, 522, 369, -32, 738, -993, -666, -522, -166, -278, 206, -305],\n [-348, -310, -115, 651, -179, -521, 179, 467, 65, -138, 217, -187],\n [109, -506, 73, 280, -525, 880, 554, 289, -17, 452, -365, 537],\n [-384, -700, -298, 987, -593, -290, 569, 905, 155, -48, 199, -100]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"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, 282, 132, -608, -131],\n [803, -1255, 17, 107, 318, -1320, 1298, -173, 1257, -134, -346, 88],\n [-234, -829, 1458, -553, 316, 232, -12, -286, -1057, -578, -337, 982],\n [-196, -284, -229, 657, 3, -380, 871, 195, 924, 235, 754, -171],\n [-522, -838, -822, 321, 592, -1203, -54, 449, 196, -101, 201, -726],\n [516, -310, 539, 456, -95, 522, 304, -1170, 500, 364, 305, 1028],\n [-204, -64, 416, -1302, 114, -119, 454, 1022, -1267, -790, -339, -434],\n [-106, -739, -1207, 1703, -710, 768, 188, -535, 666, 1583, 1389, 579],\n [273, -101, 192, -760, -133, 637, 215, 248, -1158, -61, -37, 97]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"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, 655, 145, 448],\n [-463, -146, 481, 143, -110, -70, 568, 699, -274, -184, -332, 190],\n [291, 180, -200, -227, -91, 247, -694, -806, 250, 233, 112, -96],\n [632, -12, -3, -162, -3, -181, 129, -124, 810, 1137, 745, 1021],\n [-251, 125, 48, 298, -245, 1279, -892, -1193, 182, 350, -641, 372],\n [551, -575, -1206, 706, 1391, -760, 413, 577, 1151, 192, 1335, 477],\n [173, 37, -339, -252, 212, -2, -957, -767, 500, -97, 274, -353],\n [438, -447, -419, -59, 863, -1064, 92, 517, 1303, 368, 1312, 534],\n [223, 222, -344, -93, -73, -205, 207, 85, -742, -503, -83, -835]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"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, -744, -67, 118],\n [1308, 72, -240, -321, 377, 1227, -692, -741, -1082, -631, 635, 436],\n [692, -429, 14, 500, -169, -563, 771, -383, -514, 1313, -384, -513],\n [-896, -245, -192, -699, -539, 197, -458, 794, 770, 388, 12, 554],\n [1547, -178, -487, 321, -163, 709, -98, -547, -1332, -254, -481, -517],\n [398, -240, 348, -727, -1140, -585, 178, 669, 99, 915, -1994, -866],\n [171, 530, 670, 28, 1156, -103, 465, -592, 1, -802, 846, 122],\n [671, 587, 121, -684, 855, 1132, -245, -446, -730, -1318, 494, 375],\n [475, -189, 839, -151, 17, -863, 190, -350, 352, 943, 110, -67]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"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, 412, -410, -78],\n [59, 636, -186, -1087, -1, -502, 660, 635, 177, -1119, 283, -500],\n [-534, 6, -672, 532, -132, -98, 157, -40, 150, -407, -153, 557],\n [-352, -341, -485, -195, -305, -319, 578, -471, 764, -916, -18, -763],\n [303, -250, 59, -26, 1203, -451, 457, 406, -1389, -517, 603, 1103],\n [-433, -668, -693, -738, 166, -537, -21, -111, -153, -1172, 524, -534],\n [-1018, 603, -769, 543, -2157, 649, -1350, -287, 1838, 420, -1430, -401],\n [1028, -975, 757, -596, 1260, -77, 402, -101, -1306, -96, 798, -183],\n [323, 553, 332, -1176, -397, 329, -753, 649, 58, 429, 191, -963]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"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],\n [297, -481, -126, -465, -156, -169, 351, -358, 350, 537, -255, 160],\n [-53, 107, -360, -189, -187, 5, 64, -228, -361, -237, 109, -87],\n [236, -454, 734, 670, 409, -304, 93, 600, 71, 608, 542, 305],\n [-331, 711, 226, 203, 268, 459, -569, 318, 402, -539, -391, -380],\n [-47, 443, 88, 21, 280, 257, -268, 197, 197, -213, 21, -424],\n [318, -344, -1162, -988, -628, -308, 705, -983, -887, 64, 440, -98],\n [332, -712, 400, 364, 128, -460, 368, 244, -148, 716, 552, 444],\n [-23, 200, 54, -197, 94, 221, -165, -26, 518, -25, -432, -199]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"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],\n [601, -320, -402, 827, 276, 666, 128, 487, -242, -140, 147, 57],\n [-1321, 369, -394, 377, -163, 8, 608, 772, -852, -996, -273, 62],\n [1195, -162, 384, -783, 1083, -1179, -683, 689, -1037, 587, 592, -634],\n [-881, 976, -228, -781, -288, -582, -232, 568, -716, -140, -378, 771],\n [-87, 961, -146, 426, -816, 378, 659, -195, 81, 448, -395, 937],\n [-96, 336, -56, -61, 607, -19, -665, 258, -774, -669, 142, 1043],\n [-243, -227, 1076, 402, 660, -788, 444, -1866, 307, 61, 554, -630],\n [133, 108, -1360, -759, 215, -259, -1306, 1666, -943, 364, -385, 507]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"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, 190],\n [180, -162, 450, -648, 666, -180, -900, 342, -54, -18, 270, -486],\n [500, -426, 146, -408, 458, -380, -724, -106, -558, -218, -210, -390],\n [610, -507, -407, 240, -179, -400, 58, -689, -897, -355, -765, 33],\n [80, -56, -536, 640, -632, 0, 784, -552, -296, -120, -520, 424],\n [-490, 410, 201, -34, -15, 335, 156, 433, 674, 266, 505, 83],\n [400, -340, 80, -280, 320, -300, -520, -120, -460, -180, -200, -280],\n [520, -442, 104, -364, 416, -390, -676, -156, -598, -234, -260, -364],\n [110, -99, 275, -396, 407, -110, -550, 209, -33, -11, 165, -297]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"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],\n [-60, 100, 273, 24, 232, 329, 549, 454, -296, -741, 330, -29],\n [-43, 87, 275, 31, 223, 309, 551, 458, -298, -730, 317, -48],\n [-441, 309, -198, -207, 129, 384, -342, -348, 210, 81, 189, 543],\n [-204, 156, -24, -84, 108, 240, -24, -48, 24, -132, 156, 228],\n [314, -186, 317, 178, 34, -111, 593, 542, -340, -499, 44, -447],\n [-337, 213, -271, -179, 13, 183, -499, -466, 290, 362, 23, 456],\n [172, -188, -272, 20, -300, -472, -560, -448, 296, 844, -428, -92],\n [140, -140, -154, 28, -196, -322, -322, -252, 168, 518, -280, -98]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"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, 653, 1069, 764, -600],\n [237, 6, -608, -373, -300, 221, 185, 21, 211, 461, -952, 455],\n [275, 1036, -339, -390, 197, 582, 3, 1605, -1442, -1435, 43, 501],\n [-949, 525, -161, 356, -191, -160, 1146, 455, 252, -1468, -447, 265],\n [-53, 537, -386, -254, -149, -630, -672, 226, 543, 724, -1137, 745],\n [33, -1550, -248, -801, 1501, 1269, 1304, -692, 514, 50, 751, 314],\n [-167, 1867, -670, 733, -1649, -195, -1085, 1528, -918, -1674, -758, -713],\n [404, 394, -1125, -353, 329, 32, -147, 510, 207, 117, -1720, 1187],\n [-1048, 1977, -897, 1848, -685, -412, -138, 477, -474, -960, -738, -295]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"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, 130, 858, -174],\n [-755, -119, -582, -170, -1794, -828, -1041, -1046, -221, 303, -1023, 939],\n [362, -543, -65, 719, 369, 810, 912, 110, -449, -940, 237, -309],\n [-1242, 82, -892, 1071, -765, 953, -847, 1004, 1039, -380, -627, -876],\n [401, 1220, 1518, -1540, 615, -1037, -108, -144, -186, 422, 169, 575],\n [279, -979, -1530, 378, -227, -187, -544, -154, -252, 316, 602, -107],\n [886, -1020, -312, -514, -117, -1176, 330, -719, 304, -45, -99, -384],\n [1804, 953, 598, 372, 890, 213, -20, -527, -955, 638, 1305, 1274],\n [-888, 464, 812, -1858, -591, -357, -883, 598, 332, 541, -1480, 338]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"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, -2372, -219, 1274],\n [19, 672, -182, 318, -1143, 310, -1395, -44, 83, -1414, -249, 101],\n [353, -1338, 495, -41, 1386, -187, 295, 138, -730, -419, -627, 1200],\n [-229, -42, 199, 197, -219, -1497, -651, -668, -690, 799, -1128, -679],\n [-43, -874, 885, 465, -944, -957, -960, 111, -270, 386, -1960, -611],\n [-852, 1134, 140, -14, -281, -1206, 135, -1619, -949, 1035, -78, -1117],\n [-355, 475, -405, -375, -569, 897, 213, 876, 581, 926, 187, -600],\n [746, -606, -390, -630, -628, 188, -216, -388, -239, 1132, -918, -271],\n [253, -310, 116, 425, -1043, -833, -108, 371, 963, 1196, -750, -1076]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"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],\n [-348, 485, -97, -1006, 808, 291, 437, 831, 575, -685, -385, 1088],\n [1007, -851, -22, 974, 1043, 1056, 1592, -1215, 637, -31, -247, -729],\n [-936, -203, -718, -1925, -397, -121, -402, 931, -624, 165, 340, 166],\n [-866, -483, -225, -1631, -230, -526, 339, 586, -733, -1257, -6, 406],\n [-311, -90, 567, -670, 242, -276, -123, 528, -113, -499, -29, 358],\n [-394, -78, -384, -968, 327, -143, 478, 396, -339, -853, -141, 283],\n [-212, 620, -173, 512, -1015, -82, -187, -106, 673, -180, -235, 965],\n [-822, 357, 41, -1295, 612, 252, 116, 859, 115, -506, -184, 1040]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"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, 398, 43, 866],\n [478, 866, 246, 528, 255, 335, 722, 675, -557, 147, 692, -518],\n [559, -345, -653, -129, -206, -33, -47, 582, -717, -528, -751, -872],\n [75, 912, 336, -567, -401, 1729, 330, -887, -561, 320, -399, 860],\n [98, 641, -119, -4, 108, 242, 32, 28, 115, 508, 199, -550],\n [-312, 651, 70, 361, -42, 1551, -233, -660, -286, 399, 731, 863],\n [525, -18, -454, 154, -65, -739, 18, 293, 286, -187, -423, -1024],\n [338, -1724, -1369, -64, 695, -379, -808, 1709, -1537, 122, -2273, -1261],\n [-175, 1511, 809, -368, -80, 1375, 830, 285, -1124, 310, 404, 785]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"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, 476, -1086, -143, 650, -1270, -69],\n [1840, 1050, -1418, 1048, -1538, 539, 1019, 230, -738, -1224, -1087, -620],\n [155, 115, -243, 394, -69, -388, -1280, -546, -566, 92, -1575, 1268],\n [-1224, -568, -388, 1093, -683, 1318, 1115, -598, -1335, -764, 682, -80],\n [178, 5, 251, -119, 395, -379, -799, 71, 365, -95, 390, 408],\n [-1297, 187, 258, 919, 855, 29, 933, 792, -483, -855, 2047, -386],\n [1655, 1480, 59, -892, -753, 60, 965, 575, 232, -505, -796, -521],\n [-975, -814, 731, -947, 430, -10, -887, -210, 699, 1042, 1006, 743],\n [-1807, -552, 443, 716, 1256, -442, 635, 965, -1276, -988, 847, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"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, -288, 1288, -1029],\n [-166, 48, 502, 596, -702, 617, -499, 151, 303, 145, -363, 221],\n [-274, 501, 544, 1348, 17, 509, -1574, -533, -558, 238, -723, 441],\n [-226, 66, -559, -1152, 1203, -1043, 1748, -387, -124, -158, 1574, -444],\n [926, -814, -1069, -643, 228, 197, 682, 823, -555, -474, 531, 78],\n [-724, 220, 921, 635, -1276, 767, -1162, 721, 710, -292, -722, -77],\n [-529, 699, -1454, -1435, 403, -597, 627, 454, 234, -420, 526, -325],\n [151, 1056, -565, 1584, 473, 1436, -1551, -1468, -2184, -628, -570, 819],\n [330, -997, 1070, 165, 622, -638, 622, -802, 110, 685, 219, -739]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"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, -949, 26, -460, -798],\n [1190, -110, 647, -423, -498, 921, 972, 1556, -1155, 649, 557, -729],\n [-874, 125, -424, -806, 334, 507, 787, 900, -827, 785, 1460, 67],\n [-160, 1310, 1287, 971, 810, -593, -55, -607, -1396, -1108, 1018, 258],\n [-123, 40, 541, 231, 155, -1059, 822, 275, -1508, -1951, 337, 310],\n [-105, 274, 366, 61, -1170, -565, 882, -2017, 1521, -494, -498, 141],\n [-511, -293, 949, 418, -403, 315, -203, -1345, 764, -835, 280, 1060],\n [936, -675, -1163, -64, 931, -1552, 12, 1534, -974, 23, -1152, -1053],\n [-694, -956, -704, 160, 1337, -486, -446, 362, -34, 362, 85, 517]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"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, -312, -635, 480, -631, 125],\n [-215, -88, 228, -614, 732, -359, -1076, -700, -279, 414, 189, 302],\n [91, 669, -625, -887, -608, 284, -198, -302, -497, -573, 1491, 16],\n [1644, -352, 451, 786, -887, 446, -423, -155, 69, 111, -1230, 1733],\n [81, -552, 678, 580, -279, -169, -2474, -674, -1218, 606, -122, 1682],\n [130, 889, 566, 775, -1341, 1144, -722, 500, -1511, 508, 695, -269],\n [466, 205, -40, 652, -600, 414, -896, 1096, 12, -249, 773, 1496],\n [-444, -37, 996, 1592, -65, 1255, -577, 520, 452, 500, -524, 329],\n [2181, -154, 166, 686, -851, -893, -770, -414, 19, 790, -752, 3125]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"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, -1206, -1132, 0],\n [-69, -754, -177, 257, -604, -187, 487, -748, -288, -806, 301, 80],\n [525, -429, -289, 224, -498, 120, -632, -90, 495, -774, -308, 442],\n [-586, 476, 52, 120, 754, 502, 562, 76, -644, 1218, -96, -544],\n [184, -398, -123, 357, -109, 345, -356, -7, 25, -537, -303, -56],\n [-20, 96, -189, 561, -83, -284, -511, 250, 539, 199, 696, 638],\n [94, 80, 160, -1078, -206, -126, 889, -554, -421, -42, -575, -354],\n [-785, 14, 544, -106, 527, -181, 975, -34, -1008, 211, 496, -964],\n [-664, -87, -96, 485, 68, -183, 766, -424, -498, 518, 844, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"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, 13, -84],\n [58, 396, -184, -387, 172, -104, -62, -224, -925, 43, 293, -203],\n [-158, 264, -136, -353, 108, -316, -218, -156, -435, 137, -13, -217],\n [258, 138, -48, -20, 68, 262, 192, -70, -542, -116, 354, 28],\n [231, 33, 0, 77, 22, 275, 198, -11, -286, -121, 264, 77],\n [-76, 6, -8, -43, 0, -98, -70, -6, 57, 43, -77, -35],\n [517, -297, 176, 561, -110, 781, 550, 187, 176, -341, 374, 385],\n [-29, 333, -160, -363, 142, -185, -122, -191, -706, 79, 164, -203],\n [335, -87, 64, 253, -26, 459, 326, 61, -118, -201, 304, 189]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"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, -154, 276, 109, -957, -71],\n [-171, -989, 24, -684, -1053, -763, 413, 733, -110, 208, -208, 306],\n [-358, -479, -273, 2, -443, 290, -209, -326, 583, -473, 367, 421],\n [-496, -828, 712, -695, -904, -509, 1035, 131, 438, -2, -758, 339],\n [118, -725, 482, -203, -380, -975, 1371, 453, 162, 540, -960, -147],\n [42, 294, 910, -817, -193, 192, -465, -417, -263, -187, -442, 326],\n [-1164, -175, 758, -553, -570, 121, 899, -455, 514, -512, -784, -89],\n [29, -1152, 484, -585, -747, -779, 914, 523, 623, 243, -166, 1167],\n [-533, -532, -807, -267, -629, -322, -187, 915, -255, -69, 789, 293]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"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, 301],\n [592, 144, -605, 791, -942, -681, 1416, -102, -558, 4, 573, -619],\n [26, -146, -166, 103, -1068, -346, 1543, -608, -190, -1050, 945, -704],\n [-267, -142, 702, -825, -42, 219, 566, -128, 527, -694, 273, -722],\n [495, -1129, 191, 354, -187, 782, 513, 253, -981, 112, -203, 361],\n [-988, 982, 1241, -413, -150, 95, -104, 94, 752, 816, 219, -1367],\n [-170, 53, 51, 1265, -283, -20, -157, 1434, -957, 947, 500, 45],\n [-1930, 395, 1361, -917, -431, 607, -1222, -1365, 651, 143, 44, -223],\n [-252, 401, -162, -576, -6, 1110, 334, -1591, 489, 856, -1391, 277]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"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, -388, -593, 513, 473, 336],\n [-204, -140, -70, 408, 454, 94, -316, 102, 470, -20, -382, -332],\n [753, 215, 151, -6, -628, -130, 181, -9, -257, 203, -278, -10],\n [170, 272, 133, -408, -951, -286, 386, -545, -619, 566, -91, 733],\n [250, -674, 742, -1064, 414, -169, 1056, -22, -868, -162, 666, 303],\n [315, -713, 797, -1050, 368, -272, 1031, 43, -699, -279, 544, 226],\n [-569, 213, -418, 602, 259, 354, -481, -318, 110, 613, -345, 61],\n [-883, -28, -207, 290, 354, 200, -217, -600, -57, 791, -373, 403],\n [519, 323, -73, -110, -346, 272, 256, -74, -801, 365, 388, 155]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"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, 29, 280, -227],\n [-264, 112, -728, 232, 868, 964, -140, 724, -216, 8, -284, -624],\n [50, 500, -646, -136, -175, 455, -421, 151, -86, -80, -559, 36],\n [12, 345, -683, -68, -279, 440, -596, -11, -47, 65, -620, 89],\n [-310, -214, -532, 338, 785, 767, -181, 481, -140, 184, -157, -558],\n [252, 376, 66, -309, -719, -358, -126, -336, 74, -141, -183, 460],\n [-60, 453, -583, -28, 465, 676, -40, 605, -187, -203, -304, -347],\n [-70, 409, -741, -6, 250, 713, -327, 422, -153, -69, -495, -239],\n [-358, -942, 174, 519, 606, 111, -21, -61, 46, 477, 336, -378]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"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, 421, -311],\n [46, 394, -119, 333, 100, 125, -472, 74, 265, 91, -735, 466],\n [-151, 52, -393, 65, 282, -126, -323, -21, -114, -56, -701, 523],\n [74, 94, 123, 71, -84, 87, -8, 30, 123, 49, 67, -74],\n [307, 272, 579, 193, -402, 336, 131, 105, 444, 182, 551, -487],\n [83, 150, 112, 118, -74, 107, -71, 41, 163, 63, -28, -15],\n [-316, -522, -455, -407, 304, -397, 202, -148, -593, -231, -7, 132],\n [417, 590, 658, 452, -446, 503, -129, 179, 727, 287, 238, -325],\n [-259, -232, -487, -165, 338, -284, -107, -89, -376, -154, -459, 407]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"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, -298, -1281, 945, -949, -219, 889],\n [27, -1634, 308, -211, -754, 226, 577, 556, 621, -1453, 544, -1936],\n [-1398, -402, 938, -1085, 647, -1086, -1045, 604, -513, -1100, -672, -1092],\n [-390, 151, 546, -744, 941, -1637, -411, -20, -194, -816, 879, -1301],\n [804, -347, 601, 160, 208, 495, 460, 15, 460, -150, -28, -207],\n [-519, 173, 365, -849, 962, -903, -165, 591, -802, 392, -486, 17],\n [325, -61, 292, 30, 831, -1224, -794, -1127, 104, -18, -260, 115],\n [759, -436, -432, 627, 141, 933, -271, -628, -334, 390, -303, 1061],\n [219, -124, 431, -208, 856, 806, 44, 445, -782, 86, -621, 421]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"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, -838, 219, 7, -116, -91, 620],\n [625, -677, 456, 1411, 879, -1344, 365, -1128, -154, -216, 1514, 860],\n [897, 355, -109, -699, -1526, 109, 659, -1232, -564, 1283, -783, 29],\n [-360, -764, 603, -459, -308, 243, 659, 400, -399, -50, -68, -625],\n [-1053, -406, -1291, 580, 181, -315, -620, 930, 235, 246, -738, 39],\n [-70, -326, 750, 1542, -197, -1615, 279, -84, -158, 1248, -740, 422],\n [-342, 97, 671, 543, 337, -1387, -552, -556, -173, 92, -111, -234],\n [478, 313, 936, 309, 608, -864, 270, -327, -716, 31, 628, -51],\n [756, 693, 1511, -1535, -30, 656, -140, -1203, 57, -763, 547, -1142]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"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, 377, 31],\n [557, 48, 252, 80, 126, -802, -605, -931, -397, -976, -530, -55],\n [44, 671, -225, 143, 446, 434, 606, 303, 247, 300, -181, -248],\n [-315, -650, 217, -164, -622, -129, -423, 25, -283, 94, 433, 199],\n [58, 257, -347, 41, 486, 358, 516, 367, 595, 268, -115, 30],\n [-362, 687, -222, 109, 162, 871, 854, 775, 169, 874, 200, -320],\n [-88, 223, 237, 59, -266, -28, -106, -137, -525, -8, 45, -240],\n [56, -416, 123, -82, -200, -343, -406, -266, -108, -290, 33, 174],\n [294, 1021, -102, 255, 574, 201, 502, -79, -41, -58, -484, -452]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"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, -296, -246, 186],\n [-279, 551, -40, 147, 112, 292, -207, -22, 748, 154, -429, 15],\n [26, 20, 854, -543, 485, 81, -956, 796, 264, 52, -488, 48],\n [410, -90, 544, -616, 298, -614, -314, 296, -284, -616, -38, 362],\n [26, -769, -31, 111, -220, 228, 124, 169, -741, 433, 448, -378],\n [157, -1044, 737, -413, 143, 215, -631, 901, -871, 469, 227, -383],\n [-226, -541, 201, 119, -40, 632, -344, 481, -229, 777, 52, -502],\n [115, -209, 986, -655, 502, 26, -1021, 932, 14, 52, -391, 17],\n [426, -162, 832, -793, 441, -571, -624, 582, -274, -562, -156, 344]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"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, -424, 684],\n [-1337, -256, -197, -778, -510, -407, 892, 28, 303, 146, 1310, 12],\n [-204, -332, 14, -888, -776, -593, -849, 668, -480, 839, -313, -152],\n [-831, 129, 206, 256, -28, -9, -200, 274, 549, 187, 629, 968],\n [-277, 35, 268, -472, -655, 101, 2363, 260, -137, -574, 1434, -582],\n [-274, -693, -392, -258, 341, 139, -2641, -422, 854, 157, -1323, 544],\n [469, 501, 833, -113, 6, 645, 880, 1257, -916, -202, 608, -679],\n [-1203, -373, -524, -361, 417, -335, 563, -728, 521, 151, 214, 131],\n [1143, 1056, 829, 1087, 586, 625, -581, -445, -734, -903, -860, 402]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"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, -878, 612, 124, -86, 69],\n [581, -24, -702, 586, -141, 879, 1384, -1671, -1546, -572, -199, -491],\n [-1220, 480, 1290, -490, 1144, -842, 106, 592, 608, -344, 448, -418],\n [30, -56, -279, -415, 44, -1391, -154, 164, 180, 2021, 699, -817],\n [-146, 46, 1194, -14, 1032, -734, -1053, 311, 1311, -29, 507, 11],\n [155, -432, 711, 524, 673, -585, 620, 365, 982, -1708, -587, 388],\n [137, 136, 812, -449, 179, -1390, -1110, 1116, 897, -151, -185, 183],\n [-1038, 809, -664, -350, -714, 624, 502, 218, -857, -998, -403, 1567],\n [-142, -255, -34, 413, -164, -110, 80, 155, -116, 709, -1006, -728]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"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, 939],\n [-253, -118, 389, 532, -766, 201, -552, 509, -312, -533, -182, -640],\n [337, -403, 371, 149, -460, -214, 283, 261, -454, 305, 561, 1144],\n [-751, -413, -527, 722, -577, -476, -322, 214, 12, -703, -819, 322],\n [-550, -160, -456, 385, 62, -58, -416, -559, 390, -9, -743, -341],\n [279, -125, 660, -53, 579, -719, -549, 746, -869, 639, 237, 432],\n [721, 328, 323, -458, -572, 230, -462, -126, -457, -334, 582, 805],\n [-519, 212, 359, -42, 137, -147, 1157, 556, 855, 447, -202, -2060],\n [813, 719, 415, -854, -1072, 400, 491, -34, 193, -804, 742, 283]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"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, -36],\n [208, -67, 418, -93, 364, 565, -321, 702, -202, -318, -248, 328],\n [192, 180, 144, -106, -188, 58, -256, 124, 136, 170, 154, 202],\n [48, -249, 330, -2, 590, 578, -113, 668, -358, -521, -427, 173],\n [-336, -513, -54, 202, 758, 278, 415, 212, -502, -677, -583, -271],\n [-144, -393, 150, 101, 700, 451, 149, 466, -446, -622, -524, -44],\n [48, 327, -246, -50, -658, -526, -17, -580, 410, 583, 485, -67],\n [-160, -170, -100, 90, 200, -10, 210, -60, -140, -180, -160, -160],\n [-48, 81, -162, 16, -226, -256, 85, -304, 134, 199, 161, -103]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"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, -30, -57, 742, 409, -329],\n [-258, 187, 207, -631, -51, -158, 89, -6, -1107, 266, 47, -721],\n [-2, 830, 460, -326, 582, 898, -312, -640, 630, 386, 1158, 202],\n [376, 5, 72, 27, -426, -206, 162, -126, 89, -56, -465, 140],\n [-26, -557, -34, 207, -157, -333, 271, 529, -132, 90, -298, -113],\n [934, -786, 1135, -240, -700, -385, 1190, 1163, 833, 1266, -519, 282],\n [-504, 1020, -1053, -15, 771, 583, -1208, -988, 379, -1262, 288, 602],\n [-478, 967, -93, -498, 639, 639, -650, -826, -382, -168, 885, -240],\n [739, -156, 381, -370, -561, -340, 512, 501, 695, 309, -859, 553]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"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, 115, -598, -368, -483, -552],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n [-250, 450, -400, 75, 200, 350, 275, -125, 650, 400, 525, 600],\n [20, -36, 32, -6, -16, -28, -22, 10, -52, -32, -42, -48],\n [-40, 72, -64, 12, 32, 56, 44, -20, 104, 64, 84, 96],\n [160, -288, 256, -48, -128, -224, -176, 80, -416, -256, -336, -384],\n [-210, 378, -336, 63, 168, 294, 231, -105, 546, 336, 441, 504],\n [70, -126, 112, -21, -56, -98, -77, 35, -182, -112, -147, -168],\n [-90, 162, -144, 27, 72, 126, 99, -45, 234, 144, 189, 216]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"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, -1253, 888],\n [-1122, -817, -133, -343, -325, 398, 164, -210, -808, 851, -1017, 1135],\n [672, 251, 258, -910, 1019, -1295, -1067, -886, 900, -315, -1108, -703],\n [719, 242, -268, -752, 1418, -522, 270, -709, 653, -375, -795, 361],\n [-1072, -806, -162, -1343, -247, -219, 1418, 7, 304, -279, 485, 168],\n [241, -1009, -600, -953, 1244, -389, 984, 624, 461, -593, 402, -189],\n [-546, -354, -13, -803, 1497, 364, 549, -503, -22, 1049, -768, -1370],\n [610, -416, 117, 1088, -1414, 715, -210, 723, -27, -993, 996, 1313],\n [766, 16, -177, -1032, 1689, -1004, 547, 19, 1700, -1323, -146, -612]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"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, -780],\n [127, -30, -246, 16, -34, 312, 76, -652, -366, 506, 507, -513],\n [134, -12, -252, 16, -20, 288, 56, -616, -348, 468, 494, -474],\n [44, -132, -132, 11, -110, 363, 176, -671, -363, 583, 429, -594],\n [-59, -18, 102, -6, -10, -78, 4, 186, 108, -128, -169, 129],\n [700, 708, -1020, 49, 518, -111, -656, -397, -321, -139, 975, 162],\n [-114, -48, 192, -11, -30, -123, 24, 311, 183, -203, -299, 204],\n [-174, -180, 252, -12, -132, 36, 168, 84, 72, 48, -234, -54],\n [335, 282, -510, 26, 202, 66, -244, -398, -264, 124, 585, -117]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"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, -30, 345],\n [18, -30, 60, -387, -186, 441, -3, 339, 150, 369, 48, -495],\n [36, 20, -70, 246, 58, -138, 104, -112, -160, -102, -14, 150],\n [10, -30, 65, -385, -175, 415, -20, 320, 160, 345, 45, -465],\n [-28, 20, -30, 262, 146, -346, -32, -264, -80, -294, -38, 390],\n [50, 2, -36, 13, -58, 137, 109, 99, -74, 129, 16, -159],\n [46, -10, -5, -139, -117, 277, 84, 208, 0, 243, 31, -315],\n [-112, 8, 51, 130, 197, -466, -227, -345, 94, -420, -53, 534],\n [160, 16, -138, 164, -134, 316, 362, 222, -292, 312, 38, -372]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"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, 95, 1],\n [-230, -179, -326, 284, 443, -451, -480, -211, -20, -671, -247, -521],\n [-370, 450, 330, 155, -100, 145, 675, 35, 350, 300, -215, 155],\n [-282, 336, 221, 137, -108, 95, 472, 36, 273, 226, -138, 138],\n [-212, 402, -17, 296, -872, 132, 191, 307, 439, 614, 371, 769],\n [-268, 115, 25, 177, 213, -134, 114, -99, 131, -191, -245, -211],\n [494, -543, -83, -438, 581, -31, -415, -184, -565, -427, -56, -508],\n [318, -139, -48, -198, -277, 151, -160, 125, -150, 229, 309, 267],\n [-124, 489, 91, 207, -1129, 314, 362, 419, 473, 923, 517, 1043]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"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, 742, -948, 1635, 417],\n [7, 214, 148, -108, -717, 1193, -900, 903, -1279, -653, -822, -528],\n [-1981, -82, 365, -769, -369, -1200, -40, 128, 778, -361, -27, 836],\n [276, 227, -250, 568, -272, -696, 695, -237, 319, -184, -338, 4],\n [-1794, 1764, -293, -114, 403, -239, 739, 854, -868, -279, -1052, -169],\n [1382, -310, -291, -284, -948, -208, 736, -459, 369, -623, -854, 115],\n [691, -88, 1060, -650, -610, -582, 511, -1500, 241, -423, -158, -168],\n [-1047, -263, 838, 199, -389, 403, -886, -34, 510, -886, 975, 500],\n [432, 1110, -188, -820, 689, 3, 92, -167, -797, -345, -363, -685]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"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, 233, -29, -325, -358, 380],\n [346, 154, 868, -1227, -1311, -17, 444, -337, -468, 2089, 412, -763],\n [-1469, 396, -431, -263, -1135, 1021, 163, 758, -400, 817, -745, -66],\n [427, -1071, 239, -1183, -356, 534, -377, 101, -619, -320, -1179, 62],\n [-173, 488, -434, -770, -893, -968, 848, -102, -155, 1263, -135, 749],\n [199, -1008, -340, 68, -440, 132, -589, -178, 580, -907, -113, -903],\n [131, -90, -1003, -104, -483, -771, -23, 414, 28, -546, -690, 650],\n [-41, 922, -187, 591, 640, -678, 628, 344, 233, 362, 1393, -145],\n [74, -62, -175, 1108, 379, -235, -259, 783, 233, -524, 1384, -1313]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"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, -490, -476, -533],\n [-33, 830, 129, 453, -99, 44, 372, -308, -202, 17, -250, 380],\n [-368, -1122, -697, -874, 129, 43, -986, 915, -269, -120, 796, 196],\n [175, 6, 208, 231, -12, 39, 66, -347, 329, 5, -86, -200],\n [170, 235, 345, 52, 559, -5, -20, -48, -279, -817, -364, -227],\n [212, -420, 110, -156, -402, -242, 514, -46, 552, 784, -158, -646],\n [276, -424, -385, -1318, 389, -1017, 126, 1505, -825, -478, -16, -746],\n [-484, 319, -73, 76, -136, 319, 224, 82, -431, 318, -190, 554],\n [479, 63, -703, 205, -577, -540, -688, -151, 666, 188, 1240, 349]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"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, -41, 306, 1329],\n [-505, -1210, -419, 365, 669, 576, 69, 1497, -168, 224, 237, -36],\n [529, 1338, 281, 58, -21, -662, 1598, -714, -825, 467, 202, 963],\n [-1603, 754, -257, 478, -367, -166, -62, 877, -152, -186, 102, -490],\n [-150, 303, -554, -117, -419, -734, 27, 278, -789, 61, 345, 933],\n [-5, -307, 764, -79, 764, 865, 689, 445, -319, -214, 671, -313],\n [-309, -467, 405, -540, 44, -241, 1252, 1323, -1003, -112, 593, 889],\n [1185, -813, 582, 551, 285, 1581, -603, -349, -864, -1212, 1366, 938],\n [-908, 689, -546, -697, -539, -245, 2051, -803, -962, 1352, 852, -300]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"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, -357, 438, 839],\n [100, -206, 334, -134, 347, -157, -643, 265, -68, -993, -403, 332],\n [63, 302, -609, 405, 379, -497, 424, -123, 263, -194, 408, 823],\n [96, 332, -194, 607, -526, -330, 416, 36, 676, 518, 1033, 417],\n [383, -163, 451, 239, 128, 74, -9, 179, 219, -393, -318, 41],\n [451, 128, -131, 623, 318, -134, 733, -74, 419, -27, 29, 403],\n [-231, -305, 691, -514, -268, -146, -1485, 519, -135, -1007, -77, 94],\n [-225, 319, -779, 121, 591, -911, -300, 24, 99, -954, 523, 1381],\n [-448, -136, 240, -569, -119, -423, -1495, 419, -212, -1075, 182, 459]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"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, -38, 342, -228],\n [-38, 100, 246, -387, -406, 403, 108, 730, 557, -453, 465, -1075],\n [382, -205, 241, 189, 164, -605, 350, 662, -372, -107, -507, -412],\n [-53, -435, -599, 1166, -286, -694, 121, -151, -337, 135, -313, 683],\n [-329, -115, -497, 895, -292, -523, -77, -335, -24, 4, -138, 492],\n [582, -275, 246, -214, 414, -95, 275, 300, -556, 245, -367, 96],\n [61, 80, 218, -252, 8, 62, 63, 307, 110, -153, 37, -446],\n [247, -465, -289, 241, -364, 329, 201, 269, -50, 104, 294, 138],\n [105, 190, 340, -301, 378, -223, 15, 71, -155, -20, -312, -199]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"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, 562, 329, 441, 362, 258, -133],\n [-477, 200, -651, -826, 574, -1025, 1312, -1159, 572, 398, -629, 1076],\n [-115, -129, 171, -368, 162, 1211, -711, 148, -16, -159, -585, -57],\n [-354, -538, 831, 314, -505, 1, -172, 768, 67, 536, -249, -29],\n [-582, 174, 79, 146, 544, -455, 237, -383, -631, 340, -1111, 1303],\n [1014, 886, -98, 394, -328, 619, -771, -276, -439, -947, 392, -746],\n [354, -423, 572, 318, -557, 1092, 68, -48, -779, -1077, 649, -648],\n [-60, -533, -803, -375, 208, -893, -179, 1010, 1334, 1058, 901, -732],\n [747, 301, -473, -170, 96, 631, -843, -308, -328, -455, -541, -233]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"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, 547, 280, 244, 705],\n [-120, -81, -538, -460, -277, -643, -265, 118, -1097, -642, 298, 174],\n [-701, -1097, 309, 508, 183, -157, 434, 12, -293, -58, -652, 859],\n [777, -182, -536, -166, 152, 404, -265, -1204, 566, 827, -1033, 185],\n [-242, 594, -205, 617, -245, -935, 349, 139, -240, 679, -346, 560],\n [0, 1108, -317, 643, -956, -746, 952, 598, 590, -17, 366, 30],\n [890, 834, -627, 173, -633, -184, 179, -451, 639, 387, 109, -107],\n [1643, 1061, 57, 570, -211, 218, 116, 183, 598, -191, 669, -537],\n [1172, -34, 1091, 543, 658, 762, 996, -165, 1306, -404, 548, -521]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"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, 707],\n [-277, -522, 219, 187, 272, 226, 607, -546, -257, 306, -230, 915],\n [-511, -958, -633, -125, -294, -428, -693, 290, -498, -865, -667, -675],\n [-768, -260, -1046, -10, -123, -50, -798, 1019, -596, -153, 158, -119],\n [-549, 778, -505, -37, 241, -48, -84, 1319, -402, 699, 932, -214],\n [627, 1038, -283, 656, 496, -38, -702, 557, 548, 762, 761, 136],\n [-453, 622, -817, -277, 821, 1838, -409, -618, 1075, 2299, 665, 1223],\n [-219, -639, -1190, 767, 961, 74, -1489, 309, -176, 619, -301, 215],\n [751, 282, 1317, -168, -133, 104, 965, -841, 681, 109, -114, -160]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-612, 120, -194, 362, 664, 626, 652, 990, 46, -318, -38, 180],\n [222, 308, -73, 489, 612, -483, -432, -33, -27, -493, 439, -156],\n [-99, 848, -429, 1805, 927, -1313, 797, 141, -431, -112, -540, 14],\n [110, -764, 328, -1234, -542, 630, -477, -98, 821, -92, 853, 305],\n [737, -40, 121, 183, -273, -1427, -511, -1067, 385, 53, 488, 110],\n [-302, 336, -207, 625, 464, 9, 483, 443, -290, -75, -362, -29],\n [-472, -304, -54, -38, -652, 110, 1318, 160, 210, 785, -794, 542],\n [476, 280, -6, 390, 144, -854, -532, -572, -164, -131, 168, -232],\n [103, 316, -47, 181, 569, 159, -624, 173, -332, -500, 267, -401],\n [-80, 800, -384, 1584, 688, -1128, 720, 44, -580, 50, -724, -88],\n [-492, -356, 41, -565, -290, 1007, 520, 555, 151, 214, -225, 222],\n [-373, 460, -219, 537, 917, 543, 36, 823, -458, -527, -71, -293]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-330, 647, -165, -257, -455, 83, 138, -456, -182, -331, 669, 84],\n [-60, 142, -45, -67, -100, 13, 18, -81, -22, -56, 144, 9],\n [22, -61, 22, 32, 43, -4, -4, 29, 4, 19, -61, -1],\n [-382, -159, 368, 458, 117, 174, 424, -599, -624, -539, -59, 331],\n [328, 260, -392, -496, -188, -160, -400, 524, 592, 484, 164, -316],\n [-290, 195, 85, 85, -135, 105, 230, -430, -330, -355, 245, 170],\n [28, 166, -122, -162, -118, -26, -76, 56, 116, 66, 146, -64],\n [4, 598, -371, -501, -424, -53, -178, 53, 278, 108, 548, -157],\n [-224, 548, -179, -265, -386, 47, 62, -301, -74, -206, 554, 29],\n [-496, -184, 464, 576, 136, 224, 544, -776, -800, -696, -56, 424],\n [-42, -517, 348, 466, 367, 62, 192, -105, -296, -145, -465, 165],\n [-120, -252, 240, 312, 180, 72, 192, -204, -288, -204, -204, 156]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-147, -56, 182, 175, 168, -133, -91, -119, -168, 77, 14, -84],\n [-147, -56, 182, 175, 168, -133, -91, -119, -168, 77, 14, -84],\n [42, 16, -52, -50, -48, 38, 26, 34, 48, -22, -4, 24],\n [483, 184, -598, -575, -552, 437, 299, 391, 552, -253, -46, 276],\n [-525, -200, 650, 625, 600, -475, -325, -425, -600, 275, 50, -300],\n [21, 8, -26, -25, -24, 19, 13, 17, 24, -11, -2, 12],\n [231, 88, -286, -275, -264, 209, 143, 187, 264, -121, -22, 132],\n [357, 136, -442, -425, -408, 323, 221, 289, 408, -187, -34, 204],\n [-378, -144, 468, 450, 432, -342, -234, -306, -432, 198, 36, -216],\n [525, 200, -650, -625, -600, 475, 325, 425, 600, -275, -50, 300],\n [-168, -64, 208, 200, 192, -152, -104, -136, -192, 88, 16, -96],\n [168, 64, -208, -200, -192, 152, 104, 136, 192, -88, -16, 96]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[591, 565, -636, -529, 460, -235, -225, -760, 128, -478, 434, 457],\n [78, 454, 602, -185, 118, 431, 1609, 1129, 67, -867, 964, 542],\n [517, 873, -235, -418, 441, -263, 444, 72, -217, -428, 656, 299],\n [-209, 495, -434, 122, -872, -640, 346, 1518, 1013, -421, 1208, 867],\n [160, -671, 396, 478, -43, 775, -748, -659, 425, 779, -308, 398],\n [-851, -332, 120, -565, 88, -344, 335, 661, -29, -310, 645, -351],\n [16, 83, 438, 230, -284, -59, 581, 327, -11, -265, -420, -837],\n [-230, -200, 637, -280, -384, 154, 45, 787, 348, 109, 442, -151],\n [739, -233, 515, 342, 606, 693, -797, -1293, 197, 681, -137, 218],\n [-718, -1089, -129, 3, 200, 144, -770, -764, -874, 137, -1256, -419],\n [-559, 164, -1520, -644, -167, -1201, -655, 18, -188, -553, 135, 260],\n [887, 405, 236, 1543, 298, 134, 138, -629, -190, 195, -717, 104]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-760, 128, -1104, -161, 471, 1128, 1290, 492, 306, -94, 1001, -613],\n [-284, -61, -255, 615, 1068, -783, -799, 862, 1047, 896, 1496, -1509],\n [195, -865, -309, 523, 307, -880, -883, -422, -766, -98, -1185, 180],\n [536, 364, 706, 386, 80, -763, -765, 356, 403, 780, 41, -1160],\n [-123, 1086, -127, -542, 213, -386, -233, 423, -379, -633, 28, 1256],\n [1046, -705, -408, 1061, -182, -718, -771, -209, -596, -725, 227, -501],\n [625, 15, -1389, -123, 294, 61, -90, 148, 64, -818, 287, -93],\n [585, 959, 340, -433, 467, -117, -638, -330, 674, -791, -141, 898],\n [-616, -727, -164, 391, -156, -535, -335, -79, -748, 435, 598, 249],\n [-1299, -162, 234, 18, 659, 877, 678, -625, 49, 649, -49, -34],\n [272, 794, 703, -2, -543, -320, 29, 336, 651, 1326, 915, -1554],\n [174, 691, -519, 344, 540, 194, -266, -116, -469, -711, 1110, 129]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[114, -209, 38, -76, -57, 133, -380, 209, 190, -437, 133, 285],\n [-30, 55, -10, 20, 15, -35, 100, -55, -50, 115, -35, -75],\n [-24, 44, -8, 16, 12, -28, 80, -44, -40, 92, -28, -60],\n [78, -143, 26, -52, -39, 91, -260, 143, 130, -299, 91, 195],\n [108, -198, 36, -72, -54, 126, -360, 198, 180, -414, 126, 270],\n [144, -264, 48, -96, -72, 168, -480, 264, 240, -552, 168, 360],\n [-30, 55, -10, 20, 15, -35, 100, -55, -50, 115, -35, -75],\n [-132, 242, -44, 88, 66, -154, 440, -242, -220, 506, -154, -330],\n [24, -44, 8, -16, -12, 28, -80, 44, 40, -92, 28, 60],\n [-84, 154, -28, 56, 42, -98, 280, -154, -140, 322, -98, -210],\n [6, -11, 2, -4, -3, 7, -20, 11, 10, -23, 7, 15],\n [-42, 77, -14, 28, 21, -49, 140, -77, -70, 161, -49, -105]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1350, -154, -51, 1082, 269, 386, -605, -440, -67, -3, 667, 1093],\n [957, -735, -1762, -663, -961, 1435, -1201, -953, -547, 495, 1052, -37],\n [437, -553, -924, -559, 444, -402, -434, 172, -542, 716, 31, -66],\n [825, -1189, 278, 359, -10, 472, 1097, -58, -849, -296, -152, 1204],\n [1044, -354, 301, -846, 129, -115, -729, 334, 417, 516, 60, -370],\n [299, 241, 1369, -350, 500, -747, -142, 715, 704, 605, 971, 337],\n [-128, 26, -821, 653, 674, 839, -34, -125, -562, -966, 33, -66],\n [-667, -1337, -557, -412, 662, 64, 763, -63, -1469, 132, -115, 964],\n [-819, 1170, 1382, 1475, 988, -740, 388, 1190, 720, -697, -1307, -49],\n [1050, 862, 209, 136, -1854, 178, 581, -1212, 764, -145, 375, -353],\n [-216, 298, 792, -90, 1837, -1004, -239, 1636, 859, -175, -405, 121],\n [561, 379, -132, -255, -654, -604, -334, -104, 975, -5, -373, -1093]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[677, 294, -467, 856, 389, 122, -17, 500, 83, 319, -688, -306],\n [-150, 467, -55, 372, 302, -217, -293, 475, 463, 301, -366, -579],\n [-153, -962, -161, -599, 13, 271, 533, -473, -34, -551, 814, 82],\n [-629, -180, 478, -729, -399, -95, -48, -441, -96, -233, 556, 316],\n [438, -279, -183, -311, -24, -222, 327, -220, -378, -289, 208, 331],\n [-1113, 685, 1112, -346, -817, 43, -764, -279, -60, 336, -6, 479],\n [7, 843, 269, 122, -101, -569, -451, 283, -44, 338, -488, 33],\n [-611, -338, -22, 67, 211, 431, -4, 73, 596, -13, 272, -574],\n [-237, 301, 360, 258, -333, 367, -324, -43, -92, 284, -262, 255],\n [740, 660, -81, 154, -20, -688, -121, 218, -452, 172, -554, 324],\n [-137, -440, -169, 324, 127, 716, 137, -10, 251, 3, 88, -236],\n [-406, 1021, 724, -19, -496, -420, -710, 84, -156, 443, -454, 343]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[126, -28, -98, 7, 70, -49, 126, -168, 98, 154, -98, 98],\n [432, -96, -336, 24, 240, -168, 432, -576, 336, 528, -336, 336],\n [-180, 40, 140, -10, -100, 70, -180, 240, -140, -220, 140, -140],\n [18, -4, -14, 1, 10, -7, 18, -24, 14, 22, -14, 14],\n [216, -48, -168, 12, 120, -84, 216, -288, 168, 264, -168, 168],\n [-432, 96, 336, -24, -240, 168, -432, 576, -336, -528, 336, -336],\n [-378, 84, 294, -21, -210, 147, -378, 504, -294, -462, 294, -294],\n [342, -76, -266, 19, 190, -133, 342, -456, 266, 418, -266, 266],\n [252, -56, -196, 14, 140, -98, 252, -336, 196, 308, -196, 196],\n [-378, 84, 294, -21, -210, 147, -378, 504, -294, -462, 294, -294],\n [432, -96, -336, 24, 240, -168, 432, -576, 336, 528, -336, 336],\n [468, -104, -364, 26, 260, -182, 468, -624, 364, 572, -364, 364]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[596, -584, -648, -510, -646, 614, 162, 166, -230, 396, 556, 458],\n [-802, 302, 842, 196, -92, -595, 268, -643, -93, -231, -624, -156],\n [134, 348, -116, 371, 807, -91, -445, 453, 347, -210, 2, -353],\n [422, -368, -456, -315, -367, 413, 69, 157, -125, 252, 382, 281],\n [504, -462, -546, -399, -483, 504, 105, 168, -168, 315, 462, 357],\n [710, -180, -740, -85, 255, 485, -325, 645, 155, 150, 530, 55],\n [-840, 318, 882, 207, -93, -624, 279, -672, -96, -243, -654, -165],\n [-372, 454, 410, 409, 581, -426, -191, -26, 218, -303, -370, -371],\n [464, -350, -498, -291, -295, 428, 21, 220, -92, 243, 406, 257],\n [8, -384, -32, -388, -756, 188, 380, -324, -316, 240, 104, 364],\n [-398, 120, 416, 67, -105, -281, 163, -345, -71, -96, -302, -49],\n [-686, 384, 728, 295, 171, -569, 103, -441, 25, -276, -566, -253]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[416, 291, -270, -545, 277, -336, -447, -405, -642, -640, -307, -33],\n [318, -826, 180, 185, 756, 448, 26, 202, 69, 359, 30, 592],\n [-78, 720, 236, -103, -300, -301, -1, 111, -88, -254, 14, -275],\n [-613, -112, 290, 500, -491, 324, 568, 457, 716, 599, 367, -85],\n [-173, 529, -72, -231, -364, -244, -5, -94, -114, -313, -26, -304],\n [-606, -629, -170, 256, -299, 517, 514, 148, 596, 512, 271, 62],\n [-334, 1036, 368, 361, -890, -482, 114, 230, 281, 67, 148, -624],\n [674, -27, -350, 139, 185, -484, -693, -541, -412, -108, -351, -105],\n [-610, -335, -270, -517, -71, 512, 499, 47, 132, -168, 161, 131],\n [508, -49, -650, -257, 135, -423, -646, -732, -559, -401, -397, -140],\n [270, -536, -344, 281, 138, -12, -268, -316, 7, 261, -128, 70],\n [165, -33, 108, 445, -70, -133, -128, 25, 149, 316, 0, -61]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[751, -561, 730, 1166, -425, -199, 787, -200, -142, 780, -45, 323],\n [-203, 87, 1218, 521, 1865, 788, 958, -421, 346, 684, 369, 203],\n [496, 436, 1279, 531, 1029, 677, 1107, 320, 853, 299, -311, 696],\n [-530, 405, -1103, 8, -626, -46, -519, -368, -2031, -1359, -450, -734],\n [922, -1428, -824, -632, -388, 594, -1138, -856, -226, -734, 862, 572],\n [277, -950, -989, -167, 54, -968, -1076, -1130, 961, 1089, 1544, -719],\n [-234, 668, -198, 247, 2080, 328, -358, 451, 370, 713, -368, 1109],\n [365, 1, -863, -324, -858, -2215, -428, 1288, 492, 1402, -387, 951],\n [-3, 686, 605, 1772, -269, -37, 722, 1030, -477, 841, -1478, 607],\n [1678, -1982, -1216, -140, 16, -722, -1104, -810, 1322, 1510, 1600, 543],\n [-1391, 1080, -750, 385, 1032, -962, -766, 665, -889, 819, -828, 468],\n [-1340, 17, -1018, -591, 1202, -157, -1485, -110, 1228, 1183, 1447, -1049]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[326, -603, 136, -881, 995, 361, -341, -23, 72, -678, -800, -677],\n [792, -353, -762, 584, -159, 807, -761, 530, -363, 123, 152, -5],\n [-1049, 486, 57, 430, -427, -110, 1077, 920, -790, -341, 638, -107],\n [-175, -44, 609, -789, 673, -126, 155, -61, 141, -290, -484, -375],\n [804, -416, 160, -561, 838, 684, -804, 367, -35, -57, -596, -456],\n [994, -390, -643, 442, 43, 963, -963, 655, -367, 197, 25, -88],\n [-159, -498, 463, -1222, 1111, -70, 127, -336, 242, -911, -918, -745],\n [-595, 54, -215, 206, -319, -300, 597, -106, -128, -377, 236, 19],\n [223, 169, -150, 421, -433, -66, -219, -166, 141, 512, 275, 404],\n [24, 314, 294, 78, -132, -104, -24, 72, 62, 458, 150, 218],\n [-6, -517, -128, -504, 691, 431, 9, 370, -319, -875, -464, -695],\n [-1068, 453, 788, -529, 59, -921, 1039, -461, 266, -222, -38, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[363, -172, -395, 219, 150, -4, 549, 401, 29, 10, -327, 535],\n [401, -213, 471, 316, 433, 652, -371, 464, -104, -612, -70, -491],\n [-190, -287, -251, -164, -296, -368, 543, -193, 68, 175, -37, 782],\n [-318, 392, 363, -183, -75, 40, -709, -368, -37, 63, 330, -810],\n [-26, 510, -162, -16, 38, -88, -262, -68, 8, 300, 40, -466],\n [-85, 414, -32, -50, 7, -52, -316, -123, -2, 211, 95, -469],\n [-74, 711, -80, -37, 65, -48, -522, -133, -7, 340, 121, -810],\n [713, -41, -525, 460, 433, 204, 545, 772, 8, -48, -514, 349],\n [-794, 31, 569, -514, -490, -240, -577, -859, -6, 59, 565, -350],\n [315, 46, 445, 261, 408, 588, -559, 351, -101, -458, 3, -761],\n [-584, -119, -13, -418, -520, -504, 173, -631, 66, 287, 253, 460],\n [134, 433, -609, 58, 22, -288, 281, 103, 62, 489, -193, 106]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1635, 1791, 389, 715, 1093, 210, 507, -110, -1519, -875, 511, 1695],\n [-69, -898, -1040, -293, 222, -541, 632, 697, -167, 687, 907, 302],\n [53, -358, -1685, 896, -1007, -625, 166, 98, -134, 1162, 1075, -276],\n [-1491, 842, 275, 466, -395, 392, 815, 949, 224, 134, 914, 1697],\n [-600, 968, -208, -170, 1349, -764, 84, 742, -1146, -895, 55, 1788],\n [343, -705, 904, -175, 856, 132, -116, 245, 507, 196, -119, -742],\n [-1061, 1412, -21, 770, 1106, 239, 363, 43, -2158, -578, 499, 2008],\n [-118, 540, 1177, -742, 467, 108, 1186, 349, 689, -637, 125, -71],\n [419, 173, -773, -428, 868, -580, -25, -472, -1136, -509, -72, 171],\n [386, -446, -325, 569, 963, 469, -454, -1369, -1214, 503, 356, -751],\n [-740, 571, 160, 924, 262, 3, 63, -687, -518, -102, 238, -775],\n [1083, -452, -951, -1192, -630, -929, -195, 73, 537, -317, -724, -193]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1056, -1398, -718, 226, 307, -497, 175, -175, 214, 113, -129, 153],\n [-404, 96, 631, -65, -389, -197, 734, -292, -177, -80, 348, -1069],\n [-316, 636, -34, -522, 66, 490, -296, 268, 166, -344, 188, -46],\n [115, 8, -816, -1284, 730, 471, 204, 567, 264, -907, 632, -637],\n [433, -433, -798, -832, 582, 196, 150, 330, 296, -603, 396, -380],\n [-195, 339, -508, -146, 745, 121, -107, 593, -446, -46, -129, 675],\n [515, -970, -123, -279, -86, -353, 747, -338, 257, -272, 421, -1111],\n [-675, 1171, 61, -917, 81, 811, -352, 446, 195, -607, 388, -261],\n [-105, 504, 371, 499, -512, 259, -905, -172, 259, 380, -447, 861],\n [-170, -343, 202, 368, 162, -607, 908, -89, -676, 246, 26, -415],\n [903, -1527, -378, 508, 151, -829, 657, -375, -80, 296, -109, -203],\n [979, -1419, -671, 203, 347, -579, 398, -172, 91, 93, -58, -39]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[789, -11, 350, -249, -490, 72, 379, 266, -211, 886, -88, 1246],\n [541, -487, 231, 153, -500, -609, 158, 93, 16, 454, 355, 1132],\n [596, -1607, 1057, -232, -477, -407, 361, 1266, -233, 1239, 250, 970],\n [-568, 561, -884, 302, -119, 167, 339, -847, -2, -833, 426, -889],\n [-1368, -210, 123, 1196, 1280, -407, 478, 457, -781, -692, 861, -111],\n [-883, 657, 513, 637, 532, 807, 365, 18, -1417, -68, -8, -211],\n [407, -456, -457, 820, 72, -1534, 1405, 422, 31, 393, 1547, 2667],\n [74, -479, -489, -98, -535, -492, 1500, 442, -317, 725, 1107, 967],\n [231, -977, 904, -771, 368, -839, -757, 1334, 153, 1136, -413, 766],\n [29, 244, -644, -1124, 118, -876, -944, -3, 916, 221, -407, -149],\n [905, -881, 796, -944, -585, -263, -806, 649, 451, 1040, -694, 389],\n [794, -487, 153, -597, -556, 415, -289, 91, 729, 185, -535, -482]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[290, 45, -235, -145, 20, -105, 495, -275, -350, 255, 230, -75],\n [697, -28, -637, -693, -301, 136, 487, -300, -430, 548, 646, -501],\n [283, 103, -198, 8, 171, -271, 788, -425, -520, 277, 184, 66],\n [-719, 40, 663, 743, 339, -172, -445, 280, 410, -560, -674, 543],\n [267, 44, -215, -127, 25, -104, 469, -260, -330, 236, 210, -63],\n [-6, 71, 43, 185, 184, -203, 361, -185, -210, 29, -54, 171],\n [420, 96, -324, -132, 108, -240, 876, -480, -600, 384, 312, -36],\n [712, -131, -705, -967, -570, 431, -31, -35, -130, 511, 730, -753],\n [631, -141, -638, -920, -569, 453, -156, 35, -40, 441, 664, -726],\n [-631, 141, 638, 920, 569, -453, 156, -35, 40, -441, -664, 726],\n [488, 86, -390, -218, 60, -206, 886, -490, -620, 434, 380, -102],\n [586, -130, -592, -852, -526, 418, -140, 30, -40, 410, 616, -672]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-58, 742, 377, 1842, 232, 146, -71, 534, -1361, 416, 314, 17],\n [-257, 197, -1273, 363, -99, 1035, -50, -36, -627, -236, 543, 614],\n [-121, 769, 873, 566, 190, -73, -237, 59, 25, -30, -267, -729],\n [-353, -931, 1721, -57, 512, -1619, -974, -782, 681, 114, -24, -874],\n [-383, -176, -4, 198, 153, 1238, -1022, 443, -1573, -27, 814, -858],\n [-456, 409, 589, -200, 790, 1082, -556, 792, -591, -614, 699, -815],\n [-266, 724, -676, -437, -17, -1161, 953, -977, 1380, -527, -317, 666],\n [-623, 502, -52, 370, -17, 429, 449, -203, 789, -683, -356, -160],\n [664, -312, 1155, -107, 464, -1031, 213, -565, 382, 127, -218, -120],\n [-821, -589, 1292, 1073, 320, -333, 33, 513, 385, 385, 869, -545],\n [84, 47, 219, -498, 205, 232, -920, -25, -980, 1, 324, -741],\n [818, 1090, 1118, -569, 1175, -372, -732, -1272, -430, -877, -163, -466]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[585, -77, -644, 279, -141, 489, -50, 334, 781, 687, -530, -344],\n [115, 489, 224, 508, -400, -158, 840, 157, 639, -183, -758, -303],\n [826, -97, -626, -454, -943, -154, 534, 3, 723, -207, -664, -483],\n [-695, -213, 686, 536, 601, -300, -201, -162, -738, -4, 830, 323],\n [845, -186, -1268, -347, -35, 427, -553, 752, 665, 819, -708, -205],\n [-580, 107, 900, -40, -17, -115, 437, -782, -604, -777, 577, 269],\n [421, 416, -252, -498, -833, -803, 689, 383, 475, -646, -951, -327],\n [56, -324, -244, 1111, 529, 503, -664, 411, 478, 1336, 238, -314],\n [-283, 197, 796, 861, -400, -68, 504, -500, 441, -36, 243, -539],\n [108, -165, -388, -559, 394, -362, 209, 433, -686, -443, -331, 752],\n [-392, 243, 540, -79, 211, 1479, -317, -1107, -40, 86, 632, 94],\n [532, -493, -832, -79, 210, -346, 13, 731, -78, 275, -413, 259]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-34, 1061, -402, -682, -469, -786, -454, -595, -1163, -876, 149, -1224],\n [71, -522, 23, -771, -1214, -211, 270, -583, 1173, -430, -147, -274],\n [-237, -340, 368, -65, -401, -164, 707, -486, -55, 450, -305, -71],\n [613, -823, -263, -261, -1513, -421, 604, -860, 1016, -400, -126, -128],\n [-111, 68, 1382, 283, 527, -176, -343, 642, 19, 986, 659, 289],\n [697, 408, 624, 384, 56, -708, -664, 288, -399, 283, 1083, -205],\n [1537, -280, 110, -257, -1133, -1672, -843, -234, -669, -474, -805, -303],\n [126, -670, -506, 203, 730, 919, 801, 9, 750, 1272, 301, 236],\n [-573, -654, -699, -282, -506, 641, 1469, -957, 584, 166, -585, -107],\n [-573, 994, 526, 340, -673, -569, -912, 257, -661, -2071, 31, 210],\n [351, -179, 590, -195, -687, -984, -317, -121, -567, -216, -899, -9],\n [1009, 73, 279, 201, -1461, -1312, -878, -123, -57, -1477, 70, 26]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-40, 28, -24, -8, -92, 48, 16, -60, 96, -40, -8, -72],\n [220, -154, 132, 44, 506, -264, -88, 330, -528, 220, 44, 396],\n [110, -77, 66, 22, 253, -132, -44, 165, -264, 110, 22, 198],\n [200, -140, 120, 40, 460, -240, -80, 300, -480, 200, 40, 360],\n [-190, 133, -114, -38, -437, 228, 76, -285, 456, -190, -38, -342],\n [-200, 140, -120, -40, -460, 240, 80, -300, 480, -200, -40, -360],\n [-250, 175, -150, -50, -575, 300, 100, -375, 600, -250, -50, -450],\n [30, -21, 18, 6, 69, -36, -12, 45, -72, 30, 6, 54],\n [-140, 98, -84, -28, -322, 168, 56, -210, 336, -140, -28, -252],\n [-40, 28, -24, -8, -92, 48, 16, -60, 96, -40, -8, -72],\n [20, -14, 12, 4, 46, -24, -8, 30, -48, 20, 4, 36],\n [110, -77, 66, 22, 253, -132, -44, 165, -264, 110, 22, 198]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-475, 114, -190, 361, 0, -380, -152, 399, -342, -323, 152, 171],\n [-125, 30, -50, 95, 0, -100, -40, 105, -90, -85, 40, 45],\n [650, -156, 260, -494, 0, 520, 208, -546, 468, 442, -208, -234],\n [50, -12, 20, -38, 0, 40, 16, -42, 36, 34, -16, -18],\n [-625, 150, -250, 475, 0, -500, -200, 525, -450, -425, 200, 225],\n [350, -84, 140, -266, 0, 280, 112, -294, 252, 238, -112, -126],\n [550, -132, 220, -418, 0, 440, 176, -462, 396, 374, -176, -198],\n [575, -138, 230, -437, 0, 460, 184, -483, 414, 391, -184, -207],\n [450, -108, 180, -342, 0, 360, 144, -378, 324, 306, -144, -162],\n [-650, 156, -260, 494, 0, -520, -208, 546, -468, -442, 208, 234],\n [425, -102, 170, -323, 0, 340, 136, -357, 306, 289, -136, -153],\n [-175, 42, -70, 133, 0, -140, -56, 147, -126, -119, 56, 63]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[338, -540, 1136, -346, 574, 774, 808, -86, 213, 368, 954, 548],\n [-1017, 435, -75, 210, -777, -783, -109, 105, 272, -34, 32, 266],\n [35, -217, 428, 614, 159, 293, 56, 124, 213, -1034, -483, 570],\n [854, -240, -832, -246, 452, 614, -628, 184, -1067, 644, 72, -858],\n [-471, -368, -32, -411, -486, -551, 39, 325, -282, 1364, 1280, 157],\n [1336, -492, -758, -626, 782, 507, 214, -49, -253, 1230, 758, -309],\n [-370, -613, -82, 735, -495, -455, -779, 628, -637, -636, -451, 176],\n [-283, 370, 631, 851, 86, 463, -196, -96, 198, -1956, -1411, 203],\n [-972, 222, 411, 86, -620, -494, 75, 105, 195, 68, 329, 354],\n [-441, -292, 462, 95, -305, -384, 265, 159, 285, 84, 445, 589],\n [60, -8, -164, 284, 142, 212, 426, 148, 519, 112, 562, 910],\n [-1647, 511, 157, 902, -1248, -1021, -861, 340, -180, -1288, -1087, 55]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[327, 157, 147, -312, 411, 444, -205, -209, -242, -174, -708, 572],\n [-22, -486, 487, -250, -556, -235, 49, 384, 66, 574, 197, -493],\n [85, -286, 344, -392, 59, 313, -461, -206, -88, 211, -526, 417],\n [149, 181, 115, 26, -159, -184, 445, 381, -80, 12, 198, -406],\n [-681, 1030, -27, 388, 247, 266, -544, -718, -260, -661, 37, 726],\n [-520, -154, -1175, 675, 468, -32, -445, -777, 491, -438, 360, 451],\n [26, 710, 742, -149, -312, -27, 316, 383, -445, -42, 27, -248],\n [38, 95, -269, 94, 264, 105, -44, -181, 20, -213, -108, 223],\n [1, -241, -532, 186, 243, -13, -54, -197, 236, -108, 51, 109],\n [-580, -179, -365, 402, -182, -245, -284, -287, 316, 23, 562, -75],\n [274, 216, 482, -133, -408, -279, 678, 717, -201, 192, 237, -708],\n [128, -201, 1021, -664, -354, 239, -328, 161, -306, 501, -516, 111]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-444, -451, -924, 59, -219, 172, 194, -198, 39, -499, 492, -299],\n [76, 116, -222, -1218, -420, 209, 276, -782, 548, -617, -399, 167],\n [106, 318, -164, 186, 206, -70, -368, 104, -618, 272, -670, -272],\n [75, 162, 276, 648, 486, -213, -534, 432, -654, 591, -411, -219],\n [146, 419, -124, -247, 307, -82, -614, -194, -663, 225, -1238, -339],\n [-180, -363, 282, -959, 101, 19, -194, -696, 615, -390, -261, 106],\n [290, 209, 79, -734, -797, 254, 974, -273, 908, -516, 593, 607],\n [127, -39, 375, -748, -349, 110, 452, -365, 818, -358, 285, 461],\n [274, 426, 30, 248, -70, -19, 68, 274, -322, 257, -207, 29],\n [848, 1143, 146, -473, -765, 176, 798, 88, 87, 37, -362, 531],\n [-113, -167, 49, 774, 207, -102, -92, 473, -264, 300, 419, -103],\n [-13, -156, 189, 387, -118, 0, 330, 311, 253, 49, 741, 210]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-586, -276, 448, 548, 722, 127, -101, -153, -336, 266, 98, -662],\n [-21, 624, -26, -64, -668, -484, 158, -286, 1278, -668, 153, 750],\n [304, -352, -213, 28, 562, -215, -440, 243, 738, 189, 479, -280],\n [-244, -268, 240, 488, 1060, 177, -490, 352, -226, 484, 336, -808],\n [243, -267, 383, -385, -277, 652, 277, 252, -1174, 1122, -473, -959],\n [-527, -379, -766, -477, 811, 760, 656, 726, -800, 109, 488, -49],\n [579, -179, -509, 823, 923, -155, -927, 952, 163, 396, -236, 243],\n [434, -799, 73, 819, 1303, -346, -1389, 84, -235, 294, 39, -611],\n [-1332, 467, 899, 1189, 411, -145, 194, -599, 197, -335, 7, -157],\n [798, 426, -963, 315, 104, -448, -514, 1034, 1422, -175, -5, 1180],\n [-986, 1618, -187, -362, -654, 575, 1365, 734, 519, -454, 564, 780],\n [887, -454, -510, -292, -460, -224, 51, -151, -271, -16, -22, 268]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[82, 337, -105, 702, -676, 702, 312, 914, 479, 267, 108, -332],\n [-465, -248, -50, 101, 229, 44, 114, -408, -314, 131, -135, -337],\n [-319, 267, 513, -437, 409, 1310, -1330, 382, 227, 154, -1057, 1551],\n [661, 126, -80, 370, -543, -804, 401, 33, 536, -14, 528, -374],\n [201, -216, -106, -98, -131, -525, 635, 58, -751, 82, 506, -1051],\n [21, -145, 418, 861, -904, -37, -73, -47, 575, 774, -32, -693],\n [723, 506, 154, 132, -1324, -84, -28, 741, 1540, -391, 969, 575],\n [-482, -498, -223, 309, -510, 555, -129, 118, 161, -358, -216, -90],\n [345, 212, -304, 980, -606, 658, -498, 695, 1409, -275, -770, 895],\n [-45, 540, 767, 130, -674, 231, -178, 82, 878, 754, 605, 110],\n [258, 740, 231, 1236, -561, 370, 433, 618, 811, 1156, 47, -635],\n [-888, 286, 1321, 35, -811, 336, -96, -593, 529, 1439, 1004, -622]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[345, 826, -453, 379, 764, 686, 248, -75, 218, 211, 215, 882],\n [-303, -329, -101, -927, -441, -1137, 92, 140, -1059, 489, 573, -428],\n [-671, -1090, 409, -485, -301, -747, -473, 593, -897, 70, 81, -766],\n [-291, -204, -203, 153, 712, 523, -431, 331, -349, -189, -346, 332],\n [259, -211, 1047, 1039, -130, 437, -390, 500, 485, -222, -814, -172],\n [-634, -1075, 115, -637, -669, -563, -292, -133, -81, -476, -114, -981],\n [-682, -828, -110, -678, -92, -555, -209, 238, -623, 48, 481, -536],\n [277, 76, 463, 1, -463, -524, -138, 195, -578, 164, -620, -140],\n [303, 227, 324, 750, 122, 649, -4, -12, 801, -220, -312, 177],\n [459, 319, 751, 1121, 199, 621, -2, 406, 699, 127, -147, 254],\n [0, 761, -1148, -694, 647, -106, 587, -317, -468, 608, 1185, 746],\n [59, -607, 1070, 806, -329, 296, -771, 474, 122, -605, -1564, -427]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-214, 574, -38, 352, -572, 1413, 551, 1259, 477, -229, 984, -708],\n [232, -27, 326, 675, -290, 268, 76, 244, -277, -646, 208, -403],\n [40, 442, -246, -596, 540, -809, -527, -519, -23, 657, -310, 908],\n [447, 411, 86, 345, -582, -383, -171, -497, -435, -183, -87, -235],\n [-282, 408, -20, -48, 538, 648, -2, 978, 400, 60, 582, 388],\n [305, 335, 178, 305, 86, -339, -335, -137, -341, -219, -5, 257],\n [315, 727, 228, 541, -27, 110, -269, 373, -255, -374, 415, 149],\n [480, 185, 442, 761, 19, -308, -351, -79, -596, -688, 20, 83],\n [-379, 261, -334, -627, 403, 225, 22, 348, 510, 619, 179, 425],\n [323, 1460, 44, 416, -192, 309, -319, 619, -88, -93, 757, 246],\n [-182, 472, -150, 118, -638, 1043, 491, 799, 419, -3, 692, -658],\n [373, 69, 276, 207, 631, -942, -671, -513, -553, -202, -383, 783]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[724, 529, 519, -13, -1103, -362, 314, 44, -141, -189, 637, 385],\n [181, 109, -1710, -523, -455, 1048, -392, -208, 868, 1382, -1093, -111],\n [744, -879, 855, -1306, -309, 272, 188, 142, 1058, 36, 321, -12],\n [368, -148, -301, -1019, 13, -628, 48, 62, -1205, -400, 2050, 564],\n [-504, 1547, 601, 812, 148, -615, -57, -592, -1705, -679, 537, 627],\n [-180, -897, -628, 120, -141, -23, 257, 16, 277, 758, -186, -542],\n [-703, 81, 153, -337, 654, -710, 3, -187, -705, -1074, 291, 471],\n [760, -118, 436, -274, -963, -285, 1671, 456, 557, -165, 638, -363],\n [-49, 106, -372, -156, 669, 659, -1260, -146, -171, 391, -161, 204],\n [650, 1472, 1692, 209, -97, -42, 324, 373, 13, -1514, 297, 544],\n [353, 1130, -322, -859, -424, 1125, 44, -835, 134, 1185, -370, 224],\n [-21, -817, -896, 576, 50, -115, 671, 390, -278, 774, 607, -849]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[128, 380, -504, -364, -268, 148, 204, 232, -348, -284, 84, 56],\n [138, 327, -108, -87, 57, -21, -153, -192, 99, 33, -225, -240],\n [-193, -501, 381, 283, 103, -66, 17, 35, 112, 133, 148, 177],\n [-267, -589, -21, 7, -293, 136, 493, 605, -442, -243, 602, 623],\n [203, 350, 531, 356, 632, -317, -816, -983, 897, 586, -831, -829],\n [231, 476, 195, 118, 394, -191, -578, -703, 575, 348, -649, -661],\n [-110, -152, -486, -332, -500, 254, 612, 734, -702, -472, 594, 586],\n [10, -53, 396, 277, 325, -169, -357, -424, 447, 317, -309, -296],\n [-312, -767, 390, 299, -13, -13, 221, 286, -65, 39, 403, 442],\n [156, 310, 192, 122, 314, -154, -442, -536, 454, 282, -482, -488],\n [186, 494, -426, -314, -146, 88, 34, 26, -172, -174, -100, -130],\n [235, 592, -369, -278, -50, 41, -102, -139, -33, -88, -249, -281]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[1131, -1077, -632, 750, 154, 336, -927, -78, 477, 12, 320, -549],\n [-1121, 1185, -437, 323, -1397, -321, -31, 429, -982, -383, -569, 158],\n [745, -344, 793, 632, -78, -431, 1242, -177, 603, -534, 29, 396],\n [40, -530, 494, 199, 1191, -296, 1634, -1093, 527, -760, 1153, -1004],\n [261, -659, -395, 40, 1633, 347, -638, 10, -73, 1095, -132, -394],\n [666, -888, -1080, -449, 545, 682, -1496, 179, -1007, 223, -1021, -34],\n [1199, -54, 784, -438, 575, -85, -117, 152, 524, 662, -23, -117],\n [-827, 185, -784, 94, -64, 725, 112, 426, 176, -263, 906, 67],\n [-1282, -167, -442, -243, 754, 184, -336, -428, -216, 543, 441, -39],\n [-1789, 1147, 1068, -552, 1160, -539, 575, 451, 521, 1665, 301, 334],\n [992, 75, 422, -284, 1343, 662, 1471, -58, 716, 29, 1207, -216],\n [178, 175, -414, 982, 45, -594, -262, 425, -420, -195, -438, -1423]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-169, 247, -156, -312, -156, 312, -39, 325, 247, -247, -286, 312],\n [312, -456, 288, 576, 288, -576, 72, -600, -456, 456, 528, -576],\n [-91, 133, -84, -168, -84, 168, -21, 175, 133, -133, -154, 168],\n [104, -152, 96, 192, 96, -192, 24, -200, -152, 152, 176, -192],\n [-13, 19, -12, -24, -12, 24, -3, 25, 19, -19, -22, 24],\n [52, -76, 48, 96, 48, -96, 12, -100, -76, 76, 88, -96],\n [-169, 247, -156, -312, -156, 312, -39, 325, 247, -247, -286, 312],\n [-286, 418, -264, -528, -264, 528, -66, 550, 418, -418, -484, 528],\n [-234, 342, -216, -432, -216, 432, -54, 450, 342, -342, -396, 432],\n [260, -380, 240, 480, 240, -480, 60, -500, -380, 380, 440, -480],\n [-182, 266, -168, -336, -168, 336, -42, 350, 266, -266, -308, 336],\n [195, -285, 180, 360, 180, -360, 45, -375, -285, 285, 330, -360]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[292, 809, 463, 540, -226, -422, 295, 256, -280, 443, 391, 179],\n [-111, 638, 355, 161, -212, -455, 41, -259, 660, -314, -47, -269],\n [-378, 314, 128, -78, -368, -398, -376, -662, 612, -634, -292, -72],\n [149, 897, 557, 444, -146, -514, 338, 106, 424, 70, 231, -232],\n [-472, -656, -158, -392, 165, 151, -396, -472, 811, -843, -448, -317],\n [-90, 98, 705, 679, -107, -434, -184, -15, 27, -216, 279, 359],\n [275, 524, 801, 695, 275, -348, 565, 555, 505, 143, 445, -348],\n [-196, -385, 217, 248, -68, -88, -391, -164, -194, -261, 45, 427],\n [-27, -699, -122, -71, 321, 348, -66, 185, -135, -38, -2, 53],\n [261, -371, -308, -7, 64, 361, 26, 361, -1062, 625, 206, 494],\n [152, -540, -134, 110, 130, 308, -76, 314, -866, 396, 206, 498],\n [-682, 577, -419, -668, -921, -491, -831, -1444, 607, -918, -769, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-582, 906, -634, -884, -659, 481, 458, -799, -427, 52, -240, 521],\n [110, -468, 413, 104, 512, 107, 254, 646, -191, 246, -460, 47],\n [126, 666, -44, -393, -29, 146, 156, -745, 521, 344, -18, -28],\n [-1236, 1490, -595, -437, -1404, 712, -1738, 1304, -192, 370, 970, 534],\n [422, -123, 402, -349, 761, 403, 357, -971, -224, 109, -1911, 891],\n [110, -318, -447, 92, -564, -551, 23, -396, -759, -1111, 332, -149],\n [-816, 1138, -535, -930, -1142, 831, -1427, 820, -938, -35, -334, 1141],\n [-220, 648, -250, -750, -458, 528, -548, -227, -719, -177, -928, 963],\n [32, 830, -310, 85, -1038, -807, 28, -44, -102, -660, 1908, -1191],\n [-614, 1299, -689, -735, -1758, 159, -1538, 610, -1550, -1022, 351, 661],\n [-606, -36, -427, -71, -758, 94, -660, 1289, -686, -265, 686, 89],\n [-546, 33, -421, -197, 250, 417, 1087, -603, 1033, 1002, 379, -154]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1231, -1434, 678, 466, -1425, -1144, 685, -225, 275, 466, -701, -254],\n [-904, -206, 277, 281, 68, -54, -287, -342, -480, 1159, -800, -199],\n [42, 59, 1077, -254, 727, -768, 322, 992, -968, 324, 81, -1199],\n [-267, 139, 407, -227, -335, -234, -343, 1002, -587, -528, 233, -1415],\n [34, 1080, 163, -1542, 845, -359, -1918, 959, -1517, 111, 900, -1610],\n [550, 187, 827, -372, 958, -699, 650, 755, -567, 114, 411, -638],\n [-294, 767, -988, 365, 98, 953, -1619, 117, -957, -42, -853, -275],\n [1029, -644, 733, 914, 185, 399, 443, 475, -591, -128, -874, 313],\n [503, -335, 242, 402, 234, 679, 1234, -815, 1296, 197, 247, 1335],\n [-1398, -220, 561, -945, -143, -873, -936, -255, -204, 1095, 372, -649],\n [-38, -383, 791, 589, 281, -569, 843, 554, -758, 446, -780, -605],\n [502, 602, 112, -1353, 424, -253, -651, 278, -268, -131, 1263, -616]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[286, 346, -1118, 597, -23, 503, -253, -243, -521, 839, -226, 5],\n [-556, -112, -348, -60, 97, 269, 68, 248, -86, 340, -667, -38],\n [-262, 464, -636, 411, 777, 40, 63, 54, 159, 369, -344, 511],\n [-56, -209, -501, 789, -1165, -1095, -1190, 280, 661, 418, 573, 24],\n [-324, -114, 488, 351, -654, -1381, -503, -396, 1367, -185, 435, -477],\n [552, -172, 271, 367, -1307, -1013, -715, -240, 308, -84, 984, -336],\n [322, -162, 1049, -410, -98, -580, 86, 185, 157, -887, 836, 267],\n [-825, -629, 710, -694, 609, 215, -367, -110, -141, -493, 596, -303],\n [-22, 224, 61, -366, 735, 457, 523, 173, -880, -99, -82, 517],\n [-63, -253, -673, 415, 66, 216, -938, 472, 197, 233, 376, 331],\n [-279, -503, 1041, -952, 311, 144, 339, 654, -328, -880, 234, 324],\n [469, 654, -864, 652, -642, -641, 285, 907, -455, 611, -527, 1145]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-487, 372, 15, 664, 117, -3, 16, -88, -239, 25, 367, 46],\n [-384, 6, 878, -446, -595, 368, 564, -109, 826, 942, -440, 594],\n [398, 148, -786, 502, 350, -256, -248, 118, -712, -804, 330, -488],\n [-433, 314, -65, 639, 203, -52, -92, -77, -304, -70, 397, -20],\n [210, -460, 122, -665, 69, -39, -264, 18, 255, 73, -238, 0],\n [561, -324, 95, -761, -346, 104, 240, 104, 406, 120, -533, 54],\n [1010, 48, -634, -136, -298, -22, 400, 244, -214, -566, -322, -332],\n [-607, -220, 631, -297, 74, 80, -224, -164, 422, 584, -5, 334],\n [321, 468, -697, 775, 50, -112, 192, 116, -650, -648, 283, -354],\n [-489, 472, 125, 667, -86, 94, 264, -86, -112, 170, 261, 150],\n [-610, 596, 414, 628, -392, 262, 616, -114, 162, 506, 98, 376],\n [-754, 466, 340, 669, -66, 129, 220, -151, 1, 375, 302, 274]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-460, 520, 180, -260, -320, 240, -420, -440, 200, -340, 340, 140],\n [207, -234, -81, 117, 144, -108, 189, 198, -90, 153, -153, -63],\n [46, -52, -18, 26, 32, -24, 42, 44, -20, 34, -34, -14],\n [230, -260, -90, 130, 160, -120, 210, 220, -100, 170, -170, -70],\n [506, -572, -198, 286, 352, -264, 462, 484, -220, 374, -374, -154],\n [207, -234, -81, 117, 144, -108, 189, 198, -90, 153, -153, -63],\n [-92, 104, 36, -52, -64, 48, -84, -88, 40, -68, 68, 28],\n [414, -468, -162, 234, 288, -216, 378, 396, -180, 306, -306, -126],\n [-253, 286, 99, -143, -176, 132, -231, -242, 110, -187, 187, 77],\n [483, -546, -189, 273, 336, -252, 441, 462, -210, 357, -357, -147],\n [92, -104, -36, 52, 64, -48, 84, 88, -40, 68, -68, -28],\n [161, -182, -63, 91, 112, -84, 147, 154, -70, 119, -119, -49]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-764, 263, -681, 57, 397, -524, 803, -98, 101, 334, 417, 413],\n [1409, -803, -510, 165, -193, 601, 52, -1000, -42, -303, -187, -414],\n [157, -155, 88, -297, 189, 77, -362, -54, -48, 265, -423, -122],\n [232, -273, -390, 561, -1249, 1098, -296, 78, 659, -171, -139, -1144],\n [-605, 237, -718, -388, 1206, -1139, 1048, -421, -329, 444, 443, 1035],\n [-664, 391, -32, -914, -398, -30, -722, 951, 166, 264, -361, -541],\n [57, 308, 912, 184, 457, -608, 216, 124, -530, -530, 492, 913],\n [1116, -159, 615, -463, 352, -381, -161, -264, -754, -768, 157, 530],\n [-183, 302, 172, 288, 866, -979, 1016, -322, -511, -328, 844, 1272],\n [-789, 260, 15, 1075, -212, 116, 597, 91, 407, 84, 466, 155],\n [-655, 513, 860, -168, -287, -66, -626, 983, 18, -56, -91, -52],\n [-552, 364, 1713, -134, 411, -107, -1121, 866, -207, 381, -690, 282]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-15, 346, -389, -795, -315, -70, 712, -1038, 63, -101, -586, 485],\n [-259, 125, 578, 219, -686, -543, 56, -310, -115, 308, -210, -683],\n [765, 281, -599, -432, 502, 875, 664, -4, 81, -905, -270, 286],\n [258, 118, 285, 176, -49, 377, -5, 458, -246, 24, 145, 144],\n [253, -197, 243, 727, 297, 540, -567, 526, -815, -152, 865, -245],\n [252, -40, -103, 80, 330, 410, -82, 431, -48, -176, 200, 221],\n [666, 116, -316, 17, 494, 1006, 148, 211, -546, -633, 366, 356],\n [-1, -39, -750, -530, 362, -259, 430, -551, 779, -547, -582, -241],\n [-423, 25, 433, -10, -514, -493, -132, -14, 69, 689, -110, 186],\n [-156, -131, -492, -419, 336, -404, 185, 53, 1074, -138, -563, -14],\n [321, 11, -543, -151, 399, -46, 475, -308, 621, -942, -517, -961],\n [124, 623, 1143, 76, -1216, -206, 595, 121, -110, 449, -653, -417]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-251, -88, -968, 134, -619, -330, 107, 314, -618, 771, 86, -42],\n [670, 695, -54, -510, -262, -255, -690, -839, -118, 723, 623, -277],\n [-636, -1124, -260, -28, 320, -457, 106, 342, -812, 490, -104, 378],\n [-82, -281, 359, -92, 37, -11, -121, -468, 110, 567, 605, -87],\n [914, -218, 1030, -804, 1124, -278, -578, -351, -707, -679, 207, -1114],\n [85, 216, -214, 455, -664, 281, 295, -442, 714, 198, 486, -128],\n [193, -659, 1863, 23, 870, 685, 529, 210, 322, -575, 650, -1213],\n [-175, -495, 137, -314, 628, -950, -462, 1331, -1717, 187, -786, 781],\n [-684, 1368, -2077, 916, -2287, 97, 132, -221, 1036, 1458, 51, 1441],\n [981, 624, -147, -641, -305, -775, -890, -555, -766, 490, 611, -586],\n [293, -490, 811, -548, 756, 735, 799, -74, 445, -1332, 180, -1585],\n [1137, -25, 857, -23, 828, 240, -343, -1178, 324, -679, 378, -823]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[207, 244, 87, -372, 521, 340, -153, 205, -329, 244, 215, -418],\n [212, 314, 43, 5, -44, 351, 90, -15, 4, 8, 77, -229],\n [-51, -144, 20, 83, -147, -147, 43, -130, 59, -152, -160, 227],\n [644, 229, 509, -594, 539, 584, -34, -330, -635, -330, -374, -38],\n [-31, -454, 194, -9, -137, -363, 35, -410, -79, -476, -552, 663],\n [260, -199, 332, 189, -563, -39, 308, -755, 59, -830, -795, 771],\n [-439, 41, -428, -4, 346, -198, -273, 735, 118, 794, 761, -598],\n [4, 258, -135, 323, -408, 161, 182, 15, 320, 32, 147, -147],\n [484, 185, 356, 85, -419, 385, 324, -635, -21, -670, -579, 363],\n [486, 41, 432, -9, -329, 287, 282, -715, -127, -766, -719, 517],\n [-54, -375, 129, 120, -291, -330, 96, -390, 51, -450, -486, 612],\n [-4, 170, -82, -132, 274, 144, -112, 280, -82, 316, 312, -372]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[421, 95, -438, -644, 216, -798, 323, 490, -705, -247, -564, -784],\n [991, 1219, 665, 188, -585, 482, 305, 553, -212, 150, 868, 564],\n [-1203, -462, -319, 134, 255, 12, -378, -805, 709, -231, -296, -280],\n [-152, 71, 666, 346, -158, 910, -307, -446, 649, -131, 602, 400],\n [191, -171, 820, -336, 218, 962, -355, -142, 541, -615, 390, -292],\n [-235, -386, -369, 114, 118, -196, -25, 294, 19, 516, -169, 372],\n [153, -539, -415, -364, 306, -558, 110, 318, -464, 59, -557, -348],\n [47, -136, -204, 114, -45, -284, 103, 13, -258, 201, -159, 116],\n [584, 228, -414, -358, 51, -606, 371, 1006, -645, 395, -228, -6],\n [-427, -550, -591, -38, 208, -660, 23, -292, -239, 14, -637, -332],\n [-787, -952, -559, -252, 563, -242, -286, 28, 342, 127, -577, -238],\n [-1056, -182, -781, 522, -26, -442, -75, -191, 344, 670, -246, 518]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[315, 462, -273, 420, -399, -63, -189, 168, -42, -210, 105, -63],\n [-225, -330, 195, -300, 285, 45, 135, -120, 30, 150, -75, 45],\n [-60, -88, 52, -80, 76, 12, 36, -32, 8, 40, -20, 12],\n [105, 154, -91, 140, -133, -21, -63, 56, -14, -70, 35, -21],\n [165, 242, -143, 220, -209, -33, -99, 88, -22, -110, 55, -33],\n [-60, -88, 52, -80, 76, 12, 36, -32, 8, 40, -20, 12],\n [390, 572, -338, 520, -494, -78, -234, 208, -52, -260, 130, -78],\n [-30, -44, 26, -40, 38, 6, 18, -16, 4, 20, -10, 6],\n [-345, -506, 299, -460, 437, 69, 207, -184, 46, 230, -115, 69],\n [45, 66, -39, 60, -57, -9, -27, 24, -6, -30, 15, -9],\n [45, 66, -39, 60, -57, -9, -27, 24, -6, -30, 15, -9],\n [-210, -308, 182, -280, 266, 42, 126, -112, 28, 140, -70, 42]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[111, 1534, 581, 21, -471, 389, -75, 533, -175, 109, 1832, -475],\n [904, -152, 596, 469, -633, -221, -755, -270, 93, -754, 52, -295],\n [38, -474, 382, -189, -422, 131, 570, 886, -589, 820, -549, -138],\n [-22, -983, -103, -740, -341, -300, -294, 903, -399, 1478, -675, 200],\n [256, 602, -3, -633, 1347, 1965, 604, 87, 244, 658, -1784, -1453],\n [-711, -195, -540, 1057, 249, 492, -422, 65, -517, 497, 96, -784],\n [894, -134, -679, -112, 74, -1070, -327, -23, -601, 463, -325, -91],\n [-341, -214, -366, -609, 268, -33, 1673, 750, -755, 747, -1048, 128],\n [-1483, -187, -1113, -102, 197, 819, 773, -440, 7, -1230, -466, 845],\n [-194, -59, -331, 281, 0, 437, -515, -188, -36, -175, 4, -131],\n [-926, 505, 151, 1239, 51, 1084, 20, -1070, 650, -2081, 750, 27],\n [-1001, 1217, -1240, -821, 1807, 1186, 1098, -310, 276, 500, -320, -94]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-102, 268, -36, -39, 496, -322, 364, -216, -35, -468, -198, -444],\n [-979, -468, -135, -20, -563, 406, -955, -240, 787, 831, 365, 1087],\n [-229, 1422, 554, -6, -1304, -651, 889, 431, 201, -813, 29, 353],\n [68, -552, 216, -190, -949, 696, -923, 171, 376, 1384, 344, 1164],\n [1679, 577, 442, -88, 0, 213, 150, 571, -1152, -171, -591, -160],\n [29, -641, 678, 83, -957, 1067, -1171, 318, -925, -491, -541, 162],\n [-302, 276, -529, 616, -272, -294, 325, 428, -55, -709, 380, -8],\n [282, -425, -53, -172, 1229, 372, -611, -491, -522, -57, -664, -437],\n [463, 329, -545, 158, 378, -416, 515, 187, 238, 453, 419, 134],\n [598, 17, 1117, -533, -194, -50, 742, -32, -685, -767, -648, -1277],\n [903, 424, 1567, -614, -917, 424, 35, 232, -1047, -673, -1033, -427],\n [-517, 16, -1315, 519, 1040, -831, 764, -145, 773, 98, 847, -253]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[306, -85, 357, -374, -221, 102, 340, 340, -340, -204, 0, 323],\n [270, -75, 315, -330, -195, 90, 300, 300, -300, -180, 0, 285],\n [162, -45, 189, -198, -117, 54, 180, 180, -180, -108, 0, 171],\n [108, -30, 126, -132, -78, 36, 120, 120, -120, -72, 0, 114],\n [108, -30, 126, -132, -78, 36, 120, 120, -120, -72, 0, 114],\n [468, -130, 546, -572, -338, 156, 520, 520, -520, -312, 0, 494],\n [432, -120, 504, -528, -312, 144, 480, 480, -480, -288, 0, 456],\n [396, -110, 462, -484, -286, 132, 440, 440, -440, -264, 0, 418],\n [36, -10, 42, -44, -26, 12, 40, 40, -40, -24, 0, 38],\n [-396, 110, -462, 484, 286, -132, -440, -440, 440, 264, 0, -418],\n [342, -95, 399, -418, -247, 114, 380, 380, -380, -228, 0, 361],\n [180, -50, 210, -220, -130, 60, 200, 200, -200, -120, 0, 190]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[436, -471, -113, 1506, -316, 26, 1053, 692, 452, 305, 1203, 189],\n [1608, 1362, -54, 745, -1659, -1328, -570, 422, 935, -507, -205, -838],\n [-49, 908, -122, -587, -339, 945, 1065, 901, -155, -1962, -288, -485],\n [-32, 586, 989, -617, 415, 261, -195, -1340, -58, 166, -1032, -1202],\n [694, -422, 718, 199, 178, -1134, -1145, 906, 1827, 360, 771, -88],\n [-457, -1451, 1776, -2215, 1878, -85, -2077, -446, 490, 703, -117, 240],\n [-103, -991, 595, -952, 657, -697, -1263, -665, 6, 1466, -45, 462],\n [-815, -1239, 31, -805, 1134, -646, -1051, 713, 999, 881, 603, 959],\n [134, 314, 225, 505, -493, -781, -606, -849, 424, 612, -206, -365],\n [165, 20, 1186, 167, 234, 928, 971, -480, 7, -386, 132, -919],\n [-946, 421, -391, 631, 21, 1437, 1366, -133, -655, -1312, -33, -139],\n [985, -1209, 1219, 662, -119, -13, 2, -978, -616, 1383, 824, 123]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1459, -619, -405, 728, -676, -876, 1047, -589, -780, 342, 127, -166],\n [-1073, -417, 1584, 414, 833, 42, 234, -809, 878, -1534, -62, 39],\n [259, -1310, -563, 1087, 1028, -734, -325, 522, -1196, 64, 1377, -239],\n [136, 1320, 941, -1940, -461, 549, 121, -413, 423, 100, -548, 333],\n [143, 28, -1006, 181, -752, -250, 402, 588, -551, 374, 176, -13],\n [47, -32, 574, 438, -326, -479, -160, -799, 1027, -59, 341, -247],\n [556, 462, 213, -777, 801, 881, 926, 788, -398, -89, 375, -255],\n [10, 690, 272, -419, -1021, 680, 1011, -386, 1043, -318, -1261, -312],\n [752, -481, -1318, 257, 333, 360, 69, 1061, -1054, 677, -49, -511],\n [1166, 278, -787, -914, 389, 1429, 476, 942, -606, 758, -640, -640],\n [-828, -61, -369, 443, 316, -91, -1166, 128, -140, 243, 258, 883],\n [933, 738, 644, -282, -151, 1323, 944, -1124, 772, 190, -1052, 684]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-240, 180, -108, 180, 108, -264, -288, -252, -192, -84, -252, -72],\n [-160, 120, -72, 120, 72, -176, -192, -168, -128, -56, -168, -48],\n [480, -360, 216, -360, -216, 528, 576, 504, 384, 168, 504, 144],\n [300, -225, 135, -225, -135, 330, 360, 315, 240, 105, 315, 90],\n [-440, 330, -198, 330, 198, -484, -528, -462, -352, -154, -462, -132],\n [-160, 120, -72, 120, 72, -176, -192, -168, -128, -56, -168, -48],\n [320, -240, 144, -240, -144, 352, 384, 336, 256, 112, 336, 96],\n [240, -180, 108, -180, -108, 264, 288, 252, 192, 84, 252, 72],\n [-440, 330, -198, 330, 198, -484, -528, -462, -352, -154, -462, -132],\n [500, -375, 225, -375, -225, 550, 600, 525, 400, 175, 525, 150],\n [-300, 225, -135, 225, 135, -330, -360, -315, -240, -105, -315, -90],\n [-160, 120, -72, 120, 72, -176, -192, -168, -128, -56, -168, -48]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[575, 405, 498, 566, -174, 338, 385, 160, 515, -471, 454, -730],\n [-230, -396, -30, -212, -204, 106, -172, 278, 28, -24, -448, 310],\n [-410, -152, -454, -412, 284, -382, -264, -314, -504, 460, -168, 510],\n [-90, -73, -71, -88, 16, -43, -61, -11, -71, 65, -82, 115],\n [130, -39, 207, 136, -192, 211, 77, 227, 247, -225, -46, -155],\n [-490, -383, -397, -480, 104, -249, -331, -81, -401, 367, -430, 625],\n [180, 146, 142, 176, -32, 86, 122, 22, 142, -130, 164, -230],\n [-275, -75, -324, -278, 222, -284, -175, -250, -365, 333, -82, 340],\n [240, 433, 17, 220, 236, -131, 181, -319, -49, 43, 490, -325],\n [550, 345, 507, 544, -216, 367, 365, 215, 535, -489, 386, -695],\n [-530, -661, -251, -504, -176, -15, -377, 273, -187, 173, -746, 695],\n [-310, -107, -349, -312, 224, -297, -199, -249, -389, 355, -118, 385]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[55, -90, 320, 355, -75, 530, 40, 70, -395, 365, -15, -130],\n [-101, 163, -474, -511, 40, -696, -128, -299, 389, -443, -77, 41],\n [107, -173, 518, 561, -56, 776, 128, 293, -459, 501, 67, -71],\n [38, -63, 262, 296, -87, 466, 8, -13, -394, 334, -48, -161],\n [-9, 11, 134, 173, -148, 368, -96, -291, -487, 313, -169, -303],\n [-125, 199, -450, -463, -68, -528, -224, -575, 77, -275, -221, -187],\n [17, -29, 158, 183, -74, 308, -16, -67, -297, 231, -59, -143],\n [-6, 12, -144, -174, 102, -324, 48, 156, 366, -258, 102, 204],\n [-153, 241, -422, -407, -194, -332, -336, -897, -287, -79, -389, -453],\n [116, -186, 484, 512, 6, 652, 176, 434, -268, 388, 144, 58],\n [-100, 160, -400, -420, -20, -520, -160, -400, 180, -300, -140, -80],\n [102, -164, 448, 478, -14, 628, 144, 348, -302, 386, 106, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[288, 384, 156, -348, -84, -432, -336, -408, -480, -324, 216, -540],\n [-310, -461, -178, 634, -59, 652, 523, 584, 656, 456, -381, 771],\n [208, 260, 109, -157, -115, -244, -184, -242, -296, -195, 102, -321],\n [572, 702, 297, -361, -357, -620, -462, -626, -776, -507, 240, -831],\n [136, 112, 59, 213, -257, 68, 76, 18, -24, 3, -114, 21],\n [550, 677, 286, -358, -337, -604, -451, -608, -752, -492, 237, -807],\n [544, 604, 269, 3, -539, -340, -224, -402, -552, -339, 30, -537],\n [6, -31, -5, 205, -124, 144, 125, 110, 104, 81, -117, 144],\n [594, 779, 319, -647, -214, -840, -649, -802, -952, -639, 405, -1062],\n [106, 7, 29, 603, -452, 368, 331, 258, 216, 183, -339, 336],\n [-168, -224, -91, 203, 49, 252, 196, 238, 280, 189, -126, 315],\n [-492, -526, -239, -113, 551, 228, 134, 302, 440, 261, 36, 405]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[792, 158, 553, -1015, -236, 340, 689, -969, 1308, 69, -226, -920],\n [449, 1839, -536, -1159, 66, -220, 479, -1436, 294, 860, -444, -960],\n [-862, -755, -584, 845, 213, 139, -1119, 1247, -293, -684, 530, 745],\n [-352, 488, 178, -119, 871, -781, 468, -23, -978, 822, -834, 215],\n [730, -813, -10, -196, -902, 1130, -688, 317, 1500, -617, 502, -859],\n [-393, 477, -242, 325, 824, -484, -97, 359, -748, 345, -753, 443],\n [129, -122, 534, -299, -26, -146, 243, 224, -870, 1023, -463, -781],\n [175, -802, 96, 284, -573, 771, -386, 215, 1095, -1115, 676, 44],\n [514, -679, 490, -256, -836, 850, -187, 144, 621, -157, 334, -1077],\n [-462, 177, 60, 706, 296, -206, 343, -280, -79, -965, 172, 1137],\n [-469, 92, -211, 4, 292, -510, 25, 68, -649, 319, 133, 396],\n [1619, 1275, 545, -933, -1281, 495, 1284, -2057, 818, 370, -77, -1376]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1044, 653, -872, -975, 403, 1154, 719, -1084, 400, 16, -581, 312],\n [-132, -161, -363, 290, 1286, 909, 889, 240, -25, 51, -1416, 1283],\n [418, -240, -667, -573, -52, -282, -482, 804, 593, -200, 743, -322],\n [-143, 433, 857, 396, -257, -226, -521, -89, -623, 249, -149, -586],\n [516, -267, -252, -331, 715, 842, 2408, 1137, 94, 141, -556, 1396],\n [513, -647, -679, -386, -254, -777, 519, -507, 73, -452, 531, 551],\n [1058, -514, 48, 18, 81, 337, 1038, 1380, -1062, 1191, -431, 836],\n [-364, -1517, 214, 439, -249, -521, -1198, 427, 976, 672, 1403, 911],\n [241, 903, -46, -1147, -368, 664, 1438, 308, -874, 616, -394, 44],\n [-673, -472, -831, 526, 1830, -571, -346, 338, 743, 331, -1445, 936],\n [60, 55, -744, -340, -596, 659, -1767, -89, 59, 407, 492, -1015],\n [-675, 774, -810, -1785, -195, 1910, 548, -336, 535, -109, 142, 671]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[845, -195, 989, 1091, 1031, -1303, 1140, 278, -10, 466, 844, 1774],\n [1191, 205, 1345, -1082, 650, 658, 172, -1133, -83, 1043, -67, 894],\n [-362, 450, -1464, 981, -501, -67, -225, 34, 1096, -788, -268, 408],\n [165, 899, 250, -46, -100, -836, -1042, 656, -62, -393, -169, 399],\n [-60, 1121, -1921, -388, -746, 1831, -1177, 443, 985, -962, -417, -814],\n [-666, -1300, 891, 1607, 710, -1335, 699, 1453, -962, 300, 1219, 1812],\n [868, 492, 520, -35, -665, -836, -654, 303, 749, -251, -1221, 985],\n [757, 492, 495, -398, 1086, -389, -14, 150, -618, 444, 732, 255],\n [1411, 199, 32, -1471, -336, 260, 647, -872, 107, 279, -545, -1543],\n [-1267, -431, -1266, 1089, -1763, 504, 308, 357, 1411, -834, -875, -152],\n [-418, -163, -1484, 157, -861, 167, 864, -150, 1590, 444, -1121, 129],\n [184, 1541, -2266, -1986, -432, 1400, -1381, 281, 325, -232, -609, -2182]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[24, -252, 180, 216, 204, -252, 204, 216, 12, -96, 0, -48],\n [34, -357, 255, 306, 289, -357, 289, 306, 17, -136, 0, -68],\n [36, -378, 270, 324, 306, -378, 306, 324, 18, -144, 0, -72],\n [-34, 357, -255, -306, -289, 357, -289, -306, -17, 136, 0, 68],\n [-24, 252, -180, -216, -204, 252, -204, -216, -12, 96, 0, 48],\n [44, -462, 330, 396, 374, -462, 374, 396, 22, -176, 0, -88],\n [4, -42, 30, 36, 34, -42, 34, 36, 2, -16, 0, -8],\n [-30, 315, -225, -270, -255, 315, -255, -270, -15, 120, 0, 60],\n [2, -21, 15, 18, 17, -21, 17, 18, 1, -8, 0, -4],\n [38, -399, 285, 342, 323, -399, 323, 342, 19, -152, 0, -76],\n [10, -105, 75, 90, 85, -105, 85, 90, 5, -40, 0, -20],\n [-50, 525, -375, -450, -425, 525, -425, -450, -25, 200, 0, 100]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[32, 168, -272, -40, -8, 264, -152, 448, 88, 264, 568, 24],\n [-43, -211, 359, 53, 22, -346, 197, -599, -107, -339, -755, -26],\n [26, -188, -78, -16, -254, 22, 36, 298, -176, -132, 280, -118],\n [-22, 740, -190, -16, 658, 326, -316, -134, 592, 732, 88, 346],\n [31, -678, 107, 4, -649, -243, 266, 263, -556, -642, 80, -333],\n [-77, -6, 479, 76, 323, -399, 170, -997, 92, -210, -1144, 111],\n [25, 264, -271, -38, 95, 285, -184, 377, 170, 348, 518, 75],\n [-31, 855, -185, -13, 784, 348, -353, -227, 691, 831, 19, 408],\n [13, -212, 13, -2, -217, -59, 76, 125, -178, -192, 74, -109],\n [34, 267, -328, -47, 59, 333, -205, 494, 161, 375, 653, 63],\n [25, 500, -375, -50, 275, 425, -300, 425, 350, 600, 650, 175],\n [-4, -257, 138, 17, -179, -173, 135, -104, -191, -285, -203, -103]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[535, 675, 721, 1233, -831, -98, -193, 1442, 73, 506, 265, -1027],\n [-617, 181, -635, -20, -879, -357, -916, 26, -645, 778, 480, -384],\n [-95, -1313, -1024, -807, -128, -256, 1735, -2282, 1110, -751, 854, -1164],\n [245, -471, -340, -905, -49, -872, -813, -700, -367, 754, 397, 814],\n [1647, -1172, 887, 16, -425, -1167, 2187, -423, 1890, -367, 1961, -819],\n [377, -89, 120, 134, 103, 415, -316, 212, -585, 44, -958, 353],\n [869, 497, 799, -315, -715, -1193, 844, -835, 1102, 1316, 1579, -80],\n [-252, 587, 191, 437, 183, 654, 1497, -323, 871, -179, 211, -540],\n [-565, 691, 1, -202, 257, 1126, -94, -274, -726, 745, -1485, 1270],\n [-1200, 423, -241, -792, -691, -567, -172, -861, -292, -17, 1074, 173],\n [-582, -177, -727, -807, -142, -660, -734, -931, -228, 185, 468, 3],\n [-372, 81, -550, 9, 477, 924, 456, 7, 269, -54, -306, 425]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[1182, -1008, 1405, -620, -869, -769, 85, 740, -199, 218, 126, -551],\n [352, -990, -258, 1021, -563, 426, -153, 975, 174, -271, -234, -384],\n [575, -173, 1005, -1226, -1236, -678, 1033, 1484, 171, -487, -398, -1230],\n [-294, 572, -59, -344, 583, -287, -240, -590, 899, 445, 106, 921],\n [822, -835, 761, 557, 415, 575, 481, 951, 836, -1672, -34, -17],\n [2339, 446, 2438, -1017, -1114, -180, -495, 2310, 124, -761, -164, -925],\n [-384, -287, 27, 395, -937, 413, -64, 349, -824, -374, -404, -1607],\n [737, -1372, 318, 571, -798, 686, -644, 1514, -498, 85, -266, -677],\n [-414, 820, -954, 174, -459, -296, 2386, 48, -410, -1913, -347, -1075],\n [1013, 549, 1152, -1523, -1048, -744, -1097, 772, -564, 1705, -172, -125],\n [-963, -485, -650, 1741, 1390, 985, -1689, -672, 926, 834, 432, 529],\n [-217, -956, 229, 151, -334, -283, -378, 237, -141, 949, 283, -745]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[640, 137, 200, -140, -601, -329, 227, 79, 899, -154, 402, 668],\n [-498, -501, -35, -291, 530, 877, -711, 725, 1198, 816, 180, -523],\n [-600, -160, 470, -1284, -496, 654, 321, 489, 1050, 27, 232, -164],\n [931, -153, -331, 821, 178, -632, 159, -654, -498, 171, -26, 503],\n [793, 335, -114, 1058, 267, -364, -386, -35, -149, -16, 224, 574],\n [-666, -65, 132, -711, -184, 188, 540, -236, -685, -264, -325, -414],\n [1472, 833, -311, 1151, -434, -1357, 99, -357, -62, -1006, 125, 1237],\n [-342, -130, 512, -319, -43, 561, -17, 199, -12, 492, 305, -154],\n [1350, 393, -609, 1156, 69, -1148, 223, -671, -484, -695, -169, 963],\n [-562, 585, -96, -302, -31, 171, -296, 646, 451, -865, -196, -202],\n [1309, 104, 975, 636, -1002, -706, 420, -585, -395, 722, 1015, 1113],\n [225, 217, -32, -213, -68, 29, 325, 40, 283, -502, 2, 418]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1041, -382, -360, -321, -133, -80, 438, 72, -435, 1009, 525, -961],\n [558, -701, -148, -960, 663, -48, 31, 209, 102, 750, 533, -383],\n [-194, -10, 367, -184, -171, 103, -141, 353, 682, -340, -632, 590],\n [-162, 164, -5, 239, 638, 184, -468, -390, -545, 38, 814, -13],\n [1346, -181, -74, -82, -809, 100, 483, 361, -164, 986, 25, -793],\n [-128, -175, 234, -378, 573, 166, -417, 101, 264, -20, 201, 365],\n [73, -403, -114, -570, 1095, 61, -372, -172, -264, 427, 960, -169],\n [-143, 315, 469, 289, -285, 295, -344, 190, 359, -369, -410, 600],\n [185, -10, 122, -42, -768, -73, 367, 393, 522, -97, -847, 110],\n [-110, -555, 183, -945, 1351, 174, -645, 83, 273, 246, 723, 330],\n [540, 138, 385, 133, -628, 298, -56, 386, 305, 168, -386, 159],\n [-321, 369, 135, 478, -764, -58, 203, 97, 290, -557, -834, 327]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[86, 293, 317, -152, 345, -8, 268, 269, 286, 236, -165, -144],\n [631, 842, 746, -108, 764, 123, 777, 594, 400, 318, -509, -72],\n [785, 445, 235, 445, 648, -160, 214, -343, 280, 94, -473, 587],\n [-61, 221, -529, 556, -81, 143, -151, -701, -156, -290, 98, 512],\n [-304, 237, -324, 112, -363, 413, 111, 6, -355, -308, 243, -40],\n [866, 924, 786, -26, 702, 234, 898, 674, 214, 180, -568, 10],\n [887, 979, 760, 44, 773, 214, 890, 574, 267, 194, -594, 88],\n [-108, 764, -64, 59, -221, 725, 605, 430, -404, -332, 113, -159],\n [532, -337, 89, 348, 659, -760, -460, -803, 596, 352, -385, 628],\n [-62, -76, 593, -726, -94, 113, 371, 1075, -19, 208, -10, -770],\n [603, -161, 172, 384, 861, -778, -366, -822, 747, 442, -478, 676],\n [-117, -943, -124, -253, -602, -235, -499, 76, -371, -146, 233, -195]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-555, -454, 768, 214, -515, -315, -664, -582, 125, 222, 533, -415],\n [431, -270, 279, -838, -204, 817, -755, 505, 1018, -392, 230, 842],\n [215, -236, 32, -613, 556, 529, -72, 68, 68, -109, -121, 543],\n [-21, 243, 1204, -440, -216, 656, -1013, -8, 190, 1048, 311, 324],\n [-268, 347, 595, -526, 1011, 428, -397, -365, -326, 201, -81, 149],\n [47, 1005, -836, 4, 1234, 479, 659, 214, -786, 90, -507, -286],\n [-8, -48, 903, 304, -580, -1791, 180, -447, 257, -751, -357, 420],\n [-368, -897, 1714, -210, 132, -377, -494, -1184, -693, 1209, 116, 280],\n [106, -1255, -558, -108, -67, 602, 483, 10, -445, 802, 154, 53],\n [-368, -139, -2466, 190, 935, 710, 1045, 482, -253, -1130, 60, -967],\n [166, 823, -79, -74, 410, -112, 725, 447, -574, 639, -613, 333],\n [-894, 205, 779, -494, 648, 969, -1114, -395, -96, 626, 633, -460]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[699, -471, -354, 105, 585, -1139, -341, 212, 901, -147, 213, 325],\n [-377, 648, 620, 517, -1710, 309, 201, -44, -1489, -1268, 902, -1068],\n [28, -378, 556, 1441, 404, 1077, -194, 287, -466, 39, 7, -1226],\n [1262, 6, -664, -1819, -303, -170, -414, -959, 658, 2130, -685, -606],\n [-854, 75, 161, -24, -704, -259, 222, 111, -660, -320, -52, 461],\n [-543, -27, 820, -861, -1610, -57, 80, -1167, -832, -1124, 283, 534],\n [282, 873, 41, 411, -273, 44, -334, 283, -576, 526, 1005, -1070],\n [-298, 68, -132, -527, 38, -1280, -787, 396, 490, -226, -387, 1215],\n [-654, -846, -566, -57, -693, 605, -369, 591, -203, 790, -2297, 1158],\n [-768, -87, 625, -313, -379, 494, -553, -602, 429, 200, -763, 913],\n [-597, -533, 345, 729, 302, 289, 483, 264, -716, -818, 374, 30],\n [-1690, 46, 636, -515, 749, -16, 311, -139, 430, -551, -531, 1432]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-453, 53, 407, 749, 580, 1563, 350, 1167, -67, -676, 235, -531],\n [362, 296, 1333, -1052, -795, -1447, 292, -917, 915, -138, 403, 727],\n [-75, -446, 833, -516, -995, 877, -470, 1132, 1193, -1106, 187, -752],\n [212, -241, 49, -564, 593, 479, -638, 263, -382, -371, -451, -415],\n [834, 223, -43, -1095, -594, -197, -696, 849, 747, 36, 386, 243],\n [316, -454, 1401, -451, 32, -1153, 460, -798, -141, -742, -202, 274],\n [897, -153, 193, -58, 563, -627, 582, 87, -862, 71, -26, 251],\n [-552, 397, 491, -94, -985, 797, 134, 551, 1409, -616, 172, -989],\n [524, 556, -1096, -1343, -635, 776, -1258, 826, 834, 606, -46, -748],\n [908, -758, 1009, -889, -117, 335, -244, 1054, 26, -983, -12, -446],\n [645, -327, -661, -452, 183, 971, -780, 1087, -382, 455, 266, 69],\n [-494, 318, 237, -432, -1049, -1305, -318, -1008, 1243, -314, -244, 98]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[46, 258, 186, -67, 156, 130, -273, -45, 216, 72, 203, 236],\n [278, 24, 510, 372, 552, 460, -538, 170, 40, -272, -220, 12],\n [322, 486, 774, 199, 756, 630, -955, 65, 424, -104, 177, 436],\n [-11, -198, -99, 85, -72, -60, 164, 50, -164, -80, -177, -182],\n [25, -240, -51, 156, -12, -10, 127, 85, -196, -136, -248, -222],\n [-70, -120, -174, -36, -168, -140, 218, -10, -104, 16, -52, -108],\n [-172, -276, -420, -98, -408, -340, 522, -30, -240, 48, -110, -248],\n [229, -588, 177, 614, 300, 250, -3, 315, -468, -504, -754, -550],\n [273, 534, 705, 107, 672, 560, -898, 20, 460, -32, 265, 482],\n [285, -30, 501, 409, 552, 460, -512, 190, -4, -304, -277, -38],\n [-26, 12, -42, -42, -48, -40, 40, -20, 8, 32, 34, 12],\n [-119, -72, -243, -128, -252, -210, 275, -55, -68, 88, 36, -62]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[319, 83, 31, 405, 82, 151, 29, -81, -255, -267, 240, -354],\n [-979, 192, -696, -374, 587, -82, -598, -186, 474, 288, 1031, 1341],\n [-991, 874, -116, 443, -456, 540, 447, -727, -668, 313, 337, 377],\n [152, -1259, 205, -633, -712, 227, 592, -520, 1562, -665, 766, 423],\n [368, -366, 157, 547, -126, 633, 699, -544, 316, -374, 913, -545],\n [260, -10, 138, 109, -1440, -49, -34, -679, -547, -683, -375, -191],\n [182, -157, 92, -123, -949, -657, -715, 607, -932, 266, -1119, -72],\n [-253, 174, -83, -598, 135, 604, -273, -869, 729, -441, 37, 621],\n [-891, 94, -680, -73, -226, -681, -339, -48, 14, -103, 1221, 1288],\n [-1326, 1462, -549, 252, 432, 181, 396, -915, -286, 14, 845, 868],\n [685, -552, 682, -602, -830, -193, 217, 296, 120, 63, -1799, -768],\n [-120, -222, -398, -409, 1580, 358, 48, -328, 1603, -257, 1353, 566]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[690, 573, -1082, -73, 318, -734, -1406, -1261, -899, -446, -646, 279],\n [633, -574, -984, -25, 495, 794, -905, -329, -151, 850, 402, 638],\n [-406, 458, 1507, 180, 307, -515, 601, -248, 362, -680, 378, -761],\n [-991, 505, -182, 369, -366, -1765, 99, -1427, -645, -1723, -1409, 364],\n [111, -721, -2411, 971, -620, 1188, -1045, -1173, 13, -992, 336, 512],\n [753, 749, 128, -844, -49, -991, 503, 544, -691, -481, -1199, -606],\n [343, 144, -151, -1075, -158, -1558, -256, -1194, -893, -824, -934, 556],\n [192, 1532, 989, 1362, 1150, 446, -984, -54, -144, 398, 1018, -1496],\n [-306, -37, 1236, 154, 50, 897, 1095, 1396, 775, 844, 892, -646],\n [1430, 785, -799, -1051, -326, -263, -1184, -640, 943, -544, 366, -26],\n [-1159, 1302, -518, 174, -1899, -41, 441, 982, 1297, 252, -336, 248],\n [921, -221, -139, 167, 929, 540, -1085, 615, -758, 903, -41, -685]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[85, -95, -270, 215, 75, 155, 35, 155, 75, 145, 55, 150],\n [222, -98, 180, 238, -50, -118, 94, -118, 302, 50, 242, 296],\n [92, -154, -594, 343, 165, 346, 37, 346, 45, 269, 26, 195],\n [-307, 135, -252, -328, 70, 165, -130, 165, -418, -68, -335, -409],\n [40, 44, 396, -90, -110, -236, 18, -236, 98, -126, 84, 14],\n [99, 19, 450, -29, -125, -271, 43, -271, 179, -115, 149, 92],\n [-26, 70, 324, -154, -90, -190, -10, -190, 6, -134, 10, -72],\n [-100, 180, 720, -400, -200, -420, -40, -420, -40, -320, -20, -220],\n [-136, 94, 90, -219, -25, -46, -57, -46, -161, -105, -126, -203],\n [-17, 77, 396, -168, -110, -233, -6, -233, 26, -156, 27, -67],\n [-151, 121, 198, -279, -55, -109, -63, -109, -167, -153, -129, -236],\n [-46, -10, -216, 16, 60, 130, -20, 130, -84, 56, -70, -42]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[447, -847, 115, -1115, -251, -407, -986, 146, -141, 388, 390, -558],\n [31, 237, -78, 463, -142, 402, 225, -99, 126, -33, -138, 206],\n [501, 51, -444, 4, -833, 237, -391, 334, -65, -138, 229, -126],\n [79, 713, -561, 846, -366, 4, 386, 369, -384, -687, -277, 10],\n [-62, 134, 128, 662, 340, 124, 338, -274, -188, -46, -592, -12],\n [94, -508, 109, -839, 110, -638, -541, 178, -244, 112, 239, -436],\n [373, -681, 120, -805, -186, -246, -763, 55, -98, 345, 244, -430],\n [-631, 541, 4, 266, 531, -313, 705, 68, 15, -380, -31, 318],\n [-142, 787, -397, 997, -63, 62, 647, 190, -279, -634, -396, 166],\n [-200, -115, 134, -119, 618, -833, 36, 79, -576, -229, -344, -426],\n [951, 149, -644, 659, -1336, 856, -453, 231, -104, -119, -98, -138],\n [-113, 318, -298, -352, -562, 303, 43, 310, 564, -76, 806, 484]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[43, 345, 198, -809, -353, -807, -519, 507, 333, -426, -472, -199],\n [-184, -63, 53, 184, -357, 388, 155, 389, -410, 54, 212, 1],\n [-757, 694, -508, 579, 529, 1353, 1193, 501, 613, -524, -309, -4],\n [-149, -839, -66, -459, -1545, -755, -551, 873, -1019, -86, 880, -985],\n [-131, 482, -272, -157, 521, -24, 253, -50, 799, -456, -450, -136],\n [643, 243, 75, -700, -290, -939, -618, -85, -269, -520, 347, -854],\n [-696, -270, -315, 647, 573, 753, 687, -137, 698, 406, -468, 721],\n [-38, -919, -56, -225, -356, -863, -522, -224, 10, 452, 104, -10],\n [792, 870, 49, 431, 1253, 623, 367, -1119, 90, -178, 98, 113],\n [75, -609, -48, -56, -307, -449, -301, -174, -267, 272, 332, -168],\n [872, -453, 678, -475, -492, -1063, -1130, -466, -824, 528, 332, 144],\n [-158, 519, -138, 297, 1232, 464, 502, -585, 1170, 28, -885, 752]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1025, -578, 531, 214, 759, -573, -268, 948, -862, 1205, -321, 874],\n [121, -823, 219, 190, 34, 1432, 564, 620, -157, -329, 191, -1648],\n [59, -1, 438, 6, 515, 169, -685, -94, -815, -85, -524, -208],\n [-95, 503, -492, -251, -609, -1057, 491, -162, 1087, 537, 593, 1335],\n [372, -237, 257, -25, 768, -794, -677, 84, -421, 178, -124, 615],\n [510, -415, 1001, -103, 1181, 646, -1395, 243, -1829, -197, -1083, -748],\n [-324, -485, 232, 1670, 778, 399, 184, -25, -1169, 129, -551, -785],\n [543, -19, -152, -1288, -923, 265, 597, 680, 1167, 317, 750, 244],\n [-80, 545, -43, -204, 250, -1486, -537, -479, 240, 416, 94, 1548],\n [526, -137, 172, -950, -342, -193, 394, 673, 841, 755, 759, 603],\n [-399, 493, 233, -57, -252, 504, -62, -319, -234, 73, -289, -243],\n [-843, 723, 403, 67, -367, 522, 312, -498, 86, 490, 70, -166]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[94, 394, 350, 267, -301, 549, -236, 842, 484, 115, -647, -170],\n [138, 453, 418, 297, -338, 613, -219, 920, 501, 107, -733, -150],\n [276, 271, 410, 88, -449, 656, -139, 948, 261, -190, -568, 30],\n [-440, -583, -34, -722, -359, 126, 453, -359, 496, 383, 248, 463],\n [268, 1051, 359, 1065, 359, 42, -305, 410, 106, 274, -863, -530],\n [-2, -756, 52, -967, -499, 181, 666, -312, -154, -287, 459, 836],\n [390, 1152, 166, 1323, 691, -279, -512, 241, -299, 68, -677, -767],\n [588, 663, 745, 351, -311, 578, 293, 675, -55, -199, -867, 299],\n [512, 500, -34, 654, 644, -564, -24, -424, -978, -428, 54, -180],\n [-554, -439, -642, -125, 62, -109, -841, 271, 468, 154, 467, -687],\n [-230, -292, -199, -212, -443, 529, -766, 1055, 600, -118, 0, -435],\n [-250, 731, -110, 951, 664, -417, -439, -203, 320, 692, -397, -781]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[675, -138, -276, -456, 300, 1397, 242, -40, -542, 592, 405, -5],\n [-199, 146, -58, -140, 244, 313, 370, 166, 286, -52, 253, 239],\n [565, -1030, -605, -832, 88, 293, -508, -412, -682, 465, -625, -957],\n [204, -864, -433, -1050, 422, 160, -124, -50, -222, 719, -258, -828],\n [664, -409, -103, -621, 38, 293, 58, 428, -296, 1047, 138, -498],\n [615, -535, -481, -171, -762, -383, -172, 475, -18, 0, -726, -494],\n [-3, -811, -618, -419, -554, -1033, -262, 329, 382, -349, -1094, -732],\n [891, -648, -368, -888, 22, 575, 100, 488, -384, 1144, 21, -657],\n [486, 55, -51, 7, 272, 1224, -108, -579, -786, 212, 337, 135],\n [348, -66, -199, 307, -529, -17, -217, -53, -201, -376, -395, -11],\n [992, -809, -280, -510, 281, 1069, -875, -1118, -1601, 792, -222, -832],\n [12, -207, 106, 26, -269, -801, -301, 114, 29, 138, -322, -356]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[478, -390, 295, 143, -108, 431, 898, -1148, 131, 449, -265, -649],\n [-338, 121, -446, -747, 768, 368, -272, 426, -13, 381, -336, 411],\n [403, 55, 1128, 543, -151, -276, -169, -82, -334, -635, 507, 247],\n [125, -1184, 713, 995, 278, 1169, 475, -1052, 339, 331, -202, -322],\n [-272, 581, -213, -880, -490, -2149, -691, 1725, -347, -1222, 40, 610],\n [611, -427, 241, 334, 480, 482, 391, -814, 560, 893, -720, 392],\n [886, -178, 740, 660, -1197, 87, -171, -476, 1424, 585, 591, 531],\n [90, 500, -237, 264, -303, 779, 808, -862, -385, -177, 330, -827],\n [11, -213, -139, 505, -31, -202, 867, 64, 36, -1297, -845, 426],\n [210, -1313, 395, 168, -239, -319, 52, -460, 733, 884, -391, -397],\n [693, 165, -74, -373, -416, -564, 54, -281, 718, 945, -224, 222],\n [-213, 481, -319, 437, -72, 983, -402, -3, 168, 232, 636, 144]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[118, -241, 1319, -4, 254, 265, -812, -341, 1362, -743, 295, -1474],\n [-962, -231, 29, 666, -322, -519, 110, -875, 280, 99, 89, -386],\n [-174, -113, -219, -588, 84, 361, -876, -31, -228, 240, -616, 58],\n [-7, 90, 351, 536, -70, -302, 495, -99, 358, -325, 527, -253],\n [-400, -5, -669, 373, -202, -356, 695, -167, -573, 462, 20, 644],\n [574, 778, -862, -260, -334, -208, 480, 1000, -1213, 2, -186, 1344],\n [12, -101, 27, -596, 440, 647, -928, 161, -77, 97, -337, 26],\n [-372, 116, -92, 431, -254, -391, 279, -222, -61, -58, 156, 72],\n [93, 239, 598, 488, 296, 23, 191, 166, 425, -579, 773, -207],\n [49, -335, 296, -538, 512, 681, -869, -46, 306, 94, -244, -377],\n [503, -258, 539, -662, -104, 236, -713, -55, 642, -196, -490, -907],\n [-1089, 42, -623, 945, -204, -587, 734, -547, -513, 375, 341, 641]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-691, 928, 401, 1104, -552, 515, -90, -252, -119, 875, 339, 344],\n [-1286, -63, 1015, 252, -782, 410, -100, 617, -90, 341, 360, 765],\n [937, 75, -251, 1070, -108, -336, -449, -323, 994, 940, -1128, -57],\n [-878, -60, 157, 1919, -718, -538, 597, 144, -602, 1791, -1155, 384],\n [-1013, 583, 994, 22, -522, -60, 787, -60, 318, -423, -165, 751],\n [1463, -15, -537, -44, 318, -9, 862, -716, 135, -133, -498, -569],\n [327, 380, 476, -975, -670, 549, -687, -1207, -439, -1863, 14, 1269],\n [-537, -375, 555, -506, -549, -130, -1161, 682, 235, -645, -618, 1330],\n [-562, 1184, 151, 498, 172, -2463, 209, 608, -192, 1601, -1488, -504],\n [684, 1446, 584, -1285, 694, -1292, -335, 830, -1444, -690, 272, 461],\n [-188, -1744, -673, -44, 98, 1854, -1149, -355, -801, -733, 1240, -6],\n [-399, -504, 1349, 1492, 7, 59, -458, 479, -236, 21, -119, 1447]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[400, 600, 575, -150, 350, -475, -125, 600, -550, -250, 250, -325],\n [-320, -480, -460, 120, -280, 380, 100, -480, 440, 200, -200, 260],\n [336, 504, 483, -126, 294, -399, -105, 504, -462, -210, 210, -273],\n [-352, -528, -506, 132, -308, 418, 110, -528, 484, 220, -220, 286],\n [112, 168, 161, -42, 98, -133, -35, 168, -154, -70, 70, -91],\n [96, 144, 138, -36, 84, -114, -30, 144, -132, -60, 60, -78],\n [288, 432, 414, -108, 252, -342, -90, 432, -396, -180, 180, -234],\n [-176, -264, -253, 66, -154, 209, 55, -264, 242, 110, -110, 143],\n [160, 240, 230, -60, 140, -190, -50, 240, -220, -100, 100, -130],\n [-384, -576, -552, 144, -336, 456, 120, -576, 528, 240, -240, 312],\n [320, 480, 460, -120, 280, -380, -100, 480, -440, -200, 200, -260],\n [336, 504, 483, -126, 294, -399, -105, 504, -462, -210, 210, -273]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-255, 163, 154, 11, -371, 347, -99, -240, 24, 416, 29, -138],\n [-72, -347, -696, -396, -718, 92, -332, 352, -530, 590, -52, 202],\n [29, -478, -463, -617, -923, -709, -565, 199, -20, 241, -406, 50],\n [215, 465, 930, 105, 860, 406, -691, -1040, -743, -183, 286, 866],\n [67, 15, 268, 63, 103, -415, 75, -92, 418, -355, -122, -201],\n [8, 13, -185, -86, 129, 253, -20, 65, -213, 121, 17, 217],\n [165, -23, 313, -53, 100, -384, -319, -281, -61, -266, -41, 170],\n [194, 150, 232, 234, 773, 1, 256, -48, 75, -493, 99, 124],\n [174, -209, -51, -804, -181, -841, -674, -221, 391, -217, -727, 373],\n [-40, 388, 404, -54, 574, 318, -20, -450, 276, -117, -155, 223],\n [288, 29, 28, -310, 552, 154, -608, -326, -770, -65, 19, 931],\n [-57, 75, -586, -497, 366, 500, 89, 234, 101, 230, -379, 431]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-374, 276, 178, 389, 52, -298, -570, 208, 490, 205, 324, 532],\n [-184, -60, -196, 52, 83, 352, -132, -208, 158, 38, 225, 35],\n [-663, 369, 154, 557, 112, -221, -856, 218, 794, 354, 561, 783],\n [75, 45, -36, 534, 138, -207, -690, -342, 216, -345, 519, 249],\n [86, 192, 434, -297, -215, -574, 462, 688, -200, 277, -605, 1],\n [-211, 219, 196, 250, 6, -329, -350, 230, 296, 145, 145, 367],\n [524, -294, -342, 363, 177, 164, -406, -860, -224, -781, 477, -265],\n [787, -39, 224, 258, -41, -767, -142, -166, -454, -687, -74, -186],\n [-57, 207, 246, 251, -16, -467, -312, 230, 182, 38, 79, 305],\n [-686, 258, -28, 518, 162, 86, -832, 4, 784, 308, 656, 680],\n [-200, 240, 368, -242, -169, -384, 320, 696, 42, 460, -447, 163],\n [-197, -237, -458, -75, 137, 817, 0, -490, 92, -10, 290, -166]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[57, 163, 6, 75, 30, -143, -92, -118, 65, -15, 26, -61],\n [-134, -345, -6, -152, -86, 262, 197, 237, -114, 36, -33, 96],\n [-230, -63, 102, 76, -362, -578, 71, -153, 342, 72, 333, -492],\n [401, 552, -84, 149, 452, 149, -347, -201, -147, -117, -255, 309],\n [260, 558, -12, 224, 212, -292, -326, -342, 108, -72, -18, -48],\n [25, -54, -24, -47, 64, 181, 23, 81, -99, -9, -81, 129],\n [153, 192, -36, 45, 180, 93, -123, -57, -75, -45, -111, 141],\n [67, -294, -96, -221, 232, 775, 137, 375, -417, -27, -327, 531],\n [100, 406, 36, 208, 4, -484, -222, -334, 236, -24, 134, -256],\n [102, -183, -90, -168, 246, 666, 75, 291, -366, -36, -303, 480],\n [-276, -511, 30, -186, -258, 152, 305, 277, -32, 78, 79, -50],\n [-233, -268, 60, -53, -284, -189, 175, 61, 139, 69, 187, -245]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[19, -550, -525, -148, -162, -345, -243, 477, 353, -299, -483, 258],\n [-513, -203, 451, -725, 395, 497, -497, 63, -865, 809, 1396, 325],\n [-522, 239, -468, -314, 45, 96, 581, 156, 204, 904, 852, -818],\n [-781, -1466, 318, 309, -23, -666, -129, 1252, -693, -492, -785, 875],\n [216, -508, 1506, 829, -262, 802, 80, -391, -1485, -559, -876, 1058],\n [943, 538, -671, -820, -309, 493, 1291, -376, 123, -301, 639, 12],\n [-609, 61, 1043, 206, 149, 491, -928, -47, -731, 903, 449, 76],\n [616, 158, -189, -731, -149, -30, 1099, 55, 172, -969, 109, -1280],\n [-136, -63, 419, -384, -171, 565, -37, 107, 63, -48, 260, -597],\n [-669, -885, -708, 581, 335, 88, -368, -351, -305, 906, -7, 1359],\n [275, 887, -375, -1626, 75, -515, -243, 814, 542, 222, 1454, -987],\n [203, -453, 1305, 1081, 61, 1548, 437, -1525, -1868, 10, -301, 1566]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-145, 214, -541, -455, 684, -265, 420, 44, -324, -652, -70, -27],\n [-590, 1071, 612, 337, -363, 287, -5, 316, 598, -129, -1125, 1385],\n [584, 23, -425, -393, 172, -59, 555, -1226, -467, -235, -282, 84],\n [439, -262, -238, -48, -471, -53, 56, -621, -514, 393, -261, -141],\n [23, -5, 877, 220, -959, 344, -387, 436, 528, 629, -157, 384],\n [-61, 112, 142, -104, 574, 80, 144, -14, 414, -442, 395, 21],\n [451, -1014, 139, -58, 97, 24, -310, 98, 141, 336, 1360, -1152],\n [31, 373, 196, 330, -51, 203, 57, -623, 251, -8, -396, 531],\n [-353, 77, 146, -583, -353, -153, -11, 1362, -90, -45, -190, 104],\n [-734, 579, 11, -516, 354, -181, 191, 1367, 140, -656, -308, 443],\n [566, -879, 148, -911, -184, -82, 83, 505, -126, 134, 975, -877],\n [-447, 510, -208, 810, 741, 53, -80, -513, 294, -355, -149, 305]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[264, -318, -1000, -642, -2, -7, 206, -955, 876, 677, 155, 777],\n [337, 412, 1039, 61, 24, -34, 409, -964, -571, -543, -516, 514],\n [40, -311, -705, 389, -1, -863, -618, -452, 1037, 239, 660, -691],\n [43, -125, -148, 918, -387, -310, -372, -533, 595, -428, 909, -1064],\n [88, -60, 1426, 263, 7, -536, 605, 303, -473, -894, -859, -453],\n [-149, -1548, -1836, 321, 127, -516, -516, 466, 1201, 1667, 239, -330],\n [-110, 836, -1373, -1087, 219, -223, -1573, 1693, -943, -318, 1587, 841],\n [-289, 354, 1106, -368, 249, 974, 2490, 360, 460, 430, -2036, -584],\n [30, 680, 1028, -644, -140, 397, 1468, -49, -511, -817, -931, 434],\n [-215, 543, -1516, -572, 23, -183, 5, -676, 795, 579, 645, 330],\n [518, -406, 838, 806, -207, 212, -3, -51, -889, -327, -219, 299],\n [724, -585, 27, -335, 69, -305, -666, 446, -898, -151, 122, 1334]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1123, 347, 263, 439, 1335, 132, 551, 487, 176, -429, -455, -1117],\n [-447, 909, 238, 583, 295, -268, 316, 1375, 599, 204, 567, 31],\n [904, -484, -948, 1038, -288, -667, -1875, 649, 936, 635, 645, 312],\n [608, 360, -314, -156, -337, 361, -370, -635, 231, -379, 349, 548],\n [267, 180, -154, -821, -100, 406, 342, -1271, -879, -257, -312, 367],\n [-487, -1010, 919, -280, -211, 208, 733, -11, -49, -100, -779, -751],\n [287, 151, -866, -413, 151, -743, -249, -374, -1557, 1031, -58, 649],\n [563, 273, -634, -542, -321, 328, -427, -1251, -351, -672, 480, 705],\n [-215, -1089, 12, -456, -420, -250, -62, -451, -582, -248, 18, -137],\n [-737, -805, 852, -17, 0, -52, 701, 521, 52, -2, -519, -803],\n [-651, 611, 1195, -818, 134, 770, 1913, -307, -507, -301, -808, -273],\n [-165, -453, 729, -545, -559, 266, 751, -221, -190, -183, -283, -71]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-477, 104, -527, 589, 210, -802, 1285, 295, 1067, 565, -593, -1305],\n [31, -52, 376, -499, 773, 228, -232, 436, 796, 647, 91, 645],\n [1137, -741, -661, 286, 63, -277, -1250, -1545, -850, -4, -455, 33],\n [-212, 2, 2005, 1188, -281, -112, 510, 1116, -109, 422, -151, 977],\n [172, 1042, -162, -423, 1091, -605, 298, -206, 599, 1496, -308, 535],\n [742, 133, -466, -1284, 323, -339, 240, -714, 360, -721, 659, -299],\n [-634, -1321, 1166, 1868, 268, 1324, 710, 671, -449, -1973, 888, -187],\n [499, 518, -2018, -1216, 48, -1534, -190, -1133, 587, 667, -307, -1188],\n [-617, 388, -10, 946, -831, 1266, -1226, 1295, 102, -631, -493, -841],\n [-790, -770, -516, -397, -2382, -207, -117, 2076, -102, -1309, -1014, 73],\n [-222, -333, 554, 2232, 257, 470, -610, 286, 585, -22, -1128, -1675],\n [-978, -208, 848, 1332, -556, 1649, 162, 1068, 114, -1207, 105, -1228]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1405, 294, 362, -1041, -18, 90, 733, 19, -947, -335, -49, 460],\n [-703, 727, 1397, -474, -1553, -596, 1215, 367, 831, 218, 35, -1708],\n [-826, -385, -537, -487, -185, 1056, 1127, -1935, 1373, -502, 326, 960],\n [-532, -902, -268, 1093, 1381, -1096, -1746, 910, 384, 62, 110, -7],\n [1070, -1351, -922, -671, 475, -172, 3, -926, -968, -19, 816, 718],\n [-426, 672, 529, 1000, -856, -141, -435, 194, -511, 204, -143, -153],\n [-222, -1130, -552, 231, 1047, -304, -607, 407, -1587, 393, 662, -31],\n [289, -298, 223, -354, 906, 880, 44, -761, 349, -1630, 585, 421],\n [-1007, -689, -684, 516, 1313, 1026, -277, -219, -764, -742, 150, -16],\n [-740, 78, -80, -64, -1165, -817, 602, -385, 1219, 1404, -154, 359],\n [709, -1184, -1023, -623, 315, 124, 293, -675, -1054, -180, 372, -281],\n [-113, 845, -19, 1334, 236, 874, -1097, -287, 33, -693, -479, 1286]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[886, -66, 572, -464, 727, -358, -318, -218, -268, -25, -162, -362],\n [-982, -225, -1192, -191, -1008, -32, -645, 560, -113, -1189, -52, 425],\n [701, -459, 232, -220, 739, 716, 273, -812, -790, 246, 96, 860],\n [-724, -94, -749, 50, -685, 123, -35, 344, -123, -392, 44, 268],\n [111, -470, -426, 197, 75, 57, 487, 17, -180, -118, 559, 445],\n [624, -566, -247, -744, 437, -48, -434, -187, -978, -659, -49, 358],\n [132, 511, 923, 581, 286, 96, -39, -381, 1227, 503, -55, -155],\n [811, -308, 198, -603, 604, -374, -544, -144, -419, -520, -84, -85],\n [417, -15, 355, 118, 387, -138, 197, -131, 186, 242, 167, -138],\n [433, 226, 793, 371, 538, 230, 488, -457, 371, 854, 77, -79],\n [102, 103, 38, -357, 11, -291, -26, 233, -474, 145, -241, -539],\n [1045, -313, 675, -30, 1033, 317, 298, -774, -229, 395, 226, 438]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-10, -33, -33, 142, -45, 120, 84, -13, -141, -79, 124, 24],\n [95, 243, -39, -738, 216, -717, -328, -135, 799, 398, -661, -87],\n [-20, 39, 459, -626, 225, -390, -532, 359, 523, 367, -522, -162],\n [-110, -270, 102, 756, -216, 762, 304, 198, -838, -404, 682, 78],\n [35, 33, -297, 218, -90, 75, 256, -257, -139, -136, 171, 81],\n [50, 84, -240, -8, -18, -114, 120, -232, 84, -10, -26, 42],\n [-70, -75, 549, -358, 153, -96, -452, 481, 209, 227, -276, -144],\n [105, 204, -366, -256, 45, -405, 68, -386, 388, 117, -257, 33],\n [-35, -111, -93, 458, -144, 393, 264, -29, -459, -254, 401, 75],\n [75, 123, -375, 14, -36, -153, 200, -359, 103, -30, -17, 69],\n [55, 144, -6, -456, 135, -435, -212, -66, 488, 247, -407, -57],\n [25, 51, -75, -82, 18, -111, 0, -83, 111, 40, -79, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-188, -62, 86, 518, 849, 17, -180, 211, 651, -179, -776, -23],\n [-108, 13, 93, 208, 233, -196, -418, -14, -317, -620, -387, -506],\n [-3, 617, -508, 326, -544, 671, -518, 117, -105, 740, 624, -899],\n [-493, -216, -809, 344, 1229, -117, -136, 807, 1036, 846, -283, 69],\n [-372, -328, -1054, -468, 386, -514, 350, 622, 90, 964, 546, 178],\n [-104, -394, 128, -222, 416, -596, 260, 8, -152, -532, -410, 302],\n [-549, -62, -1328, -213, 475, -722, 610, 604, -370, 723, 83, -637],\n [111, 413, -72, 442, -173, 874, -294, 94, 746, 825, 300, -46],\n [-143, -562, -774, -1076, -251, -687, 135, 379, -502, 659, 1218, 537],\n [-309, -436, -132, 283, 1237, -170, -360, 540, 1036, 145, -517, 491],\n [-159, -262, -448, -173, 371, -46, -72, 432, 544, 719, 379, 451],\n [13, -459, 368, -354, 244, -609, 330, -147, -237, -708, -364, 525]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-10, -90, 90, -190, -90, -70, 50, 20, 220, 210, -90, -200],\n [22, 198, -198, 418, 198, 154, -110, -44, -484, -462, 198, 440],\n [-26, -234, 234, -494, -234, -182, 130, 52, 572, 546, -234, -520],\n [3, 27, -27, 57, 27, 21, -15, -6, -66, -63, 27, 60],\n [-7, -63, 63, -133, -63, -49, 35, 14, 154, 147, -63, -140],\n [-23, -207, 207, -437, -207, -161, 115, 46, 506, 483, -207, -460],\n [-4, -36, 36, -76, -36, -28, 20, 8, 88, 84, -36, -80],\n [-3, -27, 27, -57, -27, -21, 15, 6, 66, 63, -27, -60],\n [18, 162, -162, 342, 162, 126, -90, -36, -396, -378, 162, 360],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n [-1, -9, 9, -19, -9, -7, 5, 2, 22, 21, -9, -20],\n [-15, -135, 135, -285, -135, -105, 75, 30, 330, 315, -135, -300]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-93, -406, -14, 413, 750, -317, -76, 763, 347, 542, -147, 784],\n [305, 36, -588, -219, -1012, 107, -428, -736, -790, -675, 397, -593],\n [-351, 890, 915, -520, -41, 664, 385, -392, 364, -169, -349, -655],\n [-113, 234, 321, -132, 85, 148, 239, -62, 202, 27, -127, -151],\n [-63, -582, -396, 597, 672, -309, -858, 969, -3, 462, -69, 1092],\n [54, -280, -405, 245, 19, -101, -665, 283, -281, 11, 86, 395],\n [231, -786, -721, 522, 235, -570, -415, 534, -214, 267, 221, 745],\n [-498, 624, 878, -156, 574, 540, -82, 330, 542, 228, -514, 88],\n [-127, 208, 132, -59, 4, 235, -312, 34, -32, -65, -103, -7],\n [-158, 432, 292, -234, -156, 394, -180, -200, -28, -198, -126, -290],\n [-17, 378, 190, -315, -390, 283, 144, -473, -97, -306, 9, -536],\n [-44, -210, 93, 189, 457, -221, 251, 370, 316, 348, -94, 356]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[30, 48, -16, -258, -416, 432, 868, -42, 664, 548, 22, -562],\n [-734, -385, -75, -425, -625, 354, -371, -268, -136, -364, -1178, -230],\n [280, -137, 109, 393, -1, 242, 617, 278, 364, 632, 340, -584],\n [-93, 103, -51, -140, 119, -230, -437, -123, -288, -398, -85, 427],\n [-277, -285, 25, 298, 295, -358, -1161, 31, -858, -710, -445, 479],\n [27, 8, 4, 8, -6, 20, 70, 12, 47, 54, 39, -39],\n [-89, 557, -189, -767, 11, -318, -239, -436, -55, -562, 55, 817],\n [327, 585, -85, -180, 565, -642, -407, -141, -302, -478, 679, 995],\n [-331, -86, -58, -247, -178, 12, -372, -173, -202, -354, -495, 145],\n [116, 335, -75, -387, -105, 34, 441, -158, 364, 128, 256, 84],\n [-316, -667, 119, 459, -251, 358, -173, 226, -160, 160, -664, -676],\n [-379, -237, -31, -266, -501, 386, 155, -125, 188, 62, -635, -411]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-222, 82, -212, -534, 177, 417, -1252, -787, -135, 779, 579, -760],\n [-1396, -1895, 136, 610, 678, -998, -558, -608, -849, 1717, -735, -417],\n [527, 94, -50, -616, 307, 58, 595, -724, -333, -531, -139, 748],\n [17, 804, -406, -90, -580, 332, 1037, -805, 362, -773, -101, -126],\n [-520, -509, -1781, 1632, -276, 382, 302, 245, 729, 497, -654, -484],\n [117, 31, -503, -1076, 84, 741, -717, -1328, -681, -431, 396, -632],\n [313, 642, 623, -1659, 1709, -1122, -933, -681, -852, -1225, 432, 1364],\n [504, 1608, 176, 61, 105, -295, 826, 371, 680, -1231, 829, 855],\n [-212, -355, 85, 1563, -530, -152, 947, 1385, 520, 333, -141, -70],\n [513, 513, 296, -747, 1106, -905, -574, 702, -384, -1687, 308, 1291],\n [354, -598, 610, -739, 643, -48, -449, -80, -792, 254, -187, 368],\n [421, -181, -1286, 788, 318, 1246, -708, 1060, 409, 472, -606, -549]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-539, -408, -2028, 116, 1207, -732, -339, -1008, -1045, -592, -135, 837],\n [-486, 86, 589, -527, 1245, 86, -222, -11, 667, 69, -230, 236],\n [-528, 142, 613, 591, 125, 289, 1436, -975, 1189, 97, 436, 299],\n [1379, 465, 803, -816, -322, 155, 145, 948, 557, -404, -430, -792],\n [549, 252, 937, -276, -679, 666, 86, 951, 318, 486, 127, -836],\n [210, 303, -934, 199, -604, 459, 807, 318, -893, -271, 1416, 98],\n [629, -1081, 520, -1021, 353, 170, -1160, 162, -286, -465, -963, -1076],\n [-369, -157, -641, -713, 1886, -662, -665, -398, 297, -880, -101, 1230],\n [-786, 490, 28, 265, 358, 676, 818, 156, 1188, 775, 1366, 1218],\n [-78, -1202, 946, -1255, 480, 856, -1182, 566, 180, -311, 514, -38],\n [-399, -1289, 93, 537, 210, -648, -979, -1326, 406, 358, -1644, -317],\n [-41, 1088, 1496, 428, -208, 2, 661, 579, 2129, 554, 632, 709]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-165, -671, -303, -88, -76, 166, 489, -37, -272, 17, -645, 128],\n [-283, -513, 335, 376, 268, 378, 279, 229, -464, -49, -539, -320],\n [-82, -542, -430, -216, -168, 52, 426, -114, -136, 34, -506, 240],\n [173, 403, -85, -156, -108, -218, -249, -99, 284, 19, 409, 120],\n [215, 514, -88, -183, -126, -269, -321, -117, 353, 22, 520, 138],\n [-142, -556, -232, -58, -52, 146, 402, -22, -234, 12, -536, 92],\n [-126, 426, 1026, 708, 528, 264, -450, 402, -204, -102, 342, -696],\n [32, -60, -196, -140, -104, -60, 72, -80, 52, 20, -44, 136],\n [290, 405, -505, -485, -350, -405, -180, -290, 475, 65, 445, 430],\n [-98, -6, 346, 272, 200, 156, -54, 158, -160, -38, -34, -256],\n [195, 678, 204, 9, 18, -213, -477, -9, 321, -6, 660, -54],\n [73, -42, -320, -241, -178, -123, 81, -139, 119, 34, -16, 230]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[158, -126, 378, 403, 298, -8, 447, 306, -88, 386, 242, 300],\n [-478, 25, -216, -368, 432, 472, -20, 295, 27, 144, 866, -400],\n [364, -154, 534, 629, -372, -508, -175, -454, -18, 282, -284, 748],\n [149, 91, -200, -136, -199, -94, 24, -45, 6, -350, -585, -156],\n [-399, 229, -746, -839, 301, 550, 117, 441, 40, -508, 91, -960],\n [194, -198, 598, 629, -114, -328, -103, -286, -28, 510, 222, 724],\n [207, 82, -152, -68, -419, -254, -192, -300, 31, -382, -743, -12],\n [-157, 83, -288, -332, 539, 454, 572, 695, -56, -98, 233, -548],\n [330, -124, 438, 525, -230, -384, -7, -256, -34, 230, -258, 580],\n [106, -194, 538, 531, 630, 144, 735, 606, -136, 666, 662, 348],\n [312, -148, 506, 587, -460, -532, -345, -588, 8, 262, -256, 756],\n [-4, -189, 506, 471, 254, -24, 127, 73, -49, 610, 664, 476]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-45, -207, 189, -225, -99, -99, 234, -45, 144, -234, -108, -27],\n [-95, -437, 399, -475, -209, -209, 494, -95, 304, -494, -228, -57],\n [30, 138, -126, 150, 66, 66, -156, 30, -96, 156, 72, 18],\n [25, 115, -105, 125, 55, 55, -130, 25, -80, 130, 60, 15],\n [90, 414, -378, 450, 198, 198, -468, 90, -288, 468, 216, 54],\n [-35, -161, 147, -175, -77, -77, 182, -35, 112, -182, -84, -21],\n [5, 23, -21, 25, 11, 11, -26, 5, -16, 26, 12, 3],\n [130, 598, -546, 650, 286, 286, -676, 130, -416, 676, 312, 78],\n [-45, -207, 189, -225, -99, -99, 234, -45, 144, -234, -108, -27],\n [-85, -391, 357, -425, -187, -187, 442, -85, 272, -442, -204, -51],\n [110, 506, -462, 550, 242, 242, -572, 110, -352, 572, 264, 66],\n [-70, -322, 294, -350, -154, -154, 364, -70, 224, -364, -168, -42]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[434, -209, -127, -1232, -598, -769, -1368, -1100, 823, 1143, 1003, -1770],\n [211, 164, 720, -7, 10, -90, 295, -63, -408, -329, 363, 738],\n [-688, 250, -444, 1204, 576, 542, -342, 1109, -327, -648, 4, -849],\n [-1168, -343, 107, -752, 193, 292, 758, -165, -1343, -355, 1287, 928],\n [-603, 750, 930, 636, -2, -791, 1285, -207, -30, -802, -606, 537],\n [-254, 122, 533, -108, 386, -459, 1316, -275, -1457, -45, 602, 1147],\n [-1309, -158, 1604, 77, 1055, -203, -95, -233, 717, -877, 356, -690],\n [-262, 221, 663, 357, 1726, 720, -730, 655, 418, -414, -674, -1144],\n [-185, -1651, -226, 232, -1450, -365, 562, -950, 889, -38, 761, 50],\n [554, -830, -477, 971, -324, -647, 1736, -441, -1233, 384, 358, 733],\n [-610, 1484, 450, 120, 94, 282, 500, 734, -160, -952, -1051, 833],\n [479, -1231, 643, 1010, -143, -1088, 1380, -881, -479, 43, 742, 893]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[262, 42, 45, 23, 720, -288, -255, 78, 28, -325, -153, -381],\n [-414, 477, 1, -242, -881, 48, 88, 284, -119, -216, 65, 681],\n [130, -506, -266, 441, 296, 363, 312, -425, 203, 591, 251, -454],\n [-318, 6, -558, 489, -408, 567, 588, -213, 231, 423, 531, 30],\n [-20, -112, -286, 322, 124, 240, 246, -172, 156, 226, 238, -218],\n [-80, -63, -752, 783, 385, 498, 553, -292, 389, 317, 584, -522],\n [22, -600, -261, 425, -66, 522, 441, -504, 184, 821, 315, -279],\n [-226, -18, -577, 543, -148, 510, 539, -224, 262, 367, 511, -135],\n [-258, 98, -104, 7, -576, 219, 218, 3, -5, 149, 161, 328],\n [206, 493, 772, -868, 203, -915, -879, 619, -402, -1012, -751, 350],\n [-134, 400, -846, 755, 586, 279, 422, -1, 397, -219, 567, -502],\n [186, -239, 114, -6, 283, -63, -97, -109, -6, 106, -105, -208]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-700, -559, -417, 501, 548, -404, -248, -73, 18, 22, 346, -206],\n [-616, -254, -110, 112, 472, -466, 134, 314, 28, 126, 374, -114],\n [-76, 12, -546, -168, 139, 847, 260, 498, 475, -783, 70, 576],\n [-756, -536, -560, 409, 615, -176, -111, 152, 171, -204, 397, -21],\n [736, 499, 305, -412, -567, 526, 141, -39, 7, -116, -389, 229],\n [-360, 103, -101, -347, 309, 103, 546, 791, 279, -249, 298, 312],\n [-452, -25, -135, -189, 372, -52, 408, 641, 214, -158, 326, 190],\n [-68, -166, -266, 181, 73, 180, -157, -114, 81, -196, 3, 53],\n [-172, -288, -110, 364, 119, -277, -332, -362, -129, 157, 38, -248],\n [-264, 417, 259, -734, 217, -26, 917, 1147, 251, -80, 319, 361],\n [-684, -117, -21, -120, 528, -471, 417, 663, 102, 105, 465, -3],\n [-480, -55, -25, -130, 375, -280, 345, 535, 105, 30, 335, 45]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[329, 737, -15, -188, -300, 397, -1063, 563, 400, -115, -266, 936],\n [-485, 538, 454, 579, -1114, -1100, 647, 314, -524, -120, 57, -301],\n [181, 38, 38, 117, -579, -278, 254, 377, 542, 453, 71, -119],\n [-1033, 166, 36, 227, -376, -580, 1303, -122, -296, -280, -479, -1137],\n [-326, 196, -247, 43, -787, -550, 133, 985, -322, -195, -658, 169],\n [74, 170, 343, 157, -21, 80, 375, -559, 658, 377, 452, -501],\n [-74, 681, 63, -35, -430, 111, -278, 335, 420, -65, -297, 221],\n [308, 120, -10, -212, 342, 612, -376, -248, 684, 196, 108, 128],\n [-415, -561, -62, 349, -527, -1055, 992, 350, -850, -4, -60, -541],\n [-351, -192, 195, 353, -349, -704, 859, -132, -402, 56, 181, -629],\n [-515, -433, -47, 263, -368, -757, 1192, 64, -348, 100, -104, -889],\n [-271, 115, 178, 135, -27, -115, 454, -344, 46, -6, 88, -475]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-168, -108, -96, -192, 288, 108, -288, -228, -192, 36, -60, -84],\n [-196, -126, -112, -224, 336, 126, -336, -266, -224, 42, -70, -98],\n [182, 117, 104, 208, -312, -117, 312, 247, 208, -39, 65, 91],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n [-84, -54, -48, -96, 144, 54, -144, -114, -96, 18, -30, -42],\n [-350, -225, -200, -400, 600, 225, -600, -475, -400, 75, -125, -175],\n [-266, -171, -152, -304, 456, 171, -456, -361, -304, 57, -95, -133],\n [210, 135, 120, 240, -360, -135, 360, 285, 240, -45, 75, 105],\n [-280, -180, -160, -320, 480, 180, -480, -380, -320, 60, -100, -140],\n [-238, -153, -136, -272, 408, 153, -408, -323, -272, 51, -85, -119],\n [-322, -207, -184, -368, 552, 207, -552, -437, -368, 69, -115, -161],\n [224, 144, 128, 256, -384, -144, 384, 304, 256, -48, 80, 112]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[593, 1021, 552, -74, -563, 436, 591, 488, -516, 320, -614, 277],\n [302, 464, 966, -634, 47, 329, 635, 487, -35, -321, -737, -85],\n [167, 761, 371, -242, -392, 65, 354, 401, -192, 134, -481, 97],\n [279, 363, 652, -302, -29, 372, 449, 296, -152, -140, -490, 127],\n [-327, -46, 47, -290, 103, -271, -64, 56, 259, -203, -71, -143],\n [-289, -257, -825, 570, -144, -253, -532, -391, -36, 334, 585, 215],\n [-427, -187, 1392, -876, 660, 721, 504, 169, 205, -1013, -799, 736],\n [403, 729, 1207, -910, -22, 239, 836, 731, 14, -368, -991, -333],\n [-102, 602, -428, -10, -529, -609, -115, 231, 27, 401, 1, -341],\n [415, -410, -731, 456, 12, -360, -287, -215, 42, 362, 602, -794],\n [267, 124, -111, -222, -69, -481, 76, 242, 199, 93, -13, -913],\n [-319, -43, -988, 436, -308, -655, -564, -235, 93, 443, 569, -200]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[606, -314, 477, -487, -1400, 45, 738, -116, 587, -43, -717, 35],\n [-1681, 204, -112, -255, 884, -461, 1102, -710, -191, -249, -163, 623],\n [-350, 559, -1475, 23, -242, -1122, -84, -686, 1794, 705, 437, -494],\n [774, -576, 1166, -19, 738, -741, 521, 275, -627, 496, -684, 940],\n [-1586, 401, -96, 62, 396, -289, 306, -760, -522, 242, 1409, -50],\n [685, -59, 220, -521, 949, -119, -1582, 1212, -2014, 158, -302, 685],\n [593, -153, 1079, -375, -501, 196, 227, 13, -1054, 489, -258, 41],\n [-997, 724, -287, -168, 1073, 157, -511, -151, -385, 316, 84, 420],\n [-548, -540, -301, -1321, 776, 399, -1160, 996, -1341, -593, -180, 1189],\n [-87, 490, -211, -1024, -410, -1105, 1422, -248, 349, -1732, -1245, 510],\n [-245, 5, 421, -487, 884, -277, -335, -93, -1069, -831, -541, 457],\n [401, -710, 893, -573, 771, -13, 255, 269, -200, -66, -923, 1153]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-106, -81, -675, -206, 288, -1608, 287, -96, 731, -870, -321, 1284],\n [652, 516, 1078, 206, -731, -931, 49, -705, 446, 516, -409, 422],\n [92, -80, -32, -744, 121, 685, -140, 486, -149, 47, 497, 235],\n [-248, -352, -146, -362, 594, -424, 822, 618, -185, -1307, 442, 63],\n [-774, -143, -1269, 538, 182, 230, -381, 2, -5, 112, -29, -94],\n [29, -222, -325, 559, 563, 424, -891, 590, -201, 372, -259, -1267],\n [-1119, -286, -1123, 495, 321, -834, 1047, -66, -44, -1367, 239, 350],\n [500, -145, 451, 127, 256, -235, -57, -227, 62, -70, -735, -459],\n [-303, -77, -358, 147, 92, 25, 83, 53, -66, -170, 93, -45],\n [641, 329, 700, -524, -616, 1120, -716, -311, -21, 1342, -25, 128],\n [-96, -365, -17, -888, 470, 352, 741, 548, -321, -1008, 561, 252],\n [70, 354, 656, 247, -809, -566, 764, -1153, 186, 59, -325, 610]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-843, 73, 422, 124, -254, -334, -766, -922, -1253, -913, -225, -191],\n [-610, -168, 864, -204, -833, -725, -1651, -155, -916, 89, -788, -924],\n [-244, -593, -358, 250, 411, -560, 650, -402, -77, -488, -153, 565],\n [-522, -231, 562, 648, -394, -117, 327, 600, 196, -921, 272, 799],\n [-61, 1608, 550, -570, 866, 626, 1245, 337, 398, 199, 1288, -602],\n [-7, 502, 994, -79, -708, 178, -499, 797, 548, 633, 464, -548],\n [-833, -540, 356, 1084, -685, -146, -186, -604, -343, -1336, 464, 995],\n [387, 14, -256, 143, -183, 192, -114, -1255, 638, 1120, 1039, -319],\n [-99, -777, 188, 928, -820, -35, -92, 417, 795, -185, 442, 806],\n [338, 339, 336, -321, -34, -322, 429, -1589, -60, 575, 189, 360],\n [1197, -184, -646, -1046, 491, -273, 18, 670, 805, 1999, -864, -927],\n [-61, 162, -304, -670, 553, -270, -434, -98, -543, 448, -496, -1159]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[676, 364, -56, 168, -10, 664, 310, 75, -119, 288, -548, -38],\n [-835, 51, -176, -579, -418, -377, 222, 289, -247, -207, 203, -331],\n [-33, -169, 172, 141, 224, -221, -208, -211, 141, -87, 249, 165],\n [-850, 238, -112, -666, -430, -310, 434, 283, -371, -202, 162, -396],\n [20, 444, -264, -336, -422, 432, 538, 381, -353, 152, -468, -354],\n [168, 672, 56, -252, -154, 476, 742, 119, -427, 140, -392, -266],\n [-570, -326, 184, -78, 150, -650, -298, -201, 137, -286, 586, 112],\n [457, -221, 296, 501, 498, -25, -366, -407, 305, 25, 159, 381],\n [-896, -198, -76, -438, -242, -622, -66, 128, -68, -294, 448, -170],\n [308, -563, -30, 477, 267, -135, -701, -172, 458, 21, 140, 347],\n [-331, -241, -352, -195, -344, -145, -184, 312, 38, -39, -13, -145],\n [-382, 257, 246, -267, 41, -219, 337, -116, -222, -155, 238, -101]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[64, 33, -121, 177, -25, -117, -105, 143, -24, -218, -156, 22],\n [-246, -121, -207, 579, -185, 136, -2, 213, 234, -768, 231, -361],\n [-630, 44, 496, 48, -230, 343, 469, -464, 838, -226, 139, -111],\n [350, 242, 83, -336, 140, -383, -152, -34, -203, 454, -635, 500],\n [-328, 341, 735, -435, -85, -29, 403, -645, 740, 390, -568, 486],\n [76, -352, -555, 450, 0, 196, -215, 468, -437, -468, 694, -569],\n [-254, -198, 206, -282, 20, 429, 279, -286, 66, 346, 663, -275],\n [-6, 0, -63, 126, -30, -27, -36, 72, 21, -162, -33, -30],\n [210, 363, 7, 171, -45, -540, -204, 121, 160, -256, -1013, 517],\n [-40, 176, 329, -318, 20, -74, 139, -292, 211, 352, -320, 305],\n [-196, 99, 203, 39, -95, 15, 141, -163, 358, -122, -170, 78],\n [212, 110, -79, -12, 50, -242, -155, 110, -143, 40, -350, 209]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[99, -155, -258, 258, 306, -591, -50, 277, 63, 177, -422, -391],\n [-145, -179, -458, 387, -385, 404, -154, -201, -465, -201, -1371, -507],\n [822, -638, -664, 372, 626, -421, 477, -577, -175, -314, -351, -979],\n [-237, -530, -244, -141, 367, -805, -140, 1198, -375, 866, -1042, -432],\n [-1059, -266, 442, -556, -958, 1331, -286, 438, -817, 381, -405, 811],\n [60, -1185, 163, -91, 1333, -847, 191, 208, -480, 781, 121, -124],\n [-39, 350, -366, -213, -375, 809, -35, -807, -652, -351, -2027, -610],\n [-270, -1085, 568, -574, 1706, -951, 354, -115, -126, 1095, 895, 399],\n [-563, -963, -320, 687, 303, 6, -68, -523, -319, 199, -723, -229],\n [1505, 613, -932, 186, -911, 531, 712, -626, 449, -1469, 531, -955],\n [109, -131, -982, 685, -563, -138, 347, -252, 712, -464, 92, -663],\n [-109, 374, -538, 1567, -146, -1287, -522, 583, 1277, -184, 265, -304]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[59, -71, -276, 229, -224, 94, -83, -104, 139, 464, 279, 278],\n [-299, 581, -471, -151, -229, 803, -658, 407, 92, 538, 171, 112],\n [328, -512, 476, 48, 388, -724, 620, -460, -180, -632, -128, -152],\n [61, -389, 368, 160, -84, -605, 446, -44, 56, -323, -315, -121],\n [-230, -340, 585, 154, -417, -753, 479, 435, 207, -464, -812, -336],\n [-264, 16, -86, 219, -594, -7, -93, 422, 307, 363, -224, 67],\n [-485, 375, 235, -264, -263, 138, -199, 765, 83, -281, -663, -399],\n [380, -500, 390, 57, 434, -649, 577, -550, -199, -547, 4, -83],\n [-490, 350, 172, -189, -364, 145, -215, 772, 141, -151, -622, -331],\n [514, -106, -228, -72, 700, 154, 32, -836, -332, 10, 746, 254],\n [271, -309, 307, -34, 401, -428, 395, -395, -195, -479, -11, -109],\n [417, -153, -294, 93, 378, 114, 15, -678, -159, 246, 681, 336]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-184, 605, -824, 2, -868, -398, -219, 351, 85, -177, -657, 231],\n [34, -190, 16, 1050, -1007, 463, 463, 478, -891, 1178, 1079, -1029],\n [-11, 22, 1684, -337, 1316, 40, 560, -978, -45, -180, 311, -63],\n [1062, -698, -104, 655, -908, 209, -852, 975, -1300, 1550, 476, -25],\n [-643, 792, 981, 411, 104, 98, 700, -823, -532, 35, -56, -395],\n [369, 1325, -289, 324, -814, -391, -595, 525, 657, -288, 411, 611],\n [467, 116, -214, -914, 326, -682, -338, 282, 1048, -741, -231, 712],\n [-812, -1140, 76, 351, 21, 201, 1322, 10, -631, 132, 11, -1293],\n [629, -655, -604, -722, 372, -52, -498, 409, 850, -175, 264, 394],\n [-74, 1410, 872, 834, -46, -564, -709, 76, -61, -1043, -568, 1107],\n [-931, 590, -90, 222, 78, -146, 845, -204, 883, -1150, 95, -331],\n [900, 70, -824, 233, -1493, 105, -376, 942, -341, 1528, 1027, -381]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-236, -755, -655, -273, 297, -277, -728, 355, 66, -258, 84, -335],\n [-439, 707, 373, 744, 18, 505, 1361, -892, -75, -432, 204, -331],\n [-57, 364, 615, 177, -103, -230, 457, 180, 241, 397, 231, 249],\n [657, 54, 164, -201, -280, 186, -351, -33, -625, 576, -345, 673],\n [37, 130, 22, 530, -368, 798, 24, -501, -642, 711, -230, 330],\n [-179, 493, 215, 274, -346, 295, 169, 50, 737, 244, -98, -147],\n [-620, -654, -215, 583, 79, 156, -251, 47, -525, 788, 359, 73],\n [-996, -421, -350, 256, 526, -413, 287, 166, 623, -684, 607, -878],\n [-236, -1063, -413, -379, 519, -821, -734, 681, -248, 22, 418, -21],\n [471, 322, 642, -76, -273, -142, 76, 203, -214, 735, -55, 715],\n [271, -373, -239, -640, -64, -479, -1027, 858, 589, 198, -166, 75],\n [106, -10, -53, -275, 135, -244, -13, 95, 161, -394, -5, -119]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-600, -696, 700, -168, 132, 208, -88, -120, 516, 624, -536, 292],\n [564, 84, -46, -300, 390, 248, -620, 804, 150, -336, 92, -682],\n [143, -11, 23, -102, 128, 88, -197, 243, 74, -71, 0, -196],\n [-53, 353, -383, 318, -362, -304, 503, -513, -416, -127, 252, 322],\n [-234, -414, 426, -180, 180, 192, -210, 126, 360, 306, -312, 12],\n [451, -187, 236, -444, 541, 396, -809, 951, 403, -157, -110, -727],\n [497, 67, -33, -270, 350, 224, -555, 717, 140, -293, 76, -606],\n [-234, -414, 426, -180, 180, 192, -210, 126, 360, 306, -312, 12],\n [-257, 53, -77, 210, -260, -184, 395, -477, -170, 113, 24, 376],\n [-645, -471, 455, 42, -108, 8, 247, -465, 246, 549, -376, 512],\n [169, -229, 259, -294, 346, 272, -499, 549, 328, 11, -156, -386],\n [141, 219, -224, 84, -81, -92, 89, -39, -183, -171, 166, -29]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[304, -266, 152, 418, -38, 437, -247, 323, 361, -19, -171, -133],\n [-48, 42, -24, -66, 6, -69, 39, -51, -57, 3, 27, 21],\n [32, -28, 16, 44, -4, 46, -26, 34, 38, -2, -18, -14],\n [-176, 154, -88, -242, 22, -253, 143, -187, -209, 11, 99, 77],\n [-352, 308, -176, -484, 44, -506, 286, -374, -418, 22, 198, 154],\n [-352, 308, -176, -484, 44, -506, 286, -374, -418, 22, 198, 154],\n [400, -350, 200, 550, -50, 575, -325, 425, 475, -25, -225, -175],\n [48, -42, 24, 66, -6, 69, -39, 51, 57, -3, -27, -21],\n [416, -364, 208, 572, -52, 598, -338, 442, 494, -26, -234, -182],\n [368, -322, 184, 506, -46, 529, -299, 391, 437, -23, -207, -161],\n [368, -322, 184, 506, -46, 529, -299, 391, 437, -23, -207, -161],\n [-352, 308, -176, -484, 44, -506, 286, -374, -418, 22, 198, 154]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-5, -70, -32, -743, -494, -266, 697, 768, 9, -258, 247, -882],\n [-316, -422, 177, 856, 718, -161, -53, -377, 259, -299, 551, 275],\n [144, -754, 697, 540, 154, -553, -249, -93, -313, -547, -345, -429],\n [791, 438, 575, -201, -440, -361, -954, -469, 280, 463, -520, 619],\n [-84, 665, -799, -682, -387, 805, 203, 232, -333, 537, -420, 119],\n [-385, -164, -335, 75, 198, 249, 444, 215, -178, -175, 188, -263],\n [78, 210, -18, -460, -268, -178, 260, 280, 338, 52, 376, -154],\n [804, 195, 650, -163, -508, -358, -946, -365, -111, 295, -916, 302],\n [274, 713, -257, -461, -338, 313, -317, -162, 174, 612, -215, 561],\n [353, 205, 26, -955, -823, -130, 233, 603, -243, 60, -448, -660],\n [610, 422, 428, 222, -78, -108, -1110, -782, 238, 532, -512, 992],\n [34, -334, 517, 1314, 846, -177, -927, -1049, 209, -35, 5, 971]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-732, -502, 424, 98, 1017, -486, 298, -577, 843, 229, 252, 822],\n [-642, -982, 521, 26, 1037, -560, 2219, -758, 2140, 160, 572, 107],\n [-39, -361, 662, -193, 226, -1083, 795, 4, 861, 490, -294, 394],\n [-562, 257, -759, 258, -378, 574, -633, -519, -564, -497, -92, -556],\n [536, -815, 156, 405, -277, -230, 563, -597, 578, 55, 65, -233],\n [-520, -658, -40, 569, 758, 467, 1317, -954, 542, 54, 654, 21],\n [-57, -860, 319, 74, 309, -623, 638, -694, 1122, 48, 42, 134],\n [-535, 32, 884, 964, 1043, -108, 1476, 191, -648, 995, 502, 1310],\n [563, 30, -298, 178, -1027, 113, -134, 335, -149, -703, -79, -823],\n [-424, -649, 493, 815, 414, -368, 2256, -749, 600, 729, 237, 148],\n [129, 16, 353, -15, 302, 16, 974, 581, 322, -37, 407, 111],\n [-610, -235, 468, 350, 494, -508, 1506, -428, 646, 776, 54, 321]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[326, -458, -119, -100, -20, -293, 278, 418, -536, 817, 35, 245],\n [-2, 366, 568, 267, 372, -407, -52, -393, -28, -1051, 761, -467],\n [-373, 358, 257, 326, 72, -189, -322, -297, 140, -701, 200, -328],\n [-637, -123, -304, 899, -429, -735, -39, 701, -607, 1020, -163, 50],\n [157, -663, -651, -807, -527, 614, 11, 265, 391, 875, -1198, 457],\n [838, -503, -301, -413, 213, 250, 594, 557, -737, 1492, 134, 730],\n [-394, -502, -929, 287, -1062, -10, 648, 973, 386, 1226, -1094, 182],\n [700, -750, -295, -215, -254, -354, 1088, 785, -318, 966, 36, 196],\n [-209, 75, 437, -250, 409, -133, -1116, -633, -349, -467, 44, -44],\n [610, -546, -7, -265, -158, -400, 918, 387, 26, 58, 182, -152],\n [495, -229, -329, -852, -311, 855, 642, -93, 1091, -385, -598, 24],\n [383, 616, 680, 446, 808, -274, 297, -296, -476, -719, 1446, -223]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-202, -82, -618, -53, -178, -76, -375, 264, 312, -278, 322, 15],\n [760, 193, -672, 902, 197, -597, -281, -1130, 96, -367, -402, -19],\n [-263, -621, 774, -263, 537, 206, 522, 172, -270, 636, -595, 303],\n [56, -586, 492, 128, 662, -58, 414, -320, -228, 502, -812, 318],\n [6, 5, 1071, -677, 395, 136, 714, 501, 159, 445, -654, -333],\n [-403, -493, -558, 331, -135, 130, -404, -116, -342, 4, 449, 581],\n [-606, -150, 255, -889, -116, 311, 115, 1143, 363, 114, 244, -166],\n [-343, -122, -276, -204, -196, 119, -212, 410, 114, -91, 371, 71],\n [698, 474, 594, 168, 274, -234, 442, -554, -6, 72, -658, -394],\n [-364, -1427, 366, 518, 885, 133, 311, -616, -846, 881, -786, 1135],\n [-189, -231, 510, 363, -77, 422, 166, -440, -1014, 444, 247, 569],\n [173, -15, -537, 513, -63, -185, -318, -513, -99, -210, 115, 180]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-10, 787, 770, 570, 586, -1152, 264, 769, -1113, -761, -358, 418],\n [-236, 1625, -678, 329, 556, 113, -1323, -1465, 475, 1058, 351, 217],\n [786, 395, 1048, 690, -1132, -484, 577, 800, 406, -25, 241, -251],\n [753, 1069, 893, 493, -1006, -1384, 453, -541, -580, 817, 505, 1911],\n [-35, -1301, 902, 1293, 815, -2343, -40, 1025, 1284, -730, 124, -642],\n [64, -300, 1038, 99, -140, -1117, 584, 1438, 242, -924, -297, 673],\n [-648, -128, -1369, -655, 463, 835, -178, -1050, 807, 626, -683, -170],\n [-967, 92, -933, -658, -774, 1906, -63, -915, -201, 19, -90, 34],\n [-37, 353, 675, -1191, 1380, -1995, -415, -287, 666, 1134, 953, 303],\n [-348, 287, -1216, 753, 623, -32, -543, -534, -341, -1023, -517, 590],\n [162, -663, 199, -1227, 323, -227, -105, 833, 289, -205, 414, -90],\n [-777, -56, -1016, -682, 817, 194, -99, -141, -1275, -630, -443, -295]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[37, -1024, -34, 436, 250, -181, -652, -412, -290, 659, -208, 749],\n [430, -149, -128, -760, -520, 372, 397, -289, -206, -603, -55, 59],\n [273, 185, -77, -777, -891, 172, -189, -326, 338, -233, -1016, 16],\n [-756, 106, -336, -431, 194, 1360, 85, -1384, -747, -921, 412, -404],\n [-399, -387, -1607, 159, -624, 1158, -579, -150, 18, -351, -193, 329],\n [796, -714, -265, -153, -173, 285, 62, -481, -160, -483, -489, 128],\n [756, -573, 134, 784, 140, -1148, -49, 677, -8, 411, 165, 683],\n [257, -116, 691, 526, 711, -739, -21, 590, 402, 818, -173, -217],\n [-1118, 916, 201, 834, 746, -505, 231, 913, -151, 408, 1600, -163],\n [-78, 787, 497, -1013, -805, 156, -172, -1386, -85, -801, -1034, -265],\n [-30, 717, 7, 369, 335, 311, -54, -475, 336, -662, -660, -1017],\n [589, 29, 272, -44, -32, -391, 230, 390, 334, 34, -343, -180]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-115, -319, 443, -258, 343, -959, -47, -385, -507, -963, 415, 119],\n [-420, -173, -206, 20, -701, -1199, -6, -454, -657, -830, -434, -308],\n [-166, -29, -191, 235, -235, 257, 138, 280, 112, 540, -98, -134],\n [-134, 860, -487, 398, -153, 505, -474, -7, 461, -112, -387, 313],\n [264, -1138, -375, -733, -1374, -849, 793, 101, -212, -646, -224, 240],\n [496, -400, 371, -667, 160, -495, 101, -411, -312, -658, 104, 0],\n [922, -1493, -38, -1296, -985, -436, 1019, 211, 30, -546, 152, 508],\n [322, 135, -67, -36, 106, 776, 42, 245, 408, 602, -41, 49],\n [-363, 230, -469, 562, -456, 551, 78, 436, 261, 945, -347, -255],\n [478, -675, -174, -530, -627, 147, 568, 288, 187, 180, -64, 162],\n [-525, 335, -634, 547, -669, 124, -70, 302, 271, 113, -317, 199],\n [-829, 546, -488, 780, -469, -308, -312, -35, -150, -11, -454, -238]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-411, 592, 936, 738, 874, 366, -86, -36, -127, -498, 1135, -104],\n [-352, 647, 146, 178, 632, 197, 216, 546, 963, -713, 446, -45],\n [-29, 334, 196, 325, 438, -11, 485, 227, 169, -217, -39, -8],\n [-206, -464, 379, 155, -583, 416, 121, -330, 349, 23, 182, 820],\n [-136, -409, -95, -211, -329, 59, -648, -586, -345, 328, 82, 10],\n [317, -603, -102, -194, -862, -1, 206, -112, -152, 373, -415, 491],\n [361, 705, 542, 383, 580, -60, 266, 803, -475, -424, 757, -472],\n [322, -242, -609, -148, -77, -489, 547, -167, -270, 524, -1310, -107],\n [351, 398, -495, -164, 505, -533, 154, 379, -386, 90, -539, -772],\n [-66, 208, 44, 281, 366, -55, 592, 87, 279, -105, -366, 93],\n [24, 15, -564, -510, 8, -235, -655, -18, -124, 117, -94, -544],\n [-420, -61, -500, -576, -220, 175, -683, 8, 958, -261, 182, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-758, -805, 1240, 796, -449, 182, 676, -18, 1071, 478, 870, 160],\n [1220, 1076, -654, 552, -897, 804, 77, 7, 209, -1281, -405, -34],\n [739, 432, -2044, -1627, -518, 173, -1511, -827, 505, 378, -885, 579],\n [-734, -124, 582, 373, 68, 120, 400, 253, -114, -1132, 1557, 298],\n [-630, -402, 915, 1009, -1074, 153, 766, -58, 80, -490, 920, 242],\n [-673, -936, -100, -802, -840, -887, -493, -1223, 584, -737, -852, 739],\n [-707, -357, -213, 275, 759, -530, 931, 337, -696, -653, 1079, -399],\n [528, 91, 1092, 470, 1251, 486, 1064, 733, 872, 237, -23, -1621],\n [836, 629, -1432, -783, -88, 603, -1718, 361, -987, 871, -331, 309],\n [-1135, -250, 1230, 1171, -682, -251, 805, -74, 451, -475, 1505, 39],\n [-702, -229, 153, -210, 843, -975, 192, 199, 534, -78, -393, -850],\n [-179, 514, -301, 401, -644, 453, -156, 167, 1518, 502, 660, 372]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[369, 321, 399, -662, -421, 40, -680, 568, -934, -590, -1457, -231],\n [-157, -734, 508, -985, -586, 845, -1051, 1786, -166, -180, -123, -81],\n [44, 466, -537, 601, 211, -192, -493, -662, 240, -188, 689, 864],\n [-79, -84, -90, -220, 299, 376, -399, -74, -1160, -54, -762, 518],\n [-990, -881, 262, -358, 212, 465, 18, 1202, 682, 548, 1269, -292],\n [472, 562, 190, 601, 177, 483, -372, -672, 328, -446, 549, 737],\n [1792, 210, 953, 483, -342, 2185, -451, -737, 275, -915, 180, 1280],\n [-181, -421, 782, 264, 23, 719, -267, 592, 903, 234, 1176, -255],\n [416, -162, -446, -873, -783, 11, -236, 676, -191, -454, -682, 222],\n [-21, 659, 177, 442, 23, -532, -1126, -92, -310, -246, -253, -33],\n [656, 0, -116, -410, -201, 768, 571, -226, 62, -486, -173, 628],\n [-1443, -930, -476, -236, 612, -791, 671, 435, -533, 1235, 25, -804]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[502, 556, 219, 185, -152, 480, -500, -729, -1011, -24, 563, 678],\n [-816, -1051, -45, 144, 307, -450, 136, 757, 215, 36, -484, -700],\n [-642, -1024, -787, 723, -261, 295, 27, -385, -730, -516, -189, 36],\n [627, 1097, -63, -1290, -607, -885, -937, -449, -383, -943, 1111, 1282],\n [552, 297, -786, 243, -711, 597, -414, -1141, -883, -701, 527, 927],\n [448, -127, 664, -263, 464, -422, -682, 917, 83, 386, 62, -512],\n [730, 551, -792, -471, -620, -467, -227, -348, 315, -1074, 423, 658],\n [-291, -1064, 650, 496, 808, 302, -20, 1171, 310, 1189, -756, -1404],\n [-78, 250, -1593, 191, -1098, 752, 732, -1505, 117, -908, 17, 902],\n [-10, -29, -792, -787, -559, 34, 200, -14, 1034, -72, -185, -26],\n [-414, -803, 37, 680, 308, 730, 350, 242, 70, 766, -637, -786],\n [434, -1, -195, 496, -64, 609, -13, -285, -180, 102, -62, -42]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[68, -208, 413, 130, 143, 114, 351, -101, -73, 389, -400, 285],\n [137, 96, 238, -60, 332, -22, 236, 215, 248, 295, -244, -55],\n [136, -64, 420, 40, 316, 56, 380, 84, 124, 444, -416, 140],\n [-103, -112, -133, 70, -253, 36, -141, -194, -217, -184, 140, 90],\n [39, -272, 413, 170, 69, 140, 341, -182, -159, 368, -396, 350],\n [28, -272, 385, 170, 43, 138, 315, -193, -173, 337, -368, 345],\n [195, 400, 35, -250, 495, -160, 95, 520, 555, 170, -60, -400],\n [36, -400, 553, 250, 51, 202, 451, -289, -261, 481, -528, 505],\n [-6, -256, 280, 160, -36, 124, 220, -214, -204, 226, -264, 310],\n [-254, -160, -462, 100, -614, 32, -454, -384, -446, -564, 472, 80],\n [26, 288, -266, -180, 86, -136, -202, 260, 254, -200, 248, -340],\n [131, 368, -91, -230, 341, -156, -27, 430, 449, 20, 68, -390]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-645, -541, 71, -700, -226, 779, -76, -339, -537, 55, 464, 507],\n [-300, 172, -45, 113, 439, 262, -810, -24, -392, -244, 426, 88],\n [246, -158, 127, 25, -537, -412, 908, 96, 402, 128, -432, -246],\n [-177, -519, 11, -695, -401, 479, 469, -282, -89, 324, 9, 427],\n [-798, -744, 289, -652, -710, 548, 501, -267, -478, -63, 377, 266],\n [-627, 109, 259, 454, 48, -103, -484, 159, -471, -643, 504, -363],\n [-324, 250, -64, 183, 563, 276, -1001, -9, -448, -301, 495, 80],\n [-264, 240, -76, 160, 536, 256, -924, -12, -392, -252, 436, 88],\n [102, -244, -194, -609, 47, 518, 19, -279, -14, 433, -29, 538],\n [909, 509, -231, 448, 310, -627, 136, 231, 689, 253, -628, -259],\n [249, 517, 117, 902, 124, -839, -42, 417, 277, -409, -198, -719],\n [-504, 252, 338, 784, -36, -492, -298, 330, -296, -774, 350, -680]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[101, -804, -874, -1352, -636, -1188, -69, 120, 34, -293, 586, 150],\n [-348, 420, -140, -153, -311, -550, 412, 75, 342, 93, -518, 24],\n [-216, 912, 918, 1362, 612, 1300, 251, -292, 13, 366, -814, -227],\n [366, -1200, 376, -634, -466, -192, 514, -926, 512, -68, -284, -384],\n [306, -736, -300, -342, -110, -372, -690, 218, 28, -352, 528, 84],\n [-215, 292, -356, 16, 282, 612, -278, -30, -517, 31, 216, 11],\n [831, -372, -44, -561, 328, -10, 415, 399, -1233, 177, 1942, 432],\n [5, -444, -126, 354, 32, 14, -1222, 194, 449, -457, -234, -79],\n [-994, 808, -826, 68, -158, -38, -632, 130, 342, -158, -1006, -76],\n [-871, 848, -72, 428, -305, -236, 43, -92, 903, 26, -1612, -210],\n [-87, 380, -132, -662, -318, -634, 1203, -8, -208, 355, 168, 156],\n [35, -472, 42, -396, -495, -738, 229, -186, 631, -116, -406, -108]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-88, -264, 52, -2, 36, 40, 112, -16, -250, -202, -44, 6],\n [-308, 452, 10, 208, 126, -32, 306, -142, 630, 540, 190, -194],\n [-88, 248, -12, 78, 36, -24, 80, -48, 310, 262, 84, -74],\n [660, 124, -158, -275, -270, -68, -724, 236, -155, -167, -134, 245],\n [-132, 724, -62, 172, 54, -80, 98, -94, 850, 712, 214, -166],\n [-330, -206, 97, 115, 135, 52, 371, -109, -80, -47, 31, -100],\n [154, -482, 27, -144, -63, 48, -137, 87, -595, -502, -159, 137],\n [-110, -538, 91, -35, 45, 76, 153, -7, -540, -441, -107, 40],\n [528, 176, -136, -208, -216, -64, -584, 184, -40, -64, -88, 184],\n [66, -746, 79, -146, -27, 88, -25, 71, -845, -704, -203, 143],\n [418, -330, -49, -238, -171, 8, -433, 175, -545, -476, -187, 219],\n [-836, -236, 210, 336, 342, 96, 922, -294, 110, 140, 150, -298]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[915, -691, 994, 317, 567, -219, -1020, 1478, 1380, 318, -1715, -213],\n [-666, 723, -711, -34, -517, 363, 590, -1795, -2042, -480, 1700, 335],\n [-623, 614, 260, -917, -394, -735, -107, -462, -612, 249, 478, 1000],\n [-293, 112, -216, -935, -452, -653, 935, -122, 356, -182, 575, 345],\n [-985, 68, 331, -915, -803, -295, 664, 657, 509, -140, 55, 19],\n [288, 907, -87, 161, 1293, 487, -469, -487, -303, 912, 52, -74],\n [-877, -758, -340, -4, -842, -335, 187, -392, -732, 599, 570, 886],\n [-184, 393, -261, 21, 574, 614, 356, 983, 1419, 138, -538, -1182],\n [-960, 373, -1457, -746, -964, -1130, 650, -603, 217, -207, 1031, 763],\n [-1051, 430, -74, -347, -576, 221, 361, -392, -802, -20, 683, 133],\n [6, 356, 477, -143, 212, 361, 72, -493, -865, 77, 351, 81],\n [205, 312, 576, -158, 864, 617, 138, 1354, 1553, 263, -1010, -1159]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[843, 300, -226, -23, -309, -214, 1250, 393, -212, -544, 113, -130],\n [33, -182, -529, -571, -503, 972, 58, 487, -137, -191, -476, -967],\n [353, 261, -317, -324, -219, 591, 35, -10, -407, -238, -553, -1694],\n [-225, -576, 362, 115, 1264, -382, -809, -831, -454, 113, 227, 335],\n [83, -531, 430, 905, 1081, -748, 11, -849, -286, 118, 786, 1347],\n [-24, -717, 39, 450, -170, 135, 281, 225, -11, 105, 543, 1416],\n [45, 126, 294, -58, 618, -148, -775, -691, -516, 60, -286, -1085],\n [161, 309, 144, -737, 375, -571, -57, 118, -130, -312, -213, -329],\n [529, 584, 321, -314, -965, -522, 538, 801, 3, -204, -45, 129],\n [-21, 242, -85, 691, -944, 77, 695, 402, 615, 228, 331, 880],\n [-570, 605, 427, 76, -16, -789, -449, -77, 761, 397, 79, 686],\n [-547, 37, -239, 452, -312, 497, -178, -108, 585, 405, -5, 127]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[766, -789, -862, -643, -117, -1358, -1012, 766, -459, -45, -643, 23],\n [-670, -100, 1598, 430, 407, 1263, -1004, -825, 302, 174, 1897, 432],\n [1063, -241, -1004, -445, 48, -1133, -440, 519, 163, 360, -1364, 297],\n [-2108, 784, -859, 239, -50, -680, 1584, -479, -330, -305, 378, -442],\n [-236, -500, -385, 1131, -176, 309, -366, 493, 507, -735, 716, -278],\n [573, -1250, 111, 22, -1473, 454, 327, 445, -280, -91, 91, -1036],\n [522, -842, 246, -152, -1527, 1238, -582, 241, 282, 244, 1157, -462],\n [-598, -551, 1044, -1480, -509, 460, 18, -797, -254, 114, -58, 500],\n [523, -313, 768, 587, -437, 1030, -129, -142, 1073, 272, 652, 766],\n [866, -313, 986, -2029, 256, 200, -1095, -189, -939, 145, -989, 162],\n [1606, -13, 623, -1299, -608, 1072, -385, -243, -115, 967, -1128, -537],\n [-275, 830, -484, -122, -350, -457, 362, -224, 589, 731, 652, 916]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-176, 88, -104, 256, 100, 176, 268, 52, 80, -352, 308, -4],\n [142, -332, 540, -254, -517, 322, -33, 397, 294, -122, -263, -499],\n [291, 21, -119, -393, 113, -587, -560, -366, -361, 841, -500, 327],\n [12, 156, -276, 12, 264, -300, -132, -276, -228, 276, -12, 312],\n [375, -273, 371, -561, -356, -223, -511, 33, -53, 617, -661, -156],\n [297, -99, 89, -423, -86, -385, -487, -171, -203, 671, -517, 102],\n [217, -545, 891, -395, -853, 559, -24, 670, 501, -245, -404, -835],\n [155, 35, -105, -205, 100, -355, -315, -235, -225, 485, -265, 220],\n [192, -474, 774, -348, -741, 480, -27, 579, 432, -204, -357, -723],\n [-254, 460, -732, 430, 701, -338, 153, -485, -342, 10, 463, 635],\n [-94, -232, 432, 86, -413, 590, 339, 497, 426, -622, 149, -539],\n [-341, 319, -461, 523, 442, 77, 415, -149, -49, -451, 605, 278]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[87, -256, -130, 940, 89, 1043, 429, -644, 525, 770, -35, -468],\n [422, -410, 2178, 58, 452, 528, -580, 1260, -557, -358, -860, -356],\n [-811, 301, -2, -379, -427, -372, 396, -340, 101, 544, -1364, -607],\n [-275, 466, 690, -427, -65, 1944, -255, 11, -250, 128, 574, 809],\n [-347, 666, 530, 472, -284, 374, -491, 1115, -421, 506, -1578, -680],\n [34, -437, -942, 2108, -776, 121, 961, 34, -53, 279, -667, 135],\n [937, 334, 524, -900, 866, 17, 1123, 371, 479, -287, -102, -208],\n [-145, -32, -39, -1966, 162, -164, -26, -671, 410, -703, 743, 136],\n [-116, 61, 288, 198, -316, 1604, 408, -43, 72, -172, -106, -139],\n [-810, 831, -195, -1762, 532, -368, -977, 160, -968, -633, 1180, 248],\n [501, -863, 457, 460, -41, -227, 529, 283, -608, -1679, 861, 274],\n [440, -234, -381, -410, 1276, -680, -910, 1105, -655, -617, 766, -332]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[377, 601, 895, -656, -48, -47, -559, -590, 580, 316, -32, 491],\n [-213, -56, 1100, -216, 215, 584, -231, 63, -302, -99, 910, 558],\n [420, 139, -29, -110, 885, 502, -182, -182, 396, 420, 909, 325],\n [-28, 140, 1221, -276, 147, 530, -141, 468, -434, -39, 1087, 491],\n [1053, 843, 362, -632, -116, -781, 103, 367, 398, 366, -292, -56],\n [-791, -245, -220, 454, -826, 124, 37, 366, -620, -353, -349, -374],\n [-507, -74, 227, 276, -989, -188, 351, 1066, -980, -463, -222, -437],\n [-308, -360, -22, 308, -354, -186, 542, 854, -808, -456, -28, -330],\n [-920, -629, -236, 348, -1057, -587, 244, -226, -488, -751, -1444, -400],\n [440, 334, -98, -118, 713, 521, -305, -160, 470, 536, 842, 254],\n [-561, -407, -39, 242, -275, 72, 38, -124, -298, -336, -262, -55],\n [1014, 1083, -547, -252, 42, -187, -193, 404, 646, 840, 131, -309]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[556, 395, -675, 293, 813, 549, 534, 12, -752, 675, -974, 1268],\n [1308, 127, 49, -335, 641, 85, -16, 162, -156, 401, 634, 294],\n [1449, 238, -714, 110, 293, -489, -522, -640, -399, 457, 397, 310],\n [-926, -990, 14, 721, -414, -993, -1415, -478, 593, -206, -337, -1841],\n [-100, 114, 630, -431, -581, 1129, 745, 1498, -16, 342, -422, 428],\n [208, 469, 716, -1394, -98, -13, 346, 78, 373, 1204, 1533, 863],\n [1337, -559, -78, -801, 655, -1041, -963, -504, -323, 975, 1274, 375],\n [-1065, -60, 995, -330, -413, 942, 360, 1301, 694, 1241, -574, -210],\n [194, -566, -14, -192, 23, -646, -904, -174, 29, 960, 196, -216],\n [-552, 725, 489, -53, -41, 519, 575, 57, 780, 226, 265, -266],\n [-562, -1049, -456, 123, -1228, -594, -1146, 299, -558, 1037, -1158, 85],\n [535, -523, 56, -363, 255, -617, -496, -199, -189, -222, 722, -100]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-1375, -999, 516, -1447, -25, 248, -918, 63, -691, -240, -588, 160],\n [-29, -479, 560, 91, -15, -1012, 285, -134, -1275, 420, -396, -595],\n [-364, -28, 105, 1265, -54, -851, 1498, 758, 119, 352, 1670, -285],\n [175, 420, -694, -441, -494, -226, 210, -317, -622, 484, 174, 86],\n [645, -13, 44, 1053, -56, 506, 449, 426, 658, 85, -7, 301],\n [-794, -415, 119, -431, 182, -1642, -66, -141, -1820, 1193, -817, -675],\n [1236, 1065, -308, 286, -258, 351, -67, -503, 715, -211, 755, 57],\n [55, 169, -738, 492, 608, -260, -336, 643, 258, 504, -2015, -337],\n [-154, -281, -931, -211, -279, 1370, 292, 244, 31, 266, -909, 1571],\n [-328, -259, -343, -618, -790, 588, 430, 6, 206, -472, 1081, 108],\n [-650, 573, 535, -40, -315, 68, -22, 1687, 833, -1473, 1804, -488],\n [-329, 75, 368, -441, 207, -157, -1213, -138, -546, 1094, -600, 473]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1, 56, -578, 992, -392, 352, 1806, 429, -1728, 52, -203, -1173],\n [-923, -997, 753, 730, -954, -1142, -154, -728, -850, -13, 585, 1021],\n [910, -512, 321, 639, 2049, 173, 547, 224, 571, 74, 257, -1009],\n [790, 1547, -593, -105, -376, 548, -189, 851, -229, -1071, -614, -1136],\n [432, -800, -164, 130, -780, -211, -305, -149, 296, -788, 289, 524],\n [894, -1024, 62, -54, 381, -359, 116, 195, 610, -913, 328, 225],\n [824, 246, -537, 131, 1143, 576, -1235, -230, 1750, 244, -19, -273],\n [-118, -9, -1394, -336, 225, 1021, 462, 617, -165, 111, -1538, -261],\n [-2003, 1103, -618, -148, -1461, -195, -224, -85, -716, 1254, -656, 659],\n [1064, -1797, 939, -242, 760, -5, 1468, -16, -7, -1626, 1047, -83],\n [203, -1135, 557, -1271, -785, -100, 72, -507, -42, -441, 439, 1252],\n [431, 684, 24, 326, 143, -710, 1073, 117, -1959, -615, 137, -802]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-203, 76, -71, -256, 543, 409, 46, -32, -24, 1, -71, 56],\n [79, 279, 505, 118, 654, 124, -253, -679, 846, -158, -155, -25],\n [-538, 216, 488, -76, -233, -1266, 120, 361, -538, -860, -103, 298],\n [-933, 907, 197, -152, 370, -550, -1077, 437, 480, -686, 619, 679],\n [571, -697, 141, -137, -3, -102, 1168, -347, -581, 491, -411, -405],\n [-86, 222, 253, 88, -514, -1221, -329, 283, 230, 328, 936, 340],\n [-123, 85, -48, -199, 146, -213, -77, 139, 129, 673, 728, 217],\n [1187, -26, -191, -311, 257, -123, -281, -277, 919, -262, 200, -108],\n [-135, -230, 419, 515, -866, -744, 398, -3, -543, -111, -331, -146],\n [-498, -86, 160, 291, -489, -335, 196, 163, -403, 806, 424, 86],\n [1044, -564, -251, -32, 179, 752, 502, -593, 366, 937, -51, -484],\n [-545, -296, -235, 1101, -1229, 986, -36, 44, -539, 813, -356, -362]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[272, 159, -440, -251, -108, -104, 289, 703, 375, 448, -244, -78],\n [158, -6, -74, -340, -93, -242, -218, 653, 523, 462, -172, -10],\n [-158, -111, 290, 109, 57, 26, -241, -362, -160, -222, 136, 52],\n [-162, -99, 270, 141, 63, 54, -189, -408, -210, -258, 144, 48],\n [114, 87, -222, -65, -39, -6, 201, 244, 94, 146, -96, -40],\n [-132, 45, -12, 363, 90, 276, 339, -645, -561, -468, 156, -6],\n [-224, -264, 608, -56, 48, -160, -760, -248, 104, -96, 160, 112],\n [-236, -150, 404, 194, 90, 68, -298, -580, -288, -364, 208, 72],\n [224, 264, -608, 56, -48, 160, 760, 248, -104, 96, -160, -112],\n [100, 90, -220, -30, -30, 20, 230, 180, 40, 100, -80, -40],\n [-98, 60, -58, 322, 75, 254, 356, -545, -499, -402, 124, -14],\n [32, -57, 88, -179, -36, -152, -263, 271, 279, 208, -52, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-839, -436, 1477, 869, -1244, -683, -952, -56, -1279, -460, 514, 743],\n [-881, 1556, 1192, -962, 1484, -151, -480, -2138, 1108, 227, -1086, -951],\n [-1018, 1840, -557, 18, 968, -1160, 1867, 53, 862, 151, -548, 99],\n [-638, 837, 539, -116, -995, -1696, 1057, 1657, -343, -1481, 1271, 479],\n [31, 654, 951, -960, 543, -1326, -4, -278, 333, 150, -126, -922],\n [278, -1335, -74, 419, -355, 484, -1033, -58, -850, -31, -325, 1045],\n [-100, 886, 903, 992, 248, -2118, -86, 192, 421, 916, -768, -937],\n [-979, 934, -93, -641, -163, -1676, 1775, 754, 636, -1159, 310, -717],\n [726, -1685, -366, 66, -1324, 15, 73, 964, -1882, 67, 1202, 1753],\n [588, 343, -922, 314, -399, 1355, 268, -871, 314, -653, 507, 626],\n [1212, -409, -892, -541, -351, 1606, -192, 385, 93, -828, 893, 563],\n [785, 105, -30, -815, 1594, 477, -1048, -247, 10, -92, -535, -346]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[149, 1160, 869, 269, -40, 668, -711, -638, 134, 560, -306, -455],\n [831, 575, -339, -186, 97, 915, -526, -48, -35, -1908, -618, -11],\n [1419, 873, -351, -1226, -980, 773, -563, -1672, -56, -149, -566, -562],\n [1409, -199, -320, 187, 749, -5, 78, 278, -464, -510, -396, 151],\n [-819, 346, -340, -565, -113, 298, 44, -240, 405, -593, 1230, -155],\n [1101, 1238, -129, 687, 826, 736, -473, -331, 504, -142, 131, 57],\n [-333, -531, 203, 288, -86, -1372, -934, -354, 553, 644, -266, 684],\n [1151, 417, -506, -1260, -805, 1424, -713, -1469, 671, -698, 717, -458],\n [-673, -955, 735, 274, -713, -846, 1137, -231, 59, -7, 1658, 834],\n [165, 407, -141, 165, 636, 508, -773, 89, 236, 605, -151, -498],\n [-778, -406, 188, -604, -432, -13, 906, 371, -806, 45, 397, -485],\n [-358, 591, 1030, 235, -564, 689, -46, -245, -279, 933, -353, -639]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[81, 287, 30, -823, -232, -437, -392, -273, 745, 251, -763, -1196],\n [-512, -59, 117, -344, 185, 871, 13, 439, 109, -253, 446, 503],\n [-804, 38, -106, -716, 586, 694, -38, 206, 290, 186, 372, 50],\n [345, 36, -118, 585, -377, -683, 89, -25, -549, -858, -82, 114],\n [-139, 142, -274, -21, -76, -498, 90, 145, -371, -980, 76, -9],\n [-81, 294, -224, -883, -339, -479, 167, 583, 67, -1286, -42, -224],\n [1020, 74, -48, -39, -1007, -904, 699, 888, -462, -1523, 54, 570],\n [-375, -177, -324, 912, 794, -98, 44, -617, -629, 662, 359, 245],\n [-754, -187, 165, -584, 620, 1480, 132, 515, 333, 551, 750, 758],\n [-326, -8, -250, 510, 461, -273, -175, -574, -326, 274, -2, -227],\n [187, -96, 284, 702, -241, 138, -377, -411, -37, 181, -288, -81],\n [661, -320, 518, 425, -272, 670, 142, 97, 229, 1020, 46, 579]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-383, -207, 971, 959, 200, -352, 207, -69, -361, -493, -73, 1021],\n [-323, -112, 75, 580, 419, 887, 135, 95, 585, 1100, 293, -221],\n [197, -22, -892, -820, -163, 287, -452, 140, 300, 405, 135, -757],\n [422, 1124, -314, -781, -603, -1149, 226, -62, -692, -1034, -785, 47],\n [-536, 28, 408, 438, 62, -518, -472, 96, -252, -248, -218, 790],\n [129, -325, -1128, -728, -96, 709, -469, 316, 419, 632, 395, -816],\n [-424, -825, 122, -194, 72, -402, -1350, -14, 66, -123, 189, 329],\n [-422, -218, 368, 150, 189, -262, -757, -100, 175, 230, -31, 250],\n [-736, -848, -7, 268, 164, -56, -1221, 309, 33, 83, 290, 650],\n [-671, -164, -1467, 9, -71, 860, -656, 1041, 112, 722, 335, 118],\n [-125, 129, 869, 341, 27, -794, -26, -303, -338, -611, -332, 637],\n [-127, 358, -528, -29, -278, -180, 90, 436, -448, -413, -194, 392]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[122, 888, -437, 892, -611, 205, 10, -410, 913, 239, 1254, 1147],\n [278, -352, 354, -154, -212, -399, -461, -465, 737, 233, 943, -119],\n [473, -621, 90, -182, 11, -270, 36, -125, 407, 449, 31, -633],\n [960, -630, -392, -419, 190, -73, 616, 43, 380, 814, -404, -670],\n [-541, -407, 369, -88, 125, 242, -121, 530, -780, -176, -1254, -769],\n [-109, -57, 288, -307, 610, -968, -133, -499, -425, -895, 684, -10],\n [217, 314, -597, -5, -227, 733, 291, 514, 263, 412, -360, 608],\n [-188, -697, 560, 173, -465, 88, -643, 169, 479, 386, -139, -680],\n [919, 183, -407, -325, 291, -503, 609, -763, 386, 324, 880, 167],\n [-577, 448, 457, 664, -615, 242, -525, -343, 195, 36, 502, 204],\n [-757, 804, 303, 1654, -1476, 939, -692, -172, 919, 642, 611, 561],\n [71, 1541, -786, 995, -766, 831, 364, -308, 702, 452, 947, 1631]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[98, 163, -376, -251, -81, 1064, -375, -255, 442, 495, -397, -764],\n [33, 76, 24, 7, -331, 548, -684, -757, -212, -374, -231, 12],\n [-305, -490, 246, -64, -27, -84, -409, -302, 766, -591, -461, -174],\n [-109, 44, -203, -56, 162, 216, 76, 136, 419, 285, -89, -435],\n [704, 179, -222, -488, 242, 769, 354, 387, -590, 811, -54, 37],\n [-161, 162, 0, 241, 115, -394, 180, 35, -284, -148, 323, 218],\n [459, -65, 85, -225, -352, 197, 9, 168, -237, 343, -89, 156],\n [-291, -47, -6, 161, 102, -386, 148, 161, 360, -66, 96, -136],\n [21, -947, 400, -513, -36, 102, -312, 71, 1218, -324, -892, -282],\n [-87, -681, 429, -174, -283, -214, -396, -158, 741, -545, -538, 15],\n [-896, 278, -48, 780, -146, -784, -252, -464, 300, -676, 430, -136],\n [126, 204, 26, 89, -303, 271, -389, -510, -564, -228, 49, 251]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[280, 207, -708, 209, 59, -88, 266, 577, 281, -857, 320, -437],\n [401, -263, 103, 40, 484, 629, -318, -60, 454, 33, -226, 84],\n [-908, 623, -55, -192, -1024, -1203, 461, 264, -760, -33, 198, -321],\n [-791, 654, 192, -342, -790, -686, -41, 574, -136, -74, -380, -611],\n [945, -661, -34, 251, 1029, 1140, -349, -337, 657, 11, -48, 398],\n [885, -766, 92, 250, 1002, 1078, -297, -610, 432, 266, 28, 629],\n [236, -368, 10, 158, 250, 130, 146, -546, -266, 288, 316, 516],\n [-781, 586, 157, -291, -797, -765, 76, 417, -305, -6, -222, -465],\n [-30, 247, -422, 83, -183, -310, 258, 379, -9, -497, 236, -311],\n [-1291, 733, 901, -674, -1082, -757, -384, 378, -284, 597, -910, -540],\n [-257, 47, -250, 127, -391, -712, 589, -309, -775, 63, 632, 276],\n [-497, 249, 540, -337, -343, -106, -349, 139, 41, 361, -580, -218]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[532, 843, 356, 285, -227, -1379, 115, 351, 333, -652, -1834, 880],\n [33, -134, -452, -719, -22, 223, -1022, -473, 817, 724, 396, 1197],\n [-84, 311, 490, -114, 252, 367, 371, -841, -1142, -221, 1076, -1432],\n [-95, 469, 146, -271, -1007, -447, -289, 1071, 243, -589, -382, -180],\n [36, 633, 787, -492, 405, -1012, -740, -45, -77, -50, -1286, 1421],\n [463, 288, 120, -147, 860, 689, -288, -765, -261, 1150, 1190, -483],\n [216, 437, -126, 906, -489, -774, 839, 724, -76, -941, -1274, -135],\n [51, -266, 231, 5, 290, 415, 141, 127, -97, 375, 522, -687],\n [-195, -828, -206, -605, 437, 958, -544, -557, 362, 986, 1260, 76],\n [36, -245, -355, 282, -71, 1003, 430, 57, -264, 357, 1427, -1510],\n [-288, 360, -324, -179, -711, 261, -656, 1265, 121, 148, 289, 5],\n [375, -102, 262, 167, 476, -307, 436, -751, 59, -44, -362, 39]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[342, 2357, 1100, -573, 1014, 937, 515, 1799, -274, -1715, 140, 1233],\n [76, 935, -906, -542, -738, 543, 165, -879, 417, -1317, 1768, 174],\n [-486, 542, -892, -54, -807, 848, 113, -666, 368, -1179, 799, 1144],\n [537, 218, 138, -415, 529, -667, 1317, 398, -637, -167, 770, -1543],\n [-168, 857, 450, 126, 184, -114, -968, 1094, -941, -308, -219, 922],\n [-33, -515, -1146, -562, -114, -582, 758, -414, 442, -425, 1503, -1105],\n [205, 830, 494, -137, 826, 215, -46, 878, -426, 21, -225, -140],\n [5, -383, 306, -9, -548, -286, 658, -644, 303, -208, 1202, -139],\n [-221, -212, 508, -157, 100, 197, -115, 35, 1413, -719, -391, 805],\n [-323, 365, -414, 243, 501, 927, 150, 275, 511, -759, 384, 452],\n [558, 198, -174, -146, -127, -474, 863, 192, -1190, 130, 40, -791],\n [796, 2672, 944, -212, 20, 792, -453, 453, -1025, -1507, 624, 550]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-836, 471, -477, -487, -167, 959, -282, 103, -354, -957, -291, 1780],\n [1722, -806, -562, 305, 311, -250, -620, 1255, 773, 733, 1212, 621],\n [345, -653, -339, 30, 776, 219, -218, 515, 472, -219, 105, -582],\n [3163, -886, 833, 1277, 534, -724, -10, 500, -47, 634, -68, 79],\n [44, 125, 606, -138, -367, -568, 104, 211, -392, 163, -1360, -970],\n [-2349, 654, -952, -1427, -534, 533, -382, 262, -251, -540, 10, 1522],\n [-1603, 854, 23, 295, -343, 888, -451, -1684, 993, -1371, 894, 374],\n [-212, -647, -823, -559, -95, 141, -936, 89, 1461, -37, 1724, 597],\n [-1037, 825, -924, -249, -1106, 137, -869, 336, -319, 1216, 544, 620],\n [689, 910, -557, 196, -254, 1369, -225, 20, -327, -701, -184, 720],\n [91, 536, 373, 8, -116, -625, 308, -85, -1109, 465, -778, 28],\n [541, -770, -382, -210, 813, 528, 638, 899, 558, -466, 163, -670]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[191, -573, -368, 481, 1174, 321, -291, -194, -31, -213, -354, -188],\n [369, -1061, -851, 871, 1686, 1125, -69, -1301, -353, 567, -438, -11],\n [110, -897, -163, 184, 1268, 672, 110, -435, -126, 438, -593, -134],\n [342, -321, -836, 537, 823, 837, -178, -778, 478, 300, -287, -462],\n [-155, 1323, 318, -660, -1889, -773, -37, 857, 798, -400, 541, -266],\n [487, -384, 35, -153, 38, -9, -199, -199, -859, 27, -67, 288],\n [21, 113, -330, 305, -250, 292, 147, -715, -192, 398, 305, 261],\n [-365, -100, 512, -201, 254, -373, 101, 680, 63, -293, -167, 5],\n [-1305, 889, 1068, -176, -985, -1194, 565, 1124, 165, -501, 680, 583],\n [108, 249, 592, -888, -684, -499, -68, 949, 217, -257, -192, -286],\n [203, -459, 229, -148, 665, -221, -315, 542, -246, -478, -399, -129],\n [-132, -495, -176, 608, 646, 300, 192, -790, -798, 324, 143, 611]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-908, 291, 1165, -483, -1238, 249, 901, 1195, -1414, -1269, 1025, 1479],\n [-321, 829, 778, 607, -415, 584, 297, -1058, 37, -531, 444, 693],\n [-477, -1271, -616, -974, -170, 779, 1215, 282, 289, -12, 272, -362],\n [-839, 234, 159, 757, 1348, 495, 812, -588, 58, 579, -669, -383],\n [944, -383, -1327, -569, -321, -300, 41, 280, -228, -474, -207, 134],\n [1493, 1038, -811, 492, -541, -851, -1116, -146, -710, -426, 208, 378],\n [-336, -441, -821, -351, 7, -632, -577, -618, -57, 128, -313, -217],\n [-133, -298, -338, -174, 534, -756, -419, -579, 323, 415, -1245, 20],\n [-1343, -666, 341, 40, 809, 1281, 882, 317, 299, -534, 709, -482],\n [-1690, -881, 507, -93, 690, 290, -139, -1612, 1072, 749, -21, -458],\n [-819, -923, 155, -730, 1, -208, 328, -99, 57, 683, -35, 59],\n [-1109, 431, 1264, 719, 89, 898, -193, -961, 775, -309, 605, -228]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-395, 206, 1176, 894, 528, 359, 279, 238, 440, 862, -427, -732],\n [-824, -1173, 716, 13, 966, 68, 423, -200, -307, -471, -82, -103],\n [287, 578, -696, -707, -784, -387, -261, -514, -395, -31, -231, 240],\n [671, 426, -1170, 9, -311, -212, -306, 620, 346, -428, 786, 647],\n [702, 213, 313, 749, -271, 637, -180, 826, 959, 589, 367, -385],\n [280, 739, -7, 849, 167, -55, -18, 906, 1089, 507, 299, -209],\n [-524, 342, 514, -192, -41, -63, 135, -822, -777, 445, -841, -265],\n [476, -592, -525, -1095, -829, -205, -261, -390, 51, -517, 89, 82],\n [-1089, -476, 1006, 380, 1153, -264, 558, -96, 135, 87, -448, -459],\n [88, 92, -714, -269, 63, -823, -9, 422, 880, -436, 369, 173],\n [-700, -99, -213, -1119, -74, -878, 153, -1132, -800, -392, -726, 98],\n [-190, 239, -116, 826, 802, -114, 171, 792, 480, -82, 482, 217]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[201, 482, 701, -906, -531, 535, 1059, 510, 445, 147, 393, -116],\n [554, -80, 484, -470, 196, -252, -90, -68, -124, 126, 736, 192],\n [-524, 554, -329, 19, -939, 1179, 604, 354, 93, 94, -885, -996],\n [537, -184, 512, -140, 249, 307, -1223, -371, -163, 510, 675, -648],\n [-127, 179, 628, -313, -55, 383, 231, 283, 827, 196, 239, -36],\n [400, -241, -450, 144, 157, -489, -388, -365, -961, -121, 85, 60],\n [232, -198, 257, 1, 327, -151, -584, -198, 23, 154, 393, 20],\n [-386, 328, 334, -11, -433, 1153, -196, 211, 691, 405, -289, -952],\n [-1178, 127, -953, 1021, -328, 508, 74, 121, 358, -237, -1498, -376],\n [-603, 299, -258, 141, -421, 397, 739, 355, 421, -160, -691, -76],\n [68, -523, 3, 512, 783, -595, -1162, -450, 29, 50, 273, 320],\n [-355, 137, -100, 19, -125, -67, 699, 277, 361, -222, -311, 356]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-637, -354, 81, 117, -420, 1047, 659, -1043, 806, -912, -1023, 1257],\n [931, 1721, -372, -1353, 580, 598, -343, -257, 228, -880, -464, 721],\n [-96, 196, 169, -417, -1154, 117, 109, -586, 931, 201, -360, 1112],\n [-578, -1549, -1019, 937, 516, 517, -1270, 1051, 546, 141, 602, -1066],\n [-4, 255, -153, -613, 174, -1139, 77, -635, 253, -566, -1253, 5],\n [-639, -547, 240, 50, -176, 410, 564, -649, -847, 345, -1052, -924],\n [-324, -298, 709, 410, -180, 557, 565, -339, -473, -6, 87, -1],\n [351, -15, 614, 464, 520, 146, 806, 237, -1822, -338, -400, -595],\n [-567, -2060, -515, 1097, -7, 565, -1079, 818, 507, 757, 580, -1426],\n [154, 244, -1203, -593, -241, 484, -83, 525, 108, 514, -264, 277],\n [562, 218, 675, 26, 618, 142, 576, -374, -723, -961, -681, -7],\n [106, -466, -800, 94, 417, 262, 33, 467, 520, -180, 208, 281]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[319, 251, 724, -126, -1413, -155, -376, 115, 951, -273, -149, -795],\n [-101, -466, -834, 497, 1271, 38, 244, -89, 254, 1094, 244, 510],\n [-75, -552, 578, 208, -2170, 196, -810, 1330, -315, -119, -519, -267],\n [-788, -1092, -1392, -168, 1171, 147, -207, -600, -422, 996, -313, -81],\n [1040, 374, -757, -823, 1205, -891, 309, -521, -220, -300, 560, 23],\n [-470, 205, 561, 1217, -65, 1270, 605, 869, -761, 58, 569, 1167],\n [388, 1714, -71, 216, 180, -1019, -360, 591, -1675, -553, 847, -207],\n [770, 1520, -758, 759, 1598, -351, 175, 144, -1424, 333, 1516, -106],\n [359, 1739, 511, 1986, 2016, -1491, -944, -428, -841, -1354, -115, -315],\n [-617, 434, -493, -824, -261, 408, 535, -168, -215, 1064, 109, -312],\n [-1012, -1060, -64, -239, -78, -83, -272, -769, 1660, 855, -1685, -422],\n [-1209, -140, -1109, -638, 369, 1402, 1686, -1443, 1117, 1272, 233, 642]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[27, 690, -278, -787, 638, 294, 1046, -449, -105, 678, 477, 1057],\n [-964, 179, 1028, -666, -237, 1192, -793, -583, -915, 413, 10, 341],\n [-241, -186, 559, -113, 508, -278, -475, -407, 152, -492, -388, -259],\n [515, -340, -28, 554, -704, 512, 179, 262, 220, 763, 880, 425],\n [-15, 660, -412, -827, 343, 463, 533, -49, -151, -16, -68, 892],\n [-979, 344, 411, -123, -924, 1483, -387, 293, -1392, 18, -355, 154],\n [523, -337, -1372, 950, -302, -1347, 442, 1670, 331, -875, -253, -1535],\n [-912, 622, -447, -144, -216, 189, 425, 1424, -819, -684, -268, -329],\n [179, 471, -370, -235, -21, -684, -432, -583, 430, -658, -1239, 166],\n [-188, 278, 100, -921, 1347, -473, 635, -402, 199, 356, 611, 217],\n [159, -299, 551, -74, -206, 557, -397, -782, -20, 799, 451, 349],\n [-54, 13, 202, 573, -915, -362, -1031, 127, 492, -637, -818, -39]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-768, -769, -308, -261, 83, -498, 251, -1790, 41, 173, 840, 1161],\n [242, -285, 325, 743, 51, -406, 25, -184, -12, -805, -754, -62],\n [-291, -320, 540, -675, 204, 547, -104, -681, -28, 570, 634, 572],\n [301, -366, -532, -1235, 765, 158, 582, 1, 347, 920, 361, -131],\n [-613, -74, 732, -733, -519, -275, -220, -1168, -194, 792, 872, 372],\n [-372, 60, 1238, -116, -1147, -721, -849, -405, -620, 213, -28, 326],\n [-132, -1012, 553, -790, 271, -70, -749, -138, -612, 295, 371, 700],\n [405, -486, 454, -705, 529, -744, -1074, 176, -1247, 434, -482, 697],\n [-795, 447, 490, -406, -871, 149, -998, 83, -670, 598, 1227, 10],\n [-62, -353, -191, -107, 324, 82, -336, 202, -305, -78, 258, 177],\n [268, -632, 895, -368, -148, -1299, -1842, 704, -1762, -14, -566, 394],\n [-119, 64, -210, -139, 81, -958, -392, -417, -669, 210, 226, -45]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-183, 332, 317, 139, 514, 495, -659, -1050, -357, 409, -437, -267],\n [-172, 752, 193, -743, 979, -535, -1000, -383, 450, 305, -1067, -143],\n [728, -52, 1061, 790, -416, -175, -553, -824, 268, 1366, -6, -831],\n [-16, 767, 436, -286, 641, 305, 479, -737, -1699, -101, -769, -442],\n [708, 20, 645, 1029, 374, 855, 952, -188, -325, 1444, -716, -40],\n [-827, 215, -302, -1351, -31, -38, 621, 876, -229, -714, 295, -263],\n [-114, 243, 398, 248, 421, 210, -923, -1360, -429, 800, -361, -61],\n [174, -527, 325, 215, -662, -115, -93, -680, -806, -237, 635, 106],\n [-295, 420, 21, 470, 738, 1422, 1212, 342, -461, 696, -62, -623],\n [410, 405, 586, 503, 1210, 249, -661, -625, 288, 241, -558, -629],\n [-329, 920, -399, -84, -58, 163, -204, -181, -83, 317, -806, -338],\n [-291, 82, -745, 324, -595, 55, -342, -84, 481, 755, -310, 733]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-54, -268, -60, -256, -271, 62, 368, 742, 97, 147, -530, -82],\n [27, -214, -59, -241, -221, 20, 265, 526, 106, 88, -362, -20],\n [615, -145, -120, -530, -225, -260, -35, 0, 265, -150, 130, 390],\n [543, -144, -153, -319, -107, -160, -103, -586, 390, -246, 522, 292],\n [564, -248, -198, -382, -177, -130, -10, -558, 497, -249, 506, 270],\n [-549, -329, -86, 280, -78, 418, 459, 74, 230, 133, -172, -516],\n [-384, 336, 152, 536, 356, 104, -264, -424, -324, 20, 216, -184],\n [24, 142, 46, 86, 110, -52, -164, -192, -100, -38, 140, 56],\n [-381, -706, -293, 117, -264, 534, 695, -340, 757, 1, 148, -570],\n [204, -172, -92, -228, -150, -36, 104, 20, 214, -50, 28, 84],\n [-276, 43, 75, 111, 11, 78, 102, 448, -202, 153, -370, -148],\n [750, -242, -210, -534, -223, -234, -60, -518, 515, -285, 518, 410]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[307, -180, 114, -56, -197, 397, 119, 564, 198, -910, -340, 156],\n [172, 925, -64, 429, -1, -738, 342, -20, 102, 182, 1290, -90],\n [-58, -296, -387, -1359, 951, -346, -638, 299, -511, 42, 382, -57],\n [-167, -609, -323, 246, -531, 1129, -103, 523, -357, -258, -922, 399],\n [-298, -454, -646, -1180, 662, 182, -686, 162, -854, 508, 4, -66],\n [-71, 185, 285, 933, -958, 729, 552, -878, 218, 602, -864, -465],\n [229, 214, 273, 638, -783, 623, 544, -232, 316, -196, -560, -279],\n [-108, 376, 140, 833, 385, -1396, -32, 490, 423, -270, 1393, 900],\n [-202, -69, -351, -718, 440, -72, -353, -240, -507, 646, 163, -271],\n [249, 209, 12, 806, -891, 785, 521, 358, 147, -526, -325, 92],\n [176, -135, -229, -702, 246, 210, -179, 458, -249, -414, 31, -49],\n [-223, -510, 243, -463, 740, -701, -488, -108, 177, 10, -59, 271]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-209, -758, 361, -301, 940, 95, -262, -240, 389, -1064, 317, 323],\n [189, 193, 2016, 238, 834, -384, 228, 446, 826, -1227, -1013, -816],\n [1439, -1566, 222, -1436, 358, 159, -371, -954, 334, 585, -99, -326],\n [506, -948, -855, -15, -310, -44, -105, -699, -827, 534, -302, -275],\n [339, -114, 1505, -1235, 427, 198, 1627, -1489, 1629, 588, -235, -754],\n [-2465, 939, 226, 1607, 396, -535, 380, 73, -439, 141, -437, -64],\n [-1172, 739, 1471, 382, 70, -509, 1469, -560, 939, 642, -523, -510],\n [2303, 226, -521, 724, 114, 244, -572, 1427, -78, 126, -511, 735],\n [-240, 1428, -1406, 280, -982, 1030, -301, 718, -483, 455, -122, 525],\n [-618, 75, 367, -333, 1183, 550, 285, 253, -735, -537, -756, -954],\n [1746, -939, 56, -627, 14, 734, -852, 129, 430, -1175, -210, 567],\n [-138, 321, 656, 661, 1568, -493, 626, 1111, 51, -1717, 784, 128]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[384, -595, 351, -53, -222, 455, -814, 579, 92, -828, -757, 94],\n [593, -353, -101, -216, -328, 198, 124, 364, -142, -423, -306, -50],\n [-423, 914, 349, 940, 1000, -1088, 239, -35, 160, -234, -417, 810],\n [386, 727, -183, 683, 656, -845, 522, -65, 119, -491, -658, 841],\n [-91, -617, 337, -83, -266, 696, -880, 408, 156, -250, -459, -4],\n [15, -615, -65, -895, -690, 150, -540, 360, -636, -130, 925, -898],\n [-359, -483, -211, -384, -434, 1026, -868, -398, 285, 608, 269, -309],\n [-485, -575, -274, -393, -532, 434, -663, 570, -445, 406, 389, -94],\n [739, 332, -63, 146, 252, 216, 265, -987, 732, -288, -457, -12],\n [391, -294, -340, -185, -258, 333, -582, 75, 16, -347, -277, 130],\n [-122, 174, 381, 552, 428, -266, -175, 318, 172, -393, -685, 563],\n [-542, 743, -98, 522, 538, -149, 843, -855, 471, 1007, 160, 280]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-345, -267, -135, 21, -192, 222, 9, -96, -90, 684, 228, 321],\n [-235, 656, -225, -502, 350, 154, -525, -831, -254, -453, -14, -438],\n [137, 436, -197, -652, -249, -152, 215, 88, -455, -496, 94, 192],\n [101, -298, 782, 103, 1189, -619, -383, 414, 486, -743, -710, -1087],\n [281, -346, 495, -500, 216, -790, 487, 1205, -136, -581, -314, -44],\n [379, -622, 262, 163, -476, -403, 799, 1233, 45, 184, 2, 589],\n [24, 693, -274, 59, 167, 340, -500, -960, 41, -410, -6, -409],\n [-5, 49, 645, 279, 1433, -324, -851, -337, 621, -839, -736, -1457],\n [200, 20, 562, -102, 924, -546, -292, 276, 278, -922, -584, -914],\n [-299, 28, -355, -78, -399, 366, 7, -354, -227, 592, 350, 434],\n [79, -194, 762, 49, 1267, -601, -477, 282, 470, -837, -730, -1185],\n [415, 722, -177, -568, -173, -206, 165, -4, -357, -978, -34, -32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[687, 740, -311, 267, -618, 288, 512, -1044, -440, 175, -538, -434],\n [334, 79, -619, 871, -275, -643, 354, 171, 186, 563, 271, -856],\n [413, -641, 893, -601, -151, 445, -334, 72, 100, -106, -764, 620],\n [-131, 731, -261, -43, 32, 267, 212, -651, -254, -187, 39, -51],\n [793, 406, -317, 213, -875, 276, 498, -911, -810, 172, -647, -383],\n [344, 379, -245, 793, 137, -511, 242, 31, 994, 589, 175, -752],\n [22, 440, 701, -565, 391, 634, -194, -550, 560, -277, -454, 533],\n [-343, -1091, 232, -872, -421, 359, -358, 463, -1502, -602, -167, 868],\n [420, 644, -153, 189, -262, 208, 328, -751, -46, 124, -329, -294],\n [-612, 176, 172, -696, 303, 498, -214, -213, -470, -617, 101, 661],\n [12, 654, -701, 673, -24, -370, 396, -259, 114, 286, 399, -710],\n [167, 251, 251, -267, -52, 387, 12, -457, -42, -133, -367, 209]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[44, 80, -613, 253, 669, -354, -791, -180, -768, -38, -692, 166],\n [492, 231, 462, 395, -159, 106, 491, -680, 588, 419, 471, -1090],\n [104, -9, 183, -41, -167, 99, 128, 130, 164, -170, 245, 18],\n [-1012, -294, -225, -580, -212, 41, 333, 258, 32, 545, -400, 556],\n [-184, -153, -195, -272, 22, -12, -328, 604, -340, -527, -133, 804],\n [168, -17, 277, -68, -254, 152, 176, 228, 236, -299, 379, 60],\n [-124, -90, 63, -189, -161, 82, 79, 284, 56, -168, 98, 290],\n [-336, -167, -35, -332, -170, 74, 50, 432, -28, -167, -23, 540],\n [80, 76, -404, 214, 470, -246, -540, -172, -512, -14, -456, 44],\n [264, 131, -247, 304, 398, -196, -432, -260, -356, -35, -265, -172],\n [-56, 131, -457, 321, 547, -307, -368, -618, -412, 552, -627, -394],\n [372, 89, 200, 158, -52, 55, 13, -30, 124, -232, 287, -204]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[22, 6, -4, 13, -10, 8, -10, -26, 7, -25, 25, 20],\n [374, 102, -68, 221, -170, 136, -170, -442, 119, -425, 425, 340],\n [-176, -48, 32, -104, 80, -64, 80, 208, -56, 200, -200, -160],\n [308, 84, -56, 182, -140, 112, -140, -364, 98, -350, 350, 280],\n [462, 126, -84, 273, -210, 168, -210, -546, 147, -525, 525, 420],\n [-352, -96, 64, -208, 160, -128, 160, 416, -112, 400, -400, -320],\n [462, 126, -84, 273, -210, 168, -210, -546, 147, -525, 525, 420],\n [-176, -48, 32, -104, 80, -64, 80, 208, -56, 200, -200, -160],\n [242, 66, -44, 143, -110, 88, -110, -286, 77, -275, 275, 220],\n [-308, -84, 56, -182, 140, -112, 140, 364, -98, 350, -350, -280],\n [418, 114, -76, 247, -190, 152, -190, -494, 133, -475, 475, 380],\n [528, 144, -96, 312, -240, 192, -240, -624, 168, -600, 600, 480]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-696, -51, 677, 332, 183, 272, -443, 385, -198, 434, -684, 834],\n [473, -146, -678, -496, 739, -1457, 142, 306, 258, -326, 98, 523],\n [-526, -1315, 636, -680, 341, -942, 790, 943, -419, 236, -379, 632],\n [101, -385, -481, -654, 288, -961, 213, 335, -43, -544, 549, 220],\n [-972, 382, 202, -1208, 347, -855, 48, 931, -208, -6, -32, -428],\n [-647, -30, 763, -514, -1369, -195, 166, -43, -434, 411, 465, -685],\n [-535, -809, 1542, -590, -256, 600, 456, 278, -772, 530, -160, -708],\n [43, -557, -901, -746, 478, -1314, 559, 622, 120, -720, 616, 361],\n [285, 44, 535, -619, 814, -176, -267, 107, -211, -61, 594, -363],\n [809, -349, -754, 137, 883, -385, 671, 38, 435, -138, -735, 136],\n [-378, 571, 6, -1387, 285, -753, 505, 517, -94, 138, -882, -1376],\n [168, 882, -558, 1277, -1134, 1119, -290, -885, 531, 105, 626, -323]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-138, 86, -250, 148, 345, -26, 25, -202, 48, -171, 87, -192],\n [282, -59, 430, -247, -525, 134, -70, 328, -12, 369, -213, 318],\n [-28, 129, -128, 83, 242, 72, -13, -122, 92, -16, -16, -110],\n [-450, -241, -454, 235, 321, -446, 166, -280, -228, -645, 441, -294],\n [-208, -39, -260, 143, 260, -156, 65, -182, -52, -286, 182, -182],\n [54, 122, -10, 16, 105, 118, -35, -34, 96, 93, -81, -24],\n [48, 9, 60, -33, -60, 36, -15, 42, 12, 66, -42, 42],\n [-142, -228, -38, 2, -133, -246, 77, 22, -184, -229, 185, 4],\n [232, -46, 352, -202, -428, 112, -58, 268, -8, 304, -176, 260],\n [552, 551, 380, -167, 0, 724, -245, 158, 468, 834, -618, 198],\n [-370, -584, -106, 10, -331, -634, 199, 50, -472, -595, 479, 4],\n [-112, -558, 232, -178, -688, -456, 122, 292, -424, -244, 260, 244]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[517, -170, -206, 742, 149, 138, -461, -1302, 147, 703, -1197, 1356],\n [-450, -83, -87, -573, 318, -65, -17, 466, 2, -498, 333, -932],\n [48, -780, -310, 14, -323, -129, -57, 192, 133, 499, -796, -229],\n [-514, 483, -678, 443, 856, 943, -230, -157, 584, -545, -1172, 324],\n [-378, 464, -464, 382, 155, 887, 635, -178, 15, 299, -494, 141],\n [428, 144, 674, -342, -315, -13, -773, -576, -7, -567, 692, 887],\n [-509, -755, -375, -510, 206, -948, -589, 1028, 554, -1187, -291, -797],\n [319, -242, 125, 67, -545, 318, 46, -255, -115, 630, -198, 331],\n [-331, 692, -243, 697, -1092, -313, 1801, 63, -400, 226, 796, 962],\n [-378, -127, -739, 642, 18, -723, 49, -74, 534, -690, -874, 986],\n [-384, 385, -434, 367, 595, 132, -193, 123, 489, -793, -571, 326],\n [-261, 309, 273, -381, -217, -533, 932, 644, -551, -19, 1430, -932]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-81, -1072, -1207, -160, 424, -1018, 179, -97, -413, -108, 647, -131],\n [531, 146, -16, -460, -74, 377, -487, 86, -53, -36, 488, 640],\n [273, 950, 408, 356, 174, 827, 453, -288, 453, 432, -840, 376],\n [-117, -556, 45, -460, -392, -378, -713, 379, -333, -444, 799, -179],\n [78, -37, -358, 147, 310, -86, 355, -193, 11, 186, -169, 103],\n [138, 1177, 1249, 203, -384, 1117, -125, 68, 435, 174, -748, 206],\n [-282, 431, 735, 817, 174, 195, 634, 3, -157, 408, -1224, -302],\n [351, 224, -480, -474, -36, 313, -190, -255, 547, -102, 534, 418],\n [-117, 132, -270, 214, 188, -17, 448, -283, 331, 126, -292, -132],\n [-567, -210, 551, 190, -364, -306, -145, 291, -169, -240, -141, -699],\n [426, 8, -845, -250, 366, 69, 194, -367, 284, 132, 323, 517],\n [-15, 199, 85, 599, 432, 46, 679, -157, -168, 444, -856, 14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[280, -541, 477, 135, 171, 129, 57, -202, 580, 345, 470, 280],\n [44, -36, 874, 452, 152, 1259, -256, -551, -858, 391, 235, -483],\n [440, -476, -456, 226, 270, 97, 804, 230, -193, -181, 187, 56],\n [173, 1047, -298, 602, 253, -475, 83, 124, 516, 154, -842, 322],\n [-1068, -386, 472, -1322, -168, -767, 158, 457, -495, -934, 543, -97],\n [-137, -833, 1323, 247, 790, 1062, -21, -133, 255, 223, 1042, 324],\n [4, -212, -164, 404, 808, 158, 336, 593, 649, -188, 238, 785],\n [225, -677, 15, -631, -900, -575, -160, -489, 638, 249, 336, -615],\n [787, 714, 424, 380, -259, -135, -537, -1082, 723, 1073, -619, -202],\n [-1120, -1189, 1307, -825, -189, 459, -480, 197, -447, -375, 1357, 48],\n [35, 923, -368, -422, 675, -264, 339, -82, 175, -439, -681, -542],\n [549, -143, -641, 769, 250, -196, 396, 456, 306, 211, -111, 1088]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-661, -691, -26, 277, 70, 839, 139, 352, 11, -274, -875, 558],\n [690, 482, -34, 346, -22, -558, 218, 123, 247, -51, 866, -386],\n [880, 640, -208, 488, 128, -320, 584, 356, 268, 100, 872, -120],\n [-750, -878, 14, 534, -726, -315, 67, 412, 468, 2, -439, 2],\n [-55, -281, 110, 511, -474, -645, -37, 200, 429, -226, 349, -426],\n [-83, -313, 259, 416, 71, 118, -243, 72, 139, -801, 91, -250],\n [727, 977, -117, -764, 923, 665, 32, -446, -659, 201, 188, 292],\n [322, 446, -79, -351, 321, 170, 41, -192, -258, 205, 115, 106],\n [451, 541, -555, 18, 557, 903, 996, 490, -179, 691, -248, 964],\n [-184, -360, 484, 152, 292, 319, -687, -263, -91, -1199, -1, -396],\n [-19, 287, -137, -668, 355, 497, -2, -281, -454, 446, -398, 414],\n [257, 199, -28, 85, 292, 275, 129, 66, -61, -162, 119, 94]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[821, -71, 1324, -1139, -150, 345, -1084, -1605, -107, -769, -872, -955],\n [-329, -181, -757, -465, -617, 15, -1075, 416, 310, 1126, 233, 1204],\n [583, 573, 739, -1907, -195, 865, -623, -266, 504, -330, -1439, -992],\n [-298, -556, 170, 225, -1178, 140, 303, 490, -544, -759, 239, 779],\n [-1027, -545, 1004, -130, -1469, -235, 125, -566, 481, 625, -879, 317],\n [-1353, -307, -391, 1234, -362, -464, 1190, 486, 226, 715, 684, 959],\n [224, -28, -1008, 530, -508, -385, 204, 1335, -789, -561, 460, 9],\n [159, 24, 29, -508, 320, -1234, 45, 8, 1259, 1820, -1050, -446],\n [-372, -457, 236, 481, 478, -643, 933, -508, -128, -81, 139, -404],\n [-84, -568, 118, 227, -718, -724, 665, 176, -28, -1282, -25, 260],\n [-239, 1696, -809, 1332, -13, 644, 978, 994, -327, -374, 1406, -541],\n [-2327, 347, -1738, 1742, -1002, -598, -181, -413, -119, 368, 2028, 870]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-73, 94, -7, 134, 84, 174, -104, -58, 186, 24, 165, 109],\n [-204, 144, -18, 236, 102, 480, -300, -46, 538, 154, 370, 302],\n [-209, 38, -17, 114, -18, 486, -316, 60, 568, 238, 295, 307],\n [-144, -180, -9, -162, -243, 324, -234, 243, 423, 315, 45, 207],\n [126, -612, 18, -756, -648, -324, 144, 540, -252, 288, -630, -198],\n [216, -72, 18, -156, -18, -504, 324, -30, -582, -222, -330, -318],\n [201, -390, 21, -522, -378, -486, 276, 288, -492, 30, -555, -303],\n [115, -298, 13, -386, -300, -282, 152, 238, -270, 72, -375, -175],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n [-146, 416, -17, 534, 423, 360, -190, -339, 337, -119, 505, 223],\n [139, -610, 19, -758, -642, -354, 164, 532, -288, 270, -645, -217],\n [323, -38, 26, -152, 51, -750, 490, -113, -881, -383, -440, -474]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-500, 453, 175, -820, -451, -514, -353, -1167, -458, 965, 818, 763],\n [-317, -598, 468, 1143, 196, 91, 563, 748, 691, -547, -359, -313],\n [-313, -233, 540, -171, 431, 371, -701, 404, 239, 538, 365, -221],\n [-79, -37, 470, 83, 27, 249, -295, 22, 103, 68, -13, -145],\n [558, 221, 515, -62, -31, 764, -662, -5, -111, -315, -502, -539],\n [-461, -238, -637, 241, -26, -811, 901, 47, 132, 71, 325, 514],\n [-145, -651, -145, 903, 451, 9, 646, 1073, 625, -528, -301, -338],\n [72, 341, -65, -428, -283, -130, -160, -593, -341, 215, 144, 251],\n [-380, -454, -171, -22, 604, -42, -83, 771, 342, 406, 422, -71],\n [-157, 69, -1196, -463, -23, -877, 658, -194, -278, 310, 487, 643],\n [-634, -348, 10, 34, 292, -326, 96, 294, 282, 522, 566, 240],\n [196, -263, 244, 222, 423, 560, -336, 724, 280, -207, -268, -552]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1285, 671, -627, 351, 345, 671, 568, -789, -350, 243, 256, -142],\n [551, 177, -130, 812, 131, -69, -417, 327, -372, -291, -452, 178],\n [-252, -1307, -2346, 286, 1863, 530, 1586, 564, -1311, 339, 101, -730],\n [-1333, -174, 228, -1889, 467, -304, 1325, 422, 341, 915, -309, 124],\n [-1031, 337, 238, -2009, -746, -484, 1349, 124, 304, 1152, 988, -1158],\n [-154, 62, 1102, 328, 62, -107, -595, 839, -805, 79, -637, 1190],\n [128, -277, -504, 81, -402, 387, 374, -761, 249, -166, 1351, -818],\n [395, 306, -761, 579, 844, -262, -1207, -137, 1142, -437, -662, -194],\n [-733, 511, -382, -1138, 1129, -940, 50, 561, -211, 950, -643, -1002],\n [-488, 756, 1343, -612, 359, -533, -509, 350, -98, 500, 2, 416],\n [725, 858, -950, 261, 80, 82, -215, 1769, 724, 940, -275, 371],\n [-1432, -1147, -1385, -1544, 135, 325, 747, 377, 118, 1341, 961, -1111]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-143, -169, -312, 312, 221, 312, 299, 39, 247, 325, 182, 104],\n [253, 299, 552, -552, -391, -552, -529, -69, -437, -575, -322, -184],\n [132, 156, 288, -288, -204, -288, -276, -36, -228, -300, -168, -96],\n [-66, -78, -144, 144, 102, 144, 138, 18, 114, 150, 84, 48],\n [-132, -156, -288, 288, 204, 288, 276, 36, 228, 300, 168, 96],\n [187, 221, 408, -408, -289, -408, -391, -51, -323, -425, -238, -136],\n [220, 260, 480, -480, -340, -480, -460, -60, -380, -500, -280, -160],\n [-66, -78, -144, 144, 102, 144, 138, 18, 114, 150, 84, 48],\n [110, 130, 240, -240, -170, -240, -230, -30, -190, -250, -140, -80],\n [165, 195, 360, -360, -255, -360, -345, -45, -285, -375, -210, -120],\n [110, 130, 240, -240, -170, -240, -230, -30, -190, -250, -140, -80],\n [-220, -260, -480, 480, 340, 480, 460, 60, 380, 500, 280, 160]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[112, -24, -443, 519, 518, -199, 814, -235, -581, -44, 371, -180],\n [5, -225, 242, -1020, -27, 419, -751, 70, -164, -608, -391, -390],\n [49, -74, -362, 309, 350, 196, 810, -332, -958, -268, 595, -536],\n [-302, 126, -102, 958, 55, 29, 1147, 47, -188, 170, 635, 193],\n [-159, 109, -253, 997, 401, -418, 1061, 119, 103, 260, 284, 470],\n [-378, 151, 581, -38, -848, 423, -340, 296, 591, 226, 66, 287],\n [412, -285, -542, -477, 768, 58, 148, -481, -1186, -646, 85, -879],\n [332, 76, -429, 437, 327, -532, 235, -264, -89, 366, 56, 57],\n [81, 351, -413, 1487, -88, -499, 1080, -288, -11, 942, 767, 335],\n [498, -241, -439, -602, 841, -484, -431, -191, -275, -364, -607, -252],\n [-111, 273, 130, 662, -503, -177, 141, 72, 564, 692, 219, 476],\n [477, 30, -136, -497, -458, 250, -750, -606, -568, 180, 217, -764]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-206, 369, -366, -48, -996, 81, 706, 264, 213, 1272, 616, -536],\n [703, 934, -1253, 144, -1004, 1097, 939, -982, 296, 954, -302, 60],\n [-671, -70, 419, 337, -560, 376, -393, 190, -66, 270, 332, -25],\n [248, -877, 206, 147, 628, -912, 144, 338, -1180, -149, 91, -680],\n [-905, -20, -20, -520, 148, -1304, 18, 932, -16, -733, 342, -169],\n [-297, -526, 1193, 23, 750, 1044, -427, -618, 610, -94, -114, 841],\n [323, -536, 360, -229, 304, -330, 596, 146, 45, 528, 101, -419],\n [1326, -486, -80, 473, 335, 1262, 297, -1638, -150, -773, -1802, 575],\n [710, 163, 214, 43, 194, 756, -349, -506, 410, -506, -824, 246],\n [-168, 682, -772, 595, -1055, -639, -965, 858, -162, 679, 926, -25],\n [247, -95, 448, -158, 775, 1403, 106, -1318, 385, -989, -1147, 781],\n [-836, 263, 130, -75, -412, -224, -593, 404, 931, -317, 199, 787]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-259, 974, 714, -298, 298, 1095, 1069, 201, -1518, 1314, -96, 346],\n [726, -707, -208, 232, -275, -397, -155, -415, 500, 226, 40, 91],\n [-188, -973, -512, -686, 350, -2071, -873, -756, 1123, -1050, 423, -2154],\n [202, -524, -466, -780, 148, -163, 549, -911, -714, 1047, 434, 526],\n [-463, -353, -1556, -1208, -403, -653, -607, 57, 524, -741, 282, -735],\n [-622, 420, -170, -669, -246, 342, 283, -410, -721, -264, 110, 299],\n [134, 26, -1184, -494, -268, 553, 485, 319, -52, 1322, 186, 549],\n [-31, 517, -684, 389, -691, 877, -204, 923, 221, -84, -301, 760],\n [1, 342, 1192, 818, 684, -46, -464, 846, -244, -559, -378, -362],\n [-273, 332, -16, 76, -639, 483, -397, 346, 136, -1230, -297, 414],\n [174, -908, 962, -1253, 1890, -824, 221, 232, -817, 548, 357, -868],\n [-604, 223, -818, -692, 73, 190, -196, 348, -649, -204, 151, 472]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-364, 134, -164, 201, -405, -694, 1143, 199, 189, -428, -1349, 979],\n [-560, 1085, -1106, -185, 734, 331, -522, -244, 453, -92, 244, 214],\n [928, 326, -59, 1465, -268, -486, 330, -359, -536, -743, -583, 808],\n [-113, -286, -185, 1144, -638, -131, -544, 630, -453, -161, 180, -209],\n [-994, -799, 871, 56, -493, -451, -8, 947, -46, 794, 304, -114],\n [286, -223, 125, -1042, -718, 1205, -740, -138, -92, 399, 545, -1467],\n [556, 130, -377, -678, -446, 754, 300, -582, -253, 102, -276, -639],\n [544, 1078, 13, -433, 681, 938, 138, -788, -10, 800, 424, -637],\n [647, 337, -352, -165, -644, 294, 411, -940, -472, -79, -461, 269],\n [511, 152, 479, -201, -135, -141, 788, -209, 397, 93, -580, 595],\n [-223, -337, -1537, 392, 240, -790, -394, 91, 387, -1276, -253, 1318],\n [847, 1521, -93, 1106, 621, 418, -605, -856, -190, 301, 739, 393]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-603, -1242, -150, -262, 1414, 902, 364, 677, -390, 342, -109, -194],\n [-757, -152, -584, -989, 109, 973, -547, 493, -132, 719, 306, -27],\n [229, 390, 1554, -1302, -283, 309, -1042, 905, -1370, -119, 485, 1490],\n [-444, 766, 177, -455, -855, 238, -273, -449, 376, -6, -197, 374],\n [-879, -360, 1119, -846, 509, 955, -49, 431, -549, 5, -458, 871],\n [320, -85, -70, -220, 252, 909, 775, -747, 470, -675, 523, 61],\n [-790, 1022, 942, -229, -1092, -588, -575, -148, 30, 86, -1197, 917],\n [-18, -1447, 322, 205, 1802, 795, 1128, 241, -310, -419, -134, -38],\n [25, -130, 410, -383, 87, 526, -116, 142, -263, -72, 459, 137],\n [-1145, -791, -61, -124, 728, 712, 133, 387, 8, 566, -526, -352],\n [-392, -320, 38, 864, 353, -251, 852, -544, 606, -235, -924, -362],\n [635, -67, -1725, 541, 275, -524, 469, -310, 581, 40, 114, -647]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[339, -479, -347, 136, 5, 1692, 1577, 475, -865, 52, -1170, 224],\n [-567, 337, 612, -209, 79, 319, 973, -267, -622, 785, -215, 114],\n [-844, -94, -461, -458, 310, -424, -23, 467, -843, 966, 769, -1305],\n [-1139, 317, -30, -411, 312, 273, 472, 113, 322, -405, -582, -196],\n [1597, 542, -385, 93, -1212, -71, 43, -875, -606, -532, -445, -657],\n [-618, 580, 378, -204, -511, 401, 1121, 823, 395, 756, -278, 2034],\n [-376, -202, 674, -958, -940, -257, 4, 807, 326, 55, -997, 1770],\n [1154, 1165, -1133, 822, -1248, -455, -199, -503, -419, -1177, 428, -1069],\n [-149, 146, 84, 117, 1444, 219, -495, -284, 1357, -404, 991, -757],\n [-539, -378, -292, -457, 1198, -308, -107, 622, 97, -170, -76, -279],\n [211, -604, -583, -1228, 614, 819, 1441, 1728, -590, 1025, -879, 785],\n [-260, 1080, 491, -432, 425, -955, 20, -731, 449, 222, 295, 47]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[733, 151, 227, -917, 1030, 205, -7, -1454, 298, 1163, 762, -404],\n [489, 39, -837, 478, 202, -41, 637, -662, -273, 474, -697, 562],\n [484, -536, -371, 818, -712, -378, 164, 617, 176, -1095, 1254, -1491],\n [-827, 46, -307, 333, -1041, -879, -212, 1098, -14, -1045, 1321, -1362],\n [-825, 222, -553, 51, -331, -767, 42, -578, -1038, 637, 131, 68],\n [193, -46, -546, -623, -262, -259, 272, -1212, -448, 942, 113, -271],\n [-120, 382, -154, -641, -331, -220, -26, 607, 1013, -475, 867, -1010],\n [1583, -119, 108, -280, 1392, 825, 333, -1332, 553, 889, -277, 344],\n [715, -229, 1209, -980, 659, 1337, 43, -731, 447, 940, -1403, 1464],\n [331, -882, 1688, -1138, -841, 1231, -300, 212, 361, -41, -832, 496],\n [-193, 1061, -923, 2302, 1654, -850, 390, 1186, 609, -994, 1085, -105],\n [103, -588, 166, 1341, -357, -159, 98, 637, -426, -840, 475, -299]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[327, 731, -86, 637, 678, -670, -935, 394, -923, -940, -412, 768],\n [-721, -172, -50, -1325, -552, 1111, 105, -184, 579, 1755, 91, -152],\n [-540, 1026, 1406, -335, 35, 183, 744, -930, -771, -542, 39, 741],\n [1008, -557, -1282, 313, 96, -160, -332, 41, 420, 13, -545, -1019],\n [634, 514, 77, -198, 371, -1032, 95, -758, -473, 621, -336, -1445],\n [-183, 402, 328, -118, 521, -724, -1200, -587, -778, -379, 488, 1120],\n [479, 81, 64, 464, 0, -609, 860, 1092, 285, 246, -561, -1542],\n [-269, 94, 72, -728, -715, -419, -1115, -2298, -625, 210, 1599, 576],\n [-476, 1038, 593, 245, -398, -283, 219, -478, -1162, 291, 506, -50],\n [-766, -520, 144, -679, -247, 1217, -103, -395, 511, 14, 417, 1376],\n [650, 841, 69, 1119, 1521, -1890, -666, 716, -1283, -312, -661, -493],\n [-1100, 154, 612, 265, -759, 953, 552, -264, -373, -326, 936, 1241]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[280, 104, -710, 577, 145, -243, 15, 449, -26, -384, 244, 582],\n [188, -509, -1495, 279, 1888, -666, 310, -7, -391, -399, 503, 834],\n [1240, 649, -509, 1645, 815, 465, 19, 138, 148, -1782, 731, -22],\n [-60, -311, -45, -265, 245, -127, -147, -186, 370, 184, -435, -766],\n [-419, -360, -1376, -638, 1477, -1106, 1003, -1240, 873, -136, -709, 877],\n [308, 613, 1121, 428, -1164, 741, -920, 448, -229, -106, 446, -174],\n [-689, 462, -1064, -633, 190, -1176, 413, -570, 1138, -54, -267, 2027],\n [-62, 448, -56, 135, -206, 160, 1148, 347, 198, -485, 82, -90],\n [293, 408, 720, 324, -464, 717, 1, -11, 274, -511, 232, -947],\n [-273, -59, 111, -354, -504, -207, -1085, 96, 474, 462, 59, -23],\n [713, -426, -574, 805, 713, 172, -198, -380, 88, -632, 104, -695],\n [151, -72, 624, -8, -46, 181, -621, 468, -737, 434, -176, -245]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-136, 564, -128, 486, -144, 90, 716, -152, -579, 593, 9, 5],\n [283, 77, 73, -267, -7, -180, -136, -275, 21, -36, 284, 15],\n [85, -146, 848, -378, 414, -542, -231, 958, 298, -516, -440, 295],\n [-39, 643, 265, 490, -238, -691, 1186, -264, -1196, 865, -186, 391],\n [232, 794, 775, 94, 30, -946, 910, 198, -938, 516, -98, 510],\n [-397, -656, -194, 258, -462, -432, 61, 6, -642, -18, -288, 493],\n [-153, 667, -415, 470, -194, 597, 348, -20, -344, 381, 398, -127],\n [-350, 423, -65, 418, -84, 419, 117, 830, -269, -44, 91, 167],\n [238, 10, 307, -343, 187, -185, -254, 153, 260, -250, 75, 25],\n [33, 24, 1040, -200, 216, -1038, 203, 1008, -388, -260, -508, 683],\n [14, 645, 1004, 204, 532, -639, 1031, 642, -270, 461, -848, 124],\n [-412, -383, 36, 55, -111, 158, -585, 1149, 40, -693, -59, 407]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[655, 1250, -1445, 1471, -1282, -634, 2072, -241, 1146, 283, -152, 171],\n [331, -533, -211, 588, -368, 1265, 617, 726, 840, -185, 298, 80],\n [-432, 1304, -1047, 393, 803, -184, -523, 772, 341, -14, -89, 1021],\n [881, -951, -289, 1113, 408, 568, 295, 58, 1576, 1081, 296, -1072],\n [-764, -789, -16, 935, 186, 326, -577, -659, -519, 631, -168, -1483],\n [-726, -1130, -906, -142, 871, 1159, -678, 505, 542, 254, 722, -923],\n [1003, -412, 513, 324, -1404, -680, 1089, -409, 376, 85, -368, -522],\n [10, 352, -445, 816, -240, -491, 1165, -1012, 879, -554, 60, -276],\n [237, 698, -111, 236, -63, 738, 70, -316, 592, -1367, -952, 1447],\n [142, -1053, 433, 1362, 41, 205, -327, -140, 1352, 120, -28, -892],\n [-1578, -1184, 745, -461, 639, 1457, -1379, -153, -294, -742, 89, -455],\n [344, -7, 936, 1502, -1249, -1062, -134, 793, -225, -17, 369, 361]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[556, -216, 261, 315, -34, -639, -1024, -198, 766, 551, -245, -329],\n [923, 143, 507, 0, -625, -92, 578, -49, 23, -822, -1143, 923],\n [231, -855, -517, 407, -371, -203, 124, 395, -429, -509, -156, -129],\n [-289, -76, 718, -284, 889, 239, 1140, -213, -225, 386, 11, 1226],\n [568, -617, 450, -847, -590, -45, 1626, 251, -695, 144, 935, 725],\n [-181, 124, -537, -440, 207, 60, 63, 149, 725, -467, 196, -374],\n [1070, 55, -542, 834, -373, -300, -626, 481, -359, -542, -983, 91],\n [183, 345, -397, 221, -775, 369, 400, 430, -752, -913, -671, 176],\n [880, 144, 295, -1185, -636, 12, 1409, 584, -300, 476, 838, 798],\n [-245, 1320, 150, 747, -557, 410, -880, -104, 56, -417, -1727, -60],\n [-339, -251, -1191, 969, -131, -61, -1100, 735, -345, 85, -270, -977],\n [-279, 210, -714, 145, -643, 444, 597, 649, -669, -769, -210, -272]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1314, 448, -783, 221, 664, 309, -11, 528, 526, -198, 1396, 670],\n [1237, 43, -136, -647, -231, -2576, -1488, 905, -676, -407, 20, -21],\n [104, -759, -372, -1364, 986, -1258, 274, 338, -375, 114, -1123, 68],\n [15, 166, 989, 949, 1184, -97, 667, -281, 268, -1037, -488, 997],\n [-374, 1254, 867, -191, -353, -1149, -919, -222, 622, -413, 381, -432],\n [824, -496, -1428, 308, 1020, -195, -48, 239, -20, -716, 459, 413],\n [1426, -237, -1070, -853, 2113, -455, -259, 193, 351, 939, 804, 1305],\n [232, 78, 111, 74, 92, -528, 200, 206, -1018, -1503, -72, 53],\n [-553, 766, 2307, 125, -739, -1940, -1189, -727, -286, -235, 492, 32],\n [-1146, -1472, -1470, -865, 2092, 1176, 712, -1362, 558, 1504, 122, 1006],\n [365, 402, -1248, 382, -350, 731, -623, 586, 694, 79, -436, -212],\n [-694, -142, 359, 236, -109, 1125, 1572, -41, 736, -779, 61, 47]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-26, 1028, 620, 575, 571, 187, -1093, -812, 195, 639, -1036, -483],\n [902, 99, 309, -439, -606, 936, 708, 85, 568, 473, 734, -178],\n [62, 71, 405, -232, -139, -300, -106, -14, 1152, 610, -86, -58],\n [34, 12, 50, -684, 652, -608, -110, 352, 312, -394, 370, 4],\n [694, -394, -492, -149, -430, 354, 869, 395, 364, -405, -24, 499],\n [332, -242, -476, -475, 455, -315, 355, 512, 5, -897, 110, 383],\n [369, 268, -291, 714, -73, 583, -15, -333, -239, -141, -1007, 202],\n [729, 84, -157, -251, 147, 80, 311, 209, 800, -256, -379, 306],\n [-248, -2, 488, -562, 81, -443, -176, 115, 527, 434, 688, -300],\n [430, -232, 144, -1157, 108, -83, 580, 614, 355, -229, 1386, -100],\n [51, 446, 919, -903, 296, 80, -270, -23, 218, 630, 1381, -799],\n [519, 1238, 1433, -214, -52, 1245, -566, -811, 225, 1513, 809, -1249]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-412, 499, -89, 226, -59, -204, -202, -283, 239, 10, -423, 345],\n [-8, -409, 494, 269, 29, 264, -158, 373, -59, -40, 243, -345],\n [-388, -24, 501, 525, -20, 124, -372, 180, 150, -38, -102, -90],\n [-48, 171, -144, -45, -15, -96, 18, -135, 45, 12, -117, 135],\n [284, -793, 593, 128, 73, 428, -26, 601, -233, -50, 561, -615],\n [328, -856, 614, 110, 80, 456, -8, 640, -260, -52, 612, -660],\n [84, 232, -377, -257, -12, -172, 164, -244, 2, 30, -114, 210],\n [-620, 365, 323, 584, -61, -60, -446, -77, 301, -22, -405, 195],\n [-48, 546, -588, -282, -42, -336, 156, -474, 102, 48, -342, 450],\n [-432, 664, -260, 148, -72, -304, -160, -424, 272, 24, -528, 480],\n [160, 305, -556, -403, -13, -240, 262, -341, -17, 44, -135, 285],\n [-80, 410, -388, -154, -34, -240, 76, -338, 94, 32, -270, 330]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-544, 184, 242, -42, -506, 157, 348, 279, -606, -210, -141, 365],\n [75, -935, 265, -605, -155, -155, 490, -870, -80, 135, 175, -475],\n [-79, -199, 618, -625, -612, -136, 177, -206, -752, -798, -329, 201],\n [797, -308, -1, 20, 100, 100, 141, -280, 234, 191, -305, -289],\n [-381, 448, 193, -42, -284, -29, -179, 407, -440, -535, -136, 434],\n [-186, -227, -35, 61, -120, 169, 452, -105, -56, 397, 75, -93],\n [764, -682, -78, -94, 236, 32, 280, -632, 436, 490, -48, -572],\n [-375, 10, -26, -180, 137, -254, -294, -79, 64, -164, 354, -8],\n [-271, -848, 224, -648, -99, -269, 340, -822, -78, 70, 407, -417],\n [561, -279, 336, -217, -350, 126, 347, -214, -312, -212, -517, -43],\n [-270, -193, 173, -87, -374, 170, 528, -62, -370, 113, -78, 56],\n [317, 84, -206, 106, 395, -132, -420, -19, 428, 36, 98, -140]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-160, 41, -86, -887, -303, -475, 523, -570, 541, -188, -275, 20],\n [-820, 1110, 592, -779, -115, -935, -359, 250, 374, 256, 125, -990],\n [-257, 382, 88, -348, -354, 9, -345, -796, 485, -301, 462, -695],\n [-1078, 808, 887, -996, -281, -733, 80, 359, 340, -32, -372, -368],\n [-1397, 1479, 1292, -733, -524, -1074, 235, 226, 23, 587, -373, -729],\n [-340, 363, -40, -996, 122, -388, -789, 110, 848, -539, 442, -867],\n [-784, 270, -451, -1498, -784, 23, 214, -117, 652, -99, -54, -1039],\n [-1018, 806, 1273, -438, 153, -613, -430, 901, 78, -138, -246, -146],\n [605, 99, -136, -587, 1002, -1174, -881, -22, 981, -623, 489, -131],\n [-801, 333, 521, 78, -802, 452, 576, -79, -481, 375, -382, -91],\n [-393, -329, -62, -184, -766, 807, 644, -376, -143, -126, -348, 184],\n [95, -265, -284, 502, 69, 383, 289, 876, -722, 592, -308, 236]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[594, -1369, -1336, -90, 440, 798, -1409, -815, -474, 838, 436, 44],\n [35, -84, -342, 610, -54, -650, -76, -403, 1414, -140, -413, -567],\n [483, 612, -184, 125, 112, -515, -81, 259, 92, -219, -455, 175],\n [170, 511, 387, 431, 508, -142, -272, 1108, -415, 835, -661, 649],\n [-377, -284, -2062, -1115, -858, 87, -265, -1231, 0, -343, 6, 124],\n [211, -263, -321, -683, -292, 876, -83, -634, -1044, -455, 779, -30],\n [1063, -248, 720, 953, 1410, 553, -971, 799, -896, 602, 306, 854],\n [-1069, -239, -19, -70, -281, 29, 563, -481, 642, -548, 397, 176],\n [1704, 781, 488, 1230, 1217, -30, -356, 185, -79, -946, 408, 307],\n [-166, 483, 137, -484, -569, 1015, 688, -117, -725, -29, 559, -115],\n [272, 979, -649, 302, -555, 543, 634, 158, 1014, 1174, -328, -195],\n [295, -593, 417, 260, -106, -613, 234, -441, 1673, -568, 321, -181]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-719, 12, -285, 31, -54, -71, 206, -484, -465, 247, 543, 410],\n [-817, 415, -461, -65, -263, 407, -251, -935, -432, -600, 257, 38],\n [-233, -15, -236, 183, 24, -101, 379, 19, -302, 432, 371, 221],\n [-48, -169, 680, -674, -55, 24, -1017, -543, 555, -937, -572, -82],\n [-1009, 241, -394, -105, -206, 203, -141, -981, -518, -316, 463, 299],\n [440, -6, 171, -16, 33, 44, -122, 298, 282, -148, -330, -251],\n [-504, -532, 635, -572, 95, -468, -456, -504, 180, 14, 94, 569],\n [94, -204, 321, -194, 63, -158, -196, 32, 222, -32, -144, 65],\n [96, 6, -441, 528, 105, -156, 882, 558, -402, 936, 486, 153],\n [25, -301, 581, -451, 53, -191, -547, -187, 402, -318, -305, 94],\n [338, 399, -318, 236, -111, 410, 19, 169, 9, -355, -246, -482],\n [432, 240, -456, 528, 24, 144, 624, 624, -192, 432, 96, -264]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[372, 449, -350, -78, -59, -109, -78, -16, -339, 5, 319, -88],\n [-464, -481, -523, -20, -521, -707, 330, 589, -687, -231, 596, -337],\n [840, 586, 489, 568, 174, 312, -258, -575, 362, 670, -313, 557],\n [1021, 814, -10, 495, -137, 64, -114, -396, -188, 689, 282, 399],\n [219, -43, -119, 471, -512, -325, 282, 113, -405, 470, 496, 182],\n [946, 686, -324, 680, -292, -792, -258, -50, -688, 426, 398, 174],\n [699, 312, 21, 900, -219, -891, -297, -36, -423, 432, 27, 282],\n [-1017, -859, 82, -444, 46, 96, 249, 353, 244, -521, -203, -303],\n [-223, -362, 139, 110, -367, 331, 495, 38, 71, 388, 307, 186],\n [-273, -46, 67, -558, 127, 865, 261, -136, 377, -60, 43, -44],\n [598, 584, 446, 73, 400, 729, -249, -605, 575, 373, -406, 382],\n [-306, -109, -676, -356, -223, -567, 78, 482, -653, -507, 487, -496]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-173, 359, -548, 222, -734, -46, 386, -545, -332, -978, -128, 1018],\n [323, -701, 176, -156, -289, -236, 358, -187, 290, 123, -271, 92],\n [465, -701, 114, -292, 331, -331, -133, 204, 124, 435, 108, -530],\n [510, -260, -986, -174, -25, -677, -179, -179, -716, -813, 470, 296],\n [-291, 349, 32, 184, -309, 228, 198, -181, 34, -225, -179, 384],\n [-253, 17, 310, 178, -682, 247, 595, -392, 366, -138, -537, 608],\n [603, -783, -122, -344, 343, -505, -187, 172, -48, 255, 230, -482],\n [545, -545, -466, -264, 185, -557, -179, 26, -316, -183, 320, -154],\n [-30, -276, 258, 54, -579, 57, 543, -345, 348, -63, -462, 456],\n [-660, 1050, 102, 318, 195, 579, -267, 183, -108, -9, 90, -12],\n [597, -997, -178, -246, -488, -565, 467, -382, 98, -240, -215, 352],\n [-51, -189, 382, 10, -176, 131, 251, -62, 354, 264, -295, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-237, 246, 426, 474, 459, 309, 612, -261, 582, -621, -72, -63],\n [416, -572, -416, -520, -624, -338, -546, 156, -520, 624, -78, 78],\n [-145, 84, 418, 438, 367, 286, 625, -303, 594, -601, -141, -54],\n [-154, 194, 196, 232, 254, 151, 269, -96, 256, -290, 3, -33],\n [-296, 478, 128, 212, 352, 137, 121, 42, 116, -208, 159, -39],\n [235, -474, 122, 42, -157, 29, 260, -237, 246, -149, -264, 9],\n [515, -788, -326, -466, -669, -302, -375, 21, -358, 507, -213, 78],\n [-90, 248, -204, -164, -26, -108, -350, 234, -332, 278, 198, 12],\n [194, -462, 268, 192, -38, 127, 481, -348, 456, -358, -321, -9],\n [-120, -48, 624, 624, 456, 408, 960, -504, 912, -888, -288, -72],\n [-336, 604, 0, 104, 320, 66, -94, 180, -88, -32, 270, -30],\n [408, -632, -240, -352, -520, -228, -268, 0, -256, 376, -180, 60]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1107, 314, -610, -864, -1568, -585, 1708, 44, 221, -34, 190, 744],\n [-576, 207, 47, -126, 718, -805, 1013, -708, -105, 374, 1004, 64],\n [854, -568, 106, -94, -64, 6, -78, 590, 756, -427, -1183, -629],\n [1156, -774, -76, -911, 311, -182, -55, -575, 387, 281, -434, -202],\n [867, 74, 212, 714, 1384, 221, -926, -443, 729, -107, 126, 68],\n [882, -321, 411, 282, 1008, 332, -999, -166, -62, 149, -238, -442],\n [-15, 173, 923, -819, 249, 71, 674, -401, 466, 524, 72, 1338],\n [-618, 330, -446, 447, -181, -259, 257, 44, -110, -248, 528, -85],\n [-1073, 690, -216, 59, -91, -800, 1611, -196, 479, 223, 165, 30],\n [-21, -91, -881, 761, -471, -295, -22, 679, 436, -898, -382, -992],\n [317, -309, 731, -494, 718, 212, -393, -457, -974, 918, -15, -303],\n [477, -386, -340, -242, -10, -558, 614, 10, 1084, -578, -111, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[802, -511, 391, -298, -539, 348, -1238, 594, -83, -145, -331, -30],\n [238, 779, 122, 566, -578, 680, -362, 1014, -1084, 1326, 970, -432],\n [-117, -20, 1243, 271, 96, -570, -1046, 705, -2443, 234, -32, -1185],\n [-911, 1269, 827, -830, 624, -805, 1444, -696, -1458, 1213, 489, -951],\n [782, -468, 213, 220, -323, 294, -984, 553, -119, -181, -606, 24],\n [-655, -786, -5, 219, 628, 120, 59, -423, 30, -390, -986, -604],\n [176, -530, 359, -916, -680, 1505, -122, -469, 1146, -52, -455, -391],\n [1864, 1139, 1513, -64, -1154, 31, 335, -298, -234, 702, 143, -113],\n [-1513, -51, -210, -936, -736, -58, -663, 107, -262, -1273, 1275, -652],\n [-1770, 401, 218, -672, -612, 160, 181, -386, -392, 171, 1945, -1499],\n [-1633, 291, -1316, -843, 69, 348, 328, 216, 448, 189, 1354, 107],\n [-357, 15, 223, -611, 776, 2, 572, -326, -345, 855, -581, -360]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1038, -1, -241, -472, 234, -581, -712, 358, 378, -73, 339, -748],\n [-841, -37, -281, -682, 456, -397, -647, 444, 424, -233, 647, -606],\n [-323, -608, 237, 773, -2, -654, 481, -31, -354, -203, 1260, -515],\n [-337, -769, -424, -706, -150, 307, -1180, 925, 1116, 874, -46, 20],\n [-670, 595, 310, 1003, 54, -477, 829, -688, -1650, -1370, 835, -671],\n [-384, -29, -285, 415, -182, -249, 57, 708, -189, -308, 626, -175],\n [-973, 33, -669, 331, 222, -167, -1155, 1, -522, -121, -652, -93],\n [-1371, 418, -190, 240, 168, -1274, -54, 369, -259, -709, 832, -1138],\n [265, 139, 572, -200, -156, 19, 369, -722, 95, 227, -384, -160],\n [-359, 601, -354, -1528, 358, -111, -940, 408, 1221, 358, -886, -174],\n [59, -1242, 965, 495, -222, -854, 580, -827, 457, 905, 816, -727],\n [-316, 1136, 38, 442, -230, 124, 617, -142, -1228, -1207, 0, -184]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[637, 92, -372, -555, -178, -289, 166, -424, -543, -623, 535, 558],\n [720, -512, -64, -12, 148, -968, -644, 364, 340, -412, 940, 412],\n [-297, 252, -930, 49, -153, 520, 1107, -1209, -217, -53, -265, -72],\n [182, 384, -236, 502, -602, -228, 414, -330, -78, 26, 610, 108],\n [-335, 513, 824, 347, -397, 306, -168, 615, -138, 514, -280, -297],\n [744, -216, -582, 272, -245, -929, 11, -303, 210, -450, 1220, 472],\n [402, -260, -376, -252, 130, -362, -38, -230, -8, -400, 400, 310],\n [411, 465, 354, -415, -430, -45, -65, 144, -706, -266, 270, 359],\n [-321, 472, -232, 511, -468, 327, 680, -482, -77, 299, -55, -210],\n [305, 261, -74, 373, -494, -369, 135, -84, -54, -46, 670, 177],\n [-79, -253, -1450, 43, 182, 129, 1053, -1456, 162, -310, 50, 61],\n [-90, 139, 830, 354, -172, -126, -573, 880, 165, 381, 35, -187]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-198, -391, 414, 1089, 945, -64, -277, -720, 143, -420, 249, 236],\n [-1048, -514, 530, 684, 380, -986, 469, -256, -372, 486, 323, 1275],\n [-718, -473, 40, -144, -226, -1207, -509, -156, 145, -83, -632, 940],\n [433, 222, -495, 410, 592, 63, -693, -305, 738, -719, -666, -453],\n [63, 37, 18, -884, -819, -20, -186, 285, -65, -174, -53, -44],\n [718, 339, -47, 271, 312, 732, -207, -100, 756, -1212, -54, -533],\n [1055, 378, -70, -7, -424, 872, 378, 245, 193, -792, 559, -851],\n [136, -258, 386, -95, -36, 105, -890, -422, 563, -1342, -139, 33],\n [-101, -115, -187, 702, 592, 46, 617, 81, -202, 1058, -187, 50],\n [68, 791, -397, 628, 595, 211, 1159, 198, -606, 933, 951, -365],\n [250, 40, -220, -805, -397, 245, -1023, -274, -514, 221, 158, -947],\n [-964, -509, 675, -378, 60, -11, 145, 30, -534, 1004, 3, 764]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[289, 85, 408, 34, 306, 442, 391, 0, -17, -408, -17, 204],\n [323, 95, 456, 38, 342, 494, 437, 0, -19, -456, -19, 228],\n [102, 30, 144, 12, 108, 156, 138, 0, -6, -144, -6, 72],\n [-51, -15, -72, -6, -54, -78, -69, 0, 3, 72, 3, -36],\n [-289, -85, -408, -34, -306, -442, -391, 0, 17, 408, 17, -204],\n [-34, -10, -48, -4, -36, -52, -46, 0, 2, 48, 2, -24],\n [238, 70, 336, 28, 252, 364, 322, 0, -14, -336, -14, 168],\n [-289, -85, -408, -34, -306, -442, -391, 0, 17, 408, 17, -204],\n [204, 60, 288, 24, 216, 312, 276, 0, -12, -288, -12, 144],\n [-187, -55, -264, -22, -198, -286, -253, 0, 11, 264, 11, -132],\n [17, 5, 24, 2, 18, 26, 23, 0, -1, -24, -1, 12],\n [-255, -75, -360, -30, -270, -390, -345, 0, 15, 360, 15, -180]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1784, 305, -297, 614, -2026, 311, 249, 830, 844, -302, 71, -1013],\n [193, -1160, -412, 1394, -128, 1010, 348, 406, -800, 730, -798, 1312],\n [-904, -101, 374, 723, -547, 249, 599, 474, 255, -68, -108, -500],\n [-403, -949, 133, 132, 1528, -261, 95, -918, -1052, 1050, -761, 1437],\n [-834, -928, 586, 1387, 283, 1008, 350, 665, -319, -157, -798, 512],\n [-529, -90, 601, 58, -393, 581, -694, 715, 1025, -1055, 661, -518],\n [1206, 307, -610, -257, 384, -308, -87, -834, 262, -62, 572, 311],\n [-657, 155, 220, 350, -29, 172, -9, -15, 699, -747, 230, -377],\n [-249, 1005, -109, -670, -623, -334, -19, 449, -185, -442, -472, -1045],\n [-37, -614, -778, -289, 457, -253, -546, -916, -452, 914, -108, 1371],\n [-720, 69, 2, -830, -363, -490, -193, 258, -765, 777, -591, -130],\n [-107, 436, -429, 248, -238, 28, 380, 96, -484, -105, -814, -176]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-24, 0, -7, -9, 11, 6, 11, 10, 12, 14, -6, 22],\n [-480, 0, -140, -180, 220, 120, 220, 200, 240, 280, -120, 440],\n [-336, 0, -98, -126, 154, 84, 154, 140, 168, 196, -84, 308],\n [-336, 0, -98, -126, 154, 84, 154, 140, 168, 196, -84, 308],\n [600, 0, 175, 225, -275, -150, -275, -250, -300, -350, 150, -550],\n [-168, 0, -49, -63, 77, 42, 77, 70, 84, 98, -42, 154],\n [168, 0, 49, 63, -77, -42, -77, -70, -84, -98, 42, -154],\n [-408, 0, -119, -153, 187, 102, 187, 170, 204, 238, -102, 374],\n [552, 0, 161, 207, -253, -138, -253, -230, -276, -322, 138, -506],\n [600, 0, 175, 225, -275, -150, -275, -250, -300, -350, 150, -550],\n [240, 0, 70, 90, -110, -60, -110, -100, -120, -140, 60, -220],\n [600, 0, 175, 225, -275, -150, -275, -250, -300, -350, 150, -550]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-339, -515, 469, 739, -554, 132, 381, 219, 431, 257, 506, -521],\n [87, 402, -189, -261, 234, -203, -263, -138, -30, -128, -68, 317],\n [-113, 326, 372, -11, -446, -27, 357, 412, -348, 89, -247, 182],\n [750, -301, -368, 73, 1383, 700, -474, -1094, -375, -539, 1023, 13],\n [-172, -97, 585, -159, -512, 107, 259, 222, -638, 256, -626, 4],\n [-619, -223, 1155, 41, -1094, -128, 219, 249, -503, 591, -754, -125],\n [254, -369, -619, -196, 478, 141, -156, -163, 187, -136, -81, -197],\n [-324, -651, 206, -304, -593, -38, 117, 271, -166, 441, -1078, -382],\n [-9, -10, 673, -107, 624, -37, -1127, -1484, -474, -10, 436, 297],\n [579, -292, -793, -120, 1154, 341, -466, -717, 127, -432, 559, -68],\n [681, 429, -625, -252, 1423, 163, -783, -1040, -151, -627, 831, 486],\n [-235, 714, -465, -126, -261, -718, -69, 487, 764, -16, -155, 302]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[548, 415, 79, 213, -685, 213, 123, 400, -565, 58, 239, 261],\n [485, -39, 20, 363, -81, 421, 7, -287, -990, 204, -624, 246],\n [1019, 465, 855, 612, -1365, 126, 185, 35, -616, -118, 395, 1309],\n [-1078, 418, -1040, -210, 1060, -1744, -1230, -966, 1168, 392, 106, -188],\n [429, 425, 785, -1413, -225, 156, 643, 903, 406, -141, 849, 590],\n [234, 1365, -663, 540, -599, -451, -559, 727, 54, 66, 887, -595],\n [791, -922, 672, -124, -449, 622, 550, 21, -741, -29, -799, 1021],\n [289, 118, 129, 321, 91, 344, -34, -332, -610, 76, -384, 58],\n [-49, 69, 177, 532, 447, 535, -71, 177, 430, -482, -123, -1082],\n [614, -401, 158, 945, -653, 537, 75, 424, -295, -335, -422, -156],\n [-91, -35, 249, 446, 1143, 671, -203, -459, 162, -352, -715, -1074],\n [377, -389, 1060, -147, 106, 739, 521, -72, 57, -415, -235, 302]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[826, 822, -858, -1347, -205, -41, -1205, 527, -1089, 579, 742, -278],\n [-321, -85, -392, 441, -509, -154, -257, -835, 802, 152, -85, 351],\n [-235, 312, 400, -436, -530, -290, 390, 132, 92, -418, -11, -168],\n [122, -175, -94, 542, -72, 714, 20, 33, -206, -309, -183, -553],\n [721, 550, 992, -1026, 161, -625, -1081, -1128, 153, -574, 563, 587],\n [-971, 111, 815, 1478, 633, -535, 812, -260, 390, -109, -948, -145],\n [1443, -1550, 366, 583, -112, 27, 646, 104, -425, 827, -144, 2141],\n [284, 452, 255, 133, 423, -70, 402, -599, 55, -10, -181, 225],\n [93, -290, 235, -377, -502, 258, 715, -870, 909, 20, 336, 796],\n [487, -220, -757, -1672, -8, 581, -841, 462, 24, -850, 861, -519],\n [217, 673, 3, -158, -405, 165, 355, 275, -846, 1209, 249, 5],\n [10, -1009, -16, -229, -300, 673, 679, 686, 133, -249, 188, 62]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-251, 182, 498, -147, 159, 350, -102, -147, -221, 195, -415, 233],\n [348, -398, -593, 536, 360, -493, 7, -257, 585, 152, 486, -9],\n [270, -300, -654, 250, -394, -351, -21, 467, 513, -92, 492, -470],\n [200, 48, -388, -236, -644, -251, 87, 541, -139, -532, 402, -298],\n [-463, 194, 601, -211, 75, 591, 169, -122, -283, 230, -707, -176],\n [-197, 300, 304, -429, -107, 218, 372, -113, -650, -358, -291, -79],\n [405, -162, -822, 13, -305, -614, 518, 105, -45, -681, 673, -471],\n [644, -436, -1214, 364, -332, -894, 226, 302, 518, -488, 1048, -474],\n [-120, -218, -323, 80, -784, 180, 6, 884, 522, 112, -20, -985],\n [-545, 420, 1003, -417, 109, 758, -144, -125, -539, 275, -861, 314],\n [-550, -38, 240, -102, -590, 708, 262, 614, 203, 307, -696, -1126],\n [176, 400, 39, -544, 100, -302, 510, -482, -1051, -895, 214, 429]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[104, 282, 317, 306, -203, 9, 526, -261, -468, 310, -158, 158],\n [888, -196, 679, -276, 619, 392, 242, 213, -49, 310, 402, -597],\n [-176, 910, 428, 462, 272, 155, -122, -132, -803, 290, -302, -47],\n [-24, 382, -6, -110, -614, 84, 359, -668, -560, 283, -385, 709],\n [688, 138, 445, -482, -43, 426, 367, -431, -459, 443, -9, 188],\n [-40, -122, -341, -502, -207, 79, -294, -187, 166, -132, -54, 316],\n [-240, 770, 124, 290, -656, 17, 462, -748, -913, 394, -574, 767],\n [224, 260, 486, 130, 1025, 260, -538, 562, -61, 23, 272, -855],\n [112, -266, -71, 94, -957, -216, 1051, -563, -143, 237, -185, 680],\n [72, -262, 250, 570, 136, -238, 491, 348, 164, 25, 207, -423],\n [56, 116, 306, 292, 620, 47, -223, 436, 11, -13, 185, -600],\n [-352, 134, 154, 824, 319, -293, 42, 458, 26, -95, 52, -482]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-502, 581, -277, -183, 287, 121, 410, -221, 246, -549, -420, 155],\n [-536, -33, -271, 474, 295, 471, -349, -915, 739, 290, -316, 103],\n [617, 372, -833, 61, 995, 79, 257, -202, -13, -396, -127, 951],\n [452, 326, -1631, -755, 21, 146, 197, -899, 470, -643, -321, 1614],\n [766, 625, 1220, 527, 515, -588, 1046, 1638, -1582, -88, 223, -1050],\n [1195, -622, -449, 1514, 455, -268, -792, -1126, 73, 1360, -54, 471],\n [325, 912, -1159, -810, -310, 52, 936, -448, -75, -838, -505, 1036],\n [383, 830, 394, -548, -70, -349, 1332, 1195, -981, -871, 26, -345],\n [-515, -1175, 864, 496, 527, -217, -1203, 339, 560, 466, 549, -691],\n [40, 251, -1192, -930, -245, -174, 393, -630, 635, -955, -329, 1096],\n [-149, -950, -902, -725, -849, 227, -1186, -916, 910, 292, 228, 938],\n [-251, 343, 186, -527, 249, -352, 891, 600, 154, -1128, -45, -229]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[437, 207, -230, 322, 69, 575, -276, -161, 207, -575, 414, -529],\n [228, 108, -120, 168, 36, 300, -144, -84, 108, -300, 216, -276],\n [-475, -225, 250, -350, -75, -625, 300, 175, -225, 625, -450, 575],\n [342, 162, -180, 252, 54, 450, -216, -126, 162, -450, 324, -414],\n [-361, -171, 190, -266, -57, -475, 228, 133, -171, 475, -342, 437],\n [323, 153, -170, 238, 51, 425, -204, -119, 153, -425, 306, -391],\n [-494, -234, 260, -364, -78, -650, 312, 182, -234, 650, -468, 598],\n [266, 126, -140, 196, 42, 350, -168, -98, 126, -350, 252, -322],\n [247, 117, -130, 182, 39, 325, -156, -91, 117, -325, 234, -299],\n [266, 126, -140, 196, 42, 350, -168, -98, 126, -350, 252, -322],\n [-418, -198, 220, -308, -66, -550, 264, 154, -198, 550, -396, 506],\n [342, 162, -180, 252, 54, 450, -216, -126, 162, -450, 324, -414]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1162, 662, 488, -574, -227, -1522, 183, -852, 231, -667, 21, 226],\n [230, 352, -396, -637, -991, 446, -1007, 634, 270, -416, -288, -603],\n [-864, 654, 593, -737, -44, -457, -417, 404, 928, -1440, -836, 816],\n [525, -114, 220, 414, 17, 411, 246, 1510, 858, -452, -696, 665],\n [-319, -561, 889, -476, 63, 420, 494, -121, 2, -715, -241, 117],\n [-151, -299, -1077, 678, 456, 110, -35, -69, -75, 694, 400, 159],\n [-768, 735, -264, -611, -130, -572, -825, -521, 122, -421, -59, 34],\n [141, 412, 5, -744, -733, 57, -744, -433, -411, -31, 129, -874],\n [533, 204, 226, 891, 916, -187, 427, 514, 258, 368, -248, 898],\n [-372, -147, -251, 95, 1544, 823, -564, -725, -433, 198, 8, 693],\n [141, 274, -35, -287, -731, -657, -14, -957, -738, 602, 658, -1067],\n [-568, 44, -401, -128, -45, -578, -21, -1133, -542, 434, 638, -437]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[119, 276, -250, 540, 102, -104, -653, 402, -413, 236, -326, -156],\n [-152, -29, -155, 281, 231, 157, -323, 221, -253, -151, -354, -107],\n [-194, -237, 665, -759, -265, -561, -159, -555, -109, 471, 314, -559],\n [-413, -183, -383, 555, 579, 569, -412, 441, -382, -611, -772, -69],\n [324, 240, 104, -96, -314, -367, 23, -90, 93, 451, 348, 22],\n [196, 86, 434, -494, -424, -599, -5, -380, 65, 623, 496, -236],\n [257, 162, -60, 6, -172, -52, 269, -12, 229, 100, 250, 242],\n [-187, -180, -62, -12, 172, 291, 186, 0, 76, -363, -134, 94],\n [549, 506, -188, 334, -292, -328, -139, 220, 21, 520, 242, 178],\n [493, 529, -427, 659, -91, -94, -271, 467, -91, 304, -36, 249],\n [-501, -413, 39, -103, 357, 383, 2, -49, -108, -533, -368, -143],\n [-305, -245, -105, 65, 295, 390, 75, 65, -25, -480, -300, 35]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-382, 102, 16, 200, -191, -117, 197, -236, -328, -490, 155, 268],\n [110, -217, 114, 31, 262, 118, 223, 412, 168, -258, -310, -215],\n [-403, 577, 120, 338, -190, -79, 124, -298, -694, 165, 745, -6],\n [297, -224, 54, -109, 275, 140, 24, 398, 322, 93, -320, -275],\n [455, -245, 208, -50, 561, 290, 179, 810, 378, 203, -390, -646],\n [564, -225, 222, -87, 627, 333, 126, 888, 432, 408, -375, -765],\n [687, -606, 86, -293, 608, 303, 41, 890, 818, 103, -845, -551],\n [153, -98, 234, 125, 410, 203, 321, 614, 70, -87, -185, -473],\n [163, -83, 324, 200, 530, 263, 446, 794, 30, -117, -185, -628],\n [131, -146, -106, -165, -38, -19, -165, -62, 226, 67, -175, 97],\n [-557, 182, -274, 35, -681, -362, -188, -966, -378, -425, 330, 853],\n [107, -259, -268, -304, -234, -125, -342, -342, 350, -29, -285, 404]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[980, 198, 744, 1792, -732, 1759, -189, -767, 84, -19, 687, -299],\n [499, -828, 729, 1154, -103, 741, -40, -292, 788, 954, 670, -360],\n [496, 544, -297, 24, 251, 528, -1145, -47, 201, 493, -20, -679],\n [-724, 250, -949, 29, -1193, -55, 1776, 947, -1052, 137, 552, -315],\n [-361, -304, -386, -524, 644, -449, 31, 237, -91, 1015, 940, -501],\n [838, 682, 493, 1397, -1123, 557, 729, 5, -1174, -478, 264, -47],\n [-60, 91, -979, -451, 970, -1365, 46, 1043, -773, -155, 395, 451],\n [439, 522, 147, -114, -322, 669, -118, -451, -427, 71, 516, -463],\n [-785, -256, 480, -1747, 120, -231, -391, -710, 828, 512, -843, -462],\n [-356, -229, -523, -473, -225, -1380, 1219, 987, -453, -157, -239, 430],\n [812, 403, -1088, 1688, 147, 192, -373, 1324, -534, 59, 457, 9],\n [-391, -8, 401, 303, -522, 562, 922, -395, -875, 192, 1053, -296]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[1180, 404, 1250, -404, 663, -454, 678, 321, 366, -620, 1155, -1068],\n [63, -261, 1419, 1012, -318, -131, -804, 972, 45, -183, 604, -410],\n [-161, -397, 31, 756, -43, -413, 572, 41, 269, -139, -1541, 88],\n [1458, -96, 461, -224, 624, -1450, 379, 668, -320, -710, -306, -79],\n [-1246, -96, -28, 157, -1221, 1512, -1348, -860, 354, 1651, 454, 1047],\n [374, 1017, 943, 50, 515, -294, -528, -633, 691, -618, -394, -714],\n [-46, 560, -572, -668, -384, 309, -409, -713, -160, 914, -112, 684],\n [-1026, 713, -1006, -277, -853, 986, -619, -1098, -53, 1359, -649, 810],\n [-79, -147, 428, 761, -343, -312, -324, 301, 16, 136, -844, 182],\n [917, -729, 1053, -230, 327, -350, 55, 174, 453, -187, 923, 128],\n [741, -700, 1076, -113, 361, -166, 321, 433, 396, -364, 1285, -297],\n [284, 6, -65, -494, -372, 107, -246, -283, -90, 846, 258, 715]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[162, -588, -445, 544, 525, -1187, 1012, -709, 548, -479, 419, 1183],\n [-593, -535, -230, 296, -118, 422, 1278, -1, 1020, -1677, 768, 420],\n [-432, -736, 2213, 724, 797, -570, -171, 779, 1830, -750, 588, -996],\n [606, -153, 935, -196, -714, -249, -258, -347, 710, -40, 1831, -1617],\n [618, 143, 1156, 53, 361, -825, -255, -1074, 1223, -218, 991, -216],\n [-342, -487, 2238, 851, 433, -1291, -587, 226, 545, -496, 727, -732],\n [-572, -204, -1131, 379, 279, 485, -38, 1155, -1327, 427, -668, 588],\n [-244, 467, -1209, -610, -1400, 1235, 351, -533, -680, -602, 462, -52],\n [465, -288, 985, 347, 1188, -1840, -130, -813, 1911, 321, -46, 54],\n [282, -56, 683, -464, 517, 833, -447, 1570, 651, 257, 324, -1807],\n [174, 247, 142, -408, -1068, 404, -96, -552, 195, -322, 1165, -1006],\n [-427, 619, -446, -756, 367, 1020, 514, 878, -87, -791, -1291, -208]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[386, -136, 395, 353, 21, 162, -26, -8, -2, -95, 290, -466],\n [60, 76, 71, -53, -265, -20, -56, -34, 46, 5, -130, 36],\n [-207, -30, -222, -75, 273, -39, 69, 39, -48, 30, 30, 135],\n [-429, 222, -432, -471, -219, -213, -9, -15, 36, 120, -450, 597],\n [585, 10, 620, 295, -565, 145, -155, -85, 100, -100, 50, -465],\n [-150, -104, -169, 37, 425, 10, 94, 56, -74, 5, 170, 6],\n [-196, 176, -190, -298, -306, -132, -44, -32, 52, 70, -340, 356],\n [-442, 260, -442, -520, -312, -234, -26, -26, 52, 130, -520, 650],\n [-411, 90, -426, -315, 129, -147, 57, 27, -24, 90, -210, 435],\n [-568, 152, -586, -466, 102, -216, 64, 28, -20, 130, -340, 632],\n [-107, -18, -115, -36, 148, -19, 37, 21, -26, 15, 20, 67],\n [62, 176, 83, -163, -543, -66, -110, -68, 94, 25, -310, 146]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[874, 674, -92, 212, -104, 340, 164, 116, -782, 180, 854, -528],\n [-184, 85, 449, -452, -340, 215, -584, -212, -112, 450, -1094, 942],\n [-538, -513, 1, 44, 176, -305, -48, 24, 526, -222, -348, 174],\n [607, 570, 545, -41, -377, 455, -723, 42, -907, 663, -513, 672],\n [511, 383, 226, 140, -146, 250, -304, 110, -617, 312, 41, 132],\n [-947, -1092, -215, 415, 563, -745, 173, 214, 1075, -689, -87, -160],\n [582, 602, -232, -128, -156, 320, 392, -100, -442, 96, 722, -528],\n [14, -417, 249, 758, 318, -305, -466, 472, -102, -104, -36, 122],\n [-589, -476, -433, -98, 260, -355, 586, -110, 815, -516, 271, -450],\n [1176, 1153, 373, -157, -543, 775, -419, -44, -1370, 795, 106, 240],\n [-664, -885, -201, 503, 525, -635, 161, 268, 798, -605, 126, -268],\n [728, 881, 197, -393, -483, 615, -167, -204, -850, 583, -22, 200]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[290, 480, 837, -258, -19, 214, -445, 274, 274, 122, 512, -493],\n [9, -282, 325, 149, 683, -20, 263, 555, -116, 518, -211, -206],\n [-42, 64, -243, -66, -283, 26, -29, -210, -42, -218, 60, 123],\n [242, 736, 458, -644, -622, 554, -446, 190, -78, -242, 930, -458],\n [-52, -194, -80, 203, 186, -185, 86, -80, 83, 71, -272, 123],\n [-92, -404, 31, 104, 659, 62, 481, 632, -390, 502, -246, -121],\n [-297, -326, -928, -71, -198, 136, 536, -15, -652, -178, -155, 353],\n [-212, -460, -529, 316, 219, -262, 361, -160, -122, 34, -526, 363],\n [-202, -250, -709, 241, -251, -287, 131, -590, 33, -331, -396, 508],\n [21, 98, -57, 87, -239, -170, -223, -417, 294, -232, -51, 150],\n [-272, -552, -726, 408, 178, -364, 406, -328, -100, -44, -668, 514],\n [-258, -888, -369, 702, 927, -546, 609, 78, -30, 474, -1032, 381]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[222, 9, 270, 263, 550, 557, 80, -45, 554, 444, -739, 278],\n [-472, -471, -37, -215, -1185, -553, 83, 246, -494, -295, 352, -655],\n [516, -298, -265, 182, 425, 578, -137, -203, 102, -65, -539, 229],\n [485, -80, -669, 100, -407, -934, -35, 697, -173, 46, 835, -10],\n [-118, 910, 152, -181, 556, -260, -263, -519, -457, -448, 738, -1],\n [335, 540, 347, 327, 182, -467, -216, -74, -277, -43, 214, -475],\n [-221, -1342, -314, -68, -914, 488, 402, 548, 497, 379, -856, 111],\n [-986, 108, 0, -601, -344, -166, 375, 221, 257, 164, 552, 441],\n [-62, 60, 235, 183, 7, -184, 354, 644, 769, 853, -187, 286],\n [-148, -802, -94, -29, -218, 700, 295, 207, 577, 380, -864, 327],\n [-329, 417, 496, 0, 47, -172, 89, -18, 105, 196, 72, -136],\n [265, -1309, -1147, -213, -937, 45, 11, 388, -303, -408, 46, 76]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[686, -503, -347, -218, -1018, -79, -182, -202, 737, -838, 931, 414],\n [643, -516, -492, -441, 12, -427, 306, 488, -517, 786, 395, -731],\n [-260, -36, 633, -168, 485, -625, -359, -380, -30, 833, -152, -763],\n [678, -15, -40, 203, -546, -373, -875, -195, 548, -1587, 764, 988],\n [25, 132, 194, 305, 368, -204, -587, -297, -270, 439, 197, -305],\n [-739, 1431, 309, 132, 1771, 643, 716, 993, -1513, 956, -1385, -446],\n [-1261, 72, 260, 101, 590, 463, 858, 4, -327, 1176, -1371, -501],\n [902, -45, -321, 201, -727, 118, -770, -365, 418, -774, 1352, 411],\n [-14, -108, -263, -449, 34, 114, 841, 603, -235, 253, -377, -202],\n [340, -374, -705, 879, -880, 514, -617, -493, 333, -881, 789, 946],\n [461, -515, -524, 484, -810, -177, -542, -130, 452, -1498, 473, 1201],\n [-444, -342, -291, 300, -779, 554, 352, -217, 673, -898, -326, 933]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-401, 559, -1228, 345, -759, 1178, 521, -117, 13, -699, -15, -106],\n [216, 1161, -27, 837, -1264, -447, -172, 348, -104, -596, 225, 1182],\n [743, 353, 948, 166, 710, 976, 773, -233, -489, 319, 126, 503],\n [610, -56, 405, 864, -117, 234, 477, -365, -252, -218, 27, 921],\n [243, -971, 600, 242, 740, -941, -200, -159, 194, 257, 161, 313],\n [677, 1612, -381, -306, -407, 1118, 186, -881, -1461, -1246, -246, 67],\n [-140, 1459, 604, -958, -308, -335, -571, 887, -49, 638, -10, -243],\n [-139, 575, 777, -491, 762, -1076, -410, 360, 595, 1071, -80, 200],\n [-119, -1120, 398, -839, -303, -318, -699, 706, -91, 487, 4, -1402],\n [945, 242, 679, -457, 304, 465, 143, -1111, -1179, -170, -785, 10],\n [524, 924, 540, -154, -228, -370, -268, -266, -588, -153, -288, 524],\n [370, -222, 342, 347, -9, 811, 501, 144, -652, -606, 575, 587]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[126, -1042, -1029, 1185, -123, 269, 215, -80, 459, -277, -709, -709],\n [-202, -604, -824, 658, -183, -106, 72, -145, 499, -105, -559, -507],\n [481, -852, -605, 976, 216, 186, -298, 252, 626, -692, -163, 277],\n [-361, 420, -27, -292, 544, -432, 1166, 34, -738, 240, 431, 621],\n [179, -126, -412, -693, 428, 233, -219, 837, 530, 284, 1557, 29],\n [415, -93, 551, -269, 463, 667, 669, 487, -544, -1798, 1319, 494],\n [277, -393, -339, 500, 100, 285, 183, 70, -45, 303, -195, -252],\n [230, -354, -16, -646, -216, 858, -440, 568, 522, -850, 1290, -886],\n [113, -496, -544, 265, -527, 222, -1043, -1, 947, 631, -474, -965],\n [-574, 316, -377, 488, 365, -1206, 655, -447, -247, 593, -930, 1067],\n [175, 26, 170, 309, -58, -345, -849, -107, 460, -98, -533, 655],\n [249, -346, -292, 485, -246, 83, -733, -67, 528, 550, -635, -323]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-388, -292, -422, 123, -1325, 133, 211, 756, -279, 108, 441, -120],\n [-350, -260, -194, -64, -924, 295, -194, 902, -89, -459, 348, -584],\n [-161, 137, -305, -381, -462, 151, -285, 1067, 237, -934, 252, -620],\n [-574, -499, 740, 280, 111, 734, -253, -110, -1036, -171, 174, -346],\n [-625, -431, 762, 205, 404, 669, 402, -702, -1357, 505, -105, 355],\n [136, 625, -51, 151, 646, -267, 91, -171, -385, -210, 264, 623],\n [-183, -347, -58, -365, -434, 237, 144, 258, 251, 67, -279, -379],\n [-33, -537, 452, 4, 193, 250, 7, -630, 80, 535, -480, -201],\n [503, 174, -417, 329, -337, -577, -296, 69, 715, 111, 216, 24],\n [141, -153, -72, 608, -387, -262, 3, -354, -104, 631, 252, 329],\n [-135, -466, 309, -539, 267, 326, 446, -541, 218, 572, -840, -112],\n [-461, -303, -191, -392, -885, 439, -28, 995, -31, -521, 129, -680]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[175, -626, -268, 18, 967, -168, 767, -620, 749, -631, 1058, 112],\n [-201, -423, 386, -202, 368, 746, 331, -458, -59, -60, -329, -343],\n [-112, -260, 192, -474, 56, -79, 206, -67, 60, 143, 8, -50],\n [28, -956, 126, -552, 366, -19, 488, 37, -116, -43, 396, 370],\n [467, 177, 360, 610, 992, 476, 1009, -298, -463, -1118, 191, 1113],\n [493, 1493, -248, 476, -292, -1304, -21, 532, 19, -366, 391, 1025],\n [-245, -1423, 1, -1077, -155, -186, 2, 300, -41, 639, 293, -129],\n [159, -398, -264, -546, 583, -1036, 707, -264, 869, -283, 1222, 316],\n [-47, 635, 211, 208, -322, 203, -252, 108, -313, 97, -603, -57],\n [538, 1556, -536, 814, -340, -1306, -258, 528, 170, -410, 528, 876],\n [312, 120, -666, 863, 509, -182, 74, -327, 626, -643, 854, 48],\n [-57, -247, -759, 732, 360, 280, -310, -667, 993, -234, 599, -981]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-339, 331, 491, -687, -277, 154, 530, -362, -322, -329, 81, -620],\n [324, 336, 79, 925, -369, -27, -463, 276, 580, -244, 564, 20],\n [111, 196, -708, -448, -298, 1060, 478, -529, 128, -495, 237, -498],\n [-618, 209, 405, 123, 304, -120, 689, 1275, 295, 978, -18, 1537],\n [401, 584, -978, 23, 287, 1733, -308, -852, -1251, -224, 704, -726],\n [-442, -156, 967, 116, -621, -278, 543, 512, -233, -926, 228, 208],\n [-902, 287, -375, 176, 241, 1587, 137, -600, -1040, -403, 217, 223],\n [1041, -349, 385, -221, 802, -435, -512, 17, -437, 1045, 179, -254],\n [678, -309, 601, -187, -737, -680, -66, -513, 1388, -654, 160, -1122],\n [1241, -148, 236, -130, -132, -48, -430, -597, 337, -164, 568, -1216],\n [-975, -693, 415, 504, 351, -569, -118, 370, 276, 250, -718, 1240],\n [-97, 563, -197, 387, -221, 908, 319, 601, -1171, -522, 728, 365]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[29, -1196, -1053, 37, -1276, 939, -497, 1706, -793, 497, 121, -696],\n [489, 228, -264, -421, -906, -333, 127, 877, -701, -35, -793, -605],\n [-707, -268, 808, -310, 91, 1114, 1592, 168, 95, -364, -882, -139],\n [411, 39, -236, -396, 773, 155, -217, -300, 215, -378, -186, -261],\n [-176, 1160, 926, -488, -276, -103, -18, -944, 661, -290, 202, -338],\n [572, 510, -609, -66, -1089, 665, 83, 421, -367, 408, 31, -866],\n [262, 292, -334, -549, 1625, 926, 1065, -758, -240, -947, -779, 571],\n [-1356, -473, -196, 104, -325, 561, -170, 338, 858, -76, 680, 93],\n [-128, -666, 825, 933, -708, 416, -13, -86, 147, 805, 719, -348],\n [-1255, 204, 1110, -581, 1478, -482, 289, -1044, 1597, -1149, -223, 452],\n [840, 751, 275, -713, -73, -527, -1141, -615, -76, -263, 202, -492],\n [-48, -128, 93, -39, 1224, -1063, 444, -337, 103, -1107, -906, 553]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-135, -85, 282, 105, 1007, -221, -992, 100, 251, -345, -102, 386],\n [481, -201, 91, -193, -547, 246, 461, 128, 190, -142, 173, 93],\n [-491, 174, 597, 638, -1274, -497, 64, 195, -190, 216, 454, -29],\n [259, -407, 112, -723, -370, 284, -110, 1053, 530, -641, 181, -367],\n [605, -466, -396, -816, 564, 708, 603, 235, 335, -239, -85, 100],\n [467, -426, 601, 319, 131, -103, -757, 70, 111, -309, 220, 1077],\n [-54, 521, -652, 252, -721, -48, 488, -751, -770, 677, -299, -569],\n [101, -594, 458, -288, 1435, 131, -733, 542, 658, -623, 108, 835],\n [75, -278, 380, -84, 859, -181, -1399, 490, 380, -657, -65, 399],\n [23, -471, 156, 76, -588, 95, 11, 419, -384, 180, 328, 552],\n [690, -306, 255, -692, 271, 472, 629, 379, 1080, -723, 156, -30],\n [378, 591, 157, 254, -566, -22, 1261, -896, 492, 78, 36, -381]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-849, -144, -791, -785, 467, -1047, 141, -480, 1898, -1459, -1387, -382],\n [565, -439, 716, 36, -1421, 1068, 536, 732, -442, -356, -228, -1694],\n [394, -436, -647, 384, -238, 370, -654, -1092, -343, 909, -69, 140],\n [1586, 1187, 477, -1072, 562, 466, -1593, 27, -948, 774, -483, 459],\n [-20, 338, -170, 554, -1107, 1380, 653, 614, 388, 1464, -487, -309],\n [-993, -694, -2226, 1259, -869, 614, -955, -48, 1078, 757, -17, -41],\n [-871, -1991, -2469, 1543, -1451, -385, 863, -552, -207, -54, 949, 768],\n [527, 854, 1999, -86, 302, 747, 148, 1080, -1004, 822, -248, -276],\n [188, -407, -348, 1457, 989, -823, 997, -1957, -1029, 668, -387, 758],\n [207, 497, 1116, 922, 1958, -985, -1067, 81, -9, 1706, -1216, 1087],\n [128, -881, 843, -70, -498, 354, 694, 396, -352, 242, 458, 181],\n [840, -236, -377, 757, 405, 116, -1031, -890, -1067, 1308, 38, 768]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1200, 928, -1192, 284, -70, -218, 42, -429, 37, 409, 451, 1653],\n [159, -417, -386, 156, 727, 705, 343, 468, -310, 453, -174, 424],\n [1712, 100, -1732, -440, -351, 486, 1375, -1032, 320, 365, -121, 673],\n [723, -682, 185, -676, 459, 319, -561, -754, -461, -448, 877, 122],\n [-667, 274, -69, 1120, -1081, 1470, -4, 283, -16, 34, -225, 339],\n [595, -90, -961, -1118, -820, -69, -729, -711, 1721, 746, 1438, 586],\n [67, -1438, -1280, -1016, 118, -606, 185, -406, 929, 340, -117, -1031],\n [-10, 702, 1612, -170, 262, 412, -1349, -430, -539, -724, -22, -171],\n [-394, 139, -1314, 934, -1680, 511, 41, -236, 1756, 918, 116, -433],\n [-276, -57, 212, 785, -1213, 790, 704, 1028, 892, 1158, -376, 328],\n [-390, 49, -44, 318, -411, 1189, -324, -157, -699, -686, -401, 76],\n [1386, -641, -926, 1821, 576, 601, 196, 293, 268, 1647, -813, -463]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[108, 9, -9, 144, -54, -36, -54, -144, 135, 108, -99, 54],\n [132, 11, -11, 176, -66, -44, -66, -176, 165, 132, -121, 66],\n [-228, -19, 19, -304, 114, 76, 114, 304, -285, -228, 209, -114],\n [144, 12, -12, 192, -72, -48, -72, -192, 180, 144, -132, 72],\n [24, 2, -2, 32, -12, -8, -12, -32, 30, 24, -22, 12],\n [-180, -15, 15, -240, 90, 60, 90, 240, -225, -180, 165, -90],\n [-108, -9, 9, -144, 54, 36, 54, 144, -135, -108, 99, -54],\n [276, 23, -23, 368, -138, -92, -138, -368, 345, 276, -253, 138],\n [-96, -8, 8, -128, 48, 32, 48, 128, -120, -96, 88, -48],\n [108, 9, -9, 144, -54, -36, -54, -144, 135, 108, -99, 54],\n [72, 6, -6, 96, -36, -24, -36, -96, 90, 72, -66, 36],\n [-264, -22, 22, -352, 132, 88, 132, 352, -330, -264, 242, -132]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-58, -557, 212, 502, 998, -648, -449, 498, 273, 93, -289, 204],\n [700, 552, -277, -803, -1005, 1084, 129, -313, 51, 213, -51, 204],\n [86, 161, 277, -508, -519, 544, 281, -513, -471, 75, 309, -185],\n [-38, 629, 342, 351, -178, 12, 611, -769, 489, 423, -868, -136],\n [464, -256, -392, -253, 110, 196, -563, 640, 177, -31, 73, 411],\n [-726, -209, -483, 174, -83, -512, 8, 390, -516, -740, 917, -354],\n [-220, -616, -123, -519, -55, 76, -351, 433, -969, -539, 1269, -158],\n [224, -538, -207, -102, 443, -104, -630, 721, -24, -122, 258, 307],\n [452, -74, 542, -395, 24, 492, -37, -340, -105, 439, -203, 133],\n [576, 622, 111, -555, -801, 916, 352, -656, 150, 426, -393, 95],\n [282, -115, -38, -511, -258, 452, -171, 71, -309, -23, 370, 90],\n [10, -429, -415, 37, 331, -260, -524, 757, -12, -302, 350, 202]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1213, 315, -126, 846, -342, 870, 1207, -2122, -371, -941, 1454, -163],\n [1001, 1324, 246, -128, 1408, 301, -714, -1320, 984, -893, 640, -982],\n [-280, 59, 904, -31, -1575, 565, 645, -598, 794, -52, 179, -37],\n [-436, 56, 1239, -810, -655, -410, 351, -2181, 313, -964, 362, -504],\n [-1779, -125, 882, 982, -1161, 1682, 672, -1854, -690, -685, 736, -1109],\n [-410, 185, 164, 387, -616, 361, 1072, 20, -388, 9, 233, 377],\n [787, -234, 965, -603, -1145, -1833, 606, -87, 340, 300, -678, 1459],\n [-173, -238, 101, 825, 734, 345, -735, 165, -581, -22, -325, -648],\n [149, 574, 1714, -83, -400, 301, 540, -1527, -298, -975, 83, -783],\n [1011, -9, -416, -330, 1921, 214, -750, 1492, -303, -296, -373, -908],\n [-115, 165, 132, -119, 288, 248, -616, -132, -632, 40, -250, -564],\n [-1327, -1636, -37, 30, -204, -345, 32, 483, -1054, 1023, 404, 134]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[878, -847, -1169, 501, 425, -430, 591, -1241, -452, 276, 674, -139],\n [-202, -384, -323, -40, -329, -773, 266, 131, -94, -582, -36, -68],\n [185, -150, -280, -450, 215, -405, 495, -585, 15, 70, -355, 25],\n [-432, -353, -246, -436, -457, -1138, 449, 232, 10, -834, -431, -40],\n [-432, -1068, -161, 5, -612, -92, 342, -181, 1028, -350, 9, 771],\n [514, 693, -183, 81, 551, -228, -113, -51, -1056, 208, 114, -751],\n [-677, -447, 473, -757, -464, 187, 324, -64, 1355, -126, -767, 902],\n [-112, -159, 168, -468, 19, 204, 263, -366, 630, 206, -429, 436],\n [275, 554, -86, 490, 211, -101, -415, 431, -979, -42, 447, -697],\n [54, -640, -187, 243, -114, 326, 132, -413, 550, 170, 273, 463],\n [348, 1034, 372, -787, 759, 213, 72, -348, -372, 636, -723, -335],\n [-636, -69, 401, -108, -554, -39, -179, 687, 462, -472, -205, 258]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[582, -601, 587, 1092, -587, -2, 1431, 681, -216, -2229, -1287, 698],\n [-669, -528, -860, 100, -338, -545, -1063, -825, 433, 166, 1013, -373],\n [-110, -427, -331, -372, -515, 49, 365, 576, 422, -77, -670, 148],\n [-388, -417, 264, -290, -482, -28, 1451, 1049, 102, -868, -1037, 171],\n [1039, 90, 414, -448, 816, 997, 458, -77, 167, 624, -932, 1061],\n [338, 379, 123, -756, 1065, 658, -97, -324, 170, 1362, -237, 399],\n [50, 441, -349, 83, -545, -1243, 648, 529, 214, 1604, -97, -803],\n [-945, 280, 556, -1074, 131, 456, -500, -481, -561, 172, 1734, -302],\n [-103, -16, 259, -38, 1029, -112, 453, -850, 97, 507, 300, 306],\n [-798, -846, -1156, -407, 122, -153, -833, -658, 952, 383, 142, 11],\n [400, -832, -431, 1182, -944, -418, 244, -41, 238, -517, -1183, 288],\n [357, -661, -476, -885, 581, 1179, -598, -477, 795, 320, -533, 1095]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[741, 219, -1036, -365, -605, 200, -691, 906, -296, -549, -309, 40],\n [-1223, 140, 286, -627, -274, 152, 273, -471, 276, 212, -478, 869],\n [-371, 76, 93, -659, 225, -186, 156, -964, 162, 188, 587, -370],\n [182, -478, 132, 453, 1146, 653, 1136, -997, 742, 2154, -659, 708],\n [-85, 665, -1407, -87, -762, 677, 281, 1907, -963, -602, -286, 655],\n [158, -533, -18, 396, 73, 282, -260, -1089, -1, -477, 590, -1743],\n [539, 1205, -340, -876, -391, -549, -682, 859, 303, -1670, -226, 13],\n [822, 596, -1176, -417, -195, 523, -1035, 213, 397, -1013, -1627, -980],\n [-44, -147, 698, 221, 486, -146, 530, -860, 562, 303, -1572, 113],\n [940, 413, -1551, -553, -527, 529, -835, 383, -61, -1191, -560, -1085],\n [1605, 865, -462, -1254, -118, -840, -449, 495, 764, -878, 136, 621],\n [-296, -420, -494, -130, 887, 815, 1163, -1209, 383, 1886, -129, 115]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[569, -179, -588, -493, -538, -864, 68, 277, 1252, 388, -1164, -883],\n [-518, -11, -618, 249, -165, 525, -941, 419, -281, 564, -111, -232],\n [-143, -153, -201, 319, -93, 380, -17, -146, -348, 57, 451, 617],\n [475, 1592, 938, 732, 424, -707, 97, 125, 356, 522, -553, -99],\n [1781, 473, -1213, 866, -700, 213, 337, -1118, 449, -1081, 1149, 448],\n [-176, -1030, -1478, -330, 1006, -477, -584, -567, -397, -200, -385, -413],\n [889, -355, -108, 609, -143, 401, -755, 130, 70, 27, 334, 117],\n [-670, -82, 325, 371, 315, 852, -1480, 833, -695, 717, 133, -91],\n [-817, -119, 1110, 159, 638, 111, -300, 545, -559, 859, -55, 776],\n [947, 50, -969, 533, 34, 397, 28, -1041, -278, -1089, 1293, 537],\n [256, -626, -108, -742, 644, -951, 195, -167, 313, -390, -990, -1098],\n [785, -612, -1577, -538, -912, -226, -3, -224, 922, -549, -480, -1177]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[882, -331, -300, 713, 216, -569, -197, 489, -361, 410, 207, -69],\n [1047, -365, -488, 1017, 346, -729, -690, 1154, -38, -215, 307, -173],\n [499, 142, 659, 191, 25, -906, 222, -143, -988, 1305, 683, -451],\n [-259, 944, 200, 359, 54, -171, -883, -283, 951, 307, 259, -942],\n [160, -172, -381, -441, 484, -159, 110, 1437, 205, -1755, -423, 332],\n [-340, -401, -658, -544, 339, 884, 445, 379, 493, -1302, -1086, 865],\n [-35, 192, -235, -999, -743, -306, 488, 77, -126, -1149, 289, -87],\n [993, 283, -117, -75, 96, -1178, 385, 340, -637, 445, 343, -514],\n [-297, 204, 657, 67, -193, -54, -40, -627, -308, 935, 423, -265],\n [-382, -259, -363, 202, 53, 647, -556, 453, 772, -1108, -308, 336],\n [-454, 103, -749, -594, -185, 1041, 580, -1053, 708, -160, -1020, 436],\n [-230, 9, 298, 920, 294, 342, -783, -277, 391, 866, 58, -155]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-105, 999, 312, 129, 246, -706, 310, 1318, 283, 370, -646, 1253],\n [2, -879, 452, -254, 894, -1, -1339, -149, -738, -553, -1371, -751],\n [678, 1244, 383, 172, 225, 805, -838, 504, -938, -698, -1016, 418],\n [-151, -1281, -463, -382, 468, -358, -285, -780, -298, -617, -541, -466],\n [-404, -718, 833, 540, 149, -66, 411, -6, 356, 523, -212, -477],\n [-472, -532, -85, 61, -534, 244, 561, -982, 838, 71, 1331, -585],\n [-321, 89, 1527, 995, 1888, 453, 678, 414, -212, 1211, -1556, -634],\n [-19, -746, -272, 464, -531, 79, -25, 597, -390, -656, 12, 1045],\n [186, 959, 1178, 998, 448, 508, 647, 1000, -112, -878, 228, -102],\n [-595, -277, 973, 1043, 1323, 1070, 691, -6, -389, 863, -1128, 53],\n [31, -699, -473, -133, -1077, -597, 47, -461, 600, 1111, -241, 495],\n [-608, -405, -450, -501, 57, -1152, 379, 172, 920, 151, 775, 218]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-448, 317, -188, 633, -107, -272, -175, -186, 500, 225, 683, 59],\n [440, -319, 232, -621, 142, 295, 206, 198, -505, -237, -691, -106],\n [360, -163, -416, -517, -356, -115, -268, -34, -235, 11, -307, 528],\n [-216, 78, 372, 312, 309, 141, 249, 60, 105, -48, 132, -441],\n [288, -159, -156, -411, -147, 12, -87, 30, -240, -51, -321, 243],\n [232, -162, 84, -328, 45, 133, 81, 92, -255, -112, -348, -17],\n [-352, 198, 168, 502, 162, -28, 90, -44, 300, 70, 402, -274],\n [440, -308, 164, -622, 89, 255, 157, 176, -485, -214, -662, -37],\n [0, -143, 884, 13, 689, 520, 637, 286, -260, -299, -377, -897],\n [-248, 92, 412, 358, 343, 153, 275, 64, 125, -50, 158, -491],\n [360, -207, -144, -513, -144, 45, -72, 54, -315, -81, -423, 252],\n [144, -162, 432, -198, 324, 306, 324, 180, -270, -198, -378, -396]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[629, -168, -751, 130, 415, -622, 77, -504, 881, 424, -630, -26],\n [283, -307, 327, 946, -386, 1121, -220, 691, -129, -1348, -71, -25],\n [-253, 259, -359, -667, -749, -944, -437, -340, 505, 286, 351, 483],\n [-453, 211, 971, -169, -332, 116, 515, 660, -1060, 715, -397, -53],\n [418, 292, 334, 657, 281, 507, 391, 557, -829, 260, -509, -51],\n [-120, 118, -268, -502, 1110, -340, 364, -648, -116, 862, 200, -344],\n [114, 704, -150, -108, -469, -470, -206, 110, -354, 463, 181, 529],\n [752, -566, -288, 1044, 1080, 1030, 190, -18, 300, -874, -380, -552],\n [527, -376, -701, 347, 487, 27, -172, -453, 894, -483, -118, -148],\n [-91, -35, -383, -282, -77, -281, -330, -387, 489, -223, 428, 110],\n [-89, -163, 849, 594, -366, 965, 194, 879, -738, -584, -286, -132],\n [-296, 30, -566, -508, 446, -86, -464, -750, 409, -448, 1161, -31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-482, -294, 799, -893, 295, -1001, 1031, 533, 700, 1133, 319, -29],\n [-46, -1255, 992, 3, -276, -668, -5, 124, -69, 897, 828, 541],\n [741, -166, 598, 535, -342, -659, -734, -406, -772, -797, -449, 839],\n [135, 111, -326, -8, -808, -904, -42, 981, 346, 2, 208, -74],\n [-1024, -397, -319, -520, 555, -617, -172, -640, 58, 289, 392, -150],\n [-171, 642, 328, -909, 152, -414, 873, 1037, 304, 301, -277, 1436],\n [1685, -311, 544, 962, 650, 205, -238, 1539, -640, 84, -1266, 20],\n [-388, 1054, -682, 44, -128, 817, -574, -243, 745, -71, -83, 32],\n [1323, -1128, 1139, 1087, 660, -1279, 82, 257, -662, 21, -729, -44],\n [-786, 604, -999, -71, -1571, 772, -217, -779, 229, -931, 749, -121],\n [1340, 356, 477, 704, -498, 75, -664, 421, -890, -1156, -1331, 288],\n [-249, 707, -278, -387, 449, 387, 979, 905, 773, 505, -195, 420]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-379, 491, 136, 857, -230, 789, -1043, -325, -70, 156, -1400, 219],\n [-1369, 125, 307, 347, -479, 318, -845, 80, 245, 675, -488, 411],\n [796, -216, -469, 72, 223, -521, 576, 15, -145, -571, 498, -326],\n [503, -1007, -1459, -109, -449, -496, 19, -170, -745, -127, 944, 743],\n [-415, -607, -32, -1225, -206, -273, 407, 265, -60, 568, 1242, 551],\n [684, 732, 748, -155, 323, 1485, -675, -600, -179, 222, -1670, 62],\n [-592, -757, -694, 675, -510, -213, -833, -229, 27, 561, -82, 266],\n [85, -392, 54, -334, -48, 454, -480, -358, -7, 674, -297, 191],\n [-826, 565, 412, 424, 33, -650, 516, 639, 448, -483, 376, -426],\n [-594, 548, -66, 548, -266, -58, -92, 286, -132, -444, -160, 266],\n [-132, 886, 307, -373, -78, 506, 211, 257, -442, -483, -152, 608],\n [-70, -221, -83, -482, 86, -811, 890, 462, 119, -270, 1218, -160]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-994, -368, 457, 1144, -2061, 483, -538, 411, 126, -150, -720, 273],\n [958, 570, 780, -340, 1988, -51, 136, -142, -605, -247, 1290, 223],\n [904, 72, -928, -1455, 678, -632, -91, -1, 793, -464, -159, -488],\n [-23, -1248, -528, 379, -1719, 67, -122, -573, 1105, -462, -493, -699],\n [-975, 159, 395, -1010, 972, -475, -377, -735, -375, 1632, -974, 860],\n [-209, 740, -1058, -693, -121, -381, 1127, 709, 1593, -267, -450, -492],\n [1291, -458, 962, -668, 1323, -5, -615, -1363, 106, 343, 932, -701],\n [-540, 481, 21, 811, -1231, 1063, -229, 926, 263, -502, -17, -250],\n [-294, 194, -148, 930, 859, -5, 666, 891, -426, 782, -252, 484],\n [-476, -1715, -458, -1002, 961, -1105, -577, -1122, 360, 1055, -1305, 900],\n [387, -602, -449, 847, 64, 135, -245, 434, -535, -228, -179, 60],\n [-177, -211, -1200, 797, 6, 19, 987, 449, 364, -599, -22, -709]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-532, 669, 391, 12, -132, 372, -436, 85, 97, 267, 1630, -508],\n [570, 370, 80, 386, -937, 840, 1281, 1186, -1315, 775, -378, -551],\n [-549, 1309, 48, 414, -683, 395, -341, -10, -1119, 683, 1361, -740],\n [-565, 541, 14, -723, 12, -165, -502, 124, 44, -275, 584, -573],\n [66, 643, -1486, -26, -838, -960, -1124, -197, -893, -282, -35, -33],\n [257, -890, -822, -328, 302, -699, 29, -112, 294, -773, -1292, 480],\n [398, 155, -117, 487, -573, -134, -221, -71, 28, 163, 341, 347],\n [113, 660, -613, 974, -1798, -415, 452, -76, -1017, -115, 263, 207],\n [699, -313, -198, 314, -258, -701, -53, -594, 145, -193, -1315, 925],\n [347, -195, -808, -123, -809, -1161, -480, -216, 516, -949, -330, 668],\n [108, 779, -240, 802, -1048, 52, -233, -41, -706, 461, 953, -29],\n [-666, -243, -131, -40, -145, -1104, 429, -1211, 148, -1194, -1234, 609]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-96, -48, -240, -240, -312, -108, -228, -24, 180, 24, -48, 24],\n [-636, -296, -424, -138, -10, 258, 134, 94, 538, -292, -164, 500],\n [-208, -100, -308, -256, -302, -57, -195, -6, 271, -30, -76, 114],\n [178, 84, 180, 115, 111, -21, 49, -13, -185, 58, 54, -122],\n [402, 188, 316, 147, 91, -123, -17, -49, -367, 166, 110, -302],\n [-704, -328, -488, -176, -44, 270, 122, 100, 606, -316, -184, 548],\n [-742, -348, -636, -337, -261, 183, -43, 79, 707, -286, -210, 542],\n [58, 28, 92, 79, 95, 21, 63, 3, -79, 6, 22, -30],\n [-570, -268, -524, -303, -263, 111, -83, 53, 563, -206, -166, 406],\n [286, 128, -80, -275, -473, -342, -442, -101, -90, 236, 38, -304],\n [-390, -172, 244, 543, 883, 579, 793, 167, 47, -374, -34, 454],\n [-498, -232, -344, -123, -29, 192, 88, 71, 428, -224, -130, 388]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-711, 1079, 126, 294, -761, 207, 674, 425, 200, 366, 26, 1483],\n [2023, -613, 415, -1524, -745, 1120, 1061, -706, -1261, 1062, -1185, -820],\n [1100, 309, 235, -691, -871, -39, -236, 1192, -1334, 1119, 255, -871],\n [-318, 438, 687, 367, 152, -690, 276, 319, -484, 320, 1170, 153],\n [-925, -822, -101, 468, -543, 739, -175, -872, 555, 604, 225, 19],\n [19, 1556, -400, -103, -329, 306, -221, 199, 712, -341, -457, 1409],\n [-814, -92, -1202, -42, 869, 34, -1835, -184, 1871, -1763, -297, 274],\n [-234, 1049, 468, 81, 353, 134, 310, 401, 774, -78, -8, 1508],\n [56, 114, -802, -369, 723, -507, -977, 168, 583, -1603, -402, -149],\n [49, -290, 390, -837, 823, -215, -536, 684, -507, -1158, 64, -527],\n [-976, -845, 431, 292, 164, 418, -316, -724, 418, 777, 454, 177],\n [-1053, 495, 572, 212, -306, -151, 1137, 946, 116, -204, -234, 1628]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[108, 566, -154, -124, -220, -164, -544, 236, 234, -198, -516, 184],\n [476, 345, -373, 366, -424, 312, -582, 598, 227, -153, -722, 604],\n [-504, -204, 372, -456, 408, -408, 480, -600, -180, 108, 648, -624],\n [446, 594, -388, 228, -466, 162, -774, 616, 314, -234, -872, 592],\n [16, -407, 47, 190, 92, 212, 334, -66, -149, 135, 278, -20],\n [-112, -350, 126, 28, 168, 56, 364, -196, -154, 126, 364, -168],\n [-14, 299, -33, -142, -66, -158, -244, 46, 109, -99, -202, 12],\n [70, -581, 35, 322, 98, 350, 448, -42, -203, 189, 350, 28],\n [126, -406, -28, 308, 14, 322, 266, 56, -126, 126, 168, 112],\n [-209, -139, 162, -166, 183, -143, 245, -260, -95, 63, 308, -264],\n [-226, 322, 108, -380, 78, -382, -134, -184, 74, -90, -8, -240],\n [26, -490, 52, 236, 106, 262, 398, -72, -178, 162, 328, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[243, -309, 375, -473, 1304, 763, 76, -49, 575, 424, -459, -873],\n [-449, 1554, 225, 126, 213, 241, -66, 542, -219, 571, 321, -2160],\n [-1003, 422, -1250, 147, 2, -279, -190, 566, 460, 1128, -937, -346],\n [797, -539, 410, -48, -46, -98, -738, 229, -416, 503, 388, 169],\n [-387, -1272, 321, -817, 1019, 1681, -420, -252, 957, -1290, -747, 63],\n [-746, 502, -1038, 335, 873, -1382, -632, -591, 546, 1410, -314, 926],\n [-14, 996, 207, 75, 1864, 176, 419, -1053, -461, 1164, 308, -762],\n [664, 1049, 274, -980, 74, 498, 569, -1380, -966, 1175, 1546, 816],\n [-11, -916, 1525, 1043, 1955, -335, -908, -991, 1383, -376, -1207, -1524],\n [365, -23, 77, 1670, 1491, -1877, 173, 2, -328, 977, -105, 4],\n [-280, 882, -400, -716, -2393, 131, -137, -483, -31, 57, 939, 685],\n [-601, -273, -1085, -691, -402, 602, 439, 162, -851, -1027, -696, 1418]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-74, 230, -44, 90, 152, -308, -236, -44, 332, -138, -164, 22],\n [520, -500, 680, -80, -300, 140, 860, -20, -320, 160, 320, -60],\n [-632, 585, -834, 86, 349, -129, -1029, 31, 348, -178, -372, 71],\n [43, -325, -38, -147, -220, 526, 274, 82, -538, 219, 238, -29],\n [-154, -215, -322, -156, -161, 617, 5, 113, -560, 216, 176, -13],\n [316, -440, 368, -116, -276, 332, 620, 28, -440, 196, 296, -48],\n [-140, -410, -364, -248, -294, 950, 158, 166, -896, 352, 320, -30],\n [-187, 55, -286, -33, 22, 176, -220, 44, -110, 33, -22, 11],\n [608, -630, 780, -116, -382, 246, 1038, -10, -456, 220, 408, -74],\n [409, -450, 516, -91, -275, 213, 717, 1, -354, 167, 294, -52],\n [248, -125, 362, 18, -65, -139, 329, -43, 52, -6, 68, -19],\n [-151, -320, -352, -207, -233, 803, 83, 143, -746, 291, 254, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-56, -112, -161, -28, -154, 182, 154, 161, -154, -63, -70, -168],\n [152, 304, 437, 76, 418, -494, -418, -437, 418, 171, 190, 456],\n [56, 112, 161, 28, 154, -182, -154, -161, 154, 63, 70, 168],\n [-24, -48, -69, -12, -66, 78, 66, 69, -66, -27, -30, -72],\n [184, 368, 529, 92, 506, -598, -506, -529, 506, 207, 230, 552],\n [48, 96, 138, 24, 132, -156, -132, -138, 132, 54, 60, 144],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n [136, 272, 391, 68, 374, -442, -374, -391, 374, 153, 170, 408],\n [32, 64, 92, 16, 88, -104, -88, -92, 88, 36, 40, 96],\n [-48, -96, -138, -24, -132, 156, 132, 138, -132, -54, -60, -144],\n [128, 256, 368, 64, 352, -416, -352, -368, 352, 144, 160, 384],\n [-112, -224, -322, -56, -308, 364, 308, 322, -308, -126, -140, -336]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[784, -576, -1125, -120, 970, 463, -1089, 153, 191, -220, -365, 437],\n [-1423, -236, -193, -145, 1445, 1619, 882, 492, -566, 368, 206, -60],\n [2038, -661, -1288, -216, 507, 263, -469, 964, 806, -323, -168, -670],\n [-557, 1109, 24, 526, -761, -855, -389, 20, -1291, 851, 382, 1187],\n [502, -116, 465, -655, -687, 51, -157, -1013, 274, -1079, 286, -213],\n [-800, 322, 113, -41, 473, 670, 553, -250, 528, -295, 96, -527],\n [-26, 158, 84, -205, -310, 208, -91, 327, 47, 173, 214, -95],\n [293, 997, -375, -187, -539, 132, -301, -202, -233, -230, 673, 149],\n [183, 415, -546, -356, 190, 1027, 720, 875, 521, -557, 817, -958],\n [785, 1491, -807, 346, 41, -644, -842, 486, 825, 797, -256, 47],\n [441, 31, -1932, 1, 1163, 1563, -136, 1314, -707, 180, 691, 63],\n [244, 628, -385, -313, 741, 678, 302, 523, 683, 288, 22, -611]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-50, -763, 671, 658, -663, 1182, 1157, 510, -475, 1187, -1470, 241],\n [1342, 325, 449, 350, 1061, -588, 1223, 69, -321, 651, 107, 539],\n [182, 127, 340, -839, -544, -1137, 643, 977, 933, -1464, 809, -973],\n [-339, 558, 856, -592, 1697, -402, -1034, -1683, 211, 286, 428, -697],\n [-429, 109, 260, -286, -788, 267, -400, 2068, -33, -1144, 134, -305],\n [-224, 47, 1472, -49, 600, 436, 223, -898, 268, 302, -15, -878],\n [703, 962, -539, -2382, -1502, -1418, -669, -169, 513, -302, 2270, -673],\n [-696, 163, 1380, -1386, 40, 89, 446, -225, -51, 431, -17, -1132],\n [-269, 185, -723, 724, -243, 653, -1540, 109, -11, -1186, 624, 303],\n [-999, -118, 158, -1610, -113, -376, -339, 194, 1090, -331, 843, 539],\n [-117, 573, -674, -610, 639, -944, -857, -1337, 748, 618, 217, -780],\n [1800, 123, 303, 238, -49, -1007, 1562, -40, 353, 1404, 268, 363]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[398, -446, 248, -128, -420, -212, -24, 416, 300, 424, -202, -132],\n [-425, 395, -20, 410, 105, 200, -15, -545, 30, -505, 460, -135],\n [-114, -10, 344, 500, -462, 16, -62, -290, 508, -210, 472, -430],\n [-133, 245, -372, -280, 546, 102, 56, -20, -514, -80, -221, 370],\n [620, -540, -80, -720, 0, -280, 40, 840, -200, 760, -780, 320],\n [-230, 404, -584, -418, 861, 170, 87, -59, -804, -151, -323, 573],\n [-252, 140, 272, 560, -336, 88, -56, -440, 424, -360, 556, -400],\n [-713, 621, 92, 828, 0, 322, -46, -966, 230, -874, 897, -368],\n [295, -401, 396, 142, -609, -180, -53, 221, 526, 269, 62, -337],\n [-76, -58, 384, 506, -525, -6, -67, -257, 560, -173, 469, -461],\n [100, -102, 32, -66, -63, -50, -1, 117, 32, 113, -81, 1],\n [421, -471, 260, -138, -441, -224, -25, 441, 314, 449, -216, -137]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[996, -80, 1102, -768, -854, -324, 178, -855, -239, 582, 691, -91],\n [736, -1261, -941, -112, 1002, 286, -1385, 409, 790, -1087, 354, 76],\n [-333, -1011, 1024, 215, -756, -172, -159, -1047, -2013, 1607, 602, -108],\n [780, -989, 162, -637, -1281, 122, -201, 438, -155, -444, -1000, 1022],\n [-1336, 890, 667, 704, -1348, -266, 1593, -265, -802, 581, 716, 224],\n [-364, 416, -380, 212, 1014, 295, 1515, 1396, 1086, -217, 594, -108],\n [-75, -1031, 302, 551, 662, 389, -892, -614, -849, 461, -438, -1009],\n [-1144, 884, 383, 1178, 818, -26, 295, -470, -523, 463, 333, -1317],\n [-89, 777, -262, -630, -1325, 321, 1241, 356, 742, -453, -1675, 1028],\n [-210, 951, -1024, 72, 250, -786, 162, -603, 848, -255, -73, -390],\n [-640, 1181, 831, -155, -375, 769, 2065, 396, 989, -63, -583, -712],\n [224, -601, -64, 531, 631, -75, -277, 328, -541, -167, -423, 127]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[266, -98, 126, -224, -70, -308, 238, -98, 56, 112, 98, -350],\n [57, -21, 27, -48, -15, -66, 51, -21, 12, 24, 21, -75],\n [266, -98, 126, -224, -70, -308, 238, -98, 56, 112, 98, -350],\n [-399, 147, -189, 336, 105, 462, -357, 147, -84, -168, -147, 525],\n [-342, 126, -162, 288, 90, 396, -306, 126, -72, -144, -126, 450],\n [38, -14, 18, -32, -10, -44, 34, -14, 8, 16, 14, -50],\n [-323, 119, -153, 272, 85, 374, -289, 119, -68, -136, -119, 425],\n [-380, 140, -180, 320, 100, 440, -340, 140, -80, -160, -140, 500],\n [-38, 14, -18, 32, 10, 44, -34, 14, -8, -16, -14, 50],\n [209, -77, 99, -176, -55, -242, 187, -77, 44, 88, 77, -275],\n [-247, 91, -117, 208, 65, 286, -221, 91, -52, -104, -91, 325],\n [399, -147, 189, -336, -105, -462, 357, -147, 84, 168, 147, -525]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-598, 1223, -59, -43, 768, 1448, -1006, -1176, -119, -258, -702, 1231],\n [-527, -337, -790, -966, -515, 1046, -1484, 702, 487, 606, -220, 1177],\n [972, 912, -489, -111, 978, 1151, -532, 1499, 643, 163, 27, -259],\n [-784, -746, 349, -480, -556, 122, -911, -855, -19, 296, -448, 776],\n [-1481, -743, -126, -393, -1145, -199, -613, -914, -473, 307, -305, 1160],\n [-158, -619, 88, 537, -298, -1235, 1345, 473, -644, -531, -141, -978],\n [-713, 775, 218, 650, 238, 132, 68, -673, -832, -100, -304, 360],\n [-430, 565, 42, 942, 30, -843, 886, -1113, -440, -453, 283, -580],\n [-271, 896, -277, 139, 181, 242, 48, -960, -36, -180, 152, 434],\n [-1606, -555, -553, 202, -567, 88, -741, -1091, -102, -540, -552, 550],\n [524, 773, -798, 668, 277, 112, 48, 718, 550, 106, 1033, -713],\n [1487, 1102, 5, 1632, 868, -813, 1325, -13, 499, -361, 1711, -2018]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[857, 442, -67, -535, 207, -627, 577, 946, 815, 239, -658, -216],\n [-75, 307, -84, 135, 223, 216, 419, 561, 460, 685, -878, 642],\n [-937, 98, 1097, -30, 253, -167, -40, -51, -619, -191, 209, 343],\n [-903, -680, 156, 275, -72, -1171, 526, 35, 880, 301, -192, -602],\n [1552, 915, -691, 102, -573, 1495, -33, -536, -1356, -113, -278, -10],\n [-808, -563, 457, -112, 356, -1799, 458, 611, 1055, -80, 12, -630],\n [377, -269, -418, -344, 5, -898, -96, -100, 250, -469, 575, -925],\n [-253, -614, 381, 334, -427, 952, -1041, -810, -752, -827, 1144, 138],\n [646, 674, 704, -1055, 610, -697, 280, 1211, 593, -37, -295, 182],\n [5, 652, 387, -341, 732, 187, 164, 1119, 406, 444, -718, 1156],\n [-1152, -419, 412, -438, 959, -400, -1118, 48, -91, -649, 1322, 683],\n [1148, 631, -934, 448, -173, 767, 325, 324, -324, 168, -840, 196]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -237, -475, 437, -920, -19, 420, 135, -526, -82, 565, 1521],\n [129, -21, 582, 1007, -204, -204, -530, -1169, -543, 88, 1001, 627],\n [896, -9, 725, 388, -309, -1063, 567, -300, -1452, 302, 1349, 754],\n [798, 379, 740, 235, -625, -20, 346, 538, -1078, 703, 839, 275],\n [-629, 158, 257, -76, 332, 363, 67, -382, 416, 67, 132, 161],\n [311, -684, 466, -657, 856, -657, -824, 465, 753, 137, 472, -1076],\n [-469, 1218, -270, 71, -1127, 1383, 115, -101, -547, 605, -368, 1422],\n [523, 735, 1336, -234, 854, -492, 1019, 1, -648, 816, 784, 50],\n [90, 165, -942, 807, 285, -216, -1007, -769, -251, 787, 1398, 755],\n [1435, -160, 507, -1072, 180, -764, -230, 969, -316, -277, 138, -774],\n [311, 646, 774, -110, 1017, 295, -299, -721, 421, -294, 237, -158],\n [-258, 316, -641, 152, -1532, 636, -818, 88, -594, 703, -162, 1119]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[15, 64, 354, 1, 474, -114, -240, -399, 686, 118, 34, -402],\n [168, 277, 162, -158, 24, 66, -153, 120, 521, 199, 178, -156],\n [246, 407, 162, -244, -24, 114, -171, 222, 679, 269, 254, -156],\n [75, 54, 472, 54, 45, -6, -368, 82, 322, 209, 131, -371],\n [-435, -936, 980, 822, 171, -318, -646, -322, -892, -95, -287, -685],\n [120, 169, -48, -111, -255, 114, -3, 327, 7, 94, 121, 89],\n [117, 120, 688, 44, 189, -30, -530, 4, 648, 311, 191, -579],\n [-381, -625, 34, 416, 309, -252, 67, -566, -673, -332, -371, -47],\n [282, 332, 482, -111, -375, 180, -442, 641, 370, 399, 351, -291],\n [441, 874, -700, -720, -255, 318, 428, 452, 834, 185, 335, 505],\n [-141, -219, 366, 196, 477, -192, -219, -510, 253, -18, -111, -383],\n [-147, -176, -692, -6, -201, 18, 538, -14, -748, -339, -219, 591]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[613, -1008, -216, 969, -716, 97, 1026, 1046, -219, -132, 401, -954],\n [-80, 333, 159, -252, 256, 82, -258, -262, 18, -15, 29, 99],\n [341, -285, 131, 277, -169, 306, 295, 183, -299, 210, 33, -390],\n [-604, -111, -647, -88, -199, -857, -121, 107, 596, -342, -244, 732],\n [38, -354, -334, 406, -292, -354, 436, 660, 298, -558, 456, -342],\n [-294, 1255, 541, -866, 960, 208, -874, -782, 208, -349, 385, 205],\n [-35, 1028, 664, -687, 826, 487, -688, -732, -87, -50, 279, -16],\n [-10, 63, 169, -214, 62, 250, -244, -472, -304, 609, -553, 339],\n [194, -587, -297, 542, -448, -188, 570, 670, 68, -247, 247, -401],\n [-265, 913, 439, -761, 698, 243, -790, -862, -11, 143, -130, 439],\n [295, -2, 154, 235, 40, 179, 278, 378, -5, -394, 621, -656],\n [61, -319, -71, 117, -239, 64, 101, -51, -219, 442, -435, 158]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1220, -864, 232, -1308, 264, -120, -666, 1253, 200, -679, 1165, -1218],\n [325, 1810, 187, 1676, -505, -668, 73, -517, 34, 83, -355, 762],\n [674, 525, -278, 1049, -417, -585, 857, 110, 505, -612, -192, 236],\n [693, 206, 371, 194, -626, -1204, -477, -666, 520, -1116, -1244, -1],\n [-721, -182, -717, -931, -120, 26, 310, 686, 1458, -1540, 292, -1171],\n [-190, -584, 322, 687, -128, 358, 336, 1062, -760, 517, 259, 546],\n [78, 404, 447, 351, 503, 1292, -31, -1721, 438, 591, -816, 56],\n [261, 239, 205, 942, 942, 985, 974, -181, -784, 1258, -654, 1043],\n [704, -1065, -858, -1299, -324, -1908, -836, 2124, -1243, 440, -665, -443],\n [-217, -197, 447, -56, 962, 376, 972, -561, 1007, -907, 734, 1110],\n [-144, 1628, 6, 1689, -787, 626, -225, -1546, 129, 337, 129, 473],\n [81, 612, 1098, 584, 342, 1706, 211, -2393, 250, 954, 247, 889]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[772, -342, -980, 663, -334, -563, -203, 260, 462, -96, 17, -78],\n [-387, 307, 265, -623, -26, -970, 9, -380, -1306, 748, -1103, -1353],\n [-860, 488, 1485, -1641, 44, 212, 350, 1074, -552, 901, -1002, -451],\n [923, 482, -864, -1181, 327, -608, 297, -299, -298, 203, -788, -75],\n [-381, -140, -211, -712, 973, 775, 1273, 1534, -2247, 1131, -169, 426],\n [-1054, 1111, 1357, -414, 231, -1724, -635, -187, 585, 1032, 59, -1749],\n [-467, 121, 373, -1229, 378, 214, 897, 821, -623, 537, -435, 325],\n [-602, -218, 215, 104, -238, 706, 550, -1290, -4, -1049, 338, 888],\n [1180, -1088, -1395, 1166, 742, 1109, 911, 634, 819, -1273, 1084, 1567],\n [655, -1428, 543, -1226, 255, -89, 712, 730, 108, -486, -1871, -465],\n [350, -525, -8, 517, -5, 230, -467, -193, -1112, -11, -764, -909],\n [-191, 1101, -118, -1493, -980, 616, -44, -689, -322, 120, -512, 1067]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-498, 216, 281, 253, -327, 45, -517, 246, 128, 274, 135, -57],\n [-285, 426, 484, 418, -65, -45, 149, 16, 98, 893, 409, -885],\n [311, -524, 365, 239, -47, -22, -106, -861, 274, 377, 364, 730],\n [-794, 165, -13, -1125, -376, 492, -526, 167, -1105, 130, -106, -1284],\n [-945, 316, 220, -328, -561, 257, -780, 422, -373, 174, 19, -735],\n [-191, -1235, -557, -1502, -771, 778, -460, -786, -963, -784, -426, 122],\n [863, 183, -1158, 48, 1254, 51, -965, 25, -403, -565, -1065, 812],\n [-601, 160, -3, 16, -137, -42, 444, 484, 336, 134, -348, 99],\n [282, -1318, -265, -949, -491, 624, -170, -1482, -654, -114, -58, -17],\n [5, 80, 311, 689, -111, -289, 166, -542, 644, 416, 276, -962],\n [230, 255, 520, 84, -153, -40, 178, 6, -306, 316, 865, -811],\n [-150, 1545, 564, 1091, 1012, -1239, 738, 1097, 1208, 190, 107, -334]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[914, 661, 140, -137, -127, 560, 136, 473, 418, 503, -270, -578],\n [-750, -428, 1289, -238, -670, -1133, 752, -1499, -1163, -686, 115, 114],\n [175, 217, 357, 357, 877, -430, 373, 306, -105, 168, 722, 447],\n [-363, -163, 527, 140, -514, -696, 1196, 46, -1353, 270, 481, 208],\n [728, 168, -143, 1263, -309, 531, -257, 616, -123, 1029, 90, 397],\n [19, 55, 406, -237, -598, 329, 92, -462, 267, -95, -609, -587],\n [691, 505, -77, 653, 1066, 506, -770, 375, 1174, 253, 66, 259],\n [-264, -500, -13, 315, -375, -203, 455, 153, -714, 299, 380, 209],\n [543, -784, -828, -1092, 732, -413, 115, 802, -282, 17, 1401, -157],\n [785, 691, 437, -186, 1353, -900, -157, -41, -83, -256, 925, 580],\n [-676, 135, 130, -965, -306, 82, 657, -157, 181, -485, -634, -762],\n [-15, -34, 1111, 1509, -778, 168, 401, -518, -374, 652, -251, 290]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-284, 654, -583, 154, 249, 530, -1095, -129, 293, 832, -465, -407],\n [0, 72, 950, 462, -531, -1012, 650, -303, -573, -1413, -113, 325],\n [128, -396, -949, -316, 369, 881, -263, 288, 637, 1151, 326, -239],\n [104, 312, -355, 208, -1, -67, 298, -70, 564, -360, -127, -328],\n [84, 4, -425, -214, 242, 185, 383, 211, 618, -26, 165, -136],\n [-282, 176, -651, -216, 474, 452, -142, 277, 803, 336, 134, -17],\n [-920, 438, 557, -684, 668, -98, -290, 464, -71, -254, 89, 851],\n [728, -994, 538, 570, -902, -623, 928, -361, -710, -673, 321, 50],\n [216, -274, -191, 158, -151, 52, 182, -57, 100, 53, 122, -116],\n [1000, -988, -317, 700, -831, -115, 797, -392, -71, -81, 290, -507],\n [184, -772, 676, -224, -246, -226, 323, 76, -821, -39, 377, 471],\n [-298, 886, -610, 496, 128, 70, -404, -209, 802, -188, -467, -428]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[692, 488, 72, 772, 5, 207, 195, -327, 158, 18, -221, 408],\n [-678, -554, -875, -571, 787, -1337, 625, 1068, -445, -896, 784, 47],\n [329, 343, -88, 374, 35, -302, 58, -75, -229, -266, 181, 476],\n [-704, 4, 509, -495, -22, 174, -588, -9, -429, 190, 321, 103],\n [219, -219, 261, -45, -478, 901, -137, -411, 694, 670, -751, -733],\n [615, 377, 188, 844, 236, 623, 407, -276, 493, 260, -472, 196],\n [150, -270, 302, 16, -263, 1077, 33, -327, 848, 754, -839, -794],\n [533, 467, 79, 321, -524, -171, -381, -459, -294, -106, 69, 425],\n [521, 11, 117, -11, -916, 417, -441, -615, 314, 390, -521, -441],\n [8, 376, -234, 418, 688, -728, 388, 378, -522, -636, 618, 874],\n [-39, 427, 571, 329, 149, 504, -222, -258, -116, 264, 8, 429],\n [-349, -99, -544, -154, 623, -1064, 400, 681, -535, -762, 721, 436]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-176, -643, -166, 512, -71, 148, -239, 172, -122, -226, -503, 426],\n [-772, 427, 268, -240, 578, -788, 246, 317, -547, -1339, -661, -328],\n [-1301, 308, -1032, 1161, 113, -585, 193, -110, -1023, 213, -985, -857],\n [-287, 675, 348, 484, -1111, 99, -373, -43, 204, 478, -56, 341],\n [571, -373, 412, -154, -535, -5, -77, 103, 602, -506, -68, 245],\n [998, -29, 282, -133, -1109, 164, -15, -244, 990, 424, 457, -80],\n [-359, 205, -472, 952, -946, -264, -16, -198, -32, 441, -539, -474],\n [689, -984, -106, 306, -429, 678, -343, -20, 502, 461, 142, 674],\n [445, -774, -302, -99, 251, -326, 347, 20, 170, -691, -330, -492],\n [1430, -318, -570, 322, -1482, 153, 282, -686, 1191, 1324, 561, -925],\n [-1440, 916, 236, 183, 506, -446, -116, 316, -974, -612, -596, 144],\n [810, -521, 120, 364, -1351, -77, -55, -92, 933, -160, -264, -81]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[188, 99, -57, -412, -271, 371, 422, 573, 284, -360, 374, -385],\n [451, 434, -378, -374, -259, 564, 539, 18, 102, -192, 171, -20],\n [-71, 676, -77, -600, -835, 360, 568, 164, 27, -960, 735, -756],\n [127, -468, 15, 201, 445, -112, -242, 267, 137, 516, -348, 300],\n [-543, 208, 163, -436, -767, -292, -84, 620, -1, -816, 587, -1024],\n [328, -509, -71, 373, 719, -13, -224, -28, 104, 828, -587, 703],\n [11, 28, -186, 227, 157, -210, -311, -417, -234, 372, -390, 350],\n [84, -805, 178, 619, 927, -323, -523, -40, 67, 972, -697, 757],\n [11, 144, -601, -159, -267, -380, -554, 223, -227, 324, -440, -96],\n [304, 298, 196, -539, -352, 866, 1066, 425, 452, -828, 859, -470],\n [127, 510, -61, -184, -295, 402, 504, -422, -63, -432, 333, -58],\n [40, 139, -622, -139, -233, -371, -559, 190, -233, 372, -479, -43]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[1301, 419, -409, 105, -1298, -234, -599, 81, 453, -975, -206, -465],\n [916, 878, -473, -698, -644, 1477, -550, -782, -580, -755, 1008, -579],\n [-1164, 282, 1008, 926, 502, -225, 299, 694, -49, -441, -586, 813],\n [1577, 2444, 654, 1257, 1076, -1217, 1662, -1648, 113, -351, 123, 604],\n [-1410, -102, 1009, -110, 1333, -368, -391, 422, -1156, 1369, -938, 1303],\n [114, 175, 847, 402, -1679, 700, -62, 394, -682, -525, 455, -1042],\n [-166, -510, 652, 759, 148, -1097, 179, 1072, 293, -16, -592, 845],\n [-20, -1509, -348, -658, -594, 123, -531, 934, 266, 69, 386, -277],\n [1685, 1295, 10, -164, -288, 847, -5, -724, -1157, -240, 687, -129],\n [-1703, -101, 189, -248, 897, 408, 59, -323, 47, 309, 70, 242],\n [-205, -753, 196, 666, -254, -518, 1400, 129, 436, 544, 644, -465],\n [-365, -63, -778, 9, 436, 470, 314, -566, 1260, -956, 175, -694]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1056, -878, -1185, 159, 13, -1619, 555, 379, -1177, 266, 951, -363],\n [470, 1259, -406, 148, 338, 276, -608, 162, 119, 1305, 1378, 107],\n [254, 161, -1330, 762, 153, -1387, -623, 24, -502, -18, 400, -459],\n [-619, -333, 1366, 587, 994, 1367, 900, 545, 482, -750, -1330, -374],\n [-201, 617, 627, -715, -1087, 982, -534, 440, 1174, 289, -186, 182],\n [-287, 658, 309, -1414, 350, -106, 493, -12, 201, 729, 1257, 1028],\n [-2, 1361, -790, 637, 466, 405, -936, -421, 305, 569, 1152, 51],\n [560, -883, 661, 100, 357, 61, -341, 1021, 280, 616, -504, -83],\n [421, -780, -1216, -446, 963, -1638, 436, -183, -616, 127, 2223, 447],\n [1057, -559, -383, -1066, -328, -817, 301, 762, -110, 1151, 1267, 464],\n [-705, -841, -1093, -1310, 157, -2223, 801, -992, -1089, -979, 1575, 1227],\n [400, -514, -322, 1873, 92, 301, -258, 683, 686, -444, -1142, -1532]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[262, -61, -163, 270, -235, -200, 527, -296, 509, -131, 278, 485],\n [-1186, 406, 154, 565, 290, 610, 568, -193, 690, -588, -745, -122],\n [-813, -348, -221, 393, -605, 470, 384, 378, -698, -600, 173, 192],\n [74, 495, -611, -596, 505, 127, 61, 83, -482, -281, 80, 408],\n [-228, -415, 481, 258, -377, 67, -379, 286, -228, 233, -115, -552],\n [747, -735, -856, -257, -658, -728, 131, 91, -737, 327, 1468, 771],\n [39, -572, -63, -141, -182, -39, -189, -615, -526, -67, 264, 61],\n [953, -787, -108, -317, -293, -1113, -734, 116, -169, 1324, 1087, -240],\n [-286, -136, -678, 70, -288, 463, 904, -733, -501, -1188, 266, 1063],\n [61, 287, 1110, 211, 555, -105, -598, -308, 1239, 676, -999, -1062],\n [1143, 540, -355, -604, 15, -501, -330, 1416, -383, 610, 526, 175],\n [-949, 392, 99, 326, 418, 516, 401, -356, 549, -503, -682, -100]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[291, 509, -191, -34, -63, 523, -12, -1116, 932, -1206, -770, -788],\n [-1368, 542, -56, -359, 449, 337, -541, 668, 317, 727, 619, 333],\n [-535, -697, -842, -809, -75, 799, 262, -913, 200, 37, 31, -450],\n [3, -472, -505, 755, -647, 752, -396, -413, 712, -46, 366, 785],\n [1, 1093, 211, 756, -987, 611, -924, 648, 1182, -790, 250, 660],\n [-313, -323, -1031, 135, -926, 1163, -156, -413, -184, -696, 308, -319],\n [-1679, 255, -1405, -1005, -189, 275, 967, 596, -194, -295, 1029, -1470],\n [-148, -911, 232, -443, 38, -157, -306, 519, -236, 1418, 298, 829],\n [-115, 311, 455, 222, -77, 813, -1183, 14, -209, 183, -95, 936],\n [257, 474, 581, 142, -55, 278, -582, 72, -311, -175, -199, 563],\n [468, -1095, -366, -797, -760, -110, 207, 158, -65, 255, -317, -747],\n [397, 405, 370, 40, -48, -1049, 489, 955, -369, -187, -25, -559]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-710, 165, -174, 230, -359, 237, 112, 630, 293, -1, -56, 902],\n [762, -349, 253, -128, -3, -591, 0, -555, -435, -115, -510, -538],\n [450, 32, -368, 838, -312, 210, -300, -66, -666, -166, 120, -496],\n [-394, 98, 342, -994, 694, 48, 196, -100, 764, 272, 372, 52],\n [-363, -42, 165, -315, -60, -171, 210, 204, 339, 39, -270, 576],\n [356, -110, 216, -396, 354, -198, 0, -416, -6, 54, 40, -500],\n [-541, 292, -283, 279, -70, 525, -58, 450, 223, 59, 434, 356],\n [791, -247, 201, -169, 223, -384, -86, -640, -394, -52, -162, -830],\n [312, -113, 503, -1114, 885, -273, 108, -663, 399, 223, 246, -698],\n [-130, -41, -101, 336, -419, -75, 40, 263, -127, -107, -330, 438],\n [-78, 5, 249, -632, 455, -57, 104, -187, 379, 151, 178, -126],\n [783, -87, 2, 69, 305, -42, -238, -607, -464, -28, 244, -1082]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-422, -370, 191, 75, -284, 90, 206, -83, -35, -445, 50, 165],\n [554, -89, -27, -370, 780, -845, 177, 715, 530, -413, 582, -202],\n [76, 447, -28, -15, -224, 475, -275, -338, -345, 764, -466, 11],\n [174, -90, -456, 519, 123, 177, 225, -162, 333, 393, 66, -492],\n [204, -137, 569, -778, 277, -214, 454, 434, 182, -3, 137, 7],\n [-172, -965, -499, 860, 221, -230, 826, 92, 880, -685, 695, -615],\n [-68, -565, 372, -222, 20, 249, 949, 87, 422, 175, 123, -346],\n [42, -112, -405, 568, -56, 394, 264, -316, 240, 508, -63, -468],\n [462, 446, -78, -153, 141, 371, 19, -132, -11, 1101, -330, -338],\n [960, 74, -831, 330, 1137, -985, -5, 651, 874, -126, 762, -701],\n [-166, -63, -59, 41, 76, -597, -417, 252, -89, -978, 307, 395],\n [-100, -902, -574, 843, 360, -516, 630, 241, 885, -957, 827, -523]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-790, -374, -605, 739, -654, -494, -108, 237, 1075, 18, 564, -315],\n [147, -251, -958, 268, 173, 368, 2, 410, -280, 367, 879, -538],\n [547, 266, 515, -479, 728, 732, 594, -25, -834, 359, -446, 658],\n [-587, -28, 423, 239, -487, -730, -87, -190, 1105, -472, -430, 368],\n [331, -136, -245, -8, -12, -345, -249, 129, 157, -720, 89, -259],\n [620, -378, -330, 132, 73, -126, 347, 557, 23, -933, 124, -126],\n [312, 261, 284, -368, 572, 182, 39, -181, -156, 11, -315, 501],\n [232, -37, -712, 8, 360, 134, -327, 117, -112, 117, 591, -333],\n [-803, -183, 386, 418, -1133, -994, -302, -180, 1054, -619, -331, -222],\n [71, -51, 147, 66, 312, 371, 700, 240, 7, 205, -136, 588],\n [-289, 128, 245, -6, -15, -209, -98, -220, 446, 31, -227, 323],\n [519, 300, 154, -420, 1139, 558, 393, -31, -202, 254, -238, 953]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-651, -112, 69, -41, 447, -159, 480, -288, 830, 1148, 639, 498],\n [-664, 44, 236, 503, -472, 698, 929, -122, 747, -42, 1146, -352],\n [739, -810, -1212, 245, -702, -778, -2070, 412, -251, 154, -810, 210],\n [-425, -169, -143, 385, -360, 332, 130, 41, 555, 114, 332, 11],\n [420, -1157, -950, 1, 247, -749, -751, 35, 294, 704, -263, 437],\n [-130, 1011, 764, -283, 189, 489, 315, 95, -648, -772, -781, -79],\n [761, -924, -561, -382, 718, -811, -269, -90, -224, 351, -340, 237],\n [-118, -566, -661, 16, 128, -675, -878, 0, 526, 1163, -148, 691],\n [214, 10, 432, -242, 515, 254, 1090, -178, -271, -551, 207, -355],\n [152, 304, 27, 140, -573, 27, -434, 102, -275, -300, 175, -320],\n [619, -362, -370, 206, -443, 226, -421, 330, -543, -1119, -685, -423],\n [-545, 16, 444, 67, 318, 428, 1368, -314, 611, 224, 990, -126]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-551, 110, 423, 200, 148, -356, 43, 443, 60, 310, -135, -48],\n [121, 499, 268, -26, -508, 713, 26, -682, -34, 641, -137, 301],\n [580, -34, 63, -199, 230, 571, 421, -957, -414, 629, 580, 746],\n [-234, 930, 22, 192, -1132, 778, -748, -182, -118, -126, -576, -732],\n [-270, -207, 215, 207, 446, -286, 487, 327, 382, 433, -98, 539],\n [-423, -105, 191, 348, 292, -241, 463, 515, 646, 414, -393, 513],\n [-343, 1052, 63, 194, -1300, 752, -939, -101, -162, -228, -665, -984],\n [-556, 294, 646, 65, -156, -249, -25, 214, 127, 549, -267, -53],\n [256, -303, 218, 14, 596, 165, 902, -446, 258, 938, 258, 1245],\n [-87, -464, 77, 81, 874, -505, 415, 287, -216, 130, 495, 348],\n [501, -99, -109, -65, 314, 488, 383, -687, -352, 382, 515, 635],\n [688, -755, -459, -184, 662, -41, 724, -291, 355, -2, 331, 914]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[180, 36, -18, -36, 144, -54, -99, -207, 144, 171, -171, -189],\n [-460, -92, 46, 92, -368, 138, 253, 529, -368, -437, 437, 483],\n [-340, -68, 34, 68, -272, 102, 187, 391, -272, -323, 323, 357],\n [-200, -40, 20, 40, -160, 60, 110, 230, -160, -190, 190, 210],\n [-220, -44, 22, 44, -176, 66, 121, 253, -176, -209, 209, 231],\n [-120, -24, 12, 24, -96, 36, 66, 138, -96, -114, 114, 126],\n [20, 4, -2, -4, 16, -6, -11, -23, 16, 19, -19, -21],\n [-380, -76, 38, 76, -304, 114, 209, 437, -304, -361, 361, 399],\n [40, 8, -4, -8, 32, -12, -22, -46, 32, 38, -38, -42],\n [-420, -84, 42, 84, -336, 126, 231, 483, -336, -399, 399, 441],\n [60, 12, -6, -12, 48, -18, -33, -69, 48, 57, -57, -63],\n [-500, -100, 50, 100, -400, 150, 275, 575, -400, -475, 475, 525]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[85, -195, 767, -1242, 619, -216, 480, 240, -466, -1176, 974, -500],\n [-452, 150, 299, -201, -80, -741, -349, -361, -690, 300, 503, 767],\n [835, -110, 612, -542, 749, 104, 560, -495, 399, -191, 244, 185],\n [987, -225, 579, -471, 1008, 423, 799, -452, 623, -618, 54, -328],\n [687, -139, 882, -398, 1266, -124, 612, -1125, 147, -506, 277, 239],\n [812, -8, 389, 250, 765, 86, 350, -1125, 587, 388, -303, 627],\n [892, -107, 285, 115, 749, 395, 523, -703, 742, 1, -344, 69],\n [-363, 80, 328, -174, 133, -588, -196, -405, -587, 21, 418, 491],\n [-488, 199, -737, 1074, -726, -6, -614, -39, 43, 909, -710, 365],\n [-635, 207, -817, 744, -1085, -30, -694, 524, -108, 858, -460, 224],\n [-176, 51, 232, -569, -192, -373, -109, 250, -411, 19, 569, 270],\n [753, -180, 78, -129, 450, 633, 561, 51, 720, -381, -258, -549]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1172, -115, 84, 849, -280, -757, 70, 742, 1031, 585, 115, 753],\n [-135, -251, 343, 339, -215, -286, -235, -56, 421, 100, 345, 493],\n [278, -305, 819, 239, -202, 133, -475, -269, 552, -228, 1032, 669],\n [67, -180, -294, -64, -207, -363, 20, -283, -375, 82, -583, -122],\n [492, -85, 7, -356, -159, 282, -48, -386, -410, -373, -16, -169],\n [-357, -185, 7, 453, 7, -682, -139, 22, 277, 502, -207, 283],\n [526, 161, 7, -135, 774, 27, -211, -357, -398, 282, -134, -465],\n [-131, 78, 917, 307, 36, 602, -242, 419, 1038, -284, 1524, 700],\n [554, -157, 21, -431, -360, 347, -39, -457, -458, -536, 10, -119],\n [586, 86, 308, -307, 221, 577, -159, -263, -160, -357, 494, -144],\n [679, -62, 1092, 122, 441, 547, -642, -341, 533, -214, 1469, 440],\n [-78, -43, -700, -72, 65, -626, 175, -205, -643, 410, -1185, -469]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-37, 217, -105, 489, 137, 388, -578, 187, 452, 231, -469, 179],\n [15, 119, -57, 245, 1425, 375, 683, -205, 400, 1382, 63, -98],\n [-685, 95, -205, -955, 1, 436, 733, -1097, -293, 311, 1017, -367],\n [-288, -241, 323, 136, -18, 319, -13, -442, 1126, 602, -151, -326],\n [-404, 343, -369, -284, -237, -513, -30, 688, -331, 0, 680, -270],\n [-320, 189, -261, -112, 153, 560, -350, -202, -415, -789, -735, -238],\n [207, -2, -157, -219, -287, -712, 8, 943, -1566, -1253, -427, -39],\n [216, 479, -946, 120, 577, -174, -888, 531, -903, -945, -118, 484],\n [993, -370, -40, 95, 117, -1023, 71, 63, -19, 105, 979, 844],\n [-626, -546, 690, -130, -839, -324, 100, 402, 558, -394, -853, -1136],\n [293, -860, 475, 331, -51, -538, 19, 210, 263, 550, -559, 198],\n [-260, 202, -190, 36, -140, -408, -378, 539, 532, -207, 260, -405]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[227, 200, -397, -919, 88, -3, -536, -484, 542, 364, -249, -501],\n [100, 345, 48, 738, 314, 356, -4, 551, -587, -174, 262, 711],\n [322, -217, -325, 497, 244, 469, -378, 487, -361, -197, -364, 268],\n [-246, -443, -91, 47, 1340, 1227, -686, 373, -803, -495, -560, -120],\n [82, 654, -44, -506, -73, -248, -61, -351, 355, 373, 348, -7],\n [519, -32, -625, 341, 748, 945, -916, 584, -502, -168, -557, 307],\n [1102, 516, -920, 598, -1, 412, -841, 663, -131, 205, -276, 755],\n [-249, -185, 272, 572, 318, 312, 192, 381, -561, -351, 73, 299],\n [-333, -64, 129, 315, 1326, 1135, -426, 482, -972, -484, -141, 251],\n [201, -64, -331, -1153, -596, -613, -196, -816, 1046, 508, -275, -847],\n [-353, -824, 164, 434, 636, 680, -80, 400, -672, -585, -469, -110],\n [377, -81, -360, 876, 644, 880, -546, 843, -791, -351, -337, 629]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[672, -238, -1824, -45, -590, 248, 646, -434, -184, -766, -609, 1024],\n [-8, -708, 871, -481, -327, 135, -1237, 360, 118, 1044, -82, -1320],\n [-75, 1439, -47, -1285, -2078, 625, 1109, -758, 1230, -1141, 456, -1227],\n [198, 350, -1024, -109, 1080, -732, 94, -1828, 54, 364, -435, -670],\n [681, 466, -179, -573, -2794, 1532, 899, 1447, 319, -1005, 403, 673],\n [-535, 384, 424, 642, 294, -713, -14, -954, 449, 212, 931, -309],\n [1395, -373, -300, -234, 1195, -371, -1850, -436, -226, -228, -551, 308],\n [432, 76, -493, 1387, -641, 254, -218, -111, 325, -729, 401, 1039],\n [111, -21, -574, 970, -114, -689, 263, 162, -145, 620, -153, 813],\n [-970, -967, -33, 266, 1560, 165, 201, 550, -1411, 962, 54, 385],\n [275, 1593, -183, -912, 229, -2, 711, -1598, 299, -615, 1022, -916],\n [-1120, -580, 584, 202, 519, -134, -401, 80, -431, 612, 881, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-65, 10, 495, 734, 498, 47, 821, 560, -499, 155, 413, 670],\n [393, 718, -1007, -407, -349, 43, -213, -1169, 187, 401, -202, -463],\n [334, 112, -475, -693, -110, 26, 212, 686, -271, -191, -258, -62],\n [372, 434, -83, 1213, 356, -194, 155, -754, 417, 373, 111, 770],\n [-221, -1220, -5, 662, 455, -267, 409, 766, -215, -336, -485, 800],\n [984, 424, -571, 757, -400, -653, -422, 586, 486, -240, -634, 825],\n [-191, -627, -295, -184, -519, -264, -141, 105, -1069, -311, -932, -141],\n [987, -278, -9, 500, -185, -1327, -377, 467, 502, -811, -1148, 579],\n [-19, -89, 196, 1308, 443, -254, 681, -114, -88, 355, 295, 738],\n [-30, -550, 148, 322, -423, -151, -1077, 61, -226, -613, -1058, 458],\n [381, 614, 881, 245, 572, -498, 24, -1253, 1114, 67, 519, -240],\n [1299, 848, 648, -723, -445, -1237, 383, 1877, -135, -832, -214, -207]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[303, 629, -60, 74, 558, 479, 158, 265, 194, -583, 627, 911],\n [406, 306, -312, -540, 236, 342, 332, -390, 84, -230, 350, 86],\n [83, -179, -168, -398, -182, -65, 122, -415, -62, 201, -149, -493],\n [615, 356, -519, -946, 255, 458, 527, -740, 92, -238, 432, -97],\n [-152, -281, 45, 4, -247, -221, -87, -85, -86, 257, -283, -384],\n [70, -205, -165, -400, -205, -85, 115, -425, -70, 225, -175, -530],\n [588, 371, -483, -868, 273, 455, 497, -665, 98, -259, 441, -28],\n [216, -120, -288, -624, -144, 24, 240, -600, -48, 168, -72, -552],\n [-492, -225, 441, 828, -147, -333, -435, 675, -54, 129, -291, 204],\n [515, 478, -357, -578, 385, 484, 401, -370, 136, -384, 526, 299],\n [42, 176, 30, 116, 162, 116, 2, 160, 56, -172, 168, 314],\n [-238, 99, 303, 648, 127, -45, -257, 615, 42, -151, 49, 538]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[123, 1003, 506, -327, 15, -710, -187, 77, 591, -337, 1148, 525],\n [413, -315, 85, -368, 152, 168, -44, 905, -148, 273, 230, 707],\n [458, -1073, -24, 115, 67, 788, -269, 1181, -306, 673, -211, 579],\n [52, 598, -485, 299, -311, -494, 139, -816, 19, -706, -48, -410],\n [246, 438, -711, -1131, 227, -662, 973, -212, -713, -646, -374, 178],\n [-298, -1437, 53, 366, 162, 1158, -126, 439, -387, 960, -1000, -343],\n [-165, -572, 65, 711, -149, 564, -365, -26, 86, 372, -323, -358],\n [321, -1573, -40, 635, -35, 1250, -489, 1137, -317, 961, -572, 261],\n [730, 634, -619, 565, -553, -542, -219, -184, 131, -844, 492, 226],\n [62, 490, 235, -1197, 423, -518, 479, 360, -117, -103, 415, 608],\n [31, -510, -4, -490, 282, 298, 246, 506, -373, 365, -334, 242],\n [204, -391, -77, 498, -176, 346, -318, 273, 23, 173, -51, 53]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[319, 621, -1071, 576, 221, 80, 407, 566, -598, -783, -244, 293],\n [-267, -138, -542, -355, 428, 598, 169, 677, -533, -621, -791, 883],\n [230, -186, 595, 91, -204, -295, -202, -500, 334, 405, 479, -516],\n [-250, 261, -14, 460, -663, -753, -356, -477, 659, 365, 744, -658],\n [-305, 339, 4, -175, -107, -27, 171, -8, 186, 420, -39, -117],\n [665, -87, 119, 332, 161, -26, 59, -108, -244, -235, 184, -179],\n [336, 738, -371, 193, 224, 131, 627, 248, -344, 53, -163, -101],\n [-120, 246, -763, -299, 580, 719, 521, 856, -748, -615, -943, 893],\n [90, -432, 28, 248, -148, -216, -433, -156, 90, -350, 264, -7],\n [-161, 249, 504, -295, -133, -73, 173, -294, 352, 822, 137, -411],\n [141, 381, -889, -32, 589, 626, 587, 844, -844, -747, -820, 773],\n [-9, -459, 2, -633, 643, 821, 209, 542, -608, -432, -865, 861]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[531, -97, -610, 478, 1143, -82, 671, 14, -542, -990, 1019, -475],\n [-552, -468, 691, 814, -289, 1625, 283, 159, 194, -334, -178, 444],\n [381, 1187, 525, -83, 806, 84, 1263, 410, -644, 767, -409, 702],\n [2080, -758, -293, 430, 204, 365, 107, 559, -2309, 871, -605, -26],\n [1331, -727, -137, 138, -239, -625, -1031, -4, -1054, 145, -1447, -255],\n [593, 421, -242, 392, -59, 1891, -194, -56, -605, -367, -273, -1165],\n [1019, -278, -407, 917, -845, 602, 718, 484, 92, 903, -739, 175],\n [21, 863, 573, -534, -450, -686, -743, -174, 396, 615, -1761, 93],\n [169, 185, 6, 28, -303, 1241, 808, 433, 50, 293, 479, -607],\n [524, 467, -66, -381, -48, -502, 1356, 528, -22, 573, 254, 68],\n [-1245, -991, 346, 974, 449, -863, 231, 873, 1105, -75, 399, 2006],\n [139, -335, -79, 200, 1094, -2483, 214, 443, 181, -602, -231, 1009]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[757, 498, 454, -330, -939, -948, -181, -195, -555, 213, 403, -640],\n [-167, -634, 83, 568, 1145, 985, 979, -661, -832, 1085, -886, -104],\n [336, 754, -307, -220, -763, -446, -317, 271, 222, -263, 331, 411],\n [-284, -500, 273, -745, 707, 436, 595, 199, 260, -303, -1018, 90],\n [140, 248, 273, -701, -1497, -1476, -401, 875, -396, -671, 1082, -822],\n [522, -82, -115, 1078, -737, -14, 181, -435, -4, 283, 679, -387],\n [378, -209, 98, 235, 267, 550, 829, -497, -132, 478, -705, 2],\n [-450, -651, -27, 403, 240, 266, 90, 138, 149, -189, 219, -255],\n [-319, -338, -17, 771, 295, 133, -537, -281, 56, 135, 613, -261],\n [432, -602, 933, 228, 60, -245, -126, -802, -78, 222, 140, -1174],\n [-558, -98, 504, -2225, 29, -743, -27, 1295, 237, -1251, -669, -72],\n [656, 161, 349, 380, 219, 175, -19, -993, -112, 676, -266, -187]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-1016, -97, -25, -833, -129, 151, 157, 1029, -206, -126, 422, 393],\n [-688, -322, 452, -262, 295, 29, -1617, 196, -197, -443, -1408, -982],\n [-235, 583, 91, -1366, -757, 424, -45, 154, -522, -768, 189, 772],\n [-14, -400, 128, 256, 25, 45, 292, 208, -102, -192, 878, -1039],\n [-633, 18, 291, -1768, -1273, -336, -1388, 38, 272, -27, -890, 693],\n [-179, -348, 118, -727, -1440, -247, 205, 507, -759, -389, 471, 170],\n [-62, -53, 150, 895, 1117, 875, 797, 1273, 161, 377, 786, -665],\n [-534, 248, 1714, 308, -542, -887, -78, -694, -269, 635, 812, 1319],\n [1735, 20, -1427, 433, 383, -390, 239, -311, 959, 255, -759, 334],\n [787, -156, -496, 400, 638, 671, 683, 1236, 708, 307, 684, -715],\n [-1061, 667, 1034, -1083, 371, 535, -1266, 569, 77, -136, -732, 748],\n [229, 413, 14, -1067, -930, 857, -799, -309, 1088, 765, -778, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-197, -525, -616, -544, 823, 687, -1175, -340, 302, -295, 1134, 882],\n [1104, 762, 622, -120, -483, 433, 617, -376, 552, 438, 379, -154],\n [-500, -1401, -599, -1169, 647, -100, -793, 220, 111, 307, -286, -410],\n [926, -619, 537, -491, -189, -196, -550, 173, -1220, 32, 107, 523],\n [-524, 126, -227, 183, -72, -103, 71, 488, 86, -280, -660, -194],\n [682, -617, 279, -924, -142, -68, -77, 105, -80, 557, -269, -457],\n [-143, -1745, -799, -1195, 450, -47, -1553, 408, -342, -149, -13, 142],\n [192, 666, 426, -181, 451, 770, -248, 69, -151, -306, 489, 1061],\n [438, -96, 281, -379, 10, 213, -435, 312, -526, -184, 10, 542],\n [-238, -604, -262, -363, 346, -95, -276, -164, 54, 207, 137, -154],\n [1174, 37, 136, -768, 344, 1092, -811, -738, 447, 103, 1703, 1016],\n [160, 511, 295, 340, 142, 322, -212, -42, -477, -430, 508, 960]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-581, 1145, -1127, 688, -672, -219, -338, -675, 134, -561, 326, -375],\n [110, -582, 549, -470, 83, 141, -1012, 897, 904, 402, 492, -943],\n [913, 300, 781, 528, 1336, -784, -134, 394, -215, -1118, -808, 787],\n [-346, -633, 371, -666, -402, 1150, 663, 183, -77, 1032, 322, -1139],\n [610, 36, -76, 746, 150, 1997, 665, 1360, -573, -486, 4, -1773],\n [-23, 1229, 644, -1862, -193, -58, 770, -371, -149, 409, -266, 331],\n [110, 409, -585, -248, 663, -75, -1518, 1038, 329, 681, 1113, -176],\n [285, 3, -67, 740, 1149, -837, -903, 91, -147, 92, 184, 434],\n [-810, -1389, -470, 398, -500, -116, -1228, 80, 984, 818, 992, -595],\n [-130, -259, 905, -878, 237, 508, 44, 724, 497, 187, 274, -1117],\n [736, -720, 127, 1179, 1336, 140, -537, 476, -701, 805, 86, -194],\n [79, -1254, 854, -592, 351, 242, -665, 593, 500, 1405, 439, -650]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1146, 31, 380, -535, 1163, 820, -944, 673, -814, 799, 171, 580],\n [731, 613, -186, -896, 925, 791, -990, 290, -635, 416, 473, -105],\n [-514, 579, -560, 576, -478, 264, -434, -162, 331, -545, 511, 1017],\n [-866, 247, -147, 132, -600, -751, 102, -639, 880, -967, 92, -319],\n [-430, -1154, -251, 188, 159, -561, 1462, 92, 163, -621, -143, 410],\n [164, -426, -855, -905, 561, 1249, 934, 320, -1712, 652, -505, -145],\n [963, -574, 1373, 171, 821, -588, -712, 491, 434, 306, -13, 507],\n [624, -259, 2130, 47, 94, -708, -1210, -110, 364, 544, -1071, -264],\n [618, 1049, 277, -4, -104, 413, -1328, 77, 2, 723, 358, -439],\n [-621, -60, -663, 424, -559, 722, 461, -79, -589, -97, -341, 975],\n [37, 152, 502, 1376, -1382, 69, 71, 47, 96, 998, -554, -53],\n [-1028, 113, -599, 500, -632, 387, 68, -373, -54, -817, -182, 1417]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-299, -399, 366, 394, 418, 143, 100, -340, 586, 23, 672, -100],\n [8, -57, -336, 208, -675, -296, -322, -475, 536, 413, 555, -45],\n [-275, -253, 91, 277, -242, 138, -216, -710, 300, 780, 512, 16],\n [-32, -885, 406, 858, -709, -378, -524, -722, 707, 331, 447, -403],\n [-280, 1012, -773, -755, 972, 281, 726, 353, 341, -267, 898, 540],\n [400, 982, -831, -764, -249, 115, 28, 654, -442, -301, -459, 161],\n [26, -567, 517, 551, -349, 341, -466, -415, 186, 278, -51, -439],\n [487, 563, -878, -263, -1079, -291, -450, 139, 147, -9, -61, -95],\n [-197, 1417, -939, -1105, 1354, 510, 960, 802, 148, -656, 728, 616],\n [203, 367, -129, -300, -11, 400, -60, 332, -392, -126, -467, -59],\n [-537, -953, 1084, 687, 919, 239, 260, -452, 358, 49, 455, -133],\n [128, 10, -114, -297, -197, -902, 222, 353, -803, -114, -821, 373]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[60, -564, -858, 157, 366, -52, -1369, -1952, -1137, 891, 35, -782],\n [12, -418, 318, -354, -146, -246, 285, 460, -22, -513, -18, -234],\n [-15, -78, -386, -300, -149, -308, -369, -434, -524, 286, 143, -76],\n [-111, -330, 248, -431, 89, 206, 236, -222, -551, 65, -246, -70],\n [-56, -50, -174, -75, 54, -695, -147, 554, 670, -514, 477, -94],\n [-251, 239, 457, -212, 291, 389, 704, 462, 314, -99, -164, 494],\n [-55, -556, -588, -151, 327, -431, -911, -1020, -542, 271, 250, -612],\n [-215, 512, 150, -248, 107, 837, 467, -472, -649, 815, -439, 720],\n [86, 283, -727, -317, -540, -122, -580, -994, -1234, 981, 18, 180],\n [112, -569, -169, 533, 494, 205, -710, -948, -165, 142, -106, -760],\n [-185, 19, -711, -126, 339, -723, -723, -346, 236, 110, 606, -88],\n [60, -370, -266, 639, 632, 469, -774, -1282, -288, 493, -187, -592]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-282, -306, 518, 286, 105, 473, 321, 16, 58, 496, 239, 214],\n [642, 288, 26, -98, 312, -274, -576, -734, -842, -56, -88, -578],\n [137, 162, -291, -157, -69, -256, -161, 15, -5, -276, -131, -101],\n [277, 342, -631, -337, -159, -546, -331, 55, 15, -596, -281, -201],\n [142, -72, 406, 162, 252, 206, -76, -394, -422, 344, 132, -158],\n [414, 306, -338, -226, 39, -413, -417, -268, -334, -352, -191, -346],\n [-265, -72, -149, -23, -192, 21, 220, 383, 429, -100, -16, 249],\n [131, 126, -193, -111, -27, -188, -143, -35, -55, -188, -93, -103],\n [-280, -360, 680, 360, 180, 580, 340, -80, -40, 640, 300, 200],\n [-762, -414, 182, 214, -273, 467, 711, 748, 874, 256, 185, 670],\n [114, 90, -110, -70, 3, -125, -117, -64, -82, -112, -59, -94],\n [-707, -414, 257, 239, -213, 492, 671, 643, 759, 316, 205, 615]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-413, -368, -960, 887, -283, -185, 1200, -970, -764, 743, -1175, 117],\n [880, -232, -668, -170, -148, 765, 8, -280, 781, 586, -614, 1017],\n [-560, -65, -560, 523, -62, 296, 379, -486, -450, 373, -903, 115],\n [-719, 258, 422, -16, 309, 223, -846, 797, -90, -336, 193, -403],\n [1207, -217, 766, -992, 326, 91, 767, -267, 114, -860, 1455, -91],\n [345, -117, -49, 34, 42, 189, 594, 210, 123, 112, 120, -154],\n [-216, -125, 651, -145, 191, -931, -150, 316, -500, -543, 935, -616],\n [221, 252, 183, -223, -160, -84, 163, -400, 116, -215, 205, -6],\n [-83, 186, -663, 336, -551, -150, 131, -1060, 44, 518, -986, 563],\n [-802, 249, -1076, 882, -543, 179, -279, -616, -5, 978, -1796, 555],\n [-223, -471, -436, 498, 91, -83, 845, -210, -626, 332, -396, -130],\n [627, -448, -29, -105, 396, 657, 439, 964, 363, 167, 335, -83]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-363, 280, -1409, -487, 449, -146, -424, -56, 986, 35, -282, 729],\n [-986, -547, 1164, 276, -420, 428, 38, -249, 232, 916, -487, -1163],\n [-1196, 362, 358, -23, 710, -748, 594, 19, -42, -1144, 368, -581],\n [569, -1374, 902, -543, 1357, 492, 3, -519, 35, -1089, 1221, 380],\n [434, 865, -861, -96, -1542, -1162, -1237, -379, -822, 598, -259, -1158],\n [170, -348, -1417, -942, 764, -282, -1587, -357, 1735, -584, 1061, -597],\n [-384, 571, 544, 898, -798, 651, 1164, 1099, -516, 778, -796, 246],\n [212, -405, 1227, 19, 1066, 59, 540, -347, -972, -1594, 991, 94],\n [-820, 399, 295, 285, -636, -734, 763, 176, -467, 535, -811, -228],\n [683, 1272, 682, 1473, -362, 441, -79, -67, -1426, -796, -248, -382],\n [1180, -839, 1193, 464, -241, 709, -341, 45, -748, -130, 732, -551],\n [1608, -1281, 518, -621, 1557, 717, -945, -533, 47, -1907, 2271, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-294, 117, 83, 153, 245, 38, 235, -141, 64, -4, -53, 30],\n [-641, -124, 539, -127, 457, -226, 488, -237, -273, -181, -139, -80],\n [-373, 214, 47, 302, 92, 229, 287, 2, 184, 297, 325, -22],\n [-213, 682, -569, 590, 547, 804, -240, -368, 727, -113, -547, 622],\n [291, -575, 350, -701, -543, -265, -312, 401, -530, 31, 360, -260],\n [698, 229, -719, 70, -37, 334, -773, -96, 378, -332, -659, 452],\n [-388, 543, -333, 409, 374, 911, -244, -171, 591, 92, -161, 526],\n [281, -332, 229, -33, -669, -658, 452, 421, -347, 501, 891, -688],\n [177, -155, 78, -34, -27, -517, 244, -56, -202, -123, -96, -230],\n [421, 370, -631, 388, 213, 116, -252, -278, 429, -279, -645, 318],\n [230, -477, 285, -621, -525, -78, -363, 409, -416, 100, 405, -182],\n [274, 410, -518, 643, 181, -157, 247, -263, 407, -36, -310, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-27, 325, -444, 703, 180, -57, 103, -282, -953, -900, -755, -1674],\n [154, -614, 855, -905, 71, -200, 294, 1187, 898, 628, 1246, 517],\n [497, 97, 1357, -266, -553, 1333, 1183, -863, -1451, 280, 1145, -45],\n [50, -836, 438, -598, -117, 809, 619, -1274, -94, -49, 335, 721],\n [18, -195, -237, -367, 320, 1171, 11, -891, -2143, -1059, -556, -1447],\n [1074, 491, 568, -300, 304, -1398, 215, 1193, 801, 964, 203, 752],\n [-532, -633, -136, -188, -484, -68, -835, 357, 1687, 530, -245, 781],\n [-135, 88, 10, -406, 251, -667, -171, 920, 938, 660, 778, 1248],\n [-844, -90, -628, -9, 365, -333, -65, -267, -75, -447, -39, -335],\n [116, -1189, -57, -1039, 295, 454, -146, -779, -91, -416, -709, -157],\n [-112, 351, 498, -357, 188, -582, 542, 567, 18, 566, 1129, 403],\n [-949, -545, -351, -97, 135, -368, 44, -49, 1025, -101, 472, 408]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[1325, -512, 84, -331, -347, -537, 1061, -103, -570, 545, 112, -840],\n [-435, 744, 370, -415, 659, 1492, -937, 1438, -342, -480, 443, -110],\n [-1428, 73, -1660, -706, 1890, 123, 339, 105, -214, -856, -373, 25],\n [-608, 111, 600, -46, -363, 1623, -1497, 1303, -834, -1629, -330, 379],\n [255, 489, -614, 612, 721, -23, 80, 396, -1483, -686, -493, -369],\n [-1346, 10, -790, -632, 604, 76, -376, -346, 475, -220, 48, 180],\n [1269, -1994, 513, 1066, -735, 459, 416, 442, 624, 275, -330, 404],\n [-18, 731, -530, -1027, -331, -253, -86, 108, -235, -127, 161, -956],\n [-272, -41, -667, -270, 288, -850, -53, -725, -507, -1684, -924, -246],\n [-1038, 659, -130, -154, 703, -4, 180, 75, 535, -215, -58, 752],\n [-63, 746, -540, 14, 220, 1200, -1034, 1295, -367, -1201, -343, -333],\n [806, -1538, -1579, -590, -263, 56, 667, 669, -45, -1198, -973, -1020]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-773, -301, -714, -8, -1140, 15, -268, -175, -177, -101, 708, -940],\n [3, 723, -1479, -784, -721, 23, 262, 362, 107, -226, -98, -263],\n [-520, -759, -962, 449, 655, 868, 571, 233, 468, 332, -430, 119],\n [70, 685, -791, -162, -459, 192, -559, -260, -260, -383, 764, -751],\n [808, 926, -379, -849, 1443, -304, 98, -1063, -179, 305, 259, 461],\n [-298, 1058, 451, -105, -442, 313, -155, -386, 317, 251, 341, 583],\n [-1, 1446, 783, -766, 790, -790, 355, -1595, -14, 836, 245, 1486],\n [-491, 1279, 1055, -299, -172, -1500, -351, -2450, -1244, 1113, 777, 1175],\n [451, 927, 201, -1141, 1003, -1174, -106, -1542, -320, 604, 377, 665],\n [723, -136, 799, -468, 341, -1082, 849, -390, -493, 107, 260, 184],\n [-662, 846, -1002, -1034, -1174, 446, -1248, -361, 784, 1029, 370, 189],\n [-578, -884, -1435, 439, -1151, 470, 1107, 1550, -14, -1217, -466, -1230]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-238, -722, -209, -285, -70, -327, -556, -322, 299, 284, 23, 27],\n [-223, 370, 172, -27, 563, 393, 491, 617, 161, -511, -367, -270],\n [296, 1066, 319, 393, 188, 519, 854, 548, -391, -478, -91, -81],\n [410, 760, 190, 380, -170, 240, 490, 130, -460, -130, 140, 90],\n [344, 76, -38, 190, -480, -174, -132, -384, -322, 308, 326, 234],\n [557, 796, 175, 462, -373, 168, 437, -31, -598, -1, 278, 189],\n [-129, -180, -39, -106, 89, -36, -97, 11, 138, -3, -66, -45],\n [530, 1012, 256, 498, -202, 330, 662, 194, -598, -190, 170, 108],\n [77, -212, -89, -10, -245, -192, -251, -287, -46, 239, 158, 117],\n [177, -204, -105, 42, -393, -252, -303, -411, -138, 339, 258, 189],\n [-202, -404, -104, -194, 66, -138, -270, -90, 230, 86, -58, -36],\n [549, 456, 57, 380, -565, -54, 113, -319, -552, 243, 396, 279]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[322, 17, 822, 151, -394, -222, -671, -289, 638, 45, 175, -307],\n [622, -179, 111, -109, -217, -696, 141, -2, 379, -156, -80, 57],\n [-292, -869, -208, 570, 164, 91, 666, -77, -269, -225, -460, 292],\n [34, -372, 52, 673, 636, 485, 659, -40, -599, 666, -733, 1111],\n [-400, -53, 802, 126, -400, 212, -847, -186, 461, -336, 456, -899],\n [582, 491, -105, -429, -239, -499, -238, -29, 355, 139, 176, 14],\n [-322, 180, 261, -563, -441, -206, -596, 226, 388, -802, 732, -1256],\n [926, 271, -350, -336, 100, -671, 442, 129, 48, 337, -263, 695],\n [876, 1058, -437, -1271, 93, -757, 111, 657, -5, 39, 371, 10],\n [-848, -261, -162, 477, -206, 605, -338, -432, -5, -116, 92, -349],\n [-230, -266, 352, 1211, -478, 554, -824, -1249, 561, 771, -297, 402],\n [-576, -7, 278, 101, -150, 411, -478, -94, 69, -218, 304, -589]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-243, 618, -637, -121, 83, 433, 311, -499, 273, -229, 398, -674],\n [95, 414, 477, 62, 299, 238, -473, 1135, 485, -581, 697, -297],\n [968, -135, 1388, -273, 580, -393, -1193, 741, 1000, 626, 1361, 639],\n [-354, 553, -978, 193, -928, 754, 112, -496, -927, -759, 209, -101],\n [318, -255, -1036, 232, -426, -32, 383, -298, -823, -237, -269, 167],\n [-27, -516, -183, 487, 470, 927, 531, 792, 487, 281, -23, 164],\n [234, -320, 500, 125, 269, 428, -237, 424, 509, 507, 486, 495],\n [267, -1418, 1847, 15, 1151, -210, -138, 641, 1407, 1927, -351, 1087],\n [-614, -615, -826, 252, -31, 801, 1206, -1114, -74, 914, -930, 191],\n [420, 629, 74, -136, 925, 109, -202, 927, 1177, -415, 1135, -864],\n [-1009, -188, -311, -21, -226, 250, 872, -1174, -257, 499, -1240, -139],\n [394, 220, 442, -284, 677, -324, -304, 260, 893, 201, 672, -315]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[668, -117, 832, -204, 51, 614, 221, -469, 633, 408, -66, -714],\n [-341, 23, -598, -264, 54, -824, -161, 409, -513, -9, -183, 722],\n [-448, -283, 104, 157, 152, -320, -316, -376, -112, -762, 117, 138],\n [-257, 188, 154, 667, -135, 1119, -56, -308, 61, -370, 858, -263],\n [-415, -320, -71, 472, 84, -431, -263, -106, -52, -1071, -253, -17],\n [17, -180, -583, -34, -23, -1338, 96, 671, -90, -232, -1217, 70],\n [-171, 317, 50, -491, 63, 656, -156, -252, -398, 701, 1134, 676],\n [435, -343, 642, -192, 274, 354, -197, -267, 229, -287, -119, 32],\n [164, 126, -555, 1128, -483, -265, 573, 740, 512, -442, -1166, -1213],\n [-428, 343, -984, 110, -209, -568, 65, 727, -537, 182, -80, 512],\n [554, -54, -55, -717, 172, -355, 8, 485, -133, 578, -531, 547],\n [-405, 584, -1266, 1467, -689, 105, 502, 1098, -47, -380, -398, -673]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[400, -339, -407, 646, 20, 772, -578, -22, 1340, 153, -681, 423],\n [-232, -360, -934, 118, 244, 377, -153, -142, 724, 703, 923, 555],\n [-634, 1411, -4, -364, -441, -1176, -3, 546, -1695, -565, -304, 648],\n [-2, -1044, -1021, 765, -1293, -34, -530, 527, 1197, 691, -22, -427],\n [-198, -132, -845, 549, -1244, 918, -1057, 649, 571, -526, -1096, -299],\n [-286, -44, 1195, 137, 968, -73, 630, -742, -397, 444, 505, 277],\n [-392, 942, -418, -929, 383, -701, -273, 721, -1270, 575, 1192, 1471],\n [301, -475, 23, -519, 356, 260, 645, -687, -19, 240, 1142, -969],\n [576, 481, -579, -1418, 167, -862, -93, 891, -868, 198, 960, 444],\n [547, -238, -626, 104, -102, -1071, 327, -11, -37, -432, -867, 134],\n [792, -767, 308, -58, 1611, 888, -377, -214, 381, 297, -480, 1386],\n [545, -520, 305, 455, -353, 442, 58, -292, 718, -648, -1154, -1064]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-245, -74, -412, -156, 459, 89, 482, 184, -565, -132, -172, -188],\n [820, 1100, 650, -25, -920, 205, -445, 655, 470, 1415, -300, -180],\n [-203, -642, -184, 84, 25, -489, -538, -603, 65, -643, 206, 483],\n [896, -175, -813, 486, 1173, 473, 119, -286, 645, 278, 823, 473],\n [1214, 140, -578, 522, 102, -148, -806, -322, 388, 977, 495, 495],\n [-35, 596, 614, -54, -1153, -221, -166, 317, -445, 673, -496, -613],\n [-725, 175, 267, -877, 128, 113, 286, 759, -156, -458, -778, 120],\n [35, -39, -77, 272, -422, -310, -119, -265, -512, 222, 18, -333],\n [349, -179, 193, 481, -956, -701, -1026, -706, 64, 267, 252, 139],\n [-306, -393, -7, -679, 269, -358, -824, 68, 605, -769, -306, 1175],\n [-595, -283, -81, -612, 684, 156, 257, 305, 174, -842, -276, 459],\n [555, 125, 267, 295, 110, 367, -168, -132, 1032, 208, 515, 286]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-50, -100, 220, 70, -240, 200, -160, 40, 260, -120, 240, -180],\n [-80, -160, 352, 112, -384, 320, -256, 64, 416, -192, 384, -288],\n [10, 20, -44, -14, 48, -40, 32, -8, -52, 24, -48, 36],\n [35, 70, -154, -49, 168, -140, 112, -28, -182, 84, -168, 126],\n [120, 240, -528, -168, 576, -480, 384, -96, -624, 288, -576, 432],\n [50, 100, -220, -70, 240, -200, 160, -40, -260, 120, -240, 180],\n [110, 220, -484, -154, 528, -440, 352, -88, -572, 264, -528, 396],\n [105, 210, -462, -147, 504, -420, 336, -84, -546, 252, -504, 378],\n [-5, -10, 22, 7, -24, 20, -16, 4, 26, -12, 24, -18],\n [90, 180, -396, -126, 432, -360, 288, -72, -468, 216, -432, 324],\n [90, 180, -396, -126, 432, -360, 288, -72, -468, 216, -432, 324],\n [90, 180, -396, -126, 432, -360, 288, -72, -468, 216, -432, 324]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-657, 589, -639, 201, -861, 493, -828, 449, -652, 31, -545, -69],\n [-17, 857, 715, -223, 35, 637, -144, 1015, -978, 63, 87, -307],\n [-440, -483, -153, -230, -454, -100, 663, -48, 133, -270, -254, -194],\n [-1042, 18, -119, -58, -742, 662, 140, 521, -929, -2, -810, -549],\n [208, 604, -306, -161, -610, -40, -162, 423, 69, -13, 344, -45],\n [-204, 256, -518, 457, -192, 313, -762, -124, -339, 527, -326, -131],\n [30, -49, -681, 510, -30, -47, -681, -553, 187, 480, -166, 80],\n [-492, -332, -1013, 390, -518, -153, -580, -582, 307, -56, -538, 287],\n [-1185, -250, -19, -3, -505, 642, 139, 339, -922, -151, -1001, -398],\n [166, -481, 290, -560, -152, -448, 1219, 21, 570, -412, 380, -145],\n [1122, 304, -349, 298, 490, -622, -694, -575, 941, 282, 830, 575],\n [252, 631, -132, 3, -174, 13, -561, 317, -31, -83, 256, 246]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-111, -413, -1321, -690, 160, 749, -305, 1488, 401, -648, -672, -722],\n [594, -175, 885, -518, -695, 801, 453, -708, 731, 472, -557, 813],\n [-1593, -351, 864, -924, -216, 666, 1392, -232, 571, -10, 282, 654],\n [-1055, -647, 524, -238, 657, 1014, -552, -519, 1214, -271, 970, 393],\n [-1481, -710, 266, -25, 1476, -832, 526, 220, -371, 517, 1504, 611],\n [-404, -1426, 1425, -664, -159, -322, 1598, -185, -192, 954, 545, 401],\n [190, -411, -675, 748, 242, -1300, 507, -431, -2311, 114, -396, -942],\n [-1116, 1017, 437, -475, -1196, -185, 135, -528, 68, -621, 1274, 750],\n [44, -194, 71, -230, 329, 195, 597, 449, 478, -77, -647, 449],\n [-443, -2245, 1094, -397, 616, -522, 1533, 875, 219, 430, 119, -45],\n [-759, 491, -1195, -30, -838, -145, -225, -1004, -1411, -578, -1284, 37],\n [121, 147, -676, 1207, 289, -1021, 870, -76, -1566, 572, 205, -479]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-60, -104, 64, 40, -84, 76, 88, -16, -8, -8, -96, -92],\n [63, 122, 16, -378, -187, -115, -342, -92, -318, -414, 136, -41],\n [246, 444, -148, -626, -34, -360, -704, -84, -416, -548, 442, 188],\n [168, 288, -200, -28, 304, -204, -184, 72, 104, 128, 260, 292],\n [81, 154, 2, -411, -179, -140, -384, -94, -336, -438, 167, -22],\n [372, 652, -350, -437, 366, -491, -686, 38, -134, -188, 615, 493],\n [-423, -742, 394, 513, -403, 560, 792, -38, 168, 234, -701, -554],\n [-261, -442, 346, -99, -589, 302, 180, -158, -300, -378, -389, -512],\n [165, 306, -46, -635, -199, -264, -632, -126, -488, -638, 319, 38],\n [-147, -242, 240, -238, -481, 151, -34, -148, -346, -442, -200, -363],\n [-420, -736, 396, 490, -416, 554, 772, -44, 148, 208, -694, -558],\n [300, 504, -424, 220, 764, -336, -128, 216, 448, 568, 436, 632]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-337, 373, -645, 203, 1053, 27, 391, -412, 453, -181, 296, 1084],\n [1183, -1335, -266, 87, -595, 986, 304, -409, 184, 1193, -211, -825],\n [-768, -197, -285, -261, -131, 256, -436, 955, -564, -70, -110, 235],\n [-430, -398, 953, -28, 758, -1527, 922, 471, -1077, 970, 265, 300],\n [244, -61, 923, 242, -844, -384, 651, -266, -212, -710, -377, -438],\n [965, -1, 547, 33, -508, -920, -370, 615, -1234, 848, 660, -175],\n [273, 602, 377, 346, -1683, 1313, -254, 242, 716, -1521, -718, -400],\n [-1588, 57, -449, -464, 771, -5, 201, -541, 1158, -787, -707, -584],\n [68, 685, -982, -832, -1160, 788, -901, -146, 865, -771, -1044, -555],\n [980, -29, -658, 43, -19, 376, -352, -786, 527, 376, 20, 144],\n [-325, 837, -965, -1465, 958, -58, -892, -941, 1270, 594, -213, -1211],\n [-915, -1035, 1060, 408, 442, -769, 818, -246, 45, -101, -196, -980]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1934, 334, -427, 877, -787, 765, 817, 509, -434, 126, -214, -1173],\n [535, -860, 428, -1056, -792, 135, 479, 53, 428, 1452, 1181, 681],\n [299, -638, 281, -520, -85, -606, -392, 857, -206, -135, 270, -166],\n [812, 594, -106, 870, 38, 40, 1043, 520, -87, 207, 402, 98],\n [902, -339, -325, -354, 979, -591, 21, -484, 204, -712, 458, 59],\n [183, -1411, -265, -500, 499, -1079, 377, 1002, -518, -294, 46, 529],\n [-314, 784, 249, -404, -507, 909, -426, -1182, 669, 994, 359, -124],\n [902, -198, 655, -1169, -936, 530, -396, -1150, 1150, 1527, 1047, 850],\n [151, 1057, -470, 887, -40, 845, 604, -1508, 759, 25, 137, -19],\n [-436, -504, 718, -886, -782, 120, -1515, -304, 255, 307, -668, 470],\n [1000, -514, 797, -959, -1147, 525, 269, -255, 746, 1318, 1466, 365],\n [644, -235, -423, 317, 83, -593, 153, 9, 370, -431, 237, 120]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[27, 605, -358, 171, 278, 265, -235, 474, -90, 51, -2, -556],\n [28, 698, -1019, 289, -422, -250, -766, -270, 480, 323, -633, 373],\n [-545, -440, 1000, 876, 822, 85, 624, 203, 698, 721, 180, 350],\n [-308, 328, 155, -1090, -1475, 335, -403, -610, 438, 496, 139, -132],\n [-382, 109, 943, 385, 370, 232, -30, 778, 1642, 1203, -1039, 284],\n [-635, 226, -290, 87, -634, -433, -197, 834, -260, 707, 190, -439],\n [508, -1478, -138, 193, -233, -111, -479, 250, -1074, -1054, 633, -417],\n [-167, -1415, -342, 981, -705, -435, -1197, 1340, -437, 146, 285, -589],\n [-551, 841, -102, 149, 84, 101, 587, -566, -546, 347, 1092, -70],\n [361, -342, 396, -426, -235, 409, -140, 174, -613, -470, 472, -447],\n [-247, 855, -150, 111, 659, 377, 309, 600, -297, 124, 389, -897],\n [-176, 505, -1438, 454, -119, -748, -210, -655, -9, -20, -271, 486]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[22, -414, 37, -397, 146, 428, -353, 96, -633, -49, -140, 344],\n [42, 14, -447, 246, 94, -487, 103, 97, 560, 73, 312, -316],\n [0, -248, -6, -243, 107, 220, -196, 74, -353, -7, -72, 175],\n [694, 98, 323, 836, -720, 551, -431, -565, 110, -863, 152, 690],\n [808, -192, -178, 893, -541, 312, -600, -410, 327, -867, 440, 607],\n [-542, 518, 635, -421, 42, 2, 577, 14, -253, 457, -508, -300],\n [156, -652, -642, -192, 340, -46, -446, 274, -124, -26, 288, 104],\n [610, -178, -417, 755, -309, -45, -405, -219, 527, -580, 504, 269],\n [72, -184, 264, -198, -62, 488, -260, -68, -538, -158, -192, 386],\n [-50, 490, 53, 401, -182, -410, 407, -126, 625, 59, 92, -352],\n [48, -120, -34, -45, 21, 92, -116, 14, -111, -49, 8, 97],\n [-518, 502, 409, -316, 97, -222, 609, 68, -2, 490, -356, -441]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-369, -40, 144, -589, 191, -113, -183, -530, 138, -175, 563, -366],\n [-473, 44, 305, -183, 197, 159, 416, -170, -814, -134, 280, 210],\n [379, 752, 691, 1515, -629, 360, -543, 354, -568, 551, -134, 1026],\n [-394, 404, 295, 372, -86, 1025, -104, -142, -240, 574, -5, 418],\n [535, 1306, 971, 1281, -1000, 130, -1822, -98, 900, 884, 278, 635],\n [-165, 1218, 619, 345, -580, 890, -726, 90, 760, 1052, -282, 599],\n [-516, 406, 463, -424, 75, 44, 560, 80, -668, -22, 27, 389],\n [-895, -630, -117, -755, 766, 301, 1469, -174, -1590, -561, 200, 1],\n [242, 136, 484, 1165, -249, 8, -307, 3, -957, 1, 319, 598],\n [657, 184, -654, -337, -327, -230, -230, 678, 1796, 390, -1053, -332],\n [-456, -148, -49, 323, 243, 1007, 705, 67, -1003, 219, -208, 424],\n [494, -100, -350, -80, -160, -421, -473, 100, 1030, 3, -192, -408]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[266, 20, -72, 6, 178, -98, 226, 186, -191, -61, -44, -169],\n [366, -28, 80, -206, 302, -414, 214, 478, -185, -211, 124, -143],\n [170, 174, -566, 626, -52, 748, 426, -526, -348, 330, -564, -368],\n [164, -56, 176, -260, 180, -404, 20, 388, -22, -194, 200, 6],\n [671, 67, -235, 79, 432, -164, 599, 403, -505, -116, -166, -453],\n [-225, -105, 345, -345, -60, -360, -345, 195, 285, -150, 330, 285],\n [50, -24, 76, -106, 62, -158, -6, 146, 3, -75, 84, 13],\n [249, 31, -107, 53, 154, -30, 233, 125, -196, -29, -82, -178],\n [386, 76, -256, 190, 210, 94, 410, 82, -343, 19, -220, -321],\n [-18, 20, -64, 82, -34, 114, 22, -98, -17, 53, -68, -23],\n [157, 7, -27, -15, 110, -82, 125, 129, -106, -47, -10, -92],\n [380, 130, -430, 400, 150, 370, 500, -140, -415, 145, -400, -405]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[264, -1343, 685, 280, 738, 193, 546, 764, 39, 1968, -967, 13],\n [1021, -392, -1370, 36, 136, -336, 269, 426, -183, 947, 1127, -104],\n [-344, -1395, 107, 716, -92, 136, 343, 712, 812, 848, -919, -458],\n [1070, -77, -389, -588, 595, 81, 239, 488, -95, 707, 343, -13],\n [443, -351, -217, -274, -123, -139, -262, 237, 457, -160, -146, -591],\n [15, 1074, 467, -521, 604, 239, -76, -844, -1117, -39, 372, 724],\n [-413, -1312, -138, 620, 676, 173, -126, -918, -260, 1551, -629, -461],\n [-97, -1004, 259, 402, 414, -172, 34, -78, 132, 1177, -672, -206],\n [220, 727, 472, -378, 62, 32, -14, -108, -937, -52, 428, 540],\n [-101, 716, 1029, -463, -484, -747, -566, 125, 758, -1463, -616, -16],\n [998, -16, 142, -352, 319, -287, 494, 1120, -51, 811, 264, 433],\n [1078, 1015, -302, -566, 458, -394, 208, -33, -1440, 670, 1486, 958]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[137, 163, 374, -185, 207, 271, -274, -353, 175, 159, 177, -18],\n [-36, -194, -76, 51, -17, -255, -37, 158, 102, -111, -103, -117],\n [180, -170, 548, -237, 367, -111, -637, -298, 606, 33, 89, -333],\n [54, 196, 128, -75, 49, 267, -13, -196, -60, 123, 119, 99],\n [159, 271, 422, -216, 220, 414, -259, -445, 123, 222, 236, 45],\n [169, 251, 454, -229, 243, 395, -302, -457, 167, 219, 237, 18],\n [65, 535, 110, -95, -15, 685, 200, -365, -365, 285, 255, 360],\n [-97, 327, -330, 124, -256, 346, 513, 59, -557, 90, 40, 369],\n [115, 55, 326, -154, 194, 128, -289, -261, 227, 96, 118, -81],\n [-126, -204, -336, 171, -177, -315, 213, 348, -108, -171, -183, -27],\n [48, -248, 176, -60, 148, -276, -316, 8, 360, -84, -52, -252],\n [114, 76, 320, -153, 187, 153, -271, -268, 204, 105, 125, -63]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[586, 229, -1624, -213, -619, 285, 506, 108, -68, 296, -728, 1110],\n [-908, 1306, 43, 911, 451, -119, -944, -37, -617, 195, -287, -637],\n [-246, -582, 495, -1152, 387, -1321, -480, 235, 376, 565, -190, -101],\n [-567, 120, -1673, 367, 101, -197, -910, 215, 1777, -401, 241, -1237],\n [-527, 671, -1321, 1333, 852, -776, 212, 419, -239, 587, -1196, 497],\n [1488, 170, 292, -336, 61, 1336, 764, -60, -1044, -132, 197, 213],\n [127, 99, 1106, 28, 124, 794, 131, 483, -1175, -117, 230, 627],\n [122, 771, -235, 1171, 1831, -223, -1050, 192, -640, 1635, -1394, -1],\n [1021, 99, -389, 727, 923, 459, 386, 815, 5, -606, -364, -167],\n [-372, -301, -452, 1339, 791, -1232, -1001, -1172, 772, 806, -440, -1085],\n [1763, -1055, 1258, -432, 82, -315, 104, -872, -38, 450, -898, -1088],\n [185, -883, 1151, -747, -583, -1049, -956, -971, -64, 844, -546, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-191, 250, 234, -345, 57, -226, -33, 64, -157, -133, -196, 88],\n [-26, -477, -150, -8, -318, -206, -27, 119, 178, -286, 29, 96],\n [-159, -263, -162, 101, -105, -320, -36, 743, -317, -27, -363, -188],\n [-43, 612, 19, 311, 548, 176, 32, 614, -705, 666, -412, -486],\n [141, -1161, -329, -27, -814, -198, -31, -431, 871, -748, 505, 438],\n [49, -695, -274, 117, -425, -160, -20, 87, 307, -315, 133, 100],\n [-311, -226, -55, -121, -146, -552, -68, 896, -421, -180, -530, -130],\n [-88, 664, 380, -344, 316, 72, 4, -328, -136, 92, -48, 88],\n [-159, -441, -130, -63, -293, -396, -50, 485, -61, -287, -217, 12],\n [421, -403, -521, 857, 14, 558, 83, 7, 175, 472, 339, -322],\n [-29, -556, -163, -31, -380, -240, -32, 98, 233, -354, 52, 134],\n [140, -686, -164, -56, -508, -36, -10, -518, 676, -492, 446, 352]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-828, -125, 1285, -1888, -415, -362, -654, 230, 331, 532, -302, 291],\n [-442, -1436, 1040, 40, -513, -461, -411, -361, 1424, -271, -47, 241],\n [-20, 127, -512, 1095, -324, -345, 215, -978, 326, 398, 592, -1099],\n [-594, -610, -807, 1651, 146, 135, -12, -1369, 426, 286, 360, 35],\n [-346, 1159, 121, 381, -522, 1025, 13, 1570, -215, -1662, -497, 598],\n [-579, -212, -342, 214, -53, -213, -515, -546, 1035, -474, -582, -1986],\n [-373, 370, -280, 832, -564, 135, 115, -35, 678, -396, 463, -1009],\n [901, 856, -680, 1151, -1543, 480, 776, 1137, -723, -1295, -1413, -499],\n [1480, 744, -1468, 1198, -155, 306, 1209, 730, -1180, -369, -131, -523],\n [740, -2220, 2087, -1688, 275, -1650, 347, -526, 833, 1559, 981, 1355],\n [1423, -734, 51, 338, -693, -522, 1084, -101, -52, 114, -717, -276],\n [-722, 1414, -711, 73, 129, 855, -780, 51, -541, -316, -148, -502]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[187, -220, -141, 2, -188, 167, 132, -86, 256, -41, 223, -177],\n [462, -198, 60, -639, 525, 177, 546, 243, -90, -384, -360, 81],\n [-132, 22, -58, 247, -249, -27, -178, -115, 98, 138, 194, -75],\n [0, 66, 78, -123, 189, -45, 42, 87, -138, -54, -174, 99],\n [-407, 484, 313, -14, 424, -367, -284, 194, -568, 85, -499, 393],\n [11, -110, -123, 181, -289, 76, -54, -133, 218, 77, 269, -156],\n [-132, 198, 150, -81, 255, -147, -66, 117, -270, -6, -270, 189],\n [132, -66, 6, -165, 123, 57, 150, 57, -6, -102, -78, 9],\n [649, -440, -107, -596, 274, 359, 664, 128, 212, -407, -79, -129],\n [165, -110, -25, -155, 75, 90, 170, 35, 50, -105, -25, -30],\n [-143, 66, -13, 189, -149, -58, -166, -69, 18, 115, 99, -18],\n [143, 44, 143, -394, 464, -17, 236, 214, -248, -205, -389, 183]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-25, 25, -54, -50, 15, 0, -49, -55, -43, 42, 97, 69],\n [86, -72, -8, 46, -60, 42, -28, -4, -94, -14, -38, 74],\n [-148, 146, -292, -278, 90, -6, -262, -298, -220, 230, 532, 364],\n [-209, 193, -230, -274, 135, -48, -185, -239, -83, 202, 473, 221],\n [458, -391, 62, 313, -315, 201, -43, 83, -370, -145, -362, 226],\n [82, -89, 274, 227, -45, -21, 259, 277, 262, -203, -466, -382],\n [-319, 263, 86, -134, 225, -168, 161, 71, 419, 14, 55, -365],\n [353, -281, -234, 58, -255, 216, -319, -217, -637, 78, 151, 627],\n [83, -66, -56, 13, -60, 51, -76, -52, -151, 19, 37, 149],\n [-44, 63, -358, -259, 15, 57, -353, -359, -404, 251, 572, 544],\n [-282, 264, -360, -402, 180, -54, -300, -372, -174, 306, 714, 378],\n [-352, 279, 250, -47, 255, -219, 335, 233, 656, -89, -176, -652]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[901, 493, 715, -538, 509, -308, 855, 446, 71, -639, -905, 226],\n [-860, 494, -339, 78, -1383, -339, 331, -1210, 296, 1049, 546, -650],\n [-922, -1002, 381, 1165, 7, -774, 721, -568, 177, -267, -931, -180],\n [1533, 17, 202, -354, 951, -10, 110, 573, -299, 513, -57, 512],\n [-232, -320, -1165, -95, 644, -179, -54, -157, 575, -389, 453, 244],\n [1181, 439, 130, -344, -99, 273, -276, 1052, -673, 214, 875, 714],\n [-1523, -1171, -780, 934, 647, -998, 791, -727, 1077, -922, -549, -24],\n [-1512, -834, -874, 420, 246, 593, -1096, -411, 336, -871, -2, -430],\n [1017, 900, 380, -379, -1168, 343, -271, 58, -876, 1433, 887, -22],\n [499, -279, 183, 322, 472, -625, 638, 861, 13, -91, 317, 854],\n [913, 283, -158, 37, -875, 466, -770, 464, -1068, 1104, 1432, 412],\n [481, 601, 933, -363, -197, 137, 91, 142, -86, 1313, 10, -220]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-394, -226, 458, -166, 307, 283, 855, 653, 678, -1080, -734, 1628],\n [141, -250, 662, 193, 7, -870, -534, 522, 559, -1409, 889, 112],\n [881, -788, -92, -682, -651, -137, 1161, 65, -1347, -125, -1023, 151],\n [320, 416, 140, 877, 117, 483, -770, -33, -41, 687, -332, -1197],\n [228, 99, 484, 180, -192, 148, -1070, -261, -238, -560, 738, -302],\n [124, 627, 864, 324, 509, -863, -1507, -326, 1517, -1882, 1255, 479],\n [-1508, 57, 1847, -738, -1554, 64, -1019, 1222, -78, -1176, -236, 713],\n [-1125, 652, -230, 954, 89, -1209, -65, 340, 1509, 450, 49, -544],\n [452, 690, -708, 752, 1644, 1094, -115, -633, 997, 347, 606, 408],\n [25, 1188, -386, 544, 101, 1299, -558, -224, -131, 1114, 596, -358],\n [333, 193, -180, 756, 294, -120, 477, 384, 397, -576, 484, 366],\n [765, -290, 125, -477, 303, 58, 381, -558, 77, -846, -113, 978]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[255, -241, 325, 335, -323, 400, -159, 165, 85, 427, 7, 232],\n [-140, -502, 45, -32, -561, -173, 505, -166, 491, 27, 153, 698],\n [222, -591, 514, 264, -417, 378, -173, -61, -47, 464, 15, 402],\n [184, 408, -65, 225, 102, 233, -160, 362, 76, 137, -33, -237],\n [-152, -82, 453, -645, 464, -553, 374, -504, -194, -377, 239, 369],\n [237, 556, -311, 515, -306, 352, 106, 732, 680, 281, 24, -14],\n [440, 323, 179, 552, -94, 631, -388, 577, 96, 515, -58, -174],\n [-199, -124, 29, -282, -313, -488, 887, -122, 747, -223, 326, 849],\n [-337, 685, -728, -248, -163, -687, 1147, 313, 1207, -540, 308, 467],\n [22, -199, 38, 72, 11, 158, -329, -101, -339, 92, -133, -222],\n [350, -322, 185, 635, -356, 785, -738, 260, -310, 639, -251, -281],\n [615, -371, 450, 948, -533, 1167, -931, 489, -259, 1010, -254, -189]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-544, 902, 738, 1007, 425, -230, -68, 499, 841, -501, -698, -1348],\n [275, -386, -334, 599, 286, -883, 42, 692, -100, 719, -1435, 418],\n [157, 351, 862, 22, -337, -193, 150, 345, 669, 299, -336, -130],\n [802, -381, -109, -328, 401, -1010, 388, -700, -57, 764, -563, 1084],\n [-230, -155, -604, 454, 408, -109, -240, 331, -208, -323, -596, -424],\n [-245, 313, 1215, 777, -299, -343, 375, 306, 266, -97, -373, -185],\n [444, -781, -320, -975, 237, -707, 692, -112, -41, 706, -162, 1168],\n [-117, -508, -400, -160, 625, -734, 455, 517, 169, 44, -869, 69],\n [-549, -171, -333, 486, 178, 140, -10, 367, -411, -392, -9, -272],\n [703, -126, -164, -308, -1407, 767, -668, 727, -321, 1546, 339, 1048],\n [-645, 172, 172, -227, 334, 131, 237, 490, 635, -847, -34, -1043],\n [-138, 211, 251, 953, -694, 290, -416, 1048, -181, 623, -381, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 677, 921, 802, 333, -315, 1958, 987, 286, -921, -459, 200],\n [-99, -815, 30, 330, -1352, 1506, 573, -103, -641, -151, 656, -107],\n [773, -734, 583, 171, -846, -843, 159, -205, -54, -438, 1280, 83],\n [1456, -428, 954, -1397, -781, -628, -557, -323, 50, -1012, 318, 17],\n [-618, 178, -842, -203, -616, -417, -478, -1115, 878, 870, -371, 1316],\n [359, 348, -143, 286, -740, -106, -229, -202, 188, 288, 613, 1459],\n [439, 304, 1213, -56, -9, -398, -1102, 72, 21, -411, -157, -349],\n [783, -517, 854, 218, -115, 307, 308, 1087, 446, -876, 324, 486],\n [-279, 189, 106, 141, 870, 1200, 868, 1198, -28, -469, -930, -399],\n [152, 77, 1095, -36, -289, -530, 1492, 181, 260, -1097, -493, -353],\n [-66, 13, -466, -375, 1377, -393, -286, 377, 21, 151, -373, -755],\n [1147, -77, -719, -1279, 666, -158, -298, 301, -398, -160, 424, 61]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[629, 550, 1197, 1475, -2088, 699, -105, -271, -191, -1356, 70, -449],\n [340, -702, -644, -55, 634, 79, -33, 718, -392, -229, 271, 800],\n [-198, -84, 701, -197, 134, -1183, 837, 75, 295, -137, 621, -381],\n [-934, 635, -867, -1097, 46, -24, 644, -501, 740, 751, 693, -132],\n [-537, -904, -395, 1070, -985, 644, -1065, 1139, -323, -97, -139, -397],\n [526, 403, 934, 619, -893, 596, -15, 448, 290, -1045, 38, -293],\n [-369, 1377, 988, -354, 665, -229, 315, -251, -71, -506, -679, -856],\n [1205, -667, -464, -1039, -275, -684, 302, 607, -266, 244, 855, 1364],\n [28, 347, -32, 504, 1116, 759, -23, 744, -793, -1103, -128, 513],\n [762, -224, -73, 265, -127, -581, -1074, -913, -212, 529, -458, 455],\n [-161, 415, -124, 837, -771, 8, -1091, -1709, 752, 345, -425, -620],\n [-323, 370, 678, 1494, -68, 82, -1190, 228, 1386, -537, 781, -224]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[151, 696, 287, 555, -594, -686, -656, 353, 511, -458, -311, 633],\n [-78, 719, -106, -163, -775, -547, -528, 43, 49, -358, 12, 407],\n [81, 401, 492, -517, 111, -219, 101, -794, -239, 361, 811, 272],\n [1153, 1524, 434, -388, -359, -1071, -265, 336, -565, -292, -289, -511],\n [283, 670, 169, 71, -346, -550, -302, 313, -111, -582, -543, 91],\n [-443, -1004, -927, -395, 269, 900, 510, 164, -398, 170, -174, -792],\n [558, 1051, 257, 418, -744, -894, -755, 408, 549, 12, 138, 351],\n [-28, 303, -35, 258, -353, -315, -305, 425, 36, -727, -752, 203],\n [96, 154, 208, 254, 37, -195, -56, 269, -67, -585, -692, 88],\n [-414, -345, 41, -366, 277, 316, 311, -517, -316, -68, 135, 142],\n [332, -526, 5, 577, 453, 339, 171, 343, 476, 672, 178, -390],\n [51, -50, -630, 378, -595, 12, -461, 544, 709, 597, 428, -124]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1687, -1316, -470, 911, 1514, -531, -1152, -1351, 1152, 1002, 527, 909],\n [-523, 191, 20, -33, -209, -726, 412, 529, -506, 10, -1666, -400],\n [630, -437, -1183, -28, 443, -320, -308, -597, 94, 871, 168, 77],\n [-502, 205, -19, -149, -1414, -272, 1471, -430, 458, -369, 310, -1399],\n [692, -937, 565, -155, 2173, -11, -588, 365, 551, 1456, 664, 461],\n [-1095, 412, -313, -882, -1439, 881, 1927, -130, -729, -829, 719, -895],\n [-811, 1564, 193, -222, -960, -1189, -554, 670, -759, -374, -1648, -767],\n [189, 638, -912, 274, -728, -97, -463, -276, -560, 921, -400, 7],\n [-1254, 749, 942, -889, -1033, -251, 1284, 457, -360, -641, 176, -1015],\n [40, 592, -241, 210, -349, -16, -512, 296, 236, -802, -164, -537],\n [-336, 112, 499, -4, 81, 820, 686, -206, -815, -671, 11, 241],\n [-1069, -147, 53, -415, -1656, 96, 944, -109, 553, -1199, -621, -479]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[384, -540, 675, 1623, 659, -382, 651, 546, -413, -539, 367, -629],\n [-1015, -1235, -1445, 1214, 768, -262, -521, -1376, 723, 555, 523, 292],\n [-474, 266, 968, 14, -435, 21, 766, -602, 186, 1600, -372, -620],\n [-210, -643, 557, 288, 971, -775, -738, -17, 138, -1174, 826, -488],\n [-101, 218, -342, 274, -98, 831, -745, -183, -801, -135, -480, 48],\n [377, 385, 1182, 1092, -134, -400, 1329, 312, -534, 678, -239, -383],\n [248, 366, -1162, -614, 266, 693, -683, 282, -803, 215, -667, 166],\n [356, -595, 16, 870, 1165, 98, 49, 1120, -374, -1418, 193, 142],\n [815, -481, -952, 281, -122, 224, -27, 995, 185, -1529, 1069, 436],\n [-435, 995, 66, -53, 741, 734, 148, 973, -841, -545, 11, 2124],\n [297, -196, 404, 774, -247, -1076, 190, -977, 4, 895, -949, -629],\n [526, -565, -651, 551, 232, 439, -676, 421, -378, -901, 341, -199]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -133, 44, 170, 171, -46, 50, -424, 307, -299, 145, 260],\n [146, -67, 240, -36, 433, -88, -778, -474, -255, -29, 55, -10],\n [-367, -193, -422, -8, -283, -379, -547, -408, -583, 182, 288, 117],\n [89, 230, -264, -177, -629, 284, 665, 727, -195, 75, -34, -98],\n [-441, -343, -258, 290, 35, -421, -135, -722, 223, -140, 278, 359],\n [935, 474, 570, -359, 194, 771, 140, 661, -166, -218, -248, -281],\n [-554, -568, -198, 346, 423, -757, -1097, -1498, -91, -125, 462, 461],\n [-789, -509, -18, 505, 559, -755, -276, -853, 791, 131, -23, 187],\n [209, 352, 106, -258, -248, 349, 497, 1048, -72, 339, -397, -457],\n [-831, -533, -102, 511, 475, -785, -276, -903, 731, 115, 41, 237],\n [-367, -265, -630, 120, -539, -307, -91, -616, -375, -202, 552, 477],\n [-75, -269, 58, 131, 407, -305, -840, -947, -161, -185, 281, 261]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[156, 677, -400, 20, -442, -121, 761, -319, -916, 357, 524, -563],\n [-1474, 716, 399, -67, -943, 213, 728, 183, -931, -740, 79, -677],\n [666, -659, -226, -1367, -645, -193, -77, 197, 1812, -125, -467, -630],\n [195, -463, 1165, 512, 1725, -1111, -413, 462, -315, 1071, 819, 956],\n [440, -1444, 626, -116, 612, -42, -1176, 418, 1418, -168, -816, 884],\n [194, -654, -55, 955, 1061, 643, -1282, -69, 477, -298, -705, 1349],\n [-200, -505, 419, 515, -683, 382, -69, -42, -881, -409, -571, 204],\n [-382, -127, 430, 422, 727, -30, -435, 209, -5, -53, 15, 594],\n [774, -1061, 623, 333, 1500, -527, -1037, 300, 770, 653, -26, 1171],\n [-912, -376, 1259, -1039, 320, -882, -44, 949, 1178, -134, 228, -246],\n [-907, 1053, -364, -300, -346, 191, 573, -19, -97, -409, 332, -665],\n [546, -1279, 934, -50, 1002, -613, -891, 495, 926, 425, -200, 869]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[409, 413, 777, -684, 406, -929, 142, -46, -5, -241, 506, -828],\n [347, 256, -253, -284, 322, 1186, -373, 421, 173, 976, 131, -150],\n [354, -234, -582, 412, -235, 236, 140, 373, -22, 59, 61, -125],\n [-633, -282, -297, 424, -289, 434, -127, -260, -19, -25, -506, 829],\n [572, 265, -68, -332, 307, 499, -135, 426, 108, 590, 344, -529],\n [-394, 142, 598, -296, 124, -566, -12, -444, -30, -334, -76, 128],\n [698, 349, 282, -508, 369, -225, 51, 330, 54, 212, 540, -871],\n [212, 331, 164, -460, 375, 549, -269, 164, 124, 600, 174, -233],\n [-541, -53, 99, 52, -56, 157, -146, -328, 1, -33, -328, 550],\n [457, 137, -351, -112, 185, 881, -202, 469, 119, 726, 181, -259],\n [763, 14, -301, 36, 22, -32, 185, 523, 5, 126, 413, -694],\n [93, 33, 277, -96, 9, -687, 194, -95, -61, -394, 153, -275]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[47, -158, -57, -110, 599, -300, -248, -214, 75, -278, -419, 644],\n [296, 393, 337, -83, -78, -42, -16, 388, 146, -70, 213, -291],\n [519, -16, -4, 51, -131, 96, 207, 443, 414, -508, 327, -183],\n [63, -636, -484, 75, 405, -72, 19, -297, 194, -508, -301, 673],\n [-141, -392, -313, 54, 203, -24, -10, -308, -23, -118, -233, 392],\n [653, -180, -100, 25, 159, -24, 145, 397, 558, -804, 169, 155],\n [-151, -669, -521, 76, 417, -78, -31, -479, 32, -310, -408, 726],\n [-301, 664, 456, -5, -727, 240, 79, 227, -390, 844, 427, -967],\n [63, 206, 279, -270, 823, -516, -484, -154, 7, -150, -551, 692],\n [-85, -491, -379, 52, 323, -66, -25, -337, 44, -258, -300, 546],\n [-280, 829, 576, -8, -892, 294, 115, 353, -411, 952, 565, -1204],\n [451, 212, 183, -10, -149, 48, 122, 472, 309, -310, 323, -296]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-11, -68, -54, 93, 81, -205, -240, -154, 40, 6, 222, -245],\n [-375, 15, -441, 81, -312, -504, -72, -117, -342, -423, -75, -516],\n [-122, -161, -243, 246, 117, -625, -600, -403, 10, -93, 519, -725],\n [-441, 42, -504, 63, -399, -525, 0, -84, -420, -504, -168, -525],\n [-23, 161, 69, -207, -230, 414, 552, 345, -138, -69, -529, 506],\n [-249, 3, -297, 63, -198, -354, -72, -93, -222, -279, -27, -366],\n [105, 135, 207, -207, -96, 528, 504, 339, -6, 81, -435, 612],\n [-372, 139, -363, -84, -473, -155, 360, 157, -430, -453, -481, -95],\n [-435, 0, -522, 117, -339, -633, -144, -174, -384, -486, -30, -657],\n [-87, 29, -87, -15, -106, -46, 72, 29, -98, -105, -101, -34],\n [390, 25, 483, -138, 271, 637, 216, 211, 326, 429, -55, 673],\n [-526, 202, -510, -126, -676, -204, 528, 234, -612, -642, -698, -116]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[147, -126, 182, 56, -84, 0, 77, 91, -49, 140, 49, -28],\n [231, -198, 286, 88, -132, 0, 121, 143, -77, 220, 77, -44],\n [-84, 72, -104, -32, 48, 0, -44, -52, 28, -80, -28, 16],\n [420, -360, 520, 160, -240, 0, 220, 260, -140, 400, 140, -80],\n [189, -162, 234, 72, -108, 0, 99, 117, -63, 180, 63, -36],\n [399, -342, 494, 152, -228, 0, 209, 247, -133, 380, 133, -76],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n [273, -234, 338, 104, -156, 0, 143, 169, -91, 260, 91, -52],\n [189, -162, 234, 72, -108, 0, 99, 117, -63, 180, 63, -36],\n [546, -468, 676, 208, -312, 0, 286, 338, -182, 520, 182, -104],\n [-84, 72, -104, -32, 48, 0, -44, -52, 28, -80, -28, 16],\n [147, -126, 182, 56, -84, 0, 77, 91, -49, 140, 49, -28]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-298, 153, 196, -1258, -122, -417, -798, -218, 600, 744, -37, 589],\n [752, -1240, -941, 1144, 347, -343, 319, -79, -369, -231, -197, -692],\n [1207, 608, 837, -808, 503, -757, -176, -395, -282, 1279, 817, 654],\n [-2057, -578, -859, 132, -200, 980, -563, -815, -32, -1190, -1137, -1219],\n [-870, 205, -242, 349, 452, -217, 122, -783, -639, -493, 20, -71],\n [679, 36, -321, 45, -325, 585, -371, 486, -988, -332, 781, -213],\n [-144, 368, 327, 307, 642, -412, 565, -1970, -125, 1625, 683, 74],\n [583, 728, 506, 557, 500, -296, 755, -619, -517, 773, 930, 341],\n [1063, -331, 73, 776, 885, -1057, 628, -113, 541, 731, -249, 74],\n [-1078, -758, -1499, 1200, 881, -174, -307, -1231, -418, -579, -584, -1039],\n [-913, -74, -126, -296, -137, -74, 17, -1546, -81, 959, 446, 153],\n [-442, 485, -207, 1056, 516, 708, 198, -517, 303, 122, -234, -816]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-252, 822, 466, -627, -162, -684, 1214, -75, -18, 872, 33, -1185],\n [-670, -1057, -63, 836, 621, -849, -543, 516, -586, -132, -174, 891],\n [-570, -582, -911, -227, -651, 1339, -43, 276, -1153, -893, 272, -41],\n [40, -1175, -533, 842, -29, -875, -781, 556, -493, -189, 18, 1148],\n [709, 76, 537, 150, 438, 515, -265, -1031, -44, 360, -258, -861],\n [169, -181, -647, 554, -380, 1455, -280, 556, -169, -881, 478, 1202],\n [-591, 258, -504, -102, -287, 1479, 388, 838, -538, -658, 381, 101],\n [931, -461, -192, 257, 335, 832, -1194, 780, 30, -286, 23, 41],\n [-363, -265, 317, -317, 325, -484, -66, -670, -201, 187, -372, -681],\n [1310, -374, -158, -597, -700, 32, -280, -73, -106, 332, 263, -783],\n [350, 574, 705, 487, 422, -888, 306, -395, 869, 643, -94, 431],\n [-641, 573, -129, -527, -93, 1771, 438, 116, -130, -708, 196, -305]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 60, 192, 72, -36, 276, -312, 24, 252, 216, 132, 132],\n [22, -110, -352, -132, 66, -506, 572, -44, -462, -396, -242, -242],\n [-16, 80, 256, 96, -48, 368, -416, 32, 336, 288, 176, 176],\n [19, -95, -304, -114, 57, -437, 494, -38, -399, -342, -209, -209],\n [-22, 110, 352, 132, -66, 506, -572, 44, 462, 396, 242, 242],\n [13, -65, -208, -78, 39, -299, 338, -26, -273, -234, -143, -143],\n [-2, 10, 32, 12, -6, 46, -52, 4, 42, 36, 22, 22],\n [-3, 15, 48, 18, -9, 69, -78, 6, 63, 54, 33, 33],\n [-10, 50, 160, 60, -30, 230, -260, 20, 210, 180, 110, 110],\n [23, -115, -368, -138, 69, -529, 598, -46, -483, -414, -253, -253],\n [-8, 40, 128, 48, -24, 184, -208, 16, 168, 144, 88, 88],\n [20, -100, -320, -120, 60, -460, 520, -40, -420, -360, -220, -220]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[436, -4, -225, 176, 272, 334, -100, 58, -1073, -114, 343, -462],\n [89, -368, 472, 657, -273, 460, 890, -652, -270, 495, 666, 663],\n [-685, -223, -62, 450, -308, -441, -258, 136, 433, 410, -91, 83],\n [-820, -204, -486, 944, -227, 211, 244, 149, -83, 808, -391, -765],\n [591, 144, 304, -576, 224, -259, -323, -153, 25, -705, 247, 518],\n [194, -197, 173, 705, 7, 503, 710, -654, -440, 159, 296, 170],\n [111, -26, -2, 588, 123, 466, 647, -616, -148, -31, -174, -107],\n [839, 67, 381, -389, 206, 375, 335, -350, -508, -396, 550, 453],\n [-319, -278, 43, 728, -149, -226, -63, -260, -21, 201, 173, 199],\n [26, -181, -407, 860, 248, -122, -557, -33, -1031, -127, 235, -555],\n [-252, 267, -300, 207, 320, -490, -418, -317, 816, -753, -1052, -309],\n [-789, -238, -476, 1259, -209, 534, 684, -152, -180, 907, -448, -827]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[694, -546, -119, 808, -216, 503, -644, -998, 31, 232, 328, -959],\n [-899, 293, 29, -403, 354, -334, 229, 1175, 68, 246, 161, -134],\n [181, 1189, -71, -435, -448, 468, 1611, 61, -874, -113, -1142, -511],\n [416, -1543, -509, 58, 852, -118, -1121, 422, 314, 558, 880, 24],\n [259, -76, -777, -175, 36, 136, -633, -1002, -284, -162, 194, -617],\n [669, 79, 193, 35, -474, 669, -187, -1089, 206, 489, -273, 548],\n [-1121, 925, 1153, -954, -474, -196, 202, 1126, 763, 784, -319, 1499],\n [-283, -521, 15, 1095, 860, 262, -12, 733, -13, -14, 380, -930],\n [-28, 408, 380, -21, -826, -319, -493, -1150, 317, -607, -41, 662],\n [-626, 3, 323, -144, -62, -539, -667, 10, 658, -84, 469, 877],\n [217, 401, -96, -859, -10, -124, 1342, 731, -330, 226, -629, 838],\n [-49, 212, 156, 822, 424, 653, 793, 368, -257, 78, -310, -620]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[588, -904, -731, 1658, 88, 607, 1066, 90, -15, 633, 362, 1954],\n [278, -787, -167, 168, -1189, 456, -379, 296, 117, 179, 65, 622],\n [150, -852, -1551, -863, -1106, 1428, -45, 765, -449, -465, -375, -163],\n [-127, 548, -728, 127, 88, -641, 720, 11, 20, 844, -1473, 300],\n [-304, 897, 2086, -793, -903, -364, 269, -1322, -264, -208, -866, 157],\n [-999, 752, 916, -941, 305, -20, 132, -196, 3, -395, -1261, -487],\n [327, 567, 1857, 58, 217, -446, -621, -547, -152, -12, 552, -506],\n [-1740, -44, -233, -1809, -627, -1060, -1071, 119, -455, -1445, -898, -862],\n [203, -1146, 571, 87, 892, 451, 39, 1214, 2466, 1412, 845, 235],\n [-1793, -9, -202, -1539, -542, -675, -1107, -38, -694, -1762, -927, -602],\n [-541, 518, -229, 368, 481, -1067, -620, -1056, -752, -576, 740, -229],\n [-704, 356, -74, -252, -37, -548, 380, -231, -180, -220, -486, -58]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[598, 276, 674, -1524, 776, -70, -260, -252, 76, -78, 662, -306],\n [-561, 456, 560, -728, 606, 448, 54, -758, 161, -63, -49, -50],\n [64, 566, 107, -462, 894, -221, -268, -60, 1039, 176, 60, -617],\n [-917, -126, -176, 776, -293, 379, 277, -461, -198, 92, -674, 530],\n [-296, 706, 155, -428, 711, -412, 419, 237, 836, 247, 151, -815],\n [-496, 804, 104, -246, 717, -339, 447, 197, 977, 247, 23, -868],\n [-615, -363, -201, 193, 524, -410, 282, -576, 120, 791, -717, 805],\n [-1, 145, -274, 703, -533, 220, -87, 425, 130, -336, -8, -368],\n [-127, -250, 478, -560, -191, 511, 63, -603, -904, -236, 110, 578],\n [1150, -104, 103, -962, 343, -946, 53, 781, 22, 227, 825, -446],\n [-718, 331, 109, 507, -282, 1014, -258, -582, 57, -508, -384, 12],\n [-429, -56, -470, 858, 43, -121, -29, -49, 488, 310, -606, 165]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[222, 51, 420, 95, 458, 168, 25, 921, -545, 1121, -238, 821],\n [-1063, -1171, -556, -145, 834, -128, 521, -1708, 1353, -710, -1099, 177],\n [137, 579, 407, -472, 382, 515, 656, -1010, 335, -497, 60, 625],\n [682, -50, 324, -818, -1260, 1692, -829, 1490, 509, 251, 807, 998],\n [371, -667, 242, -276, -471, -68, 595, 640, 483, 707, -329, -1064],\n [-1200, -126, 380, -20, 959, 156, -618, 1278, -423, 1062, -1373, 1925],\n [1065, -308, -19, 582, -533, -306, 320, 1079, -327, 702, -190, -1061],\n [617, -489, -173, 290, 1006, -733, 608, -907, -204, -830, 105, -1229],\n [646, -913, -563, 50, 1276, 314, 133, -524, -1003, 103, -82, -765],\n [-631, -1430, -1005, -63, 90, -456, -170, -736, 1325, -735, -574, -924],\n [-417, 1156, 268, -359, 611, -746, -19, -137, 320, -174, -81, 564],\n [1693, 933, -663, 490, -1757, 583, -486, 711, -52, 86, 1369, -243]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-121, 2199, -805, 561, -390, 977, 920, 325, 255, -490, -128, -94],\n [-317, -607, 655, -848, 113, -245, -128, -303, -718, 81, -183, -445],\n [506, 177, 28, -19, -680, 56, 1014, 62, 461, 223, -401, -722],\n [879, -1829, -346, 693, -939, -1373, -1209, -449, -285, 980, 763, 605],\n [-323, 305, 110, 239, 869, 457, -241, 51, 101, -248, -237, 1365],\n [805, -716, -597, -148, -454, -717, -751, -718, -220, 656, 245, -71],\n [317, -118, -99, -198, 201, 239, -234, -679, 580, -92, 48, -132],\n [190, -701, 967, -182, 199, 372, 185, -1008, 261, 161, -654, 1177],\n [800, -1489, -409, 595, -1031, -1294, -999, -356, -468, 949, 662, 426],\n [251, -830, 142, 365, -322, -391, -419, -279, 4, 300, 261, 493],\n [-150, -808, -46, 200, 465, -454, -940, 214, 11, -13, 553, 293],\n [503, 624, -372, 411, -197, 385, 723, 121, 861, 13, -302, 44]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1254, -953, -25, 888, 400, -499, -418, 556, -244, -652, -45, -938],\n [590, 170, -381, -144, 309, 562, -734, -351, 1376, 37, 359, 634],\n [99, -276, -931, -95, 0, -845, -832, 1186, 577, -482, 228, -151],\n [481, 392, -24, -579, -370, 1080, -392, -718, -310, -65, 920, 20],\n [-222, -1189, -929, 487, 603, -1221, 412, 1718, 253, -795, -1064, -279],\n [-617, -378, 849, 1154, 1044, 1015, 176, -1068, 714, -449, -443, -102],\n [1088, 626, -1510, -1773, -718, -724, -1380, 1503, 254, 345, 1446, 44],\n [357, 390, -562, -314, -229, 397, -1195, -2, 441, -993, 1074, -264],\n [955, -635, -752, 214, 682, 433, 738, 920, 506, -597, -1016, 868],\n [-432, 1333, 846, 324, 707, -1034, -175, 327, 934, -518, -203, -637],\n [417, 130, -151, -860, -1523, 109, 552, -726, -1557, 544, 331, 209],\n [-557, -49, 68, -191, 66, 154, -437, 821, -1161, -200, 803, -946]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-749, 971, -27, 285, -1448, 776, -488, -292, 607, 20, 42, 516],\n [1009, -74, 13, -459, 1748, 721, 744, 1046, -1165, 1055, -1059, -1381],\n [-88, -672, 1731, 637, -2108, -1435, -933, -259, 787, -768, 413, 1656],\n [-659, 1185, 1196, -211, -1218, 464, 359, -386, 656, 153, -70, 517],\n [-1649, 1226, -2007, 909, -1046, 923, -1069, -498, 325, 861, -384, 376],\n [40, -1185, 866, -55, -12, -995, -490, -618, -521, -798, -184, 774],\n [947, -1079, -1458, 240, 1022, -652, 264, 1342, -1054, 407, 156, -1672],\n [253, 848, -707, -57, -642, 1990, -554, -68, -254, 237, -846, -537],\n [-691, 183, 108, 266, -1745, 546, -218, -820, 201, -371, -422, 826],\n [247, -826, 544, -762, 1433, 42, 1137, 618, 347, -516, 810, -49],\n [657, -773, 843, -1818, 723, 358, -789, -760, -286, -1818, 328, 134],\n [-96, 1133, 335, -197, 58, 246, 140, -202, 285, 251, -164, 508]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[152, 286, 974, 166, 300, -132, -214, -272, 408, 248, 112, -296],\n [-359, -163, -279, 365, -721, -92, -170, -270, 319, 71, 743, 40],\n [-305, 782, 381, 551, 257, -881, -551, -411, 25, 545, -460, -467],\n [-146, 1080, 1881, 701, 228, -737, 34, -1121, 1066, 400, 189, -1251],\n [266, 91, -679, -537, 340, -274, -224, 560, -218, 79, -501, 1],\n [-297, 279, 393, 531, -231, -372, -327, -458, 313, 304, 308, -233],\n [-2, -480, -578, -213, -384, 400, 251, 219, -78, -295, 339, 323],\n [458, -31, 1124, 45, 512, -25, -1067, 126, 430, 630, 391, 201],\n [964, -338, 237, -811, 754, -5, -1421, 1017, 332, 655, 264, 486],\n [-613, -368, -587, 352, -853, 589, 1247, -464, -363, -781, 194, 125],\n [-266, 283, -1051, -92, 142, -368, 255, 213, -790, -136, -1016, -24],\n [470, -452, 34, -594, 42, 546, 256, 378, 266, -280, 378, 156]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, -336, 504, 672, 660, 48, 480, -36, 696, 552, 672, -156],\n [-293, -482, -222, -8, -31, -718, 488, -339, 362, -76, 370, -29],\n [-18, -75, 60, 96, 93, -33, 96, -24, 120, 75, 117, -24],\n [-234, -260, -380, -272, -286, -604, 208, -262, 20, -280, 36, 38],\n [126, -47, 508, 544, 545, 371, 160, 128, 392, 479, 369, -112],\n [-306, -274, -604, -496, -512, -806, 176, -338, -116, -482, -90, 82],\n [295, 395, 370, 200, 220, 745, -360, 335, -170, 235, -185, -15],\n [-198, -539, 196, 448, 425, -433, 640, -244, 704, 323, 693, -124],\n [187, 88, 498, 472, 479, 512, 8, 201, 242, 434, 220, -89],\n [-180, -321, -96, 48, 33, -435, 336, -210, 276, -3, 279, -30],\n [135, 205, 130, 40, 50, 335, -200, 155, -130, 65, -135, 5],\n [-78, -182, 28, 112, 104, -178, 208, -94, 212, 74, 210, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-76, -453, -558, 160, 262, -454, 301, -631, -295, -320, -688, 370],\n [197, 444, 281, -394, -249, 385, -117, 779, 278, 198, 738, -139],\n [-173, -609, 120, 473, 344, -143, -172, -512, -395, 134, -461, -196],\n [-70, 57, -148, 68, -36, -140, 105, -259, 47, -156, -228, 116],\n [-218, 36, 1094, 516, -38, 486, -722, 94, 40, 628, 332, -882],\n [60, 630, 51, -273, -363, 156, 60, 324, 420, -84, 357, 51],\n [-138, -300, -385, 241, 169, -382, 208, -656, -186, -272, -645, 247],\n [-229, -318, 711, 574, 169, 203, -521, -241, -196, 442, -70, -629],\n [55, 1161, -73, -444, -671, 141, 220, 352, 781, -302, 428, 219],\n [-229, -36, 562, 465, 6, 147, -381, -269, -4, 270, -85, -474],\n [224, -192, 45, -287, 123, 188, -54, 570, -154, 204, 427, -35],\n [211, -120, -821, -434, 85, -337, 529, 33, -98, -422, -182, 655]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-127, -1061, 1047, 1357, -1354, 1299, -162, -187, 337, 1251, -312, 562],\n [679, 1649, -171, -1090, 696, 568, -348, 704, 520, 77, 672, 1388],\n [1274, -195, 289, 516, 532, -553, 39, -911, 319, 736, 552, -379],\n [-414, -156, -1689, -1265, 47, -411, 1244, -484, -1448, -196, 1026, -13],\n [789, 710, -1169, -615, 401, -1321, 584, -1086, -630, 478, 1172, -642],\n [460, 204, -270, -570, 1246, 3, 520, -598, 13, -314, 571, -78],\n [-299, -1051, 986, 1262, 365, -631, 12, 728, -1181, -224, -710, -1716],\n [-347, -1502, 1228, 1659, 67, 253, 42, -286, 629, 40, -1343, -1138],\n [109, -506, 80, 262, -1076, -781, -591, -113, -458, 116, 387, 463],\n [-497, 475, -376, -908, -542, 169, -409, 1046, -418, -1014, -12, 797],\n [1318, 1043, 520, 110, -145, 771, -154, 88, 544, 85, 345, 657],\n [190, 2022, -217, -547, -248, 344, 203, 907, -73, 169, 405, 1621]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-33, -485, 390, -753, 1088, 258, -79, -1011, -82, 236, -183, -155],\n [588, -94, 290, 420, -494, 222, 154, -846, 112, -128, -90, 68],\n [-445, -343, 104, -519, 355, 731, -496, 197, -64, 499, -564, -820],\n [123, -31, 75, -51, -292, 451, -282, 524, -128, 342, -328, -337],\n [-464, -522, -198, -134, -27, 1017, -434, -220, -40, 363, -752, -1046],\n [-42, 745, 323, 330, 19, -1459, 552, -41, 518, -756, 1060, 1075],\n [-535, -171, -450, -407, 680, -96, -32, 187, -188, 46, 14, -80],\n [368, 49, -685, 64, 73, -369, 303, 469, -528, -78, 257, 638],\n [195, 286, 738, -69, -158, -109, -129, 175, 284, 93, 97, 49],\n [235, -4, -35, -239, 138, 56, -75, 456, -288, 245, -49, 114],\n [519, 253, 212, 587, -960, 98, 29, 187, 122, -62, -23, 75],\n [431, -269, 806, -719, 755, 277, -163, -621, -90, 407, -173, -13]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[72, -87, -228, 313, -208, -180, 261, 361, 75, 260, -227, 65],\n [9, -59, 10, -163, 51, 93, -285, -311, -135, -314, 193, -194],\n [-180, 405, 420, 5, 220, 0, 585, 485, 375, 700, -295, 625],\n [18, -93, 0, -221, 62, 126, -405, -437, -195, -448, 271, -283],\n [54, -149, -104, -117, -22, 66, -357, -349, -195, -408, 215, -303],\n [144, -249, -396, 311, -296, -180, 27, 167, -75, -20, -109, -185],\n [-423, 763, 1138, -781, 819, 453, 129, -257, 315, 286, 175, 676],\n [-99, 264, 198, 176, 55, -99, 594, 572, 330, 682, -352, 517],\n [-18, -27, 96, -283, 130, 162, -387, -451, -165, -416, 281, -221],\n [-18, 83, 8, 179, -46, -102, 339, 363, 165, 376, -225, 241],\n [-135, 190, 406, -474, 347, 273, -312, -478, -60, -294, 302, -9],\n [-306, 581, 800, -443, 546, 258, 285, 29, 315, 416, -7, 611]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[813, 267, 960, 197, -1154, 442, 109, -730, 147, 51, -178, -142],\n [80, 562, 1063, 249, -408, 539, 802, -1223, 103, -28, 302, -498],\n [546, -478, -95, 269, 106, -866, -224, -187, -69, -166, 134, 373],\n [273, 574, 329, 796, 128, -619, -274, -650, 207, -584, -401, -232],\n [151, -289, 136, -486, -476, 497, 254, 46, -159, 424, 313, 113],\n [-176, -590, -600, -444, 102, 97, -196, 926, -64, 276, 4, 347],\n [299, -257, 213, 449, 244, -672, 166, -529, 64, -262, 217, 129],\n [198, 612, 740, 852, 252, -570, 338, -1354, 144, -558, 96, -386],\n [-352, -222, -1324, -296, 858, -793, -896, 1058, -328, -56, -168, 361],\n [-430, -988, -1345, -1318, 280, 225, -329, 1571, -563, 789, 445, 634],\n [-303, -859, -1152, -187, 880, -791, -483, 1144, -105, -13, 26, 575],\n [1147, -68, 215, 558, -566, -898, -748, -368, 45, -342, -425, 301]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[266, 271, -23, 961, 373, 650, 455, -245, -500, -1436, -160, -416],\n [48, -578, -73, 329, -711, 128, 438, -966, -98, -526, -1150, 431],\n [-175, 796, 440, 626, 287, 45, 798, 39, -650, -433, -1, -271],\n [738, -746, 267, 106, 676, -71, 283, 121, -72, 335, 1074, -308],\n [314, -1040, 101, -755, -892, -1018, -1605, 487, 485, 1332, -2, 694],\n [237, -597, 467, -380, -70, -716, 119, 116, 25, 1236, 497, 235],\n [717, -902, 41, -264, 210, -336, -936, 539, 273, 580, 909, -42],\n [266, -432, 572, 392, -57, -296, 1029, -519, -465, 232, -84, 125],\n [536, -654, 264, 435, -409, -311, -471, -27, -258, -207, -234, 219],\n [-137, -55, -570, -89, -246, 462, -406, -261, 340, -616, -553, 79],\n [-305, -379, -1118, -999, -115, 622, -703, -268, 1119, 36, -231, 132],\n [137, 724, 1190, 1056, 141, -639, 794, 363, -1230, -73, 195, -177]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[640, 1677, -170, 512, 229, -1581, -76, 1622, 372, -1142, 1555, 1757],\n [24, -520, -427, -343, -492, 316, 303, 133, -249, 872, -218, 295],\n [778, 1307, 278, 252, -1523, 533, -827, -88, -574, -418, -431, 455],\n [-746, -1066, -266, -1172, -702, 466, 428, 1026, 252, 1264, -384, 48],\n [-215, 363, -316, 211, -490, -520, -668, 600, 21, -687, 711, 356],\n [803, 1681, 1057, 438, -199, -402, -76, 14, -411, -138, -506, 135],\n [-538, 20, -21, 592, -176, 515, -1161, -1017, -229, -851, 291, -246],\n [654, 58, -930, -187, -1527, 739, -169, -275, -125, 42, -666, 503],\n [-202, -289, -488, 84, -33, 256, 161, 183, 475, 719, -123, 827],\n [2154, 136, -501, -863, 1002, -611, 1706, 848, 450, -1662, 890, 6],\n [-262, 212, 268, -73, -429, -33, -102, 945, -169, 995, 152, 764],\n [294, 282, 248, 433, -386, 176, -114, -215, -659, 976, -349, 283]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[480, -505, 526, 20, 484, 508, -57, -227, -818, 21, 181, 628],\n [1133, 1798, 982, 1056, 1103, -237, 862, 7, 1070, -1352, 1302, -827],\n [1008, 822, 1067, 365, 802, 408, 673, 90, -86, -1153, 641, 31],\n [317, -1039, 909, 254, 80, 292, -1119, -572, -1572, 403, -418, 757],\n [-1065, -1698, -1157, 406, -281, -1063, -448, -1209, 1764, 400, 687, -1221],\n [-432, 157, -294, -63, 656, 314, 143, 88, 352, 382, 208, -289],\n [-258, -129, -919, -969, -1123, 281, -393, -616, 372, -118, 41, 25],\n [838, 227, 829, 13, 372, 525, 1173, 313, -664, 106, 293, 950],\n [-1106, -1052, -1028, -264, -107, -367, -786, 366, -2, 378, -814, -344],\n [14, -197, -665, 126, 656, -76, 161, -205, 662, 151, 774, -221],\n [256, 737, -25, -151, -14, 3, 777, 783, 42, -298, -129, 181],\n [-281, 273, 121, 935, 1111, -249, 527, -909, 1748, 392, 1463, -1210]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1353, -320, 346, 788, -1090, -184, -866, 1423, 294, -1094, -904, 965],\n [774, 228, 1066, -960, -280, -641, 166, 268, -1176, -804, 260, -860],\n [453, 126, -756, 95, -1624, -534, -425, 1250, -1311, -2107, -561, 964],\n [-1243, -326, -2049, 47, 873, -48, 811, -984, -218, 240, 42, -206],\n [-247, 1632, -160, -836, -312, 233, -407, 16, -641, 384, 419, 851],\n [786, -1074, 238, 411, -449, -95, 103, 639, -2266, 272, 419, -217],\n [-286, -562, 968, -1305, 1445, -10, 790, -525, 549, 667, 542, -1873],\n [-250, 130, 1174, -398, -106, 266, -111, 737, -497, -810, 899, 168],\n [206, -355, 1187, -207, 1406, 629, 506, -512, 191, 242, -402, -311],\n [572, 104, -679, -618, -897, -53, -1139, -221, 66, -383, -724, -156],\n [535, -157, -347, -392, -1664, -1011, 111, 1130, -1550, 107, 367, -585],\n [-388, 5, -192, 63, -346, 1045, -485, -62, -402, 321, -479, 909]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-43, 109, -57, 97, 18, -293, 67, 232, 512, 412, 398, 465],\n [631, -799, -587, 547, 676, -74, -562, -453, -1017, -660, 567, -1165],\n [1543, 52, 1198, -335, -722, 964, -189, -321, 957, 1194, 124, 1374],\n [923, 269, 249, -3, -93, -740, -459, -470, 888, 1002, 742, -207],\n [-17, -218, -34, -322, 571, -296, -76, 602, -100, 295, 1075, 22],\n [-1260, 593, 260, -435, -592, -769, 1140, 901, 338, 288, 134, 1274],\n [137, -207, 7, -581, 808, -250, -408, 405, -285, 292, 1115, -663],\n [-25, -221, -471, 1078, -310, -1015, 659, 434, 634, 319, 946, 1547],\n [-298, -203, -509, 688, 63, 822, -44, -47, 29, -634, -970, 255],\n [-290, 223, 139, 198, -534, -758, 751, 554, 642, 422, 373, 1313],\n [-242, 415, -92, 615, -779, 98, 378, -367, 832, 308, -606, 1136],\n [304, -702, -561, 210, 760, 152, -606, -552, -1427, -897, 294, -1641]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-174, 197, -1134, 1138, 9, 473, -729, 266, 1336, -302, 384, -86],\n [-9, -757, 731, 1226, 273, 51, 953, -824, -539, 1250, 724, -816],\n [312, 1251, 292, 1016, 1061, -77, 1134, -110, -122, -328, 426, 83],\n [-196, 728, 327, 829, -523, 8, 740, 286, -951, 26, -361, 678],\n [850, 688, 631, 454, 141, -478, 326, 144, -312, 685, 840, -22],\n [-429, -528, 278, -388, -655, -158, -196, -380, -863, 101, -520, -54],\n [-1223, -296, 218, 89, 312, 951, 1165, -319, -797, -1272, -1660, 1192],\n [201, 541, -333, -431, 1776, 939, 112, -7, 1376, -1114, 558, 42],\n [240, 751, -482, -368, -97, -288, 63, 740, 65, -263, 162, 774],\n [-344, -391, -1672, -231, -1722, -1821, -552, 179, -1105, 443, -524, -650],\n [-608, 222, -525, 408, -846, -1648, 1000, 0, -653, 1087, -152, -1447],\n [909, 664, -81, -680, 97, -1349, -551, 291, 604, 376, 505, -920]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[441, -399, -462, -210, -84, -525, 0, -126, -420, 546, 231, -21],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n [546, -494, -572, -260, -104, -650, 0, -156, -520, 676, 286, -26],\n [252, -228, -264, -120, -48, -300, 0, -72, -240, 312, 132, -12],\n [-84, 76, 88, 40, 16, 100, 0, 24, 80, -104, -44, 4],\n [231, -209, -242, -110, -44, -275, 0, -66, -220, 286, 121, -11],\n [-336, 304, 352, 160, 64, 400, 0, 96, 320, -416, -176, 16],\n [-252, 228, 264, 120, 48, 300, 0, 72, 240, -312, -132, 12],\n [-21, 19, 22, 10, 4, 25, 0, 6, 20, -26, -11, 1],\n [-336, 304, 352, 160, 64, 400, 0, 96, 320, -416, -176, 16],\n [-420, 380, 440, 200, 80, 500, 0, 120, 400, -520, -220, 20],\n [420, -380, -440, -200, -80, -500, 0, -120, -400, 520, 220, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[490, -311, -678, 52, 1022, 43, 48, 333, -209, -27, 266, 4],\n [396, -434, -737, -266, 697, 134, -19, 506, -27, -186, -11, 115],\n [-222, -441, -456, 231, 317, -52, 337, -160, -171, -135, -72, -9],\n [186, -158, -338, 235, 609, 13, 69, 43, -210, 54, 244, -59],\n [-409, -134, -27, 675, 149, -89, 306, -533, -317, 121, 188, -173],\n [260, -285, -516, 103, 763, -80, 209, 96, -183, -61, 138, -3],\n [-122, 62, 212, -437, -581, -51, -13, 67, 288, -170, -382, 131],\n [495, 257, 55, -171, 239, 194, -432, 420, 40, 158, 276, -1],\n [169, 386, 384, 132, 137, -354, 194, -300, -52, 137, 163, -79],\n [764, 92, -356, 286, 1298, -118, 18, 182, -332, 220, 624, -118],\n [132, -67, -99, -311, 134, -342, 356, -34, 116, -215, -263, 110],\n [156, 383, 478, -420, -240, -603, 404, -257, 253, -139, -312, 98]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-772, 499, 21, -676, -1908, -172, 407, -1042, 611, 923, 1552, 170],\n [-303, 597, -112, 635, -508, 887, 1042, 1096, 195, 767, 242, 484],\n [-1044, 251, -639, 391, 226, 957, -1477, 487, -82, -152, -342, -1251],\n [244, -542, 653, -53, 464, -1275, 1208, 420, 481, 712, 183, 1470],\n [470, -74, -711, -1064, -363, 551, 922, -322, 638, 582, -63, 850],\n [-202, 433, 735, -1483, -1174, -449, 1841, -323, 1292, 1472, 494, 1435],\n [241, 398, 1348, -571, -162, -1188, 1044, -565, -185, -492, 241, 289],\n [-2152, 444, 389, -781, -1217, -1068, 314, -798, 765, 1653, 1503, 381],\n [-1001, 630, -698, 2198, -652, -27, -220, 911, -1118, -329, -7, 272],\n [-134, -849, -247, -1419, 10, -1171, -841, -1163, 976, -118, -26, 757],\n [-2002, -333, -1311, -754, -426, 35, -316, -327, 1206, 1482, 1512, 658],\n [-813, -737, -1270, -1027, 100, -17, 271, 449, 1729, 1199, 349, 1610]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[849, -286, 349, -73, -165, -337, 1471, -395, 655, 569, 1025, 955],\n [34, 811, 872, -1324, 798, 123, 745, 443, 515, 2255, 409, -281],\n [575, 432, -791, 950, 28, -319, 616, 479, 652, 522, 369, -501],\n [384, 205, -48, -1014, -1363, -371, 564, -1605, 679, -1007, 536, 994],\n [856, 1106, 74, -469, -968, 654, 439, -849, 84, -587, 605, 347],\n [136, -1237, 172, -426, 414, -265, 940, 950, 520, 1039, 865, 425],\n [-451, -54, 357, -1208, 1284, 7, -195, 507, 56, -27, 73, 256],\n [-717, 545, 435, 763, -488, -657, 48, 48, -1609, -665, -649, -377],\n [-1018, 437, -268, 1094, -490, -214, -1074, 689, -739, 787, -1220, -1363],\n [87, 284, -627, 688, -203, -856, 401, 1110, -152, 1040, 354, -534],\n [-76, -905, 516, -866, -629, 481, 438, -891, 962, 101, 25, 200],\n [1188, 288, 1140, -1154, -56, -12, 744, -693, 530, -785, 809, 743]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[566, -586, 164, -280, 171, 478, -365, 760, -349, -93, 166, 1512],\n [926, -279, -91, 507, -1079, 566, 520, 51, 814, -136, 348, 0],\n [89, 79, -377, -103, -284, -139, -19, -107, 475, 85, 506, -347],\n [82, -852, 997, -169, -838, -109, -236, -769, 73, -697, 331, 97],\n [2184, 692, -866, 1591, 588, -663, 52, 1634, 784, 871, -134, 581],\n [150, -979, -675, -1265, -285, 686, 1543, -275, 643, 703, -915, 512],\n [235, 714, -854, 787, 724, -139, 169, 965, -244, 380, -510, 53],\n [291, 873, 317, 1347, 352, -1281, -279, 125, 813, -261, 1050, -1100],\n [1281, -708, 236, 1865, -1185, -297, -1146, 1039, -743, -956, 456, 1491],\n [1661, -333, -802, 693, 25, -409, 811, 682, 1444, 285, -50, -28],\n [-769, -43, 146, -400, 87, 337, 1171, -318, 533, -501, 391, -550],\n [-128, 353, 305, -667, -889, -299, 453, -868, -742, 154, -608, 66]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[114, 478, 155, 322, 4, 0, -110, -115, -800, 337, 655, -764],\n [341, 727, 225, 567, -195, 351, -321, 290, -580, 738, 165, -601],\n [-279, -905, -167, -673, 189, -453, 293, -284, 718, -852, -237, 673],\n [242, 534, 175, 410, -124, 216, -226, 165, -500, 521, 215, -512],\n [-78, -986, 50, -698, 178, -666, 166, -340, 520, -884, 10, 358],\n [-55, -609, -59, -409, 29, -189, 89, 12, 706, -460, -469, 613],\n [97, 289, 230, 169, 105, -303, -62, -360, -1005, 96, 1035, -1002],\n [-770, 604, -641, 236, 218, 432, 503, -292, -411, 140, 314, 87],\n [27, -541, -55, -329, -63, -15, 10, 215, 905, -309, -780, 788],\n [51, -125, -67, -41, -119, 225, -50, 311, 613, 43, -692, 568],\n [-417, -335, -266, -331, 225, -237, 347, -377, 94, -501, 204, 229],\n [-423, 609, -455, 341, 7, 615, 230, 115, -45, 391, -230, 288]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-33, 249, 764, 1017, -157, -904, -1271, -444, -1538, 843, 1280, -960],\n [772, -314, -1189, 26, -1166, 1644, -2046, -929, -1350, 918, 460, 802],\n [-57, 571, 1262, 457, 97, -1007, 109, 709, 280, 476, -361, -1244],\n [-724, -412, -25, 1286, 152, 1135, -760, -1163, -574, 479, -637, 620],\n [724, -390, 224, -267, 414, -399, 932, 336, 675, -515, 568, -65],\n [-84, -102, 541, 336, 901, -193, 678, 165, 369, -774, -83, -21],\n [870, -338, 489, 1003, 240, 589, -1280, -581, -405, 593, -595, -260],\n [-417, -103, 1115, 883, 66, -39, -951, -89, 147, 339, -1091, -1009],\n [366, -469, 708, 874, 1259, 389, -224, -52, 404, -809, -150, 228],\n [658, -537, 140, -20, -114, -352, 740, -140, 289, 217, 662, -208],\n [-933, -46, -388, 62, -694, 23, 191, -491, -879, 220, 1153, 213],\n [1133, 108, 396, 712, 1262, -69, 141, 326, 25, -308, 994, 600]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1169, 833, -157, -324, 627, -261, 441, 674, -583, -219, 908, -175],\n [519, 155, -120, 469, -256, -962, 1137, 503, -1298, -42, 598, -168],\n [-866, 277, 454, -460, 278, -1269, 109, 466, 70, -76, -633, 572],\n [278, 709, -518, -231, 218, 440, -141, 218, 128, 268, 506, -591],\n [-313, -526, 523, 86, 31, -192, -222, -326, 253, -241, -491, 535],\n [1241, 550, -540, 859, 92, 293, 496, -101, -854, 164, 1503, -1002],\n [155, 753, -71, -852, 759, 399, -653, 274, 753, -27, 65, -11],\n [970, 57, 250, -265, 798, 1066, -841, -426, 728, -392, 378, 135],\n [-98, 81, -202, 265, -306, -404, 487, 190, -516, 168, 158, -231],\n [198, 453, -26, -110, 208, -611, 399, 450, -428, -30, 286, -36],\n [245, 629, -430, -121, 282, 566, -329, 3, 296, 252, 496, -584],\n [271, 1010, 227, -384, 1017, -610, -204, 354, 163, -131, 460, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-965, -343, -1559, 2569, 1661, 931, -351, 148, -152, -834, 1078, 876],\n [808, 321, 594, -565, -536, -993, 1308, 185, -983, 21, -194, -1167],\n [440, 330, -716, 309, 263, -127, -322, -654, 327, 822, 376, 653],\n [639, -450, -1001, 943, -130, 1046, -51, -196, -569, -23, -377, -648],\n [-1478, -459, -1143, 493, 930, -1080, 369, -1453, -1329, -976, 59, 458],\n [601, 676, 293, -1560, -738, -779, 151, -958, -75, 36, -339, -417],\n [-301, -94, -187, -997, -684, -898, -823, 605, 832, 366, 552, 870],\n [-1124, -285, 360, -84, 559, -1316, 1120, -174, -187, 752, -582, 333],\n [314, 1079, 193, 630, 350, 207, 1158, 725, -244, -1525, 835, -617],\n [-83, -265, -152, -163, -259, -429, 370, -529, -1190, -937, -371, -589],\n [1061, 599, 702, -1883, -1126, -1322, -28, -1072, -50, 876, -513, 72],\n [147, 492, 565, 488, 275, 908, 334, 1332, 491, -792, 532, -706]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, -6, -1271, -205, -160, 698, -1519, -125, 1216, -927, -671, 290],\n [-1237, 628, 843, -307, -275, 959, 146, -2082, -125, -748, 396, -588],\n [-486, -399, -703, -51, 511, -1075, -1117, -375, 449, 707, 503, -1060],\n [-296, -995, -1198, -1030, 1018, -658, -527, 182, 507, -1361, 914, -208],\n [884, 720, -994, 841, 491, 136, -800, 640, -186, -243, 639, 288],\n [893, 1738, 526, 1087, -194, 848, 94, 258, 299, -566, -472, -664],\n [-1389, 886, 803, 134, -933, 417, -570, -1292, 100, 831, -396, -1466],\n [811, -1347, -1255, -757, 1187, -931, 97, 1845, 291, -894, 1211, -440],\n [-464, -533, 71, -418, -539, 727, 430, -1095, 452, -419, -929, 188],\n [-170, 1184, 208, 478, -676, 719, -464, -132, 743, 67, -1125, 848],\n [-889, 557, 251, 592, -598, -410, -371, -16, -1593, 1867, 545, -763],\n [654, -1202, 380, -873, 414, -120, 1856, 153, -152, -1171, -97, 1304]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-630, 126, -336, -102, 270, 372, 594, -186, -144, -684, 126, 168],\n [340, 84, 213, -11, -67, -170, -345, 142, 170, 380, -106, 55],\n [690, 294, 458, -76, -72, -320, -720, 322, 420, 780, -246, 230],\n [555, -399, 236, 215, -387, -386, -477, 85, -48, 582, -39, -424],\n [485, -777, 117, 374, -560, -424, -348, -43, -302, 478, 73, -781],\n [-40, -672, -163, 289, -335, -114, 147, -198, -422, -92, 178, -641],\n [590, -294, 278, 172, -344, -384, -528, 126, 28, 628, -74, -326],\n [-905, 189, -481, -150, 392, 536, 852, -265, -202, -982, 179, 249],\n [-135, -525, -187, 218, -228, -32, 216, -191, -366, -186, 165, -493],\n [-265, 189, -113, -102, 184, 184, 228, -41, 22, -278, 19, 201],\n [440, -672, 113, 325, -491, -378, -321, -30, -254, 436, 58, -677],\n [-630, 294, -301, -175, 357, 406, 567, -140, -42, -672, 84, 329]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[206, 306, 542, 405, -809, -352, 707, 1005, -424, 1351, -852, -340],\n [428, 216, -352, -93, 1222, -426, 497, -1090, -260, 153, 929, -18],\n [-23, 499, -730, 115, -858, 533, 203, -348, 801, 73, 271, -293],\n [13, 29, -339, 17, -1175, -26, 957, 215, 286, -568, -266, -343],\n [332, 592, -223, -320, 1075, -377, 1310, -933, -387, 43, 863, -54],\n [-267, -76, 644, 71, -406, 71, 666, 490, -324, 457, -180, -87],\n [-744, -482, 868, -639, 422, 236, 1019, 6, -549, -1197, 419, 339],\n [733, 1057, -1123, 344, -652, -94, -578, 104, 724, 803, -604, -343],\n [115, 362, 638, -307, 942, -541, 1808, -226, -984, 393, 446, -21],\n [-310, 1326, -90, -540, 113, 808, -410, 403, 389, 60, -381, 331],\n [120, -423, 723, -32, 425, -681, 223, 595, -841, 31, -528, 127],\n [500, 53, -147, -64, 764, -765, 1047, -604, -521, -13, 455, -143]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[362, 641, 484, 197, 310, 448, 882, -575, 537, -583, 209, 824],\n [-783, -1241, -245, -343, 117, 55, -868, -292, 253, -307, -651, -213],\n [688, 75, -554, -315, -394, 84, -109, 225, -214, -92, 138, -186],\n [-794, -1400, -531, 73, 333, 109, -750, -137, 397, -134, -436, -267],\n [-573, -220, -67, -425, 87, 557, 161, 448, 327, -756, -58, 618],\n [526, 119, 28, 112, -651, -464, -392, -324, -681, 502, 93, -751],\n [-472, -365, 1060, 896, -323, -322, -255, -1588, -236, 167, -66, -455],\n [1255, 1439, 46, -434, -859, 18, 613, 517, -719, -28, 611, 94],\n [-351, 328, -82, -527, -414, 570, 394, 1058, -165, -686, 352, 578],\n [-500, 29, 344, 624, -270, -690, -314, 270, -735, 1028, 204, -791],\n [-200, -641, -536, 659, -125, 218, -84, 153, -5, 37, 414, -290],\n [-158, 534, 775, 517, -634, 749, 940, -429, -69, -952, 769, 707]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1134, -819, -636, -1322, 1462, 551, 868, -628, 324, -539, 347, -985],\n [-949, -863, -952, -363, -720, -648, 395, -740, 60, 575, -924, -68],\n [-262, -402, -869, 74, -1234, 237, -661, -565, 3, 364, -259, -1272],\n [271, -551, 12, -727, 207, -1492, -12, 255, 47, -447, 622, -45],\n [-126, 446, -479, -942, -1067, 269, -550, -899, -745, -740, 747, -740],\n [782, 917, 1069, 354, 327, -222, -37, 755, -213, -202, 657, 1228],\n [14, -661, -323, -1117, 511, 200, 1199, -401, 308, -278, -724, -573],\n [510, 424, 641, -1516, -285, 202, 543, -630, 278, 49, -799, 122],\n [512, -753, 0, 1064, 1010, 1060, -629, 1905, 181, -508, 611, 257],\n [-1, -317, 131, 392, 2185, -483, 745, -76, 984, -74, 101, -113],\n [-508, -34, -929, 115, 650, -546, -1163, -719, -530, -1341, 1556, -866],\n [-230, -820, -287, 1289, -92, -1390, -41, 1150, -506, -258, 260, 853]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-154, -284, -414, -78, -67, 100, 380, 52, 276, 266, -268, -149],\n [68, 202, 69, 483, 434, 43, -94, -500, -495, -244, -169, 607],\n [142, 260, 253, -161, 133, 111, -452, 24, -65, -316, 421, -208],\n [-88, -199, -299, -457, -160, 198, 93, 312, 497, 147, 133, -640],\n [80, 98, 414, -38, -304, -304, -150, 224, -74, 14, 166, 44],\n [-56, -84, -138, 154, 52, -6, 188, -120, -50, 88, -222, 186],\n [80, 184, 322, 526, 128, -262, -40, -328, -542, -108, -202, 742],\n [240, 460, 529, 71, 252, 5, -644, -148, -391, -494, 467, 127],\n [74, 141, 460, 516, -109, -461, 25, -176, -522, 15, -228, 780],\n [334, 693, 529, 191, 709, 268, -943, -476, -625, -847, 615, 225],\n [-72, -92, -598, -378, 396, 630, -44, -72, 402, -136, 158, -650],\n [-132, -251, -414, -230, -54, 187, 265, 124, 370, 201, -112, -359]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[191, 1440, 237, -286, 1795, -1351, -383, 1329, 362, 1101, -608, -862],\n [-289, -814, -52, 164, -839, 350, -483, -559, -268, -577, -138, 318],\n [248, 401, 273, -269, 224, 330, 272, -349, -273, 393, 283, -460],\n [-219, 929, -872, 1010, -447, -330, 600, -350, 160, 97, -241, -213],\n [289, 99, 801, -1288, 1057, -598, -695, 1600, 924, -488, 68, -392],\n [628, 583, 826, -1377, 817, 21, 204, 1062, 923, -450, 675, -777],\n [323, -107, 469, -275, 371, 443, -58, -416, -649, 731, -58, -265],\n [-858, -875, 76, -552, 293, -267, -1330, 378, -468, -346, 258, 919],\n [517, -1738, 643, 81, -372, -224, -164, 551, 677, -459, -703, 602],\n [-90, 883, 703, 229, 502, -1213, -117, -575, -173, 1032, -58, -1085],\n [-512, 497, -586, 10, 122, -306, -211, 454, 182, -366, 202, 241],\n [-426, -635, -307, 1119, -1172, 24, 84, -1411, -613, 111, -233, 352]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-959, -71, -955, -699, 269, 867, -692, 513, -1123, 426, -65, -270],\n [-253, 277, 167, -713, -191, 379, -988, 1421, -1061, -870, 361, -978],\n [-289, 357, -318, -240, -155, 446, -205, 109, -350, 62, -308, -303],\n [596, 275, 94, 583, -309, -274, 667, -836, 803, 51, -519, 359],\n [108, 698, -1092, 30, -522, 1250, -432, -450, -500, -320, -958, 222],\n [732, 961, 112, -20, -885, 1002, -987, 428, -521, -1751, -290, -306],\n [-187, 1207, 325, -303, -677, 665, -316, 195, -187, -446, -497, -918],\n [700, 115, 512, 453, -265, -654, 535, -246, 695, -279, -125, 45],\n [-879, 509, -816, -865, -139, 1207, -1012, 838, -1369, -105, -269, -766],\n [539, 182, 1025, 108, -254, -259, -259, 389, 240, -993, 508, -225],\n [78, -347, -1696, 414, 149, 601, 308, -1141, -68, 756, -892, 1184],\n [-1131, -352, -533, -760, 528, 451, -555, 659, -954, 647, 348, -351]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[482, -9, 1331, -242, -9, -576, -1263, -742, 107, -104, 315, 154],\n [357, -615, 850, 948, -1287, -362, -409, 1649, 473, 620, 161, 111],\n [-85, 673, 23, -80, 912, 114, 208, 82, -53, 1353, -487, 11],\n [-146, 86, 824, 743, 959, -697, 42, -524, 538, 38, 1088, -623],\n [134, -589, -506, -391, -655, 85, -525, 140, -726, -538, -414, 1026],\n [-588, 65, -238, -243, 966, -920, 524, 138, -735, 493, 389, -163],\n [-215, 537, 1098, 3, 1772, -623, -982, -1515, -350, -6, 595, 368],\n [28, -447, -13, -453, 490, -1499, 627, -143, -284, -7, 1098, -1055],\n [-1425, 134, -968, -203, 948, 371, 1034, -968, -753, -527, 120, 400],\n [549, -854, -606, -1138, -1137, -588, 925, -87, 42, -316, 377, -1160],\n [184, 276, 827, 134, 568, -249, -814, -180, -72, 724, -93, 466],\n [355, 1005, 889, 95, 792, 188, -1211, -247, 149, 314, -448, 276]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[447, -248, -802, -990, -650, -902, 1365, 1218, -791, 1414, 226, 1],\n [288, 90, -1096, -258, -331, -498, 1139, 1500, -594, 711, 111, 725],\n [306, -965, 186, -454, 205, -354, 448, 24, 51, 507, 77, -625],\n [-193, 405, 820, 781, 617, -606, 198, 863, -355, 633, -129, -1037],\n [610, -151, -897, -1151, -676, -190, 1092, 427, -200, 919, 90, 448],\n [936, -696, 417, 39, -91, -854, 165, -659, -137, 499, -145, -493],\n [267, -484, 73, 1044, 23, -1043, -637, 98, -930, -779, -123, 342],\n [-275, -305, -1143, -225, -405, 67, 335, 625, -68, -119, 429, 943],\n [-476, -350, -449, -470, -212, -136, 611, 359, 312, 527, 340, -27],\n [440, -757, -174, -473, -458, -1263, 866, -372, 39, 487, -386, 154],\n [125, 892, 288, -816, -421, -57, 679, -369, 308, 901, -431, -329],\n [242, 1266, 714, -310, -85, -105, -278, -207, -745, -531, -1127, 90]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1076, -765, -1012, 494, -477, 1162, -892, -171, 470, -123, -421, -443],\n [-517, 52, -714, -538, 166, 80, -412, 869, 374, 345, -170, -412],\n [-312, 51, -195, -155, 168, 74, -161, 1161, 30, 66, 323, -449],\n [-721, -641, -196, 1196, -1131, 1189, -535, -738, -83, 421, -464, -300],\n [1066, 321, 947, -123, 102, -693, 858, -38, -523, -265, 273, 651],\n [-285, -675, -380, 112, -149, 431, -323, -402, -203, -179, -454, 360],\n [1171, -570, 348, -556, -50, -403, 728, -341, -756, -708, -627, 1646],\n [-274, -1145, -565, 319, -942, 1021, -323, 48, -362, -113, -927, 598],\n [-253, -294, 4, 390, 300, 80, -285, -1497, -59, -291, -36, 165],\n [446, 231, 101, -195, -236, -76, 381, 622, 224, -198, 62, 60],\n [-346, -249, -9, 531, 446, 120, -351, -1745, 138, -536, 169, 3],\n [107, 235, 210, 100, 37, -118, 124, -54, 80, -10, 221, -143]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-123, -410, -960, -907, -339, 571, -284, 526, -116, 486, 367, 128],\n [851, 905, 302, -793, -49, 648, 96, 532, 410, 237, -436, -992],\n [-37, -132, 125, 1918, 82, 490, 47, 460, 16, -1117, 99, -374],\n [145, 320, -180, -509, -219, 276, -393, 1056, -95, -983, -608, -1101],\n [-753, -519, -61, -729, -726, -57, -661, -444, -470, -548, -147, 671],\n [-1017, -1166, -1608, -1063, 317, -562, -1398, 342, -579, -39, 146, 34],\n [542, 566, 331, 141, -15, 479, 204, 396, 272, -159, -236, -653],\n [1002, 990, 237, -1055, -9, 1015, -170, 484, 542, 513, -428, -1151],\n [-663, -396, 265, 118, -316, -466, -335, -576, -378, -691, -163, 586],\n [-351, -428, -891, 284, -124, -342, 211, 1416, -422, -1007, 15, -430],\n [-198, -96, -92, -1261, -358, -452, 162, -326, -186, 558, 13, 627],\n [-459, -153, 787, -285, 148, -1165, 59, -1736, -126, 602, -25, 1229]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-533, 1343, 320, 34, 347, -845, -1166, 992, -1152, 86, 1277, -323],\n [-56, -387, 634, -199, 424, 300, -273, 486, -448, 798, -724, 119],\n [60, 795, 875, 1348, -428, -1501, -1822, 640, -897, -77, 416, 0],\n [-20, -481, 150, 750, -343, 340, -321, 16, 388, 191, -211, -30],\n [-404, 1000, -280, 53, 722, 177, 63, 259, -956, -348, 322, -143],\n [209, 716, 109, -1030, 1019, 766, 18, -461, 109, 214, 264, -687],\n [121, 187, 695, 570, -467, 634, 675, -386, 96, 295, -1536, 1177],\n [-361, 429, -676, 146, 718, -435, -824, 523, -729, -528, 1396, -1091],\n [-222, 839, 411, -179, 661, -294, -815, 596, -926, 263, 473, -337],\n [-207, -862, -366, -201, 140, -1202, -838, 988, -600, -4, 883, -634],\n [193, 152, 13, 335, -1528, -1032, 6, -327, 937, -391, 627, 560],\n [-436, 1047, 319, -816, 222, 542, 279, 261, -120, 517, 421, 252]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-64, 128, -208, 184, -200, -48, 168, -8, 136, -72, -176, 8],\n [-64, 128, -208, 184, -200, -48, 168, -8, 136, -72, -176, 8],\n [-120, 240, -390, 345, -375, -90, 315, -15, 255, -135, -330, 15],\n [-144, 288, -468, 414, -450, -108, 378, -18, 306, -162, -396, 18],\n [112, -224, 364, -322, 350, 84, -294, 14, -238, 126, 308, -14],\n [16, -32, 52, -46, 50, 12, -42, 2, -34, 18, 44, -2],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n [-176, 352, -572, 506, -550, -132, 462, -22, 374, -198, -484, 22],\n [-8, 16, -26, 23, -25, -6, 21, -1, 17, -9, -22, 1],\n [24, -48, 78, -69, 75, 18, -63, 3, -51, 27, 66, -3],\n [-104, 208, -338, 299, -325, -78, 273, -13, 221, -117, -286, 13],\n [48, -96, 156, -138, 150, 36, -126, 6, -102, 54, 132, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1032, -451, -1313, -468, -386, 548, -401, 472, -686, 212, -152, -525],\n [354, 643, -422, -330, 364, 1008, -945, 1329, 352, 241, -113, -628],\n [412, 6, 19, -80, 187, 278, -63, 110, -502, 322, 4, -125],\n [2, 102, -106, -185, -93, 676, -288, 343, -387, -563, 403, -338],\n [323, 151, -550, -174, -123, 899, 166, 578, -894, 521, 164, -443],\n [-8, -375, 337, 631, -652, 550, 377, -218, -968, -114, 670, -416],\n [545, -530, -468, -34, -378, -733, 11, -381, 582, 446, -121, -49],\n [-162, 299, -481, 256, 334, -796, -277, -282, 310, 164, -946, 209],\n [143, 459, -981, 926, -311, -977, -1702, -59, 1734, -214, -527, -1118],\n [1075, -917, -431, -901, -713, 1357, -135, 573, -983, -564, 1121, -560],\n [82, -503, -213, 1427, -1275, -344, 162, -666, -81, 378, 486, -939],\n [950, -244, -533, -365, -451, 1190, -662, 739, -532, -153, 805, -1014]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-66, -114, -66, -96, -156, -30, -54, 54, -96, -42, -102, 126],\n [-253, -437, -253, -368, -598, -115, -207, 207, -368, -161, -391, 483],\n [88, 152, 88, 128, 208, 40, 72, -72, 128, 56, 136, -168],\n [-286, -494, -286, -416, -676, -130, -234, 234, -416, -182, -442, 546],\n [187, 323, 187, 272, 442, 85, 153, -153, 272, 119, 289, -357],\n [22, 38, 22, 32, 52, 10, 18, -18, 32, 14, 34, -42],\n [-110, -190, -110, -160, -260, -50, -90, 90, -160, -70, -170, 210],\n [154, 266, 154, 224, 364, 70, 126, -126, 224, 98, 238, -294],\n [231, 399, 231, 336, 546, 105, 189, -189, 336, 147, 357, -441],\n [-33, -57, -33, -48, -78, -15, -27, 27, -48, -21, -51, 63],\n [44, 76, 44, 64, 104, 20, 36, -36, 64, 28, 68, -84],\n [-99, -171, -99, -144, -234, -45, -81, 81, -144, -63, -153, 189]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[621, 662, -866, -299, 1376, -21, 172, -434, 1014, 1663, -1192, 554],\n [-47, 424, -477, -61, -218, 936, -514, -75, -13, 225, -90, -298],\n [-593, -892, -429, 438, 1204, -329, -630, -239, -131, -852, 462, 1235],\n [-744, 1022, -455, -197, -859, 122, 506, -105, -605, 1297, 255, -7],\n [447, -464, 773, -323, -714, -893, 21, 294, -45, -1533, 201, -628],\n [-122, 79, 102, -401, -906, 96, 32, 167, 108, 51, 285, 554],\n [-1164, -1172, 116, 717, -936, 89, -510, 352, -182, -1141, 599, -9],\n [630, 349, 598, -289, -588, 334, 612, 609, 452, 491, -441, -344],\n [-959, 1466, -603, -496, 881, -1295, 846, 220, 944, 274, -606, -469],\n [-908, 1319, -1335, -606, 316, -101, 24, -440, 1429, 1412, -737, 400],\n [1054, -742, 188, 124, 260, -302, -111, -192, -127, 20, -422, 13],\n [386, -864, -337, 787, 937, 669, 5, 217, 820, 1307, -1095, 669]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-357, -348, -121, 462, -635, -226, 813, -156, -461, 834, -184, -1012],\n [-1196, -597, 55, 663, 54, -53, 781, -890, -714, -925, -414, -622],\n [-1707, -1250, 134, -785, -954, -473, -92, -461, 1045, -660, -635, -1237],\n [-90, 10, 642, -314, -732, -571, 680, -323, -148, 177, 191, -290],\n [-1316, -904, 791, -307, -161, -74, 59, -494, -5, 69, 237, -1272],\n [323, -299, 151, -122, -134, -338, -898, 753, 388, 156, 890, -39],\n [336, 22, 715, 526, 1426, 1324, -314, 30, -540, -1311, 28, 906],\n [593, 155, 797, -208, 653, 675, -717, 918, 155, -308, 465, 615],\n [58, -830, -1051, 1259, -683, 1420, -573, 642, 159, 363, 966, 749],\n [-223, -383, -579, 1276, 381, 666, -219, -219, -688, -609, 770, 607],\n [-571, -1083, 213, 531, -57, 14, -272, -629, -213, -305, 530, -131],\n [186, 574, -319, -374, 234, 971, -268, 330, 338, 935, 41, 354]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1247, -1391, 507, 951, -247, 362, -374, 1068, 27, -885, 1369, -291],\n [-132, 24, 333, -170, -2015, 841, -265, 163, -1323, -1607, 893, -618],\n [567, -287, 531, -607, 222, -309, 1557, 801, -652, 260, -1777, 502],\n [-638, 1324, 177, 144, -1222, 935, -313, -159, -1009, -346, 740, 670],\n [-172, -336, 967, 1396, 709, -321, -997, -115, 234, -1039, 359, -114],\n [-669, 624, -322, -414, -664, 449, 649, 171, 10, 526, -695, 1040],\n [488, 836, 1402, -9, 613, -724, -243, -1627, 120, -186, -1210, 26],\n [1210, 1037, -230, -843, -935, 299, -761, -465, -325, 777, -698, 173],\n [-1117, 707, -168, 786, 198, 493, -389, -306, 64, -71, 937, 1321],\n [-478, -27, 791, -443, -700, -632, 285, -746, 117, 432, -243, -339],\n [726, 956, 727, 319, 117, -475, -187, -645, -427, 191, -618, 1042],\n [-329, -341, -121, -551, -1630, 220, 1597, 54, -1307, -1762, 421, -68]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, -18, -12, -24, 8, -34, -42, -6, 12, 2, 2, -34],\n [-72, 162, 108, 216, -72, 306, 378, 54, -108, -18, -18, 306],\n [-28, 63, 42, 84, -28, 119, 147, 21, -42, -7, -7, 119],\n [92, -207, -138, -276, 92, -391, -483, -69, 138, 23, 23, -391],\n [-64, 144, 96, 192, -64, 272, 336, 48, -96, -16, -16, 272],\n [-32, 72, 48, 96, -32, 136, 168, 24, -48, -8, -8, 136],\n [48, -108, -72, -144, 48, -204, -252, -36, 72, 12, 12, -204],\n [-68, 153, 102, 204, -68, 289, 357, 51, -102, -17, -17, 289],\n [-88, 198, 132, 264, -88, 374, 462, 66, -132, -22, -22, 374],\n [48, -108, -72, -144, 48, -204, -252, -36, 72, 12, 12, -204],\n [-16, 36, 24, 48, -16, 68, 84, 12, -24, -4, -4, 68],\n [-84, 189, 126, 252, -84, 357, 441, 63, -126, -21, -21, 357]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[406, -915, 709, -284, 557, -489, 303, 243, 66, -194, 966, 214],\n [-193, 1403, -857, 401, -297, 423, -99, -744, 498, -575, -455, -818],\n [527, 83, 252, -859, 1099, -186, 1395, -63, -738, 202, 445, 159],\n [880, 635, 463, -164, 251, 249, 587, 321, -432, 414, 196, -150],\n [48, 503, -169, -198, 334, -177, 659, -339, -276, -163, -107, -341],\n [-723, -866, -112, 601, -561, -476, -1076, -211, 930, -784, 178, -143],\n [465, -831, 918, 124, -350, 22, -508, 986, -243, 742, 218, 564],\n [706, 1001, 302, -49, -216, 508, 422, 551, -921, 1033, -645, -34],\n [-1010, 560, -1235, 186, -482, 551, -558, -593, 288, -103, -988, 39],\n [871, -103, 938, -264, -87, 332, 264, 1156, -1095, 1439, -211, 637],\n [-591, 678, -764, 267, -680, 570, -508, -123, -126, 393, -1131, 48],\n [-739, -810, -481, -445, 515, -279, 148, -462, 180, -403, 198, 432]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[34, 1, 291, 188, -307, 287, -272, -272, 239, 329, -277, 183],\n [161, 69, 469, -74, 541, -217, -168, -720, 399, -251, -700, -445],\n [233, -418, -484, 18, 186, -392, 124, -174, 54, -312, -419, -154],\n [-200, 355, 221, -182, 175, 56, 102, 275, -191, -50, 485, -85],\n [47, 188, 474, -98, 424, -98, -124, -466, 256, -158, -371, -336],\n [-51, -204, -306, 294, -840, 420, -96, 372, -120, 528, 267, 612],\n [-454, 779, 713, -162, -129, 532, -50, 495, -255, 354, 955, 155],\n [-218, 298, -302, -486, 714, -469, 554, 669, -558, -633, 854, -416],\n [97, -22, -32, -184, 566, -399, 134, -217, 46, -439, -237, -412],\n [311, -411, -239, 58, 277, -385, -24, -528, 279, -299, -778, -253],\n [-526, 786, 162, -522, 450, -7, 470, 1027, -718, -267, 1502, -188],\n [-45, 35, -213, -176, 283, -238, 234, 241, -211, -284, 266, -169]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1244, 535, 54, 781, -461, 44, 983, 864, 572, 243, -749, -75],\n [-232, 458, -978, 801, 209, 93, -524, 750, 64, 1863, -202, -109],\n [829, 708, -645, 481, 252, 499, 222, 387, 178, 584, -180, -450],\n [221, -145, -613, 553, 906, 255, -101, 989, 324, 560, -170, -329],\n [508, -742, 807, -526, -154, -190, 690, -307, -411, -1879, 746, 377],\n [205, 55, -389, 741, -944, -695, 983, -603, -464, -719, 1095, -183],\n [-362, 315, 423, -965, 405, 821, -69, -153, -657, -321, -1065, 473],\n [413, 438, 487, -636, -631, 442, 1242, -1373, -1612, -1464, 337, 637],\n [668, -110, 435, -342, -981, -325, 818, -282, -663, -1772, 936, 361],\n [77, -592, 221, 425, 944, 137, 1014, 135, 192, -685, -651, -208],\n [1180, 465, 1230, -1012, -646, 577, 243, -80, -192, -460, -571, 840],\n [-225, -143, -52, -841, 447, 197, -1711, 199, 499, 513, 490, -177]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[100, 69, 26, 35, 19, -208, 90, -7, -21, 2, 82, 215],\n [-520, -159, 109, -293, -454, 571, -357, 325, 420, -77, -271, -563],\n [240, 162, 58, 86, 52, -490, 214, -22, -56, 6, 194, 506],\n [480, 261, 39, 207, 216, -819, 393, -135, -210, 33, 339, 837],\n [80, 192, 188, -48, -228, -516, 148, 192, 196, -44, 172, 552],\n [500, 210, -35, 250, 335, -695, 375, -230, -315, 55, 305, 700],\n [460, 60, -195, 304, 545, -299, 271, -404, -497, 95, 177, 274],\n [160, 222, 178, -6, -168, -618, 206, 150, 140, -34, 218, 654],\n [340, 6, -191, 246, 471, -123, 179, -354, -427, 83, 101, 96],\n [-520, -267, -23, -233, -262, 847, -417, 169, 252, -41, -355, -863],\n [520, 222, -32, 258, 342, -732, 392, -234, -322, 56, 320, 738],\n [220, 258, 187, 18, -147, -729, 257, 138, 119, -31, 263, 768]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[284, 193, 797, -23, 526, -388, 452, -109, 745, 271, 335, 982],\n [52, -616, 427, 552, -222, 267, -580, -526, 796, -495, 870, -349],\n [-666, -278, 1282, -1240, 1398, -432, 304, 647, -660, 680, -1077, 889],\n [626, 1078, -718, -45, -131, 158, 83, -507, -563, -441, 117, -613],\n [-172, -769, 1204, -877, 98, -887, 589, -398, -93, 422, -569, 625],\n [-131, 737, -411, 567, 891, 148, 578, 1363, -450, -256, -402, -313],\n [167, 385, -275, 452, 393, 371, -582, -234, -1097, -728, 176, -1195],\n [-63, -552, -646, -423, -129, 428, -625, 325, -1227, 753, -305, -1047],\n [518, 967, -952, 77, 200, 100, 1332, 719, 712, -457, -766, 603],\n [177, 2205, -1602, 15, -232, 479, 625, 758, -111, 530, -63, 153],\n [-172, 403, 443, 749, 711, 515, -948, 594, 123, 249, 1301, -723],\n [959, -512, 1047, 630, -293, -1200, -161, -1315, 451, -1055, -261, 340]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-392, -211, -352, -863, -507, 44, -814, 564, -108, -31, 565, 630],\n [-579, -662, 167, -933, -1231, -345, -346, 182, -68, 611, 435, 668],\n [216, 131, -88, 545, 313, 241, 362, -167, 102, -15, -174, -324],\n [184, 238, 282, -29, 166, -700, 585, -284, 155, -51, -233, -35],\n [-113, -97, 589, -354, -136, -461, -200, -152, -216, -2, -196, 58],\n [333, 672, -1305, -39, 423, -201, 738, 438, 708, -351, 561, 384],\n [-167, 53, -737, -624, -316, -107, -158, 520, 246, -44, 626, 616],\n [-519, -945, 893, -103, -1006, 335, -559, -278, -489, 755, -179, -89],\n [-2, 116, 484, -563, -176, -1127, 421, -229, 97, 23, -132, 271],\n [389, 386, 433, 642, 867, 14, 187, -371, -143, -404, -599, -617],\n [444, 311, 150, 1228, 1087, 914, -57, -290, -233, -418, -606, -949],\n [524, 796, -484, 246, 826, -565, 908, -49, 486, -490, -59, -58]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-315, -332, -165, -137, -187, -222, -788, 463, 280, 320, -232, 580],\n [-207, 180, 463, -527, 603, -140, 462, -417, -376, -478, -82, 398],\n [216, 436, 371, -440, -83, 414, -107, 699, -81, -88, -325, -617],\n [-30, 88, 121, -203, 46, 6, -50, 89, -5, -16, -161, 31],\n [-144, -552, -422, 227, -125, -451, -501, -136, 322, 277, 137, 691],\n [-262, 802, 308, 339, -5, 676, 1076, -400, -436, -34, -238, -932],\n [680, -420, 176, -643, 373, -284, -473, 544, -76, -648, 556, 264],\n [9, 140, 450, -333, 362, 352, 203, 502, -557, -636, 331, -233],\n [239, -10, -207, -153, -319, -291, -459, -37, 582, 509, -511, 93],\n [52, 1114, 655, -420, -95, 795, 582, 353, -247, 7, -802, -1206],\n [53, -206, -533, 296, -546, -351, -550, -187, 730, 801, -431, 209],\n [624, 24, -403, 251, -538, -106, -264, -75, 629, 544, -223, -479]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-16, -34, -36, -28, 36, -2, -42, 26, 34, -50, 4, 42],\n [176, 374, 396, 308, -396, 22, 462, -286, -374, 550, -44, -462],\n [-152, -323, -342, -266, 342, -19, -399, 247, 323, -475, 38, 399],\n [-96, -204, -216, -168, 216, -12, -252, 156, 204, -300, 24, 252],\n [80, 170, 180, 140, -180, 10, 210, -130, -170, 250, -20, -210],\n [-16, -34, -36, -28, 36, -2, -42, 26, 34, -50, 4, 42],\n [128, 272, 288, 224, -288, 16, 336, -208, -272, 400, -32, -336],\n [40, 85, 90, 70, -90, 5, 105, -65, -85, 125, -10, -105],\n [-32, -68, -72, -56, 72, -4, -84, 52, 68, -100, 8, 84],\n [-96, -204, -216, -168, 216, -12, -252, 156, 204, -300, 24, 252],\n [208, 442, 468, 364, -468, 26, 546, -338, -442, 650, -52, -546],\n [96, 204, 216, 168, -216, 12, 252, -156, -204, 300, -24, -252]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-660, -203, -520, 129, -271, 178, -1384, 830, -1458, 236, 1899, 1522],\n [782, 1298, -562, 1227, 640, 983, 675, -905, 952, 799, -585, -343],\n [-792, -178, -592, -352, -212, -96, -299, -295, -888, 217, 944, 1001],\n [-242, 406, -1132, 821, -383, 494, 507, -727, 312, 1063, 61, 328],\n [1507, 159, 1069, 520, 418, 406, 852, 38, 1985, 14, -1876, -1617],\n [-313, -754, 154, 188, -728, -984, 280, 154, 710, -200, -827, -785],\n [85, -983, 493, -479, -75, -74, 372, -788, 373, 608, -439, -8],\n [-1223, -33, -781, 23, -163, -436, -1250, 326, -1121, -194, 1817, 1798],\n [8, -797, 650, -787, -23, -494, 804, -806, 1120, -97, -1075, -346],\n [-394, -1794, 668, -520, -726, -870, -258, 46, -172, 280, -122, -112],\n [-897, -624, 73, -918, -578, -940, -580, 894, -1205, -961, 662, 202],\n [225, 1021, -168, 469, 777, 198, -110, -306, 82, -273, 84, 65]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-347, 883, -125, -597, 649, -1388, -692, 658, -194, -561, -953, -116],\n [-500, 393, 77, -302, 127, -450, -153, -310, -534, 291, -743, -54],\n [-571, 409, 27, -369, 201, -548, -152, -250, -544, 289, -897, 50],\n [512, 199, -90, 38, -146, -488, -668, 730, 303, -439, 82, 21],\n [-808, 670, 102, -518, 374, -764, -188, -396, -758, 276, -1096, -170],\n [-419, -107, -214, -253, 90, -238, 99, -14, -231, 417, -898, 713],\n [497, -868, 210, 702, -1044, 1398, 412, -768, 39, 821, 893, 131],\n [457, 150, -56, 62, -298, -406, -662, 548, 163, -201, -33, 95],\n [-785, -58, -37, -287, 121, 4, 402, -644, -595, 746, -955, 453],\n [-764, 52, -510, -646, 1522, -564, 776, 680, 424, -802, -604, 488],\n [-721, 479, -299, -674, 1197, -932, 195, 518, 33, -630, -836, 145],\n [49, 578, 32, -212, 322, -710, -492, 436, 29, -571, -79, -435]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[63, -1541, 300, -390, -1098, 187, -286, 198, -34, -1235, 446, -988],\n [743, -7, -114, -509, -5, -7, 466, 487, -434, 257, -115, 480],\n [-707, 443, -38, 131, 21, 150, 816, -292, 569, -124, -324, -194],\n [-606, 758, 413, 83, 523, -343, 292, 241, 93, 475, -694, -58],\n [55, 172, -103, -596, -129, 341, 1560, -61, 79, -152, -118, 499],\n [-305, -477, -271, -393, -886, 54, -470, 860, 20, -1788, 106, 698],\n [61, -902, 578, -553, 682, 279, -725, -694, -745, 546, 571, -503],\n [-152, -577, 628, -1761, 916, 409, 602, -11, -1037, 77, 255, 875],\n [583, 740, -1131, 246, -77, 501, 835, -355, 328, 299, -63, 677],\n [-300, 685, -200, 927, 149, -1074, -1064, 845, 689, -288, 240, 979],\n [-1305, 1260, 0, -779, 257, 1238, 363, -149, -970, -278, -2165, -185],\n [94, 263, 100, -1574, 888, 1107, 797, -298, -1446, 765, -950, 249]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-540, 805, 26, 287, -1071, 2271, 1265, -513, -28, -1127, -2334, -1018],\n [1021, -358, 281, -374, 490, -566, -599, 1073, -761, 1570, 1532, 310],\n [707, 176, -327, -761, -723, 1111, -1129, 491, -1271, 1638, 161, 283],\n [205, -569, 662, -166, 834, -2304, 1, -319, -638, 276, 2134, 137],\n [1123, -284, -1470, -1227, 182, 502, -1658, 853, 918, 294, 341, -979],\n [213, -230, -1143, -444, -845, 1409, -1025, -85, 242, 35, -847, -1281],\n [769, -694, 7, 362, -925, 338, -141, 227, -930, 941, 559, 489],\n [-538, -503, 1650, 1982, -65, -1063, 671, -790, 47, -1175, 380, -411],\n [49, -45, 1761, 1007, -1435, -335, 1792, -509, -956, -48, 330, 1709],\n [-1951, 103, -1334, 288, -692, 908, 149, -1836, -5, -679, -2416, 24],\n [-1040, -908, 250, 1216, 800, -2287, -851, -1630, -1001, 13, 1430, 62],\n [321, -1378, -16, 792, 889, -1080, -488, 989, 100, 573, 1170, -414]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1417, -1025, -1238, 1017, 132, 1501, 759, -753, 1254, -612, 1226, 391],\n [110, 648, -472, 775, -439, 345, -229, -572, -386, 184, 243, 296],\n [-576, 461, 675, 60, -326, -662, 66, 264, 37, -701, 346, -1132],\n [859, 581, 517, 350, -330, 502, 265, -253, -247, 199, -466, 956],\n [-1497, 866, -256, -1328, -829, -754, -361, -80, -576, 1147, -1189, -794],\n [-56, 4, 317, 559, -169, 32, -768, -57, -742, -591, 710, -527],\n [-582, 707, 405, 587, -29, -464, 531, -291, 404, 166, -140, -431],\n [964, 367, 353, 76, -629, 757, 136, -304, -132, -255, -84, 391],\n [788, -10, -849, 311, -441, 777, -465, -231, -450, -290, 599, 578],\n [-393, 28, -96, -375, 262, -190, -1180, 223, -477, -662, 631, -571],\n [756, -623, 797, 599, 1140, 441, 708, -189, 1194, -436, 216, 319],\n [-1137, 607, 441, -277, 826, -1396, -128, 698, -86, 389, -577, 162]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, -435, 370, -388, 1125, 399, 1279, -521, -469, -1746, -542, 676],\n [-146, -470, -503, 128, 978, -142, -101, -319, -614, -390, -316, 358],\n [715, -89, -604, 449, 527, -434, -382, 199, 601, 481, 629, 1317],\n [8, 449, -67, 127, -662, -117, -567, -132, 498, 1223, 589, -677],\n [-124, 136, -270, -1055, -769, 392, 602, -888, 893, -181, -40, -496],\n [540, -1123, 975, -116, 418, 595, 333, -759, 583, -52, 86, -53],\n [563, -1089, 1533, 21, 376, 42, 487, 239, -27, -783, -1012, -109],\n [657, 724, -462, -19, -1032, 149, 656, 1142, -884, -1005, -1032, -317],\n [-191, -452, -160, -465, -82, 190, 73, -653, 345, 461, 38, -21],\n [653, 508, -582, -535, -714, -379, 871, 741, 145, -771, -916, 671],\n [-144, 701, 182, -164, -622, 340, 358, -181, -204, 2, 57, -987],\n [628, -674, 82, 943, -247, 533, -1042, 219, -412, 1233, 443, -676]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-174, -317, -370, -171, -621, 3, -101, 88, 501, 1062, 106, -503],\n [573, -399, 607, -125, -572, -764, 686, -56, -99, -870, 286, 871],\n [35, -839, -142, 459, -503, -1365, -471, -237, 1019, 546, 800, 848],\n [533, 735, 1622, -615, 417, -181, -147, 506, -1777, -1162, -107, 32],\n [-828, 841, 367, -840, 922, 533, 119, 783, -1425, -595, -872, -1183],\n [-357, 714, 162, -449, 567, 931, 111, 294, -924, -298, -633, -929],\n [513, -113, -253, -161, -74, 398, 562, -39, -305, -756, -737, 237],\n [-1046, -811, -992, 818, -87, 52, 147, -1507, 1252, -290, 191, -8],\n [-133, -202, 752, -618, -437, -1262, -474, 798, -340, 649, 435, -178],\n [-762, -555, -1478, 104, 314, -96, 338, 58, 735, -28, -810, -53],\n [-1208, -740, -1240, -72, -137, -42, -19, -350, 697, 450, -594, -831],\n [875, 251, 480, -356, -498, 28, -532, 687, -295, 1114, 212, -146]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[480, -396, 669, 1112, -436, -437, 80, 672, -309, 884, 915, 509],\n [-552, 1215, -606, -1791, 1856, -31, -290, -323, -832, -1229, -1871, 232],\n [481, 44, 676, 241, -491, 115, -614, -245, -238, -393, 68, -719],\n [77, 251, 1239, 533, 807, -208, -602, 712, -1377, 372, 191, -179],\n [-66, -227, -19, -12, -454, -71, -12, -219, 661, 75, 147, -246],\n [503, -533, -535, 467, 696, 391, 806, -431, -579, 996, 216, 711],\n [463, -321, -78, 469, -92, -789, 200, 438, -49, 680, 321, 1219],\n [247, 546, 145, -925, 1361, -882, -262, -52, -1078, -595, -1225, 1249],\n [125, -316, 699, 663, -91, -254, -474, 451, -297, 553, 561, -174],\n [711, 178, -881, -451, 567, -1448, -598, 569, -533, -190, -796, 2106],\n [773, 103, -734, -533, 156, -540, -366, -304, -353, -679, -804, 1081],\n [-347, -64, -373, -510, 128, 872, 304, -804, 219, -504, -314, -719]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-448, -372, -1701, 450, 965, -457, -496, 635, 485, 760, 295, -997],\n [-230, -820, -148, 166, 682, -385, 85, -235, -1248, 384, 346, 93],\n [620, -233, -950, 282, 1288, -157, 642, -192, 455, 484, 787, 171],\n [656, 167, 457, 793, 385, 31, 831, -455, -32, 369, 605, 479],\n [473, 243, -47, -86, 554, -881, 1373, -125, -198, 627, 1141, 657],\n [466, -1142, -240, -349, 1184, -544, -446, -810, -1085, 340, 584, 182],\n [913, 229, 412, -121, 87, 63, -442, -533, 522, 11, 213, 51],\n [779, 938, 1396, -212, -187, 555, 419, 121, -979, 444, 451, 197],\n [-214, 502, -169, 389, 38, 97, -251, 721, 443, 383, -101, -622],\n [272, 482, 1265, -1391, -72, -209, 399, 296, -1544, 170, 348, 496],\n [531, 376, 219, 138, 68, -480, -489, -75, 133, 669, 546, -422],\n [1100, 856, 319, -408, -179, 226, 1437, -452, 1051, -344, 557, 1044]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-92, 370, -164, 171, -137, -334, -82, 4, 109, 73, -93, -60],\n [-24, -102, -11, -36, 47, 107, 54, 13, 25, 46, 56, -61],\n [-889, 548, -239, 6, 528, -31, 574, 643, 16, 748, -215, -1112],\n [14, -612, -806, 194, -378, 342, -8, -418, 1026, 458, 816, -288],\n [410, -782, -275, 10, -345, 403, -182, -495, 521, -72, 608, 305],\n [152, -144, -241, 119, -268, -25, -152, -249, 328, 3, 239, 125],\n [673, -930, -186, 4, -493, 404, -352, -676, 493, -304, 653, 641],\n [974, -1098, 365, -220, -355, 527, -434, -663, -53, -762, 422, 1109],\n [423, -26, -344, 296, -637, -330, -468, -526, 477, -208, 271, 505],\n [-524, -70, -720, 155, 35, 190, 326, 88, 737, 769, 435, -864],\n [90, 44, -469, 271, -422, -225, -216, -305, 546, 115, 281, 47],\n [-861, 622, -267, 53, 459, -125, 516, 607, 41, 721, -232, -1060]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-536, 344, -374, 56, 780, -682, 58, -772, 46, 228, -548, -286],\n [96, 369, 711, 544, 427, -528, 714, 311, -491, 364, 642, 232],\n [176, -72, 581, 149, 98, -133, 234, 223, -113, 233, 307, 296],\n [22, 335, -1083, -267, -348, 154, -102, -112, 92, -150, -171, -779],\n [64, 350, 525, 771, -216, 253, 522, 851, -769, -513, 945, 376],\n [-102, 306, 82, 400, 53, -26, 283, 244, -389, -229, 346, 54],\n [-252, 695, 114, 512, 783, -869, 703, -193, -450, 402, 248, -187],\n [-758, 463, -700, 125, 758, -569, -51, -862, -19, -88, -677, -392],\n [36, -649, -941, -1097, -387, 386, -997, -736, 1013, 93, -1131, -465],\n [-102, 322, -474, 298, -447, 482, 29, 406, -381, -723, 316, -176],\n [-128, -269, -65, -109, -173, 342, -367, -60, 143, -341, -243, 167],\n [242, 383, 145, 518, -436, 314, 471, 837, -616, -391, 890, 36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-176, -464, -224, 810, -319, 685, 597, -438, 195, 1003, -355, -726],\n [-307, 693, 559, -1, 945, -749, 271, 1213, -372, -707, -409, -182],\n [-1342, -75, -101, 134, -427, -176, 394, 211, -256, 39, 369, 1321],\n [-180, -1047, -950, -684, -1502, 239, -544, -731, -305, -1257, 1276, 593],\n [-1110, -1499, 645, -291, 172, 1060, -1532, -1298, -501, 781, -812, -27],\n [673, -212, -665, 998, -124, -359, 849, 562, 96, -1088, 385, -1289],\n [200, 950, -15, -951, -61, -528, 383, 501, 285, -33, 589, 844],\n [-501, 530, 138, 1403, 248, -23, 1477, 1137, 181, 227, -1106, -1512],\n [-998, -376, -101, -820, 242, -410, 796, 1248, 861, -607, 287, -1313],\n [-280, 913, -337, -758, -724, 719, 708, 1091, -230, 318, -1111, -1241],\n [509, 297, -26, 765, -30, 33, 361, 119, -428, -286, -361, -581],\n [312, 291, 466, 513, 1075, -1021, 787, 224, 1171, 341, 680, 183]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-275, -506, -442, 105, -341, 587, 224, -119, 299, -198, 275, -114],\n [-364, -136, -210, 48, -140, 316, 158, -110, 510, 116, 86, -68],\n [613, -122, 107, -21, 31, -229, -175, 154, -934, -444, 38, 60],\n [-155, -26, -67, 15, -41, 107, 59, -44, 224, 72, 20, -24],\n [416, 80, 187, -42, 116, -296, -161, 119, -599, -186, -59, 66],\n [314, -196, -39, 12, -62, -2, -55, 67, -507, -322, 89, 10],\n [414, -60, 88, -18, 34, -174, -124, 106, -626, -284, 14, 44],\n [-129, -318, -264, 63, -207, 345, 126, -63, 123, -150, 171, -66],\n [92, 632, 473, -114, 384, -596, -195, 81, -1, 394, -333, 110],\n [-463, 62, -102, 21, -41, 199, 140, -119, 699, 314, -13, -50],\n [115, -134, -58, 15, -59, 53, -4, 19, -199, -162, 65, -6],\n [144, -480, -292, 72, -256, 336, 76, -4, -316, -424, 244, -56]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[322, -483, -200, 906, 659, -624, -957, 156, 1253, 247, 428, -982],\n [395, 66, 220, -600, -66, -195, 649, 263, -196, -44, -895, 549],\n [-54, 1008, 77, 447, -1001, -93, 1044, -97, -2091, -344, 540, 306],\n [2, 744, -353, 71, -399, 1222, -733, 482, 687, -1038, -520, 122],\n [-1127, -140, 710, -835, 536, 555, -804, -1065, 996, 260, 580, 102],\n [125, 159, -13, -213, 427, -432, 63, -190, 574, -184, -480, -252],\n [-649, 482, -316, -438, 26, 622, 281, -557, -297, 335, 624, -308],\n [379, -125, -334, 625, -119, -269, -230, 372, 60, -604, -377, -121],\n [-447, 1018, -98, -1039, -484, 1026, 892, -247, -843, -89, -193, 497],\n [-891, -432, 320, -965, 54, 290, 482, -847, -695, 615, 441, 499],\n [-230, 331, 749, 390, -782, -268, 272, -257, -1379, -548, 368, 734],\n [-509, -320, 564, -751, -258, 333, 228, -365, -556, -10, -146, 936]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[11, -2274, 136, 277, -483, -160, -678, 1007, -306, 812, 285, -2334],\n [774, 0, -906, 192, -213, 44, 813, -757, 397, 44, -1510, 109],\n [-393, 899, -1161, 891, 746, -201, 437, -404, -161, 519, -1705, 1363],\n [418, -642, -1011, 403, 467, -86, 514, -154, -200, 243, -1056, -147],\n [-202, -1138, 154, -89, -393, 599, -309, 306, -92, 89, 492, -1074],\n [-1273, 717, 106, 412, 42, 436, 503, 4, 105, -41, 399, 555],\n [659, -1222, 719, -927, -223, -225, -1465, 840, -292, -618, 1703, -888],\n [-346, 466, -152, 136, 800, -644, 555, 548, -275, 36, -77, 501],\n [-45, -225, 53, 371, 539, -584, -997, 286, -593, 578, 151, 100],\n [-675, 1163, 656, -254, 111, 61, 182, 214, 54, -58, 290, 659],\n [830, -1701, -662, -703, -1057, 1285, -193, -406, 425, -935, 197, -887],\n [1173, -199, -863, -682, -988, 1301, 1525, -1727, 792, -560, -1264, 207]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-399, -171, 152, 418, -133, 190, -19, -171, -209, -57, 171, 399],\n [-189, -81, 72, 198, -63, 90, -9, -81, -99, -27, 81, 189],\n [-294, -126, 112, 308, -98, 140, -14, -126, -154, -42, 126, 294],\n [-378, -162, 144, 396, -126, 180, -18, -162, -198, -54, 162, 378],\n [210, 90, -80, -220, 70, -100, 10, 90, 110, 30, -90, -210],\n [63, 27, -24, -66, 21, -30, 3, 27, 33, 9, -27, -63],\n [336, 144, -128, -352, 112, -160, 16, 144, 176, 48, -144, -336],\n [21, 9, -8, -22, 7, -10, 1, 9, 11, 3, -9, -21],\n [399, 171, -152, -418, 133, -190, 19, 171, 209, 57, -171, -399],\n [483, 207, -184, -506, 161, -230, 23, 207, 253, 69, -207, -483],\n [-189, -81, 72, 198, -63, 90, -9, -81, -99, -27, 81, 189],\n [-147, -63, 56, 154, -49, 70, -7, -63, -77, -21, 63, 147]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[24, -117, 416, 285, -48, 240, -526, 102, -88, -285, 704, -123],\n [-46, -316, -344, 550, 84, 127, -480, -655, 300, 573, 326, 486],\n [399, -715, 374, 1485, 27, 908, -505, -1025, 507, 377, 1131, 65],\n [288, -59, -441, 726, 282, 253, -180, -877, 581, 748, -34, 550],\n [-25, 580, -269, -527, 150, -345, 66, 414, -59, -106, -525, 155],\n [-259, 359, -540, -245, 104, -308, -494, 243, 12, 98, -49, 521],\n [768, 529, 450, 145, 814, -172, -760, -934, 332, 675, -440, 317],\n [20, 852, 29, -1031, 252, -637, 28, 679, -303, -305, -814, -35],\n [-236, -294, -306, -208, -63, -281, 163, -295, -43, 398, -330, 146],\n [583, -111, -107, 1326, 345, 710, -435, -1059, 772, 645, 505, 470],\n [-623, 120, -900, -766, 42, -830, -362, 59, -166, 503, -561, 692],\n [958, 164, 989, 531, 494, 400, -42, -766, 295, 172, -92, -381]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[275, -700, -680, 640, -830, -549, 264, -862, -322, -821, 15, 1071],\n [693, -431, -1180, -1787, 348, -893, -631, -204, 83, -497, 224, -612],\n [-1020, 417, 630, 697, 105, 668, -672, 256, -799, 7, 614, 622],\n [949, -537, -703, 996, -837, -658, 1285, -992, -203, 1632, 225, 167],\n [1176, -10, -582, -2286, 974, -686, 156, -777, -132, 614, -1120, -837],\n [-4, 1421, 604, 10, -890, 868, 552, -307, -811, -1215, -423, -321],\n [200, 1691, 5, -117, -352, 532, 89, 96, -1353, -624, 1105, -599],\n [1220, -1665, -249, -453, -593, -1334, 1092, -629, 491, 347, -1082, -821],\n [-86, 1253, 0, 418, -468, 158, 494, -48, -1657, -749, 253, 580],\n [768, -217, 17, -1397, 1923, -647, 228, -356, -373, 1770, -924, -173],\n [11, 888, -595, -332, -830, 393, -307, -189, -427, -2005, 861, -42],\n [204, 1205, -303, -2043, 631, 146, -390, -43, -818, -411, -285, -729]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[324, -707, 465, -875, 246, -832, -845, -233, 449, -466, -732, -1055],\n [50, -527, -533, -368, 241, -335, -714, -594, 180, 71, -208, -331],\n [41, -171, 468, -512, -97, -568, -261, 257, 441, -185, -545, -594],\n [394, -661, -91, -316, 503, -157, -678, -726, -156, -359, -68, -437],\n [-184, -63, -3, -392, -211, -505, -240, 212, 510, 151, -458, -345],\n [-363, 406, -247, 203, -353, 74, 344, 370, 172, 411, 47, 351],\n [485, -580, 511, -451, 415, -306, -530, -368, -58, -605, -265, -675],\n [-185, -139, -230, -357, -138, -451, -338, 24, 452, 212, -381, -282],\n [-554, 79, -1015, -89, -322, -270, -241, -49, 505, 770, -170, 201],\n [337, -651, -64, -411, 428, -287, -710, -632, -16, -318, -191, -520],\n [-69, 450, 231, 423, -165, 408, 606, 372, -246, 27, 309, 429],\n [289, -670, -71, -513, 375, -418, -776, -582, 116, -277, -309, -609]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[555, -172, -1296, -1232, 1198, 697, 1130, 495, 1259, -241, 1553, -472],\n [-918, 388, 734, -168, -614, -152, -388, 296, -738, 113, -247, 92],\n [-19, -988, -162, 182, 57, -3, -21, 125, 425, -611, -32, -486],\n [151, 509, 103, 671, -815, -672, -909, -114, -155, -161, -843, -177],\n [387, 450, 217, -588, 627, 622, 949, -15, 1044, 628, 1096, -165],\n [1192, -144, -1200, 465, 247, 246, 642, -896, -825, 662, 397, 954],\n [-52, -336, 192, -291, 896, -448, -945, 771, -192, -885, -685, -465],\n [658, -300, -1007, -34, 844, 221, 1104, -608, 201, 521, 482, 833],\n [-693, 346, 843, -164, 226, -967, -27, -449, 991, 401, -288, 133],\n [-981, 239, 1230, -378, -621, 628, 456, 512, 973, 137, 499, -665],\n [-678, 488, 153, -45, -1142, -371, -1015, 507, 765, -920, -517, -1036],\n [670, 510, -703, -337, 662, -59, -710, 513, 264, -731, -347, -413]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-289, 1031, 126, -555, -143, 95, -838, -255, 47, 373, 263, 473],\n [1002, -416, 1389, -1147, 187, 583, 289, -980, -483, -1, 80, 1765],\n [-890, 662, -1133, 732, -260, -413, -521, 771, 406, 134, -38, -1309],\n [356, -246, 574, -160, 174, 755, -290, -6, -114, -112, 308, 780],\n [-457, 849, 218, 535, 1169, 13, -637, -106, 200, -76, 363, -288],\n [-226, 648, 673, -567, 15, 773, -808, -143, -504, 184, 138, 814],\n [-232, 803, 1007, -358, 789, 810, -804, -316, -588, 48, 65, 708],\n [-95, -108, 416, -1094, -1383, 619, -175, -103, -820, 310, -36, 1118],\n [-53, -164, -25, 78, -421, 56, -266, -74, 402, 12, 1068, 655],\n [441, 7, 477, -611, 291, 19, 416, -387, -498, 48, -917, 111],\n [633, 16, -659, -185, -290, -270, -45, 220, 756, 170, -278, -256],\n [727, -839, 400, 43, 369, -174, 738, -461, 213, -267, 271, 471]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[533, -1291, 1037, 376, -763, -390, -416, -273, 619, 1070, 319, -171],\n [-753, -257, -343, 426, -203, -408, 274, -199, 252, -475, 790, 202],\n [-486, -193, -37, 158, -848, -622, 142, -710, -381, -198, 918, 185],\n [515, -406, 244, 351, -740, -877, 258, -807, -274, -610, 453, -456],\n [121, -1473, 109, 506, 941, 651, -329, 454, 143, 898, 368, -653],\n [665, -1721, 1012, 797, -694, -310, -70, -392, -180, 1634, 450, -858],\n [143, 228, 177, 761, -1480, -392, 864, -459, 291, 77, -83, -231],\n [-269, 468, 892, -139, 1, 1005, 1127, 1431, 1180, 126, -1448, 303],\n [-360, 968, -136, -864, 1839, 1568, 606, 1715, 239, -281, -1609, 128],\n [605, 48, -1431, 310, 191, -437, -971, -1192, -41, -103, 668, -499],\n [-81, -380, 312, -124, 770, 954, 1152, 691, -411, -230, -493, -772],\n [30, 968, -501, -470, 189, 441, 524, -25, -365, -673, -540, -148]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[546, 267, -255, 416, -1154, -674, -219, 135, 748, 366, -244, -868],\n [988, 471, -402, -74, -897, 342, 457, 309, 917, 810, -99, -556],\n [-569, -584, 717, -857, 472, -240, 461, -559, -901, -442, 379, -466],\n [-30, -34, -820, 976, -401, -295, -279, 681, 282, 104, 58, -57],\n [640, -144, -798, 390, -926, 76, 97, 510, 673, 469, -148, -688],\n [234, 46, 600, -388, -436, -224, 215, -202, 385, 243, -396, -518],\n [331, -701, 254, -860, -452, 60, 256, -584, 23, 57, -364, -1078],\n [290, 709, 600, -605, 273, 592, 813, 55, 307, 555, 74, 382],\n [-18, -630, -398, 151, -396, -244, 103, 318, -317, -282, 419, -622],\n [-33, 146, 561, 354, -167, -393, -622, 110, 159, -409, -324, 457],\n [369, 562, -231, -32, 32, 134, -536, -519, 126, 4, -42, 318],\n [39, -686, 364, -313, -466, -287, -97, -318, 217, -17, -706, -805]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-341, 134, 34, 143, -37, 579, 145, 146, 667, 34, 750, 480],\n [-80, -243, -827, -617, -35, -253, 118, 292, -1017, 440, -148, 284],\n [-855, -743, -166, -1363, 46, -506, -199, 424, -1004, -60, 677, -65],\n [-199, 501, 235, 410, -752, 548, 1181, -670, 1149, 324, -282, -591],\n [-702, -444, -1126, 262, 19, -350, 515, -333, -602, 1072, 395, 1077],\n [136, -404, -864, 872, 41, -894, -235, -993, -721, 1314, -565, 218],\n [-475, -478, 20, -1332, -13, -250, -342, 535, -765, -231, 465, -328],\n [246, -45, -254, -547, 35, 104, -551, 441, -445, 89, 88, -51],\n [868, 595, 1130, -94, 241, 641, -692, 704, 748, -1354, -163, -578],\n [62, -41, -433, -102, -256, -348, 498, -290, -518, 411, -678, -262],\n [-527, -63, 48, -1046, -399, 303, 391, 346, -9, -89, 409, -389],\n [-678, 124, -675, 764, -662, 273, 1317, -973, 711, 1279, 130, 338]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[286, 38, -123, 103, 82, -488, 94, -278, -49, 260, -107, -279],\n [-606, 147, 593, 290, 213, 209, -66, -25, 670, -882, 193, 537],\n [-304, -705, -486, -125, 27, -21, 1008, -143, 41, -134, 98, -666],\n [-195, -382, -61, 511, 457, -912, 745, -764, 464, -51, -185, -645],\n [693, 406, -40, 310, 240, -1276, 167, -735, 182, 129, -40, -400],\n [91, -233, -317, -20, 71, -465, 737, -338, 128, -181, 147, -525],\n [20, 120, 30, -312, -295, 746, -582, 577, -399, 238, -14, 418],\n [-438, 439, 735, 290, 180, 171, -352, 10, 673, -924, 235, 755],\n [455, -476, -823, -437, -289, 34, 335, 148, -808, 967, -195, -735],\n [-205, -468, -146, 360, 319, -544, 519, -490, 177, 253, -286, -574],\n [-148, 214, 185, -207, -155, 462, -94, 307, 144, -596, 341, 433],\n [346, -120, -306, 144, 157, -818, 492, -517, 9, 260, -94, -622]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[330, 862, -193, 630, -68, -318, -406, -373, 810, -861, -581, -1557],\n [509, 334, 331, -665, -38, -58, 71, 362, -602, 370, -872, 370],\n [-665, 340, -102, -390, -806, 420, 146, 50, 455, 32, 34, -402],\n [502, 1035, 16, 912, 508, -175, 860, -471, 321, 124, -112, 293],\n [-785, -470, 75, -422, -418, 167, -299, -37, 90, 123, 508, 427],\n [-635, -1477, 52, -1369, -144, 334, -502, 919, -571, 570, -71, 641],\n [-366, 259, 1034, -925, -415, -311, -710, -361, -593, 406, -1115, 1337],\n [370, -92, 742, -82, -390, -108, -510, -443, -1297, -217, -999, 51],\n [126, 1229, 363, 1407, 173, -525, 82, -1402, 533, -507, -16, 112],\n [-558, -888, 111, -1078, -505, 433, -424, 631, -457, 251, -689, -153],\n [-194, -1113, 104, -639, -146, 60, -866, 397, -566, -162, -463, -353],\n [-713, -472, 116, -408, 156, 31, -179, 113, 303, 407, -92, 767]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[566, 768, 662, 263, 628, -506, 891, 138, 273, -778, -239, -371],\n [444, 165, -251, 45, 727, -745, 82, 63, -843, -589, -1421, 565],\n [-937, -535, 142, -370, -326, 1241, 86, 87, 949, 1161, 532, -838],\n [-431, 756, 319, 124, 1711, -791, 832, -722, 375, 831, -315, -266],\n [351, 333, -753, -542, 558, 43, 537, -175, 279, 95, -739, -147],\n [73, -796, -216, 135, -1479, 564, 3, 80, -428, -1000, -338, -130],\n [124, 26, -439, -52, 676, -707, -320, -232, -362, 149, -474, 571],\n [-498, -123, 564, 639, 979, -1085, 287, -559, -411, -35, -736, 136],\n [167, -330, -2139, -603, -1101, 354, 378, -1313, -297, -146, -474, 103],\n [719, 289, -498, -267, -782, 447, 1263, -350, 887, -1025, 110, -933],\n [98, 799, 1038, 87, 493, 211, 579, 445, 875, 169, 800, -680],\n [563, -60, -741, 109, -436, -640, 176, -667, -168, -875, -50, 232]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[722, 342, -282, 43, 16, -186, 72, 704, 1103, 40, 613, 536],\n [71, -108, 653, -254, -182, -942, -290, 643, -925, -566, -671, 88],\n [370, -26, -880, -176, -320, 589, -129, -376, 586, 564, -321, 72],\n [-32, -21, 746, 1286, -250, -352, -306, -510, 16, -176, 159, -746],\n [-383, 140, 761, 747, 375, -790, 701, -164, -666, -191, -188, -747],\n [293, 538, -135, 191, 406, -137, -545, 653, -100, -1034, -91, -160],\n [-73, -618, 73, -951, -580, -222, 238, -23, -402, 750, -539, 588],\n [-251, 148, -719, -399, 449, 1106, -5, -178, 496, 39, 674, 247],\n [7, 314, 307, 227, 313, -334, -493, 496, -520, -1005, -152, -253],\n [683, 306, 65, 807, -238, -256, -586, 281, 762, -346, 284, -112],\n [689, -66, -289, -87, -484, 30, -18, 263, 1236, 630, 559, 688],\n [-237, -286, -343, -942, -85, 423, -118, -14, -403, 161, -320, 409]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-68, -285, -226, -231, -708, 375, 27, -266, -639, 314, 140, 537],\n [-380, 606, 112, 452, 682, -1483, -854, -977, 233, -648, 131, -929],\n [462, -330, 7, 71, 246, -460, -603, -476, -74, -1000, 152, 272],\n [141, 1073, 688, 167, 926, 298, -90, 465, 622, -60, -318, -325],\n [430, -373, 671, 166, 669, 403, 852, 301, 317, -1282, -443, 208],\n [913, 283, -375, 359, 384, 39, -94, -435, -299, 97, 348, 1425],\n [-686, -639, -24, -777, -1482, 253, 59, -618, -833, -140, -470, -159],\n [-724, -86, -67, 28, -129, -1050, -1406, -456, -66, -197, 632, -1230],\n [-78, 62, 136, 59, 230, -758, 120, -642, 198, -834, -530, -378],\n [302, -204, 13, -210, 40, 1073, 794, 1526, 599, 763, -194, 108],\n [451, 892, 905, -190, 936, 1408, -131, 1957, 1108, 405, -268, -376],\n [222, 568, -371, 49, 188, 35, 454, 436, 497, 989, -302, 146]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-69, 1496, -771, -306, 608, 97, 388, 489, 94, 576, -580, 684],\n [-1987, -1824, 825, 442, -274, -257, 2578, 635, 2109, -233, 1099, -1487],\n [511, 1204, 237, 1103, 636, 587, -1159, 367, 1291, -2111, 72, -45],\n [436, -481, 21, -39, 1018, 85, -578, -1561, 70, 590, -1454, 1257],\n [-12, 215, 243, -152, 579, 62, -1626, -1174, -601, 485, -1079, 2013],\n [-398, -639, 1597, 392, -799, 791, 557, -682, 2028, -1085, 394, -1267],\n [-474, -731, 98, -366, 131, 718, -29, 7, 957, -416, -373, -146],\n [34, -635, 309, -1088, -957, 733, 46, -481, -581, 1050, 92, -330],\n [-676, -154, -200, -254, 1067, 628, -641, -424, -424, 1313, -84, -577],\n [433, -132, 351, -634, 166, 1594, -514, -678, 681, 407, -276, 254],\n [-274, -755, 474, -266, -176, 88, 291, -1322, 197, 683, -960, 952],\n [-950, -1583, -312, 41, -172, 286, -138, 264, 82, -630, -11, -1811]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[613, 905, 472, 215, -476, 737, 105, -164, 730, 1059, 456, 287],\n [-213, -1197, -1017, -1392, -474, 10, -379, -350, -88, 1436, -921, 256],\n [848, 1023, -188, 1095, 260, -1085, -20, 994, 305, -889, 160, 555],\n [-342, 447, 659, 1635, 15, 935, -386, -221, 286, -1135, 1530, 324],\n [755, 324, -1120, -405, 524, -625, -302, 124, -371, 965, -70, 338],\n [1054, 123, 1009, 74, 61, 65, -672, 857, -440, -881, -665, 130],\n [-869, 645, 73, 306, 940, 378, 936, -973, -474, -298, 1323, -996],\n [-307, -740, -181, 161, 161, 124, -749, 177, 224, 455, -128, 322],\n [1004, 1252, 1167, 1063, 1277, -603, -112, 572, -789, -277, 734, -677],\n [-561, 895, -635, 1035, 480, -587, 828, 254, 986, -674, 644, 189],\n [-546, 501, 363, 1295, 534, -69, 271, 362, 579, -1246, 660, -17],\n [1000, 837, 504, -765, 253, 405, 284, -352, -966, 262, 66, -556]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[173, -84, 321, -260, -578, 93, 49, -512, -120, 705, 739, -471],\n [29, 1030, 142, -423, -594, -950, -433, 164, 669, 740, 531, 29],\n [288, -1014, 261, 165, -48, 933, 414, -732, -675, 75, 384, -636],\n [435, -409, 225, 212, 52, 331, 102, -401, -144, 17, 349, -529],\n [-644, 178, -22, -646, -740, -42, 94, -82, -246, 726, 196, 324],\n [-216, 794, 102, -550, -716, -686, -270, 70, 378, 818, 472, 128],\n [9, 388, 116, -249, -382, -348, -151, -42, 219, 462, 359, -63],\n [566, 222, 65, 411, 436, -311, -240, 140, 459, -373, 10, -262],\n [246, -815, 157, 221, 110, 739, 319, -497, -507, -109, 170, -454],\n [234, 442, 376, -406, -784, -404, -188, -386, 258, 980, 950, -454],\n [110, -428, -62, 300, 396, 370, 146, -28, -204, -454, -270, -58],\n [-164, 678, 185, -587, -832, -575, -218, -96, 285, 959, 644, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[352, 1140, 684, 206, -260, -602, -336, -1133, -1004, -1148, 255, 113],\n [862, 29, -14, -1343, -273, 221, -464, -972, -21, 798, 698, -33],\n [3, -495, 313, -416, 284, 497, -258, -974, -271, -1063, 1036, 937],\n [1235, 1218, -727, 383, -1063, 250, 1309, -173, 455, 964, -973, -766],\n [-432, 768, 803, 1411, 1450, -398, 479, 1338, 158, -611, -194, -1140],\n [486, 441, -268, -651, -1388, -736, -985, -620, -74, 645, -4, 196],\n [1022, 374, -36, -693, -508, -386, -340, -669, -697, -188, 187, -284],\n [-1222, -1066, 353, 262, -32, -14, 195, 473, 697, 251, -397, 1474],\n [185, 910, 1310, -201, 740, -233, -330, -589, -670, -711, 1011, -511],\n [-388, 308, 182, -292, -346, 95, -368, 447, 796, 1110, -748, 8],\n [335, 486, 628, -639, -784, 64, -228, -641, 401, 286, -20, 691],\n [155, -157, 554, 174, 515, 182, -84, -409, -559, -1891, 1107, 358]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[16, -240, -232, -168, 544, -744, -16, 464, 8, 360, -584, -40],\n [384, -558, -213, -207, 255, -159, -333, 171, -216, 276, 60, -348],\n [154, -270, -133, -117, 216, -221, -134, 166, -83, 185, -101, -145],\n [-492, 750, 309, 291, -413, 323, 427, -293, 274, -410, 18, 450],\n [14, -108, -98, -72, 225, -304, -13, 191, -1, 151, -235, -23],\n [-16, 36, 22, 18, -42, 50, 14, -34, 8, -32, 32, 16],\n [412, -570, -199, -201, 203, -73, -357, 123, -234, 250, 142, -370],\n [-612, 816, 264, 276, -226, 4, 530, -118, 350, -322, -294, 546],\n [462, -402, 21, -51, -356, 725, -398, -362, -281, -101, 801, -387],\n [-438, 450, 51, 99, 168, -453, 378, 198, 261, -15, -573, 375],\n [238, -204, 14, -24, -191, 384, -205, -193, -145, -57, 421, -199],\n [-516, 702, 237, 243, -225, 51, 447, -129, 294, -294, -210, 462]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[162, -540, 99, -225, 551, 79, 126, 3, 200, -448, -104, 140],\n [-207, -144, -57, 357, 323, 262, 117, -444, -271, -277, -593, -148],\n [45, 36, 12, -78, -76, -59, -27, 99, 59, 65, 133, 32],\n [264, -876, 161, -367, 893, 127, 204, 7, 326, -726, -166, 228],\n [-180, -252, -39, 321, 437, 283, 144, -453, -238, -370, -626, -124],\n [-150, 348, -79, 221, -323, -7, -66, -83, -188, 260, -36, -124],\n [-63, 144, -33, 93, -133, -2, -27, -36, -79, 107, -17, -52],\n [-303, 96, -109, 497, 95, 250, 69, -488, -391, -93, -601, -228],\n [-90, -72, -24, 156, 152, 118, 54, -198, -118, -130, -266, -64],\n [-93, 84, -38, 148, -38, 53, 3, -121, -119, 27, -137, -72],\n [33, -420, 46, -20, 494, 151, 129, -163, 35, -407, -291, 40],\n [-171, 792, -123, 219, -855, -180, -207, 114, -207, 699, 303, -156]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-571, 756, -661, 37, -64, 51, 316, -335, 458, -277, 982, -167],\n [-650, -963, -370, 467, -1855, 81, -104, -937, -734, 1047, -790, -191],\n [175, -1137, 318, -202, -1392, -332, -597, -737, 201, 1426, -242, -158],\n [-847, 124, -1141, -57, 545, -151, -216, 1247, -110, 221, 439, -429],\n [-1493, 653, -454, -298, 130, -149, -300, -254, -301, 224, -706, 129],\n [208, 54, 735, 122, 68, 359, -368, -968, -249, 101, -962, 341],\n [-849, 200, -765, -59, 219, 127, -1585, -391, 403, 966, -462, -234],\n [-332, 356, -95, -126, 467, 44, 68, 229, -338, -684, -446, -283],\n [-805, -610, -853, -6, -324, -5, -363, 493, -643, 592, -198, -1067],\n [1332, -1092, 806, 634, -617, 293, 789, 135, -744, -146, -297, 235],\n [-422, 631, 171, -1013, 894, -427, -943, -2, 617, -324, -437, -479],\n [611, -359, 843, 222, -81, 169, 1141, 159, -958, -709, -433, 149]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-57, 160, -114, 108, 35, -320, 418, -74, 121, 381, 107, -75],\n [38, -186, 117, -166, -71, 375, -503, 99, -131, -446, -119, 16],\n [-224, 316, -577, -121, 73, -558, 394, -106, 327, 526, 225, -686],\n [-99, 272, -437, 35, 160, -492, 406, -134, 248, 469, 176, -347],\n [-314, 130, -392, -387, -194, -199, -13, 57, 216, 168, 134, -870],\n [-180, 368, -190, 238, -14, -752, 1056, -144, 278, 944, 258, -208],\n [-215, 74, -404, -369, -81, -75, -231, 43, 163, -27, 79, -729],\n [235, -438, 162, -299, 71, 909, -1339, 159, -325, -1177, -313, 233],\n [342, 28, -235, 277, 557, -6, -226, -190, -29, -196, -59, 512],\n [-154, -6, 197, -60, -287, -31, 239, 85, 1, 174, 33, -144],\n [-23, 360, -494, 216, 317, -668, 634, -226, 287, 651, 213, -165],\n [-419, 166, -301, -394, -356, -297, 235, 89, 246, 367, 180, -971]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -743, 745, -106, -698, -1864, -495, 330, -331, -417, -574, 1558],\n [408, 820, -1131, -302, -766, 420, -462, -239, -135, 302, 909, -209],\n [1492, -1065, 330, 177, -527, 113, -72, 425, -647, -86, 130, -162],\n [-1547, -148, 914, -277, 82, -1211, -633, -774, 334, -911, -961, 390],\n [471, 342, -326, 294, -864, -625, -701, 183, 410, 532, 1167, -848],\n [92, -553, -651, -274, -709, 304, -93, -816, -94, -136, 111, -203],\n [910, -351, -678, 463, -253, 1090, 841, 365, -1079, 901, 312, -124],\n [1048, -1252, -374, 12, 482, -702, 710, 164, 1300, -318, 270, -590],\n [-777, -931, -225, 50, -918, 1076, -76, -1039, -728, -415, -1272, 361],\n [917, 11, -366, 667, -243, 1223, 640, 510, -729, 766, 612, -714],\n [1161, 697, 274, -25, -825, 447, -444, 1503, -1145, 335, 571, 1170],\n [-152, -261, 376, 237, -574, 1274, -232, 135, -159, -282, -703, 265]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[537, -218, -322, -289, 155, 370, 175, 67, 194, 26, 28, -164],\n [51, 70, 302, 77, 203, 64, -239, -17, 116, 188, -176, -164],\n [-741, 202, 82, 285, -419, -542, 37, -67, -374, -238, 156, 388],\n [-102, 58, 122, 74, 5, -65, -80, -17, -19, 29, -38, 4],\n [582, -32, 400, -78, 592, 466, -386, 20, 430, 446, -372, -512],\n [-189, -108, -564, -111, -438, -189, 459, 24, -267, -387, 354, 360],\n [-258, -28, -332, -14, -350, -220, 290, 2, -236, -284, 248, 296],\n [-381, -26, -434, -3, -485, -320, 385, -1, -332, -388, 336, 412],\n [456, -170, -218, -228, 163, 319, 106, 53, 181, 53, -6, -164],\n [393, -8, 320, -37, 428, 319, -299, 10, 305, 329, -278, -368],\n [0, -132, -484, -152, -274, -42, 372, 34, -142, -270, 260, 216],\n [-357, -28, -420, -7, -462, -301, 371, 0, -315, -371, 322, 392]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-334, 426, 267, 471, -160, 768, -611, 724, 72, -627, -340, 305],\n [-314, 858, -255, -425, 920, -834, -165, 142, 431, -307, -733, -131],\n [112, -157, -228, 33, 45, -88, -151, -209, 210, 138, -585, -4],\n [404, 637, 42, -835, 1461, -854, -561, 450, 561, -147, -1209, 162],\n [1170, -362, -506, -378, -138, -42, -54, -575, 856, 683, -421, -962],\n [-315, 461, 226, -33, 336, -29, -183, 461, -76, -399, -46, 253],\n [620, -638, -424, -214, 34, -352, 54, -690, 314, 652, -628, -224],\n [320, -318, 57, 607, -940, 1194, -367, 165, 192, -42, 47, -201],\n [-584, 297, 265, 188, 409, 2, -386, 510, -258, -494, -540, 763],\n [287, -51, 427, -182, 300, 161, -244, 450, -145, -81, 20, 372],\n [-30, 246, 63, -247, 560, -342, -187, 202, 73, -125, -427, 219],\n [231, 118, -187, -113, -325, 29, 325, -237, 233, 163, 621, -722]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1355, -111, -292, -444, -352, -1268, 1490, 346, 1356, -2125, -848, 606],\n [390, -158, 375, -909, -38, 214, 349, 915, -205, 1041, 533, 347],\n [-976, 694, 80, -462, 633, 173, -1019, 667, -1424, 2131, 1037, -649],\n [355, -218, -311, -430, -1501, 193, -632, -370, -425, 1005, -1096, -976],\n [-15, 574, -42, 391, -1665, 342, -246, -444, 1113, -365, -1067, 647],\n [670, -170, -180, -1591, 451, -638, -607, 25, -163, 430, 856, -924],\n [-558, -754, 902, 996, -871, 1376, -90, -578, -329, 653, -219, 693],\n [1712, -265, -960, -1549, -49, -509, 393, 309, -189, -77, -344, -1274],\n [392, -1696, 1238, -815, 1301, 152, 585, -449, -1015, -328, 1666, -114],\n [-152, 467, 1244, 1643, 861, -361, 668, -27, 842, -814, 536, 1884],\n [58, 483, -57, 546, 57, -442, -194, -688, 134, -998, -20, 9],\n [693, -250, 436, -549, 865, -1531, 220, -604, 701, -1609, 568, -69]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1756, -355, -245, -255, -197, 746, 321, 1072, 774, -428, -158, -8],\n [-219, -966, 350, 287, 708, -494, 534, 819, -475, 1323, 118, 767],\n [206, 748, 976, 852, -1661, -789, -1351, 1530, 556, 459, -270, 363],\n [463, 98, -195, -475, 604, -229, 404, -294, -1361, 423, 818, -193],\n [267, 380, 469, 859, -601, 15, -1233, -397, -484, -544, -1527, -572],\n [-639, -368, -75, 1204, -249, 1451, -577, -560, 1719, -627, -133, 194],\n [366, 253, 112, -1632, -723, 1434, 1137, -212, 912, -672, 601, -847],\n [-1417, -109, 253, 1151, 301, -59, -595, 180, -355, -293, -799, -134],\n [-134, 574, 313, -352, 249, -402, -830, -247, -277, -453, -7, 241],\n [-569, -769, 1580, 702, 250, -594, 85, -390, 343, 357, -1242, 244],\n [-258, -625, 506, -479, -764, -321, 524, -157, -405, 741, 244, -178],\n [-715, 344, 88, 2227, 850, -513, -2012, -793, -220, -156, -445, 767]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-154, 327, -212, 105, 659, 163, 526, -884, 346, 619, 943, 701],\n [-414, 455, -500, 1807, 178, -793, 599, -1694, 418, 538, 284, 21],\n [552, 399, -789, -960, -579, -5, 407, 1081, -1117, 226, -209, -48],\n [333, -270, 359, 412, -850, -140, -520, 641, -104, -351, -687, -606],\n [-684, 185, -1076, 156, 150, -1008, 363, -218, -741, -531, -1119, -661],\n [880, 249, -597, 368, -1087, 252, 94, 518, 344, -605, -392, -149],\n [193, 469, -220, -258, 280, 565, 568, -610, 699, -156, 797, 444],\n [5, 37, -471, -22, -40, -362, 117, 307, -735, 616, -122, 167],\n [280, 356, -230, 661, -199, 199, 353, -676, 777, -178, 374, 152],\n [441, -48, 189, 746, -434, 220, -164, -113, 588, 117, 223, 194],\n [-19, 226, -750, 179, 458, 119, 446, -553, 392, 239, 446, 740],\n [34, 233, -399, 223, 408, 66, 410, -515, 96, 832, 759, 784]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[373, -1332, -157, 749, -446, 634, 214, 188, 409, 208, 684, -941],\n [783, -305, -383, 916, 179, 385, -340, 136, 775, 450, 766, 206],\n [56, -1147, -545, -122, -436, 457, 1235, -16, 4, -140, 220, -719],\n [226, 88, 405, 504, 228, -374, -594, 624, 134, 835, 181, 156],\n [-847, -759, -155, -253, -790, 845, 49, -1080, -531, 219, 115, 366],\n [-363, 245, 894, 646, -431, 149, -1810, -492, 153, 541, -409, 304],\n [599, 50, -198, 590, 289, 105, -740, -5, 837, 872, 178, 819],\n [513, 970, -76, -239, 994, -755, -647, 405, 619, 959, -365, 1441],\n [135, 482, -60, 537, -123, 84, -612, -404, 341, 608, -233, 935],\n [-432, -427, -332, -842, 197, 324, 128, -447, -286, 232, 333, 657],\n [10, 924, 1186, -175, 314, -961, -977, 677, 113, -861, -1057, -1091],\n [-788, -408, 293, -927, -371, 413, -777, -1073, 47, -55, -878, 281]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[278, 487, 1093, -878, -1013, 973, 288, 1320, 638, 589, 375, 625],\n [-598, -585, 577, -197, -261, 1520, -385, 1639, 574, 417, 179, 1113],\n [58, -144, 669, -1201, 441, 242, -776, 265, 709, 329, -83, -203],\n [-60, 1382, 1108, -642, 1423, -234, 493, 51, 1176, 1490, 871, -663],\n [-207, -606, 993, 1405, -1444, 844, -1364, 852, -1380, -1369, 587, 639],\n [-624, -873, 724, -239, -18, 455, 141, -202, 262, 1027, -499, 973],\n [-766, -200, -319, 1527, -169, -316, -141, -1206, -740, 94, 138, 571],\n [-525, 1045, 46, -147, -1437, -189, 1052, 637, 364, 266, -413, 228],\n [-927, -877, -64, 156, -528, 348, 538, 17, 913, -369, -387, 491],\n [-285, -849, -1090, 465, -179, -1904, -1179, 463, -1081, -123, -1313, 880],\n [-1119, -253, 775, 794, 1464, 595, 450, -452, 1249, 324, 958, -251],\n [-881, -1534, 584, -179, 20, 746, 442, -163, 1153, -103, -389, 453]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[5, -316, -88, 319, 1726, -38, 1781, 18, 270, -672, 1948, -314],\n [778, -74, -879, -224, 1273, 437, 394, 254, -49, -678, -390, -255],\n [-907, -666, 217, -681, -550, 1401, -185, 1643, -437, -131, 390, 513],\n [-620, -996, -136, -1783, 1638, 227, 459, 194, 157, -640, 1421, -379],\n [632, 296, 206, -218, -225, -725, -609, -187, -220, 258, -951, 143],\n [263, -178, -787, -212, 1167, -127, -130, -266, 442, -550, 144, -370],\n [246, 629, -693, 260, -242, 757, 480, 1030, -476, -156, 934, 42],\n [-34, 395, -632, -1065, 193, -56, -974, -404, 524, 429, -594, -943],\n [714, -34, -501, 670, 1749, 322, 1210, -149, 379, -1006, 568, -714],\n [763, 737, -1058, 1378, -391, -775, -539, -2021, 562, 325, -1865, -203],\n [586, -371, -713, -1183, 1785, 53, 486, -226, 29, -566, -218, -478],\n [727, 111, 146, 628, 400, -108, 272, 13, -190, -839, 291, -91]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-200, -559, 531, -500, 261, -1078, 999, 714, -1323, 3, -944, 762],\n [1133, 55, -109, -221, -563, 94, 787, -1187, 1243, -740, -1055, -237],\n [-508, 372, -1471, 582, 235, 133, -148, -170, -8, 1197, 237, -1623],\n [943, 411, 627, 444, -306, -234, -1753, 952, 990, -965, -21, -61],\n [869, 599, 246, 906, 146, 233, 465, 28, 1442, -1080, -761, 537],\n [206, 606, 54, 761, 1439, -89, -427, 1163, 721, -55, -511, -895],\n [441, -681, -30, -1184, -1337, -225, 1333, -1701, 252, -746, -1237, 873],\n [-424, 952, 807, -1106, -1708, 267, -455, -1240, -406, -936, -9, 373],\n [594, 345, 666, 428, -195, 336, -1582, 77, 807, -618, 464, 364],\n [-783, 129, 616, -582, -506, 886, -2310, 422, -553, 266, 2211, -316],\n [497, -1, 952, -378, -894, 404, -1616, 213, 1117, -1428, -364, 751],\n [46, -1285, -898, -918, -133, 860, 183, -976, 197, 1083, 1376, -1074]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-80, 746, 21, -223, 820, -87, 1059, 415, -118, 877, 619, -941],\n [819, 590, 721, 264, 215, -137, 379, 12, -579, 304, 245, -338],\n [33, -26, -32, 187, -111, -91, -354, -147, -73, -210, -2, 362],\n [-314, -567, 175, 341, -589, -40, -534, -196, 383, -472, -545, 618],\n [-820, -223, -11, 125, -31, -88, 240, 164, 621, 158, -195, -20],\n [-1172, -1192, 62, 202, -880, 102, -362, -30, 1188, -494, -1054, 550],\n [-52, -1064, 588, -4, -992, 342, -180, -80, 588, -506, -1140, 134],\n [531, 328, 453, -64, 185, 47, 517, 126, -305, 328, 109, -538],\n [-125, 487, -37, 334, 358, -320, 0, -11, -162, 199, 441, 161],\n [538, 584, -205, 27, 390, -138, -185, -119, -650, 50, 589, 88],\n [483, -408, 298, 135, -579, 117, -562, -277, -141, -536, -452, 432],\n [-1231, -898, 287, 388, -663, -55, -55, 68, 1171, -212, -885, 382]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-813, -90, -431, 57, -677, -994, 135, -121, -629, 220, -497, -85],\n [-104, 84, 355, 689, -330, -411, -265, 330, -92, -656, -136, -328],\n [98, 664, 30, -216, -794, -810, -412, -266, -634, 272, -130, -744],\n [219, -182, 286, 308, 419, 299, -82, 213, 301, -446, 137, 241],\n [483, 340, 306, -67, 12, -221, -440, -109, -166, -115, 132, -195],\n [329, 564, 279, 88, -484, 208, -199, 115, 88, -47, 150, -817],\n [285, 480, -243, -792, -264, 60, -27, -441, -216, 801, 126, -363],\n [190, -334, -338, -735, 774, 389, 223, -392, 110, 566, 170, 809],\n [-607, -276, -198, 331, -263, -310, 235, 161, -105, -132, -289, 66],\n [531, 736, -78, -829, -373, -148, -297, -513, -371, 760, 173, -572],\n [610, 598, 29, -614, -144, 742, -10, -202, 246, 582, 374, -607],\n [785, 484, 344, -435, 174, -899, -868, -499, -668, 37, 118, 49]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[859, -632, -202, 1170, -966, -1282, 611, 720, 277, 417, -26, 31],\n [731, -696, 878, -74, -627, 26, -511, -301, -237, -12, 898, 91],\n [-84, 102, -312, -548, 240, 676, 114, 262, 356, -344, -1016, 678],\n [-408, 218, -208, -323, 351, 1176, 261, 455, 405, -3, -1583, 881],\n [158, -7, 446, 11, -529, 501, -242, 17, 74, 37, 20, 277],\n [-220, 315, 1169, -495, -34, 155, 108, -1104, 117, -664, 973, -930],\n [658, -303, 1152, 69, -957, 63, 764, -293, 704, -799, 378, -205],\n [-1147, 716, -853, 434, 910, 169, -448, 239, -664, 1080, -374, -178],\n [-380, 388, 299, -1008, 639, 222, 61, -847, 134, -860, 283, -514],\n [-46, -427, 195, 349, 7, -22, -1298, 66, -932, 1491, 136, 307],\n [-221, 865, 714, -1142, 8, 95, 549, -1298, 633, -1902, 1145, -1164],\n [442, -317, 291, 31, -557, 273, -479, 115, -132, 128, 271, 403]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[15, -1390, -168, 1254, 422, 1660, 821, 554, 609, -691, -1026, -1569],\n [6, -1097, 248, 758, -1307, 524, -2, 1914, 209, -1342, 1219, -953],\n [37, 519, -747, 851, -1557, 795, -848, 308, 706, -1550, 831, -372],\n [1025, -286, -735, -513, 153, 89, -132, -18, -136, 587, 805, -461],\n [-1061, 626, -606, -787, -24, -967, 947, -699, -272, 278, 570, 239],\n [-854, 348, 780, -1324, 1067, -1309, -128, -991, -432, 1249, 172, -20],\n [-182, -410, -854, -1098, -456, -1029, 536, -411, -262, 163, 347, -325],\n [472, -954, 252, 606, -931, 168, 700, 1078, 392, -871, 435, -205],\n [-223, -792, -642, 6, -36, 64, -271, -210, -798, 158, -347, -2],\n [-409, 1044, 509, 751, 978, 307, -197, 690, -769, 453, 441, 76],\n [-642, 501, -162, -1026, 1230, 58, -2211, -294, -1610, 1543, 300, 250],\n [622, 797, -1258, -319, -680, 89, -348, 425, -271, 591, 611, 799]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[265, -615, -143, 283, -79, 914, -1092, -479, 733, -2419, 104, 196],\n [-301, 212, 660, 157, -900, 45, 206, -351, -49, 86, 884, -1184],\n [330, 366, -485, 313, -915, 762, -484, -532, -54, -321, -533, -233],\n [-689, 1237, 1654, 221, -1839, -676, -99, -1284, -391, 287, 593, -1030],\n [55, -99, -471, -411, -2, 537, -1450, 1049, 22, -429, -196, 1498],\n [156, 793, 488, 965, -1472, 905, 168, -405, -172, 1190, 605, -857],\n [-86, -171, 139, 45, 106, -250, -6, 1009, 338, 890, 579, 378],\n [-574, 306, 9, -360, -483, 344, 436, -301, -997, 1116, -820, 285],\n [-243, -233, -330, -904, 1174, -1036, 800, 614, -507, 738, -269, 69],\n [-120, -457, -646, -714, 1069, -645, 217, 1088, -84, 717, -555, 990],\n [676, 139, 182, 419, 1184, -1316, 449, 171, 714, 66, 439, -136],\n [-847, -178, 477, -17, -1318, 365, 753, -427, -247, 770, 315, -1138]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[588, 660, -285, 660, 96, 48, 99, -81, -273, -510, -438, -354],\n [-1010, -1110, 77, -264, 169, -337, 420, 173, -532, 105, 654, -499],\n [-57, 913, 13, 1150, -333, 0, -491, -525, -379, -764, -924, -849],\n [-232, -804, -445, -404, 574, -532, 1097, 764, -648, 120, 1093, -326],\n [61, 171, -87, 506, -1, -126, 507, -121, -429, -738, -100, -653],\n [-127, 79, -24, -34, -46, -147, 13, 106, -27, 43, 122, -54],\n [677, 595, -395, 716, 287, 283, -568, -105, -237, 22, -748, -83],\n [30, -274, 262, 382, -24, 577, -571, -663, 37, -130, -779, -20],\n [462, 318, 56, 162, -125, 54, 624, -159, 64, -723, -65, -143],\n [495, 229, -478, 172, 407, -45, 19, 351, -257, 214, 11, 29],\n [649, 819, -745, 358, 433, -216, -343, 594, -298, 468, -85, 51],\n [-630, -738, 61, 240, 165, 31, -116, -199, -504, -15, -78, -503]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[120, 75, -90, 30, 120, 10, 20, 85, -40, 90, 100, -125],\n [-480, -300, 360, -120, -480, -40, -80, -340, 160, -360, -400, 500],\n [72, 45, -54, 18, 72, 6, 12, 51, -24, 54, 60, -75],\n [264, 165, -198, 66, 264, 22, 44, 187, -88, 198, 220, -275],\n [-24, -15, 18, -6, -24, -2, -4, -17, 8, -18, -20, 25],\n [-456, -285, 342, -114, -456, -38, -76, -323, 152, -342, -380, 475],\n [-48, -30, 36, -12, -48, -4, -8, -34, 16, -36, -40, 50],\n [72, 45, -54, 18, 72, 6, 12, 51, -24, 54, 60, -75],\n [-72, -45, 54, -18, -72, -6, -12, -51, 24, -54, -60, 75],\n [72, 45, -54, 18, 72, 6, 12, 51, -24, 54, 60, -75],\n [-528, -330, 396, -132, -528, -44, -88, -374, 176, -396, -440, 550],\n [-552, -345, 414, -138, -552, -46, -92, -391, 184, -414, -460, 575]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-182, 63, 147, -42, 119, 63, -168, -49, 84, 168, 133, -168],\n [-390, 135, 315, -90, 255, 135, -360, -105, 180, 360, 285, -360],\n [598, -207, -483, 138, -391, -207, 552, 161, -276, -552, -437, 552],\n [-156, 54, 126, -36, 102, 54, -144, -42, 72, 144, 114, -144],\n [104, -36, -84, 24, -68, -36, 96, 28, -48, -96, -76, 96],\n [234, -81, -189, 54, -153, -81, 216, 63, -108, -216, -171, 216],\n [-182, 63, 147, -42, 119, 63, -168, -49, 84, 168, 133, -168],\n [442, -153, -357, 102, -289, -153, 408, 119, -204, -408, -323, 408],\n [-182, 63, 147, -42, 119, 63, -168, -49, 84, 168, 133, -168],\n [468, -162, -378, 108, -306, -162, 432, 126, -216, -432, -342, 432],\n [234, -81, -189, 54, -153, -81, 216, 63, -108, -216, -171, 216],\n [494, -171, -399, 114, -323, -171, 456, 133, -228, -456, -361, 456]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-303, 832, 370, 268, -793, 904, -502, 741, -281, -954, -91, 141],\n [-590, 362, 674, 212, -762, -1247, 98, 275, -371, -37, -481, -1142],\n [-84, -60, -86, 266, 15, -149, 544, -182, 44, 218, 240, 730],\n [130, -805, -4, 12, 657, -777, 857, -836, 91, 953, 446, -217],\n [239, 270, -276, -546, -317, -656, -1064, 455, 62, -315, -1221, -1294],\n [-454, 481, 918, 122, -258, 1402, 447, -240, -807, -307, 940, 529],\n [1252, 265, -858, 228, -443, 666, 467, -677, -193, -163, -611, 160],\n [111, 531, 386, 500, -459, 1738, 563, -245, -584, -533, 735, 786],\n [615, -788, -1001, 47, 527, -1294, -20, -92, 894, 571, -572, -290],\n [289, 404, -121, -213, -477, -264, 168, -366, -462, 21, -674, -286],\n [-971, -176, 332, 376, 31, -1227, 198, 570, 393, 258, 286, 492],\n [-961, 537, 1288, -718, -314, -235, -107, -161, -1081, 82, 61, -831]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[514, 259, 213, 250, 143, -131, 141, -961, -66, -490, 1028, -768],\n [871, 1041, -977, -430, 1353, 373, -222, -340, -1569, -817, 112, -981],\n [-513, 208, 602, 729, 193, -187, 182, 46, -130, 7, -505, -398],\n [443, 337, -652, -457, 130, 1025, -250, -123, -487, -1111, 150, -350],\n [678, -81, -238, -389, -73, -523, -5, 233, 116, 1499, -872, 401],\n [-575, 454, 856, -225, 76, -686, 747, 382, -103, -28, 422, -160],\n [-912, -990, 64, 604, -824, 595, -543, 341, 827, -260, -377, 734],\n [-1199, -584, 290, 150, -354, -302, -522, 602, 21, -614, 594, 298],\n [1011, 713, -777, -450, 621, 709, -30, -356, -765, -449, -240, -577],\n [-227, -319, 1267, 260, -1302, -124, 503, -264, 1146, -2, 463, -101],\n [592, 298, -22, -386, -120, 250, 295, -335, 56, -193, 322, -247],\n [140, -381, -493, -604, 159, -986, -277, 711, -65, 1599, -535, 909]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-545, 549, -154, -348, 454, 409, -289, 195, -98, 68, -673, 153],\n [269, 89, 228, -112, 139, -301, -261, 174, 406, -177, -132, -317],\n [228, 194, 245, -249, 66, -122, 169, 165, -437, 460, -299, -222],\n [-343, 535, 161, -269, 663, 101, -308, 605, 289, 213, -669, 85],\n [545, 121, 107, -397, -215, -312, -346, -362, -14, -444, -207, -751],\n [97, -209, 162, 276, 67, -216, 53, 259, 437, 18, 276, 115],\n [-117, 255, 252, -60, 462, -72, -71, 574, 263, 317, -325, 97],\n [475, 173, 268, -342, -35, -310, -99, -15, -169, 48, -282, -555],\n [-24, -300, -48, 348, -54, -96, -64, 14, 556, -314, 418, 176],\n [750, -636, 243, 325, -662, -452, 669, -275, -479, 352, 745, -204],\n [-262, -32, -157, 97, -15, 233, 149, -39, -192, 128, 62, 284],\n [580, -446, 552, 390, -155, -516, 784, 459, -270, 919, 505, 72]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[1079, 375, 463, -378, -10, 897, -1189, 981, 1501, -239, -295, 1574],\n [-61, 778, 195, -1025, -380, 198, 582, -913, 106, -1645, 251, -60],\n [-75, -5, -228, 1794, -315, 540, -806, 1481, 476, 1071, -69, 947],\n [-180, 99, 824, -373, 1067, 720, 827, 242, 293, 155, -305, -13],\n [103, -254, 646, -88, 814, -727, -324, 802, -124, 913, -906, -289],\n [338, -449, 667, -636, -582, -277, -238, 56, 1217, -1031, 966, 943],\n [698, 1516, 309, -403, 55, -216, -391, -563, -517, -735, 147, 3],\n [1358, 1176, -973, 563, -515, 1289, -1504, -56, 203, 82, 318, 1171],\n [-478, -1863, 75, -924, -413, 230, 257, 608, 1650, -394, -430, 521],\n [-382, -1024, -54, -203, 38, 1334, 502, 572, 1337, -6, -219, 699],\n [-413, 507, -286, 95, -526, -598, 13, -164, -585, -467, -458, -521],\n [455, 356, 130, 774, 49, -440, -678, 266, -336, 596, 487, 232]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1299, 88, -175, -302, -182, -530, -1079, -549, 1277, 203, -625, 749],\n [743, 6, -97, 1207, 936, -1103, 27, 315, 388, 552, 739, -345],\n [-49, -1354, 521, -79, 875, 28, -422, 869, -649, -87, -110, -533],\n [-1432, 961, 259, -487, 380, -539, -76, -37, 1068, 6, 295, 88],\n [-204, -129, -109, 191, 285, -205, 281, 173, -692, 400, -39, 223],\n [-123, -884, 431, -1024, 937, -313, 144, 525, 482, -240, -91, -338],\n [742, 283, -192, -754, -105, 934, -318, 1231, 90, -728, 864, -671],\n [-135, -254, 1387, 476, -802, -679, -1494, -37, -1234, -181, -47, 1051],\n [649, 800, -26, -1041, -5, -387, -47, -49, 969, 118, 807, -246],\n [-1424, -566, -272, 552, -298, 766, -23, -168, -541, -550, -1502, 309],\n [732, -429, -81, 417, -906, 182, -645, -562, -1200, 188, -141, 511],\n [988, -27, -474, 28, -490, 1359, -693, 72, -264, -48, 1413, -967]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-560, 8, 82, 158, 470, -337, -171, -23, 141, -394, 851, 245],\n [21, 37, -123, -62, 58, 950, -20, -410, -782, 339, 8, 539],\n [139, 43, 155, 54, -242, -930, 120, 446, 770, -179, -260, -743],\n [-414, -106, 108, 128, 332, -968, -154, 302, 734, -612, 604, -152],\n [99, 199, 203, 104, -260, -679, 183, 317, 493, 13, -197, -716],\n [401, -467, -319, -296, -92, 331, -147, -1, 15, -89, -575, 364],\n [-378, -164, -83, 18, 436, 92, -229, -147, -95, -313, 600, 543],\n [-426, -90, 0, 78, 414, -183, -189, -45, 87, -360, 657, 333],\n [307, 95, 117, 6, -382, -544, 188, 326, 474, 75, -506, -695],\n [187, -473, -171, -178, 10, -612, -176, 346, 734, -501, -286, -43],\n [95, -629, -337, -260, 232, -29, -327, 71, 303, -503, -107, 562],\n [118, 310, 170, 96, -272, -66, 222, 50, -46, 310, -206, -464]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[41, 143, -186, -371, 52, 759, 7, 114, -124, -221, -227, 399],\n [-394, -364, 255, 235, 91, 120, -170, -111, 53, 52, 298, 138],\n [13, -41, 72, 167, -34, -393, 11, -48, 58, 107, 89, -213],\n [516, 542, -433, -523, -81, 322, 216, 209, -143, -202, -512, 76],\n [-118, -118, 90, 100, 22, -30, -50, -42, 26, 34, 106, 6],\n [297, 325, -269, -344, -39, 281, 123, 133, -97, -143, -319, 95],\n [-319, -183, 37, -178, 139, 917, -149, 19, -83, -187, 33, 551],\n [-308, -372, 332, 472, 20, -548, -124, -172, 140, 220, 396, -236],\n [252, 240, -174, -174, -54, -24, 108, 78, -42, -48, -204, -60],\n [540, 548, -424, -484, -96, 196, 228, 200, -128, -172, -500, 4],\n [128, 150, -131, -181, -11, 194, 52, 67, -53, -82, -156, 80],\n [395, 261, -98, 107, -152, -883, 181, 10, 64, 161, -105, -547]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[542, -199, 534, 77, -463, 275, 236, -730, -558, 69, 378, 450],\n [560, 2, 1010, -378, -988, 1154, -956, 238, -333, -304, 345, -772],\n [650, -1434, 28, 577, -750, 660, 695, -522, -483, -96, -610, 110],\n [515, -506, -545, 530, -204, -181, 1127, -396, 109, -210, 132, 639],\n [-10, 1030, 743, -1027, 116, -49, -1704, 714, 266, -468, -92, -1036],\n [-279, -227, -822, 765, 235, -287, 1809, -1344, -347, 504, 625, 1913],\n [-524, 988, -314, -182, 989, -1129, -678, 1270, 694, -145, 63, 116],\n [-1698, -416, -1227, 593, 958, -143, 477, 408, 183, 721, -803, 518],\n [-1012, 67, 175, -468, 313, 452, -1020, 238, -141, 351, -797, -810],\n [-731, 394, -111, -50, 383, 8, -115, -354, -297, 221, 99, 985],\n [448, 151, 220, -936, -281, 205, -795, -94, 418, -703, -763, -1636],\n [1519, 294, 146, 73, -468, -576, 302, 378, 477, -943, 786, 227]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[374, -410, 360, 1269, -1357, 378, -293, 112, 89, -5, 595, 327],\n [-1720, -652, 420, -960, 1552, -1000, -150, -64, -144, 355, 850, -172],\n [40, -28, -205, -742, 557, -917, 262, 35, 315, -1356, -1392, -703],\n [-329, 518, 226, -914, 851, -140, 1821, -410, -293, 747, -877, -353],\n [1142, 864, 325, -612, 535, 14, -26, 188, 327, 244, -359, 21],\n [-597, -692, 106, -612, 1244, -265, -247, -265, -144, 655, 872, -960],\n [298, -886, -541, 1404, -1794, 557, 1596, 328, 343, -1047, -1042, -1158],\n [-1469, -991, -519, -315, -7, -641, -1870, -542, -682, -5, 471, -69],\n [-372, -436, 325, -1438, 1654, -1468, 236, 474, 483, -1358, -777, -965],\n [-886, -355, 599, 757, -870, -484, 621, -665, -266, 15, -680, -126],\n [697, 16, -156, -225, -232, -361, 342, -131, -151, 670, -832, 111],\n [-404, 374, 971, 215, 100, -423, -561, -130, -192, 1380, 949, 1578]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-875, -328, -551, -190, 1181, 461, 341, 688, -51, 1116, 381, 103],\n [365, 675, 719, 466, 758, 80, 603, 982, -824, -115, -1039, 169],\n [-603, -1366, -176, 96, -113, 295, -1337, 246, 907, -566, 1312, 844],\n [-1046, -320, -223, -322, 136, 543, -772, 23, 125, 20, 1327, 164],\n [-218, 292, -204, 274, -458, -198, 1129, 601, 288, 1639, -768, -39],\n [-540, 878, -62, -670, -282, 481, 454, -480, 982, 1236, 595, 498],\n [1436, 334, 781, 572, -733, -236, 15, -175, -482, -1504, -1145, -129],\n [899, 7, 407, -101, 129, -128, -166, -403, 1035, -550, -177, 979],\n [-486, 709, 536, -194, -206, 151, -39, -231, -81, -15, 246, -48],\n [478, 399, 2, -191, 555, -140, 559, -231, -46, 197, -543, -57],\n [-580, -56, 148, 60, 785, -398, -595, 493, -936, -400, 352, -242],\n [550, -141, 417, 264, -524, 612, -705, -208, -524, -1691, 135, -134]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-159, 182, -93, -290, -466, 490, -107, -277, 274, -405, -503, -70],\n [364, -175, -340, -272, 102, -285, -269, 183, -332, 411, 479, 25],\n [-149, -151, 681, 988, 700, -511, 586, 270, 38, 210, 166, 115],\n [4, -198, 444, 756, 788, -686, 414, 370, -248, 426, 558, 110],\n [-94, 79, 30, -52, -250, 277, -1, -153, 232, -237, -373, -25],\n [19, 151, -471, -673, -240, 156, -361, -100, -288, -60, 269, -90],\n [-150, 176, -178, -326, -92, 122, -116, -94, -168, -150, 152, -70],\n [-375, 314, 75, -224, -778, 892, -5, -505, 670, -801, -1109, -100],\n [195, -208, 217, 358, -114, 60, 109, 11, 422, 51, -519, 80],\n [150, -31, -94, -209, -758, 644, -188, -307, 666, -339, -1030, -10],\n [1014, -580, -550, -317, -188, -295, -539, 278, -42, 786, 119, 125],\n [1005, -472, -849, -743, -286, -239, -758, 233, -284, 765, 376, 65]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[656, 72, 52, 1266, 76, 953, -32, -408, -479, -518, 99, 1128],\n [-589, 95, 476, -968, 226, 239, -514, 383, -273, 849, 479, -275],\n [-358, 613, 267, -428, 324, -1, -64, -251, -393, 948, 489, -263],\n [59, 427, -199, -1212, 1069, 442, -99, -666, -1036, 274, -1511, 111],\n [225, -812, 369, -48, -526, -319, -142, 87, 485, -114, 207, -469],\n [-857, 30, -158, -1077, -206, -985, 196, 801, 1649, 901, -47, -1181],\n [-965, -550, -537, -920, 0, -332, -74, 1743, 1246, -393, -263, -254],\n [472, -552, 626, 129, -892, -506, -1, -64, 868, 495, 597, -781],\n [691, 222, 102, 641, -537, 794, -638, -1249, -352, -498, -1649, 720],\n [281, 60, -29, 607, -652, -669, 383, -315, 827, 114, 167, -467],\n [-580, 109, -135, 87, -1102, -1023, 23, 544, 1365, 161, 329, -812],\n [811, -669, 1028, -1685, 466, -87, -139, -908, -469, 1333, -434, -1153]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[904, 102, -473, -392, 1230, 793, -704, 185, 30, 307, -989, 1604],\n [427, -50, -44, 415, -709, 111, -869, -719, -680, 1063, -661, 471],\n [-438, -921, -439, -235, -49, 350, -467, -74, -122, -678, 517, -141],\n [-1632, -114, 134, -347, -1392, -59, -439, 50, -227, -99, 1185, -1964],\n [337, -125, -98, -34, 77, -564, 206, 158, -478, 478, -861, -293],\n [927, 189, -28, -59, 900, 357, 65, -202, 579, -193, -186, 1010],\n [-71, 75, -361, 52, 155, -231, 445, 437, -626, 447, -799, -176],\n [665, 652, -957, 686, 792, 459, 210, -888, -355, 1169, 139, 570],\n [-225, 194, -150, -971, 636, 181, -219, 647, 285, -149, -66, -569],\n [137, -721, -708, 25, 508, 297, -71, 303, -613, -159, -767, 786],\n [-579, -770, -564, -409, 825, 71, -73, 842, -194, -771, 162, 177],\n [310, -338, -224, 347, 192, -659, 275, 228, -749, 473, -927, 246]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1646, -175, 1752, 292, 1002, 474, 23, -820, 135, 102, -669, -202],\n [-474, 372, -55, 356, 429, 990, -540, -199, -164, -443, 584, -1150],\n [-1118, 915, 799, 2380, 499, -261, 1950, 71, 193, 447, -542, -1114],\n [-427, 1676, 334, 696, 230, 65, 742, -222, 592, 367, 399, -1033],\n [-852, -517, 753, 271, 59, -638, -922, -33, -173, 497, -586, -218],\n [-353, -442, 488, 1154, -618, 125, 554, 106, -1218, 649, -416, -1183],\n [407, 673, 809, -566, -43, -136, 537, -791, 65, 596, 631, -920],\n [-484, 1028, -203, -306, 804, 128, 1391, -775, -227, 1768, 188, 361],\n [926, -13, -169, 56, -480, -796, 606, 391, 386, 420, 37, -33],\n [-497, -293, 30, 757, 499, 820, 383, -577, -1495, 952, -76, -1197],\n [26, 454, 588, -984, 808, 384, -29, 172, 1054, -134, 646, 683],\n [542, -364, -804, -461, -687, -32, 102, 426, -756, 534, 945, -194]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[540, 373, 625, 352, -313, 232, -156, -351, 660, 127, 5, 1020],\n [309, -331, 124, -64, -421, 86, -135, 284, 668, 305, 249, -514],\n [-551, -897, -353, 151, 405, -214, -183, 1219, -552, -227, 154, -428],\n [1052, -36, 800, 292, 19, -307, 216, 907, -502, -125, -269, 632],\n [-39, 332, 45, 146, -142, -411, 420, -76, -637, -290, 838, -492],\n [402, 717, 456, 281, 83, -41, 180, -920, -243, -140, -227, 1091],\n [223, 355, -410, -469, 89, -36, 374, -489, -1483, 162, 955, -1494],\n [736, 962, 117, -428, -439, -104, 635, -485, -674, 109, 689, -991],\n [-1136, -921, -585, -254, 714, 1069, -1088, 264, -726, 528, 1278, -131],\n [50, -608, 131, 174, 245, 895, -1021, -889, 863, 698, -352, 1116],\n [1600, 532, 975, -882, -943, -50, 614, 510, 546, 528, 78, -734],\n [252, -359, 418, 736, 90, 641, -881, 234, 1097, 205, -719, 1831]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-1256, 340, -358, -683, -228, -1183, -243, 1118, 1875, -541, 1327, -1003],\n [1050, -664, -326, 337, -233, 111, 503, 362, 343, -947, 1480, 158],\n [134, 1083, 795, 373, 550, -420, -799, -725, 503, -586, -865, -196],\n [897, 799, 549, -126, 433, 82, -1344, 2080, 444, -534, 2012, -738],\n [-728, -109, 1019, -594, -229, -317, -1615, -583, 182, -2582, -253, 1588],\n [333, -85, -795, 146, 594, -620, -272, 1249, -412, 1355, 280, -689],\n [-818, 875, 573, -339, 432, -231, -1222, 421, 90, -185, -455, -72],\n [564, 1000, -359, 484, 221, -93, -916, 447, 276, 1534, 278, -1552],\n [261, -364, -1035, -243, -206, -146, 874, -921, 1254, -271, 605, 392],\n [1736, 1500, 427, 288, -440, -280, -158, -355, 1143, -284, 1236, -805],\n [1170, -121, 666, 215, -615, -152, -60, -442, -120, -751, 407, 257],\n [1011, 499, 840, 69, 522, 511, -1198, 17, -458, 126, -251, 45]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[108, 59, -27, 12, 26, -736, 354, -109, -28, -571, -135, -321],\n [334, -743, 506, -813, -162, 338, 729, -33, -1112, -227, 258, 634],\n [-244, 162, -276, 494, -36, -236, -198, -66, 432, 26, -36, -4],\n [-296, -19, -279, 538, -130, -260, -60, -127, 308, -33, 45, 259],\n [-110, -607, 127, -97, -261, 515, 234, -69, -508, 199, 327, 937],\n [-88, 44, -91, 166, -17, -49, -75, -20, 140, 30, -3, 23],\n [322, -40, 248, -483, 91, -219, 348, 22, -376, -352, -84, -308],\n [154, 322, 38, -147, 183, -91, -144, 96, 160, -26, -174, -554],\n [156, 736, -50, -62, 356, -16, -546, 212, 568, 188, -330, -1038],\n [396, 391, 144, -390, 271, -659, 213, 55, -8, -545, -324, -984],\n [-106, 806, -335, 465, 270, -368, -621, 96, 932, 104, -339, -937],\n [126, 94, 179, -343, 120, 690, -315, 192, -68, 468, 15, -99]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-587, 927, 208, -156, -260, 301, -477, -623, 859, 456, -88, 1129],\n [1080, -444, 459, -1172, 961, 342, 405, -353, -596, 171, -281, -665],\n [-276, 392, 54, 662, -1429, -752, -933, -817, 62, -46, 1024, -597],\n [-381, -196, 646, -333, -444, 1737, -31, 12, 1411, -485, -1741, 873],\n [608, -573, 641, 84, -1264, 677, -677, -504, 295, -362, 203, -716],\n [-1466, 242, -233, 1080, -290, -566, -420, 452, -20, 807, 491, 560],\n [-1153, 662, -441, 752, -376, -216, -27, 268, 766, 196, -213, 1115],\n [-111, -292, 700, 147, -1772, 432, -266, -1176, 1081, 489, -781, -337],\n [-266, -1221, 166, 1071, -1016, -408, 271, 156, -198, 1403, 109, -816],\n [-38, 888, 223, -212, -64, -408, -848, -826, -114, -259, 923, -342],\n [-414, -262, -250, 648, 149, -803, -203, 488, -908, 502, 950, -409],\n [559, 63, 115, -229, 345, -339, -558, -174, -893, 367, 1370, -323]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-161, -389, 746, -835, 1105, 411, 759, -490, 228, 139, 756, 960],\n [267, 875, 1037, 28, -530, -286, 886, 37, -1856, -976, 677, -735],\n [-1891, -12, -731, 1080, -602, -624, 590, 725, -236, 861, 341, 933],\n [562, -324, 114, -990, 111, 1006, 149, 369, 1469, -422, -782, 232],\n [-1115, 393, -421, 1375, -1903, -958, 246, 45, -1362, 441, -597, 298],\n [1254, -341, 1667, -863, 141, -6, -291, -1671, -890, 1015, -39, 818],\n [657, 539, 934, -1157, 331, 135, -876, -410, 499, 1418, -166, 1289],\n [1613, 29, 201, -405, -124, 1044, -158, 176, -261, -997, -624, -1044],\n [-318, 1123, -1769, 920, -558, -573, -1753, 15, 715, -98, -1069, -573],\n [350, -990, 608, -436, 709, 770, 530, 415, 409, -354, -456, -1414],\n [-318, -585, -537, -19, 1104, 438, 589, -174, 341, -513, 882, 494],\n [-1019, 403, 362, -569, 196, -718, 352, -375, 670, 93, 354, 944]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-240, 513, 644, -66, 222, 340, -326, -872, -102, -571, -897, 185],\n [1356, -185, 6, -845, -1555, 533, 24, 360, -740, 998, -557, -1314],\n [812, -833, -36, -19, 89, 1355, 558, 760, -130, 478, 689, -1134],\n [-687, -390, -467, 853, 977, -490, -250, -1010, 203, -1425, 198, 46],\n [-989, 44, -782, 1335, -541, -1234, -560, -1046, -707, -42, -815, 853],\n [1384, -518, 854, -739, -1021, 260, 513, 876, -1318, 132, -133, 208],\n [564, -439, -229, 4, 736, 9, 617, -62, 127, 430, 953, 818],\n [-711, 836, -449, 134, -975, -1547, -1371, -262, 129, -114, -1073, 198],\n [478, -1115, 638, -731, -832, -631, -288, -1202, -1351, -650, -877, 791],\n [985, 21, 1041, -660, -706, 1268, 150, 762, -219, 490, -790, -1276],\n [295, -132, -532, -1198, 20, 607, 16, 848, 1503, 1136, 1026, -1440],\n [-699, 703, -394, -238, -761, -900, -642, 576, 315, 1593, -330, 709]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[87, -164, -814, -361, -189, 1001, 527, -433, -422, -379, 402, -204],\n [-384, 514, 872, -522, 374, -240, 32, 799, 358, 212, -421, 361],\n [373, -394, -324, 1046, -531, -662, -252, -947, -264, 355, -254, -624],\n [393, 23, -1118, -81, 127, 1122, 502, -448, -514, -413, 787, 74],\n [491, 750, -368, 127, 65, 601, 239, 12, -536, 319, 279, 37],\n [-510, -348, -26, -240, 552, -182, 746, -499, 310, -300, -449, 129],\n [-203, 947, 739, -166, 873, -358, 458, 483, 226, 478, -586, 534],\n [-39, -393, -634, -476, -517, 897, 289, -324, -340, -411, 319, -386],\n [-598, -457, 286, -208, -2, -457, 513, -522, 270, -44, -826, -307],\n [-316, 4, -318, -1020, -404, 1150, 726, -84, -360, -274, -48, -370],\n [391, -183, -541, 990, -151, -428, 192, -1116, -348, 316, -235, -449],\n [546, 465, 196, 348, -268, -37, -923, 753, -136, 314, 541, 160]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-371, -721, -756, 475, 60, -472, 553, -965, 143, -225, 569, 368],\n [-394, -332, -454, -366, -247, -281, 329, 336, -236, -291, 297, 376],\n [773, -89, 91, 527, 311, 477, -323, 139, -252, 579, -86, -232],\n [-251, 43, -192, -493, 102, -50, 31, 495, -389, -379, -97, 256],\n [-217, -583, -765, 365, 829, -377, 67, -837, -368, -959, -78, 852],\n [-495, 355, 271, -441, -39, -325, -104, -156, 257, -740, -370, 258],\n [338, -770, 33, 383, -331, -584, -582, -46, 111, -1053, -364, 1402],\n [-483, 471, 556, 254, -220, -357, 137, -1357, 1141, -102, -66, -426],\n [771, 109, 519, 351, -333, 459, -342, 436, 137, 880, -24, -478],\n [993, -5, 684, 33, -1006, 528, -446, 1450, 10, 1144, 79, -382],\n [-65, 963, 621, -881, 34, 452, -276, 1019, -232, 160, -485, -572],\n [201, 207, -84, -105, 56, 528, 238, 516, -316, 942, 319, -774]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-82, -387, 523, 688, 306, 994, -1468, -190, 531, 183, 344, 867],\n [-1029, 98, -403, -239, -57, 204, 305, 513, -481, -789, 543, 1],\n [468, 94, 309, -725, -222, -318, 1139, -49, -184, -312, -694, -356],\n [-373, -735, -54, -59, -439, 738, -533, 380, 22, -854, 256, 204],\n [-918, 555, -573, 472, -631, 254, 583, 406, -1341, -650, -57, 19],\n [1036, -309, 1300, -118, 431, 401, -504, -434, 996, 525, -482, 581],\n [797, -411, -3, -421, 120, -347, 153, -226, 517, 208, -86, -308],\n [572, 291, 34, 279, 1406, -380, -591, -826, 893, 1346, 666, 244],\n [-55, -773, -31, -711, 1081, 19, -878, -246, 1363, 65, 1093, 10],\n [422, -308, 24, -1016, 387, -476, 503, -510, 528, -126, -180, -591],\n [-239, 1168, 17, 1304, -359, 61, 173, -13, -1136, 628, -527, 413],\n [-182, 267, 45, 1189, -415, 509, -733, 177, -466, 327, -84, 567]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[595, 484, -163, -538, -64, -312, -511, -150, 280, -551, 911, -178],\n [-460, -450, 196, 136, -732, 422, 640, -718, 600, 356, -576, 610],\n [620, 524, -188, -488, 136, -372, -596, 60, 80, -556, 916, -308],\n [-410, -344, 122, 332, -64, 240, 386, -12, -80, 370, -610, 188],\n [-25, 51, -59, 286, 738, -157, -209, 791, -780, 89, -159, -437],\n [180, 158, -60, -120, 100, -122, -192, 82, -40, -156, 256, -126],\n [-315, -257, 87, 282, 26, 167, 273, 71, -140, 291, -481, 99],\n [-515, -473, 191, 266, -502, 399, 617, -465, 340, 427, -697, 491],\n [590, 476, -158, -548, -104, -300, -494, -192, 320, -550, 910, -152],\n [-405, -401, 177, 102, -694, 383, 579, -685, 580, 309, -499, 567],\n [-70, -112, 70, -140, -560, 168, 238, -588, 560, 14, -14, 364],\n [220, 261, -136, 104, 822, -311, -454, 847, -780, -128, 198, -577]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-511, 231, -314, 10, -260, 682, 1219, 551, -468, 274, 259, -969],\n [-863, -1029, 114, 133, 573, 37, 91, 433, -149, 362, -203, 201],\n [925, 985, 523, 166, -800, 240, -177, -1074, -53, -622, 285, -303],\n [-855, -421, 108, 487, 480, 1075, 469, 454, 419, 479, 476, -219],\n [-762, -246, 563, 349, -307, -92, 16, -93, -802, 27, 286, -240],\n [-323, 939, -1019, -217, -68, 846, 1593, 1169, 216, 414, 362, -1067],\n [398, -512, 214, -295, 75, -340, 358, -402, -493, -359, -1010, -26],\n [298, -346, -1229, -1381, -414, 696, 14, -112, 60, 124, 579, -328],\n [527, 49, 329, 21, 403, 166, 762, -302, 250, -454, -1057, -85],\n [-1054, -334, -18, -94, 677, 402, 268, 505, 498, 123, 101, 170],\n [-830, 798, -605, -1348, -417, 1807, 1362, -200, 369, -552, 935, -1126],\n [9, -323, 283, 261, -237, 293, -717, -454, -14, 134, 625, 163]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-108, -1010, -1400, -473, 398, 196, -1883, -66, 45, -419, 1122, 147],\n [-542, 541, 467, -279, -101, 31, 145, 51, -661, -105, -48, -88],\n [962, -177, 676, -1031, -537, -235, 145, -647, -858, -196, -291, -49],\n [-118, -51, 1141, -253, -74, -1234, 1024, -404, -994, 1231, -2034, 230],\n [376, 149, -766, 219, -356, 493, -139, -47, 1134, -737, 1106, 381],\n [-396, 407, 347, 163, 340, 542, -42, 334, -274, -121, 180, -650],\n [-160, 241, 77, -435, -326, -303, 103, -439, -169, -18, -137, 468],\n [-668, 504, 184, 402, 519, 537, -19, 255, 107, 80, 62, -544],\n [-4, -645, -535, -656, 494, 402, -1477, -176, -497, -298, 670, -439],\n [678, -669, -588, -506, -302, -159, -610, -303, 63, -348, 482, 372],\n [182, -473, 680, -579, -126, -1053, 327, -383, -1094, 799, -1370, 215],\n [810, -974, 283, -1020, -310, -929, -265, -539, -1138, 352, -780, 253]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-493, -171, 360, -428, 1177, -230, -147, -104, -20, -784, 160, 526],\n [-85, 603, 759, -236, -31, -744, 107, 512, -212, -109, -1000, -375],\n [617, -276, -426, 595, -1120, 266, 207, 366, 492, 746, -83, -495],\n [555, -1265, -147, 144, 69, -480, 497, -756, -416, -685, -530, -193],\n [-483, 452, 642, -1335, 302, 192, -129, -882, -98, -134, 435, 425],\n [-380, 701, 56, 279, 249, 104, -343, 964, 360, 257, 154, 113],\n [126, 703, -147, 51, -829, 184, -21, -172, -434, 620, -96, -336],\n [102, 618, -143, 170, -856, 406, -110, 432, 344, 867, 172, -257],\n [-297, -40, 211, -538, 523, 61, -89, -450, -69, -341, 310, 366],\n [-740, 699, 996, -904, 1076, -575, -197, 84, -269, -677, -341, 347],\n [-570, 468, 782, -626, 852, -404, -172, 328, 92, -468, -208, 288],\n [75, -38, 177, 603, 230, -606, 73, 1014, 150, -217, -757, -282]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[63, -54, 78, 42, -30, -24, -51, 3, -45, 54, 30, -33],\n [-84, 72, -104, -56, 40, 32, 68, -4, 60, -72, -40, 44],\n [-546, 468, -676, -364, 260, 208, 442, -26, 390, -468, -260, 286],\n [336, -288, 416, 224, -160, -128, -272, 16, -240, 288, 160, -176],\n [-315, 270, -390, -210, 150, 120, 255, -15, 225, -270, -150, 165],\n [231, -198, 286, 154, -110, -88, -187, 11, -165, 198, 110, -121],\n [378, -324, 468, 252, -180, -144, -306, 18, -270, 324, 180, -198],\n [-63, 54, -78, -42, 30, 24, 51, -3, 45, -54, -30, 33],\n [315, -270, 390, 210, -150, -120, -255, 15, -225, 270, 150, -165],\n [-420, 360, -520, -280, 200, 160, 340, -20, 300, -360, -200, 220],\n [231, -198, 286, 154, -110, -88, -187, 11, -165, 198, 110, -121],\n [-126, 108, -156, -84, 60, 48, 102, -6, 90, -108, -60, 66]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-475, -596, -54, -681, 839, -448, -868, 465, -532, 486, 453, 320],\n [909, 442, 292, 242, -283, 668, -274, -614, 178, -846, 1345, 499],\n [-1025, 143, 586, -8, 135, -638, -633, 504, -112, 451, 291, 28],\n [378, 218, 0, 380, -432, 234, 238, -486, -58, -646, -168, -244],\n [-15, 253, 411, -284, 299, -13, -654, 124, -38, -193, 1119, 329],\n [414, -229, -39, -259, 330, 367, -372, 71, 258, 403, 1112, 893],\n [129, -922, -512, 327, -88, 257, 124, -38, 245, 1192, -134, 926],\n [945, 602, 448, 585, -607, 732, -264, -843, 198, -1068, 1395, 482],\n [-772, 172, 74, 98, -154, -620, 298, 208, -302, -132, -1278, -984],\n [416, -717, -321, 584, -330, 627, 152, -124, 748, 1393, 570, 1488],\n [902, 472, 199, 43, -153, 452, -335, -774, -383, -1568, 881, -162],\n [63, -505, -238, -629, 694, -253, -735, -74, -933, -511, 196, -151]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-858, 910, 977, 357, -1257, 484, 307, 129, 695, -130, -899, -564],\n [46, -201, -1598, 1036, 531, -1154, 707, 866, 313, -978, 842, -22],\n [508, -904, 370, 627, -374, 629, 1033, -17, -414, -884, -656, -642],\n [381, 129, 1704, -615, -87, 595, 202, -1525, 969, 884, -553, 1342],\n [311, -782, 56, -425, -700, 979, 793, -648, 528, 381, 538, 649],\n [751, -236, 342, 371, 614, -473, 279, -503, 108, -1216, 175, 316],\n [351, 887, -2126, 369, -1569, 119, 380, 989, 3, 36, 356, -1727],\n [360, -618, 375, -317, 271, 810, 322, -604, -188, 586, 258, 593],\n [198, -123, -14, 800, 457, -237, 410, 232, 1545, -2326, 1280, 1539],\n [712, -413, -1521, 144, -98, -447, 539, 501, -1684, 89, -111, -2216],\n [-296, -503, 1094, -935, 195, -20, -832, 186, 318, -762, -322, 599],\n [37, 508, -130, 1011, -103, -914, 1388, 67, -999, -942, -428, -2451]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[106, -526, -1050, -1661, 1908, 842, -1706, -196, 294, -193, 1088, -1622],\n [-450, 1021, -851, 921, -723, 72, 306, 1434, -1579, -524, -812, 199],\n [-123, -1109, 434, 120, -543, 1297, 514, -176, 1278, 87, -449, 73],\n [15, -1718, 124, -1179, -1014, 1553, 8, -221, 1779, -794, -771, -1249],\n [1187, 327, -321, 573, -871, -128, -1207, 655, -393, 337, 323, -1640],\n [-427, -971, 157, -1214, 350, 688, 173, -624, 1332, -894, -842, 479],\n [225, 728, 500, -659, 244, -888, -250, -668, -222, -376, -922, -253],\n [1397, -273, 279, -153, -1782, -360, -972, -99, 397, 81, -123, -2025],\n [497, -621, 189, 1062, -1801, -265, 86, 980, 526, 239, 190, -573],\n [509, 1516, 121, 1608, 1780, 1003, -111, 584, -834, 571, 238, 601],\n [-495, -395, -1646, -608, 756, -354, -1022, 719, -634, -60, 1450, -207],\n [-953, 1553, 4, 309, 125, 156, 510, 704, -1514, -623, -979, 640]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-573, 417, 193, 422, -199, 500, -197, -213, 196, -627, 227, -336],\n [167, 520, 632, -113, 247, -772, -887, -23, 135, -324, 342, 271],\n [-904, 5, 814, 287, 557, -107, -848, -85, 329, -704, -62, -171],\n [905, -613, -126, -846, 423, -540, 57, 679, -100, 693, -430, 208],\n [171, -451, 389, -150, 257, -626, -293, 311, 56, 123, -38, 231],\n [141, 366, -198, -481, 472, 123, -183, -62, -49, 101, -345, -80],\n [-915, -123, 854, 516, 74, 273, -661, 206, 486, -972, 172, -462],\n [-221, -217, -849, 72, -228, 1041, 961, -170, -186, 308, -407, -360],\n [-682, -170, 138, 1496, -1457, 307, 644, -421, 48, -499, 1016, 20],\n [447, 661, -248, -818, 843, -400, -421, -285, -220, 403, -439, 281],\n [-300, -334, 89, 450, -382, 186, 244, 36, 70, -158, 187, -94],\n [834, 511, -532, -1, -876, 38, 528, -54, -207, 263, 541, 160]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-578, -680, -431, 860, -770, 1792, -244, 547, -81, -585, -1284, 1016],\n [16, -115, 766, 431, 665, -88, -811, 605, 750, 111, 812, 881],\n [1374, -558, -275, 650, -377, 202, 584, 300, 518, 514, 101, -1592],\n [345, -432, 418, 905, 672, 838, 52, 1539, 1088, 329, 112, 65],\n [-654, -176, -403, 419, 144, 1391, -102, 103, -337, -185, -591, 455],\n [466, -1270, 222, -134, -124, -114, -1839, 536, 915, 44, 1143, -90],\n [-365, 33, -290, 685, -1814, 1123, -177, -339, -815, -729, -938, 1253],\n [-677, -332, -151, 119, 533, 702, -5, -27, -393, 25, -17, 351],\n [-835, -1273, 553, 670, 897, 486, 925, 455, -440, 784, 934, -122],\n [229, -1651, 133, 639, -1025, 588, -754, 133, 6, -123, 313, -177],\n [-259, 348, 176, -740, 486, -665, -1300, 73, 867, -728, -640, 696],\n [-1617, -121, 740, 891, -218, 637, -94, -837, -633, 80, 72, 603]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-960, 860, 564, 182, -902, 560, -108, -570, -408, -282, -704, 116],\n [-224, 379, 495, 135, 111, 200, -577, 499, -171, -214, -272, 602],\n [589, -925, -815, -756, -230, 385, 647, -226, 1119, 397, -187, -613],\n [-667, 673, 499, 493, 25, -205, -419, 279, -409, -412, -91, 543],\n [60, -253, -225, -97, 215, -108, -9, 435, 557, -70, -20, 174],\n [60, 121, 337, 126, 496, -52, -615, 826, -15, -175, -20, 672],\n [-552, 561, 365, 325, -259, -18, -135, -199, -457, -228, -128, 152],\n [374, -480, -404, 72, 752, -665, 10, 684, 452, -31, 522, 161],\n [487, -120, 18, 338, 770, -721, -148, 244, -628, 94, 815, 17],\n [627, -239, 27, -266, -12, 305, 57, -396, -415, 407, 131, -385],\n [-499, 220, 98, -108, -440, 409, -56, 58, 436, -204, -587, 219],\n [-1195, 1156, 778, 172, -1376, 899, -44, -1086, -748, -250, -955, -63]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"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, 201, -1042, -237, -232],\n [-113, -873, -896, -474, 178, -264, -716, 511, -466, 952, 551, 656],\n [848, 477, -947, 9, 254, 312, -1262, -79, -356, 80, 204, -351],\n [-344, -182, 367, 185, 588, 822, -62, -710, -900, -158, -249, -512],\n [281, 186, -133, -248, -834, -340, -218, 358, 221, -295, 405, 223],\n [-173, 297, -902, -171, -702, 55, -144, 1288, -378, 72, 398, 1780],\n [109, 1299, 357, 155, 588, 149, 857, 271, -881, 1544, -552, 283],\n [-2109, -728, -254, 337, -62, -575, 1618, 407, 1280, -942, -250, 832],\n [1430, 528, 91, 174, 99, -298, -933, -551, 1531, -1157, -552, -514]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"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, -147, -177, 255, 1061, -1171, 309],\n [-70, 234, 308, 487, -161, -530, 1707, -304, 1669, -175, 285, -1119],\n [-569, -73, 91, -924, -317, -732, -317, -981, 55, 689, -638, -313],\n [-470, -16, 71, -80, -793, -883, -57, 387, 1229, 565, 149, -1574],\n [475, -361, -1760, -318, 311, -1490, -793, -1882, -1585, 1204, -1397, -37],\n [434, 227, 210, 1012, -497, 294, 246, 583, -461, 352, -808, 335],\n [-762, 1316, 1000, -108, -1134, 930, -214, 388, 492, -154, 10, 164],\n [-435, 968, 928, -1422, 82, 568, -456, 125, -1469, 24, -432, 1310],\n [1087, 160, -1738, 1609, 269, -609, 540, -1314, -573, 171, -783, 85]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"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, 466, -254, -474],\n [411, -646, 390, 344, -7, 385, -420, -230, 257, 16, -549, 975],\n [-776, 85, -321, -722, 882, -183, 1545, -4, 735, 1033, -1488, -362],\n [341, -1702, 111, 256, 613, -77, -753, -582, -964, -334, 2197, 731],\n [1645, 84, -1921, -822, 192, -726, -713, 1042, -701, 66, 242, -384],\n [340, 823, -971, 186, 15, 123, 163, 770, -88, 495, -118, 19],\n [665, -420, 181, -670, 604, 660, -723, -188, 304, 326, -970, 381],\n [-601, -129, 94, -177, -278, 89, 504, -1377, 912, -208, -891, 12],\n [-189, 930, -1379, 927, -984, 351, -65, -189, -240, -1049, 419, -412]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"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, 576, -436, -178],\n [-171, -125, -383, -518, -20, -590, -756, 138, 1321, 1498, -1463, -1241],\n [26, 969, 383, 50, 135, -861, -183, 924, 790, -685, 640, 312],\n [-697, -199, 139, -561, -703, -785, -1079, 906, 959, 251, -273, -991],\n [-20, -721, 139, 203, -40, 1153, -316, -168, 567, -213, -69, 1046],\n [716, 485, -67, -830, 360, 541, 72, 108, 247, 698, 1052, 65],\n [30, -1199, -400, -319, -712, 1030, 154, -1177, 330, -127, 236, 870],\n [-695, -1787, -705, 299, -1014, 640, -430, 73, 774, 422, 211, 85],\n [437, -456, -594, 1188, 600, 1221, -735, 689, 577, 561, -1162, 1040]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"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, 315],\n [232, -202, -170, 509, -159, 339, 198, 423, -203, -496, -474, 207],\n [355, 152, -3, -133, -191, 445, 94, 67, 79, 70, -781, 261],\n [142, 124, -12, -559, -85, -2, 452, -265, 443, 508, 312, 370],\n [64, -312, -206, 655, 179, -173, -52, 355, -205, -608, 52, 137],\n [502, 495, 813, -1157, 1137, -239, -1046, -516, 691, 476, 364, 190],\n [67, -170, 31, 376, -44, 293, 24, 344, -238, -442, -145, -61],\n [-236, 60, -522, 40, -432, -396, 350, -284, 48, 424, -250, 120],\n [701, 57, 840, -818, 510, 846, 176, 197, 538, -54, 691, 413]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"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, -65, 110, -120],\n [-598, -598, -416, 494, 364, -182, -338, 208, 468, -338, 572, -624],\n [-391, -391, -272, 323, 238, -119, -221, 136, 306, -221, 374, -408],\n [506, 506, 352, -418, -308, 154, 286, -176, -396, 286, -484, 528],\n [184, 184, 128, -152, -112, 56, 104, -64, -144, 104, -176, 192],\n [575, 575, 400, -475, -350, 175, 325, -200, -450, 325, -550, 600],\n [-368, -368, -256, 304, 224, -112, -208, 128, 288, -208, 352, -384],\n [92, 92, 64, -76, -56, 28, 52, -32, -72, 52, -88, 96],\n [-299, -299, -208, 247, 182, -91, -169, 104, 234, -169, 286, -312]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"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, -42, 647, 592, 18, 258],\n [392, -1047, 569, 14, 231, -195, 323, 419, 147, -458, 396, -475],\n [786, -604, 784, 689, 411, -485, 192, -21, -80, -10, 1364, -174],\n [2, -734, 119, 273, 223, 415, 957, -24, -631, -397, -140, -733],\n [-2, 132, -545, 535, -214, 535, 761, -655, -582, 206, 234, -509],\n [-821, 16, -40, -1384, -213, 20, -772, 857, 614, -387, -1934, 562],\n [397, -922, 1449, -22, 354, -679, -350, 458, -22, -112, -27, 660],\n [729, 78, 161, 194, -150, 99, 508, 292, 446, 518, 1235, -1026],\n [210, 834, -1005, 602, -177, 476, 599, -578, -78, 414, 1128, -905]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"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, -124],\n [241, 268, -375, 341, -263, 511, 785, -633, 263, 135, -442, -288],\n [401, 68, -105, 451, 17, 371, 805, -663, 313, -15, -122, -408],\n [-187, 320, -434, -102, -431, 273, 91, -54, -30, 230, -514, 124],\n [-96, 120, -162, -66, -168, 84, -12, 18, -30, 90, -192, 72],\n [253, -92, 119, 243, 173, 63, 329, -279, 153, -95, 142, -232],\n [-456, -120, 178, -526, 32, -476, -972, 798, -370, -10, 208, 472],\n [-368, 184, -242, -338, -312, -28, -412, 354, -206, 170, -288, 328],\n [335, 116, -169, 395, -57, 385, 751, -615, 281, 25, -198, -352]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"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, -453],\n [1346, -713, 383, 340, 579, -1228, -446, 993, -136, 575, -78, 1238],\n [615, -79, 455, -1063, -190, -589, -47, 280, -567, 332, -1011, -253],\n [806, 138, 244, -334, 93, -435, -116, 411, -301, 1321, 178, 502],\n [-587, 1153, -916, -1036, -1011, 535, 889, -763, 894, -729, 118, -534],\n [-209, 2, 110, 277, -201, 370, -604, 320, -412, 62, -80, -1093],\n [-375, -372, -178, -189, -170, -295, -160, -117, 281, -1273, -720, -391],\n [606, -284, -147, 71, 333, -896, -184, 274, 427, 546, 336, 1245],\n [396, 1461, -454, 161, -431, 1158, 1431, -172, 425, 466, 1370, 409]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"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, -47, -455, 183, 286],\n [-515, -650, -58, 123, -218, 535, 312, -394, -193, -359, -214, 364],\n [57, 854, -299, -306, 416, -469, -723, 87, 398, 778, 751, -10],\n [-195, -42, 352, -265, 48, 162, 163, 59, -60, -286, 28, 168],\n [406, 852, -376, -74, 324, -642, -688, 204, 370, 822, 536, -288],\n [559, -38, -97, 378, -164, -257, 93, 191, -64, 28, -379, -446],\n [-124, 40, 6, -94, 52, 40, -50, -42, 30, 26, 114, 100],\n [-44, -184, -324, 250, -106, 59, -43, -201, -9, 127, -72, 8],\n [394, 620, 602, -454, 266, -385, -47, 571, 93, -67, 170, -244]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"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, -182, -208, -298, 380],\n [877, -117, -180, -94, -62, 926, -535, 271, -688, 148, 196, 314],\n [914, 34, -260, -51, 120, 895, -559, 252, -702, 252, 321, 222],\n [91, -308, 194, -86, -474, 391, 89, -32, -95, -322, -280, 269],\n [-347, 984, 42, 389, 502, 86, 968, -926, 389, -290, 199, -559],\n [625, -587, -312, -290, 10, -12, -1163, 945, -566, 632, 200, 360],\n [-703, 805, 244, 363, 222, -137, 1232, -1029, 648, -540, -75, -522],\n [752, -680, -288, -324, -112, 188, -1212, 976, -672, 576, 156, 464],\n [0, 244, -444, 17, 804, -821, -625, 470, 2, 820, 529, -326]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"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, 351, 475, 89],\n [1424, -393, -450, 927, 728, 44, 637, 279, -823, -33, 735, -648],\n [1098, -288, -270, 1232, 936, 366, 56, -556, -524, -428, 32, -298],\n [181, 214, -622, 543, -614, -623, 1490, -251, -431, 251, 456, -435],\n [856, -516, -71, 459, 587, 585, -588, -758, -224, -332, -550, 866],\n [-965, 516, 71, -438, -429, -262, 1033, -130, -374, 224, -20, -635],\n [1356, -501, -321, 1106, 797, 207, 106, -300, -502, -284, 265, -70],\n [-1187, -566, 1803, -1172, 953, 85, -1072, 248, 396, -290, -117, 212],\n [-16, -650, 1247, 9, 1584, 472, -1337, 76, 190, -612, -44, -86]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"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, -32, -1177, 84, -335, 166],\n [-358, -567, -792, -252, -240, -25, 428, 146, -236, 282, -134, 541],\n [13, 679, -444, 638, -28, 619, 640, -682, -861, 717, 27, -54],\n [324, -86, -64, 910, 519, -1007, 554, -625, 381, 83, 220, -227],\n [72, -502, 761, 254, 372, 325, -462, -566, 12, -1339, -252, -262],\n [275, 331, -857, 1488, -334, -12, 897, 307, -451, 159, 389, -1093],\n [435, -33, 420, 291, -155, 410, -246, -45, -191, -570, 215, -531],\n [-424, 550, -284, -1, -180, -507, -173, -985, 874, 331, -347, -190],\n [1334, -1630, 192, 528, 576, -806, 745, -748, -568, -235, 806, 688]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"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, -600, -268],\n [-242, 180, -198, -568, -452, -698, -400, -456, -1080, 862, -662, 60],\n [154, 123, 53, 266, -543, -329, 264, -846, -644, 458, -118, 403],\n [58, 121, -319, -698, 99, -153, -582, 418, 22, -14, -36, -169],\n [-900, -276, 336, 168, 228, -48, 168, 120, -408, 444, -756, -396],\n [243, 108, 249, 792, -804, -333, 714, -1404, -834, 579, -69, 678],\n [-331, -261, 352, 562, 321, 380, 444, 186, 356, -227, -17, -181],\n [-143, 14, 49, 36, -190, -205, 58, -304, -418, 337, -259, 64],\n [161, 25, 284, 798, -557, -140, 698, -1070, -518, 353, 1, 515]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"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, -630, 120, 544, 544],\n [-625, -928, 79, 142, 482, -147, -1313, -241, -722, 595, 527, -269],\n [1005, -222, 412, -850, -711, -255, 803, 587, -31, -446, -340, -430],\n [372, 146, 57, 368, -751, 395, 154, 271, 699, 238, -675, 697],\n [315, 400, -96, 14, -388, -304, 340, 158, -229, -606, -96, 260],\n [667, -188, -765, 735, -21, -73, 164, 679, 644, -197, -79, 175],\n [-164, 899, -799, 684, -475, -250, 292, 177, -559, -593, -87, -604],\n [-1460, 657, -1203, -643, -122, 1218, -309, -1231, 115, -501, 573, -42],\n [-732, 164, -237, 66, 675, 152, -760, -638, -282, 488, 125, 943]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"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, 642, 88],\n [578, -64, 58, -182, -233, 278, 335, 1058, 541, -217, 0, 262],\n [495, 511, -569, 750, -387, 231, -325, 202, -1619, -1180, -1090, -1416],\n [-845, 9, -263, 85, 142, -285, -368, -1228, -646, 369, -137, -432],\n [-627, -154, -178, -571, -238, 323, 624, 100, 765, 794, 106, 316],\n [832, 862, 159, 118, 381, 1077, 107, 488, 205, -902, -409, 616],\n [477, -663, -104, 223, -252, -628, -431, 473, 2, -131, 268, 90],\n [-465, -751, -1227, 165, -640, -221, -596, -306, -388, 321, -385, -92],\n [224, -390, 304, -94, 197, 60, 179, 236, 1283, 473, 860, 1558]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"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, -489],\n [550, 107, 422, 1492, 780, -203, 844, -510, -97, 457, -103, -837],\n [465, 189, -813, 666, 252, -840, -635, -230, -732, 201, 764, 548],\n [-369, -445, 3, 434, 10, 1132, 769, 105, 853, -41, -145, -355],\n [-221, 751, -895, -1018, -539, -271, -580, 471, -971, -562, -1, 966],\n [-280, -781, 1, 660, 533, 223, -8, -855, 132, 583, 1355, 562],\n [100, -52, 429, -269, -120, -477, -366, 243, -457, -273, -359, 135],\n [143, 1352, -414, -1339, -147, -1055, -301, -38, 118, 653, -284, -208],\n [105, -550, 122, 65, -254, -216, -257, -27, 676, 339, 87, 52]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"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, 256, 441, 268],\n [237, 250, -193, 304, 220, 179, 309, 141, 187, 304, -135, 336],\n [84, -165, 133, -101, 100, -612, 271, -31, -137, 200, 435, 598],\n [-225, -85, 80, -155, -300, 205, -440, -70, -150, -420, -180, -590],\n [-171, -68, -26, -162, 165, 302, -82, -131, 360, 65, -39, -526],\n [-333, -150, 54, -288, -75, 384, -402, -183, 204, -255, -135, -906],\n [6, -31, 94, 9, -295, -215, -162, 51, -394, -275, -3, 144],\n [-138, -144, 50, -204, 140, 6, -10, -134, 218, 84, 138, -256],\n [210, -116, 98, -8, 220, -742, 486, 18, -110, 388, 522, 936]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"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, 317, 746, 588],\n [-535, -154, 45, -174, 565, -555, 1079, -204, 1358, 510, -1663, -1931],\n [-511, -62, 173, 131, 747, 699, -291, 575, -641, -498, 1831, 2015],\n [-384, -665, 537, -769, 573, -64, 1056, -381, 602, -851, -942, -207],\n [315, -238, 144, 18, -280, 250, -75, -601, 306, 1392, 721, 379],\n [-364, 8, -1067, 481, 530, 3, 145, 450, -641, 326, -28, -1472],\n [186, 98, 369, 520, 1043, -479, -1406, 1547, -532, -434, -682, -1248],\n [33, -626, 779, 366, 335, 344, -341, 374, -275, -951, 990, 828],\n [525, 558, -382, -534, -155, 289, 437, 133, 182, -130, -268, 1062]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"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, -1214, -649, -625, -700],\n [177, -35, -381, -516, -641, 432, 430, -489, -195, -169, -40, -2],\n [493, 262, -606, 342, -816, -166, -79, -173, 402, -132, -252, -550],\n [281, 670, -681, 951, 559, 467, -509, 59, -351, 10, -706, -14],\n [81, -1304, 7, -184, -2591, -838, 424, -639, 784, 66, 385, -625],\n [193, -1234, 6, 619, -2568, -1149, 123, -469, 1056, 345, 398, -142],\n [-150, 324, 76, -122, 86, 219, -283, 82, -880, -255, -397, -67],\n [-313, -37, 41, 549, 632, 483, 398, 43, 648, 827, 73, 503],\n [336, 936, -802, 1065, 2683, 1305, -367, 330, -253, 617, -365, 916]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"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, 64, -20, 310, 298, -6, 170, -14, -276, 432, -180],\n [239, 296, 686, 780, -65, -448, 86, 30, 509, 256, 98, 545],\n [212, 164, 74, 122, -136, -187, 15, -65, 80, 150, -162, 153],\n [122, 140, 290, 334, -42, -205, 37, 5, 218, 122, 22, 241],\n [-5, 16, 106, 112, 19, -38, 12, 20, 73, 12, 54, 63],\n [282, 96, -564, -544, -278, 12, -56, -200, -354, 104, -524, -206],\n [326, 236, 26, 94, -222, -253, 13, -115, 62, 218, -290, 181],\n [-14, 76, 466, 494, 78, -173, 53, 85, 322, 58, 230, 281]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"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, 360, -144, -216, 216, -396, -216, 450, 324, -18, 216, 324],\n [-357, 340, -136, -204, 204, -374, -204, 425, 306, -17, 204, 306],\n [-210, 200, -80, -120, 120, -220, -120, 250, 180, -10, 120, 180],\n [504, -480, 192, 288, -288, 528, 288, -600, -432, 24, -288, -432],\n [273, -260, 104, 156, -156, 286, 156, -325, -234, 13, -156, -234],\n [-252, 240, -96, -144, 144, -264, -144, 300, 216, -12, 144, 216],\n [420, -400, 160, 240, -240, 440, 240, -500, -360, 20, -240, -360],\n [210, -200, 80, 120, -120, 220, 120, -250, -180, 10, -120, -180]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"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, -341, 704],\n [369, 209, -398, -989, -609, 323, 61, 699, -948, 871, 957, -588],\n [-1089, 75, -617, -505, 16, 118, -32, 1535, -1315, 1000, 1254, 583],\n [415, 89, -403, 262, -410, 397, -260, 91, -241, 1202, 428, -1005],\n [66, 761, 352, -18, 914, -648, -412, 15, 117, -489, 264, -176],\n [453, -1239, -566, 190, -1021, 451, 670, 227, 468, 147, -408, 58],\n [-620, 511, -479, 481, 621, -822, -722, -23, 94, -713, 471, 589],\n [-726, 843, 660, 1126, 1102, 646, -559, -365, 105, 969, -596, -255],\n [139, 432, 403, 73, 455, 209, -908, -130, 626, -579, 242, 58]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"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, 368, 362, -291],\n [981, 291, 4, 351, -114, -750, -741, 688, 406, -896, 294, -24],\n [294, 235, 412, -85, -606, -71, 60, -393, -20, -37, 78, 1130],\n [-1281, 1586, 363, -1189, 1077, -500, 323, 921, -1094, -196, 759, -1696],\n [1574, -47, -1070, 1701, -1365, -1176, -568, 272, 406, -986, -254, -401],\n [657, 652, 824, -447, -897, -657, 309, 361, -1132, 311, 922, -445],\n [-360, 733, 566, -650, 193, -579, 541, 992, -353, -12, 337, -131],\n [-807, -39, 485, -694, 499, -61, 929, 108, -327, 177, -706, 251],\n [726, -546, 182, 326, -626, -370, 359, 591, 207, 249, -141, 368]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"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, 816, -429, -88, -698, 187],\n [82, -861, 481, -1653, 350, -28, -475, 88, 672, 775, -70, 930],\n [633, -250, 582, 121, -367, 403, 140, -1193, 684, -797, 137, 42],\n [149, -41, 309, 359, -739, 517, 362, -158, -1520, -1194, 293, -992],\n [-460, 653, -58, -627, 714, 1488, -340, -719, -602, 146, -335, 782],\n [202, -1730, -240, 48, -217, -7, 87, -18, -887, 511, 109, 233],\n [592, -970, -629, -650, -316, 136, 511, -858, -729, -142, -635, 1275],\n [9, 415, 994, -1088, -78, -405, -809, 288, 1752, -336, 97, 72],\n [117, 437, -197, 273, 415, 1126, -723, -352, -960, 261, 184, 195]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"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, -1009, 342],\n [-299, -1831, -913, 577, -888, -76, -1062, 298, 1173, 47, 128, -296],\n [55, 959, 828, -843, 299, -910, 457, -1564, -5, 918, 447, -572],\n [-366, 153, -750, 917, -98, -241, 796, -1540, -467, -72, 69, -888],\n [-113, 955, 1072, 468, 1469, 1088, 974, -543, -93, 490, -1026, 335],\n [-129, -24, 1535, 261, 698, 967, 62, 1802, -333, -138, -1229, 356],\n [-410, 423, -1336, 1450, -623, -368, 556, 131, -339, -890, 182, -829],\n [765, -864, 684, -1066, 400, -480, -324, 94, 527, 1128, -1134, 314],\n [-257, -535, 1188, 164, 52, -340, 463, -55, 567, 1082, -643, -493]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"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, -59, -787, 584, -487, -559],\n [-120, 708, -285, -357, 1575, 1660, -427, 821, 844, 1431, -835, 419],\n [-21, -523, -409, -259, -1183, -570, 623, 188, -820, -1475, -438, 484],\n [-1440, -1037, 296, 766, -70, -227, 352, 553, -306, 1054, -175, -1190],\n [996, 377, -138, -1055, -722, -815, 1339, -879, -902, 573, 200, -1345],\n [719, 324, 589, -488, -669, -1009, 430, -380, -764, -731, 214, -412],\n [-590, 24, 316, -464, -45, 231, 196, 1418, -155, -328, -405, 1543],\n [518, -435, 205, -883, -571, -1392, 1173, 5, -1009, -915, -632, -251],\n [47, 400, 111, -48, -2165, -619, 819, -621, -1092, -1958, 1664, 377]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"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, 564, 136, 108, -816],\n [-232, 352, 164, -464, -168, 188, 456, 292, -328, -48, -56, 480],\n [-50, -136, 73, 236, -18, -185, -270, -7, 190, 108, 50, -264],\n [-27, -268, 74, 436, 7, -307, -484, -68, 342, 167, 84, -480],\n [-88, 416, 12, -624, -88, 372, 664, 204, -472, -176, -104, 672],\n [-145, -36, 148, 116, -83, -155, -160, 98, 110, 113, 40, -144],\n [852, -304, -778, 136, 532, 362, 44, -746, -12, -376, -84, -48],\n [267, -308, -206, 380, 185, -113, -356, -304, 258, 1, 36, -384],\n [-39, 580, -65, -904, -73, 586, 982, 221, -696, -299, -162, 984]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"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, 764, 563],\n [-77, 548, -814, 848, 1453, -752, 103, 736, -948, 279, 810, 1001],\n [-141, 169, -166, 518, -743, 317, -1317, -418, -353, -406, -405, -364],\n [-905, -332, -102, -401, 96, -514, -204, -884, -229, -633, -396, 348],\n [123, 348, -59, -133, -1038, 446, 306, -95, -617, -874, 1213, -917],\n [-540, -47, -168, -143, 890, -44, 970, -39, -317, -34, 660, 310],\n [50, 299, 371, 104, -629, -374, 176, -456, -483, 62, 478, -400],\n [-986, -355, 729, -958, -532, 721, 116, -1182, 322, -700, -565, -138],\n [534, 427, -126, 628, -381, 812, -348, 377, -263, 51, 271, -257]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"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, -111, -709, -605, -569, 99],\n [262, 667, 388, 607, -589, -285, 255, 362, 1380, 189, -339, -768],\n [686, -426, -1646, -1324, -307, 161, -897, 503, 1721, -777, -97, 1254],\n [887, -346, -1228, -290, 1081, -371, 642, -515, 247, 342, 920, 496],\n [90, 109, 207, 328, -716, -375, -393, 1419, 1117, -3, -329, -95],\n [-1207, 686, -149, -107, 987, -21, -436, -39, 548, -505, -679, -308],\n [-1233, 965, 956, 730, 1074, -241, 258, -1620, -2162, 361, -1941, -186],\n [-989, 248, 351, 1187, 28, -618, -99, -1137, -1464, 1083, -873, -596],\n [-821, -250, 166, -315, 59, 459, -92, -1813, -1170, 573, -953, 225]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"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, 430, 598, 55],\n [-592, 809, 142, -189, 854, 189, 296, -182, -50, 151, -972, -79],\n [-850, 487, -971, 217, -497, -1369, 597, 455, 183, -600, 295, 227],\n [201, 322, -406, 839, 44, -228, 372, 216, 1605, -265, 87, -437],\n [723, -863, -531, 630, -193, -55, -303, 807, 1024, -891, 320, -256],\n [228, 2, -67, 184, -321, 63, -120, -320, -317, -20, 203, -174],\n [-399, 465, -497, 10, 268, -448, 135, 296, -24, -410, -389, 62],\n [191, -160, 61, -144, -1109, -643, 45, -176, -61, 650, 1387, 462],\n [245, 624, 97, 505, -547, -109, 316, -758, 548, 655, 638, -289]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"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],\n [252, 143, -525, 654, -292, 607, 344, 683, -18, 535, 628, -55],\n [554, 925, 746, 243, 780, 108, -1293, 3, -704, -702, -542, 429],\n [-449, -422, -389, 62, 63, 200, 251, 246, 758, 733, 461, 219],\n [412, 473, 33, 894, -316, 801, -64, 569, -230, -279, 80, 171],\n [506, 582, 12, 80, 550, -43, -603, 205, -628, 169, 139, 3],\n [232, 116, -265, 593, -514, 538, 400, 449, -90, 36, 277, -101],\n [192, 406, 664, -126, 380, -184, -730, -334, -392, -760, -640, 202],\n [3, 53, 513, -135, -175, -155, -121, -406, -174, -836, -626, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"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, 721, -46, -758, 148, 903],\n [-748, -637, -206, -47, 206, 861, 421, 68, -242, -465, -130, 1096],\n [-300, 186, 1024, -1401, -1197, -718, 547, -959, 1129, -473, -567, -582],\n [400, -190, 317, -648, -1054, -671, 686, -633, 535, -1211, -1356, 874],\n [1157, 339, 1343, -1275, -542, -742, -717, -321, -510, -1130, -456, -164],\n [1134, 463, 376, -696, 937, 799, -470, -1053, -768, -1026, 961, -162],\n [-765, -233, -125, 944, 736, 49, 805, 201, -186, 965, 699, -612],\n [-76, -1111, -35, 536, 672, 163, 290, 152, -26, -814, 1254, -786],\n [-27, 1987, 559, -1180, -320, -858, 565, 50, 802, 1687, -549, 118]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"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, -190],\n [-20, 355, -675, -453, -398, -290, 249, 401, 400, -293, -52, -53],\n [-599, -696, 198, 205, 321, -676, 59, -2, 540, 486, 892, -24],\n [400, -292, -837, 329, -466, -90, 151, 600, 1244, 62, -117, 353],\n [-309, 272, -113, -448, -80, -212, 136, -56, -61, -76, 192, -228],\n [-148, 818, -384, -938, -297, -242, 306, 16, -725, -382, 317, -211],\n [746, -405, 310, 953, 247, 503, -423, 361, 43, -276, -1162, 412],\n [-558, -102, 420, -45, 231, 39, -141, -350, 375, 145, -261, -438],\n [-220, -816, -134, 421, 204, -807, 105, 450, 662, 335, 850, 313]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"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, 260, -274],\n [64, -764, 688, -732, -416, 144, 74, 324, 602, -170, -342, 620],\n [-108, -262, 284, -316, -148, 352, 77, -58, 121, 255, -241, 80],\n [96, 752, -736, 800, 416, -512, -136, -112, -488, -216, 488, -448],\n [86, -324, 270, -281, -174, -76, 8, 214, 294, -214, -89, 323],\n [-270, 294, -174, 159, 150, 516, 69, -444, -393, 657, -102, -489],\n [-82, -34, 62, -75, -22, 204, 37, -96, -29, 197, -96, -59],\n [-120, -648, 648, -708, -360, 528, 132, 48, 396, 276, -456, 348],\n [-74, -20, 46, -57, -14, 180, 32, -90, -34, 178, -81, -61]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"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, 112, 224, 32],\n [-320, 20, 260, 140, 420, 140, -120, 180, 20, 140, 280, 40],\n [-320, 20, 260, 140, 420, 140, -120, 180, 20, 140, 280, 40],\n [336, -21, -273, -147, -441, -147, 126, -189, -21, -147, -294, -42],\n [368, -23, -299, -161, -483, -161, 138, -207, -23, -161, -322, -46],\n [240, -15, -195, -105, -315, -105, 90, -135, -15, -105, -210, -30],\n [64, -4, -52, -28, -84, -28, 24, -36, -4, -28, -56, -8],\n [-16, 1, 13, 7, 21, 7, -6, 9, 1, 7, 14, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"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 [-61, -362, -15, 74, 78, -319, -26, 22, 75, 476, 234, -293],\n [-588, 855, 19, 48, -250, -140, -661, -390, -44, -266, -119, 232],\n [592, -978, 125, 59, -334, -110, 630, 179, 478, -409, 285, -878],\n [-447, 720, -121, -119, 319, 261, -287, -129, -311, 331, -340, 796],\n [-956, 342, 38, -788, -292, 543, 126, -367, 278, -507, -960, 332],\n [147, -842, 207, -413, -715, 253, 805, -53, 775, -1097, -290, -864],\n [449, -329, 107, 164, -367, -38, 294, 29, 325, -615, 212, -516],\n [-56, 218, 67, -493, -156, 585, 176, 60, -124, -792, -623, 320]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"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 [-238, 398, -911, -88, -50, 458, 132, -291, 29, -292, 515, 129],\n [-224, -112, -266, 0, -280, -84, 0, -182, 70, 28, -42, 14],\n [445, 575, 100, -60, 725, 540, 90, 295, -170, -275, 465, 50],\n [-67, -433, 406, 68, -275, -448, -102, 21, 56, 257, -445, -84],\n [242, 262, 116, -24, 370, 240, 36, 170, -88, -118, 198, 16],\n [-199, 347, -779, -76, -35, 398, 114, -246, 23, -253, 446, 111],\n [-371, 167, -869, -60, -295, 234, 90, -368, 85, -173, 312, 101],\n [-275, -537, 159, 68, -535, -526, -102, -148, 121, 283, -484, -71]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"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, 210, -218, -261],\n [-406, -145, 37, -541, -236, -57, 202, -383, -113, -383, -31, -298],\n [558, 652, -552, -87, 80, 267, -450, 172, -261, 188, -18, 53],\n [-265, -219, 384, 235, 216, -546, 109, 52, 13, -153, 294, 324],\n [-286, -86, -248, -366, -397, 119, 548, -437, -73, -277, -345, -233],\n [-593, -633, 512, -238, -186, -73, 309, -274, 228, -249, -10, -333],\n [-322, -320, 342, -302, -67, 9, -68, -133, 97, -157, 99, -313],\n [-77, 180, 173, -347, 243, -327, -529, 40, -250, -231, 472, 8],\n [664, 847, -757, 159, 146, 43, -248, 205, -383, 179, -39, 408]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"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],\n [-910, -251, 649, 411, -249, 322, -261, -751, 313, -358, -394, 229],\n [774, 273, -510, -387, 150, -321, 54, 684, -300, 60, 36, -9],\n [945, 200, -610, -575, 215, -140, 230, 580, -365, 10, -190, 265],\n [819, 535, -491, -346, 28, -706, -389, 1091, -370, -232, -140, -52],\n [-495, -309, 276, 254, -1, 373, 256, -604, 237, 258, 274, -124],\n [35, 69, 69, -144, -104, 12, -261, -1, -82, -528, -724, 514],\n [-843, -336, 555, 399, -150, 417, -3, -813, 330, -60, -72, 63],\n [-21, -125, 1, -38, 48, 198, 191, -209, 26, 80, -4, 88]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"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, 423, 323, 498],\n [-207, 945, -562, -184, -50, 405, -515, -522, -669, -694, -193, -142],\n [-551, 683, 74, -652, 210, 210, 414, 810, 1314, 640, -486, -1399],\n [-821, 396, -1305, 537, -944, 80, -486, 564, -31, -24, -318, -556],\n [-1339, -487, -470, 27, -1067, 693, -688, 1395, 695, 1010, -1354, -883],\n [206, 944, 492, -528, -235, -663, 751, -229, 180, 142, 524, 704],\n [1122, -804, 955, 45, 1012, -583, 728, -962, -638, -783, 1438, 1018],\n [-180, -290, -208, 231, -143, -175, -18, -281, -783, -740, 694, 450],\n [728, 884, -2059, 793, -831, 665, -1655, -985, -1643, -612, -892, -324]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"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, 50, 83, -140, 523, 209, 52, -371],\n [69, -85, -270, -78, -611, 669, -142, 177, -142, -921, 840, -759],\n [-1273, -572, 748, -904, -378, -150, -416, -93, -312, 90, -1254, 210],\n [1028, 699, 144, 930, -22, 418, 143, -503, 248, -1852, 2107, -629],\n [1221, -259, -781, -1971, -1673, -2246, 1057, -2369, 299, 217, -729, -115],\n [1320, 848, 27, 2109, 613, 1153, 396, -108, -239, -277, 1516, -688],\n [-667, -62, -133, -1044, -310, -1007, -33, -189, 428, 828, -736, 400],\n [1204, 351, -142, -774, -839, 366, 574, -770, 1026, 417, 822, -1669],\n [-386, 689, 979, 1051, -86, -157, -549, -317, 160, 1523, -275, -168]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"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, 1125, 56, -560, 285, -115],\n [-86, -646, 379, -659, -633, 110, -187, -153, 220, 28, -142, 415],\n [260, 167, -107, -918, -195, -489, -89, 656, 414, -813, 600, -5],\n [-90, -328, -219, -1248, -373, -655, 204, 915, 445, -853, 623, 185],\n [-863, 247, 158, -366, 1552, -365, 455, -70, -887, -351, 1007, -255],\n [1256, 738, 476, 152, 307, -11, -1518, -1507, 383, -594, -624, -637],\n [-742, 545, 273, -635, 429, -688, 479, 342, -291, -709, 321, -600],\n [-296, 1126, 720, 98, -80, -30, 121, 127, -143, -246, -286, -655],\n [-474, -302, -747, 309, 378, -13, 906, 1173, -212, 206, 628, 371]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"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, -579, 408, -14, 421, -674, -251, 250, -509, -58, -494, -442],\n [159, -351, 70, -142, 401, -288, 109, 378, 121, 14, -358, -418],\n [482, -185, 388, 37, 490, -256, 152, -173, 849, 85, -54, -424],\n [-343, -197, -430, -318, 183, 56, 291, 754, -29, 6, -370, -254],\n [1, 90, 104, 161, -325, -38, -339, -269, -678, -75, 128, 318],\n [32, 40, 122, 144, -264, -82, -324, -224, -650, -72, 80, 256],\n [364, 15, 406, 219, 0, -182, -226, -491, 23, -5, 162, 52],\n [647, -268, 654, 221, 269, -520, -309, -417, -46, -15, -60, -214]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"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, 1152, 149, 104],\n [226, -297, -268, -207, -153, -78, 1093, -221, 402, 812, 1281, 609],\n [115, 1706, 86, 1631, -331, -285, 72, 63, 233, 1377, 181, 425],\n [1168, -487, 672, -200, 425, 1452, 1893, 12, -205, 760, -1140, 274],\n [1462, -545, -312, -684, 1134, 1580, 638, 193, 706, 199, 241, 387],\n [674, 883, 877, 441, 226, 186, -1278, 69, 1205, -94, 154, 16],\n [-353, 572, 454, -41, -117, 515, -1118, 515, 917, 16, -601, -76],\n [12, 555, -132, 582, 78, 458, -9, 262, 384, -31, -33, -1046],\n [410, 432, 219, 414, 174, 81, 143, 931, 56, 1251, -694, 742]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"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, -240, -211, -423, 922, 432],\n [424, -231, -632, -1443, -287, -2167, -589, 949, 393, 981, 574, 907],\n [-4, 700, -412, 658, 658, 3, -460, 275, -844, 727, -773, -90],\n [-107, 63, 95, 579, 559, 1690, 454, -758, 209, -1079, 182, 295],\n [-729, 370, -506, 102, 400, 1528, 516, -642, 122, -1057, 1032, 1172],\n [-583, -244, 84, 161, -48, 667, -990, -114, -1080, 977, -52, 1195],\n [298, -250, -444, -106, 320, -513, -126, 203, -117, 170, -129, 298],\n [543, -654, 90, -49, 37, -1225, -837, 631, -391, 887, -461, -172],\n [96, -131, 126, 124, -50, -44, 466, -200, 146, -587, 85, -537]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"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, 940, 242],\n [-87, -181, 451, 352, -246, 438, 150, 283, 634, -740, 75, -825],\n [-363, -510, 827, -450, -216, -407, 674, 990, 270, -599, 369, 349],\n [-949, 742, 399, -705, 131, 301, -144, -70, -718, 29, 665, 546],\n [-219, -315, -238, 104, -211, -350, 470, 406, -236, -969, -787, 228],\n [1284, -550, 272, 1153, 93, 44, 248, -8, 1120, 108, 128, -33],\n [-517, 333, 126, -1072, 196, 404, 186, 652, 89, -177, -82, -678],\n [-294, -192, 1254, -311, -162, 432, 520, 866, 1287, -518, 727, -1341],\n [-44, -399, 511, -509, -190, 219, -229, 524, 421, 242, 672, -483]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"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, -154],\n [-26, 598, -52, 26, 338, -104, -494, -364, 442, 520, -442, 364],\n [24, -552, 48, -24, -312, 96, 456, 336, -408, -480, 408, -336],\n [2, -46, 4, -2, -26, 8, 38, 28, -34, -40, 34, -28],\n [10, -230, 20, -10, -130, 40, 190, 140, -170, -200, 170, -140],\n [5, -115, 10, -5, -65, 20, 95, 70, -85, -100, 85, -70],\n [9, -207, 18, -9, -117, 36, 171, 126, -153, -180, 153, -126],\n [-5, 115, -10, 5, 65, -20, -95, -70, 85, 100, -85, 70],\n [9, -207, 18, -9, -117, 36, 171, 126, -153, -180, 153, -126]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"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, 260, -459],\n [968, 570, 156, 1041, -896, -84, 576, 145, -1102, 117, -257, -300],\n [46, -560, -505, 9, 436, 820, -719, 1195, 46, 466, -839, 635],\n [570, 128, -583, 896, -293, 833, -384, 1435, -629, 851, -1106, 706],\n [-220, 548, -117, 400, -382, 14, 169, 20, 91, 485, 74, 196],\n [308, -174, -752, 373, 222, 886, -806, 1495, -274, 685, -1197, 964],\n [662, -140, 165, -21, 4, -228, 71, -135, -596, -570, -149, -281],\n [-8, -310, 295, -7, -58, 30, 257, -135, 27, -78, 257, -430],\n [-118, 276, -386, 820, -429, 721, -71, 985, -16, 1114, -480, 502]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"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, 339, 417, 590, 9, 602],\n [-379, -367, 1294, 567, 943, 851, 1302, 308, 314, -93, -1096, 472],\n [801, 1796, -44, -693, 546, -327, 173, -1264, -883, 81, -484, 730],\n [-359, 686, -85, -30, -209, 922, -276, -577, -1099, 838, 85, 894],\n [184, -169, -225, -638, 908, -541, 351, 45, 83, -1147, 423, -728],\n [-1041, -764, 1249, 143, 282, 180, 1066, 717, -208, -1094, 284, -53],\n [-406, -722, -115, -111, -89, 1103, 803, 1, -65, 306, 214, -145],\n [504, 297, -1182, -377, 333, 525, -582, -483, -617, 386, 178, -123],\n [-871, -1531, 454, 163, -302, -536, 364, 719, 1938, -177, -53, -572]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"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, 231],\n [-518, -58, -241, 793, 865, -181, -641, -486, 1081, -196, -953, -637],\n [124, 67, 68, -1066, -1523, -3, 571, -384, -349, -174, 178, 232],\n [-820, -580, -1044, 161, -624, 90, -765, -844, 1432, -374, -1199, -1059],\n [-274, -760, -164, 841, 580, 311, 59, 237, 81, -177, 923, 356],\n [680, 957, -1032, 193, -341, 436, 135, 579, 58, 404, -799, 57],\n [462, 803, 649, -224, 458, 121, 600, 401, -1187, 608, 518, 690],\n [-426, -689, 393, 185, 207, -240, -78, -377, 317, -458, 430, -12],\n [-124, -480, 565, -863, -915, -109, 444, -306, -557, -229, 857, 318]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"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, -62, -489, 618, 918],\n [-1131, 169, -649, 153, -285, -310, 424, -1004, 325, -671, 1327, -671],\n [444, -829, -1317, -361, -952, -251, -1172, 44, 1452, -529, -1063, -180],\n [-458, 350, 129, 262, -283, 113, 410, -1453, 878, -189, 1289, -1068],\n [-572, -924, -1663, 920, -1245, -1088, -1628, 146, 225, 551, -784, -700],\n [21, -1012, -333, -1384, 82, 1109, -878, 262, -557, -1119, -249, -230],\n [-672, -363, -276, -180, 540, -405, 242, 408, -1384, -660, 36, 942],\n [1043, 390, 222, -358, -489, -16, 185, -502, 171, -635, -106, 382],\n [-492, 231, 824, 310, 584, 239, 429, -187, 357, 1539, 768, -127]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"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, 1197, 274],\n [-696, -254, -361, -383, -465, -626, 166, -952, -995, -162, -284, -311],\n [-449, -530, -1014, -157, -643, 936, -219, 1018, 182, 456, -1064, 236],\n [-525, -1507, -1082, 800, 156, -172, 86, -539, 460, 387, 1855, -173],\n [775, 78, -419, -104, -645, 222, -534, 2009, 416, -444, -1315, -205],\n [-1599, -96, -1734, 343, -829, 1510, 601, -196, -95, 1020, -762, 162],\n [-573, -175, -313, -195, 67, -789, 793, -892, -379, -1761, -91, -489],\n [-207, -301, -561, 244, 770, 925, 1408, 597, 201, 640, -1134, -323],\n [1551, 1086, 1269, -1124, -362, -267, -458, -1189, -152, -164, 416, 386]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"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, 28, 100, 100, 12, 0, -8, 84, 44],\n [-17, 340, 272, -34, -119, -425, -425, -51, 0, 34, -357, -187],\n [14, -280, -224, 28, 98, 350, 350, 42, 0, -28, 294, 154],\n [-23, 460, 368, -46, -161, -575, -575, -69, 0, 46, -483, -253],\n [-12, 240, 192, -24, -84, -300, -300, -36, 0, 24, -252, -132],\n [26, -520, -416, 52, 182, 650, 650, 78, 0, -52, 546, 286],\n [15, -300, -240, 30, 105, 375, 375, 45, 0, -30, 315, 165],\n [14, -280, -224, 28, 98, 350, 350, 42, 0, -28, 294, 154]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"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, 279, 483, -592],\n [154, -469, 639, 350, 471, -767, 173, -148, 719, 577, -1329, -856],\n [-448, -547, 730, -138, 681, -830, -116, -410, 831, 185, -560, -31],\n [-254, 445, 1317, 913, 58, -668, 70, 621, 482, 614, -1045, -186],\n [-252, 478, 243, 133, -232, 111, -92, 359, -186, -79, 439, 503],\n [-220, 947, -329, 369, -986, 964, -223, 735, -349, -323, 43, 413],\n [-730, -63, 312, -317, 132, -169, -362, -149, 561, -251, 62, 574],\n [278, 669, -352, 199, -804, 555, 26, 663, -263, 53, 86, -134],\n [0, 514, 222, 341, -260, 132, 50, 439, -361, 54, 286, 259]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"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, 514],\n [222, 706, -524, 268, -238, 74, 238, -186, -302, 776, 266, -436],\n [168, 162, -234, 153, -167, -235, 167, -146, -66, 194, 141, -191],\n [-276, -398, 442, -269, 279, 283, -279, 238, 166, -458, -253, 363],\n [-75, -85, 110, -70, 75, 95, -75, 65, 35, -100, -65, 90],\n [120, -290, 10, 55, -105, -485, 105, -110, 130, -290, 35, 15],\n [-54, 308, -82, -1, 41, 357, -41, 52, -136, 318, 13, -73],\n [-189, -697, 488, -241, 206, -138, -206, 157, 299, -762, -242, 407],\n [210, 806, -556, 272, -230, 178, 230, -174, -346, 880, 274, -464]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"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, 401, -165, -258, 179],\n [-71, 164, -702, -552, 232, 413, 106, -344, 589, -285, -12, -44],\n [22, 36, -494, -381, 198, 174, 87, -185, 412, -208, 66, -93],\n [432, -372, -858, -621, 534, -336, 219, -9, 702, -402, 522, -501],\n [544, -632, 260, 258, 164, -992, 50, 538, -236, 52, 540, -430],\n [-92, 0, 832, 636, -360, -204, -156, 268, -692, 356, -168, 204],\n [72, -108, 234, 189, -54, -216, -27, 153, -198, 90, 54, -27],\n [130, -172, 234, 195, -26, -310, -17, 199, -200, 84, 114, -77],\n [-132, 60, 702, 531, -330, -84, -141, 183, -582, 306, -198, 219]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"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, 1179, 825, 238, -479],\n [-1907, 1322, 1313, -214, 954, 1261, -823, 432, -832, 955, 804, -1535],\n [-1670, 189, 941, 49, -478, 745, 690, 1470, 762, -827, 372, -2001],\n [1889, 329, -814, 1055, 249, 1585, 1148, -156, -107, -612, -1205, 845],\n [505, 522, -569, 1967, 922, 1081, -281, -359, 18, 1445, 637, 435],\n [-1562, -267, 1420, -1186, -1134, -1167, -413, 720, -900, -512, -355, 20],\n [408, -584, 64, -1349, -323, -1278, -643, -386, -1198, -853, -511, 1357],\n [891, 310, 522, -863, 206, 904, -67, -385, -85, -1459, -1150, 73],\n [332, 1133, -704, 929, 994, 1429, 747, 564, -523, 1835, 155, -216]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"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, 204, 323, -34, 425, 272],\n [238, -51, -357, 34, -357, 187, 357, -204, -323, 34, -425, -272],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n [-210, 45, 315, -30, 315, -165, -315, 180, 285, -30, 375, 240],\n [-168, 36, 252, -24, 252, -132, -252, 144, 228, -24, 300, 192],\n [322, -69, -483, 46, -483, 253, 483, -276, -437, 46, -575, -368],\n [-364, 78, 546, -52, 546, -286, -546, 312, 494, -52, 650, 416],\n [154, -33, -231, 22, -231, 121, 231, -132, -209, 22, -275, -176]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"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, 603, 236, 475, 326],\n [200, 41, 412, 1317, -1024, -1589, -546, 110, -284, -810, 24, 631],\n [-595, -389, 585, -978, -445, -1387, -6, -99, 49, -143, 183, 292],\n [-16, 51, 655, 62, 278, -794, -453, 42, -133, -955, 237, 876],\n [641, 219, -64, 1165, -404, 107, -138, 140, 52, -332, -17, 92],\n [243, -520, 233, 786, -1296, -480, -432, 467, 671, 426, 554, 205],\n [-109, 290, -664, -155, 771, 320, -100, -130, -458, 203, -496, -253],\n [-1174, -1022, 826, -292, -37, 361, -763, 527, 522, 886, 1259, 739],\n [-760, 134, -73, 95, -104, -165, 447, -411, -803, 93, -385, -421]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"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, 495, 347, 169, -548],\n [-527, 240, 858, -320, 236, -365, 276, 479, -112, -802, 81, 82],\n [-354, 384, 462, -188, 400, 129, 199, 460, -302, -46, -32, 204],\n [-576, 768, 816, -160, 704, 40, 680, 688, -464, -432, -144, 512],\n [124, -510, -246, -238, -342, 149, -791, -94, 140, 540, 230, -492],\n [-313, -108, 450, -396, 8, -77, -326, 333, -48, -110, 195, -234],\n [-8, -57, -6, -59, -25, 42, -126, 24, -3, 99, 38, -70],\n [-586, 303, 966, -323, 279, -436, 386, 522, -123, -961, 68, 134],\n [-399, 213, 498, -365, 313, 180, -131, 529, -287, 125, 85, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"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 [21, 148, -108, 298, -379, 227, 349, 114, 82, -261, -74, 271],\n [-243, 750, 318, 48, 139, 350, 120, 53, 616, 64, 88, -467],\n [-179, -546, -790, 894, -359, 49, 529, -46, 88, -957, -522, 1361],\n [262, -376, -853, 533, -652, -204, -189, -38, -402, -674, 486, 864],\n [-155, 29, -454, 101, 413, -366, -858, -302, 195, -227, 708, -18],\n [-380, 43, 380, -377, 960, -155, -331, -212, 407, 394, -226, -547],\n [370, -466, 380, -514, -182, -100, 228, 160, -694, 526, -360, -176],\n [-292, -129, 442, 81, 168, 375, 977, 142, 303, 60, -1218, 213]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"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, 1168, -1098, -1536, -59],\n [-1244, -322, -160, -541, 374, -380, -635, 261, 182, -1649, -212, -1005],\n [848, -382, -68, 270, -15, -394, 424, 445, 156, 247, 686, 479],\n [-533, -4, 236, -245, 83, 416, 54, -192, 7, -347, -34, -922],\n [-284, 1129, 1542, 532, -234, 273, 1302, 320, 600, 361, -663, 65],\n [188, -1248, -206, -408, -115, -56, -234, -787, 843, -211, 767, 600],\n [-1192, -438, -865, -450, 51, -842, -790, -279, 140, -223, -464, 518],\n [-350, -197, -440, -469, -218, -286, -472, -95, 190, -80, -117, 115],\n [-567, 766, 190, -152, 77, 1085, 237, -315, -712, 522, -596, -1427]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"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, 165, 433, -941, 811],\n [-853, -69, 338, -319, 430, -136, 17, -96, -672, -1314, 1225, 179],\n [-107, 909, -184, -124, 1716, -1120, -517, 548, -676, 429, 759, 246],\n [879, -261, -135, 99, 1014, -104, -988, -54, -830, 627, 481, -853],\n [-23, -269, 822, -384, 758, -368, -1076, -446, -1866, -473, 453, 527],\n [-129, -1269, -202, 348, -190, -390, -231, 1212, -965, -549, 532, -72],\n [-363, 569, -473, -126, -226, -48, 649, -394, 1250, 282, -701, -85],\n [-769, 142, -459, -708, 821, 560, 810, 1229, -677, -114, 1372, 145],\n [548, 545, -1616, -551, 241, -705, 751, 644, 1188, 710, -465, -805]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"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, -142, 600],\n [-634, 157, -312, 586, -663, 669, -641, 6, 319, -140, 20, -47],\n [-186, 51, 246, -368, 775, -183, 749, -214, -439, 1232, 762, 251],\n [628, -102, -540, -127, -39, -189, -304, -153, -481, -1354, -590, 394],\n [-71, 12, -370, -26, 48, 290, -164, -102, -214, -144, 123, 408],\n [-1047, 249, -544, 755, -756, 1106, -823, -69, 306, 118, 317, 173],\n [141, -135, -524, -147, -130, 604, -499, 205, 184, -558, -95, 533],\n [183, -227, -528, -721, 620, 738, -11, 211, -50, 310, 555, 1089],\n [131, -272, -188, -546, 214, 802, -200, 560, 648, 320, 315, 568]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"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, 322, 804, 396],\n [426, 125, 288, 608, 820, -518, -91, 996, -287, 400, -474, -44],\n [-270, 200, -106, -474, -582, 451, -112, -718, 465, -281, 411, 133],\n [226, 318, 932, 276, 780, -660, 2, 1060, -434, 582, 96, 188],\n [402, 400, 4, 468, 516, -124, -356, 556, 276, 158, -456, 8],\n [-137, -657, -566, -14, -298, 108, 317, -390, -303, -237, -198, -268],\n [184, 19, -944, 224, -236, 500, -321, -468, 641, -412, -588, -206],\n [195, 464, -250, 126, 6, 286, -430, -94, 654, -131, -228, 52],\n [59, -249, 36, 172, 212, -237, 169, 280, -362, 120, -147, -95]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"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, 117, -143, 221, -221, -91, -78, -65, -52, -13],\n [21, -140, 98, -63, 77, -119, 119, 49, 42, 35, 28, 7],\n [75, -500, 350, -225, 275, -425, 425, 175, 150, 125, 100, 25],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n [-12, 80, -56, 36, -44, 68, -68, -28, -24, -20, -16, -4],\n [-72, 480, -336, 216, -264, 408, -408, -168, -144, -120, -96, -24],\n [-66, 440, -308, 198, -242, 374, -374, -154, -132, -110, -88, -22],\n [45, -300, 210, -135, 165, -255, 255, 105, 90, 75, 60, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"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, -471, 121, 471],\n [40, -1188, 598, -490, -736, -720, 839, 546, -490, 855, 115, -1595],\n [54, -465, -96, -372, -632, -526, 361, 289, 37, 646, -556, -876],\n [27, 206, 212, 329, 501, 423, -194, -133, -162, -469, 619, 569],\n [-725, -100, 360, -575, -175, -465, 210, -355, 20, 5, -55, -405],\n [527, -104, 264, 629, 501, 595, -82, 261, -408, -303, 893, 423],\n [682, -349, -84, 364, -84, 182, 115, 525, -219, 288, 142, -198],\n [-12, -484, 446, -94, -92, -148, 323, 174, -338, 159, 411, -499],\n [-94, -460, 748, 42, 222, 58, 286, 70, -528, -140, 940, -260]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"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, -999, -1463, -702],\n [-1615, -494, -1635, 270, 82, -202, 890, 563, 480, 385, 1617, 1017],\n [592, 1158, 846, -756, 952, -356, -188, 796, -676, -226, 880, -890],\n [357, -199, 883, 366, -816, 544, 1410, -476, 373, -239, -342, -613],\n [-679, -636, 577, 677, 174, -153, -317, 146, -39, -26, -494, -224],\n [397, 318, -259, -120, -673, 592, 632, -335, 515, -851, 665, 191],\n [508, 472, 671, 29, 801, -745, -227, 258, 834, -551, -29, -1044],\n [473, 1043, -888, -1561, 747, -524, -504, 421, 338, -384, 118, -302],\n [-1191, -603, -1171, -641, 56, -1043, 799, 1161, 421, 1565, 1044, 206]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"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],\n [342, 118, -576, -15, -413, 59, -189, 427, -354, -361, -128, 330],\n [722, -194, -660, 300, -508, 64, 110, 426, -448, -582, -512, 522],\n [-684, 344, 612, -395, 351, -293, -107, -439, 118, 837, 416, -640],\n [228, -352, 252, 317, 79, -149, 461, -283, -46, 113, -400, -56],\n [19, -357, 480, 274, 276, -122, 461, -428, 167, 232, -252, -187],\n [-190, -78, 528, 27, 241, -295, 305, -463, 2, 565, -96, -402],\n [19, -243, -150, 165, 179, 553, -140, 232, 604, -724, 216, 399],\n [-57, -285, 180, 189, 285, 291, 96, -81, 501, -297, 84, 117]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"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, 472, 1864],\n [-306, 1200, -292, -551, -1141, -650, -1056, 1686, -443, -1062, 173, -423],\n [-120, -531, 954, -346, 496, 293, -853, 654, 410, 784, 45, -1238],\n [584, 542, -935, -142, -773, 66, 112, -974, -323, -301, -515, -486],\n [1707, 349, -793, -168, -674, -44, -129, 65, -1639, -1233, 346, 255],\n [1320, 6, 691, -778, -272, -591, 809, 965, -1648, -831, 866, 384],\n [-425, -1511, 1627, 164, 897, 730, -100, 802, 178, 671, 181, -1557],\n [865, 225, 567, 606, -437, -642, -667, 415, -702, 131, -336, -988],\n [828, -286, -838, -309, -457, 479, 534, -1287, 863, 313, -432, -75]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"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],\n [108, 346, -355, 446, 58, 219, 23, -272, -373, -49, 78, 249],\n [226, -344, -224, 394, 382, 422, 292, -480, -644, -56, 656, -338],\n [198, -328, 1158, -1318, -190, -12, 730, 228, 230, -194, 64, -200],\n [-187, 462, 472, -695, -507, -449, -152, 562, 730, -2, -770, 455],\n [-204, 258, -444, 444, -66, -192, -486, 114, 192, 126, -306, 204],\n [-49, -516, 13, 13, 189, -20, -41, -2, 25, 73, 256, -430],\n [-183, 671, -310, 249, -286, -243, -431, 211, 294, 61, -595, 563],\n [-163, -110, 464, -623, -239, -353, -84, 438, 586, 42, -358, -33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"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, -389, -46],\n [396, -84, 826, 52, 110, 759, 215, 637, 734, 504, -281, -14],\n [-134, 276, 973, 1091, 697, -213, 69, 434, 1052, 1372, -489, -1045],\n [-331, -79, 77, 1008, 115, -918, -481, -136, 72, 405, 426, -534],\n [-410, 217, -133, -617, -476, 642, 285, 664, -1, -923, 349, 770],\n [-165, 605, 412, -196, 806, -7, 28, 331, 528, 486, -304, -219],\n [347, -116, 599, 1407, 396, -1080, -612, 228, 131, 853, 534, -1017],\n [-105, 262, 194, -12, 427, 16, 108, -13, 333, 435, -398, -250],\n [566, 467, 45, -479, -187, 796, 1091, 725, -318, -375, -633, -337]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"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, -1416, -452, -1756, 336, 785],\n [370, 1637, 274, 162, -161, 1049, -1451, -1074, -177, 458, -280, -1341],\n [731, 10, -441, -616, 402, 1193, -581, -469, 743, -1475, 422, -378],\n [-234, -554, -187, 1084, -326, 626, 491, -554, -1783, -89, -1023, -70],\n [426, -279, -135, -533, 238, -591, -95, 977, 759, 470, 74, -133],\n [-309, -808, -769, 410, -815, 418, 1199, -118, -253, -421, -619, 209],\n [-842, -720, -792, 1141, 1261, -817, -208, 555, -663, 1186, -349, -522],\n [1127, 3, -1377, -1074, -96, 1086, -458, 209, -451, -773, -222, -1053],\n [-108, 1059, 1613, 233, -467, 266, -543, -1107, -98, 114, 217, 392]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"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, -50, -30, 110, -170, 80, -70, 140, 170, -150, 210, 160],\n [120, 25, 15, -55, 85, -40, 35, -70, -85, 75, -105, -80],\n [-168, -35, -21, 77, -119, 56, -49, 98, 119, -105, 147, 112],\n [-288, -60, -36, 132, -204, 96, -84, 168, 204, -180, 252, 192],\n [576, 120, 72, -264, 408, -192, 168, -336, -408, 360, -504, -384],\n [-120, -25, -15, 55, -85, 40, -35, 70, 85, -75, 105, 80],\n [72, 15, 9, -33, 51, -24, 21, -42, -51, 45, -63, -48],\n [432, 90, 54, -198, 306, -144, 126, -252, -306, 270, -378, -288]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"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, -55, 567],\n [-216, 43, 67, -285, 573, 627, 174, -35, 29, 699, -482, -763],\n [-342, 473, -219, -236, 197, 431, -161, -195, 740, -405, 93, 160],\n [-166, -350, -142, -225, -322, 147, 167, 784, -459, 259, -335, -778],\n [58, -470, 719, 822, 117, 8, 485, -259, -371, 398, 164, 146],\n [848, -559, 150, -178, 325, -643, 129, -120, -1142, 1204, -531, -692],\n [190, -753, 207, 242, -530, -366, 298, 779, -1089, 499, -237, -553],\n [-430, -251, 219, 466, -881, -31, -9, 1059, -580, -175, -1, 132],\n [-476, 152, -9, -311, 127, 624, -74, 603, -208, 594, -619, -697]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"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, -504],\n [-168, 656, 373, -198, -101, -77, -196, -400, 354, -229, -195, -15],\n [-643, -3, 359, 138, 252, -424, -315, -609, 28, -2, 429, 126],\n [-171, -187, 237, 70, -134, -226, -211, -189, -48, 284, 219, -204],\n [-26, -162, -166, 80, 177, 27, 96, 83, -106, -55, 84, 144],\n [-463, 489, 563, -90, -51, -325, -381, -660, 298, -77, 87, -54],\n [-342, -670, -176, 324, 397, -221, 8, -43, -354, 149, 534, 210],\n [351, -329, 54, -16, -493, 31, -53, 285, -114, 505, -48, -489],\n [-190, 554, 202, -136, 91, -31, -88, -323, 274, -333, -144, 156]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"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, 1130, -1112],\n [-736, 190, -581, 83, -679, -953, -266, -311, -918, -551, -616, 750],\n [-798, -213, -1544, -186, 2163, 469, 1437, 1095, 1708, 897, 616, -457],\n [786, -138, 896, -514, 759, -343, 36, 494, -197, 155, 784, -1085],\n [-1403, -176, -1457, 325, -180, -145, 696, 302, -168, 202, -600, 451],\n [1168, -694, 1233, 302, -156, -354, 397, 54, -553, -114, 386, -650],\n [595, 583, -165, 171, -579, -512, 902, -359, -649, -1439, -686, 776],\n [718, -231, 1087, 374, -105, 911, -624, -329, 288, 890, 1122, -1051],\n [827, 1361, 484, 465, -224, 980, -53, -717, -52, -1, 719, -770]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"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],\n [-287, 646, -173, 624, 102, -132, 145, -15, -230, -389, -83, 214],\n [242, -705, 86, -722, 30, 256, -189, -215, 522, 391, -56, -274],\n [-91, 92, -97, 60, 114, 60, -1, -165, 158, -79, -115, 2],\n [-30, -382, -186, -484, 336, 392, -172, -640, 896, 136, -362, -240],\n [370, -857, 214, -834, -114, 192, -197, -15, 346, 511, 88, -290],\n [-93, 255, -39, 258, 0, -84, 66, 60, -168, -144, 9, 96],\n [-255, 351, -237, 282, 252, 84, 36, -330, 252, -258, -249, 60],\n [14, 401, 170, 498, -318, -384, 173, 615, -874, -151, 344, 242]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"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, -29, -13, -420, -269],\n [118, 160, 333, 525, -487, -34, -151, -96, 1039, -608, -944, 690],\n [242, -297, -228, -279, 23, -1119, 1013, 216, -458, -651, -1427, -242],\n [113, -99, -612, -902, 146, -702, 311, 160, -1032, 271, 342, -419],\n [332, -23, 639, 377, -1, -220, 438, -180, 331, -613, -881, 205],\n [828, -586, 10, -477, 766, 0, -52, 139, 103, -1297, -1217, 345],\n [-76, -528, 831, 664, 588, 661, 99, -236, 1345, -1302, -1436, 749],\n [867, 749, 475, 263, 175, -698, 1126, -97, -990, -251, -916, -347],\n [239, -20, 82, 142, 747, 1263, -716, 83, 13, -19, 566, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"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, -1046, 708, 204, -369, 134, 1163],\n [1405, 154, 304, -1482, 634, 762, 190, 246, -91, 1367, -406, -1313],\n [-882, 123, 3, -1514, -901, 113, 115, -775, 964, 871, -101, 360],\n [-886, 712, 407, 1049, -396, 133, -56, 389, -1055, 261, 336, -279],\n [-132, 55, -1055, -1219, -2, 187, -614, 49, 141, 1071, -687, 381],\n [-81, 664, -377, -194, 259, 1256, -1070, 1464, -357, 872, -448, -364],\n [-836, 560, 427, -216, -469, 136, -656, -914, 1120, -129, -481, 1100],\n [931, 358, 481, -469, 766, 566, -459, -448, 744, 331, -243, -167],\n [440, -897, -310, -476, 381, -352, 761, 667, -549, 449, -112, -440]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"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],\n [256, -190, 308, -54, -232, 312, 74, -222, 94, 116, -336, -110],\n [-344, 380, -402, 202, 364, -538, -122, 328, -156, -30, 518, 54],\n [-268, -80, -349, -233, 126, -61, -27, 166, -32, -403, 203, 325],\n [288, 75, 374, 239, -140, 76, 31, -181, 37, 422, -224, -341],\n [144, -330, 152, -262, -224, 388, 82, -178, 106, -160, -308, 106],\n [-208, 10, -264, -106, 128, -116, -34, 146, -42, -240, 196, 198],\n [-68, 290, -59, 263, 162, -311, -63, 116, -82, 211, 217, -151],\n [-16, -290, -48, -310, -112, 268, 50, -58, 66, -312, -140, 234]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"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, 299, -346, 93, 7, 1336, 48],\n [-765, -173, -588, 844, 1118, 200, -632, 322, 417, -572, -201, -692],\n [555, 1259, -643, -1002, -985, 233, 587, -531, -784, -280, 574, 1192],\n [1378, 934, -565, -1488, 111, 235, -250, 192, 313, 377, -99, 234],\n [425, 261, -1419, 203, -620, -645, 429, -798, -385, -440, 1685, 532],\n [440, -870, -71, 501, 532, -531, -486, -57, 725, 525, -380, -657],\n [-520, -621, -1137, 1417, 1247, 24, -261, -189, 536, -793, 1141, -242],\n [-50, 284, 541, -1239, -46, -565, 244, 191, -569, -39, -1376, 1184],\n [490, 160, -37, -487, 732, 57, -223, 344, 273, -66, -896, 669]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"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, 603, 510],\n [601, 650, -171, 316, -306, 452, 370, -301, -35, 198, -238, 107],\n [418, -137, 58, -84, -68, 546, 581, -345, -385, -553, -126, 22],\n [912, 554, -100, 914, 177, 606, 665, -249, 235, 684, -150, -879],\n [-985, 1394, 50, 529, -575, -296, 755, -228, -1263, -786, -482, 1625],\n [-1663, 338, 231, 194, -682, -133, 1616, -547, -628, -139, -959, 607],\n [468, 958, -296, 954, 293, 98, 436, -95, -1931, 542, 145, 668],\n [-1098, 262, -841, -607, -1490, -89, -132, 556, -694, 1718, 695, 1010],\n [-409, 1431, -821, 121, -1492, 117, 1348, -503, -1303, 742, 164, 1317]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"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, -1466, 103, -5, -1208, 236, -819],\n [-92, 134, -1099, -134, 898, 1533, -2499, -2, 713, -607, -1134, 196],\n [-347, -635, -803, -280, 530, -656, 1953, -170, -67, 736, 101, -1193],\n [305, 219, 1290, 445, 19, -497, 1667, 933, 95, 2000, 423, 959],\n [-179, -342, 376, 944, 924, 1474, -1544, 887, 1249, 411, -1028, 1955],\n [1133, 872, 472, -1104, -2154, 248, -678, 821, -84, -899, -152, 409],\n [662, -2296, 391, -426, -252, -1304, 105, -221, -243, -607, 1480, 917],\n [-330, -301, 60, 591, 86, -119, -799, -162, 384, -1510, -559, 695],\n [-23, 305, 770, 810, 642, -712, 1745, -52, 44, 923, -283, 914]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"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],\n [-789, -632, -159, 627, -398, -942, 1442, 43, 1567, -221, 667, 764],\n [186, -656, -659, -526, -1123, 536, -81, -785, 473, -717, 435, 358],\n [172, 1071, 657, -309, 797, 421, -1063, -9, -687, 166, -776, -524],\n [-568, -105, 73, 38, -178, -701, 692, -39, 1183, -395, 106, 586],\n [495, -341, -487, -576, -462, 543, -432, -33, -1121, 60, -172, -42],\n [1031, -363, -422, -107, -26, 600, -663, 203, -1233, 280, 195, -773],\n [452, 640, 366, -181, 787, 238, -815, 468, -1308, 513, -652, -638],\n [311, -524, -316, 404, -42, -65, 305, 335, -369, 341, 426, -241]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"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, 336, -1344, -611],\n [1433, -1101, -1809, -129, -132, 990, 78, -105, -157, 987, -381, -1583],\n [-242, -10, 753, -996, -215, -456, 1171, -809, 357, 83, -742, -292],\n [243, -431, -840, 610, -155, -40, -1366, -458, -954, 972, 1440, 568],\n [-38, 250, 10, 1031, -1023, -753, -1031, -482, 484, 1154, 119, -586],\n [-171, 1733, 710, -649, 282, -368, 870, -165, 59, 1047, -824, 7],\n [-423, 351, -572, -427, -1391, -68, 1095, -2020, 1038, 1212, -385, 287],\n [770, 566, -196, -1053, 584, -521, -283, 146, -601, 39, -613, 231],\n [31, 51, 1291, 114, 1175, -389, 394, 68, -707, -241, -488, 1009]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"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, -49, 56, -119, -14, 140, 7, 56, 42, 126, -84, -42],\n [546, 147, -168, 357, 42, -420, -21, -168, -126, -378, 252, 126],\n [-572, -154, 176, -374, -44, 440, 22, 176, 132, 396, -264, -132],\n [-624, -168, 192, -408, -48, 480, 24, 192, 144, 432, -288, -144],\n [468, 126, -144, 306, 36, -360, -18, -144, -108, -324, 216, 108],\n [572, 154, -176, 374, 44, -440, -22, -176, -132, -396, 264, 132],\n [-494, -133, 152, -323, -38, 380, 19, 152, 114, 342, -228, -114],\n [286, 77, -88, 187, 22, -220, -11, -88, -66, -198, 132, 66]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"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, -437, 252, 176],\n [-1290, -653, -894, 256, -1124, -85, -307, -285, -447, -31, -270, -905],\n [765, 87, -68, -449, 999, 754, 502, -330, -667, 53, -193, -294],\n [-469, 125, -770, -365, -127, -764, 446, -329, 770, -188, -90, 14],\n [-436, -605, -893, -220, 253, -636, 102, 421, -290, 33, -1136, -855],\n [-171, -207, -725, -428, -502, -835, 354, 317, 709, 291, -153, 229],\n [129, 1152, 171, -312, 442, -200, 1098, -576, 423, -738, 172, 812],\n [720, 17, -54, -416, 802, 527, 575, 79, -773, 93, -458, -183],\n [-307, 451, 83, 164, 372, -387, -153, -141, 577, -386, -196, -18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"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, 354, 1044],\n [514, 790, 377, -1609, 878, 743, 275, -314, 228, -140, 24, -83],\n [1151, 370, -28, 625, 174, -271, 788, 526, -724, -494, 667, 771],\n [306, 268, -230, 1, -33, 270, 351, 455, 3, 446, 970, -310],\n [-1244, -1142, -635, -222, 118, 556, -22, -1166, 310, -567, -443, -109],\n [417, 1124, -486, -547, -46, -1117, 1294, 574, -59, -335, 898, 670],\n [-417, 12, -479, -1439, 536, -694, 712, -178, 362, -632, 499, 366],\n [1294, 968, 1767, 856, -590, -37, -187, 76, -591, 103, 47, 345],\n [596, 1647, -58, -1624, 714, -241, -131, 1554, 1031, -131, 195, 821]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"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, -501, 310, -40],\n [-1085, -782, 635, 773, -204, -1145, -430, 266, -551, 23, -364, 820],\n [-649, 58, 1137, 740, 477, -937, -691, 871, 303, 323, -474, -568],\n [-248, -635, 302, 412, -489, 151, -407, 519, 287, 422, 167, -805],\n [34, 13, -16, 234, -251, 40, 262, -664, -663, -47, -78, 606],\n [-1042, -750, -484, 874, -41, 220, -615, 203, 326, -608, 1335, -183],\n [-141, 785, 316, -489, 585, -1037, 230, 575, 522, 12, -1174, 610],\n [-1216, -1178, -436, 799, -246, -111, -357, 171, 46, -597, 1222, 17],\n [255, -1, 462, -118, -893, -653, 32, 213, 266, 1090, -685, -940]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"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, -140, -33, -320, -615, 217, -528, -180, 28, -413, -151],\n [393, 106, -180, 39, -340, -655, 189, -576, -260, -24, -421, -167],\n [-21, -34, 26, -24, 33, 64, -7, 60, 44, 17, 36, 18],\n [-63, 410, -218, 324, -169, -332, -77, -348, -412, -233, -136, -110],\n [438, -4, -130, -51, -315, -605, 224, -516, -160, 41, -411, -147],\n [-591, 506, -114, 456, 163, 304, -357, 180, -316, -333, 316, 38],\n [558, -468, 102, -423, -159, -297, 336, -180, 288, 309, -303, -39],\n [282, -220, 42, -201, -89, -167, 168, -108, 128, 147, -161, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"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, -275, 638, 521, -169],\n [-522, -78, -551, 494, -329, -251, 73, 205, 69, 472, -87, -466],\n [308, 186, 791, 580, 661, -1251, 825, 529, 57, -638, -629, -16],\n [-366, -254, -85, -142, 359, -183, -475, -739, -41, 794, 923, 210],\n [-1, -562, 901, -395, -362, 204, -913, -425, 37, -15, 37, 761],\n [-727, 319, -740, 983, 444, 459, 107, 371, 108, 192, -101, -497],\n [-641, -285, -994, 769, -98, 611, 823, 863, -516, 186, -51, -1075],\n [-1070, -1464, -620, 119, -843, -735, 15, -256, -650, 1697, 1070, -719],\n [91, 32, 89, -1009, -208, 223, -1367, -1355, 368, 708, 893, 869]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"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, 28],\n [224, -78, -296, -480, 576, 112, 186, 324, 260, -248, 58, 336],\n [471, -120, -531, -635, -128, 786, -37, 518, 245, -548, -151, 350],\n [-122, 54, 135, 242, -235, -122, -46, -175, -161, 129, -8, -168],\n [29, -399, 439, -361, 908, 406, -482, 352, 1173, 180, -16, 418],\n [64, -102, -66, -384, 1014, -212, 214, 226, 402, -26, 162, 344],\n [323, -36, -424, -407, -161, 480, 45, 321, 36, -401, -95, 202],\n [46, 135, -263, -22, -61, -198, 291, -39, -369, -133, 53, -40],\n [102, 171, -478, -270, 588, -524, 653, 62, -380, -224, 209, 148]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"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],\n [-124, -78, -221, 160, -45, 685, -470, 244, -444, -97, 546, 757],\n [210, -55, -179, -250, 25, -142, 209, -35, -200, -136, -423, -247],\n [49, -3, -1, -61, 17, -109, 86, -33, 26, -17, -137, -131],\n [433, 60, -259, -481, -193, -466, 755, -252, -310, 34, -926, -815],\n [-59, -42, 371, 11, 333, -586, 29, -82, 714, -98, -228, -409],\n [36, -72, 144, -84, 248, -372, 36, -32, 344, -156, -272, -280],\n [-73, 147, -11, 133, -301, 217, 82, -55, -154, 293, 265, 111],\n [-165, -199, 340, 101, 578, -322, -424, 129, 698, -364, 47, 48]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"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, 187, -102, 255, -664, -385, 252],\n [-19, 440, 322, -49, -888, 117, -531, 267, 3, -537, 659, 535],\n [-541, -19, 452, 299, -549, -131, 211, 302, -463, -268, 969, -1080],\n [-1304, -411, 677, 243, 365, -1083, 58, -142, -287, -1420, -1208, -842],\n [-166, 288, 4, 488, 803, -498, -1172, 829, 1252, -260, -54, 521],\n [994, 340, -177, -931, 239, -264, 293, -101, 579, 616, -1082, 566],\n [559, -365, -774, -875, -764, 1151, 789, -943, -1197, 1226, 25, -521],\n [-839, 80, 406, -432, -768, 291, -1499, 525, 358, -1795, -200, 1383],\n [-257, -413, 204, 526, 669, -650, -389, 56, 788, 427, -220, -420]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"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, 921, -310, 410, -551, -406],\n [-943, 135, 468, 0, 139, 877, 133, 251, -328, 1175, -295, 848],\n [72, 1461, 487, -105, 253, 498, -1308, -408, 102, 275, 494, -263],\n [305, -41, 515, -328, 953, -661, -690, 936, -739, 925, 15, -519],\n [-1410, 59, -213, 564, 180, 211, 1289, -661, -535, -476, 876, 1994],\n [200, 486, 405, -1180, -168, -536, -424, -618, 622, -39, 855, 21],\n [141, 759, 1220, -55, 504, 432, -942, -262, -377, -273, 713, 209],\n [-157, -252, -477, 394, 677, -138, 659, 137, -865, -106, 138, 610],\n [-1170, -1282, 400, 618, 689, -583, 1514, 517, -1267, 369, -785, 917]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"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, 1241, 175, 496],\n [126, 325, 500, -359, -728, -257, 441, -444, 106, -167, -666, 310],\n [80, 265, 294, -167, -215, -651, -365, -718, 321, -1176, -1431, -31],\n [66, -96, 363, 0, -1126, 275, 81, -820, -321, 644, -81, 578],\n [-539, -516, -97, 228, 632, 503, -149, 542, -634, 486, 1552, 80],\n [-1489, -108, -8, 211, -796, 14, 1388, -1007, -111, 241, -352, 926],\n [-2406, -608, -724, 1294, 444, 117, 589, -1007, -892, -863, -513, 733],\n [-943, -307, 44, 242, 1091, -977, -141, -9, -964, -1329, -309, -433],\n [-442, -341, 9, 282, -815, 29, 245, -915, -564, 677, -74, 401]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"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, 482, 560, -295, 1336],\n [-692, 411, -1248, 957, -72, -171, 500, 748, -13, 214, -907, -1581],\n [659, -152, 223, 574, 288, 495, -119, -61, 121, -654, 733, -629],\n [-749, -613, -72, -115, 152, -215, 80, -543, 353, -615, -366, -150],\n [1110, 824, 1046, 1020, -857, 855, -971, 1753, -889, 446, 272, -1120],\n [-367, 53, -107, 199, -1109, 201, -181, 459, 309, -225, -1229, 282],\n [-301, 206, -1190, 233, 444, -696, 694, 36, 581, -773, -116, -348],\n [1053, 392, 169, 604, -441, 1381, 442, 37, -84, 241, 832, 878],\n [988, -429, 1615, -982, -33, 449, -303, -762, -405, 116, 1262, 1378]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"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, -433, 116, 162],\n [736, 472, -70, -675, 19, -398, -389, 427, -540, 277, 352, 142],\n [8, 223, -329, -149, -322, -579, 565, -234, -668, -103, -266, -275],\n [-609, 734, -370, 358, 1015, 872, 1487, 223, -477, -782, -1009, 584],\n [-394, -367, -266, 650, -850, 529, -27, -642, 481, -162, 310, 198],\n [-1273, -1426, -95, 209, 461, -609, 822, -44, 909, -576, -612, -288],\n [-123, -68, -1417, -152, -684, -1828, 664, 491, -1080, -254, 944, -1205],\n [-701, 222, -1264, 237, -1551, -422, -644, -553, -461, 406, 1556, -850],\n [-740, -1053, 141, -185, -68, -1434, 264, -690, 57, 204, -750, -1100]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-952, 695, 191, -64, -174, 457, 518, 1373, -102, -377, -294, 921],\n [122, 353, -354, 724, -856, 206, -93, -177, 543, -532, 1081, -578],\n [-330, -337, 1006, -369, 271, 933, 58, 1440, 122, 1296, -1348, 23],\n [352, -886, 942, -455, 412, 1224, -1124, -941, 3, 60, -1385, 92],\n [-834, -1528, 623, -394, 975, -44, -980, 736, 321, 169, -483, -268],\n [-74, 1290, -827, -355, -525, 1034, -437, -546, -1093, -1808, -440, 1318],\n [-646, -1066, 1412, -105, 1029, 455, -1323, 68, 928, -1504, 670, 133],\n [1051, -314, 769, -475, -244, 1078, -160, -391, 650, 784, -954, -1182],\n [-452, -343, -493, 389, -332, 530, -538, 86, -330, 934, -575, -290],\n [-362, -408, 1710, 420, 375, 678, -20, 1258, 765, 836, 63, -288],\n [-2209, -13, -717, -421, 1152, -470, -422, 707, -388, -1159, 355, 1408],\n [351, -785, 741, -4, 82, -69, 273, 645, 170, 1588, -932, -305]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-159, -96, 108, -162, -72, -132, -180, 57, -159, 138, -189, 192],\n [-521, 205, 431, 124, 70, -162, -562, -128, -588, 279, 33, -75],\n [381, 168, -268, 310, 136, 284, 428, -99, 389, -310, 375, -376],\n [-318, 219, 277, 194, 98, -50, -338, -135, -371, 139, 138, -173],\n [17, -424, -76, -530, -248, -212, -4, 257, 73, 130, -525, 568],\n [-25, 551, 101, 688, 322, 274, 2, -334, -98, -167, 681, -737],\n [-70, -430, -10, -560, -260, -260, -100, 260, -20, 190, -570, 610],\n [-232, -427, 115, -598, -274, -342, -278, 257, -195, 297, -636, 669],\n [322, 334, -198, 504, 228, 340, 372, -200, 304, -326, 558, -578],\n [-65, -47, 43, -76, -34, -58, -74, 28, -64, 59, -87, 89],\n [-281, 505, 291, 564, 270, 118, -282, -308, -368, 19, 513, -575],\n [-250, 167, 217, 146, 74, -42, -266, -103, -291, 111, 102, -129]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-209, 1695, -1014, -215, 307, -965, -709, 1263, 621, -306, 143, -1197],\n [-1302, 557, -698, 837, 790, 199, -720, 442, -527, -84, 181, -1521],\n [400, 704, 122, -989, 515, -70, 716, 1884, 702, 208, 38, 1130],\n [910, 153, 52, -672, -771, 662, -9, 190, 876, 412, 363, 386],\n [1080, 904, 711, -301, -842, 1307, -1534, -1094, 1009, 1137, -10, 1436],\n [-467, 1706, 1369, -403, 32, -1094, 246, -7, -1900, 870, -1119, 994],\n [-415, -890, -229, 1161, 791, -1072, 1218, 861, -1304, -571, -786, -1780],\n [565, 820, 564, -503, 1749, 93, -190, 1102, -310, 372, -1203, 1198],\n [186, 701, -811, -11, 634, -817, 137, 658, -277, -135, -279, -718],\n [-883, 890, 641, -347, 1377, 127, 763, 1265, -161, 1034, -597, 1128],\n [-433, -858, -492, 427, -74, 322, 697, 679, -1113, -696, 841, -160],\n [-276, 1041, 446, -1062, -625, -2560, 73, -814, -224, -491, -242, -227]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[115, 17, 309, -447, 236, 41, -166, -546, 49, -80, -200, -158],\n [151, 586, 722, -33, 187, -403, -49, -408, 400, 276, -28, 410],\n [-599, -792, -570, -204, -124, 174, -120, 516, -582, 44, 208, -135],\n [1041, 1292, 544, 807, -163, -123, 405, -220, 914, 84, -404, 48],\n [-371, -746, -462, -456, 200, 220, -179, -141, -478, -513, 247, -148],\n [28, 574, 348, 516, -124, -434, 157, 279, 344, 411, 175, 563],\n [834, 971, 379, 576, 67, -134, 307, -456, 725, -346, -106, 190],\n [366, 710, 758, -18, 224, -330, -12, -588, 510, 128, -128, 304],\n [-112, -82, 554, -741, 189, -15, -330, -453, -60, 447, -393, -242],\n [-781, -734, -96, -582, 56, -60, -324, 236, -556, 360, 172, 49],\n [861, 898, 18, 945, -399, 115, 469, 288, 620, 76, -372, -190],\n [207, 127, 15, 93, -214, 173, 62, 184, 71, 294, -362, -348]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1047, -173, -92, 703, -386, 1022, 696, 663, -584, -88, 248, -174],\n [-296, -13, 1149, -397, 479, -781, -334, 139, -1477, -94, 213, -163],\n [469, -142, -744, 1445, -98, 814, -26, -776, 672, 307, -569, 1214],\n [-13, 705, -860, -367, 27, 14, 154, -1015, 726, 567, -705, -937],\n [209, -558, -827, -359, 124, 897, -36, 415, 1235, -207, 214, -310],\n [-892, 1024, 0, -430, 26, -397, -87, -526, -337, -203, 697, 875],\n [916, 89, 8, -586, 1466, 1189, -31, -834, 31, -1431, 1692, 1014],\n [375, 979, -339, -287, 370, 284, 535, -1089, 288, -108, 226, -96],\n [-916, 229, -261, 176, 664, 1892, 933, -117, -678, -495, 901, -332],\n [523, 360, 160, -35, 520, 66, -56, -641, -36, -385, 528, 900],\n [-1456, -131, -225, 110, 261, 276, -569, -163, -728, 340, -208, -23],\n [-1329, -88, -551, -332, 124, 1174, 557, 711, 134, 336, 92, -1141]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1147, -244, 205, 756, -112, -357, 45, -293, 173, 224, 757, -308],\n [118, -577, 362, -1193, -506, -446, 384, -1074, 306, -262, -500, 1584],\n [319, 388, -515, -917, -284, 434, -106, 322, -300, 43, -224, 878],\n [173, 54, 237, -505, -111, 391, 632, -6, -144, 874, 704, 209],\n [-822, -502, 438, 1360, 361, -970, 523, -332, 374, -49, 802, -470],\n [-244, -527, 381, -450, -197, -1000, 1385, -600, -30, -77, 583, 915],\n [-919, -742, 625, 426, -65, -1030, 243, -1077, 509, -159, 93, 445],\n [-571, -62, 88, 183, -195, 264, -1291, -439, 279, -179, -808, -374],\n [-156, 228, -429, -316, -274, 297, -305, 192, -82, -39, -2, 539],\n [-419, -251, 10, 198, -287, -601, 360, -26, -276, -955, 22, -935],\n [-616, -602, 747, -229, -23, -1331, 1092, -895, -125, -59, 89, 212],\n [28, 240, -915, -706, -615, -132, 153, 539, -505, -1226, -202, 476]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-375, -99, 169, 1192, 347, -1270, -522, 569, 623, 540, -255, 937],\n [704, -13, -1169, -464, -172, 205, -681, -200, 305, 394, -559, 202],\n [-111, 749, 198, -1356, -1057, 1353, 887, -105, -868, -661, 600, -645],\n [-230, 870, 275, 1705, -836, -1643, -413, 47, 287, -226, 17, 620],\n [-235, -1267, -443, 130, 1472, 44, -232, 1044, -282, 327, -626, 80],\n [558, 506, 16, 795, -650, -1702, -274, -96, 520, -536, -228, 487],\n [-378, 94, 71, 1410, 369, -884, 295, -386, -799, -14, -297, -558],\n [954, -718, -1300, -649, 902, 412, -1256, -150, 801, 889, -612, 235],\n [473, 108, -547, -1443, 132, 891, -40, -1284, 950, 1744, -181, 291],\n [-1139, 523, 1116, 1354, -631, -670, 377, 332, -15, -139, 483, 498],\n [54, -542, 708, 1039, -131, -1476, 456, 906, -312, -1903, -135, -51],\n [338, -320, -430, 508, 1031, -179, -952, 443, -320, -212, -26, -463]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[855, -1552, 1175, -96, -539, -167, -192, 579, 122, -325, 613, 570],\n [-1069, -3, 414, -1304, 294, 73, 341, -358, -82, -125, -403, 918],\n [136, -633, 518, -554, 1400, 72, 1120, -243, 783, -631, -110, 566],\n [252, 264, -264, -55, 746, 685, -185, -71, 670, 481, -105, -475],\n [-240, 426, -539, 347, -241, -146, 42, -107, -677, 122, -72, -105],\n [-94, 303, -132, -962, 463, 728, -764, 25, 472, 140, -624, 580],\n [362, -545, 614, 109, 513, 264, -199, 697, 493, -379, -63, 2],\n [-100, 458, -676, 740, -429, -757, 870, -696, -553, 51, 361, -496],\n [971, -762, 623, 582, -567, 22, -436, 420, 607, 301, 761, -729],\n [-392, 1109, -827, 711, 1505, 375, 624, -95, 403, 37, -494, -1070],\n [-580, -52, 295, -172, 1483, 210, 957, 104, 283, -471, -382, 74],\n [410, -964, 895, -572, -83, -323, 341, -82, 597, -507, 301, 656]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, -194, 464, -169, -262, -335, 614, -585, 18, 512, -52, -206],\n [11, -958, 52, 718, -40, -1156, 939, -271, -251, 248, -115, -917],\n [178, -587, 516, 65, -512, -851, 951, -772, -119, 601, -325, -570],\n [556, -721, 352, 588, -498, -298, 733, 27, 87, 117, -321, -376],\n [73, 190, 621, -448, -21, 508, 130, -510, -263, 202, -434, 585],\n [-26, -189, -147, 343, 701, 90, 578, 278, 445, 455, 632, -448],\n [-506, -80, -680, 284, 347, -722, 47, 326, 396, 118, 937, -803],\n [-886, 587, -334, -563, 611, -154, -264, -213, 177, 311, 882, -97],\n [-188, 795, -134, -719, 180, 642, -959, -97, -315, -331, -287, 798],\n [926, -708, 1048, 391, -481, 522, 489, -360, -902, -342, -1679, 747],\n [-72, -372, 285, 215, 7, -237, 237, -260, -520, -152, -423, 78],\n [-418, -356, 415, -75, -140, -755, 350, -800, -732, 50, -428, -61]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[213, -52, -403, 508, -833, 918, 972, 141, -594, -125, 344, 40],\n [554, -1190, 375, -766, -1057, 461, -15, -257, -397, -584, 356, -704],\n [-889, -189, 1023, -351, 204, -219, -232, -708, 316, 72, 33, 739],\n [32, 797, -1037, 397, -494, -845, -480, 679, -289, 121, -1503, -712],\n [-370, -506, 629, -790, 348, 437, 298, -888, 176, -648, 1057, 584],\n [1065, -149, -247, -234, 272, 588, 558, 212, -131, -112, 867, -158],\n [122, 392, 645, -608, 206, -252, 241, -321, -34, 286, -145, 695],\n [971, 857, -489, 175, 820, -427, -8, 734, 126, 658, -287, -85],\n [-439, -837, 456, -143, 398, -502, -1236, -124, 652, -98, 8, -565],\n [502, 63, 363, -486, 798, -360, -308, 27, 356, 267, 177, 83],\n [-300, 53, 894, 318, -564, 247, 466, -161, -224, 711, -258, 759],\n [303, 90, 398, -359, 1199, -697, -769, 108, 673, 413, 33, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[918, 49, 486, 734, 493, 1181, -641, 461, 83, 613, -55, 401],\n [379, -985, -1173, -851, 680, 336, -299, 451, -761, 5, -1010, -602],\n [91, 416, 822, 729, 1158, 1457, -59, -120, 610, -568, -114, 467],\n [-371, 601, 524, 349, 117, 110, 728, -917, 699, -477, 315, 938],\n [849, -406, -416, 94, 846, 1190, -596, 480, -382, 618, -403, -35],\n [209, 744, 134, -148, 603, 470, -42, 266, 484, -514, 165, -886],\n [-91, -737, -411, -93, -353, -305, -304, 234, -682, 550, -169, 15],\n [-613, 644, 1075, 977, 458, 766, 173, -467, 623, -387, 582, 642],\n [46, 606, 499, 279, -628, -444, -67, 133, 309, 211, 641, -207],\n [-501, -128, -905, -785, -847, -1333, 520, -430, -376, 248, 317, -277],\n [-602, -1, -567, -698, -661, -1230, 881, -810, 24, -322, 75, 236],\n [987, -182, 601, 713, 656, 1308, -751, 635, 73, 323, -458, 394]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-781, -927, -159, 219, 582, -285, -526, 315, 677, 129, 730, -504],\n [-29, -13, -240, -20, 173, 53, -367, 364, -285, 339, 350, -614],\n [101, -646, -800, -472, 896, 250, -979, -139, 172, 509, 79, -617],\n [-1134, -30, 937, 393, 963, -467, 547, 518, -226, -857, -244, -70],\n [-123, -684, -724, -1032, 400, 1058, -582, -727, 541, 467, -398, -728],\n [-1314, 204, 1014, 954, -824, -1002, 1036, 178, 1020, -1205, -383, -632],\n [2496, 1051, -1250, -740, -47, 1081, -882, -393, -1309, 1537, 174, 611],\n [-439, -966, -4, -264, 1954, 968, -912, 336, -517, 864, 605, -600],\n [1380, 175, -405, -585, 440, 45, -690, 690, -552, 503, 672, 1004],\n [-110, -130, -957, 8, 1553, 489, -177, -1033, 639, -931, -1390, 358],\n [304, 223, 282, 93, -274, -722, 510, -166, 82, -53, -315, 555],\n [396, 895, -313, 638, -1739, -2159, 558, 1070, -15, -684, 657, 622]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[158, -41, -40, 231, 49, -197, 6, -147, -54, 34, -207, 201],\n [-114, 24, -36, -126, 0, 18, -66, 0, -120, -24, 72, -48],\n [375, -90, -10, 495, 70, -305, 95, -210, 80, 80, -390, 350],\n [-231, 21, -394, -54, 175, -578, -439, -525, -1030, -46, -237, 383],\n [466, -118, -84, 660, 126, -516, 50, -378, -76, 100, -570, 542],\n [-47, 32, 242, -213, -140, 499, 217, 420, 580, -12, 336, -404],\n [-178, 64, 252, -390, -168, 618, 190, 504, 568, -40, 480, -536],\n [441, -105, -2, 576, 77, -340, 121, -231, 118, 94, -447, 397],\n [491, -131, -166, 744, 175, -692, -21, -525, -270, 106, -693, 687],\n [-610, 145, 0, -795, -105, 465, -170, 315, -170, -130, 615, -545],\n [-327, 81, 38, -450, -77, 322, -55, 231, 2, -70, 375, -349],\n [-456, 96, -144, -504, 0, 72, -264, 0, -480, -96, 288, -192]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[540, 534, -328, 168, 4, 42, -654, 138, -668, -646, 156, 428],\n [367, 356, -186, 219, -141, -101, -576, -14, -483, -591, 197, 221],\n [523, 521, -338, 105, 83, 112, -561, 193, -631, -542, 101, 453],\n [374, 391, -340, -204, 442, 425, -51, 425, -374, 17, -170, 510],\n [107, 109, -82, -15, 67, 68, -69, 77, -119, -58, -11, 117],\n [19, 17, -2, 33, -37, -32, -57, -23, -31, -62, 29, -3],\n [496, 488, -288, 192, -48, -8, -648, 88, -624, -648, 176, 368],\n [415, 410, -250, 135, -5, 25, -510, 100, -515, -505, 125, 325],\n [390, 381, -212, 192, -94, -57, -561, 27, -502, -569, 174, 262],\n [-403, -386, 178, -315, 257, 203, 726, 92, 551, 757, -281, -193],\n [392, 385, -224, 162, -52, -19, -525, 59, -496, -527, 148, 284],\n [127, 128, -90, 3, 51, 55, -108, 70, -147, -99, 5, 125]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-525, -272, -122, -440, 342, -28, 383, 66, 709, 6, -529, 823],\n [-148, -267, -278, 1193, 1710, 113, 1059, 924, 1392, 1079, -66, 316],\n [-79, -32, 11, 226, -129, 10, -138, 89, -222, 29, 380, -340],\n [-537, 546, 346, -1497, -248, -411, 680, -303, 594, 280, -738, 176],\n [-577, 370, -167, -1052, -307, -21, 29, -696, 407, 589, -512, 217],\n [518, 506, 1005, -576, 183, -235, 1194, -337, 432, 618, -775, -339],\n [-1289, -479, 133, -748, -1331, 332, -722, -1604, -581, 915, 555, -481],\n [-98, -89, -893, 178, -229, 1018, -917, -746, 76, 51, -570, 626],\n [-281, -362, -116, 208, 1260, -732, 801, 666, 929, 632, 151, 615],\n [686, 129, 45, 303, 1017, -145, 788, 954, 719, -542, -731, 676],\n [585, 1753, -179, -1205, -95, 50, 474, 439, 651, -562, -1490, 10],\n [934, 443, 356, -141, 30, 249, 329, -128, 42, -388, -914, 114]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-474, 320, 682, 498, 938, 745, 452, -233, -103, 826, 1240, -1187],\n [-425, -364, 479, 168, -875, 13, -566, 577, -176, 132, 25, 499],\n [826, 269, -1280, 67, 691, -1087, 563, -126, 775, -211, -820, 719],\n [-177, 304, -948, 147, 1056, 6, 264, 649, -140, -304, -297, -464],\n [-540, -499, 1061, 58, -775, 414, -601, 241, -488, 329, 417, -37],\n [477, 232, -942, 254, 708, -972, 511, 84, 621, 224, -348, 582],\n [-390, 89, 425, 1259, 467, 352, 146, 518, 583, 521, 402, -203],\n [222, 969, -1074, -188, 740, -661, 942, -296, 453, 533, 656, 114],\n [-1016, 236, -57, 979, -21, 926, -346, 1471, -1, -354, 26, -368],\n [-492, -425, 73, -54, 472, -192, -261, 684, -759, 439, 156, -250],\n [-107, 301, 390, 658, -703, 1031, -155, 15, 659, -735, -191, -117],\n [-288, 512, -1107, 423, 1094, 41, 358, 875, 91, -276, -223, -392]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[282, -766, 712, 160, 676, -892, 557, -1383, 453, 361, -140, -386],\n [-1448, -1197, -831, 1308, -716, 529, 613, -377, 586, 654, 738, -754],\n [155, 858, 318, -856, -41, -708, -408, -684, -392, 471, -282, -1406],\n [637, 657, -123, -345, 148, 925, 3, 533, -1169, -389, -316, 99],\n [-859, 668, -291, -719, -164, 97, -558, -714, 1003, 609, -1103, -1357],\n [674, -1263, -1, 919, 449, 811, 1199, 26, -770, -361, 1163, 575],\n [-646, 218, -643, 54, -575, -508, -42, -447, -143, 646, 217, -202],\n [-790, -416, -515, -128, -170, -1036, 317, -1595, 907, 1008, 386, -593],\n [1452, -137, 745, -925, 801, 882, 652, 487, -782, -877, -958, -134],\n [433, -812, -645, 200, 144, 615, 888, 156, -292, -227, 1419, 941],\n [50, 442, 624, -359, 96, -1609, -387, -779, -119, -24, -533, 79],\n [-613, -1025, -891, 250, -681, 391, 770, 524, 726, 646, 38, 222]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[286, 646, -618, 425, 666, 125, 184, 173, -115, -358, -588, 495],\n [77, -345, 1109, 685, 649, 1401, -691, 292, 858, -690, 79, -1192],\n [-215, -657, 317, -1461, 407, -559, -122, -1415, -28, 1743, 1916, 55],\n [-769, 500, -426, 1436, -1181, 203, 319, 954, 351, -865, -748, 159],\n [525, 958, -31, 557, -157, -1364, 333, -994, 800, -641, 1055, 226],\n [-509, -750, -161, -92, 196, -110, 68, 242, 92, -1206, 41, -416],\n [585, -747, 917, -519, -342, -508, 651, -1124, 105, 159, -299, 1239],\n [-13, 502, -264, -547, -280, -339, -776, -14, -859, 1155, -76, -105],\n [638, -399, 2120, 824, -62, 1149, 823, -411, 1498, -460, 24, 252],\n [604, -1656, -32, -285, -271, -18, -118, -228, -267, 129, -539, 4],\n [1004, 1633, -1259, 912, 656, -292, -302, 899, -134, -943, -430, -759],\n [33, 95, 138, 80, -150, 457, -919, -137, 113, -113, -725, -102]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1134, 946, -570, 1810, -228, -216, -53, -324, -226, -2061, -636, 294],\n [401, -555, 654, -1130, 303, 505, 1339, 1434, -312, 864, -169, -281],\n [773, 862, -83, -616, -370, -263, 469, 762, -691, 297, 815, 10],\n [-708, -856, 235, -1061, -40, 986, -670, -187, -233, 1162, 1069, 214],\n [-768, 370, 37, 249, 28, -409, -669, -248, 906, -37, 32, 11],\n [-58, 651, -702, -34, -163, -1502, -557, -734, 1324, 460, -14, 558],\n [289, -231, 761, 507, -747, 319, 1192, 749, -1139, -639, 74, -611],\n [1151, 400, -501, 1028, -835, 752, -509, 94, -273, -757, 1593, 1257],\n [842, 794, -182, 1964, -682, 495, -241, 1, -833, -1816, 908, 365],\n [1605, 1031, -162, 403, -520, 138, 523, 369, -1063, -1424, -349, 112],\n [289, 4, -118, -604, 1165, 131, 560, 667, -292, 487, -474, -394],\n [580, 458, 413, 1049, -882, -493, 603, -232, -550, -1248, -323, -209]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-373, 786, -372, -1417, -76, 218, -394, -2210, -159, -174, 298, -183],\n [-958, -847, 1605, -817, -1055, -737, -1051, 138, -1324, 955, -331, -500],\n [589, -78, -971, -178, -134, 472, -582, 33, 152, 293, -35, 1306],\n [-736, 28, 431, -271, 749, 82, -73, -257, 34, 21, -259, -773],\n [654, -1552, 105, -427, -1188, -1601, -1654, 96, -612, -1129, -525, 1013],\n [885, 797, -1001, -674, -53, -1070, -158, 141, -656, -449, 168, -865],\n [973, -559, 500, -787, -1494, 176, -983, -241, 983, 716, 15, 1495],\n [323, 1099, -96, 425, 161, 796, 49, -866, 518, 1184, 958, 1068],\n [-41, 350, 980, -965, -818, -252, 337, -391, -76, 87, 669, -865],\n [-320, 2, -402, -278, 519, -700, 61, -910, 51, -1764, 193, -752],\n [145, 299, -801, 1663, 1186, 239, 915, 355, 968, -821, 787, 57],\n [149, -305, 42, -2101, -1098, -710, -690, -721, -822, -992, 210, -229]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1039, 316, 463, 73, -435, 194, -365, -533, -202, -110, -493, -478],\n [-479, 204, 421, -656, 101, 788, -274, -937, -214, 0, 411, -365],\n [-354, 130, 366, 389, 417, -1153, 384, -327, -559, 441, -479, -291],\n [-691, 989, 579, 369, -130, -1158, -82, -892, -927, 329, -905, -98],\n [143, 6, 699, -383, 1124, -107, -584, -1061, -6, -358, 1457, -225],\n [-61, 129, 210, -365, -224, 123, -969, -572, -1181, -558, 599, 565],\n [989, 829, -891, 119, -3, 284, 17, 349, -202, 809, 55, 40],\n [-994, -1256, 486, -992, -537, 387, 1079, -203, -519, -171, -793, 354],\n [-1214, -801, 879, -996, -398, 180, 71, -979, -1417, -500, -206, 386],\n [-70, -298, 612, 114, 198, -552, 76, -66, 1172, -838, 104, 330],\n [85, 114, -466, -14, -913, 374, 295, 605, 226, 6, -838, 464],\n [-518, -1916, -656, -805, -695, 1425, 1180, 1109, -531, 369, -567, -103]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[32, 27, -1514, -283, 454, -48, -83, 435, -454, 425, 939, -543],\n [-216, 1216, 224, 260, -1580, -442, 234, 1619, -1207, -473, 1027, -257],\n [-1528, 1232, 486, -363, -300, 276, 916, 434, 365, -384, -281, -296],\n [85, 315, 656, -89, -128, -420, 154, 624, -12, 195, 1076, 578],\n [-235, 488, -755, 484, 298, 717, -562, -664, 390, -1147, 164, -1039],\n [-651, 437, -143, -544, -724, -51, 454, 812, -619, -256, -288, -1177],\n [355, -362, -509, -301, -1672, 488, -202, 1177, -1679, -291, 711, -823],\n [265, -292, -484, -814, -203, 227, -847, 618, 129, -530, -1257, -548],\n [-534, 97, -1207, -289, 546, -13, 559, 1005, 20, 1006, 411, -361],\n [-1512, 883, 24, 19, 1278, 320, 84, 513, -657, -291, 1075, 406],\n [831, -26, 475, 307, -964, -349, -843, 1476, -1104, -647, 851, -186],\n [-588, -397, 952, 701, 1101, 357, -282, -908, -636, -85, -528, 1254]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 2, 17, 9, 0, -22, 1, -22, -15, -25, 25, 17],\n [-132, 44, 374, 198, 0, -484, 22, -484, -330, -550, 550, 374],\n [-138, 46, 391, 207, 0, -506, 23, -506, -345, -575, 575, 391],\n [-12, 4, 34, 18, 0, -44, 2, -44, -30, -50, 50, 34],\n [108, -36, -306, -162, 0, 396, -18, 396, 270, 450, -450, -306],\n [150, -50, -425, -225, 0, 550, -25, 550, 375, 625, -625, -425],\n [132, -44, -374, -198, 0, 484, -22, 484, 330, 550, -550, -374],\n [108, -36, -306, -162, 0, 396, -18, 396, 270, 450, -450, -306],\n [-30, 10, 85, 45, 0, -110, 5, -110, -75, -125, 125, 85],\n [126, -42, -357, -189, 0, 462, -21, 462, 315, 525, -525, -357],\n [-84, 28, 238, 126, 0, -308, 14, -308, -210, -350, 350, 238],\n [-24, 8, 68, 36, 0, -88, 4, -88, -60, -100, 100, 68]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-612, 393, -276, -1453, -535, 401, 894, -158, 1376, 360, -1033, 756],\n [-691, -289, 1348, -248, 1813, -19, -66, -169, 208, -425, 672, -229],\n [-54, 145, -1092, -424, -1001, 754, 280, 386, -249, 563, 478, -1342],\n [1020, -691, 567, -441, -726, 175, -9, 323, -864, 1155, 1, 262],\n [174, 716, 98, 587, -154, -196, 162, 423, -356, 287, -869, -91],\n [-240, 269, -1189, 175, 773, -1171, 327, -1795, 371, 23, 470, 1139],\n [819, -79, 26, 20, -455, 506, -870, 1390, -546, 455, -898, -163],\n [193, -687, 901, -889, -968, 106, 370, 1054, -114, -192, -504, 273],\n [975, -226, 932, -206, 178, -308, -27, 286, -530, 574, -1036, 770],\n [-946, 1052, -214, -981, -380, -8, 1056, 723, 1182, 807, -1659, 215],\n [199, -841, 505, -1962, 619, 778, 95, -283, 439, 803, 214, 357],\n [-43, 32, 733, -1923, 637, 1257, 212, 299, 1133, 287, -1290, 173]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-390, -534, 618, 544, 222, 534, 92, 384, -726, -396, 714, -880],\n [-406, -118, 325, -375, -282, 12, -200, -47, -425, -169, 186, -178],\n [468, -565, -382, 141, -992, -120, 438, -197, 2178, 616, -1009, 1003],\n [-1057, 610, -179, 36, 507, 412, -506, 236, -706, 57, 474, 291],\n [186, 617, -679, -1071, -428, -947, -508, -305, 142, 504, -695, 878],\n [-76, -963, -312, 896, -201, -59, -108, 1030, 172, 669, 75, -152],\n [102, 68, 113, -969, -159, 246, 52, -913, -196, -267, -210, -180],\n [70, -1127, 235, 861, -771, -555, 8, 1143, 445, 398, 47, -176],\n [130, 206, -251, -745, 485, 1044, 276, -1269, -78, -217, -208, -212],\n [631, 121, 202, 56, 945, 500, 388, -486, -891, -594, 369, -1052],\n [115, -707, -81, -847, -922, -246, -140, -325, 221, 323, -493, -2],\n [516, -919, 310, -1071, -1140, -342, 118, -633, 244, -14, -547, -375]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[107, -560, -450, -1262, 1613, -798, -875, 464, 1300, 426, -159, 606],\n [925, 573, -770, -208, -838, 1035, 185, 564, -211, 175, -834, -378],\n [363, 839, 243, 48, 381, -1509, 69, -1042, -1204, 504, 288, 1283],\n [-77, 22, 30, 421, 930, 415, -189, -1278, 1901, -326, -189, 478],\n [241, 1406, 155, 2508, -853, -342, 447, -979, -520, -71, -212, 484],\n [-271, -319, 546, 189, 1023, 237, 944, -771, 743, -106, 816, 181],\n [109, 1156, 237, 1880, 159, -314, 1126, -1328, -223, 872, 541, 775],\n [197, -810, 373, -181, 58, 548, -569, 494, 181, -1414, -349, 34],\n [519, 1046, -293, 574, -57, -1067, -285, -1580, -863, 478, 515, 1010],\n [-1060, -453, 546, 18, 908, -78, 1491, -816, 439, 728, 1525, -392],\n [-406, 521, 631, 524, -965, -298, 157, 831, -621, -8, -261, -627],\n [-63, -15, 158, 1263, -577, 1654, 176, 652, 1146, -313, -592, -681]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[584, -239, -242, 310, 1053, 677, -336, 630, -500, 1228, -116, -591],\n [-342, -127, 466, -43, 841, -255, 209, 45, -94, 571, -589, 212],\n [-688, -45, 551, -57, -845, -796, 557, -897, 351, -1084, 132, 803],\n [267, 39, -202, 5, 219, 267, -185, 278, -133, 340, 35, -270],\n [-104, -42, 510, -106, 790, -280, 290, -82, -346, 776, -160, 238],\n [551, 340, 125, -337, 132, -91, 161, -134, -622, 729, 854, 18],\n [-535, 401, 738, -652, 25, -939, 580, -519, -7, -33, -22, 727],\n [-604, -850, 988, 729, 322, -546, 735, -953, -180, -49, -111, 811],\n [-141, 33, 94, -44, -335, -199, 128, -245, 103, -355, 118, 195],\n [861, 1162, -791, -990, -1330, 99, -334, 161, -96, -408, 1377, -377],\n [44, -1139, 44, 1247, 869, 663, -121, 121, -190, 501, -517, -264],\n [-163, 1094, 69, -1258, -534, -701, 142, -27, 188, -288, 233, 283]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1332, 90, -1050, -2659, 1305, -1143, 170, -469, 491, 1764, -39, -1045],\n [58, -1090, -332, -1688, 552, 414, 1627, 708, 230, 73, 391, -942],\n [807, 681, -1354, -1009, 1042, -446, -380, -1355, 696, 230, -498, -130],\n [151, -515, -657, -64, 800, -320, -80, 154, 13, 838, -661, 337],\n [602, -411, 783, -918, 18, 157, 204, 338, -453, 464, 570, -1015],\n [989, -357, 671, 540, -214, 369, -636, 1696, 112, 349, -248, -695],\n [-485, 87, -391, -872, -949, 56, 987, 202, 868, 49, 1858, -2141],\n [-159, -301, 744, -463, -239, 239, -379, -72, -423, -564, -475, -1198],\n [259, -435, -1009, -885, 371, -324, 166, 291, 682, 478, -419, -1444],\n [-208, 592, 705, 124, -818, -867, -679, -302, 540, 671, 952, -760],\n [-1594, -1017, 155, 399, -618, 722, 1824, 149, -195, -724, 1421, -616],\n [7, -242, -645, -796, 1083, -152, -199, -1300, -393, 286, -600, -260]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-188, 300, -236, -409, -135, 554, 458, 382, 71, -433, -627, 413],\n [-194, -265, 239, 510, 230, -511, -467, -282, 112, 355, 334, -383],\n [-333, 753, 598, 263, 745, 162, -503, 520, -360, 291, 368, -524],\n [404, -247, 271, 214, 132, -173, 13, -412, 6, 39, 510, 361],\n [776, -1107, -461, -70, -766, -503, 399, -974, 322, -113, 172, 591],\n [728, -456, -96, -91, -319, -208, 196, -516, -51, 1, 429, 333],\n [96, 174, -524, -733, -488, 705, 805, 319, 81, -645, -802, 712],\n [623, -1273, -42, 486, -359, -885, 10, -1253, 433, 150, 594, 476],\n [-480, 60, 452, 679, 539, -564, -856, -4, -57, 615, 463, -925],\n [-434, 335, 441, 373, 562, -12, -368, 217, -27, 172, 148, -249],\n [-708, 1265, 115, -424, 448, 953, 75, 1226, -324, -259, -666, -239],\n [-312, 508, -20, -320, 128, 692, 436, 504, 56, -476, -592, 524]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-648, -440, -4, 226, -406, -355, 391, -165, 167, -232, 200, 253],\n [682, 628, -162, -763, -125, 370, 68, -489, 369, 197, 231, 110],\n [759, 1160, -256, 126, 635, 613, 116, 530, -14, 721, -668, -738],\n [-527, -106, -451, -698, -1021, 122, 840, 447, 198, 260, 388, -109],\n [-633, 36, -412, -301, -431, 901, 244, -169, 1485, 303, -480, 764],\n [-304, 612, -679, -221, -404, 90, 302, 488, -884, 747, 605, -419],\n [998, 200, 750, 1027, 1050, -776, 276, 449, -603, -404, -726, -1208],\n [745, 628, -70, -416, 135, 97, -32, -166, -264, 207, 230, -280],\n [-159, -498, 456, 850, 198, -1142, 184, -24, -923, -556, 298, -396],\n [348, -652, 941, 1073, 1065, -178, -354, 106, 738, -772, -1380, -81],\n [-253, 298, -379, -194, -666, -65, 1243, 684, 61, 365, 43, -674],\n [664, 112, 766, 1478, 1213, -779, 191, 261, -379, -447, -925, -939]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1439, -151, -216, 678, -137, 53, -165, 1060, 563, -583, 784, -209],\n [166, 247, -637, 605, -49, -118, -611, -860, -1038, 472, -736, -325],\n [-836, -304, 381, -476, 313, 252, -6, -488, -23, 192, -302, 151],\n [-486, 283, 634, -176, -343, 55, -515, -369, -714, -284, -503, 421],\n [228, 836, 467, 142, -806, -350, -407, 110, -769, -578, -201, 388],\n [-636, -1392, -1009, -250, 1560, 368, 760, -789, 1196, 1782, -551, -633],\n [-236, -46, 106, 8, 427, 104, -352, -961, -607, 78, -65, -428],\n [326, -179, -225, 460, 72, -9, -506, -334, -196, 596, -1051, 107],\n [-782, -733, -551, -395, 408, 336, 629, 195, 813, 722, -135, 95],\n [-707, -104, 1006, -498, 196, 250, -379, -608, -342, -291, -239, 249],\n [-612, -184, 616, -692, 604, -36, 468, -508, 428, 188, 104, -88],\n [491, -346, -759, 338, 576, -146, 303, -219, 498, 841, -224, -496]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[103, -1169, -265, 96, 345, 180, 830, -339, 408, -59, -509, 248],\n [212, -225, 74, 689, 206, 387, 575, -511, 344, -125, -575, 617],\n [256, -1324, -661, -844, 230, 186, 860, -141, 221, -59, -1, -744],\n [-955, 595, 686, 1262, -893, -778, 90, -12, -647, -18, -1014, 880],\n [-52, -697, 292, 481, 282, 73, 511, -183, 356, 83, -615, 831],\n [-364, -1847, -314, -867, 1, -462, 908, 256, -9, 166, -336, -420],\n [-973, 105, 324, 1070, -991, -802, 554, -162, -695, -128, -1168, 504],\n [-156, -5, -483, -625, 209, -381, -948, 468, -61, 42, 820, -575],\n [127, -1001, 93, -474, 492, 84, 273, 185, 402, 231, 11, 206],\n [-416, 152, 115, 686, -535, -292, 399, -237, -341, -141, -677, 256],\n [-236, -623, -294, 51, -168, -213, 519, -151, -90, -105, -391, -139],\n [49, -272, -432, -23, 357, -8, -297, -34, 236, -84, 240, -62]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-151, 140, 101, -223, 103, -229, 56, 100, 84, -112, 271, -38],\n [-38, -299, -352, -266, -94, -323, -10, 342, -538, -931, -181, 623],\n [270, 586, 391, -286, 272, -101, 192, -402, 636, 950, 320, -718],\n [518, -144, -333, -200, -78, -93, 62, -107, -324, -176, -501, 267],\n [236, -49, 480, 208, -468, 775, -638, -350, 378, 503, -529, 117],\n [1541, -6, -86, -789, -457, 182, -362, -665, -108, 238, -1400, 533],\n [89, -123, -178, 373, 9, 207, 94, -102, -86, 237, -150, -141],\n [656, 183, -420, -88, 340, -281, 574, -340, -94, 551, -151, -473],\n [854, -137, 109, -84, -490, 592, -496, -497, 54, 375, -1030, 332],\n [565, 210, 434, -873, -341, -14, -502, -235, 252, -82, -478, 451],\n [171, 239, -109, -813, 225, -740, 262, 140, -122, -453, 206, 141],\n [893, 581, 489, -957, -55, -126, -172, -573, 574, 685, -321, -166]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-349, -360, 465, -242, -407, -408, 1126, 218, -35, -1369, 641, 329],\n [-113, -74, 1627, -264, -735, -319, -189, 867, -887, 1170, 672, -569],\n [115, -138, -630, 790, 833, -311, -48, -1385, -42, -1186, -369, 881],\n [-54, 38, 1165, -499, -620, -1238, -264, -49, -1932, 1057, 74, -172],\n [-650, -271, 735, 289, 58, -44, 938, -297, 489, -1313, -559, -200],\n [-388, 726, -822, 304, 410, 918, 436, -54, 360, 648, -160, 680],\n [569, -651, 237, 1056, -92, -458, 705, 275, 1453, -1143, -239, -484],\n [-119, 373, 81, -61, -59, 326, 213, 487, 221, 830, -247, -251],\n [474, 349, -1349, -310, 135, -165, 327, 162, -3, 61, 112, 721],\n [-313, 151, 50, -911, -879, -364, 15, 276, -943, 860, 199, -304],\n [-2039, 4, 213, -1305, -1455, 24, 1190, -708, -135, -336, -133, -1114],\n [-115, -6, -1202, -192, 804, 1254, 302, 77, 2153, -1529, -1347, -474]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-425, 805, -394, 1255, -543, -50, -402, 484, -955, -311, -2102, 406],\n [66, 356, 1019, 698, -891, -1552, 92, 398, -1768, 47, -351, 239],\n [65, -87, 817, -187, 701, 892, 1175, -396, 88, 963, -147, -339],\n [-1228, 339, -513, 439, 369, 936, -94, -1806, 30, 499, -550, 229],\n [1319, -1202, 448, -160, 1008, 1122, 331, 716, -31, 45, 7, 275],\n [-1197, -591, -720, -596, 87, 370, -239, -512, -131, 1203, -629, 666],\n [-1010, 477, -984, 54, 493, 1747, -213, -916, 284, 534, -1512, 31],\n [647, -859, -427, 417, -141, -1105, -1185, -13, -139, -648, 496, 1147],\n [-533, -76, 850, -829, 480, 1549, 906, -182, -1170, 303, 269, -1049],\n [216, -659, 106, 1056, 73, 530, -525, -51, -46, 330, 37, 808],\n [499, 963, -998, -915, -272, 528, -817, -343, 676, -23, -78, -590],\n [-1241, 489, 688, 382, 117, 895, 1098, -275, -880, 147, -505, -735]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-52, 22, -38, -34, 36, -34, 48, 8, 28, -22, -14, -6],\n [390, -165, 285, 255, -270, 255, -360, -60, -210, 165, 105, 45],\n [182, -77, 133, 119, -126, 119, -168, -28, -98, 77, 49, 21],\n [520, -220, 380, 340, -360, 340, -480, -80, -280, 220, 140, 60],\n [-156, 66, -114, -102, 108, -102, 144, 24, 84, -66, -42, -18],\n [52, -22, 38, 34, -36, 34, -48, -8, -28, 22, 14, 6],\n [-260, 110, -190, -170, 180, -170, 240, 40, 140, -110, -70, -30],\n [234, -99, 171, 153, -162, 153, -216, -36, -126, 99, 63, 27],\n [338, -143, 247, 221, -234, 221, -312, -52, -182, 143, 91, 39],\n [624, -264, 456, 408, -432, 408, -576, -96, -336, 264, 168, 72],\n [-156, 66, -114, -102, 108, -102, 144, 24, 84, -66, -42, -18],\n [182, -77, 133, 119, -126, 119, -168, -28, -98, 77, 49, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[577, 639, -46, -207, -809, -1056, 767, -68, 235, 1502, -118, 1295],\n [-1420, -214, 1379, 438, 923, -813, 310, 591, 98, 574, 170, -132],\n [115, 318, 59, 282, -335, -304, 292, -253, 247, -168, -170, 553],\n [2, 955, -547, -10, -201, -786, 1050, -176, -444, -932, -1058, -747],\n [-224, -494, -40, -381, -270, -141, -1428, -173, 454, 1869, -231, 1420],\n [-102, -997, -416, -246, 627, 852, -1028, 64, 106, 860, -3, 751],\n [-860, 19, 432, 799, 951, -747, -385, -169, 179, -1180, -401, -708],\n [558, -1218, 104, 334, -240, 1199, 1315, 756, -312, -69, 514, 379],\n [298, -1270, -722, -544, 388, 1382, -997, 499, -53, -268, -129, -592],\n [875, -1340, -732, 443, 985, 179, -934, -306, -32, 878, 907, -66],\n [933, -148, -1562, -372, -39, 281, 355, -585, 1032, 662, -708, 525],\n [-1019, 75, 2045, 1362, -51, -1375, 326, 539, -1141, -65, 245, -512]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-160, 250, -30, -260, -150, 110, -40, 250, 170, -20, -150, -240],\n [-240, 375, -45, -390, -225, 165, -60, 375, 255, -30, -225, -360],\n [-48, 75, -9, -78, -45, 33, -12, 75, 51, -6, -45, -72],\n [-64, 100, -12, -104, -60, 44, -16, 100, 68, -8, -60, -96],\n [-224, 350, -42, -364, -210, 154, -56, 350, 238, -28, -210, -336],\n [144, -225, 27, 234, 135, -99, 36, -225, -153, 18, 135, 216],\n [-64, 100, -12, -104, -60, 44, -16, 100, 68, -8, -60, -96],\n [16, -25, 3, 26, 15, -11, 4, -25, -17, 2, 15, 24],\n [48, -75, 9, 78, 45, -33, 12, -75, -51, 6, 45, 72],\n [-384, 600, -72, -624, -360, 264, -96, 600, 408, -48, -360, -576],\n [352, -550, 66, 572, 330, -242, 88, -550, -374, 44, 330, 528],\n [-416, 650, -78, -676, -390, 286, -104, 650, 442, -52, -390, -624]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-544, 260, 45, -308, -85, -154, 483, 326, -644, 383, 140, 361],\n [-531, 516, -351, -387, 279, 120, 321, 261, -474, -186, 489, 825],\n [1082, 165, 478, 998, -14, 111, -866, -685, 745, 203, -231, -146],\n [342, 108, 437, 542, -603, -94, -481, -246, 162, 861, 258, 243],\n [-1023, 377, -423, -940, 603, -87, 1148, 594, -1062, -417, -32, 366],\n [-541, -598, -124, -343, 624, 360, -52, 1151, 486, -1157, -743, -862],\n [530, 100, 6, 85, 779, -74, 367, -529, -42, -620, -818, -622],\n [239, 159, -356, 24, 676, 329, -201, -124, 378, -932, -56, 71],\n [695, 866, 380, 709, 322, 8, -232, -667, -76, 339, -51, 552],\n [-1138, -467, -54, -624, 595, 307, 282, 1712, 42, -947, -711, -649],\n [55, -685, -37, -39, 407, 225, -227, 460, 677, -917, -752, -1045],\n [-533, 245, 9, -259, -34, -45, 313, 415, -470, 237, 182, 396]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-756, 573, 22, 557, 149, -906, -632, 235, 1023, -1423, -880, -617],\n [186, 519, 155, 545, 822, -493, 861, 529, -450, 385, -138, 1253],\n [420, 68, 287, 636, 585, 331, 658, 481, -1000, 742, 96, 1503],\n [-1043, -1058, 560, 336, -163, 1656, -417, -1100, 400, -499, 354, -158],\n [260, -229, 636, 74, -601, 346, -331, -471, -152, -147, 493, 7],\n [-130, 877, -236, 511, -535, -432, 116, 185, 205, 47, -178, 405],\n [-362, 980, -510, 314, -520, -1014, -506, 406, 802, -738, -734, -584],\n [-437, 159, -655, 8, -713, 609, 97, -264, 214, 524, 99, -7],\n [580, -119, 425, 321, 1556, -385, 650, 853, -928, 257, -260, 1114],\n [-131, -487, 827, 1028, 731, 755, -216, 247, -605, -394, -223, 972],\n [-210, -851, 193, -36, -880, 1409, -835, -655, -63, -95, 369, -510],\n [119, 103, -948, -1317, -738, -434, 16, -333, 585, 424, 252, -1348]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-126, 28, 154, 42, 182, 196, 56, -350, 28, 0, 266, 126],\n [45, -10, -55, -15, -65, -70, -20, 125, -10, 0, -95, -45],\n [-198, 44, 242, 66, 286, 308, 88, -550, 44, 0, 418, 198],\n [-18, 4, 22, 6, 26, 28, 8, -50, 4, 0, 38, 18],\n [-45, 10, 55, 15, 65, 70, 20, -125, 10, 0, 95, 45],\n [216, -48, -264, -72, -312, -336, -96, 600, -48, 0, -456, -216],\n [216, -48, -264, -72, -312, -336, -96, 600, -48, 0, -456, -216],\n [-171, 38, 209, 57, 247, 266, 76, -475, 38, 0, 361, 171],\n [225, -50, -275, -75, -325, -350, -100, 625, -50, 0, -475, -225],\n [-99, 22, 121, 33, 143, 154, 44, -275, 22, 0, 209, 99],\n [45, -10, -55, -15, -65, -70, -20, 125, -10, 0, -95, -45],\n [-198, 44, 242, 66, 286, 308, 88, -550, 44, 0, 418, 198]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[197, 519, 369, 154, -4, 132, 835, -212, 545, 91, -471, 302],\n [-64, 188, 54, 135, 13, 26, 192, 23, 150, -46, -87, -32],\n [691, -109, 693, -179, 453, 404, 445, -447, 197, -3, -18, 726],\n [-307, -4, -441, -37, -371, -289, -273, 190, -153, 134, -63, -340],\n [-594, 574, 126, 808, 388, 196, 274, 392, 350, -610, 174, -500],\n [271, -105, 531, 138, 628, 414, 113, -126, 67, -349, 321, 294],\n [-547, 452, 171, 781, 499, 251, 159, 384, 267, -670, 303, -468],\n [-215, -381, -351, -104, -50, -144, -673, 202, -431, -61, 351, -298],\n [203, -410, -81, -332, -36, -47, -367, -97, -305, 138, 150, 136],\n [-230, 34, -36, 221, 155, 46, -138, 177, -36, -236, 201, -228],\n [-701, 646, -369, 520, -328, -239, 249, 395, 303, -110, -270, -632],\n [-255, -281, -225, 55, 115, -38, -569, 233, -337, -211, 408, -314]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[548, -458, -484, 894, -120, 501, 670, 90, -335, -305, 564, -950],\n [-965, -1127, 805, -482, -529, 426, 43, 10, 322, 120, 1012, -879],\n [1072, 1172, 433, -2140, -1583, 534, 273, -947, 691, -18, 447, -226],\n [-468, 371, -513, -2189, -1959, 706, 737, -569, 856, -51, 722, -52],\n [126, 1252, 611, -6, -687, 576, -350, -96, -115, -6, -634, -439],\n [207, -50, -431, 661, 1198, 1379, 189, 236, -1084, 468, 50, 517],\n [-112, -682, -705, 1158, 934, -217, 392, 413, -266, -649, 313, 347],\n [94, -626, -581, 405, 318, 300, -384, -402, -296, -1882, 297, -595],\n [-614, 75, -354, -280, 199, -303, -20, -183, -93, -747, -69, 793],\n [-561, 904, -94, -1200, -1705, 244, 1365, -1189, 175, 12, -825, 1239],\n [1355, 508, -506, -1071, -947, 632, 139, -550, 554, -952, 737, -1005],\n [555, -963, -394, 1029, 2405, -803, -854, 856, -515, -253, 770, 65]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-104, 52, 650, 182, -416, 624, -364, -338, -286, -494, -338, 312],\n [-61, 23, 410, 183, -284, 541, -296, -152, -99, -396, -367, 228],\n [54, -60, -211, 241, 40, 446, -174, 379, 451, -211, -567, 36],\n [-78, 48, 453, 45, -264, 258, -174, -309, -297, -243, -51, 180],\n [21, -45, 1, 314, -100, 679, -306, 281, 374, -389, -708, 144],\n [114, -84, -609, 75, 312, -54, 102, 537, 561, 159, -237, -180],\n [-134, 106, 688, -162, -328, -106, -40, -676, -726, -84, 442, 168],\n [111, -81, -596, 65, 308, -71, 108, 518, 539, 166, -213, -180],\n [135, -87, -769, -38, 436, -355, 258, 559, 550, 365, 0, -288],\n [-176, 124, 962, -58, -512, 216, -220, -794, -814, -326, 238, 312],\n [-20, 10, 125, 35, -80, 120, -70, -65, -55, -95, -65, 60],\n [11, -13, -40, 57, 4, 109, -44, 82, 99, -54, -133, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[504, 5, -11, -123, 622, -1015, -350, -11, -1096, -753, 330, 1394],\n [161, -206, -570, -473, -130, -446, -63, -1272, -305, -934, 142, 1235],\n [900, -835, -590, 245, -526, -251, 810, -669, -205, -1168, 456, -365],\n [-429, 1224, -667, 957, -711, 971, 880, 66, 1248, 150, -42, 344],\n [28, -978, -244, -1028, 350, 82, -1249, -321, 122, 398, 55, -57],\n [79, -1009, -111, -257, -324, -443, -363, -763, 135, 18, 247, 141],\n [-278, 966, -619, 943, 175, 1792, 1162, 482, 1430, -222, -182, 35],\n [-460, 57, 1025, -73, 1116, -120, -126, 387, 33, 355, -219, 919],\n [-482, 745, 557, -374, 82, 609, 291, 363, -525, 644, -533, -184],\n [-1350, -350, 179, 165, -566, 630, -1457, -1006, -25, 1869, -873, 257],\n [-1032, 829, 313, -265, -180, 287, 849, -735, 445, 197, -1030, -911],\n [797, 290, 348, 429, 869, 151, 885, 931, 538, -660, 375, 273]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-116, -481, -135, -602, -403, -452, -33, -600, -244, -203, -168, 44],\n [20, 257, 589, -5, -518, -379, 158, 234, 499, 666, 116, -421],\n [168, 706, 226, 866, 552, 630, 56, 876, 378, 328, 248, -86],\n [44, 119, -155, 268, 367, 338, -43, 180, -74, -153, 32, 134],\n [52, 185, -39, 289, 284, 283, -12, 246, 29, -20, 60, 53],\n [-8, -106, -246, 4, 218, 160, -66, -96, -208, -278, -48, 176],\n [68, 389, 427, 286, -125, -16, 113, 432, 424, 507, 152, -280],\n [12, 79, 109, 44, -57, -30, 29, 84, 102, 127, 32, -74],\n [-116, -457, -57, -617, -484, -515, -12, -582, -181, -116, -156, -13],\n [124, 491, 69, 658, 509, 544, 15, 624, 200, 133, 168, 8],\n [76, 223, -211, 452, 575, 538, -59, 324, -82, -201, 64, 190],\n [60, 363, 441, 240, -177, -66, 117, 396, 426, 519, 144, -294]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[24, -500, 362, 34, -226, -54, 0, -426, -336, -410, 34, -78],\n [614, -81, 498, 163, -333, 12, -509, -67, 251, -167, -769, 417],\n [-134, -213, 211, 117, 503, 177, -844, 421, 518, -288, -263, 980],\n [926, 249, 664, 275, -656, -200, -364, -40, 265, 126, -1244, 230],\n [58, -589, 298, 34, 270, 316, -846, 4, 308, -625, -106, 861],\n [-466, -435, -578, -367, 52, 226, 698, -568, -647, -270, 1276, -778],\n [-260, 210, -410, -78, 574, 250, -336, 514, 468, 124, 210, 476],\n [918, 667, -78, 29, -435, 100, -179, 183, 497, 465, -783, 53],\n [-264, -518, 176, -20, 39, 2, 17, -303, -316, -411, 323, -27],\n [58, -447, -149, -189, -26, 319, -63, -374, -144, -413, 468, -37],\n [464, -2, -41, -116, -646, -17, 521, -574, -409, 35, 68, -737],\n [262, 877, -301, 0, -437, -329, 810, 91, -133, 841, -227, -861]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1112, 1, -211, -459, -511, 525, -1245, -480, 253, -231, 510, 1720],\n [-672, 53, -806, 353, 316, 121, 618, -264, -594, -185, -526, -168],\n [-357, -746, -645, 282, 205, 402, 646, 370, -633, 393, -537, 119],\n [-386, 1020, 169, 595, 526, -590, 117, 29, -326, -489, 582, -165],\n [452, 259, 143, -547, -769, -276, -908, -422, 176, -547, -29, 203],\n [1154, -523, 390, 626, -707, -73, -764, 287, -417, -138, 1066, 443],\n [336, -522, -70, 121, 6, 127, -48, -66, 253, 35, -250, 42],\n [43, -1060, -565, -180, -584, 772, 327, -29, -413, 553, -395, -28],\n [956, 31, 503, 435, -777, -379, -837, -296, -23, -557, 908, -158],\n [1240, -430, 228, -5, -1020, 178, -1049, -320, 49, -231, 736, 534],\n [-106, -80, -474, -200, 901, 488, 189, -47, 507, 256, -555, 972],\n [530, 93, 1331, -82, 942, 71, -35, 937, 1245, 944, 995, 446]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[263, -14, 265, -69, -196, 204, -404, -168, -210, -50, -126, 167],\n [-136, 593, 111, -772, 30, -105, 35, 172, 433, 21, -241, -8],\n [-458, 222, 97, 49, -104, -96, 110, -304, 132, 61, 156, -401],\n [485, -440, 472, -27, 169, -232, 153, -886, -789, -118, -366, 369],\n [92, 611, -446, -626, -368, -712, 137, 638, 157, -77, -675, 146],\n [231, 8, 173, -582, 542, -311, 694, -178, 8, -33, -340, 300],\n [-414, 531, -335, -279, -175, -137, -66, 542, 540, 65, 32, -267],\n [109, 1032, -53, -904, -577, -246, 87, 718, 559, -47, -652, 42],\n [-613, -42, 509, 507, -321, 503, -809, -904, -153, 96, 610, -593],\n [167, -172, -566, 275, -262, -609, 34, 302, -396, -87, -315, 145],\n [173, -31, 50, 242, -664, -554, -251, -530, -775, -130, -473, 12],\n [-718, 275, -394, -176, 91, -489, -124, 22, 228, 84, 142, -374]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-101, -488, 489, -265, -479, -308, 1155, 288, 1311, -586, -245, 532],\n [406, 1013, 600, 283, 1097, 969, -319, 291, -802, -126, 1338, -950],\n [-491, -1603, 635, -592, -377, -1121, 1248, 30, 1497, 357, -593, 1057],\n [-413, 103, 30, 27, 119, 406, -260, -145, -429, 84, 250, 50],\n [-2, -930, -562, -689, -352, -873, 33, -115, 747, 136, -1110, 345],\n [375, -289, 464, -29, 707, -484, 49, 114, -138, 832, 406, -249],\n [280, 270, 610, 257, 923, 253, -184, 89, -584, 439, 932, -533],\n [87, 47, 177, 386, -169, 37, 185, -59, 122, -297, 63, 44],\n [358, -7, -713, -675, -42, -361, -284, 186, 205, 78, -643, -227],\n [-1008, -290, -436, 179, -911, 285, -169, -528, -107, -327, -568, 792],\n [1185, 775, -817, -901, 803, 216, -767, 515, 8, -537, -213, -1350],\n [969, -23, -1011, -104, -252, -979, -521, 16, 14, 372, -985, -367]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[98, -471, -77, -657, 125, 367, -63, 349, 762, -82, -307, 305],\n [959, 460, 50, -272, 378, -403, 286, 59, 337, -880, 1132, -674],\n [58, 1087, -411, 239, 1057, -101, -1054, -126, -910, -334, 711, 411],\n [873, 581, -837, -598, 1340, -36, -496, 165, 784, -938, 962, 604],\n [-119, -245, 1199, -275, -919, 236, 796, 65, -511, 558, -583, -825],\n [-1012, -680, -489, 328, 32, 16, -368, -262, 1078, 507, -639, 289],\n [-76, 19, -754, -18, 492, 295, -898, 290, -291, -151, -151, 1157],\n [-293, -894, -113, -245, -609, 539, 79, 394, 98, 433, -1068, 802],\n [-283, 271, -324, 239, 297, 82, -333, -174, -353, 255, -182, 576],\n [321, 389, -575, 123, 483, -80, -359, 26, -261, -358, 397, 579],\n [-228, 294, 160, -443, 329, 530, 217, -191, -135, 728, -731, 681],\n [-1028, 173, 465, -684, 806, 581, -248, -430, 899, 1038, -866, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-499, 658, -1047, -281, 299, 593, -561, 247, 1701, -293, 750, 292],\n [1156, 674, 34, -259, 261, 90, 402, -1303, 436, 1107, -299, -42],\n [297, 1008, 390, -10, 205, 576, 151, 1271, -4, -296, -426, 55],\n [664, -48, 149, 561, 83, 142, -830, -1227, 801, 554, 137, 728],\n [255, -414, -249, -227, 159, -652, 230, 649, 9, 1441, -664, -1242],\n [50, -1203, -125, 199, -627, -254, 35, 680, 507, 985, 587, -117],\n [204, 1416, 274, 527, -289, 71, 1024, 1106, -279, -412, -221, -224],\n [-503, 524, 321, -218, 405, -761, 245, 380, -943, -1051, -442, -1085],\n [378, 188, 430, 558, -692, -720, 1281, 214, 319, 858, 574, -658],\n [464, -515, 763, -850, -366, 553, 114, 358, -948, -998, 224, 655],\n [-997, -1196, 262, 433, 719, 47, -301, -773, -1600, 346, -1028, 219],\n [337, 137, 373, -492, 1234, 15, 283, -1308, -369, 1123, -785, -542]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-9, -153, 234, -207, 72, -198, 216, -81, 0, -171, 189, -27],\n [18, 306, -468, 414, -144, 396, -432, 162, 0, 342, -378, 54],\n [24, 408, -624, 552, -192, 528, -576, 216, 0, 456, -504, 72],\n [10, 170, -260, 230, -80, 220, -240, 90, 0, 190, -210, 30],\n [-15, -255, 390, -345, 120, -330, 360, -135, 0, -285, 315, -45],\n [-19, -323, 494, -437, 152, -418, 456, -171, 0, -361, 399, -57],\n [13, 221, -338, 299, -104, 286, -312, 117, 0, 247, -273, 39],\n [14, 238, -364, 322, -112, 308, -336, 126, 0, 266, -294, 42],\n [24, 408, -624, 552, -192, 528, -576, 216, 0, 456, -504, 72],\n [-8, -136, 208, -184, 64, -176, 192, -72, 0, -152, 168, -24],\n [9, 153, -234, 207, -72, 198, -216, 81, 0, 171, -189, 27],\n [-21, -357, 546, -483, 168, -462, 504, -189, 0, -399, 441, -63]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[204, 485, -295, -449, 431, 340, 6, -26, 371, 444, 261, -98],\n [-24, 150, -308, -616, 360, 126, 40, 246, 726, 314, 792, 90],\n [228, 214, -422, -400, 268, 95, -126, 155, 490, 207, 567, -187],\n [-208, -299, 235, 215, -229, -181, 60, 25, -177, -225, -130, 155],\n [-432, -417, 479, 283, -297, -201, 200, -3, -279, -257, -276, 375],\n [-432, -284, 183, -261, 19, -97, 218, 221, 370, 13, 441, 431],\n [-104, 563, -187, -875, 697, 511, 264, 65, 777, 747, 592, 283],\n [-552, -376, 442, -10, -130, -128, 296, 100, 44, -92, 48, 532],\n [-152, -266, 376, 500, -348, -166, 48, -150, -562, -306, -596, 86],\n [752, 159, -514, 406, -182, -126, -526, -106, -361, -272, -235, -822],\n [764, 331, -625, 133, 29, 14, -482, -68, -99, -58, -7, -784],\n [228, -577, -235, 463, -529, -578, -402, 232, -163, -678, 213, -404]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-156, -48, 156, -192, 144, 312, -300, 180, 192, -240, 216, -204],\n [-65, -20, 65, -80, 60, 130, -125, 75, 80, -100, 90, -85],\n [208, 64, -208, 256, -192, -416, 400, -240, -256, 320, -288, 272],\n [130, 40, -130, 160, -120, -260, 250, -150, -160, 200, -180, 170],\n [286, 88, -286, 352, -264, -572, 550, -330, -352, 440, -396, 374],\n [273, 84, -273, 336, -252, -546, 525, -315, -336, 420, -378, 357],\n [-91, -28, 91, -112, 84, 182, -175, 105, 112, -140, 126, -119],\n [338, 104, -338, 416, -312, -676, 650, -390, -416, 520, -468, 442],\n [299, 92, -299, 368, -276, -598, 575, -345, -368, 460, -414, 391],\n [26, 8, -26, 32, -24, -52, 50, -30, -32, 40, -36, 34],\n [130, 40, -130, 160, -120, -260, 250, -150, -160, 200, -180, 170],\n [-104, -32, 104, -128, 96, 208, -200, 120, 128, -160, 144, -136]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-961, -1062, 963, -294, -65, 183, -425, 650, 933, 447, 161, -76],\n [-838, -1189, 723, -652, -66, -21, -162, 369, 487, -77, -360, 138],\n [-271, 643, -306, -605, 992, 705, 1199, -125, -895, 827, -488, 79],\n [289, 16, -63, -45, 212, -260, -165, 82, 676, 1022, 822, 141],\n [-96, 554, -149, -557, 910, 292, 652, -215, -538, 746, 11, 518],\n [-104, -743, 436, 286, -735, -416, -856, 196, 656, -726, 134, -67],\n [-120, 281, 237, -37, 149, -60, -292, -281, -470, -716, -53, 673],\n [-655, -385, 873, 164, -306, 6, -852, 123, 70, -1073, -63, 435],\n [763, 459, -564, 250, -3, -331, 14, -216, 145, 444, 523, -38],\n [138, -225, -427, -650, 430, -8, 793, 40, 142, 1115, -98, -176],\n [-117, -484, 432, -255, 75, -406, -574, 114, 752, 403, 652, 526],\n [272, 1233, -257, 660, 160, 385, 54, -303, -843, -437, 58, 46]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-887, -873, 780, 934, -442, -58, -217, 865, 56, -1024, 813, 409],\n [1303, -501, 120, -359, 1054, 466, -839, -1241, -360, 718, -318, 11],\n [575, 916, 496, -809, 107, 344, 31, 187, 721, 853, -469, 462],\n [78, -860, 720, 1093, -209, 223, -110, -292, -968, -410, -1120, -752],\n [288, -605, -189, 1087, 86, -140, 306, -763, -673, 129, -833, -789],\n [-262, -1288, 656, -114, 1395, 352, -1039, -832, 477, 1147, -931, -599],\n [-131, 326, 900, -929, -613, -464, -1721, 533, -882, 748, 1466, 1517],\n [927, 140, -386, 434, 1169, 760, 1151, -1697, -995, -380, 31, -131],\n [457, -92, 1201, -161, -101, 718, -914, 204, 109, 1468, -1329, -378],\n [-633, 110, 1607, 363, -177, -207, -425, 608, 16, 687, 405, 933],\n [1827, 644, -174, -558, -569, 151, -1074, 4, -1125, 834, 638, 181],\n [-1141, -520, -1203, 545, -1044, -350, 45, 490, 165, 237, -754, -1307]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-423, -571, -12, 1274, 81, 79, -126, -1519, -155, 281, 693, -124],\n [691, 299, -148, -566, -107, 760, -208, 1086, 455, 171, -1424, 242],\n [-926, -781, 370, 17, 9, -951, -132, -331, -788, -1111, 1440, -864],\n [-476, -513, -315, 1334, 1396, -832, 88, -1455, -192, 202, 511, -1369],\n [-24, -1005, 710, -228, 148, -644, -472, 494, 122, -1323, -284, -552],\n [68, 1130, -341, -333, 13, -388, 286, 244, -371, 690, 352, 291],\n [132, -266, -259, 830, 1074, -289, 108, -1034, 613, 157, 286, -1126],\n [590, 611, -1499, 540, 28, 2232, 556, -908, 573, 1725, 73, -211],\n [-789, -229, 440, 928, 479, -1534, -596, -485, -1166, -162, 84, -224],\n [-343, -30, -580, 785, 184, 121, -87, -1269, -362, 278, 1716, -1158],\n [-336, 538, 45, 1021, 31, -1072, -741, -543, -1344, 655, 296, 204],\n [-251, -930, 128, -206, -417, 500, 111, -240, 154, -830, 862, -396]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1799, 275, -1035, 1609, 553, -908, 193, 1106, 848, 1060, -1366, -264],\n [-914, -475, 583, 199, 83, -1430, 992, 825, 767, 180, 1404, -271],\n [-1376, 13, 918, -933, -893, 793, -108, -640, 311, -201, 824, 1589],\n [-86, -13, 518, 235, 619, 553, 835, -302, -289, -927, 257, -1054],\n [99, -651, 60, -350, -320, 1090, -454, -1379, -367, 60, -268, 720],\n [698, 1062, -464, 383, 104, 722, -877, 289, 40, 563, -1132, 336],\n [-711, 312, 260, 1057, 430, -960, 79, 259, 727, 371, 825, -96],\n [-488, -702, 926, -228, -486, 847, -14, -310, 356, 338, 520, 555],\n [1169, -1077, -149, 374, 554, 155, 503, -182, -779, -727, -439, -1941],\n [1146, -1060, -584, -591, -245, -300, 128, 210, -895, -661, -635, -1136],\n [394, -959, -504, -657, -956, -335, -185, -452, 62, 223, -363, 1253],\n [530, 173, 52, 318, -272, -15, -462, 1220, 454, 738, -435, -123]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-612, 67, 98, 424, -529, -836, -55, 387, -301, -42, -916, 283],\n [706, -426, -429, -107, 427, 407, -301, -642, 435, -654, 1123, 232],\n [-941, 913, 154, 396, -635, -889, 682, 773, 349, 1680, -1163, -888],\n [117, 324, 36, -15, -264, 606, 453, 537, 240, 594, 84, -777],\n [522, -599, -120, -144, 331, 142, -391, -339, -215, -1198, 516, 731],\n [-315, 124, -111, 410, -469, -543, 91, 358, 134, 140, -430, -57],\n [-542, 445, 121, 19, 18, -463, 146, -123, 124, 968, -461, -305],\n [337, -63, -111, 115, -266, 198, 272, 586, 161, -302, 131, -178],\n [-55, 246, 251, -105, -141, 66, 427, 635, -130, 300, -405, -321],\n [-221, 22, -275, 357, -143, -854, -65, -101, 356, 44, -153, 185],\n [434, 425, -666, 495, -495, -239, 837, 836, 1441, 718, 513, -1063],\n [332, -329, -287, 165, -36, -73, -169, -64, 177, -676, 384, 307]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[118, 1221, -2785, -1404, 477, 358, -1875, 209, 13, 1137, 292, 1191],\n [359, -483, 940, 323, -12, -33, 1125, 1445, 56, 784, -72, -991],\n [51, -264, 982, 183, -851, 8, 164, 1128, -273, -46, -179, -441],\n [-46, -284, 809, -318, 864, 60, 355, -815, 521, -1904, -744, 585],\n [-998, -757, 835, 467, 250, 351, 407, 134, -827, -669, 62, -234],\n [25, 376, -133, -979, -203, -193, 698, 764, 1253, 1007, -340, 576],\n [-239, -325, 73, -385, -454, 92, -295, 560, 225, 25, 692, 384],\n [-73, 186, 135, -59, -147, 577, -444, -1236, 59, -767, -478, 554],\n [719, -575, -149, -66, 1548, 503, -142, -1667, 685, -1213, 421, 295],\n [863, 5, 62, 113, 152, 1293, 51, -936, 479, 676, -119, -104],\n [-143, 788, -823, 155, -1187, 1032, -981, -1470, -235, 1112, -8, 495],\n [-78, -723, 1168, -197, -796, 1068, 687, 780, 633, 798, 429, 44]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-184, -985, 1062, -610, -1048, 358, 620, 537, 529, 592, -1298, 840],\n [-790, -136, 224, 22, 436, -471, 503, -16, 826, 530, -378, -1111],\n [-663, 489, 863, -217, -38, 38, 367, 315, 920, 651, -29, -406],\n [451, -90, -209, 347, -752, 480, -5, -102, -339, -607, -199, 1046],\n [233, 104, -428, 228, -1053, 1128, -352, -723, -1032, -673, -351, 1537],\n [-382, -823, 487, -383, -354, 46, 460, 108, 342, 472, -1013, 73],\n [-1028, 376, -17, 795, -739, 462, 687, -619, 759, -98, -768, -71],\n [-524, 837, 374, 572, 272, 333, 563, -299, 873, -376, 68, -183],\n [-814, -118, 7, 189, -812, 274, 328, -347, 291, 374, -811, -35],\n [-608, -322, -1210, 856, -945, 506, 61, -1250, -636, -489, -985, 286],\n [-63, -676, 780, -546, -1143, 305, 275, 545, 240, 612, -871, 808],\n [66, 280, 865, -761, 318, 434, -154, 213, -49, 280, 217, 399]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-622, 176, -253, 239, 113, -279, 141, 335, -575, 144, 561, 755],\n [-148, -160, -206, 80, 36, -4, -148, 72, -52, 206, -74, 146],\n [18, 144, 115, -24, -10, -38, 130, -4, -46, -131, 137, 3],\n [-350, 112, -133, 133, 63, -161, 91, 189, -329, 70, 329, 427],\n [-232, -64, -188, 104, 48, -64, -64, 120, -160, 164, 76, 260],\n [152, 320, 324, -100, -44, -44, 292, -68, -12, -344, 236, -124],\n [628, -224, 222, -236, -112, 296, -184, -340, 600, -106, -614, -770],\n [372, -384, -50, -111, -55, 253, -335, -211, 461, 151, -622, -498],\n [696, 192, 564, -312, -144, 192, 192, -360, 480, -492, -228, -780],\n [-206, 112, -45, 73, 35, -109, 95, 113, -213, 2, 241, 259],\n [-140, -128, -178, 73, 33, -11, -119, 69, -59, 175, -46, 142],\n [-506, -80, -367, 220, 102, -158, -86, 264, -374, 307, 227, 577]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-465, -667, -318, -1012, -1033, -802, 105, -610, 18, -363, -1465, 923],\n [418, 1321, 742, -555, 991, -835, 159, 127, -668, 521, 121, -267],\n [262, 26, -257, 946, 641, 644, -175, -359, 653, -680, -650, 1438],\n [1068, 65, -67, -949, -1, -205, 309, 376, -427, 697, -584, 551],\n [-334, -667, 621, -808, -1531, 59, -255, 217, 1040, -401, -1846, 1587],\n [104, 416, 371, -1462, -1359, 212, -64, -1649, -1179, -907, -1527, 174],\n [-225, -405, 881, -402, -572, -654, 919, 1773, 892, -19, -795, 985],\n [-488, -907, -584, 525, -288, 436, -445, -391, 856, -974, -862, 1100],\n [1090, 362, 381, -884, 336, -427, 547, 774, -343, 867, -571, 764],\n [-201, -1148, -705, 61, -814, 548, -135, -319, -79, 69, -399, 316],\n [567, 704, 693, 833, 182, 1216, -238, -143, 960, -481, 91, 684],\n [874, -331, -492, -43, -132, -56, 756, 975, 595, 469, 1080, -473]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-411, 814, 278, -444, 956, 830, 182, -311, 1247, 353, -482, -96],\n [-1139, 48, 1113, 230, 552, 612, 193, -642, 508, 204, -1387, -1140],\n [224, -204, 807, 183, 294, -111, 466, -15, -60, -426, -366, -566],\n [642, -141, -187, 12, 251, -465, -401, -307, -747, 274, 994, -20],\n [982, -86, -726, -349, 963, -514, -137, 171, -160, -141, 1037, 920],\n [-995, 311, -772, -347, -268, 226, -249, 426, 219, -813, -697, 381],\n [-819, 404, -283, -702, 837, 1218, 679, 264, 763, -352, -703, -282],\n [1388, -999, -288, 131, 862, -903, 648, 625, -279, 14, 782, 1200],\n [-676, -122, -221, -343, 902, 367, 477, 427, 543, -1038, -1060, 162],\n [-371, -122, 349, 456, -1473, -134, -123, -20, -703, 408, -51, -566],\n [421, 433, 266, -246, 322, -668, 414, 574, -112, -368, 227, 478],\n [316, 817, 76, -619, -71, -86, 812, 863, -262, -256, 539, 141]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1677, -907, 366, 1582, -1566, -1476, -972, -822, 664, 1392, 512, -887],\n [1002, -345, 71, 749, -914, -403, 1252, 460, -1385, 585, -351, 1108],\n [2036, -1482, 954, 498, 1328, 2044, -624, 1086, -1592, 66, 188, -1101],\n [-1448, 731, -553, -413, -1053, -767, -898, -1244, 1493, 270, -13, 341],\n [-267, 645, -415, -139, 320, -54, 447, -236, -834, -1019, -111, 900],\n [293, 351, -153, -260, 368, 703, 444, -7, -999, -211, 381, 158],\n [-101, -552, 96, 255, -276, 107, -987, -67, 282, 233, -514, 955],\n [871, 227, 484, 1309, 1296, 890, -592, -174, -664, -1042, 341, -1072],\n [-630, 941, -430, -491, 829, 1779, 449, 490, -543, -975, -807, 593],\n [980, -159, 650, 1117, -1154, -311, 817, 525, -1505, 495, -955, 2095],\n [-310, -678, 479, -349, 144, -278, -67, -310, -755, -110, 527, -100],\n [746, -407, -80, -47, 1002, 2051, 21, 1051, -1263, -399, -669, 642]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-40, 32, 36, 38, 10, -10, -30, -42, 22, 24, 22, 28],\n [-420, 336, 378, 399, 105, -105, -315, -441, 231, 252, 231, 294],\n [-380, 304, 342, 361, 95, -95, -285, -399, 209, 228, 209, 266],\n [320, -256, -288, -304, -80, 80, 240, 336, -176, -192, -176, -224],\n [-380, 304, 342, 361, 95, -95, -285, -399, 209, 228, 209, 266],\n [220, -176, -198, -209, -55, 55, 165, 231, -121, -132, -121, -154],\n [40, -32, -36, -38, -10, 10, 30, 42, -22, -24, -22, -28],\n [-460, 368, 414, 437, 115, -115, -345, -483, 253, 276, 253, 322],\n [480, -384, -432, -456, -120, 120, 360, 504, -264, -288, -264, -336],\n [480, -384, -432, -456, -120, 120, 360, 504, -264, -288, -264, -336],\n [520, -416, -468, -494, -130, 130, 390, 546, -286, -312, -286, -364],\n [300, -240, -270, -285, -75, 75, 225, 315, -165, -180, -165, -210]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-795, 380, 510, -571, 421, -840, 8, 449, -428, 503, -665, 828],\n [470, 455, 440, 261, 902, -259, 887, 96, 480, -631, -606, 560],\n [537, -554, 254, 1070, 302, 670, -36, -840, 46, 833, 250, 269],\n [659, -574, 70, 179, 431, -437, 31, 125, 578, -198, -663, -737],\n [428, -43, 468, 535, -418, 338, 488, -732, -234, -456, 316, 593],\n [83, -1045, -82, 232, -127, 25, -857, -425, 102, 1007, -64, -819],\n [-1211, 1034, 1080, -1115, 63, -839, 407, -405, -252, -319, -544, 1500],\n [925, -1021, -438, 859, -549, 298, 60, -204, 176, -659, 145, -1131],\n [-1478, 734, -275, -852, -179, -140, -9, -72, 46, -461, -13, 181],\n [861, 1182, -1552, 251, 608, 766, 890, 1935, 446, -1394, 601, -574],\n [-54, 299, 95, -344, -501, -27, 56, 91, -336, -312, 289, 265],\n [1069, -966, -126, 617, -476, 249, -181, -319, 180, -191, 189, -933]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-289, 187, -51, 425, 68, 306, 340, -68, -102, -425, 442, 68],\n [-51, 33, -9, 75, 12, 54, 60, -12, -18, -75, 78, 12],\n [374, -242, 66, -550, -88, -396, -440, 88, 132, 550, -572, -88],\n [85, -55, 15, -125, -20, -90, -100, 20, 30, 125, -130, -20],\n [-136, 88, -24, 200, 32, 144, 160, -32, -48, -200, 208, 32],\n [374, -242, 66, -550, -88, -396, -440, 88, 132, 550, -572, -88],\n [255, -165, 45, -375, -60, -270, -300, 60, 90, 375, -390, -60],\n [-136, 88, -24, 200, 32, 144, 160, -32, -48, -200, 208, 32],\n [102, -66, 18, -150, -24, -108, -120, 24, 36, 150, -156, -24],\n [17, -11, 3, -25, -4, -18, -20, 4, 6, 25, -26, -4],\n [442, -286, 78, -650, -104, -468, -520, 104, 156, 650, -676, -104],\n [-374, 242, -66, 550, 88, 396, 440, -88, -132, -550, 572, 88]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-198, -543, 313, -376, 951, -552, -838, -118, -806, 114, -172, 1034],\n [-218, 33, -203, -225, 325, 12, -665, -484, -95, 306, -190, 65],\n [10, -478, 734, -289, -22, -490, 187, 528, -317, -364, -336, 329],\n [11, -74, -117, 98, 658, -8, -150, 151, -404, 55, 409, 680],\n [-359, 320, -87, -485, 316, 434, -225, 271, 57, 107, -151, -97],\n [154, -600, 557, -1, -37, -693, -12, 32, -371, -225, -230, 414],\n [-9, 877, -1011, 402, -18, 985, 185, -205, 564, 346, 661, -545],\n [-23, 411, -201, 22, -514, 435, 347, 61, 524, -6, -45, -715],\n [-89, -436, 67, -117, 844, -466, -781, -339, -683, 197, 19, 919],\n [-70, 298, -439, 69, -153, 265, -272, -548, 307, 289, -34, -434],\n [147, 50, 203, 121, -280, 104, 683, 613, 123, -313, 171, -101],\n [-148, -83, 145, -296, -307, -170, -352, -404, 154, 94, -570, -396]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[69, 119, -518, 320, -6, 205, -723, -156, 196, 342, 238, 109],\n [163, 803, 152, -176, 190, 330, -396, -543, 1281, 543, 11, 75],\n [-514, -206, 50, -221, -736, -54, -512, -422, -200, 134, 689, 150],\n [948, 554, 202, 230, 1080, 37, 959, 719, 451, 23, -1255, 12],\n [-458, -586, -90, -48, -536, -186, -144, -30, -776, -266, 478, -28],\n [737, -49, -377, 665, 140, -172, 121, 976, -831, 422, -665, 668],\n [-509, -571, 283, -310, -440, -264, 333, -30, -685, -508, 318, -188],\n [-118, -24, -370, 79, 644, 283, -99, -321, 559, -501, 86, -764],\n [-30, 572, 5, -191, 474, 394, -285, -663, 1316, 49, 102, -441],\n [166, 230, 367, -169, 82, -57, 378, 96, 191, 80, -297, 115],\n [-76, 428, -66, -117, 188, 308, -438, -570, 956, 174, 225, -220],\n [-510, 22, -483, 45, -738, 239, -1400, -782, 267, 530, 1047, 197]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[87, -786, 209, -848, 570, 320, -219, 473, 86, 348, 216, 401],\n [-25, 629, 348, 222, 5, 182, -216, 237, -111, -424, 349, -807],\n [-111, -366, 379, -372, -428, -452, -447, 421, -1264, 235, -460, -160],\n [-127, -423, 72, -406, 175, -126, -174, 77, -259, 123, 41, 210],\n [1094, 596, -47, 642, -365, 902, 627, 370, 1014, 145, -496, -53],\n [321, 540, -382, 630, 71, 698, 564, -109, 1360, 65, 142, 10],\n [-740, -956, -814, -274, 221, -486, 222, -682, 339, 689, -44, 1152],\n [-645, -90, 362, -398, 297, 422, -588, 881, -130, 429, 624, -736],\n [-962, -551, 248, -750, 417, -942, -732, -322, -1238, -375, 531, -62],\n [-425, -473, -399, -4, -238, 344, 87, 501, 421, 1217, -245, 258],\n [-156, 212, 430, -216, 252, -104, -402, 116, -470, -518, 444, -544],\n [-689, 39, -910, 538, 39, -486, 456, -1137, 691, 25, 159, 590]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-842, -1090, -42, -345, 305, -905, -266, 551, -1034, -440, -19, 228],\n [768, 281, -81, -210, 347, -748, 127, -639, -187, -1014, -236, 644],\n [-1027, -825, -519, -363, -580, 394, -770, 760, -313, 439, -10, -550],\n [305, -240, 765, -45, -344, -495, -428, -362, 390, 268, -1369, -153],\n [-198, 245, -299, -745, -177, 514, 390, -17, -501, -558, 422, 177],\n [-1096, -1169, 126, -454, -78, -429, -204, 664, -959, 45, -19, -67],\n [496, 1034, 31, 525, -157, 874, -225, -135, 1271, 557, -400, -489],\n [1008, 729, 542, 665, 410, -207, 679, -694, 577, 103, 103, 306],\n [1083, 1787, -128, 687, 510, 732, 396, -482, 1241, -188, 172, 58],\n [-71, -266, 773, 488, 267, -428, 208, 67, 112, 520, -248, -53],\n [653, 1025, -250, 202, -50, 543, -302, -300, 962, -108, -445, -176],\n [331, 145, 1113, 378, -79, -69, 376, -337, 515, 713, -627, -154]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[375, -150, 105, -270, -90, 195, 105, -240, 375, -300, 300, -150],\n [-400, 160, -112, 288, 96, -208, -112, 256, -400, 320, -320, 160],\n [-250, 100, -70, 180, 60, -130, -70, 160, -250, 200, -200, 100],\n [-600, 240, -168, 432, 144, -312, -168, 384, -600, 480, -480, 240],\n [-375, 150, -105, 270, 90, -195, -105, 240, -375, 300, -300, 150],\n [-575, 230, -161, 414, 138, -299, -161, 368, -575, 460, -460, 230],\n [450, -180, 126, -324, -108, 234, 126, -288, 450, -360, 360, -180],\n [-50, 20, -14, 36, 12, -26, -14, 32, -50, 40, -40, 20],\n [600, -240, 168, -432, -144, 312, 168, -384, 600, -480, 480, -240],\n [575, -230, 161, -414, -138, 299, 161, -368, 575, -460, 460, -230],\n [150, -60, 42, -108, -36, 78, 42, -96, 150, -120, 120, -60],\n [525, -210, 147, -378, -126, 273, 147, -336, 525, -420, 420, -210]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-183, -460, -471, 1213, -25, -878, 363, -591, 172, 84, 574, -523],\n [545, -95, -302, -26, -1209, 295, -385, 14, -113, 747, 640, 422],\n [812, -655, -868, 1246, 189, -984, 678, -702, -268, 262, 372, -558],\n [-667, -472, -172, -257, 1836, 478, -1189, 280, -240, -909, -1021, -735],\n [360, -304, -335, 574, -1148, -400, 1130, -232, -97, 227, 770, 299],\n [-737, -217, 319, -237, -254, 223, 130, 94, 241, -338, 53, -54],\n [-1167, 375, 753, -553, 229, 417, -859, 198, 628, -323, -202, -46],\n [-177, -172, -157, 322, -809, -43, -550, -162, 173, 685, 637, -101],\n [-253, -281, -876, 844, -52, -154, 266, 466, -837, 21, 274, 36],\n [-55, 549, -212, 286, 191, -244, -5, 482, -606, 722, -95, -32],\n [246, -621, -85, 392, -1255, -219, 1028, -646, 556, -506, 891, 407],\n [-751, -183, 193, 788, -126, -732, 150, -662, 776, -76, 544, -491]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[105, -2, -590, 735, 445, -430, -29, -754, 226, -375, 121, 230],\n [-195, 668, 496, -1071, -192, 463, 353, 353, 126, -108, 228, 512],\n [167, 956, -64, -613, 40, 5, 247, -281, 462, -584, 612, 1064],\n [-362, -858, 38, 604, 167, 47, -68, 85, -396, 467, -633, -966],\n [-577, -590, 622, -295, -141, 534, 141, 674, -490, 655, -649, -918],\n [-57, -54, 294, -327, -225, 210, -3, 390, -138, 219, -93, -174],\n [-497, -406, 136, 181, 256, 201, 192, -10, -217, 233, -448, -530],\n [216, -426, -540, 954, 246, -474, -273, -477, 3, -63, -78, -234],\n [-1070, 50, 568, -608, 424, 714, 741, 71, -145, 131, -484, -254],\n [762, 146, -580, 528, -118, -608, -445, -353, 257, -321, 470, 442],\n [58, -468, 368, -146, -448, 182, -248, 700, -366, 542, -288, -636],\n [592, -336, -648, 976, 28, -652, -500, -408, 68, -112, 140, -64]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[663, 166, 201, 256, 106, -68, 248, -512, -102, -439, 104, -431],\n [-3, 708, 478, 139, 550, -129, 1567, -850, 1066, -1131, -387, -1346],\n [791, -349, -66, -604, 225, 1721, -1318, 71, 53, 497, 1461, -513],\n [-209, -914, -196, 257, 1557, -80, 725, 1306, 176, 743, 785, -383],\n [199, -138, 211, -933, -110, 85, -394, 711, -143, -1228, -2099, 976],\n [-936, -929, -175, -246, 179, -655, 21, 1243, -676, 293, -478, 1874],\n [-1300, -396, -464, 25, -144, -637, 65, 185, -358, 787, 1191, -163],\n [530, -980, -459, 342, 611, 471, 548, 678, -246, -264, 550, 1367],\n [422, 98, 476, -545, 203, 996, -419, -261, 767, -647, 209, -1059],\n [559, -664, -538, -108, 1028, 88, 730, 847, -429, -476, -134, 252],\n [-124, -458, 761, 403, -76, -1219, -236, 2, -554, -143, 38, 74],\n [-600, -18, 269, 755, -136, -1047, 1039, 422, -62, 187, -1510, 2573]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-1166, -249, 1402, 252, -80, 1156, -736, -1596, -1169, -263, 911, 1054],\n [484, 529, -1265, -388, -654, -21, 115, 182, -98, 466, 1102, 102],\n [1316, -907, -1716, 314, 986, -872, -109, -537, -1411, -372, 1092, 5],\n [-835, 214, 894, -2, -437, 878, -251, 61, 475, 472, -784, -559],\n [38, 41, -23, -340, -103, 228, -1570, -623, 305, 977, -526, -1787],\n [-500, 902, -279, 34, -724, 653, 636, 823, 755, 24, 438, 413],\n [657, 876, -757, 491, -622, -437, 1071, 1451, 658, -1061, 574, 187],\n [570, -6, -1410, 107, -830, -392, 55, 56, -629, 350, 589, -561],\n [-1120, -1017, 1007, 573, 804, 367, 690, -883, -958, -552, 120, 1928],\n [569, -206, 193, 324, 433, 476, -835, -445, -797, -464, 372, -874],\n [-477, -1091, 738, 81, 851, -92, 764, -688, -699, -60, -161, 1623],\n [341, 667, 330, -83, 13, 805, -255, 64, -178, -581, 1068, 200]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-702, 915, 253, -698, 979, 57, 164, -179, -11, -466, -504, -821],\n [995, -29, -108, -808, -885, -1386, -536, -363, 553, -660, 533, -1681],\n [-120, -195, 857, 7, 598, -462, -82, -228, 512, -658, -1498, -433],\n [1114, 976, 7, -1230, -1125, -470, 257, -591, 1966, 35, -406, -978],\n [1194, 69, -1741, -621, -1264, -334, -1716, 1116, 193, 1117, 695, -240],\n [18, -46, -334, -1444, -710, -999, 259, -1142, -64, -614, 1371, -444],\n [721, 85, -781, 66, -365, -68, 505, 195, -552, -92, -7, -1063],\n [-157, 64, 3, -249, -564, -1448, 761, -956, -534, -1244, 402, -1066],\n [-726, 204, 53, 287, 1065, 1994, 492, 821, -5, 482, -732, 696],\n [-946, -865, 338, -418, -1031, -1009, -942, -139, -150, -907, 1341, -249],\n [-795, -576, 1112, 1770, 3, 742, 48, 823, 144, -569, -1809, -196],\n [-23, 164, -761, -899, -702, -1362, -1111, 52, -67, 348, 769, 274]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-75, -720, 423, -498, 522, 198, -150, -57, 174, 141, -66, -258],\n [61, 356, -203, 346, -336, -102, 81, 48, 52, -177, 116, 36],\n [3, 488, -299, 138, -198, -126, 88, -1, -394, 119, -122, 358],\n [-33, -748, 451, -330, 396, 198, -143, -22, 440, -55, 88, -440],\n [50, 200, -110, 260, -240, -60, 50, 40, 120, -170, 120, -40],\n [72, 512, -296, 432, -432, -144, 112, 56, -16, -184, 112, 112],\n [-73, -768, 453, -502, 534, 210, -158, -55, 226, 119, -46, -302],\n [-85, -340, 187, -442, 408, 102, -85, -68, -204, 289, -204, 68],\n [-56, 84, -66, -212, 150, -12, -1, -47, -394, 274, -218, 278],\n [26, -64, 46, 92, -60, 12, -4, 22, 204, -134, 108, -148],\n [-130, -380, 200, -640, 570, 120, -105, -105, -430, 480, -350, 210],\n [51, 596, -353, 366, -396, -162, 121, 38, -208, -67, 16, 256]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[128, 368, 416, -112, -400, 224, 384, -240, 80, 256, 96, 336],\n [-128, -368, -416, 112, 400, -224, -384, 240, -80, -256, -96, -336],\n [-120, -345, -390, 105, 375, -210, -360, 225, -75, -240, -90, -315],\n [-48, -138, -156, 42, 150, -84, -144, 90, -30, -96, -36, -126],\n [-72, -207, -234, 63, 225, -126, -216, 135, -45, -144, -54, -189],\n [-104, -299, -338, 91, 325, -182, -312, 195, -65, -208, -78, -273],\n [48, 138, 156, -42, -150, 84, 144, -90, 30, 96, 36, 126],\n [-48, -138, -156, 42, 150, -84, -144, 90, -30, -96, -36, -126],\n [-8, -23, -26, 7, 25, -14, -24, 15, -5, -16, -6, -21],\n [-16, -46, -52, 14, 50, -28, -48, 30, -10, -32, -12, -42],\n [104, 299, 338, -91, -325, 182, 312, -195, 65, 208, 78, 273],\n [-16, -46, -52, 14, 50, -28, -48, 30, -10, -32, -12, -42]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-84, 76, -56, -20, 32, -32, 40, -16, 92, 20, 68, -64],\n [-126, 114, -84, -30, 48, -48, 60, -24, 138, 30, 102, -96],\n [147, -133, 98, 35, -56, 56, -70, 28, -161, -35, -119, 112],\n [-294, 266, -196, -70, 112, -112, 140, -56, 322, 70, 238, -224],\n [-210, 190, -140, -50, 80, -80, 100, -40, 230, 50, 170, -160],\n [-210, 190, -140, -50, 80, -80, 100, -40, 230, 50, 170, -160],\n [-273, 247, -182, -65, 104, -104, 130, -52, 299, 65, 221, -208],\n [273, -247, 182, 65, -104, 104, -130, 52, -299, -65, -221, 208],\n [-189, 171, -126, -45, 72, -72, 90, -36, 207, 45, 153, -144],\n [315, -285, 210, 75, -120, 120, -150, 60, -345, -75, -255, 240],\n [21, -19, 14, 5, -8, 8, -10, 4, -23, -5, -17, 16],\n [-147, 133, -98, -35, 56, -56, 70, -28, 161, 35, 119, -112]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-496, 197, -599, 393, -1, -467, 315, 29, -690, 712, -232, 147],\n [492, -180, 552, -348, 96, 396, -336, -12, 636, -648, 180, -84],\n [-68, 107, -301, 271, 493, -413, -79, 91, -346, 400, -292, 341],\n [387, -75, 252, -93, 486, 21, -366, 63, 291, -258, -75, 201],\n [-250, 198, -572, 466, 608, -666, 8, 122, -658, 732, -438, 470],\n [196, 77, -187, 265, 955, -491, -361, 157, -214, 304, -412, 563],\n [136, -123, 353, -295, -425, 429, 19, -83, 406, -456, 288, -317],\n [488, -254, 754, -550, -370, 722, -218, -94, 868, -928, 424, -386],\n [-261, -51, 108, -213, -954, 429, 402, -153, 123, -210, 381, -543],\n [-327, 2, -45, -88, -789, 250, 403, -120, -53, -14, 263, -416],\n [-252, -21, 27, -129, -747, 291, 345, -117, 30, -96, 276, -411],\n [-100, -30, 70, -110, -430, 210, 170, -70, 80, -120, 180, -250]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[245, -139, -795, -970, 865, -1628, -659, 111, 192, -925, 882, -1036],\n [99, 215, 121, -280, -480, 2370, 967, -371, -225, 493, -51, 1128],\n [409, 356, -216, -1087, -781, -1288, 388, 1028, -1606, -1887, -92, -710],\n [-43, 343, -324, -650, -1343, 554, 1049, 87, 949, 710, -741, 52],\n [-641, -210, 381, 1550, 234, 222, -83, -49, -208, 212, -45, -819],\n [502, 448, 503, -255, 187, -9, -140, -263, -788, -7, -112, 186],\n [283, 133, 1585, 1911, 746, -537, -1117, 332, -1059, 144, 47, 121],\n [536, 549, -18, -271, 1081, -977, -816, 403, 125, -52, 1172, 82],\n [-284, -350, 433, 872, 45, 334, -344, -406, 664, 1074, -180, -391],\n [15, 1410, 727, 104, 881, 637, -472, -288, 354, 1531, 1583, 570],\n [-575, -849, -1, -401, 249, 527, -814, -317, -470, 245, 932, 240],\n [217, -20, 820, 679, 404, 155, -763, -372, 755, 1204, -134, 1112]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[936, 251, 356, -139, 1055, 1250, -464, -1709, 1195, -251, -877, 698],\n [-743, 670, 288, -1552, 566, -263, -82, -1000, -273, -210, -80, -57],\n [-1104, 390, 564, 1015, 385, 658, 832, -224, 565, 926, 423, -738],\n [-439, -55, 1139, -460, 176, 282, -1186, -541, -1211, 148, 222, -665],\n [-535, 778, -76, -1472, -109, -1742, -50, 849, -1330, -791, 853, -591],\n [-129, 26, -1329, -496, -541, -1061, 1249, 832, 435, -291, -10, 521],\n [-178, -995, -1440, -1577, -922, -726, 454, 619, 249, -780, 231, 1139],\n [79, 158, 93, -755, 288, 353, -121, -793, 639, -309, -53, 622],\n [683, -282, -627, 301, -790, -252, 1067, 225, 711, 221, -600, 756],\n [-417, 513, 1260, 40, 1303, 1696, -636, -1815, 759, 196, -75, -300],\n [-9, -202, -490, -175, -484, -182, 956, -53, 599, 255, -486, 621],\n [167, 868, -187, -258, 516, -402, 669, -41, 864, -404, 740, 209]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-693, 179, -690, -828, 271, -1325, 18, 21, -22, -161, -583, -16],\n [1035, 277, -1360, -1277, -245, -1150, -747, -1807, 1129, 1343, 196, -28],\n [708, 942, -338, 385, -687, 248, -852, -953, -610, 654, -381, 802],\n [-309, 640, 1950, 1356, 275, 1148, 26, 150, -1513, -615, 274, 532],\n [-330, -396, -604, 829, -46, 961, 311, 342, 393, -234, 264, -492],\n [-749, -314, -1188, 115, -937, 77, 734, 505, 602, -885, -1329, -304],\n [118, 2519, 625, 1202, -861, 663, 443, -1787, -753, 707, -518, -235],\n [-332, 220, 247, 869, -525, 768, -282, 502, -819, -477, -1543, 508],\n [-398, -400, -461, -296, -6, -704, -104, -341, 283, -512, 815, 137],\n [-972, -951, -1265, -160, -453, -619, 258, 456, -93, -1341, -277, 513],\n [-489, 1130, 1099, 1378, -247, 949, 211, -269, -1025, -695, -153, 536],\n [1, -186, -1247, 607, -485, 1002, 606, -569, 620, -286, -242, -31]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[245, 417, -1561, -358, -869, 425, 723, 9, 909, -579, 667, 182],\n [-213, 229, 204, -409, -352, -428, -890, 429, 187, 411, -107, -68],\n [856, 183, -261, -586, -988, -331, -1541, 1476, -145, -467, 9, 633],\n [-759, -535, 237, -136, 257, -373, 245, -975, -143, 337, -193, -1102],\n [-99, -1070, 420, 506, 14, 969, 562, -739, -968, -436, -666, -886],\n [-53, 652, -242, -568, -432, -631, -830, 663, 638, 374, 270, 344],\n [-195, -323, 79, -286, 519, -1099, -105, -463, -167, 89, 179, -450],\n [408, -730, 833, 276, 878, -659, -336, -56, -1116, -276, -263, -30],\n [-5, 618, 193, -275, -232, -345, -861, 761, 384, 458, 40, 503],\n [567, -121, 320, -451, -407, -705, -1542, 1065, -497, -191, -183, 289],\n [219, -1330, -105, 526, 109, 911, 1100, -1017, -1072, -990, -385, -913],\n [489, -765, 566, 590, 688, 211, 319, -231, -1073, -547, -308, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[125, 440, -1544, -199, -1081, 57, 261, 721, -621, 1155, -38, 730],\n [282, -713, 1037, -418, 924, 125, 563, -1170, 385, 151, 273, 312],\n [414, 58, 493, 192, 486, -170, -261, 327, -296, -355, -86, -526],\n [-465, -788, 195, 53, 261, 18, -285, 95, 683, -1159, 122, -691],\n [-341, 401, -495, 856, -213, 1372, -486, 127, -946, 781, 232, 338],\n [-621, -210, -758, -819, -991, -763, -291, 83, 1463, -1319, -18, -254],\n [399, -666, 885, -576, 951, 501, 30, -804, 69, -195, 528, 135],\n [-201, 91, 196, -944, -406, -2154, 564, 374, 1249, -1166, -618, -482],\n [-665, -724, 104, 835, 114, 107, 90, -239, 724, -433, -169, -493],\n [647, 537, -20, 760, 416, 795, 321, 373, -1829, 1821, -19, 560],\n [-756, -877, 292, 201, -76, -527, 188, -829, 1785, -1073, -202, -494],\n [58, 726, -185, -1203, -343, -316, -194, 499, -411, -246, 204, 367]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1639, 108, 307, -235, 416, 794, 711, -258, -5, -193, 320, -505],\n [-282, -186, 154, 328, 976, -184, -244, -244, 56, 188, 422, -594],\n [895, -173, 360, -523, -717, 337, 603, 222, 466, -1137, -116, 619],\n [432, -1074, 624, -449, 606, -324, 405, 582, -635, 459, 88, -1402],\n [725, 405, -577, -520, -1130, 0, 568, -48, -910, 554, -597, 41],\n [22, 285, -460, 260, 169, 886, -7, -41, 157, 948, -494, -432],\n [305, 43, -677, -78, -38, 496, 500, -368, -24, 725, -717, -745],\n [-866, 573, -777, 213, -785, 27, -431, 88, -296, 903, -658, 468],\n [34, 102, 623, 51, -189, 571, -547, 1214, -456, 769, 175, 254],\n [-369, -210, -620, -200, -605, -91, 386, -292, 467, -265, -835, 69],\n [-439, -17, 478, 827, 1676, 629, -764, 93, 479, 606, 707, -641],\n [624, 665, 99, 43, -22, -47, -130, -117, -797, 306, 579, 220]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-311, 463, 1194, 20, -884, 1408, 304, -552, -529, 896, 1188, -993],\n [1338, 404, -641, -1049, -1101, -374, -850, -514, 318, 168, 1530, 544],\n [660, -171, 543, -344, 755, -111, 214, 517, 885, -98, -960, -952],\n [-23, -264, 301, -878, 367, -18, 1373, 759, 928, -364, 530, 57],\n [-386, 1085, 458, -313, -475, 332, 30, -704, -482, 1089, 300, -135],\n [1422, -186, 875, -348, 960, 915, 1306, 323, 300, -1043, 69, -1576],\n [-940, 559, -642, -192, -509, -5, -1210, -1159, -814, 201, -900, 49],\n [1079, 201, -1195, -468, 326, -736, -467, -309, 263, -17, 381, 1543],\n [-27, 335, 330, 1198, 320, 400, -327, 75, -1092, -955, -745, -1096],\n [792, -13, 902, 263, 237, 110, 909, 554, 361, 461, 621, -474],\n [-767, -311, 206, 1960, -533, 3, -689, 4, -1281, -53, -291, -467],\n [-1599, -245, 588, 193, -1774, 1085, -493, -1135, -906, 1603, 449, -226]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[352, -686, -927, -386, -690, 893, 854, -812, -558, 337, 304, -1303],\n [81, 1228, -460, -351, -747, 970, -810, 296, -448, -651, -157, -890],\n [641, -199, 466, 461, 22, 216, 424, -661, 522, 458, -751, 231],\n [631, -1194, 94, -245, 70, 47, 1298, -730, 736, 158, 505, 172],\n [-252, 838, 665, 521, 302, -419, -960, 481, -115, 26, -901, 489],\n [692, -1090, -606, -176, -166, 358, 1450, -590, 786, 190, 590, -468],\n [-284, -405, -798, -689, -459, 666, 347, -568, -440, -103, 1282, -115],\n [-23, -231, -229, 731, 295, -364, 244, 81, 218, 666, -525, -92],\n [78, 465, -62, 203, -212, 447, -269, -220, 26, 88, -262, 85],\n [-30, 309, 494, -587, -125, 128, -399, 34, -174, -631, 314, 323],\n [5, 104, 1183, -28, 849, -1333, -307, 1139, 818, -724, -171, 861],\n [659, -21, 1115, 80, 280, -567, 27, 358, 270, -241, -1149, -310]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[51, -537, -306, 610, -87, -278, -330, -406, -14, 1107, 199, 440],\n [-35, -574, -984, 389, 34, -383, 285, -208, -489, 147, -44, 1274],\n [168, -1289, -451, -751, -74, 256, -352, 63, 967, 121, -583, -994],\n [-980, 28, 832, -72, -513, 831, 652, 557, 413, -727, 1238, 645],\n [-241, 13, -633, 993, -91, 127, 737, 440, -662, -80, 342, 124],\n [401, -532, 418, -727, -268, -23, -873, -311, 1215, 700, -341, -902],\n [-82, 349, -469, -893, -1073, -138, 344, -479, 440, -38, -359, 557],\n [-28, 418, 1001, 1112, 1336, 211, -27, 855, -887, -708, 720, -283],\n [1030, 12, 239, -268, 278, -748, -983, -348, 515, 526, -648, -335],\n [-864, -618, 341, 167, 947, 1013, 567, 973, -489, -1327, 602, -365],\n [549, -336, -1012, -592, 449, -210, -3, 42, -211, -513, -1297, -938],\n [-338, 107, 289, -1071, -109, 376, 146, -6, 312, -797, -170, -43]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[575, -219, -950, -582, -744, 162, -388, 714, -58, 158, 898, -64],\n [-21, 119, -429, 102, -192, -201, -194, 319, 153, -111, 249, -355],\n [46, 21, 155, 126, 150, -143, 59, 252, -548, -53, -542, -128],\n [-367, 145, 702, 202, 252, 18, 194, -308, -188, -474, -1228, 22],\n [241, -59, -392, -170, -276, -20, -166, 430, -198, 20, 194, -132],\n [-214, -12, 691, 249, 588, 29, 349, -627, 5, 233, -223, 326],\n [-255, 320, -474, 525, 42, -538, -192, 337, 297, -132, 295, -688],\n [-370, 290, -275, 339, -72, -273, -159, -23, 629, -301, 181, -440],\n [188, -222, 197, -607, -396, 535, -7, -125, -105, -233, -421, 460],\n [-617, 438, -71, 640, 162, -445, -83, -160, 696, -415, -98, -586],\n [-151, 41, 453, 250, 408, -87, 214, -243, -197, 63, -397, 71],\n [156, 3, -270, 123, 54, -226, -58, 363, -273, 204, 253, -216]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-596, 326, -1382, -221, 510, -1653, -330, 470, 744, 747, -68, -794],\n [-170, 2384, 316, -795, -1104, -57, -257, 172, 1039, 644, -849, 737],\n [267, -1686, 155, 381, 1262, -321, 232, -165, -484, -61, 689, -953],\n [511, 403, -1205, -108, 1621, 271, 109, -798, 149, -512, -23, -310],\n [183, -300, 15, 344, -832, 606, 431, -364, -215, -739, 307, 916],\n [-1041, -795, 620, 80, 361, -659, 344, 898, -518, -207, -387, 140],\n [-29, -464, 1069, -726, -920, 591, -141, -937, -503, -302, -191, 500],\n [-257, -379, 1314, 1202, 208, 78, 658, 1360, -705, -201, -369, 362],\n [-418, -739, -196, -431, -133, 39, 490, -834, 536, 430, 696, -457],\n [624, 374, -627, -525, -708, -16, -942, -263, 240, 1123, -624, -46],\n [1207, 2266, -438, -452, 100, -459, -929, 272, 947, 500, -343, 59],\n [395, 1352, 44, 344, 733, -215, -149, 91, -174, -756, -534, 138]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[349, -1023, -910, 182, 121, -226, -249, 1756, 322, 806, 1328, -1399],\n [610, 57, 318, 5, -160, -1281, 158, 219, -383, -1311, -248, -411],\n [312, -817, -249, -471, -576, -535, 819, 170, -341, -334, 145, -1396],\n [517, -242, -255, -437, 730, -328, 1762, -1061, -303, 64, -1645, 1009],\n [-746, -876, -1260, 657, -605, -612, -512, 1479, -125, -486, 859, -597],\n [-725, 342, 434, -732, -1455, -513, 482, 703, -68, -910, 1778, -343],\n [164, -1027, -703, 1813, 444, -847, -1552, 1146, 644, -598, -700, -1355],\n [298, 112, 120, -930, -779, 101, 581, 422, -531, 196, 1454, 735],\n [98, -664, 16, -324, -269, -716, 1317, -516, -282, -93, -610, -860],\n [293, 175, 554, 49, 762, 240, 803, -1076, 447, 772, -1184, 994],\n [103, 949, 383, -328, 258, 210, -486, -94, -197, -298, 253, 405],\n [-538, -528, -566, 490, -97, -278, -803, -12, -974, 725, 64, -1464]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-398, 364, 83, -136, -17, -762, 9, -561, -167, -270, -47, 629],\n [889, -335, 457, -206, 609, 859, -722, 847, 495, 284, -383, 382],\n [462, -1126, 2, -137, 491, -561, 547, 134, 343, -180, 348, -919],\n [276, -219, 359, -112, 772, -201, -241, -123, 401, -388, -646, 623],\n [55, 653, -747, -570, -1836, -3, 7, 557, -1180, 891, 801, -61],\n [-652, 491, 489, 397, 451, 132, 74, -833, -6, -428, -904, 264],\n [466, -971, -1033, 335, 361, -321, 888, -378, 202, -948, -740, -865],\n [1476, -727, 684, -56, 1291, 913, -586, 167, 313, 63, -71, -653],\n [54, 277, -443, 153, -454, 365, 101, -157, -446, 46, -30, -351],\n [-72, -765, -510, 278, 466, -519, 801, -335, 426, -878, -925, -324],\n [143, 279, -361, 1098, 1162, 1152, -877, -259, 1097, -654, 29, 473],\n [-35, 500, -76, -485, -1063, 37, 85, 189, -931, 536, -181, 78]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-177, -600, -498, 1099, 1179, -604, 466, 886, 165, 471, 573, -289],\n [-20, 1119, 406, 230, 355, 332, 199, 62, 595, -982, -263, -806],\n [255, -916, -302, 85, 126, -1164, -309, 76, 292, 1074, 408, 802],\n [208, -263, -24, 431, 1054, -121, 292, 730, 215, 139, 849, -22],\n [-269, 391, 593, -967, -425, 313, -536, 574, -81, 182, -145, 978],\n [218, -795, -188, -418, -490, -1058, -386, -450, -50, 1173, 200, 929],\n [615, -148, -31, 200, 204, -1174, -247, -471, 961, 297, 227, 140],\n [-13, 771, 344, 103, 665, -260, 698, -96, 63, -18, 561, -706],\n [-677, 138, 84, -202, -389, 363, -418, 784, -154, 5, -690, 512],\n [801, -964, -450, 277, -57, -276, -364, -524, 405, -23, 189, 233],\n [-172, 656, 469, 18, 776, 233, 164, 937, 308, -257, 366, -47],\n [-285, -933, -488, -51, -444, 700, -45, 162, -1006, 257, -128, 341]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-71, -1016, 735, -513, 598, -417, 772, 1761, -140, 891, 426, -1301],\n [-817, -347, 155, 749, -484, -3, 904, 1082, -361, -306, -662, -396],\n [671, 1685, -585, 552, 667, -1326, -93, -1149, -799, -723, -108, 753],\n [-238, 843, -477, 536, -246, -130, 451, 1123, -445, -988, -1057, -784],\n [98, -912, 1150, -899, -201, 192, 83, -464, -445, 318, 1361, 189],\n [-181, -640, 432, 263, 209, -473, 444, -251, -161, 601, 415, 446],\n [474, -441, 111, 787, -139, -815, 250, -2834, -309, 473, 571, 2445],\n [-209, -597, -55, 1056, 486, -1041, 878, -46, -21, 869, -287, 571],\n [-98, 741, -120, 280, 119, -251, -369, -928, -233, -371, 199, 725],\n [882, 211, -132, 231, 162, -845, 170, -1620, -440, 43, 268, 1162],\n [-103, 72, -262, 1088, 1041, -1405, 370, -631, 43, 920, -24, 943],\n [-589, -1133, 41, -56, -1075, 1415, 31, 610, 758, 112, -531, -305]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-372, -192, -36, -12, 144, -804, -84, 204, 252, 468, 300, -816],\n [204, 794, 652, 184, 392, 128, 538, -728, 236, -76, -700, 162],\n [-137, -236, -165, -47, -60, -221, -149, 223, 3, 129, 239, -232],\n [-311, -9, 109, 29, 224, -741, 38, 35, 293, 431, 133, -745],\n [-275, -321, -191, -55, -16, -513, -190, 311, 89, 299, 361, -529],\n [330, 556, 386, 110, 136, 538, 350, -526, -14, -314, -566, 564],\n [-198, 435, 474, 132, 444, -672, 339, -372, 426, 390, -258, -657],\n [-243, -456, -327, -93, -132, -375, -291, 429, -15, 219, 453, -396],\n [371, 343, 175, 51, -40, 733, 192, -339, -169, -427, -417, 751],\n [-247, 148, 229, 63, 284, -659, 141, -111, 317, 383, -15, -656],\n [-142, 92, 138, 38, 168, -382, 86, -70, 186, 222, -14, -380],\n [192, -383, -424, -118, -404, 634, -301, 326, -392, -368, 220, 621]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2157, -1054, -423, 679, -486, 34, -46, -913, 261, 267, 876, 860],\n [-1037, -1036, 329, -926, -648, -124, 673, -488, 394, -75, -68, -102],\n [152, -309, -234, 315, -447, 326, -75, -465, -902, -221, -77, 135],\n [-204, -61, -130, 217, -432, 312, -193, 155, -107, -40, 1, 490],\n [1199, 548, 1669, 9, -198, -647, 501, 1544, 550, -656, -842, 53],\n [1358, -232, 719, 742, -111, 373, 393, 643, 566, 315, 94, 10],\n [-131, 108, -871, 1313, 257, 276, 330, 332, 912, 1005, 315, 1270],\n [358, 543, 1176, -1353, 83, -341, 1048, 358, -281, -1076, -168, -1687],\n [1416, 423, 412, -854, 710, -564, -273, -120, 609, 1293, -300, -1346],\n [898, -854, -101, 2282, -1463, -737, -616, 809, -577, 476, -183, 696],\n [-435, 860, -946, 158, -9, -57, -468, 1590, 770, -107, -479, 1415],\n [306, 1015, -475, -300, -217, -1306, -808, 1723, 19, -313, -1058, 330]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-636, -901, 296, -977, 44, 132, 853, 331, 2, -1058, -58, 828],\n [1044, 1247, 873, 434, 638, 430, 43, -53, 500, -142, -300, -954],\n [-1281, -1237, 280, 124, -677, -431, 486, -310, -570, 1360, -331, -399],\n [196, -219, -704, 56, -233, 378, 950, -468, -176, -37, -171, 101],\n [945, -58, -695, -383, -707, 639, 299, -1017, 730, -345, -774, -739],\n [267, 528, -252, 225, -110, 1538, 701, 192, 526, -439, 76, -149],\n [172, -483, 347, -963, 63, -284, 425, -307, 0, 51, -355, 168],\n [809, -371, 2042, -835, 478, 107, 396, -235, 1523, 932, -683, -1895],\n [47, 1711, 539, 1214, 598, 899, -978, 1240, 180, -481, 498, 459],\n [-573, 1205, -163, 531, 766, 376, 1072, 565, -1492, -1557, 764, 767],\n [-955, -1088, -5, 68, 203, -1127, -75, 409, -278, -414, 571, 217],\n [-463, 952, 1087, 666, 1675, 211, 198, 1798, -95, -802, 1597, 304]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[139, 350, 315, -862, -287, 963, -142, -311, -536, -657, 361, -268],\n [-331, 148, 232, 400, -332, 112, -513, 46, 65, 449, 99, 232],\n [195, 14, -239, 17, 56, -169, 521, -199, 131, -46, -185, -202],\n [-4, 280, 226, -589, -39, 702, 431, -516, -443, -477, 298, -160],\n [-380, -486, 237, -303, 1021, -130, 434, 139, -445, -369, 370, 513],\n [242, 126, -9, -359, -203, 282, -150, -23, -99, -287, 12, -245],\n [358, 178, -297, 274, -578, -182, -343, 103, 426, 270, -374, -353],\n [-708, -94, 739, -238, 293, 563, -667, 191, -619, -100, 688, 668],\n [459, -180, -480, 216, -69, -615, -105, 354, 468, 111, -471, -279],\n [-414, 96, 270, 321, -108, 129, -207, -72, -48, 351, 180, 303],\n [393, 500, -324, 530, -1125, -29, -465, -114, 614, 567, -489, -529],\n [432, -654, -587, 239, 555, -1138, -72, 783, 493, 25, -510, -31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1114, -964, 541, 518, -320, 30, 103, 272, 725, -400, 686, 226],\n [904, -570, 474, -48, -243, -116, 132, 175, 326, -821, 842, -152],\n [233, 137, 587, -383, 160, 40, 514, 1113, 230, 506, -240, -299],\n [-826, 356, 307, -144, 377, -78, -136, -10, -476, 340, -651, 131],\n [-423, 589, -120, -410, -38, -100, -178, 33, -447, -512, 260, -670],\n [-156, 274, 170, -187, 179, 70, 361, 605, 88, 793, -554, -15],\n [695, -527, -940, 422, -672, -192, -51, -1736, 224, -737, 853, 605],\n [-699, 1005, -402, 1188, -1512, -344, 75, -818, 238, 563, 403, -261],\n [1409, -812, 229, -792, 402, 146, 495, 756, 432, -513, 448, -75],\n [-1076, 868, -412, 65, -183, -94, -525, -447, -630, -267, 14, -533],\n [-128, 630, -392, -656, -8, -44, 273, 157, -229, -1, 35, -531],\n [-119, -693, 699, 1137, -39, 28, -165, -155, 407, 760, -541, 1018]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1346, 98, 257, 53, 533, 133, -642, -863, -543, -217, -90, 977],\n [-87, -415, -299, 476, 354, 238, -204, 247, -268, -144, 479, 281],\n [568, -319, -138, 16, 584, -152, -353, -331, -210, -314, -134, 354],\n [-556, -596, 30, 86, 106, -484, 26, 154, -72, -424, 560, -402],\n [-624, 406, -282, -298, -482, 126, 558, 536, 642, 502, -660, -610],\n [-578, 48, 147, -217, -395, -284, 329, 191, 266, 38, 28, -573],\n [234, -513, -514, 326, 692, 125, -306, 111, -191, -229, 34, 362],\n [730, 123, 379, 121, 133, 119, -389, -554, -451, -129, 276, 615],\n [-155, -522, -254, -339, 407, -685, 41, -25, 247, -399, -387, -470],\n [-292, -551, -13, 139, 231, -353, -91, 58, -155, -401, 486, -169],\n [424, 33, -729, -113, 521, 268, -42, 144, 304, 212, -1016, 211],\n [137, 820, -58, 245, -487, 982, 142, 267, 56, 760, -177, 430]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[687, -336, -62, 175, 131, -114, -624, -393, -569, 850, 912, -3],\n [385, -302, 83, -212, 590, -603, -603, 71, 66, 440, 5, -159],\n [-45, -3, -544, 197, -503, 600, 570, -366, -412, -115, 561, -96],\n [-242, 483, 403, 567, -899, 829, 259, -193, -328, -115, 334, 587],\n [-348, 378, 198, 294, -606, 570, 390, -30, -60, -330, -24, 330],\n [338, 32, -249, 631, -847, 897, 147, -710, -961, 480, 1345, 270],\n [702, -320, -43, 221, 75, -61, -631, -426, -619, 880, 979, 34],\n [457, -352, -516, 59, 27, 68, -82, -415, -509, 470, 810, -245],\n [-335, 222, 595, -228, 334, -443, -203, 539, 662, -340, -983, 149],\n [-338, 487, 596, 358, -574, 468, 108, 83, 27, -235, -163, 543],\n [261, -323, -218, -275, 517, -478, -268, 36, 76, 225, -17, -314],\n [-279, 314, 383, 152, -286, 217, 97, 135, 134, -240, -271, 305]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[259, 275, 500, -374, -301, -458, -418, 5, 93, -229, 849, 221],\n [1008, 454, 677, 207, -110, -317, 415, -679, 11, -974, 1354, -6],\n [-168, -916, -360, 714, 426, 812, -166, 128, -388, 172, -934, -208],\n [449, -908, 1027, -393, -268, 265, -851, -205, -710, -230, 167, -318],\n [-663, 1, -771, 196, 226, 159, 64, 440, 224, 557, -792, 129],\n [-162, -28, -452, 652, 264, 52, -400, 428, 242, 32, 154, 440],\n [849, 300, 570, 332, -64, -290, -18, -388, 47, -846, 1345, 190],\n [106, 58, -12, -35, 37, 126, 601, -336, -92, -74, -265, -304],\n [200, 988, 185, -682, -315, -595, 1006, -507, 305, -184, 429, -178],\n [586, -696, 839, -254, -133, 419, 102, -645, -719, -368, -143, -654],\n [-278, 360, -758, 745, 321, -112, -111, 484, 518, 72, 217, 578],\n [528, 873, 103, -316, -74, -155, 2022, -1124, 61, -473, -17, -697]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[342, -523, -1482, -233, 566, 392, 83, 410, 477, 792, -487, 763],\n [-458, 664, -1053, -1598, -447, -591, 42, 320, 608, -1041, -882, -631],\n [1271, -1469, -872, -903, 1375, -632, -545, 1160, -441, 1051, -1220, 72],\n [362, -315, -158, -686, 378, -568, -580, -32, 572, -459, 120, -152],\n [523, -182, 405, -393, -627, -459, -351, 48, -1188, -432, -277, 60],\n [-652, -287, 1408, 967, 37, 457, 280, 552, -1372, -290, -129, -393],\n [-695, 528, 438, 1205, -499, 580, 526, -1264, 72, 201, 1214, 457],\n [370, -528, 738, 434, 188, 301, -635, 59, -863, 128, -5, 134],\n [1458, -831, -896, -717, 641, 179, -868, 728, -608, 506, -1157, 133],\n [54, 682, 590, 323, -604, 250, -693, -1202, 369, 289, 861, 327],\n [-1822, 320, 364, 168, -299, 576, 33, -353, -479, -57, 17, 257],\n [-106, -547, 1800, 725, 71, -1156, -58, 997, 286, 1773, 338, 680]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1624, 591, -1125, -52, -16, -317, 413, 1053, 135, 620, -806, 855],\n [-400, -991, 4, -603, -657, -357, -401, -1066, -733, -1166, 216, -49],\n [-238, -749, 1532, 1062, -782, 309, 234, -42, 187, 910, 167, -1108],\n [-877, 1309, -1711, -273, -114, -161, -633, 464, -182, -141, -727, -534],\n [-135, -802, 213, 1447, -293, 299, -3, 759, -283, 241, -1225, -1370],\n [-1398, 828, -28, -853, 1301, 138, 167, 352, -663, -237, 320, -260],\n [541, 1001, 509, -1173, 177, -853, -597, 994, -325, 94, 49, -384],\n [31, -471, 172, 765, -613, 409, 364, -598, 1610, 562, 1261, 742],\n [-318, -699, 1882, -535, -403, -94, -551, 788, -314, -99, 172, -673],\n [642, -501, -597, 1036, -1367, 60, 483, 91, 1363, 93, 1361, -373],\n [-1052, 291, -275, -452, -353, -462, -61, -1000, 410, -370, 1631, -314],\n [179, 201, -320, -1413, -384, -662, 377, -18, -972, 124, 27, 728]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-266, -397, -1021, -34, -181, -61, -425, 494, -301, 46, -459, -657],\n [-286, -33, -677, 50, -121, 115, -79, 84, -47, -300, -147, -823],\n [463, 511, -662, -908, -647, 513, -20, 23, 498, -408, 542, -664],\n [28, 241, 535, 136, 145, 51, 292, -343, 162, -135, 233, 188],\n [-135, -268, 607, 462, 390, -322, 33, -35, -253, 342, -239, 677],\n [-388, -158, -286, 354, 126, -60, -19, 15, -177, -143, -266, -459],\n [395, 462, 3, -546, -324, 332, 149, -173, 419, -254, 509, -127],\n [304, 624, 200, -398, -236, 398, 349, -411, 515, -453, 624, -251],\n [397, 328, 983, -114, 114, 26, 313, -359, 275, 110, 441, 845],\n [-8, -148, -324, -92, -92, -32, -182, 214, -98, 90, -140, -102],\n [290, 467, 751, -120, 39, 169, 392, -457, 370, -167, 513, 376],\n [-419, -356, -157, 486, 246, -226, -107, 121, -337, 86, -435, -151]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[844, 218, -336, 187, 293, -437, 208, -906, -590, -234, -640, -1157],\n [813, 450, -862, 91, -352, -1409, 753, -904, 196, -60, -1165, -848],\n [279, 18, 353, 663, 250, -1340, -759, 548, 591, 256, -279, 325],\n [-52, -853, -829, 850, -162, -525, 77, 331, -601, -52, -335, -1243],\n [-466, -284, -184, 510, 133, -896, 652, 1436, 1377, -802, -679, -1019],\n [-215, -421, 579, -213, 295, 253, -203, 924, 588, -539, 276, -302],\n [-807, 69, 145, -238, 442, 856, -263, 951, 493, 253, 662, -30],\n [-117, 158, 335, -317, 403, 16, -513, 203, 317, -552, -690, 1093],\n [551, 124, -562, -741, -1015, -721, 1659, -553, 858, -380, -320, -1270],\n [-295, 276, -695, 157, 10, 586, 123, -509, -776, 588, 111, -60],\n [-384, -90, -627, 1112, 268, -345, 628, 583, 18, -114, -312, -1408],\n [-441, -114, 156, 189, 258, -475, -333, 1196, 1006, 36, 21, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[347, -149, 509, -1003, -316, -800, -482, -96, 307, 648, -1764, -269],\n [-313, -287, -196, -287, 66, 315, -107, -1219, 223, 62, -518, -991],\n [95, 167, 973, 694, 246, -1364, -106, -804, 1278, 268, 105, 328],\n [186, 680, -1298, -51, 55, 354, 656, -991, 231, 1215, -500, -621],\n [-182, -721, 1286, -769, -415, 188, -1033, -458, -138, -1561, -112, -337],\n [-35, -229, -178, 397, -629, -978, -696, 565, 653, 1052, -662, -138],\n [2298, 683, -369, 1521, -761, -1410, 565, -340, 282, 1469, 803, 208],\n [1481, -124, -64, -442, -905, 304, 380, 413, -672, -182, 730, 411],\n [-1013, -1128, 932, -850, -6, -721, -535, -730, 1140, -70, -900, -133],\n [769, -504, 112, -49, -1177, -348, -488, 1146, 399, 740, -160, -112],\n [53, -650, -115, 426, -73, 431, -524, 1220, 267, 128, 125, -742],\n [1228, 616, -489, -146, -515, -390, 509, -346, -1179, 2, 343, 837]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-365, -189, -854, -1521, 299, -19, -265, -145, -227, 12, 340, -1635],\n [-712, -547, -819, -135, -97, 533, 335, 508, 203, 199, -213, 225],\n [545, 681, 675, -578, 1041, 444, 55, 1023, -160, 171, -655, 450],\n [387, -281, -939, 847, -131, 774, 1553, 483, -151, 1119, -11, 1701],\n [842, 567, 29, 541, -179, -1166, 1800, 794, 44, 1764, 134, 855],\n [516, -176, 1465, 176, 897, -111, -125, -897, -44, 98, -502, 518],\n [1204, 1251, -1572, 685, -844, -447, 357, 205, 16, -30, 815, -397],\n [-367, 40, -335, -980, 200, 451, 325, -1161, -75, 142, -305, -392],\n [347, 900, -403, 399, -470, -859, 602, 612, -1123, -544, 341, -109],\n [-401, -301, -1619, -25, 912, 771, 936, -311, 434, 197, -819, 793],\n [1296, 1168, 866, -6, -435, 107, -1620, 183, 203, -781, 743, -976],\n [-315, -995, -886, -28, 1295, 480, 1067, -364, -143, 398, -701, 790]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[104, -259, 390, 1040, 428, 12, 1049, 115, 710, -288, -483, 190],\n [-363, 931, 904, -147, -292, 221, -280, -106, -398, -137, 655, -1411],\n [-612, -745, 284, 215, 1032, -116, 849, 252, 1072, -1308, -1110, 345],\n [-3, 332, 1266, -308, -974, 270, -782, 206, -400, 384, 714, -358],\n [244, -68, -335, -281, 263, 401, -1669, -250, 544, 924, 5, -964],\n [-352, 226, 488, -267, 236, 332, -925, -549, -646, 829, 511, -37],\n [672, -222, 343, -135, -363, -872, -568, -127, -149, -36, 508, -22],\n [-1420, -172, 150, 364, 422, -503, 526, -279, 727, -647, -21, -146],\n [674, -27, -1286, 44, 535, 371, -1127, -804, -90, 402, 417, -372],\n [-423, 304, -75, 41, -935, -16, 915, -754, -1114, -857, 1300, -38],\n [-415, 669, 752, 857, -179, 254, -827, 883, 668, 1576, -163, 176],\n [-496, -354, 1460, 267, -113, -1330, 949, 643, 1499, 444, -614, -320]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[146, -779, -448, 135, 1215, 615, 306, -1721, -176, 189, -1056, -350],\n [522, 507, -381, 414, -1164, 9, -676, 278, -949, -157, 547, 290],\n [-512, -49, 64, -1146, 903, 681, 1353, -166, 587, -330, -459, -235],\n [-780, 108, -964, 994, -48, 132, 44, -41, -882, 580, 249, -532],\n [-167, 413, -686, 955, -588, 128, -273, 242, -1755, 758, 119, 78],\n [125, 479, -689, 535, -719, -145, -606, 145, -565, 145, 616, 605],\n [16, -384, -26, -504, 1212, 285, 502, -930, 434, 246, -802, 526],\n [513, 466, -221, 259, -1338, -131, -745, 444, -322, -585, 852, 14],\n [669, -178, 575, -953, 94, 491, 391, -356, 214, -725, -504, -174],\n [-1275, 737, -392, -214, -512, -97, 688, 1455, 506, -225, 1148, -399],\n [-657, -27, -771, 615, 303, -327, -222, -204, 543, 315, 483, 135],\n [-283, 488, -725, -132, 322, 312, 398, -99, -669, 616, -105, 1107]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[84, 270, -505, 332, -651, -490, 34, -581, -620, -24, -570, -426],\n [525, -279, -142, -985, 1041, 101, -332, 571, 217, -291, 24, 78],\n [-447, -124, 879, 185, 23, 384, 21, 201, 712, -209, 1178, 317],\n [-315, -229, 682, -21, 407, 583, 98, 509, 687, 169, 680, 512],\n [489, -195, -150, -853, 789, -55, -356, 359, 125, -439, 120, -66],\n [84, 103, 123, -94, -272, -425, -307, -380, -9, -822, 718, -413],\n [12, 2, 106, -64, -16, -78, -102, -56, 74, -264, 308, -82],\n [-267, 54, 17, 449, -273, 194, 295, -23, -62, 543, -354, 195],\n [45, 108, -367, 189, -231, -120, 129, -169, -364, 307, -642, -87],\n [-312, 208, 546, 416, -806, -416, -208, -650, 156, -936, 1300, -416],\n [294, -332, 174, -818, 1042, 348, -222, 702, 476, -142, 292, 298],\n [-294, -77, 546, 140, 7, 259, 35, 133, 441, -84, 700, 217]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-302, -142, -166, -198, -299, 79, -173, -313, 16, 203, 124, -25],\n [308, 252, 196, 252, 322, 14, 182, 350, -56, -322, -336, 14],\n [-156, -548, -204, -324, -230, -378, -114, -298, 184, 614, 992, 38],\n [886, 252, 446, 504, 851, -377, 499, 871, 14, -419, -42, 91],\n [992, 365, 520, 603, 966, -349, 563, 999, -15, -558, -209, 93],\n [-98, -159, -82, -117, -115, -74, -62, -134, 47, 187, 261, 4],\n [-688, -379, -392, -477, -690, 131, -397, -729, 57, 522, 391, -51],\n [-134, -530, -190, -306, -207, -377, -101, -273, 180, 591, 968, 39],\n [1160, 266, 568, 630, 1104, -550, 650, 1122, 42, -480, 70, 126],\n [440, 360, 280, 360, 460, 20, 260, 500, -80, -460, -480, 20],\n [-818, -65, -370, -387, -759, 496, -452, -756, -75, 207, -289, -102],\n [-892, -73, -404, -423, -828, 539, -493, -825, -81, 228, -311, -111]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1293, 456, 548, 433, 988, 682, -266, 973, -669, -849, -141, 423],\n [-460, -806, 366, 193, 676, 259, -897, 957, -265, 800, 468, -583],\n [-118, -349, 252, -814, 696, 267, -1273, 1286, -942, 199, -280, -929],\n [1046, -220, 410, 772, 311, 547, 201, 891, -246, -975, -99, 832],\n [172, 653, 52, -1567, 436, 524, -945, 1105, -1179, 339, -439, 143],\n [325, 284, 81, 522, -4, -174, -56, 480, -496, -189, 197, -64],\n [-519, -29, -91, 543, -936, -592, 215, 51, 361, 418, 386, 227],\n [-176, -387, -427, -1117, 86, -50, -177, -178, -556, -342, -637, -972],\n [-708, -134, -294, -18, -528, -391, 118, -328, 109, 704, 352, -116],\n [412, 289, 27, -1522, 551, 638, 175, 86, 459, -271, -818, -41],\n [40, -314, 352, 1073, -650, -420, -965, -679, -156, -1356, -530, 481],\n [394, 31, 74, 881, 573, 180, -198, -276, -816, -242, 390, 143]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-32, -241, 83, -575, -349, 199, 461, 137, 401, 173, 153, -913],\n [276, -126, 131, -146, -267, 283, -304, -310, -280, 175, -169, -612],\n [-1071, -529, 838, 28, 808, -765, 1072, 975, 644, -1054, -357, -391],\n [672, 397, -553, -179, -642, 336, -806, -733, -271, 674, 189, 554],\n [82, -146, 47, -981, -680, 22, -173, -283, 457, 410, 70, -63],\n [-134, 358, -548, 698, 591, -1, 259, 446, -94, 77, 546, 1127],\n [-563, -281, 75, -191, 376, -41, 1001, 844, 563, -76, 435, -238],\n [46, 282, 59, -625, -697, -757, -506, -665, 605, -289, -492, 734],\n [-467, -457, 420, 425, 760, 167, 820, 810, -139, -364, 42, -973],\n [-369, -422, 542, -377, 71, -188, 314, 250, 277, -289, -251, -603],\n [-622, 125, 298, -962, -497, -1351, 312, -76, 1468, -777, -463, 860],\n [713, 209, -655, 129, -239, 934, -686, -378, -757, 1091, 609, 341]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-115, 90, -10, -55, 65, 95, 0, 10, -75, 125, -100, -15],\n [460, -360, 40, 220, -260, -380, 0, -40, 300, -500, 400, 60],\n [368, -288, 32, 176, -208, -304, 0, -32, 240, -400, 320, 48],\n [-506, 396, -44, -242, 286, 418, 0, 44, -330, 550, -440, -66],\n [-345, 270, -30, -165, 195, 285, 0, 30, -225, 375, -300, -45],\n [598, -468, 52, 286, -338, -494, 0, -52, 390, -650, 520, 78],\n [-23, 18, -2, -11, 13, 19, 0, 2, -15, 25, -20, -3],\n [437, -342, 38, 209, -247, -361, 0, -38, 285, -475, 380, 57],\n [276, -216, 24, 132, -156, -228, 0, -24, 180, -300, 240, 36],\n [506, -396, 44, 242, -286, -418, 0, -44, 330, -550, 440, 66],\n [115, -90, 10, 55, -65, -95, 0, -10, 75, -125, 100, 15],\n [161, -126, 14, 77, -91, -133, 0, -14, 105, -175, 140, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-16, -453, -374, -435, 134, -308, -1876, -532, -227, -434, 1459, 38],\n [-72, 886, -1372, 1101, -633, 1221, -1877, -1008, -205, 338, 631, 299],\n [513, -665, -908, -264, -28, 561, 767, 1231, 761, -274, 357, 645],\n [1840, 824, -1436, 1304, 241, 760, -1165, -511, -557, 1020, -95, -388],\n [-6, -161, -977, -224, 291, -77, -879, -473, -512, -264, 1424, 858],\n [-297, 534, 562, 1065, -508, 129, 300, -108, 116, 661, -1639, -815],\n [386, -178, -7, -77, -237, 835, 405, 424, 451, -649, -149, -652],\n [767, 751, 949, -8, 426, 515, 406, -429, -166, -168, -852, -1246],\n [-447, -456, 0, -271, -235, 629, 159, 634, 1340, -807, 72, 71],\n [-663, 412, 331, 484, -182, -826, -954, -648, -96, 917, -329, 207],\n [816, 728, 1699, -600, 879, 220, 1094, -144, -683, -66, -1133, -1278],\n [-5, -348, -1009, 1151, -1410, 555, 565, 1106, 452, 748, -853, 35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[273, 294, -20, 117, -20, -1223, 530, 294, -223, -668, -210, 169],\n [-287, 525, -516, 978, 202, -607, -136, 682, -306, 243, 826, -546],\n [-335, -182, 2, -225, -362, 117, 785, 438, 779, 447, -510, 488],\n [-252, 183, -162, -343, 97, 295, 3, -106, 101, 64, -204, 124],\n [-21, -112, 80, -61, -268, -401, 677, 348, 395, -7, -392, 366],\n [-363, -74, -152, -161, 289, 476, -290, -384, 7, -140, -142, 51],\n [-221, 182, -85, -337, -342, 738, 202, 385, 521, 1046, 35, 42],\n [147, 230, 1, -5, -220, 90, 34, 315, 41, 522, 269, -164],\n [536, -953, 721, -183, -260, 805, -406, -635, 99, 89, -53, 10],\n [43, 233, 92, -950, -347, 216, 614, 100, 466, 289, -678, 512],\n [-39, 110, -155, 769, -112, -832, 380, 703, 23, 76, 345, -148],\n [-407, 974, -768, 821, 346, -1321, 260, 834, -407, -250, 502, -321]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[500, 64, 1035, -1722, 448, -185, 1255, 286, -405, -1821, 1570, 208],\n [-12, 467, 279, -423, 399, 590, 307, 211, -188, 53, 558, -388],\n [381, 268, 360, -432, 472, 726, 436, 399, -115, -199, 579, -100],\n [489, 1346, 861, -385, -685, 323, 565, 535, 94, 839, 137, -1623],\n [-659, 470, -164, 678, -156, -66, -261, -841, -338, 970, -444, -576],\n [-104, 541, 41, -86, 82, 476, -212, 205, -49, 788, 94, -598],\n [101, 676, 925, -557, -567, -505, 56, -229, -185, 144, 560, -751],\n [-243, 295, -23, -829, 511, 46, 818, 0, -490, -186, 307, -271],\n [-705, 218, 826, 310, 506, -241, -5, -741, -173, 600, 82, -62],\n [-476, -312, -323, 522, -119, -573, -1130, -665, -118, 1030, -562, 314],\n [-1040, 75, 632, -504, 826, -591, 406, -455, -239, 166, 259, 24],\n [183, 573, -86, -371, -770, -527, -764, -1023, -1002, 931, 182, -594]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[45, 135, -345, -180, 315, -300, 75, 90, -210, -150, 390, 195],\n [21, 63, -161, -84, 147, -140, 35, 42, -98, -70, 182, 91],\n [12, 36, -92, -48, 84, -80, 20, 24, -56, -40, 104, 52],\n [-27, -81, 207, 108, -189, 180, -45, -54, 126, 90, -234, -117],\n [-72, -216, 552, 288, -504, 480, -120, -144, 336, 240, -624, -312],\n [-27, -81, 207, 108, -189, 180, -45, -54, 126, 90, -234, -117],\n [-21, -63, 161, 84, -147, 140, -35, -42, 98, 70, -182, -91],\n [75, 225, -575, -300, 525, -500, 125, 150, -350, -250, 650, 325],\n [-18, -54, 138, 72, -126, 120, -30, -36, 84, 60, -156, -78],\n [24, 72, -184, -96, 168, -160, 40, 48, -112, -80, 208, 104],\n [45, 135, -345, -180, 315, -300, 75, 90, -210, -150, 390, 195],\n [48, 144, -368, -192, 336, -320, 80, 96, -224, -160, 416, 208]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-737, 435, 1114, -174, -936, 252, -914, 459, 268, 902, -45, 260],\n [-275, -621, -58, -611, -315, -605, -188, 405, -831, 441, -460, -753],\n [-433, -244, 1140, -698, -159, -438, -234, -387, -496, 16, -376, -722],\n [828, 17, -520, -183, 263, -58, 1, -795, 84, -277, -170, 182],\n [68, 566, 571, -356, -692, 318, -831, -282, 297, 485, 16, 404],\n [129, -583, 32, -460, -39, -653, -305, -258, -319, 428, -851, -325],\n [215, 591, -478, 269, -131, 641, 110, 201, 223, -267, 792, 405],\n [-68, 338, -433, -22, -388, 406, -1, 576, -223, -5, 674, 4],\n [530, -271, -938, -40, 477, -140, 582, -174, -398, -590, 169, -296],\n [-329, 492, 337, 32, -23, 506, 385, 171, -183, -663, 960, -240],\n [240, 463, 23, 111, 29, 406, 26, -309, 295, -314, 412, 316],\n [-870, -207, 232, -640, -715, -148, -72, 1098, -1140, 264, 413, -1020]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-587, -864, -1087, -384, -374, -1082, 554, -513, 280, 1082, 451, 164],\n [-503, -928, -529, 1225, -8, 103, -1117, -1151, 449, -90, -2306, -708],\n [-205, -712, -690, 22, -784, -1077, 178, -455, 349, 1023, 752, 31],\n [-813, -344, 90, -645, -922, -597, 35, 112, 321, 1309, 1169, -31],\n [-386, 386, -319, -8, -697, 107, -601, 1292, -894, -1536, 1113, -1521],\n [-1890, -189, -1494, 613, 640, 1, -400, -585, 447, 583, -828, -184],\n [646, -410, 195, -386, -2004, -327, -418, -504, -451, 1193, 405, -809],\n [-903, 550, 829, -1091, -20, 721, -175, -144, -331, -1442, 1036, 460],\n [488, -175, -1001, -155, -614, -372, 353, -271, -991, -1756, -833, -1532],\n [389, 944, 145, 640, 128, -61, 558, 610, 511, -1041, -578, -573],\n [272, 1514, 719, 955, 257, 859, -599, 536, -174, -425, 77, -411],\n [-1094, 1616, 20, 705, -233, -251, 57, 875, 586, -197, 1293, -615]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-829, -304, 627, -299, 778, -24, 117, -1075, -906, -117, 1898, -422],\n [1856, 1390, 1009, 1243, -281, -743, -593, 2762, 242, -1261, -1618, 1278],\n [-1333, -563, 96, -479, 531, -845, 11, -666, 5, 424, 205, -904],\n [863, -407, -1174, -461, 583, 180, -473, 469, 270, 234, -1088, -619],\n [965, -506, -695, 675, 49, -221, -1250, 787, 774, -76, -1266, 93],\n [-870, -79, -1824, -1123, 342, -363, -418, -1590, 320, 527, -652, 159],\n [-664, 56, -1515, -2312, 568, 844, 755, -1385, -312, 1122, -436, -24],\n [486, -286, 668, 776, -1162, 302, 371, -729, -441, 190, 321, 607],\n [-303, 21, -192, 172, 573, 428, -75, 24, -261, -711, 835, -144],\n [-636, -632, -710, -1072, -72, 1146, 554, -1462, 54, 934, 386, -900],\n [-1370, -427, -369, -931, 884, -784, 97, -836, -221, 455, 391, -704],\n [-15, -167, 415, 620, -574, -426, 19, -602, -366, 50, 523, 757]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 816, -140, 265, -625, -194, 1054, -331, 757, -1197, 34, -5],\n [-1057, 46, -1355, 837, 765, -1127, -280, -57, -15, 463, -217, -983],\n [-148, 409, 5, 81, -1401, -121, 368, 1187, -50, -544, -969, 919],\n [-212, 596, -475, 612, -380, -188, 346, -474, -2, -611, 346, -49],\n [-1095, -221, -230, 602, 809, -613, -946, 195, 302, 339, 200, -544],\n [1017, 86, 1172, -694, -824, 1050, 257, 864, -196, -20, -64, 1193],\n [817, 261, 203, -580, 796, 350, 584, -867, 38, 774, 1111, -183],\n [564, 36, 455, -145, -1658, 444, 688, 1350, -530, -358, -936, 1349],\n [-596, 419, 125, 70, -68, -189, 124, -308, 973, -1278, -263, -435],\n [-434, 395, -241, -222, 885, -392, 109, -783, 528, 216, 542, -699],\n [-754, -715, 729, 41, 931, -2, -976, -553, 756, -476, 335, -704],\n [1090, 29, 921, -1140, -830, 599, -226, 1904, 471, 293, -1169, 1154]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-536, 1534, 59, 752, -115, -247, 690, -159, -643, -91, -353, -927],\n [572, 1053, -8, -321, 1239, -505, -796, -603, 1302, 894, 1304, -307],\n [-261, 308, -319, -77, 216, -920, -465, -238, -32, -617, 1095, 475],\n [-122, -291, -1232, 1020, -110, -56, -54, 431, 346, 809, -149, 1303],\n [140, 1296, 760, -165, 721, 424, 597, -126, -251, 437, -45, -2033],\n [-724, 1459, -636, 501, 402, -732, 271, -1005, 366, -94, 179, -369],\n [39, -10, 650, -425, -188, -1182, -1368, -495, 464, -212, 1405, 536],\n [-1001, 484, 89, 925, -227, -954, -569, -1132, 548, 773, -396, 116],\n [-366, -1366, 954, -681, -216, -945, -1048, -180, -864, -1551, 162, 943],\n [-584, -102, 689, 372, 763, -399, -81, -92, -1188, -523, -1112, -171],\n [434, 483, -1245, 473, -489, 1053, 1167, 844, 262, 657, -4, -108],\n [-184, 177, -705, 318, -598, 337, 816, 318, -343, -392, -307, 127]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[211, 13, 137, -38, 495, -734, -512, -122, -551, -443, 20, -728],\n [-1158, -61, 592, 1022, -82, 1708, 498, -1533, -275, -1079, -878, 247],\n [174, 1005, -1030, -591, -296, -1272, -591, 262, -762, -84, 279, -389],\n [231, -714, 1337, -472, 518, -1303, -339, 388, -303, 3, 2057, -742],\n [314, -40, 523, 458, 386, 1223, -147, -838, -318, 248, -937, 60],\n [-950, 741, -527, 18, -1212, 161, 181, -343, 125, -973, -1353, -455],\n [-114, 74, 151, -395, -581, 656, 477, 332, 225, 757, 438, 140],\n [-875, -1305, 279, -393, -345, -746, 1062, 1487, 120, -52, 1330, -1346],\n [-1104, -404, -1078, 103, -490, 269, 838, 642, 426, -1102, -1555, -1049],\n [-773, 492, -966, 236, -752, 591, 577, -167, -461, 11, -295, 316],\n [72, -421, -222, 356, 581, -538, 144, 405, 362, -284, -34, -12],\n [1936, 312, 1456, -984, 546, -61, -1869, -767, 184, 848, 221, 582]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[71, -827, 457, -896, -214, -874, 751, 469, 107, 1233, 503, 426],\n [-520, 536, -1251, 468, -342, 87, -878, -598, -348, -49, -96, -588],\n [-1002, -103, 157, -83, -465, 120, 673, -565, -843, -1336, -17, -282],\n [774, -1026, 1080, -1292, 908, -1257, 876, 1113, 87, 277, 1023, 526],\n [758, 771, 31, 852, 245, 391, 55, -28, 467, 497, 81, 196],\n [829, -525, 1185, -1025, -38, -606, 350, 1146, 380, 1012, 323, 400],\n [961, 1326, 987, 641, 910, 90, 356, 1064, 720, -538, 596, -819],\n [147, -1180, 759, -1634, -679, -749, -51, 863, 119, 1367, 132, 372],\n [-1065, -1041, -2, -136, -191, -13, 988, -367, 390, 518, -563, 371],\n [85, -622, 45, -53, -140, 982, -624, -624, 260, -50, -528, 719],\n [-636, 897, -259, 1223, -140, 959, 297, -767, 297, -582, -137, -609],\n [-359, 113, -918, 402, -473, 735, -833, -1176, -357, -210, -9, 69]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1127, 255, -75, -315, 899, -653, -363, 999, -57, -368, -618, -250],\n [1283, 178, 1514, -341, -567, 632, -291, 353, 349, 305, 1077, -1216],\n [-683, -1024, -489, -112, 285, 782, 391, 1514, -932, -284, -680, 866],\n [610, -226, 116, -1297, -1772, -691, -41, -857, -272, 297, 179, 580],\n [-397, 366, -177, -32, -137, 567, -183, -33, -951, 836, 226, -512],\n [288, -425, -28, -466, -459, 1025, 324, 660, -485, 366, -1120, 464],\n [-818, 1246, 258, -617, -489, -1324, -293, -1138, -531, -263, -411, -24],\n [-1848, 1184, 879, 770, 2061, 809, 61, -216, -1099, -380, -399, -345],\n [316, -361, 923, -48, -465, 1128, -199, -537, -2, 140, 1098, 349],\n [1618, 291, 1959, -1560, -785, 791, 466, -504, -606, 729, -326, -411],\n [758, -1067, 345, -532, 242, 417, 544, 1403, -109, -98, -215, 88],\n [-875, 184, -1641, -362, -360, -1101, -279, -1820, 498, 479, 757, -821]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[100, -310, -729, 44, 249, 83, 371, 230, 459, 80, -10, -481],\n [447, 117, 411, -799, -1248, 1574, 130, -412, 670, -513, 356, -758],\n [247, -868, -784, 743, 597, -586, 494, 242, 47, 1376, -691, 27],\n [-280, -82, -661, 275, 282, -371, 256, 491, -94, 114, -152, -152],\n [763, 235, -774, -97, -430, -445, 46, -306, -178, 771, -883, -391],\n [-347, 231, -306, -67, -167, 269, 99, 328, 217, -437, 56, -487],\n [282, 274, 464, -666, -1091, 920, 19, -258, -35, -448, 349, -186],\n [111, -489, 826, 32, 238, 641, -113, -427, 624, 30, 331, 143],\n [1052, 336, -935, -126, -415, -337, -95, -640, 335, 926, -1268, -873],\n [-172, -360, 7, 423, 667, -545, 34, 159, -205, 347, 0, 489],\n [-644, -658, -265, 392, 43, 625, 638, 792, 337, 53, 263, -308],\n [326, -552, 489, 367, 1115, -73, -363, -713, 979, 428, -141, 80]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[634, 270, -600, 596, -177, -614, -323, -709, -28, -39, 1165, 24],\n [-471, -980, 1708, 540, 66, 747, 894, -484, 442, -826, -880, -468],\n [23, 89, 565, -416, -219, -541, 1553, -766, 791, 303, -236, -560],\n [396, 543, -1618, 253, -23, -496, -740, 169, -688, 563, 1329, -56],\n [144, 525, -362, 503, 625, -854, -904, -525, -342, 25, 633, 18],\n [-300, 27, 1210, -1590, 196, -682, 1086, -277, 1304, 72, -1631, -50],\n [367, -377, 80, 198, -218, 242, -1195, 203, 259, 680, -246, 209],\n [101, -598, 12, 595, -444, 353, 269, 36, -338, 295, 214, 134],\n [902, -693, -353, -634, -1463, -433, 1185, -216, 734, 883, 210, 554],\n [475, 825, 616, 123, -103, -659, 71, -919, 724, 599, -60, 223],\n [330, 445, -460, -234, -222, 188, -378, 140, 218, -427, 408, 146],\n [-1690, 1013, 415, 208, 2282, -310, 2, -23, -1019, -892, -441, -1342]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[202, -202, 821, 227, 413, -688, 184, 714, 294, 775, 433, -114],\n [40, 696, 168, -396, 326, 102, -478, -270, 122, 66, 70, -576],\n [-358, 16, -341, -119, -557, -248, 236, 150, -582, 455, 455, 114],\n [-228, 136, 256, -118, -191, -691, 199, 543, -373, 1031, 801, -168],\n [82, -167, 118, 128, 84, -46, 72, 102, 118, -19, -56, 84],\n [-228, 434, 38, -312, -149, -327, -73, 135, -341, 643, 555, -324],\n [-244, -318, -348, 108, -518, -138, 358, 162, -422, 168, 194, 360],\n [228, -239, 673, 245, 397, -472, 142, 534, 338, 470, 213, -42],\n [-384, -108, -870, -88, -769, 305, 195, -321, -621, -303, -57, 372],\n [-480, 202, -944, -302, -813, 319, 49, -435, -751, -193, 75, 168],\n [178, -248, 937, 257, 396, -889, 273, 903, 247, 1034, 616, -114],\n [158, 124, -233, -53, 190, 619, -307, -561, 279, -832, -622, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-344, 153, -192, -656, -50, 713, -76, 21, -943, 619, -193, 70],\n [1032, 378, 167, 977, 24, 337, 328, -828, 219, -101, 886, -117],\n [-230, -146, 303, -464, 221, 492, -333, 344, -743, 104, 239, -104],\n [-1114, -339, 580, -1935, 355, 128, -98, 932, 184, 343, -522, -81],\n [-1449, 359, -640, -130, -1000, -1853, -275, 1014, 170, 75, -1364, -225],\n [543, -590, -81, 1194, 155, 518, -602, -663, 400, -996, -222, 211],\n [-399, 248, 349, 213, -444, -535, -86, 242, 285, 200, -191, -464],\n [-653, 37, 73, -736, -507, -1060, 288, 480, 62, 446, -604, 91],\n [330, 139, -963, 613, -119, -498, 276, -46, -459, 72, 53, 319],\n [-244, -340, 879, -958, 293, 283, -177, 508, -600, 175, 416, -92],\n [-733, 98, -367, -904, -143, -1623, 462, 1110, 179, 266, -304, 94],\n [-200, -202, -552, -1008, 398, -412, 147, 737, -863, -61, 192, 536]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[100, 254, -124, -690, -1211, 786, -355, 1032, 353, 34, -626, 888],\n [-701, -1087, -248, -317, 654, 114, -552, 663, 346, 2028, 511, -1020],\n [-261, -374, -72, 1, 762, -288, 358, -262, -133, -406, 470, -75],\n [-597, -380, -1301, -1393, -268, 770, -1125, 35, -824, -562, 926, -244],\n [-127, -586, 327, 430, -672, 486, -35, 325, 505, 869, -1456, 206],\n [-28, -155, -54, -258, -722, 298, 571, 145, 156, -165, -887, 392],\n [558, 1119, -154, 22, -51, -464, -430, -583, -519, 89, 931, -858],\n [811, 1498, 144, -316, -560, -344, 723, -38, -141, -1496, 308, 820],\n [140, 28, 387, 607, -33, 16, -433, 77, 246, 694, -348, -132],\n [232, 109, 419, 290, -573, 66, 500, 244, 439, 272, -967, 372],\n [537, 888, 10, 302, -344, -292, -216, -686, -406, -53, 152, -567],\n [0, 138, -339, -111, -136, 194, -163, -617, -598, -1485, 44, 417]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1104, 365, 378, 1294, 512, 382, -716, -718, 876, -106, 738, 475],\n [117, -577, -475, -802, 181, -22, 591, 314, 303, 1063, 159, 613],\n [-978, -432, 53, -230, 419, 328, 95, 762, 159, 844, 1085, -20],\n [-116, 116, -355, -378, -1445, 851, -35, 243, 113, 591, 141, 530],\n [1633, 1422, -435, 1096, -595, -1727, -1413, -432, 193, -727, -1303, 486],\n [633, -589, 407, -470, 765, 609, 1282, -1659, 438, -740, -761, 70],\n [22, -736, 605, -544, 255, 401, 627, 370, -1056, -751, 120, -397],\n [753, 209, -4, 451, 199, -643, -683, 346, -424, -515, -180, 357],\n [2149, -244, -29, -1018, -157, -586, 991, -586, -257, -1059, -1909, 232],\n [1115, -382, -408, -724, 1092, 183, 354, 293, 260, 406, 70, -500],\n [744, 119, 735, -35, -148, -1635, -412, 1036, -247, -828, -311, 1037],\n [-183, 692, -48, 1213, -259, -136, -1265, -364, 397, 214, 715, 887]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-81, 153, -162, -225, 216, 99, 45, -126, 180, -27, -225, 189],\n [-180, 340, -360, -500, 480, 220, 100, -280, 400, -60, -500, 420],\n [-81, 153, -162, -225, 216, 99, 45, -126, 180, -27, -225, 189],\n [198, -374, 396, 550, -528, -242, -110, 308, -440, 66, 550, -462],\n [9, -17, 18, 25, -24, -11, -5, 14, -20, 3, 25, -21],\n [207, -391, 414, 575, -552, -253, -115, 322, -460, 69, 575, -483],\n [27, -51, 54, 75, -72, -33, -15, 42, -60, 9, 75, -63],\n [-126, 238, -252, -350, 336, 154, 70, -196, 280, -42, -350, 294],\n [-144, 272, -288, -400, 384, 176, 80, -224, 320, -48, -400, 336],\n [117, -221, 234, 325, -312, -143, -65, 182, -260, 39, 325, -273],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n [135, -255, 270, 375, -360, -165, -75, 210, -300, 45, 375, -315]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-721, -677, 501, 371, 50, 239, 866, 366, -501, 555, -798, -873],\n [322, 745, -212, -880, 1913, 449, 301, 269, 169, -1754, -575, -147],\n [-706, 793, -280, -1465, 142, 275, 1000, 859, 888, 686, 993, -64],\n [-32, -60, 590, 194, 250, -192, 824, -70, -954, -38, -1106, -754],\n [-186, -97, 580, -227, -606, -481, 2202, 593, -876, 1232, -223, -888],\n [-734, -239, -115, -720, 589, 58, 1003, 576, 38, 253, 1230, 533],\n [-66, -989, 608, 1455, -1218, -873, 471, -95, -1197, 790, -472, -611],\n [652, -946, 138, 500, -594, 757, -800, -1152, 29, 703, 656, 937],\n [390, 289, -226, -482, -236, 220, 582, 373, 768, 82, 1328, -104],\n [-601, -442, 278, 1218, -449, -1047, 255, 620, -728, -231, -643, -1013],\n [-491, 117, 724, -83, -132, -46, 558, -355, -389, 287, 728, -545],\n [1517, 205, -285, -826, 444, 1262, 417, -278, 604, -13, -498, 228]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-268, 132, -308, -661, 607, 1057, 547, 936, 347, -1363, -494, -892],\n [-1352, -592, -179, 1337, 744, -693, -1359, 341, 284, 199, 301, 555],\n [1089, -837, 286, 786, 138, -243, 39, 660, -1048, 190, 379, 367],\n [-273, 210, 950, 40, -1245, -629, -953, 300, 970, 299, -90, -212],\n [1645, 1099, -25, 849, -1068, -599, -786, -396, 130, 1097, 84, -678],\n [1033, -245, -906, 179, 670, 717, 157, 1147, -125, -351, 461, -438],\n [-647, 648, -534, -1065, -218, 200, 515, -749, 768, 40, -252, 77],\n [1038, 687, -597, -813, -947, 265, 583, -1696, 295, 785, 70, 243],\n [-887, 15, 5, -1143, 312, -386, 1174, 868, -96, -246, -258, 345],\n [-806, -196, 34, -1598, 339, 162, 1386, 228, -225, -57, 268, 569],\n [460, -211, -586, -391, 152, 619, 66, 228, 359, -335, 227, -277],\n [985, -407, 379, -508, -288, 871, 776, -1372, -745, -589, -420, -70]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[114, -77, -304, 694, 196, 344, -796, -363, 712, 761, 789, -552],\n [-487, -896, 37, 1177, -657, -1084, 644, -734, 78, 40, -135, -948],\n [-595, -230, -1188, 1188, -836, 61, -419, -78, 330, -684, 832, -102],\n [-413, 990, 2261, -631, -150, -682, 334, 160, -527, 1269, 596, 391],\n [-145, -622, -159, 805, -1500, -1255, 265, -156, -460, -44, 247, 9],\n [-818, 229, 727, 34, 423, 293, 339, -1138, 298, 981, 356, -311],\n [44, -75, -363, -625, -983, 96, 718, 202, -740, -146, 19, 519],\n [-233, 590, 711, -970, 2237, 906, -116, 997, 435, 387, -528, 1110],\n [-355, 882, 84, -487, 530, -176, -1137, -530, 491, 57, -378, 1403],\n [355, 479, 2, -1286, 1887, 728, -197, 723, 236, -312, -1409, 1281],\n [-345, 765, 1539, -363, 516, -317, 50, -122, -368, 1054, 47, 1070],\n [-427, -442, -743, 224, 207, -47, -379, -715, 924, 344, -85, -152]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[110, 122, 575, 218, 1247, -677, -395, 116, -52, 1227, -380, 317],\n [121, -131, -461, 328, 519, 143, 443, -116, 84, -311, 646, 53],\n [-507, -1483, -19, 770, 115, 218, 153, -663, -427, 143, 583, 770],\n [-347, -553, 1227, 176, 297, -139, -839, -462, -747, 1115, -728, -144],\n [432, 20, -990, 532, 1184, 44, 782, -252, 267, -614, 1150, 181],\n [-505, -146, 56, 642, 504, -366, -367, -79, -318, 467, 72, 297],\n [-1042, 854, 364, 654, 182, -185, -734, 695, -515, 558, -233, -851],\n [521, -602, -746, -418, -704, 404, 877, -191, 567, -937, 532, 622],\n [475, -344, 517, -592, -261, 1, -145, -393, 7, 215, -550, 156],\n [-747, 594, -565, 746, 83, -106, -235, 218, -284, -403, 437, -363],\n [895, -576, 83, -408, 515, 227, 619, -379, 324, 31, 202, 285],\n [59, 36, 319, 302, 793, 320, -11, -298, -419, 109, 243, -794]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-282, -596, 326, -21, -51, -48, -117, -197, -170, -656, 938, 330],\n [-709, 278, 340, -494, 238, -44, -722, 17, 195, -1332, 541, 374],\n [-217, 105, -67, 571, -58, 103, -345, 806, -513, -534, -714, -446],\n [331, 423, -793, 290, -393, -209, -752, 475, 197, 416, -214, 372],\n [-95, -804, 254, 645, -148, 86, 207, 302, -713, -363, 195, -292],\n [59, 506, -221, -450, -109, 133, 35, -517, 336, 247, -596, 210],\n [-206, 334, 452, 12, 454, 356, 706, 178, -312, -88, -1306, -1032],\n [-399, 657, 262, -632, 277, 262, 93, -385, 222, -478, -785, -156],\n [-288, -501, 182, -142, -142, -132, -405, -262, 5, -717, 1176, 642],\n [-138, -237, 195, 242, 193, -169, -218, 506, -134, -352, 599, -110],\n [150, -80, 250, 573, 175, 400, 1025, 337, -694, 464, -1566, -1258],\n [-121, -185, -69, -561, -263, -145, -429, -768, 431, -327, 1116, 1030]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[726, -467, 835, -198, -885, 242, -741, -1271, -4, -507, -924, -320],\n [-286, -116, -912, 970, 95, 274, 903, 1585, 259, 295, 1300, 1000],\n [470, -995, 799, 116, -733, 672, -787, -681, 310, -9, -654, -172],\n [1272, -598, 444, -113, -890, -423, 25, -1195, -429, -1105, -521, 232],\n [896, -234, 409, -993, -143, -954, 101, -822, -228, -1234, -747, -551],\n [-457, -78, 708, 320, -669, 1144, -984, -558, 454, 193, -483, -456],\n [-117, -74, 77, -763, 646, -626, -45, -348, -284, -193, -424, -537],\n [615, 324, 1176, -650, -468, 300, -787, -430, 723, 357, -822, -897],\n [-148, 1262, 187, -336, -378, 393, -705, 16, 590, 466, -528, -609],\n [-1025, 621, -435, 495, 563, 572, -155, 714, 111, 1335, 513, 192],\n [206, -688, 625, 882, -392, 561, 521, 203, 160, -125, 857, 484],\n [919, 246, -337, -837, -97, -1227, 292, -648, -540, -1055, -587, -61]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[77, 423, 339, 143, 936, -74, -128, -196, 415, -1035, -42, 130],\n [-947, -1136, -257, 814, -7, -203, -676, 1131, -252, -298, -335, -479],\n [-764, 810, 365, 501, -571, -306, -464, 417, 635, -824, 257, 1016],\n [-456, 580, 259, 522, -76, 511, -694, 696, -150, -1244, -70, 447],\n [373, 716, 124, -99, -226, -1710, -435, 427, 812, 762, -398, -401],\n [-303, -192, -523, 440, -777, -556, -1219, 1626, 820, 599, -356, -575],\n [582, -1279, -552, 118, 338, 226, 1231, -523, -315, 56, -221, -519],\n [-322, -453, -570, -172, 222, 1546, 1045, -824, -286, 323, 727, -492],\n [-957, -60, 1309, 750, 1236, -396, 651, -950, -335, 109, 303, -144],\n [14, 312, 421, -400, 196, -1350, -307, 66, 1071, -190, -373, 1132],\n [-44, 572, 435, -164, -329, 397, 1130, -1712, 1230, 823, 1202, 596],\n [322, 65, 946, 659, -30, 763, -1433, 895, -69, -372, -414, 361]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[24, -288, 240, -600, -216, -168, 192, -120, -552, 120, -552, -432],\n [-5, 60, -50, 125, 45, 35, -40, 25, 115, -25, 115, 90],\n [-19, 228, -190, 475, 171, 133, -152, 95, 437, -95, 437, 342],\n [9, -108, 90, -225, -81, -63, 72, -45, -207, 45, -207, -162],\n [-1, 12, -10, 25, 9, 7, -8, 5, 23, -5, 23, 18],\n [-6, 72, -60, 150, 54, 42, -48, 30, 138, -30, 138, 108],\n [10, -120, 100, -250, -90, -70, 80, -50, -230, 50, -230, -180],\n [-5, 60, -50, 125, 45, 35, -40, 25, 115, -25, 115, 90],\n [15, -180, 150, -375, -135, -105, 120, -75, -345, 75, -345, -270],\n [-10, 120, -100, 250, 90, 70, -80, 50, 230, -50, 230, 180],\n [6, -72, 60, -150, -54, -42, 48, -30, -138, 30, -138, -108],\n [25, -300, 250, -625, -225, -175, 200, -125, -575, 125, -575, -450]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-93, 126, -126, -309, -144, -150, 240, 84, -276, -159, 180, -306],\n [-231, 402, 78, -423, -408, 90, 420, 348, -492, -273, 60, -342],\n [218, -328, 152, 598, 356, 182, -498, -248, 576, 328, -280, 564],\n [211, -320, 136, 569, 346, 163, -477, -244, 552, 314, -260, 534],\n [-9, 76, 268, 217, -50, 317, -103, 108, 112, 72, -260, 270],\n [-175, 200, -400, -725, -250, -475, 525, 100, -600, -350, 500, -750],\n [75, -250, -550, -325, 200, -650, 100, -300, -100, -75, 500, -450],\n [22, -12, 108, 142, 24, 128, -92, 8, 104, 62, -120, 156],\n [-85, 176, 152, -47, -166, 179, 99, 172, -120, -62, -100, 6],\n [240, -432, -144, 384, 432, -168, -408, -384, 480, 264, 0, 288],\n [207, -460, -508, -7, 422, -599, -179, -468, 224, 108, 380, -162],\n [-5, 124, 508, 437, -74, 601, -219, 188, 240, 152, -500, 534]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-345, 713, -598, 207, -575, 552, -460, 23, -322, 391, -276, -230],\n [605, -149, -111, 29, 390, 19, 585, -864, -84, -618, 8, -40],\n [-441, 345, -168, 63, -417, 198, -474, 453, -78, 465, -108, -66],\n [423, -119, -62, 15, 281, 0, 412, -593, -50, -433, 12, -22],\n [392, 8, -182, 56, 194, 106, 358, -638, -116, -394, -40, -68],\n [294, -230, 112, -42, 278, -132, 316, -302, 52, -310, 72, 44],\n [-259, 315, -217, 77, -308, 217, -301, 182, -112, 280, -112, -84],\n [-195, 403, -338, 117, -325, 312, -260, 13, -182, 221, -156, -130],\n [-237, 301, -212, 75, -289, 210, -278, 157, -110, 257, -108, -82],\n [96, -576, 564, -192, 372, -492, 204, 276, 312, -132, 240, 216],\n [-417, 673, -524, 183, -589, 498, -518, 169, -278, 461, -252, -202],\n [159, 49, -122, 39, 53, 84, 136, -293, -74, -157, -36, -46]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[359, 839, 1097, -114, 522, -1471, 365, 797, -306, 268, 1342, -911],\n [-305, 288, -499, -315, 18, -40, -161, 772, 270, -103, -180, 21],\n [-1136, 809, -1512, -769, -184, -476, -382, 199, -322, -1168, -1380, -477],\n [954, -486, 602, 704, -599, 1260, 689, -1299, 704, 251, 534, 567],\n [-74, 129, 41, 54, -849, 529, -419, -1079, 371, -761, -735, 169],\n [-344, -158, -437, 497, 229, 1211, -795, -872, -1108, -214, -1543, 663],\n [-406, 726, -695, -87, -725, 105, 481, -1351, -390, -476, -444, -172],\n [-211, 717, -551, -813, 315, 379, 240, -379, -566, -797, -666, 10],\n [-109, -146, -288, 584, -452, 391, 191, -1933, -1315, 739, -397, 1102],\n [-21, -1600, 179, 773, 564, 378, -1333, 264, 291, 1018, -519, 958],\n [298, 1225, 715, 747, -465, 563, 515, -756, -229, -392, 263, -275],\n [-180, -411, -950, -230, -263, 222, 221, -317, 420, 111, -202, 30]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-393, 9, -826, -498, -850, 705, -650, 302, 862, -371, -34, 167],\n [-33, -63, -1016, -400, -414, 910, -856, -121, 328, 417, -75, -851],\n [-546, -366, -264, -838, -348, 683, -664, 575, 746, -72, 445, -1122],\n [1423, -190, -182, 702, -785, 523, -133, 49, -377, 127, -1598, 659],\n [134, 103, -1554, -158, -643, 1073, -901, -486, 275, 386, -411, -226],\n [-874, 305, 976, -362, 627, -981, 391, 418, 205, -206, 1123, -262],\n [337, 254, -681, 152, 231, 282, -418, -646, -443, 875, -125, -713],\n [269, 1231, 218, 270, 134, -871, -314, -16, -262, 875, 80, -179],\n [986, 558, 570, 1098, 892, -988, 674, -827, -1388, 855, -463, 345],\n [-952, 60, 360, -546, -12, -335, 108, 519, 682, -626, 825, 144],\n [58, -302, 644, 248, 264, -366, 656, 62, -232, -436, -46, 556],\n [-578, -594, -345, -706, -402, 760, -373, 431, 742, -475, 307, -495]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[868, 1002, -950, 189, -221, 1072, -561, -923, 835, 869, -1126, -488],\n [731, -1687, -272, 847, 162, -1052, -1260, 1957, 112, 862, 378, -301],\n [-999, -1120, 775, 542, 1922, -1266, -708, 1031, -670, -471, 658, 646],\n [-488, 1015, -918, -560, -890, 1353, 1598, -770, 659, -89, 453, -285],\n [757, 925, -127, 6, 1472, -572, -1259, -68, -221, -152, -500, 72],\n [245, -360, 280, -949, -711, 38, 466, 538, -655, 95, 662, -942],\n [-1040, -554, 334, 1217, 809, -342, -217, -335, 243, 137, -334, 1072],\n [1531, 553, -362, -1526, 623, -177, -939, 1037, -1005, 374, -50, -1464],\n [521, -228, 69, -839, -532, -733, -140, 1210, -318, 276, 302, -103],\n [257, -1045, -723, 1024, -790, 867, 399, 125, -299, 313, 448, -725],\n [-71, 18, 673, 208, -1114, -627, 668, -427, -268, -404, -191, 985],\n [899, -764, -17, 1331, 851, -1270, -1471, 774, 234, 701, -491, 181]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-804, -79, -592, 572, 745, 69, 167, -333, 418, 344, -79, 447],\n [636, -277, 712, -1012, -829, 391, -31, 73, -10, -360, 239, -495],\n [286, -84, 1004, -937, -523, 333, 83, 2, 169, -745, 563, -357],\n [-196, 241, -254, 509, 346, -302, -25, 59, -121, 87, -103, 201],\n [-228, 604, 672, 202, 330, -422, 58, 160, -90, -814, 514, 114],\n [-548, 462, 402, 335, 577, -283, 140, -26, 147, -611, 464, 270],\n [-100, -303, -1152, 580, 209, 13, -89, -109, -54, 1040, -719, 207],\n [-128, 585, 264, 470, 343, -541, -31, 223, -264, -446, 203, 153],\n [-184, -30, -884, 694, 352, -192, -74, -26, -118, 706, -518, 258],\n [288, 116, 528, -352, -300, -28, -28, 140, -120, -416, 236, -204],\n [232, -17, -642, 417, -32, -216, -165, 137, -333, 591, -519, 33],\n [-396, 222, 590, -111, 283, 7, 168, -98, 277, -653, 540, 102]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-430, 307, 64, 101, 221, 14, -177, -33, -148, -346, -182, 193],\n [-520, 354, 70, 132, 356, 12, -235, -104, -248, -395, -262, 226],\n [-100, 116, 34, -2, -178, 16, 13, 158, 144, -141, 66, 64],\n [360, -132, 0, -156, -828, 24, 300, 492, 624, 120, 456, -108],\n [100, 80, 50, -110, -830, 40, 225, 570, 640, -125, 410, 20],\n [120, 40, 36, -100, -708, 32, 202, 476, 544, -74, 356, 0],\n [420, -420, -114, -30, 402, -48, 27, -414, -336, 501, -114, -240],\n [-180, 248, 78, -26, -522, 40, 71, 430, 416, -307, 214, 132],\n [-330, 79, -18, 167, 975, -34, -326, -607, -740, -53, -520, 81],\n [30, -179, -72, 83, 795, -46, -179, -583, -620, 238, -370, -81],\n [-370, 117, -8, 171, 947, -30, -331, -575, -716, -98, -514, 103],\n [-20, 180, 74, -90, -842, 48, 193, 614, 656, -241, 394, 80]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-964, -939, -1425, -255, -1391, -1801, 2108, -205, 500, 1794, 573, 251],\n [-810, 303, 5, -1612, 963, -447, 564, -209, -1696, 376, 137, -1751],\n [728, -8, -257, -1455, -627, 935, -586, -852, -101, 1388, -1153, -416],\n [-37, 339, -167, -843, 777, 627, -45, 69, -557, 338, 37, -240],\n [473, 216, -333, -1935, 1061, 522, -356, -708, -884, 1226, -1052, 119],\n [-1387, -750, -1449, -716, -330, 903, 458, 90, 926, 367, 801, 2366],\n [1231, -440, -166, 601, 315, -590, 1107, 234, 52, -192, -805, 755],\n [160, 370, -248, 298, 1253, 1724, -474, 1125, -11, -352, 302, 659],\n [465, 830, 1097, -30, -263, 937, -1379, -369, 397, 18, -343, -153],\n [979, 330, -462, -179, 647, -420, -170, -113, -673, 1025, -266, -1230],\n [525, 875, 653, -347, 239, 955, 372, 418, -83, 167, 168, -119],\n [793, -349, 16, 107, -367, -544, 193, -677, -125, -1008, -369, -64]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[10, 118, 1164, -33, -444, -69, 298, -491, 526, -271, -18, -1073],\n [-663, -724, -904, -405, 720, -818, 542, 475, 259, 358, -1394, 110],\n [-393, -780, 511, 699, 477, -701, 570, -253, 37, 897, -527, -336],\n [-309, 20, -259, 50, -63, 467, -346, -426, -1039, -634, 894, 669],\n [852, 843, -661, -350, -370, 808, -787, 392, -427, -541, 537, 657],\n [88, 179, 1196, -73, -513, -39, 311, -457, 661, -173, -9, -1158],\n [-39, -153, -575, 351, 454, -152, -182, 452, -30, 357, 40, 740],\n [-1433, -1306, 33, 442, 761, -696, 613, -871, -1285, -150, -358, 230],\n [-100, -435, -129, 912, 922, -730, -116, 547, 45, 97, -570, 674],\n [177, -140, -402, 751, 536, -19, -453, 206, -873, -24, 186, 1021],\n [-232, -337, -1007, -86, 586, -422, 114, 721, 359, 637, -602, 582],\n [700, 556, -447, -1025, -509, 375, -55, 256, 102, -202, -669, -466]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-693, 87, -288, -382, -19, 488, -747, -259, 223, -1292, -333, 1427],\n [1056, 792, -585, -620, -1635, -1655, 180, 217, 1534, 799, 1356, 1102],\n [73, -1042, 63, -74, 680, 1196, 8, -824, 455, -398, -88, 995],\n [832, 324, -654, -6, -225, 552, -438, 893, -563, 308, -757, -303],\n [227, -1083, 1121, 139, 280, 1379, 410, 649, 253, -698, -1294, 288],\n [-103, -174, -19, 29, 1632, 1182, -288, 356, -1288, -1129, -1181, -493],\n [781, 1051, -863, 30, -739, -46, 469, 613, -1031, 108, -357, 563],\n [254, 332, -751, 1433, -873, 220, -1089, 600, -85, 339, -76, 216],\n [457, 419, -527, -668, 1090, -390, -129, -917, -464, -390, 187, 675],\n [636, 275, -134, 1701, -1293, 350, 467, 708, -859, -435, 383, 10],\n [-881, 627, -904, -652, -452, -1405, -55, -669, 721, 766, 1467, 735],\n [-1539, -1032, 1376, 169, 101, -755, 431, -982, 109, 350, 633, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[568, 191, -83, -34, 21, 418, -11, -415, -69, 262, 435, -324],\n [186, -240, -426, -6, 63, -426, -48, -384, 252, -723, 423, 216],\n [-419, -854, -323, 503, -70, -339, -324, 438, -571, -522, -177, -184],\n [325, 345, 154, -115, 5, 423, 73, -185, -4, 470, 132, -204],\n [427, -422, -425, 305, -8, 155, -248, -282, -413, -228, 495, -456],\n [-247, -644, -409, 271, -4, -539, -198, 100, -133, -778, 57, 112],\n [968, 320, -304, -188, 89, 340, 44, -912, 242, -9, 891, -216],\n [119, -609, -454, 355, -16, -143, -269, -79, -382, -491, 303, -268],\n [-176, 355, 169, -334, 52, -298, 229, -51, 565, -117, -144, 516],\n [-994, -64, 362, -62, -40, -554, 116, 768, 194, -132, -882, 576],\n [752, 148, -292, -80, 62, 256, -12, -692, 104, -58, 714, -224],\n [677, 459, -112, -311, 89, 187, 151, -715, 434, 28, 600, 44]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[466, -364, -376, 280, -190, -182, -390, 178, 484, 170, -184, 8],\n [571, -442, -526, -146, -277, -104, -390, -158, 580, 371, -1, -61],\n [-146, 108, 216, 648, 126, -122, -10, 510, -132, -298, -280, 104],\n [152, -112, -232, -728, -136, 140, 20, -572, 136, 328, 316, -116],\n [-478, 372, 408, -120, 210, 146, 370, -54, -492, -230, 112, 16],\n [503, -386, -518, -538, -281, 8, -270, -454, 500, 463, 187, -113],\n [-492, 376, 532, 716, 292, -54, 230, 590, -484, -516, -270, 138],\n [70, -52, -100, -284, -58, 52, 0, -224, 64, 134, 122, -46],\n [14, -4, -124, -836, -82, 200, 140, -644, -8, 286, 382, -122],\n [-685, 534, 570, -282, 291, 236, 550, -162, -708, -293, 211, 7],\n [363, -282, -318, 30, -165, -96, -270, -6, 372, 195, -57, -21],\n [-448, 344, 458, 454, 248, -1, 245, 385, -446, -404, -155, 97]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-79, -50, 302, -453, 300, -216, -334, -898, -873, 477, -445, 12],\n [-83, -1230, -787, 391, -975, 182, 11, 650, 660, -354, 722, -215],\n [-629, 725, 111, 21, -232, -142, -164, -728, -177, 979, -669, -624],\n [-376, 169, 467, -70, -968, 133, 555, 371, -149, -433, 276, 674],\n [483, -1277, -428, -843, 526, -221, -389, -249, -925, 935, 649, -408],\n [484, -783, -851, 95, -324, -723, 27, -374, -311, 275, -303, -179],\n [188, -848, -889, 171, 241, -555, -732, -140, 890, -711, 110, -475],\n [-284, -227, 307, -29, 70, 777, 357, -472, -573, -206, -499, 222],\n [-459, -826, -327, -224, -273, 642, -248, 110, -192, 160, 178, -337],\n [-348, 868, 857, -1073, 1501, -70, -775, -737, -465, 434, -72, -311],\n [-1141, -57, -162, -67, 370, 2290, 1022, 308, 278, 280, -61, -1090],\n [318, 506, 150, 359, -123, 293, 557, 575, -119, 330, -35, 269]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[986, -1454, -1523, -203, -460, 361, 550, 623, 180, 893, 745, 425],\n [-279, 136, -988, -545, -666, 1605, 295, -52, 1227, -569, 854, 6],\n [-752, 376, 858, 1043, 1692, -1199, -511, -447, -91, 715, -2026, -223],\n [-1010, 468, -941, -75, 397, 149, 198, -9, 426, -243, -671, 1049],\n [-161, -477, -1406, 799, 394, -319, 841, -146, 952, 1033, -842, 279],\n [766, -359, -2074, -451, -464, 1768, 475, -30, 411, 369, 964, -459],\n [1288, -826, 970, -279, -574, -394, -265, -128, -168, 145, 976, -684],\n [-137, -31, -414, -989, 213, 1132, 74, -453, 1195, 434, 126, -1337],\n [-458, 394, 1435, 687, 775, -938, -744, -601, 961, 767, -622, 88],\n [299, -818, -2374, -373, -230, 1024, 259, 672, -14, 787, -103, 1439],\n [-603, 827, 1908, -549, -802, -854, 216, -732, 837, -746, 255, -499],\n [666, 257, 486, 223, -876, 130, -46, 680, -2043, -936, 658, -228]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-26, -77, -91, -32, 47, 122, 78, -38, -123, 14, 5, -202],\n [-300, 145, -329, 440, 240, 93, 106, 10, -393, -377, 395, -242],\n [-828, -320, -360, 928, 94, -290, 760, -840, -408, -606, 488, 168],\n [210, -162, 216, -348, -171, -27, -30, -48, 252, 297, -306, 108],\n [144, -19, 502, -90, -359, -539, -115, -146, 648, 172, -281, 892],\n [306, 60, 140, -376, -53, 115, -240, 260, 156, 257, -216, -76],\n [-560, 9, -382, 726, 217, -71, 365, -314, -444, -544, 507, -76],\n [-128, -263, -357, -64, 190, 439, 294, -142, -477, 9, 59, -738],\n [80, -587, 268, -398, -321, -111, 347, -538, 306, 418, -481, 184],\n [-156, -523, 107, -56, -216, -159, 458, -622, 123, 155, -233, 182],\n [-24, -422, 278, -144, -304, -286, 292, -508, 342, 230, -322, 428],\n [386, 411, 296, -242, -80, -122, -551, 534, 378, 143, -123, 332]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[270, 76, 257, -523, -59, 754, 224, -496, 430, -523, 332, 344],\n [92, 88, 98, -182, 42, 292, 128, -224, 156, -182, 152, 112],\n [-60, -46, -62, 118, -16, -184, -74, 136, -100, 118, -92, -74],\n [-214, 456, -117, 383, 563, -306, 252, -64, -262, 383, 60, -316],\n [320, -366, 228, -592, -526, 636, -114, -184, 440, -592, 108, 446],\n [34, -201, -3, -53, -218, -24, -147, 124, 22, -53, -90, 61],\n [46, -611, -61, -51, -634, -224, -481, 468, -22, -51, -334, 111],\n [-68, -253, -104, 146, -219, -322, -251, 332, -144, 146, -230, -67],\n [-278, 372, -189, 511, 511, -522, 144, 112, -374, 511, -60, -392],\n [-118, 582, -9, 191, 641, 18, 414, -328, -94, 191, 240, -202],\n [166, -388, 85, -295, -471, 218, -224, 80, 198, -295, -68, 248],\n [104, -191, 62, -188, -243, 166, -97, 4, 132, -188, -10, 151]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[204, -1001, 410, -879, 377, 391, -945, -171, -322, -46, -953, 477],\n [-163, 183, -172, 1001, 262, 68, -791, -290, 189, 255, 919, -258],\n [64, 714, -144, 1288, -798, -692, -200, -858, -32, 989, 1765, -402],\n [-22, -810, -253, 100, 696, -753, 877, 384, -395, 46, -212, 572],\n [-375, -59, -242, 1394, -87, 64, 14, 173, -266, -566, 204, 755],\n [-310, 357, 142, 108, 31, 422, 616, 852, 78, -479, 527, 254],\n [-1012, -461, 587, 175, 381, 542, 935, 1448, -467, 203, -1220, 959],\n [194, -20, 378, 293, -302, -381, 358, 100, -21, -877, 1078, 236],\n [-1083, 262, 1362, 443, -310, 126, 522, 827, -302, 1519, 393, 69],\n [26, 291, 73, -326, 407, 68, -902, -507, 646, -922, -381, -906],\n [442, -604, 238, -276, -443, 340, -329, -79, -302, 149, -205, 524],\n [710, 949, -456, -652, -759, -163, 51, -697, 284, 1348, 1337, -957]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-171, -209, -475, -19, 133, -285, 399, -323, 38, -475, -209, 171],\n [-72, -88, -200, -8, 56, -120, 168, -136, 16, -200, -88, 72],\n [54, 66, 150, 6, -42, 90, -126, 102, -12, 150, 66, -54],\n [-45, -55, -125, -5, 35, -75, 105, -85, 10, -125, -55, 45],\n [45, 55, 125, 5, -35, 75, -105, 85, -10, 125, 55, -45],\n [117, 143, 325, 13, -91, 195, -273, 221, -26, 325, 143, -117],\n [-18, -22, -50, -2, 14, -30, 42, -34, 4, -50, -22, 18],\n [-36, -44, -100, -4, 28, -60, 84, -68, 8, -100, -44, 36],\n [90, 110, 250, 10, -70, 150, -210, 170, -20, 250, 110, -90],\n [36, 44, 100, 4, -28, 60, -84, 68, -8, 100, 44, -36],\n [-81, -99, -225, -9, 63, -135, 189, -153, 18, -225, -99, 81],\n [18, 22, 50, 2, -14, 30, -42, 34, -4, 50, 22, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1005, -521, 434, 288, -1080, 1053, -334, 229, -606, 270, -83, -30],\n [-174, -682, -324, 696, -174, 452, 14, -468, -172, 374, -840, 342],\n [-179, 217, -13, -37, 141, 459, 495, 448, -49, 339, 5, -833],\n [335, -507, 21, 205, -165, -57, -409, -420, 187, -9, -169, 473],\n [1028, -1051, -671, 523, 108, 174, -699, -1294, 1084, 123, -551, 224],\n [913, 14, -30, -254, 15, 291, -184, -2, 577, 18, 394, -723],\n [-529, 1144, 585, -708, -141, -337, 395, 1087, -832, -403, 809, -167],\n [440, 138, 907, -434, -651, -251, -458, 524, -487, -350, 712, 521],\n [140, 277, 81, -281, 166, 60, 155, 296, 212, 33, 335, -582],\n [-10, -733, 220, 635, -527, 1057, 231, 222, -497, 757, -653, -227],\n [-393, 1663, 90, -992, 255, -648, 419, 854, -440, -765, 1044, -443],\n [-1093, 1179, -218, -584, 697, -1098, 417, 256, -148, -639, 442, 183]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[35, -66, 427, -658, 66, 75, 671, 715, -135, 411, -139, 96],\n [38, 486, -70, 72, -343, -454, 268, 130, 332, 439, 166, -4],\n [-96, -411, 118, -104, 434, 351, -343, 272, 97, -362, 22, -264],\n [85, 312, -155, 330, -180, -277, -221, -135, 409, 31, 179, -108],\n [106, -27, 79, -180, -170, 77, 398, -263, -564, 131, -275, 401],\n [-628, 339, -685, 576, -86, -539, -432, -47, 622, 99, 609, -565],\n [589, 1122, 46, 378, -744, -895, 178, 126, 1078, 652, 290, 15],\n [29, 258, -90, -98, -457, -213, 646, -414, -626, 423, -222, 515],\n [85, 399, 297, -574, -386, -344, 1064, 539, -158, 855, -109, 314],\n [1013, -156, 706, -106, 117, 469, -280, -54, 152, -459, -434, 307],\n [-653, -672, -74, -450, 458, 441, 216, 226, -740, -114, -94, -79],\n [-1111, -639, -497, -34, 649, 244, -384, 337, -134, -296, 381, -672]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[29, 666, -696, 441, -561, -652, 592, 338, 951, -674, 497, 480],\n [-213, 1390, 514, 784, -883, -365, -169, 695, 1138, -35, 1117, -713],\n [-235, -1, 478, 844, 604, -1457, 942, 39, 1197, -263, -321, 618],\n [-213, -357, 899, -667, -79, 197, -1888, 658, -700, 1348, -181, 156],\n [1154, 1128, 57, -20, 872, 167, 114, 1366, 622, -831, 327, 1070],\n [-473, -312, 620, -25, 424, -513, 826, 32, 762, -333, -211, 751],\n [-986, -359, 483, -1093, -984, -133, 362, 971, 625, 53, -327, -131],\n [580, -606, -42, 275, 696, 565, 309, -649, -661, -267, 174, 13],\n [194, 207, -699, 905, -542, -1048, 194, 174, 689, -265, 580, 478],\n [313, -1138, 75, 653, 9, 368, -1100, -1103, -1522, 1066, 266, -997],\n [895, 205, -748, -423, 794, 267, -404, 340, -479, -272, -384, 1159],\n [-205, 687, 288, -405, -253, -483, 344, 1187, 884, -131, -505, -295]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[878, -357, 263, -1085, 601, 8, 165, 130, -222, 148, -125, 167],\n [466, -134, 556, -879, 510, -57, 264, 183, 165, -2, -147, -239],\n [-216, -763, 1056, 311, 221, -5, -21, 899, -141, 1, 164, -501],\n [556, -89, -140, -219, 89, 193, 295, -200, -390, 563, -622, -89],\n [176, 653, -522, -357, -85, 13, 233, -660, 262, 87, -372, 29],\n [602, 314, -350, -525, 94, 143, 400, -531, -109, 472, -711, -73],\n [-394, 1291, -1147, 149, -559, -56, 69, -1132, 612, -186, -193, 197],\n [476, -453, 356, -539, 401, 1, 23, 318, -228, 63, 50, 83],\n [554, 70, 469, -856, 436, 35, 510, -53, 167, 277, -591, -484],\n [18, 520, -477, 232, -306, 153, 316, -589, 15, 417, -675, -240],\n [-1376, 379, 90, 1407, -685, -107, -243, 119, 527, -427, 376, -425],\n [1060, -667, 410, -689, 521, 241, 411, 233, -695, 767, -726, -197]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[103, -74, -1, -70, -236, 137, -68, 35, 287, -196, 142, -84],\n [29, 273, 338, -88, -605, -25, -166, -358, 799, -443, -198, -523],\n [359, 384, 437, 326, -686, 425, 128, -475, 811, -278, -330, -394],\n [257, 505, 410, 584, -175, 303, 362, -512, 155, 201, -594, -117],\n [155, 528, 537, 222, -658, 125, 32, -611, 831, -310, -506, -558],\n [-50, 488, 430, 148, -314, -138, 16, -520, 430, -120, -528, -426],\n [393, -213, -274, 560, 512, 609, 510, 289, -797, 629, 128, 722],\n [-163, 200, 91, 106, 248, -233, 80, -155, -287, 226, -298, 12],\n [546, 538, 440, 920, -204, 706, 612, -546, 110, 358, -640, 48],\n [-339, -568, -469, -694, 232, -409, -432, 581, -207, -222, 662, 124],\n [-211, 427, 460, -260, -641, -381, -322, -514, 915, -553, -370, -763],\n [435, 71, 80, 476, -128, 599, 342, -85, 45, 165, -76, 178]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-629, -147, 276, 716, -491, 21, 66, -354, -466, 455, 86, -387],\n [-856, -4, 686, 1248, -573, -502, -387, -1146, -885, 887, -398, -1167],\n [-856, -17, 376, 1002, -688, 61, -92, -392, -538, 544, 205, -382],\n [-263, 58, 184, 494, -901, 64, 224, 2, -501, -54, 539, 121],\n [512, -95, -430, -794, 435, 781, 143, 1302, 762, -798, 237, 1047],\n [998, 502, -706, -1304, 634, 411, -88, 1228, 1136, -1076, 517, 1439],\n [-260, -300, -426, -288, 329, 846, 361, 874, 614, -84, 410, 719],\n [-80, -136, -76, 56, -494, 250, 448, 284, -171, -157, 498, 328],\n [291, -517, -224, -456, 27, 385, 670, 562, 51, -346, 98, 317],\n [-566, -747, 834, 1042, -339, -279, -37, -862, -1096, 694, -1081, -1511],\n [-215, -427, -150, -168, 718, 605, -19, 528, 506, 111, -368, 90],\n [123, 706, 290, 338, -446, -996, -479, -1056, -479, 200, 21, -504]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[743, -257, -881, -235, 1749, -298, 696, 84, -69, 1048, -379, -830],\n [-281, 814, 234, 303, -220, 299, -1041, 371, 468, 2, 830, -754],\n [558, -754, -1008, 763, 1224, -747, 832, 74, -379, 1153, 94, -603],\n [-57, 975, -377, -299, -663, -210, -446, 196, 763, -456, 452, -934],\n [538, -771, -1390, 958, 139, -1071, 43, -354, -550, -509, -769, 760],\n [597, -498, 135, -766, -214, 1002, -1545, -1526, -13, -208, -797, 1683],\n [839, -254, -385, -78, 132, -188, 107, -98, -272, -383, -550, 616],\n [-958, 1068, 922, 450, -902, 362, 240, 1504, 387, 1710, 2004, -1398],\n [-105, -848, -249, -225, 527, 486, -728, -747, -200, 923, -593, 1178],\n [52, 207, -1599, -452, -725, -385, -577, -419, 210, 777, -774, 713],\n [-1247, 618, 1716, 368, -145, 846, -177, 1059, -179, 237, 764, -233],\n [-819, 255, -283, -328, -699, -263, 534, 964, 496, 1258, 655, -330]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[493, 200, 160, 39, -352, 280, -198, 462, 70, 382, -1138, -274],\n [1130, 186, 152, -66, -798, -879, 400, -1024, 779, 1327, -949, 960],\n [-775, 682, -127, 495, -91, 1051, 70, 1512, -689, -1706, 675, -797],\n [325, 595, 22, 388, 487, -11, 741, -912, 1335, 180, 319, -411],\n [-142, 120, -1754, 147, 354, 676, 1489, -1058, 662, -1221, -44, -309],\n [561, 409, 1153, 312, 3, 448, 105, -68, -60, -374, 874, 863],\n [449, 215, -183, 435, -117, -638, 860, -668, 765, 934, -639, 876],\n [-764, -320, 377, 78, 202, -952, -704, 1040, -465, 906, 62, -510],\n [-1700, 849, -881, 732, 48, -602, 502, 527, 474, -519, 1031, -395],\n [8, -1000, -128, -479, 665, -851, 187, -997, 37, 806, 227, -164],\n [-389, -77, 377, 23, 938, 7, 182, -402, 445, 38, 801, -929],\n [-229, -639, -136, -24, 619, -455, -599, 441, -128, 869, -514, -271]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[680, 355, -1073, 190, 1589, 845, 190, -1277, 416, 39, -22, -346],\n [-620, 79, -450, -1375, 487, -377, -484, 432, -465, 948, 186, 277],\n [-1448, -588, -1881, 980, -434, 1078, 642, -755, 555, 1088, -458, -80],\n [681, 1400, 741, 321, 1168, 1545, -1326, 969, -785, 589, 1616, -2447],\n [-588, -1173, -752, 222, 1909, 939, 1177, -1069, 721, 519, -682, 266],\n [1392, -603, -416, 1184, -2008, -1138, 413, -787, 315, -6, -1873, 502],\n [107, -506, 842, -146, 219, 964, -1396, 1335, -153, 168, -296, -930],\n [-147, 184, 164, -763, -1096, -1054, -396, 1059, 266, 34, -694, 507],\n [-199, -33, -415, 978, -762, 1108, -68, 224, 739, -304, -329, -1090],\n [-261, 495, 376, -1624, 491, -506, -670, 758, -526, -75, 367, 276],\n [195, -627, -322, 336, 2083, 509, 307, 260, 659, 1716, 231, -934],\n [271, 2034, -475, -54, 174, -1425, 1164, -736, -190, -376, -141, 1120]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[504, -1127, 1612, -863, -1503, 511, -1387, -387, -1162, 827, 373, -907],\n [-1059, 158, -753, -566, -812, -400, -740, 332, 386, -255, -621, 476],\n [1072, -373, 220, -823, 300, -212, 410, 154, -545, -472, -593, -1010],\n [1781, 26, 1336, -1517, -542, 65, -135, 1411, 366, 663, 531, -1157],\n [561, 276, -1044, -360, 434, 314, -8, 759, -345, -803, -297, -791],\n [-1774, 36, 495, 100, -1451, -408, -888, -608, 460, 458, 30, 1242],\n [-195, -255, -537, -437, 325, 327, -467, 486, -251, -934, 482, -301],\n [-7, -197, 1048, 411, -214, -339, -112, 452, 1153, 31, 1120, -147],\n [1675, 989, -108, -1430, 503, 659, 837, 1805, 297, -494, 840, -881],\n [-214, -583, -194, -399, -1038, -580, -874, 462, 67, -567, -677, -609],\n [522, 757, -1756, -561, 300, 742, 973, -212, -681, 68, -1115, -195],\n [-1033, -145, 402, 1131, 193, -758, -485, -397, 332, 583, -138, 1421]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-392, 47, -418, 0, -24, -757, -215, 717, -534, 980, 373, -1048],\n [71, 696, 951, 60, 191, -125, -1502, -741, -1348, 949, 860, -819],\n [1362, 551, -137, 464, 746, 489, -236, -251, 550, -450, -807, 349],\n [401, 188, 87, 753, 430, 236, 1328, 454, 1532, -1098, -843, 1423],\n [-261, 575, 436, -614, 1301, -33, 469, 582, 1013, 60, -647, 1048],\n [431, 974, 1223, -646, -549, 933, -184, -2, -14, -825, 1209, 541],\n [-398, -216, -943, -755, 749, -643, -107, 194, 399, 523, -701, -554],\n [156, -1743, -979, 122, -1743, 237, -13, -190, -1257, -152, -8, -1003],\n [-429, 1133, 295, 1034, 1141, -547, -79, 920, -266, 1601, 678, 366],\n [-1643, -740, 147, -21, -711, -539, 136, -37, -668, 933, 654, -309],\n [-19, 1203, 1818, 231, 651, -907, 847, 1331, 55, -34, 546, -67],\n [-793, 478, 452, 1167, -509, 90, 1513, 710, 1103, 885, 459, 364]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-464, -78, 258, 184, 34, -109, 451, 554, -44, 56, 474, 96],\n [-228, 254, 502, 408, -364, 534, -460, -74, 287, -467, -259, -407],\n [352, 388, -60, 288, -426, 271, -539, -536, 387, -395, -581, -531],\n [-534, 822, 402, 1464, -1044, -51, 513, 576, 936, -720, 246, -1110],\n [-554, 180, 872, 464, -336, 771, -523, 134, 231, -547, -141, -349],\n [-262, 350, 570, 552, -486, 596, -502, -76, 393, -577, -301, -543],\n [-394, -658, -14, -616, 748, -413, 715, 668, -674, 674, 788, 904],\n [-171, 4, 330, 56, -49, 344, -294, -19, 14, -172, -104, -51],\n [-512, 268, 396, 672, -390, 25, 355, 520, 333, -293, 325, -381],\n [-280, -466, 334, -520, 496, 274, -176, 146, -485, 233, 161, 577],\n [-543, -66, 476, 208, -7, 157, 187, 483, -28, -78, 348, 47],\n [126, -400, -332, -576, 512, -357, 305, 82, -439, 499, 257, 577]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[130, 304, 61, 689, -226, -416, -1131, 311, -84, -147, 457, 298],\n [130, 335, -543, 207, -473, -159, -567, 422, 145, 155, 337, 73],\n [-10, 7, -22, -306, -371, 263, 86, 367, 419, -142, -414, 279],\n [-85, -138, 8, -925, -650, 731, 658, 619, 907, -275, -1094, 484],\n [-55, -131, 302, -147, 43, 146, 164, -2, 110, -181, -312, 147],\n [125, 354, -306, 23, -922, 81, -772, 931, 649, -195, -180, 600],\n [-40, -127, 567, 283, 353, -147, -197, -248, -243, -229, 19, 91],\n [15, 65, -849, -490, -195, 210, 677, 9, 122, 488, 61, -431],\n [-95, -171, 116, -857, -537, 686, 642, 524, 818, -299, -1058, 463],\n [35, 81, -765, -106, 149, -90, 449, -311, -290, 576, 489, -639],\n [20, 22, 345, 435, 200, -264, -483, -113, -244, -149, 233, 92],\n [115, 238, 14, 845, 210, -601, -944, -151, -513, 71, 816, -96]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[44, 201, -257, -246, 151, 213, 332, -86, -211, -377, -308, 154],\n [530, 528, 49, -348, -326, 531, 434, 319, -466, -368, -254, 289],\n [292, 714, -416, 8, 104, 396, 400, 328, -118, -400, -554, 218],\n [-278, -683, 370, -98, -79, -338, -310, -365, 43, 299, 490, -175],\n [616, 678, 258, 436, -538, 270, -128, 864, 102, 302, 12, 44],\n [-330, 238, -567, 656, 540, -269, -194, 105, 608, 126, -318, -165],\n [-628, 52, -816, 586, 877, -398, -138, -219, 662, -17, -429, -194],\n [272, -574, 966, -408, -776, -10, -236, -42, -386, 364, 774, -32],\n [436, 683, -11, 462, -259, 215, -60, 718, 183, 173, -164, 38],\n [218, -105, 230, -680, -254, 312, 368, -208, -593, -362, 35, 217],\n [456, 986, -366, 400, -36, 386, 212, 726, 118, -144, -534, 156],\n [50, 135, -254, -504, 154, 300, 488, -236, -409, -554, -341, 229]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-126, -56, 0, 161, 77, -14, -56, 42, -98, -28, 56, -119],\n [-126, -56, 0, 161, 77, -14, -56, 42, -98, -28, 56, -119],\n [-18, -8, 0, 23, 11, -2, -8, 6, -14, -4, 8, -17],\n [144, 64, 0, -184, -88, 16, 64, -48, 112, 32, -64, 136],\n [234, 104, 0, -299, -143, 26, 104, -78, 182, 52, -104, 221],\n [324, 144, 0, -414, -198, 36, 144, -108, 252, 72, -144, 306],\n [270, 120, 0, -345, -165, 30, 120, -90, 210, 60, -120, 255],\n [-36, -16, 0, 46, 22, -4, -16, 12, -28, -8, 16, -34],\n [54, 24, 0, -69, -33, 6, 24, -18, 42, 12, -24, 51],\n [234, 104, 0, -299, -143, 26, 104, -78, 182, 52, -104, 221],\n [-36, -16, 0, 46, 22, -4, -16, 12, -28, -8, 16, -34],\n [-306, -136, 0, 391, 187, -34, -136, 102, -238, -68, 136, -289]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[308, -456, -66, -484, 723, -205, -386, 481, 1035, -27, 505, 91],\n [103, -301, -433, 155, 1396, -405, -971, 376, 1430, 1145, -152, -1016],\n [98, 457, 472, 344, -719, -140, 1135, -987, -584, -213, -77, -17],\n [-950, -183, 688, -346, -371, -159, -112, -14, -681, 521, -323, -162],\n [-147, 696, -311, -137, -444, -179, -128, -846, -149, -1720, 164, 533],\n [-519, -497, 269, -483, 770, -679, 351, -536, 508, 95, 174, 54],\n [-190, 132, -272, 192, 83, -61, 240, -469, -235, -277, -171, 121],\n [-224, 172, 490, 4, -25, -527, 445, -798, 150, 162, -49, -383],\n [-916, 159, 920, -94, -534, -273, -564, -5, -466, 1117, -572, -948],\n [-375, 255, 235, -223, -525, 66, -720, 240, -292, -159, -125, -117],\n [753, -110, -347, 377, -360, 866, 80, 990, -431, 257, 28, 294],\n [108, -397, -60, 718, -182, 736, 676, 653, -1054, 1476, -580, -159]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-121, 196, -89, -312, -493, -307, -655, -248, 358, -228, 619, 477],\n [-252, 772, 755, -74, -355, -751, 139, 263, -210, 1020, -87, -1112],\n [-6, -397, 318, -419, 364, -200, 487, -1315, -1272, -389, -120, -1526],\n [108, -401, 395, 91, -285, 110, 401, -232, -104, -1231, 251, -49],\n [-432, 716, 1290, -91, -298, -409, 600, -1183, -1059, 351, -856, -1779],\n [-457, 820, 817, -398, 39, -1212, -14, -410, -542, 830, 213, -1936],\n [-1042, 862, 112, -314, 632, -633, -669, -1016, 450, 72, -116, -407],\n [-442, -51, -755, -406, 123, 226, -408, -1067, 99, -295, 134, 619],\n [-549, -96, -1134, 467, 1141, 796, 1046, 573, 301, 736, -792, 284],\n [-52, -403, -584, 234, 364, 895, 57, 486, 533, 443, -1035, 1381],\n [65, 292, 427, 338, -509, -63, 727, -290, -428, -913, 588, -791],\n [34, -523, -332, -173, -173, -216, 364, 577, 219, -475, 906, 63]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-344, -322, 370, 413, 147, -152, -157, 596, 658, 341, 66, -294],\n [-339, -31, 579, 734, 461, -827, -274, 634, 668, 522, 575, -196],\n [233, -415, 135, 592, 787, 31, 634, -556, -726, -286, 801, 492],\n [-470, -606, 246, 1233, 916, -159, -544, -354, 649, 525, -24, -397],\n [242, 429, -900, -906, -244, 219, -605, 366, 569, -351, -795, -227],\n [-488, 53, 780, 307, -515, -389, -104, 376, 305, 672, 47, -297],\n [268, 524, 286, -325, -433, -362, 555, -198, -908, -113, 586, 478],\n [-399, -842, 447, 663, 290, 332, 148, 320, 453, 258, 28, -255],\n [47, -382, 213, 38, 131, 157, 512, 525, -20, -188, 409, 161],\n [-288, 252, -668, -363, -452, 369, -1206, -330, 859, 297, -1518, -743],\n [503, 410, -1195, -1145, -64, 364, -418, 444, 431, -716, -680, -33],\n [225, -110, -513, -587, -290, 734, 148, -232, -245, -432, -536, 55]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-396, 153, 21, -813, -32, -572, 957, -52, 766, 400, 368, 415],\n [-76, 315, 443, 35, 53, 389, -76, -232, -270, -46, -638, 260],\n [-495, 529, 361, -372, 288, 230, -222, 129, 753, 1148, 145, -64],\n [50, -224, -110, 294, 746, 158, -384, -78, -25, 360, -127, -790],\n [343, -399, -311, 640, 319, 205, -689, 91, -411, -158, 11, -737],\n [-444, 418, 408, -736, 39, -197, 833, -256, 493, 354, -215, 601],\n [44, -163, -309, -197, -418, -430, 331, 196, 211, -200, 555, 215],\n [187, -295, -445, 456, 113, 71, -831, 431, 110, 322, 642, -757],\n [-542, 392, 232, -544, 467, -29, 101, 70, 936, 1214, 270, -161],\n [125, -106, -276, -23, -625, -259, 46, 289, 46, -314, 540, 278],\n [-97, -235, -105, -50, 892, -122, 148, -217, 228, 456, -110, -680],\n [-313, 31, -23, -552, 322, -404, 636, -89, 628, 500, 234, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[631, 805, 166, -238, 230, -379, -374, 826, -129, -450, -570, 216],\n [430, -474, 332, -348, -354, -586, 622, 508, -542, 1258, 1208, 134],\n [668, 639, -95, -278, -25, -317, 280, 338, -507, -65, 506, 546],\n [494, 880, 53, -163, 368, -103, -539, 530, -4, -740, -821, 182],\n [464, 484, -268, -76, -430, -568, 766, 320, -532, -2, 952, 638],\n [-690, -409, -214, 515, -543, -232, 411, -84, 361, -159, 37, -194],\n [242, 90, 359, -155, 152, -273, -385, 662, 74, 88, -513, -180],\n [-12, 874, -425, 181, 303, 379, -378, -330, 194, -1287, -799, 245],\n [146, 481, -153, 236, -625, -965, 554, 914, -77, -401, 152, 326],\n [-74, -94, -157, 109, -344, -225, 483, -26, -126, 128, 543, 160],\n [-280, -791, 469, -196, 581, 723, -774, -454, 315, 637, -552, -682],\n [-331, -107, -384, 278, -364, 25, 542, -454, -17, -140, 530, 176]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[58, 286, 208, 574, -25, 1418, 442, -236, -43, 555, -53, -1565],\n [890, 519, -895, 133, 1575, -19, -485, 340, 1387, 57, 892, 1090],\n [-559, -207, 762, 519, -510, 372, 559, 743, -456, -220, -69, -743],\n [-793, 127, -780, -250, 451, -81, -364, -310, 662, 1363, -538, 440],\n [-1031, -7, -364, 41, 298, -220, -305, -143, 331, 765, -803, 486],\n [246, -92, 210, -275, 184, 545, -217, -568, 128, -198, 101, 11],\n [1019, -72, 227, -551, 225, -228, -839, -21, -9, -971, 642, 602],\n [-329, -237, 160, -180, 549, 162, -711, -980, 292, -315, -473, 844],\n [-556, 18, 558, 701, 56, 1333, 811, -835, -174, -301, -852, -907],\n [-359, 256, 105, 670, -217, -245, -668, 1419, -341, 579, -74, -809],\n [-192, -614, 590, -110, -240, -330, 184, -757, -268, -913, 17, 774],\n [1049, 813, -1736, -716, 279, -1115, -470, 306, 434, 1041, 265, 336]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[371, -823, -151, -171, 1114, 360, -914, 1524, 172, -332, -302, 295],\n [-812, -1011, -157, 681, 85, 432, 206, 907, -628, -1021, -759, 300],\n [-726, 313, -288, 635, -854, -630, 658, 18, -238, -461, 267, -667],\n [23, -155, -1035, -279, -602, 384, -300, -176, 212, -282, 176, 82],\n [184, -1026, -417, -367, 936, 1040, -1009, 842, -1048, -265, -188, 1125],\n [649, 463, -258, -710, 90, 28, -483, -414, -80, 585, 760, 36],\n [68, -102, 33, 175, -310, -162, 326, 108, 1815, -286, -724, -604],\n [668, -217, 805, -263, 709, 104, 20, 231, 1674, 191, -807, -269],\n [112, -1103, 59, 164, 696, 316, -64, 1622, 1367, -1003, -1023, -504],\n [886, -276, -158, -1160, 898, 910, -807, -6, -1115, 351, 728, 598],\n [-466, -1424, -1265, 137, -144, 1036, -409, 1122, -102, -1369, -660, 391],\n [261, -525, 115, -508, -29, 1088, 190, -863, 251, -44, -650, 541]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-571, -71, 638, -849, -498, -527, 69, -402, -448, 148, -897, 175],\n [436, -347, 764, 266, 156, -439, -162, -747, 895, -1386, -133, -625],\n [981, 355, -174, 25, -634, -51, 119, 200, -860, 376, 627, -597],\n [-982, -140, 716, 189, 378, -391, 473, -534, 363, -904, -553, -183],\n [982, -323, -138, -302, 173, -520, -1930, 475, -486, 370, -228, 1004],\n [222, -620, 46, -709, -53, -744, -352, -88, 269, -162, -233, 538],\n [885, 24, 1442, 220, -93, -1207, -619, -719, -274, -1346, -251, -966],\n [250, -384, -24, 295, 332, -1539, 203, 482, -1221, -478, 567, 235],\n [194, 30, 325, -562, -75, -146, -534, 30, 141, 459, -328, 278],\n [331, -665, 54, -1915, -806, 28, -1422, -680, 1061, 361, -1288, 852],\n [-242, 56, -276, -786, -42, 379, -376, 492, 90, 1382, -322, 930],\n [-242, -545, -161, -620, 133, 475, 86, -921, 2498, -979, -265, -251]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[805, -1591, 730, -455, 1032, 308, -943, -541, 125, -605, -47, 756],\n [159, -601, 104, -351, 497, 303, -107, -52, 278, 361, 744, 536],\n [694, -638, 376, -522, 518, 3, -361, -542, -32, -144, 78, 291],\n [1020, 382, 54, -794, 185, -684, -40, -1055, -376, 495, 83, 41],\n [-795, -99, -64, 599, -181, 520, 124, 798, 456, -5, 158, 21],\n [-539, 308, -610, -64, -294, 45, 617, 476, -353, -2, 427, -254],\n [-411, -397, 374, 287, -34, 795, 140, 629, 763, -33, 301, -91],\n [643, -965, 380, -431, 495, -10, -506, -452, -464, -1069, -524, 51],\n [616, -261, 804, -141, 302, 265, -346, -423, 844, 525, 142, 226],\n [1202, 3, 690, -711, 403, -205, -275, -1050, 455, 801, 275, 233],\n [92, 1083, -222, -207, -603, -335, 683, -144, -143, 439, 43, -693],\n [-1187, 699, -478, 1081, -754, 51, 273, 951, -14, -268, -559, -423]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[1534, -1420, -245, 281, -1180, 468, 12, 1018, -72, 250, 1002, 771],\n [-332, -173, 595, 463, 1274, 723, 234, -398, -229, -894, 735, -118],\n [-38, 243, -205, 343, 689, 91, 946, -440, -184, 784, -120, 387],\n [-811, 1026, -1285, -1310, -478, -461, 61, -1195, 505, 58, -863, -470],\n [-489, -596, 257, 823, 994, 475, 439, 392, 165, 920, 273, 653],\n [391, -283, 35, 463, 48, 1273, 126, -71, -871, -841, 1475, 437],\n [-623, 517, -511, 237, -640, -73, -1162, -342, -192, -1216, 624, -318],\n [-590, 812, -541, 1, -607, -84, -1509, 185, -274, -571, -525, -146],\n [452, 16, 525, 392, 844, 608, 99, 152, -591, -566, 80, 144],\n [1535, -437, -289, -777, -1423, -142, 217, 441, -104, 410, -224, 130],\n [208, 980, 111, -523, 391, -64, 410, 1113, -262, -213, -1030, 651],\n [204, -388, 335, -570, -150, 117, -115, -1385, -6, 59, -74, -1192]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-206, 1124, -370, 318, 158, -244, -278, -343, -617, 938, -1502, 536],\n [647, -1150, 515, -904, 194, -270, 637, 550, 805, -645, 852, -194],\n [-1632, 476, 127, 1371, -721, 598, -880, -686, 252, -641, 268, 694],\n [627, 114, -358, 25, 512, 49, 1248, 839, -239, -599, -481, 54],\n [-342, -8, -89, 185, -500, -43, -949, -12, 71, 500, 367, -192],\n [733, -457, -612, 29, -33, 345, 328, 1004, -275, -100, 817, -953],\n [-240, -9, 392, -618, -33, -582, -1348, -232, -425, -31, 36, -921],\n [40, -1478, -109, 487, 465, 1569, 729, -476, 1826, 384, 528, 1652],\n [-435, -209, 41, 584, -493, 563, 24, -87, -53, -909, 1228, -501],\n [200, -688, -408, 322, 532, 993, 271, -271, 991, 983, -370, 1250],\n [1172, -430, 210, -1080, -36, -520, 900, -77, 141, 934, 534, -316],\n [636, -931, 520, -1184, 189, -333, -201, -447, 606, 820, 472, -163]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[256, -134, 60, 175, 158, -286, -91, 24, 128, -144, -296, 261],\n [-733, 88, -183, 134, -20, -414, 250, 98, 168, 520, 555, 92],\n [-269, 704, -786, 499, 943, -963, -159, 535, 481, -22, -62, -76],\n [718, -372, 520, -445, -506, 982, -103, -358, -426, -442, -368, -207],\n [0, -218, 340, -71, -270, 142, -109, -200, -304, 288, 24, 595],\n [-103, 411, -332, -111, 166, 212, -9, 145, -9, -117, 122, -557],\n [480, 431, -572, 85, 611, -61, -21, 350, 454, -865, -438, -1110],\n [-518, 1633, -1590, 640, 1685, -1219, -364, 990, 626, -105, 16, -597],\n [163, -903, 1117, -337, -1023, 655, -87, -676, -758, 557, 41, 1264],\n [20, -516, 354, -115, -458, 170, 295, -218, 62, -22, 94, -89],\n [-199, 758, -498, -82, 383, 181, -246, 237, -189, 54, 142, -325],\n [-624, 547, -586, 359, 565, -779, -15, 376, 296, 367, 312, 102]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[344, 440, 308, 572, -800, 160, -520, -576, 436, 540, -164, 400],\n [246, -110, -215, -949, 833, -94, -238, -356, -69, -369, 42, 281],\n [638, -446, 1005, 459, -794, 464, 226, -4, -7, 155, 681, 18],\n [-350, 388, -707, -395, 572, -322, -308, -174, 77, -75, -517, 116],\n [88, -313, 501, 492, -529, 223, 395, 355, -113, 76, 372, -255],\n [-166, -185, -154, -255, 363, -79, 227, 257, -192, -239, 59, -179],\n [476, -173, 427, -114, -139, 203, -105, -277, 49, 6, 304, 215],\n [322, -1148, 797, -263, 159, 344, 972, 762, -605, -563, 1056, -509],\n [164, -601, 683, 398, -458, 301, 635, 543, -269, -78, 631, -380],\n [768, -676, 1172, 316, -707, 538, 364, 68, -114, 24, 903, -23],\n [-290, -382, -323, -621, 816, -164, 418, 460, -387, -517, 127, -316],\n [70, -785, 180, -665, 685, 65, 635, 525, -510, -625, 595, -345]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[64, -76, -56, -24, -8, 84, 80, -72, 68, 28, 72, 40],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n [416, -494, -364, -156, -52, 546, 520, -468, 442, 182, 468, 260],\n [320, -380, -280, -120, -40, 420, 400, -360, 340, 140, 360, 200],\n [400, -475, -350, -150, -50, 525, 500, -450, 425, 175, 450, 250],\n [64, -76, -56, -24, -8, 84, 80, -72, 68, 28, 72, 40],\n [-64, 76, 56, 24, 8, -84, -80, 72, -68, -28, -72, -40],\n [-384, 456, 336, 144, 48, -504, -480, 432, -408, -168, -432, -240],\n [-32, 38, 28, 12, 4, -42, -40, 36, -34, -14, -36, -20],\n [208, -247, -182, -78, -26, 273, 260, -234, 221, 91, 234, 130],\n [-256, 304, 224, 96, 32, -336, -320, 288, -272, -112, -288, -160],\n [352, -418, -308, -132, -44, 462, 440, -396, 374, 154, 396, 220]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-271, -445, -708, -425, -831, -217, -217, 1337, -206, -48, 653, -319],\n [-547, 493, 822, -564, -428, -10, -804, 738, -372, -276, 554, -488],\n [767, 520, -234, -508, 12, -125, 1009, -630, 878, -26, -216, -207],\n [-471, 270, 236, 447, 112, 145, 70, -1118, 332, 248, 519, 465],\n [-670, -594, 696, 290, 167, 502, -705, 232, -572, -71, 289, 26],\n [-97, 156, 54, 14, -203, -204, -355, 206, -130, -69, 25, -38],\n [184, 578, -792, 210, -230, -829, -275, 445, -300, 135, -411, 249],\n [-427, -918, 28, 827, 1160, 519, -562, 797, -1572, 277, -792, 509],\n [-846, 1165, 1006, -341, 393, 296, -260, -202, -416, 179, 646, 34],\n [179, 286, -44, 271, 538, 70, 453, -766, 148, 220, -321, 346],\n [1341, 274, -202, -624, -586, -398, 962, -864, 1578, -424, -406, -560],\n [-410, 398, -434, 1139, 902, -210, -221, -534, -810, 614, -521, 1076]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-572, -376, 672, -332, 640, -8, -68, -184, -124, 348, -568, -456],\n [595, 368, -667, 388, -609, -52, 166, 210, 144, -455, 526, 513],\n [812, 580, -1018, 386, -1022, 132, -94, 224, 146, -308, 936, 570],\n [-542, -220, 448, -566, 272, 348, -626, -284, -206, 878, -156, -660],\n [623, 328, -619, 512, -497, -204, 410, 266, 188, -707, 390, 633],\n [-411, -84, 225, -582, 3, 480, -816, -282, -210, 999, 114, -639],\n [298, 320, -522, -56, -638, 328, -476, -4, -16, 318, 644, 30],\n [-557, -298, 560, -449, 456, 170, -347, -234, -165, 613, -362, -558],\n [-544, -416, 720, -208, 752, -160, 176, -128, -80, 96, -704, -336],\n [-307, -158, 300, -259, 236, 110, -217, -134, -95, 363, -182, -318],\n [325, 8, -97, 568, 141, -532, 886, 270, 204, -1025, -254, 603],\n [-18, -24, 38, 12, 50, -32, 48, 4, 4, -38, -52, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[596, -362, 1018, 220, -616, 416, -64, 46, -372, -468, -234, 178],\n [-461, 325, -916, -247, 575, -283, 68, -29, 276, 484, 295, -103],\n [-766, 90, -236, 358, -30, -858, -72, -114, 576, -416, -650, -518],\n [688, -63, 161, -352, 66, 786, 72, 105, -522, 422, 629, 479],\n [291, -344, 975, 393, -667, 59, -100, -2, -138, -682, -538, -42],\n [-569, 304, -853, -139, 497, -433, 44, -50, 366, 334, 118, -202],\n [-725, 105, -280, 305, 15, -795, -60, -105, 540, -340, -565, -475],\n [173, 125, -362, -329, 325, 319, 76, 47, -168, 488, 515, 229],\n [-579, 288, -807, -105, 459, -459, 36, -54, 378, 282, 66, -222],\n [573, 6, -33, -393, 183, 705, 84, 96, -450, 510, 672, 444],\n [374, -363, 1027, 370, -684, 144, -96, 9, -198, -662, -491, 7],\n [-242, 220, -622, -214, 410, -106, 56, -8, 132, 388, 280, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-203, 108, 298, 346, -335, 145, -243, -196, 302, 313, -629, 42],\n [212, -32, -228, -224, 160, -128, 236, 216, -132, -196, 484, 24],\n [-270, -80, 166, 80, 80, 128, -274, -292, -106, 54, -358, -132],\n [15, -140, -158, -250, 335, -49, 47, -4, -322, -237, 329, -114],\n [316, 24, -266, -212, 70, -170, 336, 332, -34, -176, 568, 96],\n [170, 80, -74, 0, -120, -72, 166, 188, 134, 14, 162, 108],\n [-164, -196, -51, -202, 395, 35, -134, -198, -399, -206, 98, -204],\n [-84, 124, 205, 278, -325, 83, -118, -70, 305, 258, -430, 84],\n [-27, 72, 99, 144, -180, 36, -45, -18, 171, 135, -207, 54],\n [186, -96, -270, -312, 300, -132, 222, 180, -270, -282, 570, -36],\n [-38, -32, 2, -24, 60, 12, -34, -44, -62, -26, -6, -36],\n [111, 104, 5, 88, -200, -32, 97, 130, 205, 93, -5, 114]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[407, 225, -808, -210, -568, -166, -164, -649, 154, 439, -470, -579],\n [305, -293, 530, -631, -154, -246, 30, 645, -152, -990, 782, 1072],\n [439, 149, 89, -1031, -1655, -1349, -174, -349, 431, -998, 755, 805],\n [998, -461, 371, 332, 118, 211, -616, 527, -95, -198, 542, 165],\n [-385, 170, -818, 548, 1197, 1206, 244, -192, -362, 1251, -1203, -1087],\n [-491, 53, 44, 89, -878, -1108, 430, -673, 518, -186, -6, -226],\n [-893, 624, 535, -662, -35, 20, -18, 229, -61, -443, 399, 940],\n [1013, -303, -501, -279, -234, 44, -220, 26, -107, -46, -28, -99],\n [259, 211, -111, -789, -1331, -1051, -94, -453, 371, -604, 399, 435],\n [1150, -639, 35, -9, 162, 219, -290, 563, -235, -333, 372, 220],\n [-502, 97, -475, 210, 683, 556, 430, -156, -197, 614, -753, -559],\n [313, -114, 300, 273, 906, 973, -452, 703, -400, 166, 160, 186]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[74, 174, 431, -503, -1017, -262, -63, -40, -527, -1089, 1106, 471],\n [1007, 1, -85, -1108, -286, -714, 328, 124, -652, -998, -599, 202],\n [-197, 386, -1049, -256, -349, -895, 653, -342, -726, 228, -174, 344],\n [-225, 69, 114, 80, -118, 199, 499, 523, -148, 696, -272, -86],\n [224, -577, 940, 664, 25, 583, 369, 304, -365, 215, -65, 224],\n [-251, -236, 797, 690, 172, 112, -1269, -162, 728, -635, 844, -429],\n [570, -192, -993, -569, 432, 195, 116, -173, 5, -273, -833, 70],\n [-225, -248, -23, 612, -642, 478, -574, -386, 916, -544, 2385, 503],\n [-94, 225, 882, -334, -33, -837, 65, 1127, -809, 390, -1573, -1162],\n [17, -290, 274, 562, 466, -61, -831, -98, 739, -15, 176, -611],\n [-541, 428, 579, -13, 600, -260, -610, 459, -23, -144, -1298, -581],\n [821, -425, 65, -348, 605, 241, -468, -773, 214, -124, -333, -525]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-434, -125, -403, -1010, -871, 301, 376, 35, -789, 59, 497, -381],\n [-726, -26, -195, 485, 7, -363, -597, 34, -524, 15, 723, -1070],\n [-223, -72, 360, -271, 239, 455, -260, 83, -852, -471, 1038, -729],\n [-1032, 678, -315, 705, 58, -1052, -671, 380, 283, 443, -354, -66],\n [139, -126, -725, -619, -502, 323, 960, -435, 322, 55, 116, -270],\n [-417, 802, 506, 993, 1068, -552, -920, 195, 394, -244, 211, -201],\n [227, -364, -310, -1256, -824, 461, 950, 91, -186, 316, -504, 831],\n [-684, 278, 452, -327, 426, -689, -611, -38, -75, 708, 391, 407],\n [949, -981, -796, -949, -1407, 1046, 1311, -584, -361, -239, 39, -436],\n [-126, -417, -843, -768, -757, 45, 844, -505, 87, 509, 201, -289],\n [278, 324, -148, -126, -800, -10, 65, 88, 90, -109, -692, 419],\n [263, -728, -802, 132, -116, 109, 910, -273, 555, 331, -392, -117]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[188, -68, 11, 413, -741, -467, 920, -228, -809, 793, -257, -363],\n [823, 110, -688, 329, -1345, -394, 877, -110, -904, 564, 227, -161],\n [766, -42, -263, 210, -41, -375, -382, -212, 455, -362, -75, 725],\n [381, -249, 238, 320, 212, -531, -226, -379, 383, -134, -543, 652],\n [-74, -82, 376, 289, 306, -322, 94, -192, 110, 257, -352, -30],\n [-830, 111, 160, -290, -89, 507, 481, 311, -605, 415, 234, -901],\n [-709, -289, 385, -183, -307, 158, 552, -39, -722, 353, -394, -353],\n [675, 508, -1135, -297, -748, 463, -79, 458, -149, -296, 1138, -158],\n [-541, 64, 249, -459, 1076, 571, -967, 274, 895, -742, 190, 178],\n [-180, -109, 591, 151, 1124, -196, -685, -169, 930, -314, -409, 394],\n [419, -113, -86, 174, -182, -311, -36, -203, 71, -78, -197, 410],\n [-178, 324, -230, -140, -24, 354, 122, 324, -142, 154, 552, -588]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[642, -558, -637, 894, -71, -62, 64, -701, -321, -810, 68, 365],\n [-590, 476, 349, -595, -344, -662, -95, 971, 58, 996, -173, -729],\n [126, -307, -201, 523, 338, -38, -92, -187, 258, -329, -120, 64],\n [-708, -250, -430, -344, 159, -376, -130, -111, 117, 838, -247, -540],\n [-230, -353, -987, 56, 824, 798, -521, -496, 76, -23, 732, 848],\n [170, -606, -158, 709, 353, 100, 197, 98, 212, -494, 7, -329],\n [261, 329, 498, 260, 58, -323, -153, -139, 423, -302, -552, 233],\n [-273, -394, 259, -509, -541, 225, 897, 623, -557, 347, 259, -1236],\n [595, 686, 545, 78, 20, 171, -310, -555, 239, -647, -250, 1127],\n [360, -197, 531, 136, 315, 710, 405, -577, 274, -783, -207, 197],\n [122, 4, -2, -198, -317, 390, 274, 409, -489, -62, 589, -62],\n [713, 59, -422, -153, -1182, 185, 416, -316, -1421, -368, 748, 435]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[249, -132, 106, 676, -808, -174, 714, 163, 185, -94, 189, 540],\n [-333, 1392, 443, -8, 232, -1639, -171, -226, 196, -1241, -623, 858],\n [917, -300, -263, -626, -131, 938, 831, 619, -494, 1357, 264, -479],\n [-2, -614, -263, 641, -277, 585, 94, -746, 186, 601, 20, -239],\n [-643, 132, 703, 159, 288, -146, -378, -982, 801, -215, -574, -246],\n [289, 354, 209, -853, 339, -70, 312, 669, -229, 150, -290, -147],\n [-23, 339, -384, 88, 221, -524, -635, -49, -526, -386, 286, 460],\n [-416, 64, -9, 330, -258, -59, 674, -396, 862, -379, -831, -367],\n [-320, -206, 963, -434, 216, 525, -525, -65, 521, 175, 438, -498],\n [67, -81, -508, 311, 196, -287, -517, -239, -622, -35, 74, 438],\n [-59, 108, -16, 98, -421, 580, 790, -494, 865, 405, -181, -777],\n [220, 415, -47, -734, 741, -297, 182, 19, -394, 321, -1041, -114]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-399, -251, -1050, -559, -282, 269, 733, 299, -470, 423, 889, -611],\n [316, 779, 499, 361, 788, -981, 209, -81, 129, 81, -351, 1270],\n [-597, 138, -34, -188, -511, 373, 301, 811, -127, 57, 89, 136],\n [-955, 630, 1402, 154, -509, 1043, -243, 741, -35, -734, -92, 119],\n [-729, -408, -727, -220, -839, 761, 422, 974, -500, -332, 1103, -389],\n [-645, -579, 38, -447, -727, 698, -115, 833, 238, 54, -797, -505],\n [650, 93, -787, 267, -438, 199, -181, 205, -296, -339, -223, 279],\n [-836, 910, 1505, 34, 1014, 737, 358, 522, -539, -1660, -151, 273],\n [849, -246, -521, -242, 785, -841, 10, -994, 264, 730, -745, -225],\n [576, 1148, -17, 250, 616, 3, 238, -884, -632, -201, 692, 135],\n [-1122, 125, 764, -189, -1723, 1833, -501, 919, 30, -154, -86, -801],\n [-300, 100, 644, -514, 237, 756, -127, 1, 79, -226, -1373, -709]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-357, -187, -332, -494, -1142, -1218, -168, -204, -638, -35, -173, 21],\n [81, -156, -428, -568, -443, -396, 350, 112, 279, 141, -589, 173],\n [1194, 391, -69, -201, 712, 885, 280, -234, 722, -211, 396, -436],\n [-342, 44, 219, 134, -798, -1050, 595, 832, -738, 784, -152, 737],\n [699, -74, -377, -756, -588, -552, 539, -13, 184, 59, 14, 46],\n [-1663, -1271, 178, 81, -415, -341, 214, 857, 129, 505, -1377, 874],\n [1812, 1228, -719, -782, -241, -306, 459, -465, 157, -76, 495, -485],\n [1187, 281, -184, -200, 552, 496, -103, -787, 396, -684, 1295, -445],\n [-1541, -1305, 1007, 862, 285, 362, -112, 758, -173, 274, -222, 616],\n [-431, -709, 46, -19, -359, -625, 425, 392, -75, 194, 257, 854],\n [-155, 448, -315, 117, -377, -805, -249, -276, -625, -87, 538, 269],\n [473, 615, -688, -779, -1069, -1097, -109, -478, -501, -82, -189, -416]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1189, -656, -476, -356, -369, 725, 374, 225, 100, -411, -29, 1154],\n [-387, 35, 519, -306, 183, -198, -500, 269, -607, 307, 448, 86],\n [-676, 316, -27, 377, 1125, 586, -68, 533, 404, 254, 526, 260],\n [543, -91, 380, 417, 42, 233, 492, -749, -480, 532, -1028, -25],\n [-1381, 1226, -93, 390, 418, 311, 358, -830, -973, -27, 632, -496],\n [-371, -145, -358, -359, 422, -482, -393, 639, 532, 22, 558, -561],\n [-771, 199, -143, -67, -277, -765, -106, -611, 193, -144, -231, -1876],\n [-238, 24, 514, 28, 256, -816, -985, 1393, 729, 243, 564, 723],\n [604, 84, -1108, 413, 96, 486, 797, 59, 946, -489, -97, 565],\n [144, 562, 32, 712, 1086, -834, 124, 504, 56, 1104, -116, 626],\n [-844, 593, -234, 183, 69, -363, 59, -383, 10, -125, 205, -934],\n [538, -131, -459, 184, 172, 130, 161, 589, 779, -142, 65, 801]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-145, 267, 593, -486, -377, 536, 42, 107, 313, -1116, -279, 446],\n [381, 172, 718, -668, -597, 477, 427, -566, -90, -388, -614, 600],\n [-180, 121, 27, -386, -78, 69, 41, 611, 69, -342, 423, -180],\n [-81, -30, 18, -52, -468, 616, 635, -161, 325, -753, -377, 749],\n [921, -135, 297, -2031, -334, 144, -811, -527, 198, -78, 1287, -180],\n [176, 129, -43, -237, -265, 439, 30, 189, -112, -218, -172, 131],\n [731, -169, 537, -1305, 321, -533, -1581, -982, 231, 305, 1065, -522],\n [-59, -112, -53, -95, 407, -321, -875, -89, 326, -76, 605, -345],\n [-566, -314, -68, 668, 855, -1187, -400, -169, 345, 509, 708, -580],\n [-1090, 1, 322, 709, 870, -1137, -363, 532, 459, -192, 606, -661],\n [443, 225, 80, 406, -111, -27, 377, -89, -995, 1099, -989, -162],\n [-114, 392, 550, 819, 254, -121, -357, -69, -472, 191, -1206, -122]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[156, -52, 338, 338, -78, 13, -338, -195, 338, 143, -130, -325],\n [-180, 60, -390, -390, 90, -15, 390, 225, -390, -165, 150, 375],\n [-180, 60, -390, -390, 90, -15, 390, 225, -390, -165, 150, 375],\n [-288, 96, -624, -624, 144, -24, 624, 360, -624, -264, 240, 600],\n [36, -12, 78, 78, -18, 3, -78, -45, 78, 33, -30, -75],\n [168, -56, 364, 364, -84, 14, -364, -210, 364, 154, -140, -350],\n [-96, 32, -208, -208, 48, -8, 208, 120, -208, -88, 80, 200],\n [132, -44, 286, 286, -66, 11, -286, -165, 286, 121, -110, -275],\n [-192, 64, -416, -416, 96, -16, 416, 240, -416, -176, 160, 400],\n [276, -92, 598, 598, -138, 23, -598, -345, 598, 253, -230, -575],\n [288, -96, 624, 624, -144, 24, -624, -360, 624, 264, -240, -600],\n [-84, 28, -182, -182, 42, -7, 182, 105, -182, -77, 70, 175]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[181, 277, 114, -267, -603, 117, 309, 427, 341, 711, -400, 397],\n [223, -761, -174, -285, 99, -549, -681, -539, 11, -135, 224, -461],\n [360, -328, -24, -496, -528, -320, -232, 0, 352, 608, -224, 32],\n [163, -815, -201, -198, 270, -564, -747, -644, -88, -336, 332, -560],\n [-48, 674, 183, 41, -411, 439, 638, 609, 187, 497, -380, 539],\n [-289, 17, -51, 408, 612, 102, -51, -238, -374, -714, 340, -238],\n [-156, 642, 153, 195, -153, 453, 582, 483, 33, 195, -228, 417],\n [-6, 288, 81, -3, -207, 183, 276, 273, 99, 249, -180, 243],\n [-7, 499, 141, -10, -366, 316, 479, 476, 176, 440, -316, 424],\n [-266, 706, 150, 348, 36, 528, 618, 448, -88, -24, -136, 376],\n [-337, 365, 39, 462, 450, 336, 273, 56, -308, -516, 172, 20],\n [-84, 446, 111, 101, -159, 307, 410, 357, 55, 197, -188, 311]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[233, 53, -192, 439, 566, 1, 520, -87, -657, -465, 60, 310],\n [310, 268, -254, 804, -112, 10, 182, -384, -542, -174, 414, 662],\n [-118, -49, 125, 9, -806, 134, -545, -201, 512, 426, 207, 145],\n [-88, -222, 149, 324, -1050, 369, -621, -461, 513, 392, 403, 549],\n [145, -360, -20, 774, -186, 480, 96, -529, -276, -293, 380, 906],\n [53, -528, 11, 36, 1200, 261, 801, 136, -603, -817, -323, 81],\n [-158, -640, 193, -354, 778, 299, 391, 217, -49, -466, -401, -179],\n [-71, -277, 72, -283, 630, 63, 328, 229, -119, -313, -308, -242],\n [187, 731, -235, 331, -664, -386, -317, -158, -36, 437, 367, 103],\n [-75, 371, -13, -421, -168, -360, -227, 266, 262, 355, -127, -527],\n [-97, 91, 79, -73, -692, -4, -487, -100, 450, 433, 149, -7],\n [-54, 471, 6, 51, -1320, -183, -858, -222, 639, 834, 390, 42]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[126, 336, -546, -273, 126, 189, 525, -546, -189, -42, -483, 105],\n [-120, -320, 520, 260, -120, -180, -500, 520, 180, 40, 460, -100],\n [-108, -288, 468, 234, -108, -162, -450, 468, 162, 36, 414, -90],\n [-108, -288, 468, 234, -108, -162, -450, 468, 162, 36, 414, -90],\n [-90, -240, 390, 195, -90, -135, -375, 390, 135, 30, 345, -75],\n [-42, -112, 182, 91, -42, -63, -175, 182, 63, 14, 161, -35],\n [150, 400, -650, -325, 150, 225, 625, -650, -225, -50, -575, 125],\n [108, 288, -468, -234, 108, 162, 450, -468, -162, -36, -414, 90],\n [30, 80, -130, -65, 30, 45, 125, -130, -45, -10, -115, 25],\n [6, 16, -26, -13, 6, 9, 25, -26, -9, -2, -23, 5],\n [42, 112, -182, -91, 42, 63, 175, -182, -63, -14, -161, 35],\n [102, 272, -442, -221, 102, 153, 425, -442, -153, -34, -391, 85]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-441, 830, 86, 179, -271, -481, 311, -487, 221, 174, 9, -200],\n [419, 887, 339, -625, -516, 319, 589, -478, 268, -862, -162, -119],\n [-441, -714, -43, -655, -1055, 1280, 28, 80, -1009, 137, -656, -923],\n [460, 755, 1273, 513, -93, -1193, 518, -223, -2, -312, -1130, -900],\n [-76, 328, 284, 602, 356, -728, 4, -38, 206, 500, -184, 34],\n [-180, -1236, 384, 1207, 1030, 332, -301, 365, -492, 1082, -401, 310],\n [216, -1432, -567, 193, 1353, -784, -778, 957, 538, 1708, 276, 708],\n [-604, 175, 451, 66, -783, -286, -89, 154, -625, 459, -813, -1144],\n [-534, -420, -1263, 241, 199, 1105, -381, -146, -141, 586, 956, 1081],\n [918, -420, 511, -348, 631, 39, -1318, 1920, 106, 1091, -690, 367],\n [431, 1053, -524, 75, -145, 124, 713, -1095, 471, -642, 415, 698],\n [583, 1710, -570, 1045, -541, -406, 404, -1061, -141, 25, -456, 431]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-777, -310, -516, -763, 2, 1139, 1135, 599, -285, 342, 16, 251],\n [0, -319, 615, -211, -211, 190, -334, 187, 10, -20, 0, 289],\n [-228, 56, 780, 478, -588, 70, -186, -278, 38, -130, 624, -332],\n [193, 367, -679, 334, -208, 13, 515, 99, 1145, -894, -1288, 405],\n [-281, -51, 1401, 785, 209, 1551, -1007, 545, 167, 904, 306, 164],\n [-412, -42, 628, 66, 397, 828, -292, -15, 45, -149, 17, 214],\n [502, 684, 9, 887, 193, -198, -571, -106, 572, 59, -140, 28],\n [357, 369, 962, 1309, -583, -669, -1056, -626, 551, -176, 100, -344],\n [-25, 17, 464, 456, -693, 376, -173, 387, 237, 682, 201, 101],\n [466, 49, -704, 266, 116, -567, -362, 244, -21, 1249, -624, 186],\n [-206, 301, 606, 1421, -607, 317, -226, -378, 1121, -697, -724, -289],\n [334, 835, 346, 1289, 432, 297, -726, -221, 924, -384, -337, -11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1559, -195, -307, -469, 251, 179, 555, -441, 605, 580, -242, -499],\n [-589, 578, 226, 1465, -366, -847, -1191, -368, 910, -597, 1009, -29],\n [-494, -187, -33, 453, -649, -70, 582, -289, 332, 350, -208, -695],\n [-471, -336, 3, 565, 12, -170, 315, -155, 490, 206, 517, 62],\n [-733, 224, -8, 422, -1230, -9, -1627, 620, -764, -750, -56, 531],\n [-440, -115, -201, 1121, 2, -634, 246, -255, 889, -250, -333, -1007],\n [-650, -99, 109, -85, 1667, -505, 423, 372, -183, -373, 432, 161],\n [-1096, 100, -915, 610, -229, 14, -962, 1081, -63, -335, 683, 453],\n [-411, -232, -784, 317, -260, -242, -1220, 743, 114, -372, 1037, 602],\n [-361, 926, -239, 393, -553, 1116, 241, 194, 42, 673, -151, 287],\n [443, 521, 614, -441, 860, -1214, -1253, -95, 523, -730, 1416, 869],\n [-688, 296, 126, -653, 1573, -678, 1157, 355, -111, 346, 626, -611]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[354, -39, -625, -80, 177, 541, 160, 107, 109, 644, -375, 135],\n [546, -375, -155, 104, 273, 32, 566, -23, 284, 169, -93, 405],\n [-800, 560, 200, -160, -400, -20, -840, 40, -420, -220, 120, -600],\n [508, -370, -90, 112, 254, -24, 548, -34, 272, 102, -54, 390],\n [-662, 413, 295, -96, -331, -145, -644, 3, -329, -314, 177, -465],\n [-290, 23, 535, 72, -145, -466, -122, -93, -86, -551, 321, -105],\n [380, -194, -280, 24, 190, 193, 326, 24, 173, 293, -168, 240],\n [-394, 67, 635, 72, -197, -542, -202, -105, -130, -655, 381, -165],\n [16, 248, -670, -184, 8, 661, -246, 154, -87, 683, -402, -150],\n [552, -300, -360, 48, 276, 234, 492, 24, 258, 378, -216, 360],\n [326, -5, -655, -96, 163, 577, 116, 117, 89, 674, -393, 105],\n [-258, 87, 305, 16, -129, -245, -176, -43, -101, -316, 183, -135]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-579, -613, 293, 152, -358, 461, 206, 157, 445, -608, -418, 695],\n [-825, -271, 260, 209, 152, 65, 194, 31, 748, 148, -253, 1004],\n [393, -420, 966, 396, 204, 696, -1095, -987, -987, 978, 783, 120],\n [-222, -209, 482, 560, -625, 90, -270, 245, 470, -743, -749, 64],\n [638, 536, -187, -33, 108, -461, -391, -308, -522, 193, 77, -631],\n [-256, 481, -850, -435, 192, -706, 774, 420, 568, -321, -386, 90],\n [-339, -286, -678, -581, -225, 137, 994, 560, 340, -923, -290, 228],\n [-21, -182, -325, -162, -601, -113, 216, -60, 11, -1447, -969, 263],\n [-370, -653, 970, 514, 17, 788, -488, -229, 40, 615, 401, 536],\n [126, -450, -42, -354, 42, 714, 324, 236, -390, 208, 762, -266],\n [46, -1032, 916, 400, -720, 1216, -466, -66, -410, -548, 74, 32],\n [-345, 92, -602, -257, -323, -132, 1029, 1276, 907, -730, -322, -442]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[989, 39, 269, 660, -281, 806, 209, -451, -1349, -96, 28, 30],\n [148, -84, -203, 264, -124, 472, -77, -155, -85, -216, 143, 354],\n [438, 94, 426, 138, 24, -68, 118, -78, -762, 270, -150, -412],\n [-12, -162, 177, 207, 345, -156, -615, 141, -177, 513, -24, -162],\n [1035, 157, 408, 502, -337, 626, 486, -448, -1440, -106, -67, -180],\n [-718, 124, 245, -763, 365, -1216, 13, 489, 763, 451, -268, -650],\n [-762, -172, -339, -281, 287, -384, -503, 329, 1059, 113, 86, 206],\n [-485, 163, 379, -661, 318, -1130, 105, 407, 413, 481, -303, -746],\n [51, 53, -102, -26, -169, 162, 244, -94, 30, -250, 35, 128],\n [-195, -83, -81, -15, 126, -86, -251, 99, 249, 99, 33, 62],\n [87, -147, 570, 208, 593, -542, -808, 266, -546, 1004, -187, -632],\n [233, -155, 119, 391, 180, 202, -487, -29, -431, 317, 39, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-647, 44, -894, 56, -156, 33, 975, 357, 2171, -49, -214, 352],\n [910, 1181, 732, -1594, -79, 105, -1533, 928, -581, -1182, 337, 346],\n [-374, -300, 646, -821, -135, -1218, 241, 864, -1281, -429, 1548, -586],\n [-805, -896, -919, 179, 284, -638, 1126, -127, -78, 403, 1319, 3],\n [-615, 605, -771, -503, -668, 427, 592, -227, 1077, 77, 327, 421],\n [382, -584, 105, 307, 45, 255, -390, -614, -458, 368, 672, -418],\n [-733, -1089, -169, 445, -213, 190, 1304, -507, -187, 1011, 1142, -968],\n [1061, 881, 849, -489, -143, 229, -520, 1213, 525, -1346, -695, -204],\n [1172, 1238, 908, -495, -215, 581, -955, 765, 449, -991, -831, 391],\n [-308, 6, -926, 1234, -616, 272, 619, -1017, 956, 562, -689, 352],\n [-556, -787, -590, 655, -501, -364, 825, -998, 229, 163, 608, -871],\n [1411, 933, 1528, -506, -653, 627, -1233, 637, -750, -745, -79, -457]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[215, -298, -698, 497, -399, -408, 284, -339, -290, 1169, 411, -694],\n [-747, 299, 679, 21, 76, -453, -73, -175, -367, -1003, -161, 4],\n [-375, -235, 280, -1476, 73, 1625, -180, 212, 679, -533, 622, 1367],\n [300, -102, -368, -723, 804, 891, -323, 966, 373, 337, -732, 75],\n [-425, -113, 835, -1107, 337, 1240, -375, -206, 243, -919, 75, 1293],\n [119, -241, -127, -255, -321, 1400, 232, 464, 996, 297, 574, 571],\n [-426, 43, -85, 251, 116, 268, 167, -1182, -504, 1201, -817, -620],\n [-968, 278, 543, -973, 702, 815, -279, 792, 216, -1032, -617, 342],\n [-51, 390, -286, -131, -509, -134, 349, -27, 473, -117, 330, 146],\n [357, 461, 540, 32, 400, -388, -295, -711, -242, -523, -1005, 352],\n [-383, 285, 349, -1164, 284, 925, -171, -1040, 58, -102, -562, 917],\n [-481, 497, 21, -657, -527, 559, 367, -253, 732, -415, 353, 669]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-233, 361, 265, -413, -295, -406, -446, 623, -90, 984, 168, 355],\n [-549, -54, 483, 892, 423, 709, 330, 36, -798, -208, -790, 82],\n [528, -242, -336, -266, 42, -182, 152, -428, 310, -158, 214, -604],\n [-509, 118, 470, 418, 19, 364, -3, 373, -475, 330, -431, 390],\n [48, 173, 199, -15, 341, 494, 273, -287, 172, 121, -376, -608],\n [-206, 78, -114, 98, 348, -824, -288, 236, -930, -78, 134, 44],\n [-386, 531, -21, -27, 636, -570, -293, 164, -669, -238, 9, -39],\n [478, -920, -414, 46, -1506, 430, 78, 12, 1306, -438, 646, 1244],\n [189, -65, -302, -371, -403, -551, -301, 168, 273, 34, 547, 355],\n [192, -319, -180, 337, 51, 575, 404, -502, 365, -813, -139, -114],\n [-426, -51, 387, 373, 144, -444, -199, 558, -1275, 728, -285, 139],\n [417, -451, -357, -183, -876, 262, 50, -130, 1103, -359, 495, 602]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[92, -839, 810, 140, -435, 849, 635, 310, -552, -489, -50, -12],\n [176, -141, 402, 126, 1045, 68, -795, 162, -890, 763, -314, -158],\n [1478, 114, 201, 134, 760, -237, 964, 877, -305, -92, 196, -294],\n [172, 721, -617, -236, -1188, -335, 381, -864, 1149, -553, 444, 862],\n [784, 111, 275, 103, -491, 38, 617, -368, 196, -345, 271, 761],\n [354, 1179, -1152, -702, 226, -453, -735, -33, 388, 269, 150, -264],\n [46, -62, -159, 279, -75, -491, 994, 357, 612, -388, 191, -217],\n [1168, 907, -616, -411, -218, -318, 427, 2, 487, -293, 415, 241],\n [-860, -1062, 914, 442, -62, 593, -130, -68, -608, 72, -344, 26],\n [546, 527, -332, -132, 730, -410, -343, 193, -110, 427, 10, -182],\n [-528, -1141, 1158, 783, -240, 333, 539, -240, -297, -139, -177, 471],\n [100, 179, -464, -83, -286, -293, 811, 414, 623, -503, 237, -371]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[90, -342, -396, 126, 18, -180, -162, -36, 252, 360, 288, -288],\n [-75, 285, 330, -105, -15, 150, 135, 30, -210, -300, -240, 240],\n [-105, 399, 462, -147, -21, 210, 189, 42, -294, -420, -336, 336],\n [-80, 304, 352, -112, -16, 160, 144, 32, -224, -320, -256, 256],\n [-55, 209, 242, -77, -11, 110, 99, 22, -154, -220, -176, 176],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n [-85, 323, 374, -119, -17, 170, 153, 34, -238, -340, -272, 272],\n [-130, 494, 572, -182, -26, 260, 234, 52, -364, -520, -416, 416],\n [85, -323, -374, 119, 17, -170, -153, -34, 238, 340, 272, -272],\n [-105, 399, 462, -147, -21, 210, 189, 42, -294, -420, -336, 336],\n [5, -19, -22, 7, 1, -10, -9, -2, 14, 20, 16, -16],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[455, 247, 1011, -2008, 199, 143, 435, -1163, 1070, -1183, 1142, -1344],\n [794, 596, -17, -642, 906, -102, -47, 80, 1063, 626, -1146, -82],\n [77, 1538, 633, -398, 310, 425, -346, -56, 434, -465, -86, -64],\n [-409, -533, -752, 778, -575, -125, 295, 570, -891, 411, -443, 290],\n [597, -462, -115, -446, -1227, -101, 659, -395, -339, -470, 383, -71],\n [-612, -2136, -445, 1073, -551, 98, -113, -139, -1270, 76, 1020, -84],\n [-1153, -845, 804, 202, 1229, 350, -363, -643, -91, -582, 958, -1159],\n [-733, -189, 608, -138, 113, -169, 220, -483, -27, -807, 904, -458],\n [687, 429, -53, -1055, 584, 1731, -1185, 22, 239, 269, 420, -1134],\n [-927, 677, 728, 220, 162, -729, 370, -191, 218, -782, 360, 293],\n [-303, -347, -42, 66, -85, -754, 900, -88, -15, -128, -505, -69],\n [1511, -214, -92, -278, -1124, 823, -252, -435, -395, -131, 179, 64]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[779, -317, 183, -66, -11, -691, 566, 423, -940, -947, -423, 654],\n [-42, 797, -298, 1256, -919, -239, -856, 1025, 661, 467, 224, -137],\n [87, 37, 35, 274, -357, 453, 270, 389, -248, -123, 613, 168],\n [1381, 991, 1398, 963, -1389, -51, 258, 542, -55, -764, 1040, 1119],\n [122, -7, 354, -216, -277, 363, 728, 482, 67, 71, -295, -292],\n [243, -977, -245, -343, 1065, -808, -120, 479, -1074, 307, -883, -693],\n [-559, -310, -76, -659, -677, 843, 575, -18, -39, -190, -25, 438],\n [-752, -1079, -847, -999, 1523, 686, 810, -462, -1023, -147, -33, -414],\n [1042, -596, -77, 300, -1161, -643, 447, -633, 1543, 133, 479, -925],\n [359, 379, 133, 498, 295, -366, 30, 635, 73, 202, -307, -530],\n [-419, 95, -41, -93, 25, -115, -906, -213, -531, -116, 1, 897],\n [1327, 549, 1130, 209, -624, -335, 1037, -66, 552, -691, 49, 164]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[586, -308, 548, 116, 310, 284, -96, 62, 136, 244, -170, -316],\n [257, -173, 614, 37, 468, -386, -339, 202, 6, 218, 399, -540],\n [-258, 103, 80, -63, 149, -564, -213, 123, -106, -12, 482, -206],\n [567, -285, 402, 117, 186, 450, 9, 0, 150, 198, -327, -168],\n [-244, 99, 60, -59, 127, -512, -189, 109, -98, -16, 436, -178],\n [-144, 47, 148, -39, 175, -456, -201, 117, -74, 24, 400, -226],\n [86, -7, -296, 31, -289, 556, 285, -167, 74, -76, -502, 358],\n [-530, 251, -224, -115, -39, -628, -129, 71, -162, -140, 498, -6],\n [45, -7, -122, 15, -122, 246, 123, -72, 34, -30, -221, 152],\n [341, -197, 494, 61, 336, -74, -195, 118, 54, 194, 123, -372],\n [-418, 260, -788, -68, -574, 340, 384, -230, -40, -292, -382, 652],\n [-153, 73, -70, -33, -16, -174, -33, 18, -46, -42, 137, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-695, 973, -1218, -672, 491, -671, -1392, -176, -259, -637, 858, 947],\n [-738, 541, -470, -1414, -570, 220, -1104, -248, -90, -1082, -54, 150],\n [1266, -234, -120, -1144, -184, 556, 429, 287, -934, -4, -592, -637],\n [298, 318, 17, -672, -260, 935, 404, 209, 560, -329, 951, 690],\n [-206, -888, -1149, -83, -233, 1010, 943, 6, -1650, 578, -2310, -123],\n [-19, -10, -833, 148, 1106, 624, 128, 221, -684, 1065, -821, 424],\n [-973, 49, 267, 87, -8, -1489, -1330, -429, 339, -467, 380, -33],\n [-91, -275, -636, -420, 167, 1405, 94, -55, 118, -175, -155, -1017],\n [585, -479, -1244, 131, 694, 268, 649, 179, -1740, 910, -1367, 115],\n [-1012, 891, 611, -717, -675, -983, -1446, 135, 1304, -1260, 1461, 471],\n [-525, -11, 335, -571, -62, -141, -907, -133, 901, -773, 1251, 409],\n [683, -405, -621, -356, -359, 1155, 906, 74, -871, 2, -1056, -1047]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[189, -147, 126, 420, 147, -84, -63, -378, -84, 399, 441, -210],\n [90, -70, 60, 200, 70, -40, -30, -180, -40, 190, 210, -100],\n [-171, 133, -114, -380, -133, 76, 57, 342, 76, -361, -399, 190],\n [27, -21, 18, 60, 21, -12, -9, -54, -12, 57, 63, -30],\n [-63, 49, -42, -140, -49, 28, 21, 126, 28, -133, -147, 70],\n [-234, 182, -156, -520, -182, 104, 78, 468, 104, -494, -546, 260],\n [198, -154, 132, 440, 154, -88, -66, -396, -88, 418, 462, -220],\n [-180, 140, -120, -400, -140, 80, 60, 360, 80, -380, -420, 200],\n [-144, 112, -96, -320, -112, 64, 48, 288, 64, -304, -336, 160],\n [108, -84, 72, 240, 84, -48, -36, -216, -48, 228, 252, -120],\n [-180, 140, -120, -400, -140, 80, 60, 360, 80, -380, -420, 200],\n [234, -182, 156, 520, 182, -104, -78, -468, -104, 494, 546, -260]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[755, -618, 143, 1756, 46, -1385, 779, -693, -1484, -1157, -541, -521],\n [810, -254, 714, 405, 1028, 36, -782, 89, 1094, 840, -413, 70],\n [-318, -1046, -489, 900, 769, -49, -360, 170, 216, -273, -244, 1352],\n [34, 134, 526, 86, -330, 714, 345, -5, -697, -651, 134, -474],\n [-165, 623, -197, -1281, 208, 1458, 5, 609, 453, 877, 396, 779],\n [-489, -759, -320, -139, -1027, -1659, 347, -684, -226, -602, -1000, -1425],\n [890, -222, 61, 474, 635, 141, 149, 244, 329, 224, -1072, 626],\n [140, 156, 1433, 378, 75, 395, -1318, 664, 1079, 761, -926, 1097],\n [-227, -803, -1900, -347, -24, -251, 1708, -658, -925, -803, 369, -289],\n [-880, -468, 1075, -865, -721, -1286, -775, -606, -444, 75, -779, -1398],\n [-814, -753, -107, -57, 410, -273, -542, 39, -321, 62, 78, 228],\n [-511, 92, -1390, -176, 177, 702, 723, 646, -871, -310, 475, 820]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-481, -241, -689, 336, 19, 176, 357, -41, -207, -516, -669, -185],\n [-386, 976, 683, -318, 272, 172, 264, 62, 369, -123, 336, 215],\n [-487, 1156, 613, -330, 17, 311, 68, -130, 587, 91, 433, 510],\n [443, -1020, -269, 234, 459, -427, 340, 426, -755, -475, -469, -850],\n [-78, -333, -391, 196, -4, 3, 113, 7, -197, -206, -340, -170],\n [-209, -479, -796, 354, -259, 124, 3, -169, -168, -159, -531, -40],\n [-734, 332, -215, 142, 360, 232, 684, 110, -85, -765, -536, -215],\n [-305, -368, -638, 316, 13, 91, 272, -12, -254, -422, -595, -225],\n [-623, 1279, 412, -290, -317, 484, -163, -375, 808, 319, 467, 840],\n [-87, 934, 825, -414, 65, 105, -86, -28, 487, 281, 641, 400],\n [-143, -266, 115, 94, 925, -251, 938, 600, -635, -1025, -547, -930],\n [447, -536, -185, 74, -225, -171, -352, -50, -135, 325, 63, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-305, 1406, 591, -416, -671, -151, -190, -1011, 905, -316, -241, 862],\n [125, 1154, -1117, -1180, 29, -457, 659, -821, -817, -306, -1452, 393],\n [143, 633, 602, 201, -441, 463, -221, 389, 160, -106, 373, 282],\n [452, 1255, -667, -225, 791, 206, 707, -75, -998, -911, -645, 622],\n [624, 1372, -346, -144, -486, 450, 455, -438, -743, 14, -716, 293],\n [-941, -161, 718, 77, -550, -343, -700, 50, 584, 95, 620, -341],\n [162, -26, 267, -326, -449, 302, -91, 82, 467, 137, -71, 339],\n [162, -563, 234, 799, 1205, -168, -76, 769, 177, -451, 889, 36],\n [504, 61, 705, 349, -397, 1074, -63, 345, 480, 1, 375, 504],\n [791, -1006, -901, 906, 1992, -703, 519, 532, -642, -111, 317, -421],\n [1080, -1076, -1157, -36, 273, 850, 976, -521, -761, 595, -1051, -189],\n [-365, -659, 425, 221, 206, 231, -240, 310, 410, -209, 514, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[244, 312, 253, 713, 430, 669, -753, -681, 1562, -69, 75, 77],\n [2026, -93, 1321, -424, 114, -883, 175, -133, 935, 249, 1476, 919],\n [462, -531, 1101, 967, 407, -7, -718, 7, -248, 577, 1292, -167],\n [-538, 780, -253, -159, -734, -1532, -698, -953, 860, 663, 211, 661],\n [-73, -310, 646, -899, -479, 910, 1120, 809, -274, -1120, -809, -150],\n [-146, 251, 1140, 114, -964, 1383, 1138, 1562, 674, -2260, -832, 984],\n [-867, 1049, -560, -690, -551, -166, 411, 235, -1349, -48, -672, 133],\n [501, -667, 347, -728, 232, 752, 727, 368, -844, -351, 523, -257],\n [884, -1795, 1208, -231, 1109, 638, 604, 92, 7, 103, 851, -688],\n [1178, -16, 76, -754, 573, -345, 503, -4, -570, 518, 870, 293],\n [397, -912, 748, 146, 399, 702, -191, 215, -27, 374, 453, -537],\n [-175, 124, -399, -1056, -797, -1360, 710, -24, 2, -109, 328, 997]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[1016, 1382, -477, -816, -1304, -97, 106, 200, 640, -708, 590, 289],\n [214, -297, 453, 390, 289, 217, 251, 382, 427, -174, 271, -88],\n [-718, -725, 380, 394, 807, -350, -281, 92, -151, 782, -411, -197],\n [-996, -597, 295, 797, 366, 19, 600, 96, -647, 253, -430, -42],\n [-234, 77, -204, -734, 341, -972, -1303, -194, 171, 1146, -407, -123],\n [-188, 76, -490, -214, -202, 195, -32, -589, -694, -124, -255, 86],\n [730, 800, -64, -471, -645, -225, -63, 387, 772, -277, 466, 116],\n [6, 247, -408, 8, -515, 492, 529, -382, -603, -624, -7, 171],\n [168, 134, -464, -210, -292, 466, 104, -554, -518, -470, -18, 102],\n [-24, -42, -323, -308, 72, 28, -392, -463, -330, 118, -185, -9],\n [510, 686, -439, -821, -475, -331, -609, -174, 298, 59, 121, 87],\n [252, -630, 56, 324, 450, 863, 196, -391, -296, -526, 123, -90]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-454, 91, -200, 386, -120, 171, -93, -310, 184, 53, -189, -241],\n [593, -598, 341, -266, 28, -850, -596, 976, 244, -385, -242, 495],\n [1380, -44, 13, -304, -268, 283, -979, 552, -863, -1100, 428, -539],\n [-670, -819, -761, 593, 359, -673, 321, -180, 1344, 766, -913, 265],\n [457, -441, -1313, 860, -21, -155, 212, 535, 628, 383, -1152, -73],\n [-62, 999, 171, -396, -358, 336, 204, 88, -781, 177, 129, -30],\n [405, 1107, -196, -260, -459, 270, 779, 602, -987, 471, -130, 239],\n [191, -724, 210, -66, 71, -757, -592, 456, 429, -334, -133, 270],\n [-17, 99, -463, 1490, -762, 340, -501, 518, -11, -585, -698, -386],\n [876, 917, -967, 397, -399, 848, 723, 552, -811, 311, -506, -273],\n [-434, 678, 298, -355, 123, 539, 867, -643, -449, 481, 554, 58],\n [313, 32, -564, 193, -488, 242, -673, -354, -624, -585, 353, -867]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1049, -178, -250, -713, -1121, -614, 675, -51, 527, -168, -478, -850],\n [2086, 735, -1335, 1205, 1317, -450, -786, 576, 150, 106, -801, 1063],\n [0, -1535, 461, -748, -865, -538, 1078, -1069, 668, -529, -419, -58],\n [-1337, -128, 478, -895, -1495, -487, 891, 472, 32, 509, -123, -1638],\n [401, -640, -371, 1531, 754, 465, 57, 37, -481, 222, 256, 645],\n [-430, 340, -192, 857, -284, -194, 513, -28, 1083, 706, 911, -231],\n [624, 557, 34, 575, 630, 730, -1236, 1266, 394, 382, -1147, 1467],\n [1263, 250, 507, -44, 44, 234, -593, 627, 465, -332, -446, 960],\n [1197, 533, 459, -820, 421, 239, -745, 1436, 999, -436, -1561, 1154],\n [-475, -4, 594, -662, -218, 679, -600, -597, -592, 209, 59, 562],\n [-1770, -1492, 629, -307, -880, -439, 768, -1446, -855, -548, 690, -1231],\n [937, 41, -190, 682, 1300, 915, -1176, -11, -1478, 290, -283, 1309]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-51, 174, -516, -641, -413, -281, 834, -457, 135, -36, -451, 584],\n [961, 584, -36, 115, -100, 133, 484, 27, 1320, -522, 16, 668],\n [796, 900, -69, 28, -1032, 23, 136, 363, 661, 286, -1001, -216],\n [-78, 438, -429, -380, -953, 201, -22, 1150, -1031, 1054, -1236, 623],\n [-338, -854, 250, -704, 1548, -563, -128, -54, -600, -24, 835, 884],\n [143, -1068, 461, -537, 1212, -918, 416, -213, -186, 165, 245, 375],\n [-18, -60, 78, 132, 456, 12, 201, -1196, 877, -752, 771, -293],\n [-303, 621, 1277, -69, 1295, 62, 182, -607, -229, 766, 474, 134],\n [733, 389, -563, -731, -272, -456, 565, 442, 552, -378, -330, 1178],\n [-2011, 248, 243, -83, -138, -81, -1574, -288, -401, -732, 674, -1788],\n [-882, -397, -619, -373, -422, -299, 598, -522, -46, -679, 42, 16],\n [-532, 381, 946, -236, 595, -74, -1182, 1007, -634, 768, -129, -194]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[180, 423, 9, -9, -324, -81, -378, 153, 108, 63, -351, -342],\n [70, -251, -88, -182, 93, -3, 411, 4, -201, -181, 312, 284],\n [-4, 323, 73, 143, -168, -21, -438, 41, 192, 163, -351, -326],\n [-478, -597, 92, 250, 583, 179, 297, -336, 21, 93, 364, 380],\n [48, -275, -83, -169, 118, 5, 420, -11, -198, -175, 325, 298],\n [778, 471, -260, -622, -685, -257, 189, 480, -327, -399, -52, -116],\n [-646, -604, 169, 425, 681, 228, 129, -427, 147, 226, 273, 310],\n [-370, -177, 134, 316, 301, 119, -153, -222, 183, 213, -26, 8],\n [684, 167, -283, -653, -472, -209, 498, 389, -432, -473, 221, 146],\n [-8, 369, 85, 167, -190, -23, -504, 45, 222, 189, -403, -374],\n [-556, -254, 204, 480, 446, 178, -246, -332, 282, 326, -52, 0],\n [800, 495, -265, -635, -710, -265, 180, 495, -330, -405, -65, -130]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[611, 205, 524, -309, -152, 1143, -351, -933, -914, -1277, -1458, -33],\n [-810, -1847, -374, -583, -873, 1146, 456, 456, -868, -715, -1332, 668],\n [-490, -187, 671, 1213, -871, -948, -517, -78, 826, -1153, 804, 830],\n [1383, 397, -107, 169, 264, -330, -921, -497, 383, -293, -460, -1022],\n [-716, -755, -103, -388, -608, -712, 307, 1291, 1669, 846, 1268, 1402],\n [-433, 4, 899, 1385, -136, -132, -379, -163, 665, -200, 951, -666],\n [810, -16, 211, 832, -779, -355, -1372, -535, 492, -784, -492, 43],\n [-13, -913, -999, -932, 5, 392, -17, 841, -189, 1159, -445, -576],\n [-392, -646, -597, -462, -679, -123, 487, 761, 778, 381, 324, 869],\n [1577, 361, -52, -96, 1148, -890, -1003, -129, 473, 739, -256, -876],\n [-779, -168, 1152, -1209, 353, 220, 407, 576, 52, -36, 356, 1769],\n [-1141, -1342, 600, 712, -145, 582, 878, 376, 206, -317, 273, 122]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-94, 667, -922, -34, -106, -444, 1027, 168, -1184, -394, 365, 24],\n [514, -1356, 1368, 1087, -302, 1212, -1470, -145, 735, -679, 268, -134],\n [65, -1470, -158, 1525, -1509, 1291, -716, 186, -382, -228, 91, -597],\n [536, -478, -682, 743, -742, -448, -842, -411, 387, 1277, -334, -202],\n [-735, 756, 1177, -1405, 1532, 336, 886, 898, 178, -1116, -164, 729],\n [-685, -249, -411, -34, -945, 103, -776, -243, 750, 1312, -327, 180],\n [186, -1698, -416, 396, -746, -223, -1400, -1745, -97, -561, 507, -574],\n [-567, -312, -857, 12, -573, -105, 489, -61, 359, -104, 395, -530],\n [-1157, -413, 481, -629, -80, 674, 31, -192, -295, -22, 212, -715],\n [-694, -1103, 164, -401, -343, 299, -389, -1083, 263, 173, 285, -1468],\n [711, -1421, -302, 760, -547, 227, -495, -509, -150, -5, -417, -1057],\n [-829, -1801, 71, 166, -983, 930, -675, -726, 199, 366, 17, -1693]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[36, 252, -342, 396, -450, -414, -216, -342, 54, 360, 216, -54],\n [24, 168, -228, 264, -300, -276, -144, -228, 36, 240, 144, -36],\n [12, 84, -114, 132, -150, -138, -72, -114, 18, 120, 72, -18],\n [-46, -322, 437, -506, 575, 529, 276, 437, -69, -460, -276, 69],\n [-18, -126, 171, -198, 225, 207, 108, 171, -27, -180, -108, 27],\n [-2, -14, 19, -22, 25, 23, 12, 19, -3, -20, -12, 3],\n [-4, -28, 38, -44, 50, 46, 24, 38, -6, -40, -24, 6],\n [16, 112, -152, 176, -200, -184, -96, -152, 24, 160, 96, -24],\n [24, 168, -228, 264, -300, -276, -144, -228, 36, 240, 144, -36],\n [-18, -126, 171, -198, 225, 207, 108, 171, -27, -180, -108, 27],\n [12, 84, -114, 132, -150, -138, -72, -114, 18, 120, 72, -18],\n [-18, -126, 171, -198, 225, 207, 108, 171, -27, -180, -108, 27]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-191, -434, -403, 852, -1634, -201, 767, -52, -1016, -195, -507, -888],\n [228, 1201, -346, -307, -440, -30, -1515, -528, -509, -222, 492, -723],\n [-140, -242, -7, -458, -461, -283, -708, -125, -411, 195, 343, -577],\n [-412, -490, -401, 1671, -349, 409, 1557, 9, 188, -213, -163, 2],\n [-513, 241, -780, 625, -1645, 341, -516, -451, -1407, -489, -519, -900],\n [434, -589, -394, -679, -1519, -638, -156, 715, -440, 682, 1185, -1725],\n [668, 573, 693, 420, -559, -754, -347, -90, -775, 378, 605, -1030],\n [582, 546, 446, -443, 399, -471, 5, 256, 458, 435, 887, 121],\n [-574, -448, 256, -175, 311, -153, -406, -483, 3, 41, 14, 297],\n [323, 1452, -872, 576, 471, 582, -708, -662, 654, -766, 239, -226],\n [55, 1069, -392, 240, 1110, 412, -716, -906, 806, -800, -283, 505],\n [-462, 305, -25, 408, -205, 209, -220, 61, -13, 567, 1599, -78]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[489, 115, -747, 1131, -327, 1410, 1001, -363, 82, 479, 140, 48],\n [-1144, -1449, -949, -312, -811, -445, -1084, 287, -1127, 698, -1055, 299],\n [-379, -290, -97, -966, -145, -1498, -240, 593, -160, 125, -549, -273],\n [-882, -133, -139, -505, 244, -327, 361, 251, 930, -298, 139, -1009],\n [-1583, 1009, -591, 815, 562, 506, 782, -583, 504, -668, 1617, -1074],\n [-401, 689, 295, 617, 368, 819, -351, -1849, -44, 166, 532, -506],\n [-228, 1097, 490, 726, -251, -374, 375, -520, 778, -1644, 1050, -203],\n [-517, 412, -1535, 1227, -476, 1584, 815, 518, -662, -8, 211, -942],\n [182, 537, 267, 1031, -80, 645, -822, -492, 302, 631, 32, -180],\n [184, 1138, -504, 1311, -127, 1619, 411, -845, -438, -180, 674, -391],\n [40, -720, 92, 249, -146, -421, -818, -906, -633, 1338, -493, 710],\n [135, -350, 395, -1218, 769, 374, -305, 982, 478, 147, -395, -180]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[503, 18, -571, -333, -332, 669, -559, 214, 761, -911, -480, -673],\n [-755, 1121, -105, -134, 397, 1450, 529, 364, -1, -700, 49, -28],\n [363, 432, 490, 915, 700, 676, 419, 134, -447, 236, 64, 1],\n [-598, 457, 21, -161, -537, 178, 116, 12, 34, -60, 133, 449],\n [684, -1080, 418, 187, -1115, -453, -1125, -95, -163, 630, -503, -226],\n [-474, 459, 296, 294, 743, -725, 514, -294, 61, 456, 913, 697],\n [-406, 610, -1012, -969, 53, 789, 131, 259, 855, -1384, -187, -442],\n [-88, -621, -173, -719, -365, 549, -754, 248, -34, -335, -634, -802],\n [785, -434, 279, 490, -321, -739, -814, -269, 546, 394, 194, 42],\n [-1099, 265, -336, -914, 1005, -443, 257, -126, 433, -303, 733, 44],\n [375, 293, 473, 1014, -137, 121, 751, 0, -825, 593, -82, 565],\n [375, 641, 628, 1057, 520, 750, 64, 93, -62, 211, 258, 102]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-51, 51, 204, 102, 374, -102, -204, 340, 85, 170, 442, 68],\n [3, -3, -12, -6, -22, 6, 12, -20, -5, -10, -26, -4],\n [78, -78, -312, -156, -572, 156, 312, -520, -130, -260, -676, -104],\n [78, -78, -312, -156, -572, 156, 312, -520, -130, -260, -676, -104],\n [-45, 45, 180, 90, 330, -90, -180, 300, 75, 150, 390, 60],\n [72, -72, -288, -144, -528, 144, 288, -480, -120, -240, -624, -96],\n [-45, 45, 180, 90, 330, -90, -180, 300, 75, 150, 390, 60],\n [69, -69, -276, -138, -506, 138, 276, -460, -115, -230, -598, -92],\n [9, -9, -36, -18, -66, 18, 36, -60, -15, -30, -78, -12],\n [45, -45, -180, -90, -330, 90, 180, -300, -75, -150, -390, -60],\n [39, -39, -156, -78, -286, 78, 156, -260, -65, -130, -338, -52],\n [-39, 39, 156, 78, 286, -78, -156, 260, 65, 130, 338, 52]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[590, 508, -270, -262, -2, 444, -398, -380, -348, 1030, 108, 282],\n [-86, -42, -201, -90, -150, 48, 142, -138, 143, -12, 113, 123],\n [-236, -122, -501, -220, -380, 108, 372, -338, 373, -62, 283, 303],\n [356, 302, -129, -140, 20, 252, -252, -202, -223, 602, 47, 147],\n [-439, -296, -414, -133, -383, -42, 511, -212, 495, -413, 249, 210],\n [-466, -322, -381, -110, -370, -72, 522, -178, 503, -472, 233, 183],\n [358, 276, 78, -30, 150, 156, -326, -36, -304, 486, -64, 6],\n [-94, -112, 276, 166, 146, -180, -18, 248, -34, -298, -142, -204],\n [251, 130, 531, 233, 403, -114, -395, 358, -396, 67, -300, -321],\n [-438, -396, 342, 270, 90, -396, 246, 396, 204, -846, -156, -306],\n [-454, -362, -9, 86, -134, -240, 382, 118, 351, -668, 33, -69],\n [20, 30, -105, -60, -60, 60, 20, -90, 25, 90, 55, 75]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-89, 251, 197, 382, -537, -741, 367, 280, -205, 987, -411, 627],\n [-361, 940, 807, 439, -440, -964, 279, -483, 250, 488, -1138, 341],\n [162, 443, 45, -4, -382, -316, -72, -34, 269, 362, -559, 643],\n [510, -686, -890, -425, 77, 655, -222, 683, -207, 69, 804, 252],\n [34, 410, -18, 23, -343, -461, 222, 219, -55, 721, -452, 484],\n [57, -140, -224, -203, 200, 268, -33, 101, -75, -156, 246, -222],\n [108, 380, -699, -582, 66, -114, 494, 780, -501, 982, -68, 1],\n [312, 6, -803, -765, 355, 561, -42, 445, -136, -1, 308, -221],\n [-560, 727, 1134, 846, -534, -1180, 388, -566, 132, 526, -1043, 296],\n [226, -93, -289, -208, -2, 232, -164, 134, 75, -50, 121, 173],\n [-158, 704, -78, -692, 658, 342, 10, -400, 190, -622, -352, -926],\n [163, 103, 90, -210, 183, 443, -539, -566, 588, -929, -131, -88]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[294, 663, -1601, -783, -259, -804, -82, -126, -1223, -640, -370, 260],\n [526, 732, 2112, 261, 274, 11, 434, -339, 450, -753, -1015, 484],\n [672, -236, 847, -410, 223, -396, 564, -34, -211, -511, -500, -204],\n [143, -1429, 798, 1402, 120, 1281, -462, 122, 2342, -997, 692, -373],\n [-194, 367, -525, -763, 458, -1085, 272, 178, -1956, -93, 281, 805],\n [719, -948, 1709, -734, 38, -727, 1208, 754, -547, -333, -695, -972],\n [1068, -2423, 719, -671, -389, -1692, 1168, 113, -631, -26, 440, -598],\n [234, -523, 218, 179, 128, 248, 81, 179, 359, -659, -51, -341],\n [216, -1125, 610, -358, 193, -574, 216, 634, 230, 229, -319, -489],\n [-187, 803, 160, 596, 73, 736, -184, 177, 424, -354, -191, 111],\n [170, -388, -309, -555, -431, -433, 147, -789, -152, 1129, 188, -242],\n [943, -560, 718, -137, -377, -882, 175, -246, 664, -792, -1055, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-17, -797, 505, 725, 435, 85, 341, 263, -571, -515, 237, -428],\n [-115, -201, -259, 74, -132, -200, -95, 373, -342, 227, -256, -380],\n [442, -331, 700, 589, 761, 154, 191, -101, -203, -636, 312, -39],\n [211, 802, 175, -538, -12, 307, -22, -808, 926, -113, 321, 913],\n [305, -184, -19, 298, 324, -241, -188, 370, -446, 41, -267, -427],\n [-572, -407, -554, -19, -579, -248, -13, 587, -475, 454, -342, -569],\n [838, 261, -170, 166, 594, -469, -601, 401, -402, 256, -587, -421],\n [785, 184, 467, 295, 809, -8, -164, -168, -1, -359, 50, 99],\n [89, -521, 677, 572, 502, 254, 385, -103, -196, -657, 438, -36],\n [-102, -138, 498, 136, 140, 364, 378, -406, 264, -490, 508, 360],\n [-486, -455, 606, 228, -56, 529, 675, -431, 236, -644, 739, 359],\n [395, 208, -457, -46, 112, -463, -524, 470, -358, 483, -621, -441]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-798, 347, 915, -1296, -890, -1188, -637, 1147, 1779, 136, 805, 103],\n [477, 902, -123, 491, 175, -41, 284, -477, -94, -95, 64, -832],\n [-149, 472, 1411, -1304, 189, -119, 100, 412, -60, 359, -84, 522],\n [324, 63, 45, 718, -752, -764, 163, -718, -282, 18, 662, -959],\n [176, 214, -14, 426, 1472, 967, 816, -324, -297, 722, -524, 557],\n [335, 148, 1366, -536, 148, -230, 384, -624, -1080, 346, 139, 365],\n [-238, 739, 66, -985, -733, -633, -939, 816, 1075, -855, 240, -288],\n [409, 558, 487, -778, 111, 124, -340, -175, -766, -717, -319, 229],\n [197, 898, -425, 522, 943, 437, 394, -121, 567, 213, -159, -246],\n [-390, 427, -863, -512, 200, 454, -681, 1118, 1222, -646, -494, 133],\n [479, 19, -918, 1062, 239, -10, -143, -926, -225, -559, 254, -112],\n [2, -188, -356, 707, 434, 197, 384, -286, 134, 428, 73, 51]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[368, 634, 898, -780, -575, -19, -74, -143, -635, 357, -311, -458],\n [1173, 1401, 71, 240, -481, -583, 181, 130, 145, 607, 398, -1111],\n [-680, -632, -240, 442, -238, 641, -598, 25, 1159, -1195, -36, 69],\n [-889, -729, -544, 209, 459, 163, 549, 304, -291, -243, 375, 1388],\n [-464, -404, 542, -366, -1163, 711, 162, 415, 319, -73, -69, -360],\n [46, -917, -544, 94, 949, -63, -388, -571, 285, 235, -591, 34],\n [114, 226, -187, 136, 538, -350, 52, -90, -362, 24, 130, 341],\n [-52, 21, -100, -258, 503, -328, 560, 14, -966, 562, 121, 797],\n [499, 83, 880, -830, -937, 413, -631, -458, 373, 325, -876, -1314],\n [907, 418, 52, 43, 488, -708, 111, -117, -502, 964, -102, -826],\n [712, 197, 464, -1135, -529, 129, -118, -725, -161, 1085, -876, -540],\n [-1053, -982, 94, -85, 431, 268, 259, 315, -672, -368, 45, 1023]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-244, 1757, 425, 111, -753, 667, 841, 517, -123, 1888, -224, 580],\n [1075, -627, -381, -76, -151, -1054, 451, -314, -198, -108, -638, 161],\n [379, -306, -45, 1242, -771, -1090, -1001, -294, 558, 289, 19, -68],\n [-1696, 813, -1304, -827, 1311, 15, 1437, 605, 685, -870, -440, 131],\n [-874, -292, -1298, -273, 90, -465, 272, -34, 836, 403, 283, 847],\n [-26, -578, -1427, -42, 969, -307, 601, -264, 194, -735, -727, -408],\n [-58, -170, -115, -468, 473, 1403, 1050, -521, -693, 585, 775, 46],\n [-485, -194, -492, 352, -499, -726, -693, 332, 316, 731, 855, 587],\n [-260, 862, 1384, -767, -766, 1073, -283, 143, -847, 835, 847, -565],\n [-935, -255, -887, -233, 702, 497, 19, 1416, 1946, -1543, 467, 39],\n [-842, 1082, 206, -79, -460, 579, -336, 59, 437, 18, -421, -1230],\n [335, 777, 112, -187, -1026, -464, 720, -457, -1136, 1351, -803, 242]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -325, 1567, -540, -469, -794, 852, -267, 843, 130, 899, 711],\n [358, 222, -381, 382, 365, -904, -597, -189, 94, -541, 399, 181],\n [55, -198, -85, 74, 396, -14, -336, 615, -658, -197, -101, -230],\n [-544, -116, -831, 573, -135, -105, -1207, 21, -104, -67, 239, 658],\n [405, 95, -664, 19, 404, -213, -1563, 881, 182, -905, 244, 620],\n [341, 315, -684, 33, 417, 404, -159, 257, -474, -320, -604, -802],\n [191, 445, -211, -59, 596, -204, -517, -25, 171, -392, -136, -340],\n [-200, -429, -354, 78, -350, 967, 118, -99, 296, 550, -994, 80],\n [48, -638, -807, 1040, 53, 158, 557, -865, -388, 747, -1329, -487],\n [-440, -281, -469, 379, -895, 474, 149, -458, 200, 587, -23, 654],\n [-176, -321, 722, -380, -844, 279, 1651, -296, -283, 383, -21, -571],\n [-229, -39, -1494, 471, -1108, 977, 43, -693, 304, 243, -748, 86]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[206, 144, -96, 250, 348, -14, -374, 520, -410, 398, -100, -352],\n [11, -156, -60, 355, 276, -419, -143, 388, -533, 497, -250, -274],\n [161, 114, 282, 124, -3, 331, -473, 220, -89, 44, 134, -313],\n [-1, -194, -230, 434, 429, -651, -59, 508, -707, 682, -386, -281],\n [125, 20, 20, 273, 240, -85, -329, 412, -395, 363, -102, -330],\n [126, 189, 446, -148, -306, 696, -393, -146, 364, -397, 367, -111],\n [-402, -398, 348, -282, -648, -82, 540, -860, 562, -584, 138, 482],\n [424, 321, -84, 443, 597, 134, -805, 962, -700, 670, -107, -698],\n [441, 584, -412, 17, 540, 391, -441, 660, -207, 271, 22, -290],\n [-297, -433, 188, 86, -243, -437, 306, -318, -33, -11, -119, 142],\n [-302, -298, -416, -84, 30, -702, 752, -300, -6, 58, -294, 440],\n [389, 441, -374, 167, 582, 169, -452, 738, -405, 444, -83, -373]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-499, 85, -28, 597, -346, 227, 579, -814, 370, 549, 608, -147],\n [-336, -613, -146, -544, 391, 512, 342, 151, 1226, 416, 335, 88],\n [-339, 1854, -595, 1166, -1727, 1077, 750, 603, -748, 715, -994, -970],\n [699, -655, -63, -764, 651, 123, -131, -934, 859, 803, -698, 379],\n [-166, 600, -563, 56, -411, -403, 564, 96, -622, -647, -1190, 81],\n [-170, -834, 352, -433, 676, -696, -434, 423, 307, -716, 664, 390],\n [1016, -308, 345, 260, 659, 483, -406, -300, -840, 467, 232, -49],\n [-57, -16, 5, 814, -77, -179, 88, -774, -476, 67, 604, 109],\n [244, 569, -360, 56, -222, -326, 197, 538, -1037, -672, -1302, 2],\n [1099, -432, 700, -582, 737, 663, -644, -222, 71, 877, 110, -222],\n [658, -1624, -263, -945, 1700, -499, -405, -505, 340, -545, 141, 1130],\n [-9, -328, 293, -906, 209, -654, -371, -455, 786, -190, -101, 263]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-126, -188, -112, -5, 184, 190, -292, 47, -10, 514, -449, 1068],\n [-16, -1023, -281, -195, 367, -475, 1257, -472, -258, 358, 135, -157],\n [144, -389, -194, 118, 458, 182, 868, -55, -419, 638, -304, 275],\n [844, -7, -278, 913, -286, 778, -138, 348, -333, 472, -317, -573],\n [-577, -650, -47, -367, 599, -254, 338, -332, 220, 46, 53, 1043],\n [144, -291, -222, -130, -214, -183, -65, -46, -267, 770, -502, 466],\n [55, 163, 164, 318, 394, 293, 697, 18, 62, -748, 616, -960],\n [723, -395, -349, 403, -455, 29, 311, 6, -437, 596, -213, -819],\n [413, 699, 112, 198, -386, 186, -90, 291, -262, -40, -58, -865],\n [69, 681, 185, -34, -669, -50, -1062, 230, 233, -366, 36, -324],\n [-437, -239, 107, -408, 301, -425, 415, -289, 195, -386, 368, 69],\n [-5, -78, 22, 388, 568, 521, 451, 65, 35, -230, 188, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-132, -110, -330, -220, 88, 572, 220, -418, -198, 0, -462, -264],\n [36, 30, 90, 60, -24, -156, -60, 114, 54, 0, 126, 72],\n [90, 75, 225, 150, -60, -390, -150, 285, 135, 0, 315, 180],\n [-150, -125, -375, -250, 100, 650, 250, -475, -225, 0, -525, -300],\n [-24, -20, -60, -40, 16, 104, 40, -76, -36, 0, -84, -48],\n [144, 120, 360, 240, -96, -624, -240, 456, 216, 0, 504, 288],\n [96, 80, 240, 160, -64, -416, -160, 304, 144, 0, 336, 192],\n [12, 10, 30, 20, -8, -52, -20, 38, 18, 0, 42, 24],\n [-54, -45, -135, -90, 36, 234, 90, -171, -81, 0, -189, -108],\n [48, 40, 120, 80, -32, -208, -80, 152, 72, 0, 168, 96],\n [-102, -85, -255, -170, 68, 442, 170, -323, -153, 0, -357, -204],\n [72, 60, 180, 120, -48, -312, -120, 228, 108, 0, 252, 144]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-546, 338, 364, -442, 208, 390, -104, -182, -364, 104, 468, 286],\n [231, -143, -154, 187, -88, -165, 44, 77, 154, -44, -198, -121],\n [-273, 169, 182, -221, 104, 195, -52, -91, -182, 52, 234, 143],\n [-483, 299, 322, -391, 184, 345, -92, -161, -322, 92, 414, 253],\n [105, -65, -70, 85, -40, -75, 20, 35, 70, -20, -90, -55],\n [-126, 78, 84, -102, 48, 90, -24, -42, -84, 24, 108, 66],\n [420, -260, -280, 340, -160, -300, 80, 140, 280, -80, -360, -220],\n [336, -208, -224, 272, -128, -240, 64, 112, 224, -64, -288, -176],\n [483, -299, -322, 391, -184, -345, 92, 161, 322, -92, -414, -253],\n [-525, 325, 350, -425, 200, 375, -100, -175, -350, 100, 450, 275],\n [-42, 26, 28, -34, 16, 30, -8, -14, -28, 8, 36, 22],\n [231, -143, -154, 187, -88, -165, 44, 77, 154, -44, -198, -121]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-158, 267, 9, 565, 182, 187, 126, -151, 285, 152, -510, -328],\n [912, 417, 682, 235, -209, 473, 357, 78, -546, -579, -179, 280],\n [0, 202, 230, 160, -245, 405, -34, 204, -258, -77, -362, -12],\n [-491, -437, -298, -1159, 159, -683, -994, 125, -666, 465, 697, 254],\n [690, -51, 50, -121, -357, 149, 639, 292, 198, -507, 509, 316],\n [-974, -569, -272, -167, -375, -9, -421, -12, 126, 168, -237, -78],\n [-266, -336, -340, -590, 499, -791, -500, -302, -66, 380, 568, 46],\n [609, -471, 138, 347, -795, 379, 1160, -23, 726, -1035, 211, 354],\n [-413, -205, -38, 613, 165, -67, 128, -615, 516, -8, -533, -288],\n [-40, -412, -382, -806, -605, -13, 60, 722, 72, -102, 814, 350],\n [-557, 330, 110, -398, 356, -94, -1139, 131, -990, 704, -338, -150],\n [30, 1243, 280, 257, 527, 469, -617, 516, -834, 778, -701, -438]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[566, 857, 425, 622, 755, 484, 666, 635, -348, -375, 344, -962],\n [224, -49, -160, -292, -317, -222, -583, -342, 696, 380, -924, -546],\n [163, -193, 797, 253, -1060, -33, 117, 498, -609, -1055, 33, -192],\n [327, 161, -184, 7, 269, 334, 294, 96, -27, 120, 26, -165],\n [-542, -116, -150, -192, 254, -815, -774, -611, 439, 490, -399, 322],\n [189, 55, -48, -62, -128, 151, 45, 6, -61, 109, -41, -123],\n [516, -624, -292, -592, -39, -1387, -838, -880, 76, 467, -1621, 210],\n [520, -710, -149, -481, -380, 128, 916, 191, -932, 797, 836, -280],\n [402, -8, 1054, 340, -1032, -741, -422, 203, -885, -1326, -749, -68],\n [-345, -898, 362, -306, -1287, -557, -388, -55, 37, -302, -213, 92],\n [74, -787, 174, -237, 267, -1267, -32, -219, -231, 254, -327, -196],\n [764, 267, -398, -75, 670, -581, -370, -629, -682, -174, -1169, 1089]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-233, -83, -175, 614, -188, 62, 153, -771, -105, 151, 424, -105],\n [-534, 1142, 1158, -798, 114, 214, -752, 1150, 228, -1214, 298, -574],\n [-441, 187, -931, 300, 1483, 129, 719, -522, 98, -696, 203, -887],\n [102, -755, 510, -851, -1, 177, 988, 960, 555, -1516, 614, -1028],\n [43, 777, -358, 878, 73, -1125, -944, -170, -135, 1603, -561, -274],\n [-295, 1425, 571, -1385, 542, -555, -1056, 1435, -580, 99, -111, -353],\n [-97, -1329, -704, 15, -340, -239, 759, -271, 539, -350, 453, -650],\n [200, 4, 31, -775, 353, 672, 44, 53, -718, 171, -110, 980],\n [-89, -475, -953, 1609, 41, 527, -1, -2039, -307, 1253, 55, 820],\n [-256, -144, 173, 6, -233, 813, 131, -673, -389, -231, 575, 562],\n [-47, -442, -989, 32, -113, 107, 55, -1030, -673, 936, -110, 1066],\n [-104, 361, 32, 356, 131, 71, -430, -645, -892, 1241, 478, 165]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[338, -130, 78, 221, 221, -156, 104, -169, -338, 247, -169, 143],\n [-78, 30, -18, -51, -51, 36, -24, 39, 78, -57, 39, -33],\n [-104, 40, -24, -68, -68, 48, -32, 52, 104, -76, 52, -44],\n [-26, 10, -6, -17, -17, 12, -8, 13, 26, -19, 13, -11],\n [-572, 220, -132, -374, -374, 264, -176, 286, 572, -418, 286, -242],\n [182, -70, 42, 119, 119, -84, 56, -91, -182, 133, -91, 77],\n [676, -260, 156, 442, 442, -312, 208, -338, -676, 494, -338, 286],\n [650, -250, 150, 425, 425, -300, 200, -325, -650, 475, -325, 275],\n [-338, 130, -78, -221, -221, 156, -104, 169, 338, -247, 169, -143],\n [-78, 30, -18, -51, -51, 36, -24, 39, 78, -57, 39, -33],\n [286, -110, 66, 187, 187, -132, 88, -143, -286, 209, -143, 121],\n [156, -60, 36, 102, 102, -72, 48, -78, -156, 114, -78, 66]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[167, 368, 620, 883, 24, -418, -149, -135, 386, -162, -735, 616],\n [613, -183, -240, 417, 506, 506, 682, 585, -221, 587, 29, -207],\n [5, 36, -349, -524, 266, -66, -262, 159, -195, 86, 423, -600],\n [469, -247, 368, -79, 556, -1202, -306, -439, -247, 143, 355, -383],\n [445, -383, 925, 282, 214, -1502, -139, -699, -98, 39, 19, 77],\n [292, 194, -562, 226, 786, 52, -300, -376, -58, -34, 198, 154],\n [253, -283, 156, 109, -177, 440, 771, 794, -149, 505, -88, -329],\n [-148, -425, 88, 104, -714, 920, 987, 490, -29, 247, -198, 239],\n [-743, 57, -615, -550, -676, 1114, 94, 124, 87, -293, 101, 171],\n [330, 475, 243, 269, 543, -682, -542, 194, 113, 45, -203, -325],\n [204, -365, -598, 18, 36, 1220, 949, 646, -269, 503, 200, -133],\n [-718, -12, 344, -334, -853, -218, -319, -559, 244, -570, -141, 450]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[16, 2, -25, 13, 14, 17, 24, -12, 26, -23, 15, -14],\n [-416, -52, 650, -338, -364, -442, -624, 312, -676, 598, -390, 364],\n [-272, -34, 425, -221, -238, -289, -408, 204, -442, 391, -255, 238],\n [-64, -8, 100, -52, -56, -68, -96, 48, -104, 92, -60, 56],\n [128, 16, -200, 104, 112, 136, 192, -96, 208, -184, 120, -112],\n [-192, -24, 300, -156, -168, -204, -288, 144, -312, 276, -180, 168],\n [416, 52, -650, 338, 364, 442, 624, -312, 676, -598, 390, -364],\n [288, 36, -450, 234, 252, 306, 432, -216, 468, -414, 270, -252],\n [-304, -38, 475, -247, -266, -323, -456, 228, -494, 437, -285, 266],\n [-400, -50, 625, -325, -350, -425, -600, 300, -650, 575, -375, 350],\n [-112, -14, 175, -91, -98, -119, -168, 84, -182, 161, -105, 98],\n [224, 28, -350, 182, 196, 238, 336, -168, 364, -322, 210, -196]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[539, -341, -689, -359, 120, -370, 13, 152, -617, 247, 7, 383],\n [786, -444, -800, -540, 750, 54, -218, 460, -261, 196, 713, -179],\n [159, 31, 665, 595, -222, -128, 1231, -330, 300, -221, 422, 344],\n [-371, -286, -260, -943, -172, -61, -737, 263, 7, 219, -509, 433],\n [388, -651, -1033, 38, -330, 130, -305, 280, -390, -150, -344, -67],\n [-982, 602, 1029, -556, 444, 492, -778, 71, 994, 59, 174, -476],\n [707, -414, -835, 445, -46, 12, 210, 113, -493, -144, 101, -198],\n [14, -682, -218, -1394, 542, 417, -591, 685, 700, 130, 610, 145],\n [230, 13, 8, 342, 624, 721, -148, 248, 566, -293, 838, -1040],\n [-866, -74, 446, -1132, 110, 440, -954, 354, 891, 84, -119, 37],\n [-221, 439, 998, -67, 238, -210, 633, -271, 398, 122, 452, 326],\n [245, -717, -525, -889, -374, -517, 172, 189, -381, 265, -323, 1162]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[327, -1101, -320, -677, -1361, -1257, -178, 333, -1599, 713, -1331, 190],\n [687, -395, -236, 156, 711, 277, 82, 785, 1083, 510, -82, 272],\n [129, -971, -783, -735, -29, -375, -281, 412, -450, -486, -246, 203],\n [-18, 469, 150, -260, -274, 96, -154, -648, -409, -246, 367, -536],\n [468, 78, 1400, 571, -954, 674, 320, 498, -608, 593, -349, 282],\n [206, 247, -316, -600, 604, -1244, -490, -552, 541, 190, -109, 94],\n [-536, 130, -945, 376, 469, 500, 308, -146, 550, -86, 407, -595],\n [178, 62, -624, -580, 856, -102, -376, -280, 660, -558, 560, -216],\n [132, -1104, -787, -668, 176, -292, -257, 643, -235, -579, -241, 425],\n [-1063, 926, 13, 491, 253, -385, 145, -906, 245, -142, 243, -155],\n [-362, 489, 38, 704, -150, 1212, 480, -152, 67, -30, 551, -692],\n [258, -272, 1129, 692, -306, 1076, 382, 1003, -65, -7, -99, 711]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-300, -652, -297, -382, -61, -448, -587, 13, 518, 320, 875, -308],\n [274, 354, 739, 560, -363, 279, 236, 166, -821, -957, -840, 238],\n [533, 387, 753, 82, -232, 745, 1146, -431, -504, -339, -133, -435],\n [-258, 909, -155, 408, 461, 575, -62, -71, -439, -769, -470, 699],\n [273, -28, -1002, -150, 545, 279, 131, 13, -365, 59, -863, 833],\n [69, -1613, -312, -259, 225, -1050, 59, -231, 237, 1362, 854, -653],\n [-1224, 255, -731, 754, 755, -592, -1875, 482, -210, -894, -107, 1283],\n [803, 982, -1298, -1439, -791, 277, 700, 143, 931, -235, 346, 671],\n [849, 618, -340, -558, -1369, -584, 547, 415, -8, -1219, 249, 807],\n [170, -1314, 645, -50, 371, -23, 621, -509, 159, 1746, 275, -1488],\n [-1120, 309, -124, 200, 140, -448, -1577, 390, 715, -265, 670, 184],\n [-467, -448, 470, 1017, 659, 0, -626, 75, -916, -249, -858, 177]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[461, -256, -127, -327, 218, -282, 30, 175, 373, -47, -1087, -474],\n [-996, 798, -624, 420, 61, 863, 645, 249, -408, 432, 1371, 1231],\n [-1020, -191, -652, -308, 1716, 1037, -65, 1396, -151, 681, -245, 452],\n [160, -141, -633, -942, -787, -1128, 1047, -659, 1212, 348, -999, -327],\n [-900, 738, -240, -1216, -432, -365, 665, -733, 668, 410, 121, 635],\n [-721, 98, -327, -1095, -941, -1328, 724, -783, 1509, -117, 431, -94],\n [344, 24, -104, 1510, 917, 1435, -709, 1115, -1662, 378, -469, 353],\n [-551, -324, 454, -805, 430, -63, -604, -160, -92, 458, -433, -107],\n [976, 154, 1041, -109, 516, 669, -393, -184, -502, -780, 393, -179],\n [625, -176, -110, 29, 469, 416, 151, 265, -296, 254, -888, -130],\n [179, -960, 734, -122, -298, -503, -771, -611, -415, 479, -532, -649],\n [570, -391, 575, 1115, -210, 396, -582, -112, -1083, -45, 526, -143]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-40, 250, -111, -768, -263, -220, -175, -575, 253, -255, 99, -455],\n [242, -56, 209, 30, 467, 514, -29, 19, 497, 257, -223, -167],\n [164, -452, 154, 288, -430, 324, -190, 694, 130, 390, -426, 54],\n [-283, 784, -304, -834, 408, -641, 176, -1301, -104, -723, 684, -307],\n [-78, 534, -149, -924, 187, -278, -45, -1023, 303, -435, 321, -523],\n [-121, -77, -92, 135, -339, -243, 9, 187, -330, -62, 55, 178],\n [164, -602, 183, 600, -481, 368, -153, 1003, -21, 499, -491, 251],\n [398, -569, 349, 279, -172, 798, -280, 793, 607, 660, -696, -132],\n [-221, 173, -219, -321, -426, -515, -22, -280, -317, -329, 250, -33],\n [203, -14, 178, 36, 484, 441, 4, -29, 422, 203, -160, -133],\n [-373, 304, -321, -120, -259, -763, 165, -368, -681, -500, 499, 212],\n [-169, 532, -189, -588, 309, -391, 109, -896, -13, -472, 443, -240]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[692, 51, -1053, 237, 97, 464, -1352, -774, -14, -634, -480, 8],\n [-1027, 12, -467, -514, -376, -386, -193, -656, -574, -177, -1484, 571],\n [366, -486, 860, 169, 122, 107, 528, 906, 944, 301, 180, 0],\n [-10, -193, -116, -978, -182, -105, -15, -1229, 539, 539, 13, -692],\n [776, -1160, 174, -394, -1077, 718, 435, 460, 1295, -144, -351, -29],\n [232, -17, -872, -445, -255, -80, -624, -745, -92, -416, -646, 91],\n [757, -352, 58, -852, -400, 1119, -846, -705, 222, 1225, -1273, -984],\n [-41, -514, 168, -45, -233, -407, 1104, 1264, 260, -644, 253, 651],\n [385, -521, -1086, -896, -773, -478, 504, 222, -10, -1126, -259, 535],\n [-874, -189, 156, -261, -524, -252, 395, -312, 66, 6, -551, 336],\n [-1078, -119, -251, 835, -115, 132, -454, -771, 183, -768, -360, 670],\n [-433, 931, 685, 357, 476, -85, 25, -525, -567, 1006, 1160, -771]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[115, -93, 26, -932, -489, -30, 559, -780, -478, -187, -881, -559],\n [179, -895, -469, -269, -256, -22, -158, 616, 350, -325, 570, -1262],\n [-726, 199, -99, -1507, 779, 290, 830, -670, 318, -141, 87, -1064],\n [-307, -1235, -100, -321, 896, -197, -339, -145, 1062, 392, 44, -1413],\n [1417, -116, -376, 758, -1391, -342, -76, 1692, -998, -930, -692, -401],\n [1116, -467, 227, 1325, -745, -283, -1273, 1534, -234, -589, -145, 616],\n [1533, 1071, -97, 148, -847, -808, 447, 781, -1271, -142, -951, 1020],\n [139, -657, -459, 66, 688, -617, 127, 2, 666, 739, -31, -856],\n [-390, -591, -760, 282, -359, 157, 489, -882, 551, 1235, 161, -672],\n [-683, -287, -127, 591, 1446, -11, -77, -467, 1082, -30, -350, -278],\n [1181, -224, 389, 339, -558, -330, -1071, 267, 123, 277, -755, 1068],\n [-92, -1328, 457, -254, 377, -44, -679, -1203, 809, 127, -1524, -705]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[203, -454, -459, -521, -185, 422, 475, -96, -16, 135, -135, -541],\n [4, 328, 648, 512, 320, -584, -700, 132, -128, 0, 0, 352],\n [274, -332, -72, -268, 20, 76, 50, -18, -128, 180, -180, -428],\n [-613, 654, -12, 462, -130, -14, 75, 5, 320, -402, 402, 862],\n [634, -452, 450, -130, 350, -380, -550, 84, -416, 414, -414, -650],\n [301, -18, 597, 243, 355, -526, -675, 118, -272, 195, -195, -97],\n [219, -282, -90, -240, 0, 90, 75, -21, -96, 144, -144, -360],\n [-435, 430, -75, 275, -125, 50, 125, -10, 240, -285, 285, 575],\n [-215, -150, -744, -426, -410, 662, 825, -149, 256, -138, 138, -106],\n [-768, 864, 72, 648, -120, -96, 0, 24, 384, -504, 504, 1128],\n [322, -576, -447, -603, -155, 416, 450, -95, -80, 213, -213, -703],\n [-502, 256, -555, -55, -375, 480, 650, -107, 368, -327, 327, 405]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[678, -982, -136, -478, 422, -114, 132, -214, -186, 104, 326, -348],\n [-66, -6, -48, 66, 126, 198, 276, 138, -258, -48, 78, -84],\n [467, -662, -85, -332, 267, -105, 50, -164, -89, 77, 209, -223],\n [529, -552, 23, -414, -23, -483, -506, -414, 437, 161, 23, -23],\n [-538, 499, -61, 433, 126, 606, 692, 493, -614, -187, 44, -49],\n [-492, 451, -59, 397, 124, 564, 648, 457, -576, -173, 46, -51],\n [-526, 474, -68, 426, 146, 618, 716, 498, -638, -188, 58, -64],\n [-220, 267, 13, 165, -52, 132, 104, 129, -80, -53, -50, 53],\n [7, 105, 68, -27, -185, -213, -326, -135, 311, 44, -121, 130],\n [-279, 79, -140, 259, 361, 645, 870, 463, -807, -164, 217, -234],\n [-465, 610, 55, 340, -185, 195, 90, 220, -45, -95, -155, 165],\n [291, -391, -40, -211, 131, -105, -30, -127, 3, 56, 107, -114]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[325, 86, -182, 219, -401, 1336, 471, 676, 217, 916, -4, 297],\n [-287, 81, 309, 309, 182, 215, -680, 178, 1, 488, -248, -521],\n [18, 873, -296, -675, 1, 69, 498, 1077, -205, -334, 431, 827],\n [580, -99, -286, -765, -872, -1700, 931, 1096, 52, 819, 285, -41],\n [-1448, 660, 1134, -231, 400, 128, -380, 31, 784, 490, -863, -853],\n [722, 1326, 263, -272, -631, -273, 333, -1415, 577, 25, 48, 408],\n [-777, 88, 415, -740, -348, -18, 306, 120, 930, -309, -254, -348],\n [1284, 1751, 996, -291, -1018, -488, 18, -1361, -412, 840, 1168, -126],\n [14, 895, 1379, -15, 178, -702, 141, -1531, -1390, 1009, 25, -102],\n [-756, -1746, -31, -228, -56, 319, 73, 367, -1131, -255, -357, -191],\n [-705, -692, -308, -192, 323, 338, -132, 758, -722, -9, -833, 431],\n [566, -33, 861, -319, -1009, -26, 195, -240, -318, 955, 1032, -702]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[459, -710, 23, 65, 876, 367, -110, -1145, -301, -1677, 448, 503],\n [1313, 1134, -955, -245, 349, 554, -396, -815, -310, 86, -891, 2179],\n [214, 94, -382, 615, 762, 320, -989, -447, -539, -1333, -1347, 768],\n [-988, -327, 126, 181, 645, -320, -263, -151, 253, -1230, -337, -1364],\n [555, 778, 457, 723, -415, 587, -2119, -206, -968, 173, 422, 837],\n [-737, -600, -1043, -311, 335, -937, 1295, -534, -34, 65, -732, 315],\n [504, -24, 388, 265, 686, 857, -289, 78, 482, -678, 614, -586],\n [-146, 493, 399, 753, -216, 448, -712, 313, -10, 973, 284, -384],\n [631, -133, -251, -988, 1048, -93, -240, -1548, -237, -2404, -187, 1052],\n [303, -829, -753, 842, 21, 412, 1152, 2249, 574, 1558, 116, -587],\n [-203, -346, 1110, 524, -162, 141, -1266, -22, -643, -961, 34, -210],\n [-1129, 215, -1281, -333, 401, -1036, 502, -1185, -22, -156, -615, -144]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[106, -210, 469, 220, -17, -1137, 358, -12, 723, 1040, -417, -759],\n [764, -258, 315, 838, -624, -351, -181, 220, -272, 497, -717, -800],\n [-12, -219, 262, 87, -278, 81, 139, -259, -4, -307, -197, 290],\n [-107, 636, -504, -562, 294, 909, -635, 395, -343, -158, 594, -31],\n [36, -252, 125, 224, -62, -740, 253, 424, 706, 387, -719, -1634],\n [220, -130, -478, -400, 711, 251, -359, 564, -12, -362, 100, -592],\n [-523, 363, -475, 43, -508, 1172, -61, -10, -569, -1254, 114, 301],\n [43, -51, -125, 863, -427, -547, 362, 30, -168, 237, -374, -384],\n [-292, -394, 379, 10, -142, -583, 541, -120, 774, -57, -561, -646],\n [-262, 408, 497, 80, -618, -168, 121, -328, 249, 718, -19, 87],\n [-534, 347, 366, -165, -437, 63, 246, -459, 268, 203, 151, 486],\n [-67, -67, -29, 623, -845, 411, 128, 2, -349, -716, -554, -347]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[885, 135, -905, -270, 525, 485, -285, 130, 50, 275, -965, 480],\n [65, 115, -95, 95, 0, 40, -15, -5, 0, -50, -85, 120],\n [575, -299, -483, -598, 483, 299, -207, 138, 46, 437, -575, 0],\n [-834, -102, 846, 282, -504, -456, 270, -126, -48, -276, 906, -432],\n [-47, 203, -9, 244, -105, -17, 27, -36, -10, -155, 23, 144],\n [34, 518, -174, 550, -168, 40, 18, -66, -16, -332, -106, 432],\n [196, 404, -302, 349, -21, 123, -42, -23, -2, -189, -264, 408],\n [-523, 391, 407, 674, -483, -267, 195, -142, -46, -477, 507, 96],\n [-198, -522, 336, -477, 63, -129, 36, 39, 6, 267, 282, -504],\n [705, -69, -673, -408, 483, 379, -237, 128, 46, 337, -745, 240],\n [-486, 342, 384, 603, -441, -249, 180, -129, -42, -429, 474, 72],\n [520, -568, -356, -866, 546, 258, -204, 166, 52, 594, -480, -240]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1284, 483, 426, 403, 610, -446, 276, -858, -109, 593, -444, -213],\n [-110, -774, 851, -165, 1164, -318, -158, -946, 481, 913, -907, 33],\n [168, 486, 679, 772, 1627, -1560, 706, -35, -696, 1034, -2002, -388],\n [-1, -599, -1322, -1248, -227, 1314, -428, 701, 520, 1292, -36, 989],\n [-1426, 101, -363, -352, 468, 43, 482, 486, -1598, -343, -1907, 517],\n [-1713, -1474, 41, -1240, 62, 1074, 264, -36, -831, -550, -1439, -1641],\n [-881, -825, -1310, -1387, 503, 2303, -732, 489, -298, 112, -179, 281],\n [1664, 759, 1011, 612, 357, -92, -1134, -776, 1405, 20, 1098, -449],\n [284, -171, 1505, 940, 733, -382, -1043, -1017, -514, -1023, -643, -321],\n [125, -398, 1230, 1106, 561, -1677, 1056, -700, 19, 249, 716, -1299],\n [939, -636, 230, -140, 588, -46, 355, 503, -509, -495, -157, -1333],\n [2026, 732, 1308, -29, 645, -543, -803, -609, 1608, 357, -783, -571]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[464, 108, 541, 431, 295, 284, -854, 145, -362, -23, -82, -272],\n [-791, 504, 678, 834, -624, 673, 193, 1463, 930, 0, 1304, -496],\n [1040, -433, -541, -866, 648, -740, -209, -510, -724, 281, -405, -223],\n [-32, 153, -66, -283, 102, -71, 10, -24, 224, -234, -177, -116],\n [632, -550, -755, -315, -412, -779, -457, -472, -400, -497, -80, 291],\n [216, 642, 750, -28, 801, 483, -765, 67, 122, -324, -674, -547],\n [-512, 462, 749, 331, 548, 781, 323, 86, 122, 512, -287, -88],\n [213, 181, -2, -133, 25, -87, -704, -302, 94, -803, -558, 2],\n [-105, 528, 691, 505, -57, 499, -691, 718, 456, -473, 276, -490],\n [1, -620, -640, -272, -88, -413, 847, -573, -514, 716, 6, 556],\n [-742, 9, -45, 276, -594, 158, 935, 766, 564, 417, 1033, -17],\n [1119, -1308, -1236, -94, -1077, -1350, -120, 472, -766, 327, 1627, 14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[662, 1217, 412, 1270, -507, -165, -784, -888, -86, 41, -1017, 842],\n [-401, -1382, -260, -336, -111, 891, 336, 842, 352, -583, 22, -216],\n [-1241, 756, -787, -1436, 240, -892, -1188, -2394, 1206, 1740, 486, -674],\n [631, 410, -482, -54, 30, 1038, 287, 1589, -1709, -1275, 574, 764],\n [-576, 611, 407, -979, 947, -18, -1066, -448, -657, 1124, -770, 119],\n [1355, -668, 1074, 1278, 816, 336, 775, 163, 779, 321, -1404, 138],\n [-389, -971, -254, -190, -19, 290, 486, 455, 639, 1410, 571, -295],\n [-328, 1254, -52, -527, -280, -1690, -1685, -2175, -117, 1658, 103, 186],\n [-730, 525, -1046, -1075, -347, -684, -1162, -1025, -433, -149, 424, 479],\n [268, -1201, 1113, 830, 775, 1899, 722, 1722, -80, 188, -1665, 628],\n [572, -215, -93, 4, 74, -427, 206, -589, 93, 272, 459, 431],\n [201, 2884, -312, 870, -614, -856, -1306, 1192, -2350, 192, -552, 367]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-87, 340, 234, -195, -187, 101, 304, 510, -441, 487, 54, 48],\n [103, 240, -304, 159, -459, -221, 148, -130, 193, -235, -214, 224],\n [-84, -588, -30, 941, -362, 104, -516, -364, 131, -799, 393, 785],\n [-8, 368, 152, -560, 192, 24, 336, 384, -256, 608, -136, -408],\n [303, -132, -738, 139, 11, -461, -192, -926, 961, -815, -486, -176],\n [-258, -394, 687, -192, 673, 490, -226, 438, -570, 524, 516, -216],\n [273, 588, -618, -221, -439, -491, 408, -266, 481, -155, -636, -146],\n [-3, 334, -141, 430, -878, -111, 226, 172, -140, -172, -15, 667],\n [-293, -448, 632, 299, 185, 487, -300, 406, -603, 201, 650, 328],\n [-160, -238, 181, 734, -547, 188, -206, 126, -284, -322, 424, 816],\n [105, 626, -99, -672, 16, -179, 518, 288, -66, 566, -405, -483],\n [-215, 146, 509, -61, -112, 313, 174, 688, -705, 573, 338, 196]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-284, 447, -1008, -139, -508, 1086, 217, 568, -634, -783, -244, 568],\n [-167, 701, -1101, 1218, 1239, 1105, 1032, -585, -920, -543, -328, -630],\n [-406, 489, 74, 239, -427, 623, -209, -4, -183, -787, -395, 42],\n [753, -398, -868, -844, 472, -423, -219, 364, 587, 644, 249, -10],\n [-578, -1188, 218, 24, -836, 430, 336, 1096, -518, 176, 454, 1060],\n [-52, 452, -639, 759, 829, 671, 316, -395, -272, -315, -383, -530],\n [128, -665, -310, 58, 712, -39, 1010, 79, -496, -17, 844, -146],\n [419, -295, -335, -807, 287, -400, 641, 108, -184, -337, 946, -96],\n [544, -425, 223, -659, 528, -950, 444, -248, 178, 107, 946, -408],\n [-319, -334, -684, 612, 46, 852, 211, 540, -408, 361, -353, 484],\n [-195, -453, 36, -481, -579, 30, 720, 528, -682, -363, 796, 628],\n [-129, -1761, 941, -1150, -1247, -768, 2, 1265, 119, 444, 1220, 1152]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[20, 16, 44, 2, 20, -2, -42, 42, 40, -38, -34, 38],\n [220, 176, 484, 22, 220, -22, -462, 462, 440, -418, -374, 418],\n [-130, -104, -286, -13, -130, 13, 273, -273, -260, 247, 221, -247],\n [190, 152, 418, 19, 190, -19, -399, 399, 380, -361, -323, 361],\n [150, 120, 330, 15, 150, -15, -315, 315, 300, -285, -255, 285],\n [220, 176, 484, 22, 220, -22, -462, 462, 440, -418, -374, 418],\n [-200, -160, -440, -20, -200, 20, 420, -420, -400, 380, 340, -380],\n [-220, -176, -484, -22, -220, 22, 462, -462, -440, 418, 374, -418],\n [-120, -96, -264, -12, -120, 12, 252, -252, -240, 228, 204, -228],\n [250, 200, 550, 25, 250, -25, -525, 525, 500, -475, -425, 475],\n [210, 168, 462, 21, 210, -21, -441, 441, 420, -399, -357, 399],\n [-130, -104, -286, -13, -130, 13, 273, -273, -260, 247, 221, -247]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[554, 168, -1175, 612, -287, 217, 249, -577, 140, -994, -125, 123],\n [-294, 724, -429, 13, 390, -781, 356, 79, 5, -591, -194, 398],\n [-830, -327, -60, -1323, -16, 1157, 641, 250, 727, -71, 795, 344],\n [-326, 167, -280, -343, -1327, -648, 394, 318, 812, -756, -563, 530],\n [934, -201, 410, 1294, -786, -732, -2334, -337, -831, 1010, -146, -1265],\n [-221, -140, 774, 459, 535, -2243, -1329, -208, -1226, 1329, 130, -449],\n [-1265, -29, 374, -1499, 717, -926, -115, -32, -492, 793, 1455, 400],\n [723, 252, 574, 719, 1210, -461, -720, -275, -886, 709, -457, -780],\n [156, 590, -703, -443, -687, 590, 90, 107, 419, -654, 553, 356],\n [195, -540, 198, -643, -1118, 1259, 156, -194, 423, -78, 398, -140],\n [-741, -493, -38, -90, -1002, -329, 193, 132, 282, -6, 393, 296],\n [1110, 841, -253, 1570, 438, 191, 1170, -1230, -1116, -668, 397, -670]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[284, -68, -508, 438, -35, -23, 710, 127, 73, 493, -50, 142],\n [112, -608, 354, 164, -333, 87, -1511, 246, -128, 582, 95, 66],\n [-690, -172, 503, -322, 574, -221, -2184, -494, -922, 205, 915, 28],\n [-550, -67, -500, 173, 611, -282, -867, -714, -907, 1050, 810, 354],\n [6, 111, -44, -313, -660, 249, 728, -88, 637, -246, -893, -2],\n [-226, 300, 408, -674, -518, 407, -145, -305, 394, -313, -549, 83],\n [314, -22, 440, -374, -894, 291, 768, 466, 1027, -1002, -1186, -341],\n [366, 1066, 69, -304, -210, 1019, 656, -310, 244, 767, 207, 820],\n [-420, 780, -141, -412, 468, 186, 273, -741, -354, 162, 464, 359],\n [522, 648, 133, 152, 334, 483, 411, 211, -85, 324, 692, 388],\n [814, 259, 10, 67, -842, 567, 1636, 622, 1089, -294, -959, 40],\n [-460, 585, 311, -899, -426, 458, 59, -657, 332, -316, -537, 192]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[788, -876, -368, -170, -1028, 222, -162, 488, -86, 486, 134, 558],\n [-310, 354, 168, 25, 410, -87, 29, -196, -21, -219, -131, -227],\n [-74, 162, 232, -340, 144, -18, -280, -80, -458, -282, -678, -116],\n [-180, 276, 272, -300, 280, -48, -244, -144, -424, -336, -664, -188],\n [-146, 54, -200, 515, 126, -45, 431, -44, 649, 231, 879, -17],\n [-75, 171, 252, -375, 150, -18, -309, -84, -504, -306, -744, -123],\n [-51, -45, -228, 465, 6, -18, 387, 12, 600, 270, 840, 45],\n [361, -309, 60, -490, -416, 105, -416, 184, -579, -51, -709, 182],\n [454, -474, -136, -235, -574, 129, -207, 268, -229, 189, -179, 297],\n [-151, 183, 108, -35, 206, -42, -25, -100, -72, -138, -152, -119],\n [243, -171, 132, -495, -258, 72, -417, 108, -606, -144, -786, 93],\n [-408, 396, 48, 345, 498, -117, 297, -228, 381, -81, 411, -243]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 12x12 matrix:\n[[-137, 816, 234, 1043, -1474, 112, 626, 867, -372, 793, -79, -182],\n [611, 707, -422, -113, 256, 1314, -886, -623, 54, -302, 438, 351],\n [-49, -1465, -656, -435, 674, -1716, -23, 757, 698, -302, 172, -125],\n [880, 293, -756, 668, -542, 940, -146, -388, 528, 281, -21, 13],\n [248, -440, -405, -229, 307, -648, -662, 1115, 350, -77, 890, 24],\n [-82, 1191, -163, 119, -193, 837, -552, 80, -411, -189, 251, 270],\n [-349, -1076, 27, -772, 1363, -896, -253, 30, 570, -404, -289, -382],\n [-20, -1440, 700, -512, 796, -940, 132, 380, 500, 260, 100, -540],\n [-124, 275, 708, -68, -162, 24, -232, 803, -395, 296, 662, -48],\n [-463, 565, -1082, -103, 308, -697, -871, 1318, 93, -599, 396, 164],\n [-150, 1291, -402, -40, 32, 1040, -528, -619, -461, -542, -90, 454],\n [1058, -828, -1140, -106, 636, 432, -426, -1031, 1097, -301, -105, 57]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-114, 1031, 579, 266, 12, -601, -22, -956, 461, 631, -704, -408],\n [-105, 567, 267, -594, -1616, -325, 763, 1122, -92, -942, -509, 1136],\n [1712, -154, -189, 500, -873, 722, 1095, 738, -143, -188, 1147, 381],\n [82, -1620, -1167, 514, 525, 408, -909, 405, -2471, 99, -408, -794],\n [-544, -741, 1096, 627, -1466, -317, 728, -903, 391, 955, 30, 633],\n [565, -99, 187, 269, -656, 1116, 815, -355, 959, -465, 901, 546],\n [-2540, -1618, -1113, 88, 146, -1062, 32, 286, -302, -551, -391, -6],\n [489, 1262, 161, -833, -766, 1629, 313, -165, 496, -1197, 542, 24],\n [-1504, -1119, -1020, 568, 494, -135, -542, -562, -1064, -229, -996, -978],\n [-224, -390, -1548, -217, 2031, -153, -810, -830, -1413, -697, -174, -1080],\n [-473, -969, -559, -583, 1044, 19, -74, 344, -190, -505, 303, -102],\n [-418, 788, -317, -611, 846, -2179, -999, 253, -522, -176, -638, 554]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[468, -598, -104, 338, -104, 598, -312, -364, -676, 260, -78, 442],\n [198, -253, -44, 143, -44, 253, -132, -154, -286, 110, -33, 187],\n [-468, 598, 104, -338, 104, -598, 312, 364, 676, -260, 78, -442],\n [-432, 552, 96, -312, 96, -552, 288, 336, 624, -240, 72, -408],\n [-306, 391, 68, -221, 68, -391, 204, 238, 442, -170, 51, -289],\n [450, -575, -100, 325, -100, 575, -300, -350, -650, 250, -75, 425],\n [54, -69, -12, 39, -12, 69, -36, -42, -78, 30, -9, 51],\n [18, -23, -4, 13, -4, 23, -12, -14, -26, 10, -3, 17],\n [-198, 253, 44, -143, 44, -253, 132, 154, 286, -110, 33, -187],\n [-414, 529, 92, -299, 92, -529, 276, 322, 598, -230, 69, -391],\n [468, -598, -104, 338, -104, 598, -312, -364, -676, 260, -78, 442],\n [378, -483, -84, 273, -84, 483, -252, -294, -546, 210, -63, 357]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-416, 1316, -386, 18, 100, 669, 0, 127, 649, -344, -345, 44],\n [558, 323, 505, 724, -289, 244, 30, 132, -1054, 668, 1794, 824],\n [980, 431, 636, 1493, -783, 923, -266, -106, -981, 1017, 1980, 1722],\n [-929, -636, 296, 1017, -786, -371, -163, 121, -559, 877, 531, -628],\n [-918, 292, 1113, -628, 947, -106, 412, 80, 1253, -1666, -411, 565],\n [-1101, -375, 738, -1166, 949, -1287, 287, 628, 1530, -772, -546, -230],\n [71, -28, 109, -122, -83, -217, 530, -852, -462, -291, -894, -1126],\n [-349, -603, -35, 450, -200, -702, -334, 586, 104, 466, 1032, 1121],\n [-1291, -574, -732, 323, -228, -503, -282, 713, 899, 435, -729, -282],\n [-1215, 82, 239, -301, 87, 49, 119, 135, 931, -235, -430, -947],\n [57, 366, 655, 160, 248, -499, 255, 286, 750, 64, 686, 1498],\n [-195, -203, -640, 453, -373, 20, -196, 241, -525, 465, 972, 340]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-36, 24, 20, 16, 80, 80, 24, -68, 52, -60, 80, 88],\n [144, -96, -80, -64, -320, -320, -96, 272, -208, 240, -320, -352],\n [-180, 120, 100, 80, 400, 400, 120, -340, 260, -300, 400, 440],\n [-45, 30, 25, 20, 100, 100, 30, -85, 65, -75, 100, 110],\n [81, -54, -45, -36, -180, -180, -54, 153, -117, 135, -180, -198],\n [108, -72, -60, -48, -240, -240, -72, 204, -156, 180, -240, -264],\n [9, -6, -5, -4, -20, -20, -6, 17, -13, 15, -20, -22],\n [-135, 90, 75, 60, 300, 300, 90, -255, 195, -225, 300, 330],\n [-216, 144, 120, 96, 480, 480, 144, -408, 312, -360, 480, 528],\n [162, -108, -90, -72, -360, -360, -108, 306, -234, 270, -360, -396],\n [99, -66, -55, -44, -220, -220, -66, 187, -143, 165, -220, -242],\n [153, -102, -85, -68, -340, -340, -102, 289, -221, 255, -340, -374]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[86, -6, -48, 230, 28, -188, 166, -136, -106, 60, 20, 204],\n [-150, 217, -339, 37, -72, 187, 249, 77, 71, -95, -170, -157],\n [-478, 536, -762, -212, -212, 702, 388, 366, 312, -310, -440, -650],\n [503, -483, 636, 395, 214, -794, -197, -448, -373, 330, 410, 762],\n [158, -230, 360, -42, 76, -196, -266, -80, -74, 100, 180, 164],\n [-216, 244, -348, -92, -96, 316, 180, 164, 140, -140, -200, -292],\n [63, 18, -81, 216, 18, -153, 180, -117, -90, 45, 0, 171],\n [-115, 120, -165, -70, -50, 175, 70, 95, 80, -75, -100, -165],\n [-115, 227, -384, 157, -62, 102, 349, 12, 21, -70, -170, -62],\n [147, 42, -189, 504, 42, -357, 420, -273, -210, 105, 0, 399],\n [-10, -171, 357, -391, 16, 139, -467, 149, 107, -15, 110, -189],\n [-395, 468, -681, -122, -178, 563, 386, 283, 244, -255, -380, -513]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1437, 805, 984, -485, -162, -449, 486, -53, 1068, -669, 349, -117],\n [1321, 659, 520, -189, -152, 1437, 1392, 223, 309, 258, 897, -1372],\n [-1473, -507, -679, -1459, -971, -356, -451, 666, -1208, -153, 489, 592],\n [-1163, -75, -768, -2392, -1640, -1713, -1154, 2002, -678, -1914, 106, 497],\n [-1786, -285, 198, -600, 582, -576, -1284, -889, 166, -1357, 254, -188],\n [527, 604, -81, 729, -163, 571, 803, 244, -713, 1142, 17, -1168],\n [59, -954, 460, -1432, -444, 1010, 714, 776, 614, -397, 1017, 941],\n [-43, -623, -539, 261, -213, 513, 695, 672, -87, 115, 649, -651],\n [-66, -145, -52, -259, -190, -654, -289, -362, 561, -1214, 212, 252],\n [-403, -1405, 658, -271, 1702, 154, -383, -667, -322, 379, 1176, 1920],\n [-558, -465, 212, 7, 910, -111, -538, -62, 742, 159, -805, 1482],\n [-806, -381, -125, -903, -1595, 86, 85, 953, -416, 342, 408, -1054]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-591, 319, 195, 776, -378, -132, 195, -63, -342, 282, 222, -375],\n [464, -397, 34, -568, 1352, -893, 791, 935, 492, -65, 905, -3],\n [-123, -484, -339, 314, -136, -607, 1106, 838, -428, 535, 375, 400],\n [-993, 755, 259, 429, -54, 190, -95, 221, -653, 35, 349, -1276],\n [-138, -382, -569, -90, -1474, 550, 449, 18, -407, 332, -603, 550],\n [-240, 302, -194, 88, -944, 954, -808, -578, -422, -206, -768, -214],\n [-842, 310, -30, 817, 73, -406, 689, 888, -831, 274, 807, -1004],\n [1031, -600, -735, 919, -475, 55, -45, 54, 304, -710, 342, 2],\n [-682, 296, -368, 556, -851, 536, -31, 306, -970, 15, -84, -777],\n [-240, -275, 29, -1580, 210, -23, 622, 451, -76, 624, -480, 801],\n [791, -716, -797, 321, -1027, 433, -187, -256, -93, -179, -682, 960],\n [-698, 677, 651, 8, 498, -39, -530, -371, -285, 275, -206, -275]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-549, -405, 459, 542, -253, -728, -23, 617, -202, -1563, -460, 326],\n [-272, -787, 515, -466, -775, 266, 610, -420, -327, -641, -293, -317],\n [-136, 222, 158, -352, 66, -261, -1169, 221, 8, -681, -392, 1046],\n [-111, 163, -829, 1246, -119, 641, -810, -343, -752, -589, -712, 385],\n [1495, -1056, -402, 486, -262, -1176, 2222, -1389, 1938, 670, 729, -1374],\n [-5, 230, -411, 1545, -225, 424, 725, -505, -288, -1289, -388, -2],\n [-500, 38, -853, 573, 673, 562, 597, -859, -49, -416, 422, -501],\n [292, -169, -429, -585, 464, -1647, -411, -919, 768, -187, 423, 595],\n [-1667, -205, 1357, -1780, 1428, 69, -2037, 1094, 21, -544, -185, -100],\n [-1104, -526, -4, -892, 732, 318, -797, 193, 339, -687, 486, 332],\n [1573, 146, -168, -1095, -796, -483, 655, -1024, 12, 1916, -612, -553],\n [142, -31, 222, 821, 656, -145, 310, -47, 640, -327, -418, -1039]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1149, 515, -1404, 698, -834, -768, -835, 107, -253, -409, -412, 273],\n [1381, 395, -727, -52, -400, -1584, 562, 29, 210, -701, 73, -1438],\n [198, -181, 105, -1075, 323, -847, 541, -302, -758, 507, 79, -282],\n [-729, -762, 503, 48, 1107, 541, 1063, 866, 380, 171, 9, -474],\n [-151, -745, -360, 160, 143, 486, 897, 623, 507, -716, 898, -162],\n [-883, 404, 377, -427, -215, 1175, 430, 170, 68, -597, -251, 620],\n [412, -502, 417, 312, 653, -8, -527, -1038, -84, 64, -709, -159],\n [261, 925, 0, -1556, -2236, -470, 48, -139, 472, 379, 682, -294],\n [179, -102, 790, 46, -431, -169, -583, 698, 751, -222, -427, -622],\n [-644, 218, 63, 1304, 847, -90, -1319, 1258, -1050, -686, 276, 1324],\n [-125, -855, 188, 484, 591, -90, 17, -707, -158, 573, -1136, -295],\n [867, -645, -1470, 921, 737, -478, -729, -126, -944, 504, -283, 828]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1135, 2210, 239, 677, 1113, 479, -458, 450, -977, -870, 421, -350],\n [727, -351, -113, -348, -358, 477, 316, -879, 321, 1813, 265, 1161],\n [172, 1206, 708, -624, 311, 1124, 957, -1493, -253, 738, 974, -1798],\n [-722, -897, -876, -515, -461, -701, 1122, 328, -205, 53, 652, 1218],\n [56, 314, 810, -879, 293, -573, 477, -463, -367, 752, 421, -250],\n [-1203, 437, -689, -1163, 550, -1311, 348, -8, 994, -460, 1253, -590],\n [-291, -255, 723, 298, -787, 463, 154, -502, 85, 484, -693, 496],\n [-782, -383, 620, -51, -427, 37, -202, 466, 779, -618, -731, -944],\n [-1151, -2227, 906, -1082, -482, -990, -77, 347, 1405, -3, -1042, -1309],\n [461, -971, -1545, -63, -192, 283, 585, 269, -108, 489, 753, 1249],\n [1141, 86, 1056, -433, 719, 438, -753, 239, 2046, 442, -458, -136],\n [190, -606, -601, -151, 608, 516, 114, -486, -144, -505, 887, -1450]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-221, -84, 109, 319, -21, 449, 895, -809, -120, 588, -954, 684],\n [1835, -1824, -206, -1471, -620, -442, -887, 224, -679, 955, 682, -1203],\n [-829, 943, -319, 535, 681, 199, 787, 245, -73, -383, -348, 1274],\n [-426, 1244, -176, 689, -20, 155, 862, 662, 671, -998, 42, -85],\n [-1059, 864, -737, 1028, 9, 39, 485, -445, 662, 43, -927, 1251],\n [500, -510, 836, -659, 350, -506, -638, 592, -720, -345, 477, 69],\n [127, 155, 1359, -131, 299, 229, 383, 291, -371, -715, 254, -446],\n [-25, -236, -176, 116, 141, -206, 566, -261, -396, 513, -1008, 1568],\n [-306, -152, 57, 33, 347, -185, -170, -243, -351, 258, -399, 1024],\n [-38, -561, 506, -13, -410, -440, -1268, -552, 271, 188, 9, -437],\n [79, 41, -472, -84, 93, 350, 520, -21, -123, 276, -2, 14],\n [36, -37, 246, -124, -109, -216, -795, 191, 202, -334, 583, -742]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[413, -131, -312, -308, 525, 1013, 95, 716, 64, -152, 341, -358],\n [1792, 191, 437, 1014, -1166, 1318, 209, 1303, -350, 246, 1731, -35],\n [-255, 1190, 432, -554, -374, -1111, -461, -305, 633, -927, -616, 655],\n [-2303, 543, 1436, 1065, 394, -1056, -20, 588, 1282, 534, -336, 95],\n [-898, 42, -555, -1385, 578, -709, -274, -836, -87, -733, -1079, 51],\n [883, -781, -1245, -649, 117, 536, -75, -738, -1119, -247, 219, -532],\n [175, 840, 601, 444, -1248, -876, -910, -517, -338, -589, 270, 61],\n [-64, -944, -513, 989, 422, 203, 716, -364, -125, 1129, 733, -600],\n [420, 25, 125, 404, -107, -653, 33, 543, 118, -423, -395, 1054],\n [-97, -123, -703, -420, 701, -882, -610, -516, -147, -988, -948, 252],\n [-230, -678, -555, -256, 695, -44, 435, -278, -35, 305, -502, 98],\n [-939, 70, 408, -352, 613, 167, -127, 1047, 350, -366, -478, 176]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-267, 840, -140, 216, 980, -33, -1118, -143, -656, -688, -307, -112],\n [686, 334, 646, 275, -1513, 792, 1533, -72, 547, -1429, -124, -1157],\n [560, 1020, 735, 1019, 749, -647, 2, 504, 286, -1204, -1115, 215],\n [1020, 56, -176, -626, 2969, -680, -277, -620, 697, 1025, 132, 435],\n [-644, -13, 175, -80, -337, -355, 905, 143, 1294, 658, -216, 172],\n [-137, -32, -535, -148, 192, -164, 401, -1124, 1338, 375, 248, 376],\n [-15, -524, 1095, 910, -839, -182, 687, -918, -322, -47, 601, 268],\n [1083, 384, -902, -307, 1420, -242, 437, -1224, 1734, -48, -139, 77],\n [-231, 1072, -45, 84, 1816, -709, 161, 79, 607, 235, -748, -689],\n [751, -662, -201, -59, -1691, 735, 1572, -1099, 1264, -361, 844, -272],\n [-581, 324, 224, 855, -596, -323, 648, -1235, 736, -429, 111, 166],\n [676, -783, -805, -354, -2258, 610, 4, 6, -830, -671, -662, 36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[958, 578, 432, 923, 196, 9, 693, 1213, -271, 254, -387, -842],\n [-886, 753, 714, -689, -273, 184, 749, -877, 819, -547, -805, -116],\n [-1284, -832, -709, 193, -1278, 410, 611, -161, 1377, -705, -541, 31],\n [-57, -85, 163, 120, 870, 1372, 823, 1525, -909, -579, -634, -470],\n [497, 72, 553, 263, -602, -871, 209, -241, -1269, 460, 191, 1056],\n [-551, 560, 965, 410, -1490, -1105, 1628, -308, -379, 80, -291, -623],\n [779, 596, -89, 437, 503, -821, 15, -119, -396, 686, 187, 400],\n [1343, 109, 109, -625, 1324, 55, -656, -782, -36, 179, -271, -14],\n [-47, 205, -35, -20, 229, 517, -588, -98, -2, 107, -350, 2058],\n [-75, -838, -1049, -55, -380, 609, -34, 663, 1043, -1219, 22, 477],\n [-77, -1084, -875, -503, -730, 13, -414, -280, 694, -1036, 392, 887],\n [-390, -386, -308, -163, -602, -500, -282, -644, 695, 34, 445, -694]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[275, 247, -459, -1832, 1632, -118, -577, 818, 1110, -707, 546, -218],\n [178, -208, -69, 875, -316, 422, 364, 270, -1100, 802, -20, -110],\n [-190, -1056, -125, 1420, -373, 835, -186, -129, -1537, 961, 271, -393],\n [308, -230, 337, -506, -285, -591, -149, -169, 177, -93, -653, 660],\n [-39, -84, 16, -702, 633, -219, -177, -142, 611, -436, 100, 36],\n [441, -257, 456, -930, -73, -1121, 466, -387, 447, -18, -187, 1048],\n [-367, 707, -192, 790, 355, 1115, -543, 811, -309, 183, 122, -1143],\n [123, -52, 177, -60, 279, 209, -439, 38, -64, -280, -1194, -64],\n [-210, 684, -1041, -298, 1083, 1277, -1030, 1349, 257, -492, 626, -1405],\n [-41, -1362, 818, 719, -604, -536, 284, -805, -958, 1281, 647, 736],\n [-42, 911, -142, -1462, 156, -866, 105, -207, 1810, -1311, 92, 352],\n [33, -607, 437, -732, 894, -146, -993, 638, 80, 738, 1157, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}