{"messages": [{"content": "Find the rank of the matrix:\n[[226, 270, -378, -80, 286, -296, 68, 240, 20, -20],\n [324, -20, 28, -144, 340, -312, 288, -488, -56, -312],\n [-143, -235, 329, 46, -192, 205, -13, -283, -26, -32],\n [36, 220, -308, 0, 76, -96, -72, 400, 40, 120],\n [-228, -60, 84, 96, -252, 240, -168, 192, 24, 168],\n [-65, -175, 245, 16, -99, 112, 26, -268, -26, -62],\n [414, 280, -392, -162, 487, -483, 225, 1, -8, -186],\n [-373, -85, 119, 158, -410, 389, -281, 341, 42, 284],\n [-406, -120, 168, 170, -451, 431, -293, 315, 40, 290],\n [406, 120, -168, -170, 451, -431, 293, -315, -40, -290]]\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[[569, -60, 14, -363, -532, 391, -239, -286, -512, -630],\n [80, 593, 406, -171, 130, -343, 155, -267, 6, -244],\n [229, 694, 770, 29, -476, 333, 801, 116, -150, -990],\n [-390, -47, 166, -253, 402, 187, 217, 805, 658, 204],\n [139, 764, 744, -44, -310, 146, 664, 45, -64, -828],\n [-918, 91, -80, 386, 4, 124, 16, 548, 500, 410],\n [-119, 348, 331, -341, 268, -91, 117, 230, 325, -83],\n [-742, 307, 0, 416, -84, -69, -4, 165, 267, 258],\n [-429, 111, -141, 414, 166, -370, -54, -139, 127, 451],\n [828, -184, 194, -98, -1156, 1064, 302, -8, -788, -1274]]\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[[104, -78, 130, 149, 66, 17, -327, -796, 187, -301],\n [92, 54, 1, 392, -147, 48, -368, -847, 23, -184],\n [514, 186, 226, -168, 50, 60, -478, -48, 656, -72],\n [414, 264, 68, -3, -118, 7, -367, 32, 363, 93],\n [-283, 63, -229, 563, -332, 268, 19, -300, -365, 8],\n [337, 285, 58, 45, -169, 294, -331, 303, 470, 78],\n [-400, -336, 119, 359, 106, 632, -100, -759, 170, -610],\n [-290, -312, 59, -348, 318, -115, 411, 265, -151, -87],\n [364, 324, 0, -112, -158, 46, -174, 596, 304, 278],\n [1088, 780, 22, 192, -474, -296, -960, -226, 562, 408]]\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 10x10 matrix:\n[[310, -324, -92, -229, -79, 222, -482, 319, 249, -321],\n [270, -306, -178, -296, -291, 73, -273, 381, 201, -64],\n [178, -216, -176, -253, -325, -24, -92, 313, 123, 87],\n [-188, 180, -12, 72, -106, -218, 394, -122, -162, 344],\n [258, -306, -226, -338, -405, 1, -177, 423, 183, 62],\n [-136, 108, -100, -38, -284, -270, 422, 8, -132, 450],\n [74, -54, 74, 40, 199, 171, -259, -25, 75, -288],\n [70, -72, -16, -47, -7, 56, -116, 67, 57, -83],\n [312, -360, -232, -368, -396, 52, -276, 468, 228, -16],\n [66, -54, 42, 12, 123, 123, -195, 3, 63, -204]]\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 10x10 matrix:\n[[143, -462, -187, -374, 165, -242, 209, 132, 495, -99],\n [-44, 36, 146, -76, -302, 32, -36, 62, 336, -426],\n [71, -144, -164, -32, 284, -86, 81, -17, -147, 318],\n [-138, 432, 192, 336, -192, 228, -198, -114, -414, 36],\n [61, -174, -99, -118, 125, -94, 83, 34, 105, 57],\n [81, -294, -79, -270, 17, -150, 127, 106, 429, -195],\n [-73, 192, 132, 112, -188, 106, -95, -25, -51, -138],\n [81, -204, -154, -108, 230, -114, 103, 19, 15, 192],\n [-46, 54, 139, -50, -277, 40, -42, 49, 276, -375],\n [-164, 486, 251, 350, -293, 260, -228, -109, -366, -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[[118, 274, -478, -610, 657, 205, 206, 318, -26, -48],\n [-419, 36, -592, -275, 446, 517, 80, -106, 526, 84],\n [49, 214, -539, 78, 137, -90, 450, 173, 400, 319],\n [-228, 628, -33, -611, 276, 44, 148, -209, 548, 481],\n [-668, 766, -370, -643, 863, 36, 115, -11, 701, 99],\n [-364, 35, 255, 46, -184, 78, -189, -325, 284, 81],\n [-598, 1015, -132, -732, 998, 444, -27, 140, 358, -401],\n [-217, -695, 188, -217, -193, 287, -474, -265, -181, -149],\n [-630, 716, 65, -762, 482, 484, -102, 220, 320, -435],\n [-375, 298, -64, 105, 155, -25, 29, -338, 523, 269]]\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[[42, 42, -28, 224, 182, 140, 98, 196, 0, -182],\n [-3, -3, 2, -16, -13, -10, -7, -14, 0, 13],\n [18, 18, -12, 96, 78, 60, 42, 84, 0, -78],\n [-27, -27, 18, -144, -117, -90, -63, -126, 0, 117],\n [15, 15, -10, 80, 65, 50, 35, 70, 0, -65],\n [-54, -54, 36, -288, -234, -180, -126, -252, 0, 234],\n [21, 21, -14, 112, 91, 70, 49, 98, 0, -91],\n [-54, -54, 36, -288, -234, -180, -126, -252, 0, 234],\n [-33, -33, 22, -176, -143, -110, -77, -154, 0, 143],\n [-21, -21, 14, -112, -91, -70, -49, -98, 0, 91]]\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[[-54, -221, 355, 158, 22, 258, 221, 192, 214, -426],\n [190, -170, -426, 593, 226, 26, 72, -151, -510, -327],\n [-618, -107, 313, -145, -134, -15, 359, -486, -209, -678],\n [-182, 466, -102, -238, -338, -361, 88, -259, -179, 123],\n [-106, -79, 126, -230, 32, 40, -92, -17, 142, 114],\n [-52, -212, 381, 31, 26, 253, 137, 223, 305, -274],\n [-378, -412, 77, -380, 272, 99, -217, -384, -57, 27],\n [78, -413, -11, 557, 262, 285, 195, 30, -193, -600],\n [-252, -693, 388, -370, 418, 411, -268, -6, 367, 23],\n [-422, 316, 290, -315, -390, -202, 288, -241, 10, -239]]\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 10x10 matrix:\n[[-500, -241, -498, 257, -703, -387, -278, -574, 320, -672],\n [184, 233, 1, 542, -72, 79, 306, 98, -229, -19],\n [-333, -635, -61, 797, -445, -522, -267, -743, 329, -473],\n [-509, 307, 41, -50, 641, 263, 206, 42, 383, -428],\n [-329, 208, -178, -6, -314, 95, 204, 208, 402, -900],\n [262, -92, -804, -993, -578, -489, -397, -531, -421, 196],\n [256, 510, 536, 282, 1193, 533, 650, 407, -170, 122],\n [-58, -673, 648, 270, 126, -642, 207, 233, 1484, -518],\n [-694, 234, -219, 370, -75, 318, -41, -206, -104, -260],\n [134, 40, 350, -95, 918, -242, 686, 78, 412, 31]]\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 10x10 matrix:\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n [-308, 308, -140, -266, -308, 238, 126, 154, 70, 112],\n [-308, 308, -140, -266, -308, 238, 126, 154, 70, 112],\n [286, -286, 130, 247, 286, -221, -117, -143, -65, -104],\n [286, -286, 130, 247, 286, -221, -117, -143, -65, -104],\n [88, -88, 40, 76, 88, -68, -36, -44, -20, -32],\n [132, -132, 60, 114, 132, -102, -54, -66, -30, -48],\n [44, -44, 20, 38, 44, -34, -18, -22, -10, -16],\n [198, -198, 90, 171, 198, -153, -81, -99, -45, -72],\n [308, -308, 140, 266, 308, -238, -126, -154, -70, -112]]\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 10x10 matrix:\n[[439, 260, -151, 40, 109, 327, -367, -26, -140, -364],\n [-516, 80, 103, 605, 258, 691, -218, -72, -75, 119],\n [379, 349, 68, -116, -118, 246, -242, 401, 468, 127],\n [82, -390, 134, -290, 144, -342, 156, 174, 290, 132],\n [-602, -363, 202, 347, 334, 218, 73, -44, 44, 249],\n [363, -458, -247, -290, 282, -493, 71, -429, -587, -617],\n [26, 285, -90, 195, -50, 302, -179, -80, -160, -123],\n [402, -51, -231, -228, 15, -279, -21, -249, -388, -453],\n [523, -9, 32, -386, 0, -174, -84, 303, 366, -21],\n [-69, 949, 63, 369, -478, 765, -320, 371, 403, 376]]\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[[735, -948, 182, -230, 448, -572, 95, -268, 523, -548],\n [171, 294, -25, 38, 31, 272, 61, -219, 308, 298],\n [-135, 11, -8, -130, -336, -427, 495, 686, -100, 70],\n [-587, 398, -435, 509, 188, 580, -2, 105, -449, 324],\n [717, -1114, -209, 438, 407, -1085, 1201, 360, 635, -529],\n [619, -740, 203, 110, 579, -355, -59, -370, 203, -443],\n [602, 825, 922, -68, -62, -159, -498, -342, 203, 527],\n [-63, -11, -276, 720, 642, -178, 707, 653, -275, 387],\n [-36, 216, 16, -277, 107, 753, -833, -827, 138, 27],\n [584, -699, 66, -297, 249, 108, -354, -876, 533, -560]]\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 10x10 matrix:\n[[-1121, 589, 643, 229, 195, -65, 392, 1025, -102, -971],\n [352, -353, -85, -341, 673, -112, 84, 148, -22, 220],\n [-1127, -283, 267, -363, 99, 32, 808, 1169, 263, -1108],\n [536, 30, -877, -791, -185, 192, -536, -676, -172, -101],\n [96, 758, -212, 579, 135, -159, -69, -217, -983, -372],\n [72, -169, 186, 288, 695, 320, -60, 680, -457, 153],\n [709, 257, 293, 457, 395, -941, 191, -802, -355, 51],\n [-195, 525, -463, 243, -214, -128, 233, -226, -481, -284],\n [-693, 242, -248, 159, -1263, 570, -73, -137, 223, -405],\n [492, 126, 163, 388, 637, -238, -41, -79, -819, -348]]\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[[315, 98, 780, 226, 119, -129, 431, 388, -465, -520],\n [-650, 103, -715, -533, -334, 262, -105, -191, 359, 296],\n [5, 199, 366, 25, 9, 207, 449, 627, -450, -23],\n [-415, -21, -203, -299, -171, 30, -69, -46, 106, 73],\n [-261, -380, 742, 34, 219, -670, -128, -281, -85, -455],\n [-224, 103, -889, -137, -24, 396, -191, -217, 405, 760],\n [-262, -116, 198, -182, -134, -141, -49, 133, -124, -165],\n [-337, 166, -321, -236, -111, 285, 143, 123, 51, 286],\n [644, -558, 598, 940, 902, -475, -440, -26, -230, 638],\n [21, -186, -260, 176, 223, 14, -315, -86, 117, 592]]\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[[-278, 450, -154, 322, -444, -47, 310, -88, 161, -246],\n [-142, 263, -61, 156, -215, 4, 190, -69, 108, -107],\n [299, -153, -173, -138, -17, 4, -224, 396, 80, -355],\n [-284, -370, -42, 224, -86, -396, -252, -74, -476, 154],\n [80, -66, -50, -36, -2, -14, -80, 114, 2, -94],\n [251, 7, 123, -262, 267, 242, 20, 28, 174, 85],\n [216, -425, -337, 6, -177, -291, -480, 561, -187, -503],\n [-369, 529, -67, 346, -407, -10, 416, -250, 162, -93],\n [-174, -55, -287, 294, -411, -321, -132, 201, -161, -361],\n [242, -522, -134, -134, 104, -195, -474, 380, -243, -170]]?\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[[1129, -333, -414, 18, 517, -80, 416, -471, 228, 30],\n [-469, 275, 686, 356, -314, 199, -55, -498, -138, -2],\n [-122, 121, 654, 133, -203, -368, 238, -425, -84, -133],\n [213, -92, -213, 187, 343, 318, 262, 3, 172, 126],\n [-491, 316, -6, 465, 188, 935, -140, -86, -52, 491],\n [-1109, 512, 480, 117, -297, 264, 3, 157, -82, 367],\n [-1221, 517, 1514, 695, -283, -317, -89, -123, -684, -159],\n [651, -255, -231, 47, 66, 16, -413, -284, -164, -256],\n [602, -99, 83, 456, 503, 232, 474, -597, 106, 121],\n [-585, 284, -144, 258, 218, 782, 127, 236, 136, 532]]\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[[-32, -52, -29, 50, -1, 76, 39, 45, -87, 4],\n [-223, 44, 14, -70, 181, -323, -377, -398, 222, -335],\n [-458, -130, -42, -20, 84, -410, -366, -310, 120, -408],\n [-186, -189, -3, -60, -375, -270, 174, 339, -18, 111],\n [49, -88, -6, 10, -231, 61, 255, 326, -114, 213],\n [249, 97, -47, 170, 302, 545, 55, -97, -216, 48],\n [298, 97, -65, 220, 347, 686, 98, -79, -294, 77],\n [-145, -222, -60, 70, -255, 27, 233, 348, -210, 121],\n [700, 236, 85, -10, -115, 544, 501, 411, -105, 592],\n [446, 541, 231, -340, 231, -334, -342, -503, 654, -27]]\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[[-556, 276, -828, 14, -5, -1, 638, 535, -314, -952],\n [-255, -124, -320, 390, 269, -799, -413, 285, -493, 41],\n [-310, -214, -979, 440, -301, 192, 141, 369, -38, -187],\n [-492, -3, 314, -481, 682, -419, -228, 354, 150, -301],\n [-22, 10, 454, -694, 129, 756, 177, -105, 725, -130],\n [26, -211, -725, 783, -133, 70, -374, 27, -429, 62],\n [-226, -264, 349, -376, 797, 274, -789, 13, 336, -11],\n [-99, 279, -42, -255, 254, -353, 161, 66, -429, -350],\n [20, -557, 75, -11, 472, 824, -1019, -190, 532, 370],\n [-26, 145, -8, -182, -217, -674, 420, 136, -174, 108]]\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[[-79, 39, -327, 223, -469, 97, -135, -23, 453, -39],\n [-165, 105, -10, 195, -130, 130, -125, 105, 75, -105],\n [-134, 102, 470, -34, 498, 54, 10, 194, -558, -102],\n [-480, 312, 158, 492, -142, 358, -320, 348, -24, -312],\n [-216, 132, -169, 318, -367, 187, -200, 102, 300, -132],\n [-209, 141, 216, 155, 124, 140, -105, 185, -201, -141],\n [-35, 39, 476, -151, 576, -24, 85, 131, -603, -39],\n [34, -42, -580, 194, -708, 36, -110, -154, 738, 42],\n [-366, 246, 352, 282, 184, 248, -190, 318, -318, -246],\n [-190, 114, -209, 304, -399, 171, -190, 76, 342, -114]]?\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[[-427, -227, 145, 245, -363, -4, -54, -275, 87, -6],\n [-222, -55, 98, 146, -214, 35, -60, -132, 2, -54],\n [-574, -330, 186, 322, -478, -20, -60, -374, 134, 12],\n [375, 139, -149, -233, 343, -32, 78, 231, -35, 54],\n [75, 331, 79, 43, -53, 172, -138, 99, -215, -234],\n [13, -357, -135, -115, 157, -214, 186, -55, 247, 294],\n [-314, -269, 70, 150, -226, -63, 12, -220, 134, 78],\n [9, 161, 53, 41, -55, 92, -78, 33, -109, -126],\n [-315, -329, 49, 133, -203, -98, 42, -231, 175, 126],\n [-101, 4, 55, 75, -109, 33, -42, -55, -19, -48]]\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 10x10 matrix:\n[[-131, 729, 265, -355, 25, 247, -310, -82, -612, -365],\n [222, -175, 71, 227, 54, 160, 155, 52, 206, 523],\n [356, -208, 187, 345, -491, -103, 116, 965, -267, -91],\n [112, -362, 130, 244, -524, -376, 48, 986, -90, -194],\n [131, -6, -60, 120, -36, 283, 140, 12, -138, -421],\n [230, -68, 129, -184, 248, 622, 470, -516, 634, -209],\n [-387, 88, -311, -77, 269, -74, -222, -547, -97, -116],\n [249, -183, 10, 284, 717, 1210, 513, -1045, 739, 647],\n [-48, -137, -204, 179, -277, -423, -136, 430, -348, -268],\n [87, -46, -213, 2, -443, -577, -73, 548, -426, -677]]\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[[32, -247, -97, 119, 665, 759, -604, 157, 174, -245],\n [265, -90, 281, -36, 44, -296, 59, -111, -459, 172],\n [-150, 678, 650, 426, -395, 190, -513, -292, 1029, 553],\n [271, -141, 384, 159, 448, 711, -870, 84, 408, -22],\n [-752, 200, -927, -49, -105, -106, 757, 60, 15, -274],\n [456, -381, 199, 157, 471, 21, -345, -79, -559, 46],\n [-634, 276, -534, 120, 143, 216, 272, -20, 222, -94],\n [-307, 39, -513, 172, 54, -191, 376, -102, -238, -49],\n [90, -319, -489, 31, 10, -557, 515, -65, -797, -126],\n [-335, 330, -30, -235, -414, 14, 257, 105, 499, -29]]\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 10x10 matrix:\n[[80, 988, 212, 225, -563, 533, 162, 691, -183, 9],\n [558, 149, -60, -85, -1, -58, 685, -418, 133, -286],\n [103, -523, 399, 46, 1198, 816, 542, -547, 568, 865],\n [-820, -20, -98, 411, 1191, 534, -201, 110, 15, 1293],\n [466, -586, 340, -410, 116, -220, 159, -347, -369, -313],\n [690, 756, -265, 705, -412, 275, 300, -507, -759, 75],\n [549, -1027, 141, -254, 260, -105, 21, -880, 308, -278],\n [510, 310, 861, 364, -281, 604, 403, 491, 123, 440],\n [346, 143, -797, 179, 35, -218, 61, -970, -514, -337],\n [-998, -29, 319, 20, 34, 590, -865, 697, -328, 570]]\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[[-62, 194, 49, -43, -202, 136, -159, -113, -85, -216],\n [598, 524, 529, 197, -142, 256, -339, -173, -385, -486],\n [-116, -313, -191, -19, 212, -188, 231, 145, 181, 321],\n [-302, -226, -251, -103, 38, -104, 141, 67, 175, 204],\n [436, 488, 430, 134, -196, 256, -330, -182, -334, -468],\n [-48, -84, -60, -12, 48, -48, 60, 36, 52, 84],\n [-628, -494, -532, -212, 100, -232, 312, 152, 376, 450],\n [496, 263, 367, 179, 32, 100, -147, -53, -233, -219],\n [376, 218, 286, 134, 8, 88, -126, -50, -186, -186],\n [-52, -146, -88, -8, 100, -88, 108, 68, 84, 150]]?\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 10x10 matrix:\n[[-40, -22, -54, -120, 72, 68, 200, -260, 178, -108],\n [6, 73, -78, -64, -101, -2, -30, -43, 2, 49],\n [-42, -18, -63, -132, 69, 72, 210, -279, 189, -111],\n [10, 354, -417, -380, -469, 24, -50, -345, 99, 191],\n [6, -63, 90, 96, 75, -18, -30, 117, -54, -15],\n [-22, -177, 174, 128, 253, 18, 110, 51, 30, -137],\n [22, 449, -510, -448, -605, 14, -110, -371, 82, 265],\n [-16, -342, 390, 344, 460, -12, 80, 288, -66, -200],\n [26, -188, 285, 316, 215, -68, -130, 407, -199, -25],\n [40, 396, -408, -320, -556, -24, -200, -180, -24, 284]]\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 10x10 matrix:\n[[326, -32, -118, 27, -351, 504, -279, 380, -248, -723],\n [275, -477, -382, 131, 17, -87, -200, -53, 182, -367],\n [-211, -54, 598, -47, -160, -604, 333, -284, -213, 579],\n [-22, 277, 461, -174, -87, -153, 135, 32, -62, 234],\n [-244, -286, -63, -388, 94, -947, 474, -1062, 473, 561],\n [570, -191, -441, -37, -78, 366, -422, 293, 248, -868],\n [-172, -18, -16, 867, 261, 678, -361, 960, -590, 77],\n [-340, -194, 44, 48, 542, -831, 314, -561, 450, 935],\n [-165, -89, 241, -248, -186, -524, 335, -541, -1, 321],\n [373, -113, 92, -537, -693, -125, 72, -361, -42, -661]]\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 10x10 matrix:\n[[449, 5, 152, 1220, 149, -222, -368, -96, 123, -384],\n [-339, -708, 214, 476, -287, 45, 440, -53, 187, 288],\n [1411, 727, -96, 443, 379, 172, 160, 166, -281, 82],\n [759, -195, -192, -977, 992, -218, 1031, 969, -112, 1155],\n [-1021, -267, -176, -449, -171, -285, -238, -222, 40, -58],\n [-117, 899, 458, 345, -951, 683, -574, -368, -780, -612],\n [294, 378, 129, 750, -777, 546, 417, -411, -660, 228],\n [91, -576, 78, -193, 704, -454, 599, 752, -45, 797],\n [-7, 29, -658, -694, -30, 68, 247, -463, 416, 83],\n [-451, -183, 77, -636, -277, 224, 400, 102, -182, 385]]\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[[-73, -368, -187, -20, -195, -375, -281, 226, -506, 386],\n [-328, 21, 764, -365, 323, 115, 218, 248, 169, -37],\n [-121, 48, 440, -107, 278, 228, 375, -158, 446, -258],\n [132, 687, -68, -32, 122, 460, -54, -152, 548, -498],\n [-187, 232, 62, -284, 189, 197, -187, -66, 515, -369],\n [52, 176, 192, 43, 133, 223, 276, -144, 277, -199],\n [-187, -279, 70, -126, 105, -77, 31, -130, 217, -77],\n [-221, 296, 516, -359, 166, 108, -125, 458, -70, 42],\n [33, -224, -345, 117, -26, -40, 17, -394, 297, -183],\n [235, -387, -129, 427, -100, -104, 493, -366, -111, 127]]\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[[-34, 12, -28, -32, -12, -26, -30, -32, -28, -24],\n [-238, 84, -196, -224, -84, -182, -210, -224, -196, -168],\n [85, -30, 70, 80, 30, 65, 75, 80, 70, 60],\n [-272, 96, -224, -256, -96, -208, -240, -256, -224, -192],\n [-119, 42, -98, -112, -42, -91, -105, -112, -98, -84],\n [-119, 42, -98, -112, -42, -91, -105, -112, -98, -84],\n [170, -60, 140, 160, 60, 130, 150, 160, 140, 120],\n [-323, 114, -266, -304, -114, -247, -285, -304, -266, -228],\n [-323, 114, -266, -304, -114, -247, -285, -304, -266, -228],\n [272, -96, 224, 256, 96, 208, 240, 256, 224, 192]]\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[[174, -507, 287, 298, -159, -132, 289, -197, -41, -244],\n [102, -833, 361, -368, -50, -320, 176, 187, 275, -123],\n [-88, -414, 237, 31, -260, -24, 170, -77, -26, -265],\n [162, -1256, 650, -73, -184, -170, 463, -1, 80, -691],\n [156, 150, -223, 733, -50, 196, 214, -315, -418, -245],\n [-212, 69, 4, 920, -871, -158, 246, -677, -293, 186],\n [-18, 251, -88, -143, 10, -204, -176, 42, 195, 480],\n [130, 413, -70, 813, -296, -170, 80, -542, -147, 411],\n [-386, 905, -610, 319, -327, 160, -247, -178, -265, 467],\n [-148, 611, -775, 131, 13, 92, -186, 104, -231, 384]]\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[[130, 369, -413, -311, 11, 166, -609, 110, -229, -216],\n [53, 480, -412, -237, -66, 146, -618, 264, -316, -139],\n [-485, -3, 237, -152, -189, -294, -137, 52, -235, -191],\n [-409, -549, 607, 6, -59, -362, 481, -352, 167, -111],\n [-618, 171, 67, -387, -179, -382, -609, 132, -459, -426],\n [42, 342, -303, 385, 106, -50, -203, 547, -170, 309],\n [-284, 219, -150, 8, 45, -268, -462, 331, -303, -85],\n [108, -543, 259, 389, 317, -184, 567, -230, 413, 208],\n [250, -123, 64, 128, 7, 196, 372, -137, 231, 173],\n [-136, -420, 347, 223, 106, -240, 439, -173, 222, 89]]\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[[-35, 621, -130, -239, 99, 218, -113, -203, -94, 181],\n [-52, 165, -126, 873, 317, 332, 373, 96, 580, -87],\n [-202, -758, 252, 124, 224, -108, -332, -34, -76, 222],\n [-696, -367, 28, 686, 558, -546, -93, -391, 111, 480],\n [-155, 108, 162, -313, 82, 716, 451, 471, 629, 179],\n [33, 535, -210, -128, 122, -796, -203, -784, -791, -54],\n [346, 67, -5, 136, -159, 515, 787, 374, 541, -300],\n [414, 505, -350, -178, -476, 443, 629, -380, 131, 394],\n [328, 250, 68, 149, 191, 328, -82, 327, 27, -647],\n [96, -17, 436, 116, 954, 694, 53, 205, 165, -416]]\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[[-438, -278, 105, -879, 592, -111, -770, 943, 734, 346],\n [73, 151, -185, 829, -495, -554, 217, -1030, -456, 183],\n [-634, 875, 514, 6, 507, -757, 115, -384, 1046, 577],\n [-626, -356, -22, -429, 25, -461, -798, -512, -245, 291],\n [37, 1, -89, -600, -2, -129, -99, 172, 78, -183],\n [-269, -112, -164, 168, -98, -414, -611, -571, -541, 279],\n [989, -52, -476, 779, 510, 152, 189, 824, -251, 198],\n [-329, 973, 104, 31, 159, -307, 36, -95, -224, -30],\n [-103, 811, 16, -90, 293, -569, -341, 177, 327, 288],\n [-324, 87, 435, -973, 14, 477, 170, 260, 536, -464]]\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[[-344, 50, 276, 316, 236, 174, 60, -330, -278, 234],\n [-220, 126, 740, 20, 308, 142, 296, -674, 98, 234],\n [297, -177, -108, -281, -231, -24, 114, 22, 581, -112],\n [249, -75, -396, -164, -228, -132, -129, 394, 116, -196],\n [-411, 234, 234, 367, 333, 57, -102, -125, -718, 179],\n [73, -210, 58, -57, -107, 137, 190, -245, 506, 67],\n [373, 343, 188, -569, 9, -404, -58, 274, -23, -324],\n [-203, 135, 712, 6, 298, 122, 277, -632, 80, 214],\n [223, -352, -162, -140, -280, 135, 189, -123, 763, -3],\n [-304, -582, -904, 745, -289, 424, -175, 216, -33, 232]]\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[[58, 489, -539, 252, 85, -610, 367, -988, 203, -20],\n [377, 458, 30, 29, -42, -241, -199, 166, -467, 158],\n [-420, -688, 187, -256, -118, 467, -4, 530, 77, -191],\n [-145, -282, -162, -701, -96, 216, -48, 623, -442, -124],\n [449, 582, 119, 308, -209, -341, -200, -201, -451, 151],\n [-69, 8, -147, -261, 346, 316, -187, 674, 76, 205],\n [-212, -76, 102, 375, -333, -235, 4, 361, -374, -118],\n [421, 332, 132, 76, -63, -167, -39, -618, -35, 62],\n [-508, -925, 257, -164, 131, 489, 225, 139, 655, -258],\n [-53, 325, -332, 472, 114, -459, 300, -765, 365, 7]]\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[[-151, 68, -682, -290, 398, 127, -672, 541, -327, -200],\n [131, -471, 362, 117, -269, -539, 765, 85, -220, 279],\n [221, -123, -386, -547, 317, -148, -321, 718, -423, -117],\n [-509, -32, 376, 828, -358, 96, 482, -796, 406, 160],\n [602, 101, -33, -1015, 406, 176, -368, 624, -23, -372],\n [383, 122, 287, -309, -341, 78, 508, -302, 281, 38],\n [414, -40, 600, -380, -128, 74, 508, -154, 366, -108],\n [324, 526, -491, -482, 431, 293, -1137, 377, -137, -213],\n [151, 63, -163, -672, 552, 317, -565, 553, 25, -459],\n [72, -223, 825, 377, -364, -196, 802, -512, 333, 190]]\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 10x10 matrix:\n[[-699, -234, 68, -352, 723, 154, 410, 603, -113, -543],\n [-402, -100, 460, -42, 76, 946, -117, -63, -14, -227],\n [-39, 192, -124, 140, -61, 176, -81, -268, -113, 138],\n [-75, -246, 608, -70, -151, 704, -195, 14, 175, -180],\n [-405, -53, 10, -133, 362, 198, 179, 210, -105, -244],\n [-561, -237, 522, -189, 286, 902, 23, 202, 3, -420],\n [-21, 140, -520, -26, 263, -682, 264, 151, -147, 49],\n [-348, -338, 204, -338, 446, -44, 292, 600, 64, -448],\n [-222, 58, 8, 12, 114, 286, 11, -59, -94, -55],\n [-306, -332, 96, -356, 486, -264, 354, 664, 58, -436]]\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[[-60, 55, -396, 557, -430, -154, 226, -240, 163, -290],\n [-333, 194, 342, 71, -8, 393, -263, 487, 108, 29],\n [-52, -303, 240, 123, 22, 252, 124, 302, -227, 418],\n [-291, -4, 34, 837, -512, 330, 248, 368, 110, 113],\n [695, 608, -179, 366, -400, -378, 678, -275, 510, 102],\n [583, 280, -659, -286, -8, -816, 212, -953, 238, -510],\n [-131, -438, -290, 117, -40, -107, 25, -245, -264, -109],\n [-30, 311, -191, -518, 238, -271, -431, -342, 171, -565],\n [-708, -204, 51, 361, -156, 419, -361, 364, -104, -219],\n [-53, -115, -247, 717, -474, 4, 384, -39, 47, 16]]\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[[-124, 197, 383, -435, 591, -519, -492, -412, 322, 822],\n [-525, -112, -925, 272, -467, 808, 666, 316, -603, -457],\n [-211, 235, 2, 495, -16, -219, -89, 83, 469, 13],\n [-1156, -137, 423, -375, -954, 421, -165, -684, 177, 600],\n [578, -126, 1218, -1656, 619, -122, -602, -771, 27, 578],\n [-720, 65, 554, 275, -726, -74, -708, 37, 423, 651],\n [-77, 650, 673, -268, 556, -612, -912, -176, 802, 785],\n [-67, -573, -632, -139, 122, 243, 883, -471, -631, -99],\n [-41, -1041, -207, 212, 240, -826, 480, -481, -462, 417],\n [38, -423, -420, -103, 816, -683, 458, -584, -266, 474]]?\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 10x10 matrix:\n[[796, 87, -113, -1131, -73, 232, -565, 352, 186, -231],\n [-137, -143, 67, 422, -125, -47, 88, 17, 100, 79],\n [171, 299, 351, -647, -703, -268, -315, -54, 297, -77],\n [595, -175, 475, -58, -889, -293, -672, 405, 260, 223],\n [-639, 220, 0, 219, -32, -84, 479, -419, 166, -120],\n [65, 81, -327, 240, 691, 83, 26, -59, -584, 131],\n [988, -234, 575, -182, -934, -375, -1030, 613, 14, 384],\n [112, 168, 516, -554, -712, -354, -294, -18, 102, 44],\n [228, -448, 435, -943, -474, 153, -125, 404, 389, -200],\n [-151, -186, 76, 58, -540, 128, 144, 84, 845, -240]]\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[[-76, -102, -122, -70, -8, -126, 77, -15, -89, 81],\n [-121, -224, 258, -10, 264, 179, -57, 293, -431, 208],\n [171, 444, -221, -105, 378, -248, -459, -42, 543, -229],\n [-59, -198, 49, 95, -145, 162, 247, -74, -309, 103],\n [-43, -102, 289, 43, 337, 254, -151, 260, -339, 129],\n [139, 260, -294, 58, 438, -5, -213, -263, 65, -100],\n [-25, 60, -302, -138, 148, -293, -79, -77, 119, 6],\n [-78, 10, -453, -211, 203, -433, -56, -107, 74, 63],\n [-60, -194, 104, 70, -397, 102, 310, -42, -140, 52],\n [17, -40, 245, 73, -394, 132, 145, 60, 99, -61]]\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[[-28, -42, -56, -56, -154, 196, 266, -84, 196, 224],\n [-20, -30, -40, -40, -110, 140, 190, -60, 140, 160],\n [-2, -3, -4, -4, -11, 14, 19, -6, 14, 16],\n [-42, -63, -84, -84, -231, 294, 399, -126, 294, 336],\n [24, 36, 48, 48, 132, -168, -228, 72, -168, -192],\n [12, 18, 24, 24, 66, -84, -114, 36, -84, -96],\n [38, 57, 76, 76, 209, -266, -361, 114, -266, -304],\n [-4, -6, -8, -8, -22, 28, 38, -12, 28, 32],\n [-14, -21, -28, -28, -77, 98, 133, -42, 98, 112],\n [28, 42, 56, 56, 154, -196, -266, 84, -196, -224]]\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[[-50, -25, 70, -50, 65, 40, -105, -35, -70, -70],\n [-180, -90, 252, -180, 234, 144, -378, -126, -252, -252],\n [-120, -60, 168, -120, 156, 96, -252, -84, -168, -168],\n [50, 25, -70, 50, -65, -40, 105, 35, 70, 70],\n [90, 45, -126, 90, -117, -72, 189, 63, 126, 126],\n [-120, -60, 168, -120, 156, 96, -252, -84, -168, -168],\n [-210, -105, 294, -210, 273, 168, -441, -147, -294, -294],\n [-180, -90, 252, -180, 234, 144, -378, -126, -252, -252],\n [160, 80, -224, 160, -208, -128, 336, 112, 224, 224],\n [-180, -90, 252, -180, 234, 144, -378, -126, -252, -252]]\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[[-418, 329, 66, 187, 354, -134, -103, 171, 260, -654],\n [-352, -387, -73, 115, 393, -220, 40, -1201, -561, 922],\n [99, -253, 382, -59, -96, 612, -389, 789, -127, -1206],\n [483, -6, -975, -274, 39, 96, -208, -790, 188, 639],\n [1, -574, 708, 151, -840, 776, -803, 875, -16, -920],\n [-470, -112, 543, -111, 428, 200, -98, 237, -322, -545],\n [150, 339, -529, -543, 502, -312, 265, -687, -69, 912],\n [481, 339, -709, -12, -5, -302, -6, -416, 227, 221],\n [347, 430, -398, 34, 210, -386, 710, 170, 213, 36],\n [660, 791, -833, -141, 124, -575, 262, -159, 406, 105]]\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[[674, -152, 230, -642, -744, -640, -302, -80, -268, 404],\n [208, -9, -90, -114, -173, -130, 141, 115, -306, 93],\n [-186, 100, -310, 306, 292, 280, 442, 236, -268, -160],\n [351, -111, 255, -405, -435, -390, -354, -159, 48, 237],\n [-351, 111, -255, 405, 435, 390, 354, 159, -48, -237],\n [-350, 72, -90, 318, 376, 320, 114, 16, 180, -204],\n [157, 9, -135, -51, -107, -70, 204, 145, -324, 57],\n [301, -59, 65, -267, -319, -270, -80, -3, -172, 173],\n [169, -21, -15, -123, -161, -130, 30, 43, -168, 87],\n [19, -84, 345, -195, -140, -160, -501, -296, 462, 78]]\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[[-29, -1111, -143, -315, 281, 234, 14, -476, -670, -34],\n [-34, -50, 430, -160, 204, 55, 271, -79, -506, -20],\n [-334, 126, -259, 661, -24, 65, -288, -128, 197, -328],\n [343, 857, 312, -364, -301, -368, -40, 571, 717, 522],\n [-174, -93, -298, -254, -131, 532, 161, 52, -373, -480],\n [-901, -869, -735, 925, 679, 587, -530, -745, -630, -906],\n [526, 1154, 252, -176, -710, -433, 268, 707, 908, 412],\n [238, 303, 231, -539, -147, -38, 168, 317, 80, 244],\n [-24, 931, -217, 581, -179, -58, 239, 342, 420, -346],\n [127, 41, -129, -831, -417, 453, 237, 321, -182, -142]]\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[[-120, 397, -78, 690, -93, 44, -195, -779, 523, 27],\n [-336, 406, -295, 867, -1024, -500, 19, -12, -140, 692],\n [339, -337, 456, -461, 528, 97, 164, 567, 866, -1107],\n [-411, 768, 123, -220, -500, 384, -335, 291, -671, 390],\n [109, -330, -129, 281, -151, -228, 549, -232, 284, -57],\n [-547, 124, 774, 980, 48, -76, -52, 531, -155, 624],\n [281, -276, -148, 809, -223, -1213, 3, -681, -357, 317],\n [-75, 439, 87, -97, -947, 188, -173, 1162, -208, 405],\n [1175, -631, -632, -76, -520, -778, -36, -65, 117, 52],\n [-92, 348, 380, -336, 343, 206, -154, -388, -381, -314]]?\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[[365, -504, 964, 127, 108, 666, -714, -539, 55, -198],\n [1138, 244, -206, 166, -871, -502, -753, -247, 5, -766],\n [-763, -94, 637, 80, 1235, 854, 37, 207, 98, 113],\n [-139, -486, 880, -356, 59, 111, -503, -63, -281, 375],\n [375, -192, 432, 63, -202, -158, -795, -129, -151, -200],\n [-890, 77, 634, 539, 953, 1085, 56, -446, 163, 149],\n [532, 124, 371, -360, 86, 151, -323, -386, 308, -401],\n [-108, -45, 23, -181, 27, -100, 17, 146, -265, 218],\n [-647, -192, 484, -355, -149, -160, -99, 272, -712, 794],\n [206, 444, 115, -497, 311, -50, -287, -140, -488, -26]]\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[[148, 271, -212, -92, -210, -227, -124, -314, 404, 61],\n [-45, -180, 163, 168, -56, 256, 223, 410, -604, 48],\n [-125, -186, 212, 69, 25, 102, 275, 172, -217, 84],\n [-398, -392, 369, -138, 606, -44, 144, -146, 395, -102],\n [-461, -520, 408, -54, 414, 192, 465, 64, -11, 100],\n [-142, 20, 109, -86, -458, -168, 656, -282, 303, 492],\n [463, -67, -42, 473, 85, 331, -13, 306, -255, 48],\n [-324, 150, -163, -399, -379, -166, 104, -254, 43, 132],\n [155, -206, -86, 207, 573, 402, -485, 348, -367, -375],\n [26, 184, -389, -144, -544, 68, 256, -310, 129, 418]]\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 10x10 matrix:\n[[-38, -267, 56, -440, 103, -853, 535, 295, -253, -327],\n [-206, -302, 432, -1, -709, 178, -96, 8, -256, -582],\n [181, -43, -288, 178, 302, 6, -200, 161, 16, 438],\n [89, 358, -105, 296, 159, 528, -202, -359, 345, 271],\n [35, 137, -73, 464, -180, 857, -661, -150, 138, 378],\n [-173, 394, -206, -482, 337, -245, 169, 102, 71, 335],\n [-408, 63, 268, -322, -575, 267, -209, 97, -209, -195],\n [-274, 595, -104, -500, 221, -3, 153, -103, 189, 255],\n [-156, 227, 184, -435, 68, -419, 603, -209, 103, -421],\n [133, -418, 96, 34, -37, -453, 253, 152, -191, -339]]\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[[-123, 662, 67, -266, -456, 881, -780, 67, 191, 478],\n [-294, -223, -855, 83, -345, -256, 516, 225, -476, -364],\n [-59, 215, -415, 66, -462, 798, -187, 203, 63, 199],\n [776, -476, -132, 510, 246, -430, 588, 196, 190, -704],\n [30, -233, -142, 487, -75, 61, 171, 74, 201, -207],\n [-783, 91, 459, 984, 206, 144, -18, 1129, -985, -765],\n [-707, 490, -8, 290, -676, 747, -483, 833, -363, -485],\n [-997, -378, -311, 124, -207, 150, -81, 476, -459, -248],\n [-775, 463, -414, -201, -60, -454, 716, -30, -396, 312],\n [53, 329, -631, -42, 200, -7, 565, 11, -377, 623]]\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 10x10 matrix:\n[[189, 311, 802, 663, 174, -77, 589, -220, 15, -156],\n [65, 76, -172, -19, 45, 283, 241, -335, 35, -244],\n [553, -286, 265, 111, 652, 195, -416, 705, -158, 147],\n [-645, 736, 288, -312, 16, 527, 803, -680, 10, -247],\n [-85, 118, 313, -339, -709, -379, -312, 71, 119, 427],\n [-232, -961, -617, -179, -270, 140, -634, 160, 30, -144],\n [-143, 188, -223, 258, 836, 216, 359, -309, 10, -107],\n [-189, 629, 224, 104, 286, -45, 511, -413, 67, 89],\n [250, 274, -474, -327, 184, 138, -3, 105, -97, -15],\n [-31, -808, -749, -295, -193, 9, -741, 471, -72, -29]]\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[[-522, 152, 201, 189, 369, -585, -632, 226, -115, 406],\n [241, -21, -26, 173, -329, 562, -310, -418, -363, 324],\n [1004, -705, 664, -709, 324, 343, 380, 584, -293, -61],\n [458, -32, 496, -473, 305, 9, 249, 302, 36, -340],\n [-508, -60, 455, -40, 643, -372, -165, 472, 195, -125],\n [68, -125, -35, 228, 493, 460, 423, 235, -400, -127],\n [276, -760, 208, -343, -360, 313, -101, -6, 148, 289],\n [586, 49, -74, -78, 158, 79, 477, 281, -352, -282],\n [380, -176, 376, -102, 182, 596, -3, -5, -334, 32],\n [90, -64, 90, -42, -513, -132, -341, -47, 242, -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[[537, 321, -360, -176, -79, -11, -97, -471, 19, 472],\n [151, -71, -69, 401, -209, -577, -555, -339, 311, 548],\n [-169, 211, 434, -283, 63, 667, 356, 156, -337, -560],\n [-312, -10, 122, -141, -46, 242, 297, 243, -120, -316],\n [-339, 152, 624, 152, -336, 188, -137, -93, -58, -182],\n [32, 162, 269, -125, 60, 360, 96, -18, -182, -244],\n [-52, 478, 595, -216, -244, 664, 115, -237, -300, -292],\n [284, 492, -211, -341, -330, 258, 132, -450, -92, 320],\n [-451, -203, 513, 292, -65, -41, -132, 234, 25, -312],\n [302, 857, 1, -591, -525, 703, 304, -636, -291, 210]]\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[[250, -472, -932, 157, 111, -432, -206, -75, 469, -247],\n [-269, -356, -663, -532, 153, -271, -113, -470, 646, 132],\n [404, -727, -581, 117, 126, -80, -412, 449, 577, 373],\n [-322, -274, -45, -245, 187, -222, 319, -678, 134, -521],\n [12, 550, -1098, -391, 53, -211, -863, -496, 1095, 969],\n [-138, 196, -127, -763, 359, 217, -626, 829, -130, 327],\n [303, 165, -377, -224, 23, -4, 56, -551, -233, 1256],\n [101, -77, -103, 647, -421, -63, 398, -40, 346, 381],\n [-381, -150, 927, -9, -783, 142, 747, -483, 289, 537],\n [192, -63, -94, -325, 605, 464, -135, 166, -495, 1048]]?\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[[-399, 209, -304, -57, 190, 285, -95, -133, 266, -304],\n [-45, 79, -152, -71, -34, -13, 43, -7, 22, -60],\n [75, -67, 116, 43, -8, -31, -9, 21, -46, 70],\n [159, 83, -232, -171, -242, -249, 199, 77, -130, 44],\n [255, 102, -306, -238, -357, -374, 289, 119, -204, 85],\n [57, -307, 632, 331, 250, 185, -255, -21, 2, 172],\n [-153, -100, 266, 188, 253, 256, -211, -77, 128, -33],\n [-477, 42, 78, 174, 435, 510, -315, -189, 348, -267],\n [192, -350, 676, 318, 158, 66, -196, 28, -92, 262],\n [672, -158, 100, -130, -514, -638, 348, 252, -476, 422]]\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[[194, -100, -86, -72, -30, 54, -64, -56, 140, -64],\n [170, 99, -301, 30, -138, -87, -174, -34, 85, -2],\n [143, -256, 157, -144, 87, 171, 68, -56, 140, -100],\n [-475, 132, 347, 120, 141, -51, 228, 128, -320, 124],\n [248, 189, -493, 66, -228, -159, -282, -46, 115, 10],\n [-286, -330, 704, -132, 330, 264, 396, 44, -110, -44],\n [247, 285, -608, 114, -285, -228, -342, -38, 95, 38],\n [28, -162, 166, -84, 84, 114, 84, -20, 50, -52],\n [-123, 20, 107, 24, 45, -3, 68, 32, -80, 28],\n [222, 159, -429, 54, -198, -135, -246, -42, 105, 6]]\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[[78, -99, 13, 764, 97, 111, -400, -218, 167, -175],\n [-27, -2, -23, -59, 27, 5, 16, 34, 24, -20],\n [305, 69, 264, 543, -260, -70, -114, -362, -233, 187],\n [122, -76, 107, 416, -272, -21, -145, -177, -257, 240],\n [-148, -344, -85, 54, -622, -29, -63, 141, -663, 688],\n [-123, -198, -108, 135, -147, 48, -135, 87, -147, 168],\n [-469, -159, -445, -449, 564, 197, -59, 477, 566, -493],\n [-292, -32, -264, -508, 372, 88, 92, 340, 356, -312],\n [459, 330, 387, 435, 21, -105, 12, -486, 60, -132],\n [129, 93, 77, 349, 206, 39, -143, -187, 250, -269]]?\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[[-20, 300, -564, 428, 8, 88, 500, -4, -380, -44],\n [-218, 58, 291, -109, -234, -165, -317, -321, 19, 265],\n [20, -300, 564, -428, -8, -88, -500, 4, 380, 44],\n [22, 198, -438, 314, 44, 88, 398, 50, -266, -74],\n [394, -454, 174, -322, 388, 176, -54, 550, 418, -398],\n [-420, 360, 63, 159, -426, -231, -165, -597, -285, 453],\n [-93, -277, 729, -495, -130, -176, -677, -163, 399, 183],\n [373, -403, 111, -265, 370, 176, -3, 523, 361, -383],\n [-21, -169, 378, -270, -40, -77, -344, -46, 228, 66],\n [14, 186, -399, 289, 34, 77, 361, 37, -247, -61]]?\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 10x10 matrix:\n[[-251, 764, 340, 320, -68, 64, -710, -321, -124, 128],\n [643, 60, -645, -631, 337, 297, -43, -1097, 982, 84],\n [580, 297, -595, -833, 426, 302, 97, -57, -91, 47],\n [582, -556, -585, -505, 178, 627, 433, -68, 70, -437],\n [706, -238, -550, -258, 452, 683, 154, -508, -8, -420],\n [-33, 366, -91, 261, -317, 331, -21, 443, -464, 100],\n [422, -348, -454, -549, 229, -70, 371, -188, 438, 9],\n [-553, -297, 693, 43, 157, -1041, -74, 153, 109, 80],\n [236, -406, -471, -166, -428, 562, 361, -21, 456, -121],\n [-90, 715, 20, -39, 48, 155, -457, -543, 263, 358]]\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 10x10 matrix:\n[[473, -18, 308, 275, 115, -712, 779, -132, 210, -134],\n [-543, 149, 318, 491, -496, 370, -135, -599, -351, 830],\n [-151, -805, -38, -163, -104, 542, -269, 815, 263, -167],\n [530, 634, -714, -112, 841, -347, -73, -24, -23, -30],\n [-38, -1414, 1096, -328, -1101, 245, 594, 495, -80, -435],\n [-285, 608, -362, 367, 684, -206, 475, -593, 672, 180],\n [518, -1, -293, -364, 352, -474, -283, 688, -214, 11],\n [-146, 513, -84, -283, -482, 10, -84, -677, -166, -466],\n [12, 430, -868, -459, 450, -194, -492, 385, 621, -839],\n [623, 607, 203, 79, 580, -497, -91, -302, -973, 565]]\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 10x10 matrix:\n[[297, 164, -300, -126, -59, 81, 99, 398, -141, 552],\n [-319, -214, -263, -598, -148, 578, -333, -185, -223, -380],\n [90, 132, -274, -125, -84, 169, -144, 294, -337, 174],\n [-389, -108, 5, -709, 179, 422, 85, -205, 454, 70],\n [639, -28, -11, 307, -188, 128, 288, -10, -733, 302],\n [-234, 764, 218, 746, 409, -828, -271, 757, 117, 156],\n [-679, 328, -55, -439, 360, -46, -278, 346, 651, 66],\n [298, -486, 57, 361, -439, 136, -110, -577, -703, -722],\n [208, 392, -324, 86, -3, -116, -113, 667, -257, 500],\n [-679, 156, -87, -711, 253, 474, -321, 71, 130, -134]]\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[[108, -24, -126, 66, 18, -132, 18, 84, -96, 114],\n [378, -84, -441, 231, 63, -462, 63, 294, -336, 399],\n [-108, 24, 126, -66, -18, 132, -18, -84, 96, -114],\n [54, -12, -63, 33, 9, -66, 9, 42, -48, 57],\n [306, -68, -357, 187, 51, -374, 51, 238, -272, 323],\n [270, -60, -315, 165, 45, -330, 45, 210, -240, 285],\n [-108, 24, 126, -66, -18, 132, -18, -84, 96, -114],\n [-180, 40, 210, -110, -30, 220, -30, -140, 160, -190],\n [360, -80, -420, 220, 60, -440, 60, 280, -320, 380],\n [-216, 48, 252, -132, -36, 264, -36, -168, 192, -228]]\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[[-23, -398, -349, 355, -763, -135, -43, 699, 269, 533],\n [-293, 510, 236, -307, 228, 374, 189, -528, -125, -836],\n [-58, -198, 89, 38, -814, 237, -1091, 425, 557, 325],\n [245, -7, -133, 812, 699, -434, 251, -193, -131, 67],\n [666, -263, -345, 1353, 1183, -761, 446, 84, -199, -3],\n [1191, -920, -276, 164, 782, 807, 228, -482, 51, 351],\n [-328, 234, 85, -662, -319, -141, 233, 475, 81, -465],\n [208, -69, 436, 81, -89, 80, -560, 95, -263, 352],\n [-266, 93, -23, 91, -403, -154, -479, 335, -311, 271],\n [-147, -240, 178, -426, -1008, 299, -350, 101, 209, 171]]\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[[-203, -303, -501, -247, -202, -390, -545, -490, 205, -184],\n [-348, -91, 237, -772, -647, 32, -426, -597, -225, 46],\n [777, -633, -231, 238, 193, 471, -436, -272, 957, 308],\n [160, -330, -338, -153, -1058, 223, -738, -168, -698, 416],\n [611, -130, 101, -159, 271, 106, 290, -176, 539, 307],\n [-124, 425, 1038, 252, 251, 676, 625, 496, -128, -63],\n [-15, 165, 642, -34, -43, 438, 265, 113, -73, 46],\n [610, -465, -694, -346, -485, -27, -631, -346, -65, 666],\n [641, -448, 102, -115, -155, 362, -159, -429, 630, 270],\n [384, -177, -995, -174, 334, -496, -311, -27, 111, 462]]\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[[19, 10, -185, -42, 136, 32, -152, -7, -42, -91],\n [-151, -586, 500, -113, 220, 282, 381, 172, 123, 81],\n [-995, 393, -444, 379, -62, 228, -583, 82, 69, -717],\n [-413, 129, -237, -186, 42, -178, -216, 85, -118, -361],\n [252, 129, 493, 387, -558, -18, 303, -135, 129, 360],\n [-478, 224, -74, 148, -278, -63, -390, -8, -120, -516],\n [145, 704, -450, 307, -466, -274, -583, -261, -186, -241],\n [294, -62, 232, 196, -166, 106, 60, -101, 29, 160],\n [-804, 256, -16, 710, -160, 517, -48, 79, 409, -152],\n [-244, 176, 107, 225, -200, 30, 201, 31, 187, 138]]?\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[[330, -326, 489, -264, -288, -495, 463, -485, 238, 102],\n [-46, -541, 247, -73, 89, -225, -65, -93, 306, 556],\n [-381, -152, -120, 159, -72, 9, -71, 112, 40, 24],\n [486, 230, 202, -216, -102, -120, 288, -262, -68, -224],\n [178, -95, 192, -119, -83, -174, 168, -186, 80, 42],\n [77, -487, 244, -112, 221, -153, -155, -54, 288, 634],\n [277, 166, 43, -101, 88, 48, 10, -39, -62, -38],\n [169, -6, 150, -101, -122, -147, 197, -178, 28, -72],\n [289, -200, 505, -251, -602, -618, 760, -633, 166, -278],\n [13, -370, 457, -149, -668, -654, 728, -581, 230, -218]]?\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[[35, -77, -14, -154, 119, 14, 119, -63, -126, -140],\n [70, -154, -28, -308, 238, 28, 238, -126, -252, -280],\n [110, -242, -44, -484, 374, 44, 374, -198, -396, -440],\n [-95, 209, 38, 418, -323, -38, -323, 171, 342, 380],\n [20, -44, -8, -88, 68, 8, 68, -36, -72, -80],\n [-50, 110, 20, 220, -170, -20, -170, 90, 180, 200],\n [-55, 121, 22, 242, -187, -22, -187, 99, 198, 220],\n [35, -77, -14, -154, 119, 14, 119, -63, -126, -140],\n [-105, 231, 42, 462, -357, -42, -357, 189, 378, 420],\n [-85, 187, 34, 374, -289, -34, -289, 153, 306, 340]]\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[[769, -313, 44, -244, -378, 312, 248, -126, -113, -531],\n [918, -1302, -529, 550, 176, -607, 298, 391, -719, -316],\n [353, -75, 315, -514, 688, -404, 520, -187, -722, 133],\n [-474, -133, 78, 997, 251, -309, 301, 98, 657, 677],\n [474, -940, -360, 562, -713, 165, -1050, 860, -856, -380],\n [-39, 475, -876, 66, 253, -259, 814, 112, -139, 80],\n [355, -278, 367, -368, -42, -101, -49, -456, 425, -412],\n [-471, 676, -381, -877, 291, 211, 52, -424, 3, -375],\n [559, 431, 434, -1065, -74, 496, 196, -482, -644, -463],\n [484, -1046, 423, -35, 246, -661, -745, 5, -717, 113]]\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[[389, -26, -34, -63, -321, 67, 456, 24, 84, -490],\n [-619, 55, -189, 249, 466, -323, 96, -344, 541, 337],\n [599, 70, -121, 211, 241, -412, 543, 174, 65, -441],\n [45, -172, 361, 290, -28, -469, 440, -177, 52, 136],\n [73, -218, 138, -108, -459, -111, 448, -531, 1, -56],\n [-116, -77, 336, -17, -383, 40, -455, 302, 133, 554],\n [-705, -498, 102, -164, 55, 240, -890, -494, -758, -392],\n [-42, -580, 360, 165, -626, -624, -420, 396, 310, 16],\n [-283, 153, 297, 8, -52, -628, 101, -536, -486, -269],\n [769, -430, 39, -85, -375, 507, 282, 527, -216, -287]]\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 10x10 matrix:\n[[56, -359, 124, 144, 390, 89, -394, -137, -630, 214],\n [80, 206, 28, 165, -396, -331, 138, -13, 455, 36],\n [263, 477, 141, -567, 88, 252, 210, -10, -16, -550],\n [12, -822, -413, 233, -71, 552, -279, -196, -147, 369],\n [939, 80, 22, -196, -843, 485, -409, -503, 353, -33],\n [-450, -83, 271, 326, 825, -628, 139, 180, -612, 61],\n [-205, -289, -115, -170, 542, 356, 38, 62, -479, -112],\n [154, -518, -316, -133, 122, 659, 8, -199, -205, -90],\n [-219, -362, -222, -262, 503, 571, 9, 71, -459, -115],\n [-239, -77, 48, 490, 21, -625, 179, 67, 137, 219]]\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[[27, -222, -136, -24, -123, 310, -65, 86, 171, -127],\n [415, 273, -544, -163, -47, -429, 218, 475, -783, -230],\n [51, -59, -7, 209, -238, 421, -135, -73, 215, -197],\n [5, -573, -437, 259, 205, 308, -122, 163, 56, -287],\n [33, -287, -396, -91, 350, -276, 95, 285, -310, -40],\n [-5, 40, 40, -74, -28, -27, 20, 2, 10, 43],\n [-74, -176, -105, -152, 258, -223, 72, 110, -91, 109],\n [242, 604, 227, -588, -734, 77, 140, 114, 17, 89],\n [404, 591, -177, -659, -483, -343, 290, 425, -518, 8],\n [203, -123, -421, 325, 37, 100, -48, 173, -280, -355]]\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[[22, 29, -56, -119, -60, 13, -73, -204, 24, -119],\n [-25, 506, -231, -606, -66, -661, -96, 353, 11, 32],\n [184, -654, 172, 757, 343, 531, -304, -41, 350, 422],\n [381, 419, -375, -760, 347, -216, 96, -432, 32, -533],\n [160, 411, -134, -434, 421, -285, 562, 207, -216, -354],\n [53, 450, -141, -343, -681, -91, 35, -78, -475, 193],\n [-270, -141, 200, 212, 53, 330, 171, 757, -82, 139],\n [-257, -366, 33, 42, 60, 111, -616, 5, 568, -87],\n [-211, -289, 129, -48, 531, 536, 312, 2, 170, -793],\n [188, 785, -222, -555, -442, -527, 441, 56, -659, 108]]\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 10x10 matrix:\n[[-125, -726, 366, -65, -160, 209, 287, -809, -153, 24],\n [588, 234, -271, 35, -453, -583, -369, 405, 575, -1],\n [379, 484, 324, 828, -455, -217, 215, 727, 251, -675],\n [254, -130, -338, -206, -369, -908, -262, -98, -78, -271],\n [-22, 94, -103, -358, 87, 69, 155, 145, 500, 30],\n [393, 35, 737, -310, -378, 549, -250, 182, 406, 51],\n [570, 210, 564, -244, -629, 457, -984, 359, -287, 384],\n [-300, -931, -838, 144, 275, -487, -448, -599, -298, 703],\n [-198, -434, 402, -736, 114, 503, -1048, -397, -492, 722],\n [-432, -403, 172, -512, 709, 541, -249, -422, 395, 611]]\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 10x10 matrix:\n[[-30, -54, -36, -39, -30, 54, -24, 57, -48, 51],\n [-10, -18, -12, -13, -10, 18, -8, 19, -16, 17],\n [110, 198, 132, 143, 110, -198, 88, -209, 176, -187],\n [70, 126, 84, 91, 70, -126, 56, -133, 112, -119],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n [-170, -306, -204, -221, -170, 306, -136, 323, -272, 289],\n [140, 252, 168, 182, 140, -252, 112, -266, 224, -238],\n [-90, -162, -108, -117, -90, 162, -72, 171, -144, 153],\n [80, 144, 96, 104, 80, -144, 64, -152, 128, -136],\n [-140, -252, -168, -182, -140, 252, -112, 266, -224, 238]]\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[[507, -761, -154, 234, 268, 0, 248, 191, 268, -47],\n [-407, -43, 282, 142, -360, -785, -15, 217, 536, 665],\n [1122, -686, 764, 72, -98, -432, -196, -448, -260, 16],\n [274, -653, -615, 235, 433, 203, 339, 321, 271, -301],\n [640, -546, 259, -336, -63, -334, -26, 148, -521, -628],\n [498, -125, 477, 498, 64, -295, -234, -664, 262, 743],\n [13, -148, 191, -34, -579, -730, -163, -134, 82, -171],\n [430, -606, -180, 500, 666, -601, 61, 76, 288, 470],\n [295, 64, 934, -286, -594, 602, -27, -236, -91, 187],\n [292, -977, -291, -196, -48, 122, 501, 796, 198, -639]]?\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[[147, 210, 168, -84, 399, 147, -147, -441, -147, -273],\n [-7, -10, -8, 4, -19, -7, 7, 21, 7, 13],\n [-119, -170, -136, 68, -323, -119, 119, 357, 119, 221],\n [-56, -80, -64, 32, -152, -56, 56, 168, 56, 104],\n [-56, -80, -64, 32, -152, -56, 56, 168, 56, 104],\n [-119, -170, -136, 68, -323, -119, 119, 357, 119, 221],\n [-140, -200, -160, 80, -380, -140, 140, 420, 140, 260],\n [-77, -110, -88, 44, -209, -77, 77, 231, 77, 143],\n [-7, -10, -8, 4, -19, -7, 7, 21, 7, 13],\n [-21, -30, -24, 12, -57, -21, 21, 63, 21, 39]]\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[[-27, -551, -423, -368, -337, 305, 105, -457, 659, 125],\n [-64, -38, 454, 302, 661, -199, 406, -306, -456, -495],\n [-170, -226, -297, 180, 89, 228, -337, 179, -357, 366],\n [664, 644, 564, 213, 50, -528, -94, -301, -372, -219],\n [-52, -309, -519, -248, -281, 290, -254, 370, 43, 235],\n [-23, 243, 136, 496, 1177, -328, -776, 8, -1754, 144],\n [468, 329, -395, -117, -1214, 179, -572, 553, 527, 717],\n [635, 291, 212, -145, 448, -525, -422, -889, -578, -140],\n [218, 572, 593, 60, 26, -427, 245, -365, 255, -263],\n [76, -388, -442, -448, 66, 95, -232, -296, -15, 27]]\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[[191, 193, 50, -91, -113, 240, -468, -40, 154, 78],\n [-413, 179, -497, -9, 50, -205, 298, -64, 5, -836],\n [-441, 232, 160, 440, 121, -451, 646, 347, -202, 53],\n [-320, 84, 306, 480, 82, -434, 532, 336, -242, 160],\n [35, -133, 416, 289, 7, -168, 136, 190, -168, 414],\n [224, -59, -553, -605, -41, 440, -428, -417, 283, -401],\n [-584, 106, -1, 513, 96, -609, 712, 274, -279, -479],\n [289, -157, 383, 77, -78, 105, -286, 42, -31, 460],\n [337, -67, 266, -4, -156, 216, -562, -48, 62, 211],\n [660, -144, 85, -520, -101, 649, -758, -266, 279, 636]]\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 10x10 matrix:\n[[111, -196, 62, 269, -19, -144, 693, 638, -76, 131],\n [512, 456, 787, 97, 137, -444, -59, 135, -179, 10],\n [-340, -39, 392, 398, -547, -284, 252, 205, 177, -458],\n [-464, -240, -85, 162, -572, -25, 262, 68, 127, -508],\n [-131, -492, -678, -63, -11, 286, 601, 364, -80, 125],\n [-608, -90, -417, -111, -149, 364, -695, -695, 367, -130],\n [-34, -77, 52, 51, -234, -99, 285, 178, -71, -238],\n [-158, -348, -625, 105, 481, 410, 85, 161, 229, 752],\n [-405, -219, -277, 453, 426, 289, -201, 67, 558, 813],\n [373, 445, 962, 296, -43, -559, 30, 234, -77, -111]]\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[[627, 478, -136, -375, -7, -74, -568, -259, -479, 268],\n [-339, -313, 214, 276, 175, 122, 349, 49, 284, -166],\n [443, 267, 86, -170, 217, 54, -347, -301, -306, 162],\n [422, 238, 124, -140, 258, 76, -318, -314, -284, 148],\n [67, -54, 256, 101, 329, 150, 20, -203, -3, -12],\n [204, 230, -236, -222, -236, -136, -242, 40, -190, 116],\n [276, 226, -100, -186, -52, -56, -262, -88, -218, 124],\n [21, 29, -38, -30, -41, -22, -29, 13, -22, 14],\n [61, -114, 400, 179, 503, 234, 68, -293, 27, -36],\n [-248, -127, -106, 65, -192, -64, 177, 206, 161, -82]]\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[[326, 869, 368, -92, -106, -321, 241, 512, -445, -166],\n [-254, 508, -406, -205, 49, 399, -61, -529, 0, 339],\n [-538, 20, 131, 374, -31, 504, 144, -383, 68, -161],\n [-783, 484, 836, 611, -365, 1237, -13, -396, 1230, 118],\n [-602, 34, 192, 868, -461, 945, 216, -832, 749, -348],\n [-55, 636, 1115, 544, 514, 240, -105, -231, 741, 458],\n [199, -442, 161, 198, 582, -458, -338, -342, -480, 159],\n [452, -405, -19, 571, -341, -399, 772, -321, -807, -1031],\n [-217, -235, 599, 502, -39, 37, -317, 132, 53, -184],\n [-14, -117, 4, -35, 14, -195, 94, 509, 66, -133]]\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[[-863, 349, -712, 243, 145, 1077, 382, -823, -404, -603],\n [249, 90, -355, -359, -83, -230, 503, 337, 638, -570],\n [-690, 164, 287, 649, 576, 283, -309, -663, 3, -783],\n [-110, -1012, -130, 2, -489, -462, -782, -914, 181, -26],\n [-433, 419, 350, -404, 995, 314, 522, 524, 254, -1072],\n [727, 569, 366, 267, -31, 37, -34, 478, -191, 427],\n [-637, -1, 121, 86, 530, -94, -242, -322, -56, -225],\n [557, -518, -771, 99, -1000, -220, -766, -620, -65, 664],\n [877, 79, 23, 286, -267, -452, -848, 529, 119, 708],\n [321, 273, -131, 81, 387, -493, -899, 471, -80, -142]]\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[[342, 84, -428, -336, -210, -206, 494, -608, 322, -664],\n [-241, -110, 78, 92, 171, -15, -389, 268, -91, 244],\n [152, 169, 392, 236, -147, 308, 380, 114, -185, 242],\n [-92, -52, 7, 85, 116, -157, 264, -173, 178, -284],\n [-412, -236, -86, -10, 296, -130, -868, 402, -100, 336],\n [-100, 55, 465, 287, 3, 369, -284, 547, -397, 706],\n [218, 133, 57, -61, -213, 231, -14, 91, -181, 238],\n [218, 106, -67, -157, -212, 175, -138, 65, -154, 200],\n [-149, -136, -225, -41, 193, -370, 219, -347, 353, -556],\n [-290, -193, -186, -110, 205, -136, -774, 280, -61, 230]]?\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[[117, -310, -696, 71, 340, 373, 1456, 136, 116, 848],\n [-229, -127, -409, -324, 72, 372, 260, 0, -247, 420],\n [623, 379, 395, -534, -10, 630, 966, 175, 305, 16],\n [1071, -193, 796, 592, -558, -1257, -293, 654, 244, -1085],\n [-133, -257, -115, -832, -377, 443, 104, 226, -430, 237],\n [497, -478, 145, -784, -79, 1004, 723, 143, -131, -270],\n [-143, 378, -399, -55, 541, 365, 550, -545, -330, 1373],\n [-458, 439, -348, -409, -62, -194, -515, -609, -675, 542],\n [451, -533, -432, 260, -63, -682, -153, 111, -480, 169],\n [-38, -452, 185, -434, -668, -185, -1133, 725, 31, -196]]\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 10x10 matrix:\n[[-196, -371, -11, -861, 5, -846, -1623, 166, -227, -513],\n [-168, -237, 452, -302, 122, 210, -178, 340, 291, 542],\n [-112, -215, 536, -208, 78, 150, -230, 36, 37, 94],\n [211, 27, 29, -390, 23, -68, -343, -259, -408, -579],\n [154, -16, 111, 106, -152, 438, 455, -314, -213, -119],\n [265, 277, -52, 434, -43, 554, 992, -301, -97, 6],\n [-252, -421, 430, 165, -287, 68, -206, -286, -134, -170],\n [-38, 142, -197, -439, 339, -528, -647, 488, 226, 131],\n [-82, 364, -281, 252, 338, -614, -181, 294, 281, -3],\n [434, 779, 192, 259, 641, 404, 972, 16, 126, 56]]\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[[558, -69, -292, -16, -176, 530, 228, 272, -906, 106],\n [226, -203, -69, 635, -307, -146, -719, 475, 231, -43],\n [-504, 979, 159, 862, -34, 454, 72, 795, -191, 533],\n [398, -161, -301, -214, 179, 41, 214, 16, -10, -131],\n [-60, 280, -15, -739, -399, 415, -140, -2, 151, 127],\n [573, -176, -6, 348, 181, 108, 139, 411, -687, 110],\n [34, 220, 107, -290, -421, 582, 73, 35, -806, 437],\n [-158, -179, -46, 513, 42, -318, -178, -27, 246, -294],\n [-741, 837, 456, -283, 108, 329, 439, -26, -77, 388],\n [215, -68, -382, -587, -118, 230, 172, -260, 24, 14]]\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[[154, 332, 379, -825, -160, 227, -996, 636, 9, 14],\n [-646, 81, -361, 382, 33, 770, 49, -9, -570, 211],\n [291, -434, 293, -236, -286, -349, 110, -341, 29, -65],\n [-68, -491, 495, -117, -287, -136, 129, -262, -13, 96],\n [-583, 502, -580, 274, 235, 776, -308, 424, 382, 72],\n [-148, -123, -839, 411, -506, -19, -117, -407, 318, -699],\n [-301, 581, 602, 574, -139, -124, -451, -1133, 1487, 115],\n [-105, 646, 591, -25, -570, -366, -1002, -463, 107, -333],\n [-152, 347, -49, -239, -335, 869, -493, -366, 325, -25],\n [-464, 592, -354, 144, 54, 934, -406, -321, 575, 300]]\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[[-149, -133, 247, -129, -698, 267, 413, -28, -97, 110],\n [-34, -27, -213, 651, -211, -34, -423, 177, 334, -473],\n [231, 62, -516, 649, 466, -292, 2, 391, 175, -735],\n [-159, -54, -128, 249, -196, 78, -438, -163, 181, -189],\n [109, -115, 491, 41, -9, -474, -306, 168, 487, 370],\n [-75, 92, -339, 468, -377, 401, 24, 177, -130, -502],\n [150, -330, 431, -465, -35, -507, 1018, 82, 89, 251],\n [-123, -259, -210, 333, 154, -439, -589, -300, 560, -363],\n [25, 17, 759, -178, -667, 126, 105, 302, 59, 676],\n [122, 198, -550, 316, 705, -85, -385, 44, -34, -430]]?\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[[-88, -229, -478, 730, -963, 81, -869, -577, -653, 235],\n [-645, 364, 278, 581, 25, -285, 201, -149, 178, 529],\n [170, 570, 220, 254, 606, 767, 208, 330, 149, 323],\n [206, -192, 118, -410, 138, -74, -63, 18, -79, -240],\n [-347, -750, -232, -85, -469, -663, -379, -465, 52, -307],\n [-402, -418, -527, 37, -337, 501, -255, -427, 545, -232],\n [493, 504, 287, -360, 646, -254, 890, 876, 107, -45],\n [-680, -793, -249, 563, -252, -480, -580, -586, 320, -23],\n [-448, -903, -191, 255, -348, -852, -556, -504, 56, -197],\n [-351, 578, 142, 212, -33, -299, 666, 218, 209, 347]]?\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[[-383, -1358, -912, 203, 240, 637, 414, 143, 378, -221],\n [-266, -1019, -239, -1144, 242, 378, -112, -817, 505, -419],\n [141, 87, 231, -450, -220, -436, -299, -591, 419, -538],\n [219, 380, -102, 154, 155, 354, 1148, -240, 777, 1376],\n [-494, 265, -311, 530, -174, 0, 140, 680, -277, 641],\n [-275, -50, 89, -637, 10, -427, -38, -434, 116, -243],\n [666, -324, 152, -342, 42, 713, 31, -252, -286, -74],\n [-182, -1152, -460, -286, -142, 926, 322, 96, 448, 330],\n [-54, -577, -946, -70, 508, 1257, 659, 275, 697, 429],\n [942, -290, -181, -122, 149, 664, 613, -155, 101, -371]]?\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[[-332, -157, -148, -445, -95, -323, -49, 424, 344, -295],\n [-260, -65, -52, -221, -91, -195, -65, 260, 208, -143],\n [-466, 124, 172, 133, -232, -109, -227, 167, 118, 109],\n [570, -135, -192, -126, 279, 150, 270, -225, -162, -108],\n [736, -149, -220, -107, 353, 219, 337, -322, -236, -101],\n [66, -224, -252, -473, 92, -191, 127, 233, 202, -329],\n [-412, 8, 40, -106, -176, -198, -154, 274, 212, -58],\n [34, -306, -340, -663, 102, -289, 153, 357, 306, -459],\n [176, 81, 76, 231, 51, 169, 27, -222, -180, 153],\n [-428, -33, -4, -201, -171, -247, -141, 336, 264, -123]]\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[[200, -718, -66, 438, -341, 561, -298, 56, 503, -30],\n [-308, 723, -311, -278, 577, -747, 164, -422, -580, 240],\n [71, -10, -86, 160, 171, -10, -438, -196, -418, 637],\n [-267, 704, 188, -594, 237, -509, 538, 122, -326, -350],\n [65, -630, 126, 160, -309, 562, -182, 232, 328, -191],\n [19, -399, -409, 414, 23, 133, -280, -324, 245, 166],\n [-242, 880, -140, -390, 476, -789, 360, -262, -500, 73],\n [-110, -70, -442, 220, 214, -158, -128, -400, 30, 156],\n [-358, 1037, -17, -632, 510, -874, 558, -142, -577, -140],\n [-199, 541, -417, -76, 377, -646, 300, -426, -81, -37]]\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[[227, -359, 21, -43, 497, -166, -523, -238, 116, 298],\n [867, -341, -990, 1089, -110, 132, -463, 543, -729, -459],\n [105, -120, 459, -469, 267, -31, -253, -638, 557, 98],\n [340, -69, -82, 262, -186, 253, 244, 66, 265, -640],\n [220, -159, -640, 415, -35, 125, -36, 765, -163, -265],\n [-109, -63, 66, 59, 31, -242, -609, -398, -335, 617],\n [-312, 305, 137, -200, -43, 25, 733, 266, -89, -150],\n [-215, 44, 173, -296, 286, -175, 36, -70, -76, 348],\n [86, -157, -50, -128, 15, -101, -872, -345, 61, 472],\n [567, -139, -670, 390, 56, -8, -573, 259, -611, 4]]\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[[499, -219, -402, -319, 348, -197, 115, 178, 273, 56],\n [-191, 853, -761, -124, 1099, -450, 712, -203, 340, -158],\n [-143, 395, 580, -208, 79, 124, 368, 448, -78, -400],\n [183, -422, 422, 141, 146, -312, 640, 245, -294, -620],\n [-181, 725, 121, -470, 725, -175, -814, 332, -96, 686],\n [-1184, -933, 37, 618, -50, -431, 951, -46, -187, -1012],\n [194, -332, 510, 737, -783, 603, 707, -30, -143, -873],\n [1, 944, -336, -317, 776, 281, 216, 275, 914, 53],\n [13, 347, -618, 24, 93, 550, -120, 253, 246, -14],\n [-357, -257, 66, -549, -270, -622, -574, -883, 10, 949]]\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[[640, 198, -284, 416, -116, -524, -144, -694, -374, -138],\n [446, -321, -630, 108, 90, -56, -32, -101, 117, -425],\n [146, 435, 503, -170, 135, 628, 83, 102, -391, 135],\n [-327, 83, 373, -328, 283, 871, 53, 589, -9, -33],\n [629, 50, -384, 264, 50, -125, -105, -402, -262, -318],\n [571, 31, -296, 212, -174, -477, 27, -517, -139, -17],\n [-111, -1, -172, 376, -118, -639, -249, -359, -47, -65],\n [53, 285, 283, 50, -87, -83, 6, -190, -233, 209],\n [8, -297, -468, 102, 296, 284, -205, 218, 111, -569],\n [591, -76, -267, -78, -37, 45, 188, -157, -16, -64]]\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[[417, 287, -91, 427, 65, -401, -189, 325, 188, 209],\n [244, 57, -14, 207, 177, -203, -286, 217, -61, 45],\n [446, 388, -126, 488, -32, -452, -74, 328, 326, 280],\n [119, -130, 49, 40, 284, -54, -389, 144, -273, -88],\n [-10, 118, -42, 38, -158, -26, 202, -38, 188, 82],\n [219, 75, -21, 195, 129, -189, -219, 189, -18, 57],\n [553, 455, -147, 595, -7, -553, -133, 413, 364, 329],\n [178, 448, -154, 308, -380, -264, 434, 60, 582, 316],\n [45, -254, 91, -64, 364, 38, -471, 104, -419, -176],\n [312, 418, -140, 398, -206, -358, 180, 194, 454, 298]]\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[[-104, 127, 537, -503, 343, -256, -91, 240, 717, 156],\n [570, 664, -352, 543, -604, -255, -265, -555, 62, -325],\n [-480, -453, -203, -325, -143, -296, 3, 372, -95, 148],\n [281, 194, -366, 457, -440, 78, -149, -350, -283, -208],\n [-1, -141, -355, 265, -264, 126, 9, -104, -434, -80],\n [345, 8, 296, 416, 77, 1060, -344, -378, -181, -118],\n [-217, 49, 135, -447, 20, -594, -43, 276, 504, 120],\n [169, 211, 417, -80, 103, 200, -310, -96, 456, -6],\n [73, 205, -457, 157, -283, -561, 227, -77, -170, -101],\n [292, 393, 71, 125, -241, -100, -315, -248, 343, -128]]\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[[90, -75, -45, -135, 165, 120, 255, 285, -75, 105],\n [-66, 55, 33, 99, -121, -88, -187, -209, 55, -77],\n [132, -110, -66, -198, 242, 176, 374, 418, -110, 154],\n [-36, 30, 18, 54, -66, -48, -102, -114, 30, -42],\n [-42, 35, 21, 63, -77, -56, -119, -133, 35, -49],\n [72, -60, -36, -108, 132, 96, 204, 228, -60, 84],\n [-126, 105, 63, 189, -231, -168, -357, -399, 105, -147],\n [-72, 60, 36, 108, -132, -96, -204, -228, 60, -84],\n [108, -90, -54, -162, 198, 144, 306, 342, -90, 126],\n [-120, 100, 60, 180, -220, -160, -340, -380, 100, -140]]\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 10x10 matrix:\n[[-52, -90, 8, -16, -18, 38, 56, 82, 90, 106],\n [215, 150, -160, 170, 210, 190, -120, -365, -325, -320],\n [236, 213, -148, 164, 201, 133, -156, -395, -367, -377],\n [100, -360, -320, 280, 360, 760, 160, -220, -60, 80],\n [-259, -84, 248, -250, -312, -380, 96, 451, 371, 334],\n [163, 291, -20, 46, 51, -133, -180, -256, -284, -337],\n [9, -171, -108, 90, 117, 285, 84, -36, 24, 81],\n [217, 189, -140, 154, 189, 133, -140, -364, -336, -343],\n [-53, -225, -68, 46, 63, 247, 124, 68, 120, 179],\n [-105, 147, 204, -186, -237, -437, -52, 204, 112, 39]]\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[[300, -75, -482, -405, 25, 331, 416, -246, -256, -328],\n [-426, 0, 186, 724, -57, -717, -30, 56, 278, 651],\n [39, -65, 124, -80, 68, 77, -37, -42, -10, -162],\n [435, -12, 34, -541, 15, 628, 13, 170, -68, -622],\n [456, -4, -154, -326, -93, 451, 294, 266, 48, -429],\n [147, -167, 198, -192, 139, 190, 39, -98, -20, -395],\n [-114, -27, 218, 309, -23, -253, -24, 136, 206, 172],\n [426, -203, 278, -395, 122, 489, 129, 97, 53, -742],\n [-42, 195, 340, 13, -94, 112, -474, 406, 150, 59],\n [420, 31, -436, -525, -55, 534, 297, -1, -207, -415]]\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[[191, -246, 19, 476, -40, 131, 356, 250, 765, -608],\n [306, -499, -373, 92, -125, -47, -41, -163, 831, -296],\n [-76, 6, 828, -254, -110, 412, 722, 410, 560, -750],\n [-183, -22, 820, -1046, -96, 1074, 912, -19, -433, -1053],\n [199, -13, 50, -24, 239, -453, 566, 191, 259, 291],\n [168, -879, -359, -64, 39, -428, 325, -97, -370, 98],\n [-287, 320, -233, 1004, 630, -662, -1418, 671, -126, 485],\n [-51, -275, -164, 202, 413, 358, -831, 180, 514, -955],\n [141, -26, -401, 111, -475, -423, -590, -598, 819, 505],\n [64, 42, 506, -663, 229, 360, 707, 151, 314, -575]]\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[[-57, 199, -214, 320, -520, 36, -436, -655, -1142, 870],\n [-1175, -392, -106, -1101, -976, 205, -280, -245, 247, 936],\n [1083, -65, 210, 579, -19, 829, 933, -210, -340, -449],\n [-162, 293, 273, -248, -637, 83, 206, 803, -142, -209],\n [-169, 241, 621, 429, -430, -234, 529, 263, 266, -350],\n [-384, -69, 114, -782, -117, -787, 545, 555, 1069, -3],\n [168, 196, -438, -52, 1180, 240, -37, -587, 567, -473],\n [-798, 449, -491, 433, -182, 467, 448, -511, -212, 377],\n [-452, 157, 282, -16, -108, -405, 6, 319, 224, -107],\n [273, -65, -948, 28, 454, 215, -109, -465, -124, 408]]\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[[-383, 387, -901, -547, 297, -65, 117, -650, 534, 588],\n [-648, -576, -194, 269, -475, 590, -378, 666, 81, -595],\n [483, -55, 141, 210, 496, 157, -633, 366, -143, -296],\n [-387, 109, 14, -109, -690, -163, 759, -294, -212, 239],\n [-96, -354, -225, -115, 610, 206, -642, -55, 1170, 39],\n [-514, 72, 155, 190, 53, 14, 266, 557, -133, -534],\n [221, 88, -201, -37, 1011, 435, -283, -87, 1187, 197],\n [486, -736, -548, -359, 16, 534, 62, 162, 661, 281],\n [-151, -2, -592, -316, 957, -63, 607, 337, 676, -74],\n [-10, 268, -273, 19, -193, -238, -22, -605, -370, 361]]\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[[86, -785, -375, 530, -152, 393, -506, 999, 181, 990],\n [49, -145, -486, 474, 124, -376, -365, -154, 206, -203],\n [-706, -587, -313, 461, 384, 13, -70, -117, 406, -96],\n [536, -391, 283, -552, -266, -245, 471, -601, -125, 210],\n [-40, -666, -1094, 1308, 826, 232, -562, 569, 1083, 436],\n [614, 91, 666, -691, -138, -434, 76, -786, -480, -89],\n [29, -780, -575, 434, 270, 41, -274, -41, 573, 520],\n [723, -41, 144, -265, 110, -542, -68, -774, -136, -105],\n [-63, -588, -859, 31, 184, 329, 221, 347, 112, 631],\n [-386, 444, 1005, -559, -468, -405, 325, -933, -215, -852]]?\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[[55, 68, -203, -511, 97, -323, 249, -239, 26, 632],\n [2, 357, -86, -461, -13, -210, 235, -110, -172, 707],\n [84, -254, 100, -30, 222, -112, 458, -652, 148, -134],\n [-65, -57, -433, 451, -254, 420, -385, 551, -305, -52],\n [68, -478, -60, 122, 158, -56, 2, -204, 300, -382],\n [-83, 680, 7, -227, -209, 61, 105, 187, -472, 678],\n [-124, 824, 669, -130, -169, 28, -19, 231, -252, 95],\n [-59, 539, 208, 76, -119, 223, 423, -250, -494, 284],\n [-33, 163, 121, 350, -72, 323, 290, -235, -332, -133],\n [-108, 348, 696, 22, -108, -54, -594, 640, 242, -542]]\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[[128, -180, -326, 448, -144, 102, -170, -626, -576, 76],\n [-64, 2, -113, 288, 104, 33, -311, -195, -224, -126],\n [-242, 176, 101, 109, 332, -36, -418, 235, 133, -308],\n [-30, -8, -81, 187, 52, 24, -186, -143, -157, -68],\n [262, -178, -70, -191, -364, 27, 509, -182, -71, 346],\n [-118, 102, 100, -41, 156, -33, -131, 208, 159, -134],\n [148, -160, -226, 238, -184, 72, 20, -446, -386, 136],\n [220, -242, -349, 378, -272, 111, 11, -687, -598, 198],\n [16, -28, -58, 88, -16, 18, -46, -110, -104, 4],\n [-26, 18, 8, 17, 36, -3, -49, 20, 9, -34]]?\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[[-511, 338, 269, 184, 88, 813, 689, 465, 173, -95],\n [-139, 328, 193, 444, 284, 79, 627, -73, 321, 11],\n [-986, 77, 887, 393, 214, 398, 65, -357, -140, 770],\n [-187, 24, -178, -693, 233, -893, -233, 17, -594, 165],\n [-286, -10, 101, -185, 151, 177, 62, 84, 302, 247],\n [270, 184, -197, 15, 352, -164, 602, 144, 387, -680],\n [570, -329, -224, 46, -132, -43, -335, -207, 408, -259],\n [499, 157, -335, 139, 129, -532, 248, -111, 181, -242],\n [555, -279, -143, 139, 117, -201, -134, -355, 628, -323],\n [-572, 602, 262, 201, 451, 120, 996, 283, 6, -38]]?\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[[899, 50, -317, -394, -314, 46, 476, -405, -179, 529],\n [-413, 476, -108, 342, 452, -92, 112, 344, 221, -458],\n [-722, 361, -459, -58, -276, -198, -373, 224, -498, -339],\n [398, -427, -7, -586, 156, 56, -47, -426, 428, -17],\n [659, 142, -757, 366, -830, 225, -200, -379, -93, 90],\n [-34, -320, 331, 686, 316, -292, -196, 171, 770, -107],\n [-202, -205, 10, 24, 6, -406, -265, 21, 972, -756],\n [192, -14, -168, 485, -358, 140, -235, -103, 648, -546],\n [-672, 179, -274, -1178, 162, -317, -51, 1, -132, -605],\n [112, 5, -623, 14, -265, 561, -525, -354, -686, 278]]?\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[[120, 60, -200, 150, 10, 190, 120, 150, 140, -30],\n [48, 24, -80, 60, 4, 76, 48, 60, 56, -12],\n [264, 132, -440, 330, 22, 418, 264, 330, 308, -66],\n [-204, -102, 340, -255, -17, -323, -204, -255, -238, 51],\n [-108, -54, 180, -135, -9, -171, -108, -135, -126, 27],\n [12, 6, -20, 15, 1, 19, 12, 15, 14, -3],\n [-72, -36, 120, -90, -6, -114, -72, -90, -84, 18],\n [252, 126, -420, 315, 21, 399, 252, 315, 294, -63],\n [-204, -102, 340, -255, -17, -323, -204, -255, -238, 51],\n [-180, -90, 300, -225, -15, -285, -180, -225, -210, 45]]\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[[-21, -441, -294, -63, -168, -189, -378, 441, -42, -441],\n [-7, -147, -98, -21, -56, -63, -126, 147, -14, -147],\n [8, 168, 112, 24, 64, 72, 144, -168, 16, 168],\n [-17, -357, -238, -51, -136, -153, -306, 357, -34, -357],\n [-2, -42, -28, -6, -16, -18, -36, 42, -4, -42],\n [3, 63, 42, 9, 24, 27, 54, -63, 6, 63],\n [-4, -84, -56, -12, -32, -36, -72, 84, -8, -84],\n [5, 105, 70, 15, 40, 45, 90, -105, 10, 105],\n [-15, -315, -210, -45, -120, -135, -270, 315, -30, -315],\n [-9, -189, -126, -27, -72, -81, -162, 189, -18, -189]]?\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[[530, -377, -625, 178, -429, 42, -152, -400, 85, 345],\n [-489, 464, -186, 863, 208, -98, 153, -27, 807, 86],\n [-80, -178, -147, -283, 302, -267, -453, -314, -442, -28],\n [567, -87, 154, -304, -753, 160, 261, 474, 116, -30],\n [-241, -72, 195, 234, -289, -66, -198, 238, -255, 226],\n [541, -154, -601, -114, -454, 127, 96, -399, 119, -42],\n [318, -69, 937, -58, -401, 39, 210, 1235, 323, 316],\n [332, 279, -450, -227, -859, 572, 764, -305, 75, -592],\n [-143, -160, 741, -176, -209, -158, -269, 748, -443, 214],\n [141, 483, -158, -526, -247, -80, 312, 48, 322, -732]]\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[[-15, -143, 40, -107, 122, 83, 291, 250, -746, -40],\n [303, 223, -307, -227, -229, -146, 132, 221, -546, -502],\n [33, 599, -224, -443, -472, -489, -357, -492, -428, -542],\n [-129, -434, 207, 457, 224, 430, 398, 6, 91, 841],\n [774, 467, -765, 228, -762, -53, 277, -53, 202, -166],\n [-42, -37, 46, 322, -43, 106, -118, -282, 804, 438],\n [282, 445, -348, -478, -323, -384, -124, 124, -600, -878],\n [462, 154, -395, 376, -343, 83, 45, 1, 922, 92],\n [576, 833, -700, -336, -813, -530, -286, -252, 0, -894],\n [354, 670, -503, -172, -725, -381, -173, -490, -95, -381]]\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 10x10 matrix:\n[[-327, 323, 124, -169, 474, 87, -185, 359, -309, -364],\n [-22, -79, 40, 13, -117, -9, 332, -168, 56, 404],\n [78, 159, -54, -37, -87, -47, -522, 2, 240, -400],\n [-111, -356, -580, -48, -246, -971, -142, -609, 87, 168],\n [157, -113, 8, 103, 45, 158, 16, 169, -131, -148],\n [-121, 375, 438, -65, 333, 624, 106, 469, -157, -120],\n [546, -788, -349, 404, -45, -37, 230, 167, -480, -202],\n [-27, 22, 332, 38, 3, 430, 659, 57, -51, 576],\n [-167, 356, 202, -160, -162, 69, -48, -203, 415, 260],\n [3, 318, 204, -34, 369, 422, -435, 559, -189, -704]]\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[[-374, 202, -109, -347, -549, -164, 94, 851, 512, -355],\n [-416, -540, -264, -143, -294, 887, 0, 88, 400, 46],\n [-410, 904, 145, 64, -325, -844, -406, 911, 766, -571],\n [-132, 775, 248, -104, 31, -1037, -34, 576, 508, -590],\n [127, 229, 33, 523, 160, 85, -488, 258, -201, 134],\n [-27, -1401, -702, -389, 562, 551, 207, -279, -367, 78],\n [-191, -41, -89, -338, -194, -88, 284, 360, 77, -265],\n [219, 708, 375, 778, -202, 2, -587, -516, -467, 528],\n [100, 1269, 719, 391, 101, -206, 340, 657, 158, -929],\n [-132, 83, -141, -9, -551, -23, -348, 309, 368, 254]]\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[[-608, -584, -137, -647, -391, 275, -195, 372, 483, -747],\n [-343, -160, 249, -246, -125, 246, 92, -118, -175, -398],\n [-384, -711, -438, -106, 444, 38, 12, 253, 418, -160],\n [-400, -431, -370, 36, -257, 417, -295, 136, 584, 15],\n [-9, 156, -432, 699, 95, 24, 342, 477, 266, 288],\n [283, 457, 489, -106, -314, 531, 15, 386, -319, -757],\n [392, 108, -59, -569, -191, -155, 106, 296, 51, -640],\n [51, 578, 877, -318, -794, 461, -5, -649, -725, -391],\n [-145, 97, 258, 1047, 331, 761, -587, 136, 4, 668],\n [105, 274, -732, 565, -245, -130, 559, 735, 514, 99]]\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[[-335, 151, 519, 242, 515, 205, 321, -402, -288, -278],\n [-645, 54, 513, 602, 255, -877, -242, -306, -256, 408],\n [-446, 109, 65, -76, 327, -160, -90, -219, -38, 37],\n [-393, 493, 310, 166, -24, 13, 512, -337, -138, -139],\n [118, 196, -583, -36, -246, -102, -355, 810, 536, 82],\n [107, 273, -213, -85, -184, 271, 194, 269, 211, -182],\n [-300, 110, 225, 245, 420, -38, -44, -10, -43, -95],\n [125, -113, -405, 148, -40, -329, -627, 747, 396, 231],\n [124, 201, -631, -225, -118, 146, -277, 742, 539, -67],\n [444, -102, -426, -172, -623, -82, -122, 361, 230, 195]]?\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[[-249, -422, -217, -230, 93, 186, 89, 39, -89, 380],\n [333, -242, 231, -266, 3, -101, -47, 211, 483, 24],\n [143, -284, 288, -407, -488, -558, 241, -188, 392, -130],\n [-181, -1, -514, 244, 606, 664, -92, 264, -440, 369],\n [-423, 111, 532, 76, -248, 48, -518, -154, 118, -43],\n [555, 155, 87, -93, -293, -593, 388, -99, 257, -431],\n [135, 704, -22, 493, -52, -145, 19, -174, -298, -482],\n [-131, -92, -426, -41, -64, -109, 433, -194, -374, 70],\n [-385, -7, -239, 71, -59, 65, 118, -213, -401, 111],\n [556, 98, -156, -174, -456, -838, 778, -288, 72, -478]]\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 10x10 matrix:\n[[349, -615, -446, 204, -85, 666, -707, 449, 286, 834],\n [-593, -95, -193, 103, -29, 130, -394, -804, 461, 356],\n [-344, 480, -100, 452, 39, -222, -218, -18, -706, 13],\n [112, 90, -232, 173, 225, 429, -388, 520, 580, 193],\n [-531, 357, 405, -423, -184, -219, 646, -359, 441, -530],\n [627, -215, -360, 354, 761, 558, -766, 700, 1044, -240],\n [612, -477, 421, -672, -825, -211, 799, 278, -555, 464],\n [-124, 425, 655, 209, -355, -316, -542, -215, -447, -44],\n [27, 14, 441, -745, -4, 65, 531, -255, 839, -229],\n [428, -701, 73, -92, -697, -268, 345, 115, -419, 179]]\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[[-18, -84, -111, -228, -102, 90, 159, 69, 132, 9],\n [-66, 204, -123, 180, 66, -54, -117, 9, 132, 141],\n [218, -348, 587, 52, 62, -66, -59, -185, -660, -397],\n [-243, 338, -682, -157, -112, 111, 134, 230, 770, 432],\n [135, -202, 371, 59, 50, -51, -55, -121, -418, -243],\n [-47, -198, -278, -553, -248, 219, 386, 170, 330, 28],\n [30, -244, -28, -382, -160, 138, 260, 68, 44, -96],\n [145, -326, 338, -153, -40, 27, 90, -78, -374, -284],\n [-108, 392, -169, 410, 158, -132, -271, -13, 176, 243],\n [16, 32, 75, 118, 54, -48, -83, -41, -88, -17]]\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[[459, -95, -172, -600, 176, 340, -699, -482, -193, -385],\n [231, -620, 658, 163, -364, 450, -170, 105, -566, -488],\n [-989, 45, 706, -135, -911, 544, -154, -57, 234, 789],\n [339, 410, -399, 683, 252, 111, 692, 651, 227, -310],\n [-91, -111, -534, -443, 185, -930, -514, -828, 92, -70],\n [-224, 239, 279, -135, -609, 1167, -281, -202, 100, 308],\n [-242, 682, -325, 766, 329, -501, 906, 741, 495, 298],\n [-309, 812, -736, -916, 490, -119, -841, -504, 452, -181],\n [-261, 332, 78, -314, 136, -88, -433, -301, 43, 266],\n [-286, 505, 145, -128, -151, 107, -387, 163, 374, 75]]\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[[-270, -340, -150, 210, -330, 330, -270, 120, 145, 400],\n [-564, -204, -336, 501, -168, 423, -3, 381, 114, 318],\n [46, 316, 14, -4, 322, -192, 332, 46, -121, -332],\n [26, -136, 22, -41, -142, 57, -161, -55, 49, 134],\n [-48, 148, -36, 63, 156, -51, 183, 75, -52, -142],\n [-148, 568, -116, 208, 596, -216, 688, 260, -202, -552],\n [72, -356, 60, -111, -372, 147, -423, -147, 128, 350],\n [48, 120, 24, -30, 120, -90, 114, -6, -48, -132],\n [308, -436, 208, -341, -472, 57, -605, -349, 142, 386],\n [-540, -144, -324, 486, -108, 378, 54, 378, 90, 252]]\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[[-23, -57, 39, 13, -61, 111, 53, -145, -13, -101],\n [-401, -519, -240, -335, -429, -319, 789, -287, -262, -341],\n [80, 104, -27, -26, 74, -60, -122, 148, 131, 106],\n [144, 68, -96, -253, -72, 1, -52, 37, 541, -28],\n [374, 426, 42, 14, 274, 90, -578, 346, 562, 290],\n [-183, -121, -213, -139, -21, -497, 269, 271, -257, 131],\n [13, 147, 102, 289, 245, -39, -229, 209, -370, 229],\n [9, -5, 96, 100, -3, 182, -41, -142, -55, -71],\n [-380, -532, -318, -480, -488, -388, 840, -260, -66, -360],\n [-25, -95, -285, -435, -175, -365, 255, 155, 405, -15]]?\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[[240, -36, -1086, -951, -160, -607, -533, -988, -79, -683],\n [-301, 644, -238, 626, -95, 787, -428, 427, -285, -555],\n [838, -257, 274, 538, -271, 373, 542, 282, 381, -57],\n [562, -1345, -266, -41, -367, -712, -178, -214, -620, 71],\n [187, 357, 432, 695, -552, 811, 746, 557, 85, 424],\n [109, -348, 188, -182, -201, -493, 480, -295, -161, 541],\n [178, 438, -271, 72, 195, 157, 87, -236, 441, -520],\n [88, -83, 222, -63, 135, -58, 453, -104, 32, 464],\n [-608, 12, 90, 356, 748, 208, -969, 546, -198, -483],\n [375, -428, 397, -37, -450, -77, 736, 143, 339, 670]]?\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[[780, 448, 189, 354, 333, 19, -123, -3, -78, 270],\n [532, -20, -198, 416, 304, -16, 58, 373, -573, -430],\n [464, 304, 249, 179, -29, -12, -121, -50, 249, 399],\n [307, 549, 314, 16, 277, 14, -181, -295, 189, 452],\n [-148, 516, 442, -228, -80, -68, -230, -375, 543, 558],\n [-217, 721, 259, -121, 512, -166, -242, -167, -240, -173],\n [-90, -38, -148, 112, 118, -112, 22, 296, -432, -548],\n [23, -331, 18, 1, -541, 31, 65, 56, 438, 289],\n [-465, -135, -212, -196, 221, 2, 77, -14, -348, -430],\n [-444, -1000, -489, -130, -527, 119, 339, 238, -15, -332]]?\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[[110, 110, 231, -33, 143, -176, 99, -220, 176, 66],\n [-70, -70, -147, 21, -91, 112, -63, 140, -112, -42],\n [220, 220, 462, -66, 286, -352, 198, -440, 352, 132],\n [-160, -160, -336, 48, -208, 256, -144, 320, -256, -96],\n [-70, -70, -147, 21, -91, 112, -63, 140, -112, -42],\n [-160, -160, -336, 48, -208, 256, -144, 320, -256, -96],\n [40, 40, 84, -12, 52, -64, 36, -80, 64, 24],\n [-90, -90, -189, 27, -117, 144, -81, 180, -144, -54],\n [-90, -90, -189, 27, -117, 144, -81, 180, -144, -54],\n [210, 210, 441, -63, 273, -336, 189, -420, 336, 126]]\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[[-352, 118, 73, 333, -30, -216, -140, 180, -227, 11],\n [-324, 111, 130, 108, -286, -910, -453, 529, -585, -615],\n [-647, 193, -748, 98, 771, 442, 192, -222, -385, 505],\n [-618, 568, -174, -423, 233, 746, 755, -554, -313, 40],\n [619, 318, 363, 40, -439, -249, -379, -419, -601, -566],\n [214, -198, -424, 132, 452, 508, 52, -303, 384, 587],\n [-119, 278, 263, -264, -257, -850, -617, 457, -259, -679],\n [94, -302, -504, 555, 119, -305, -359, 17, 3, 80],\n [998, -534, 172, 714, -359, -227, -343, -148, -325, 25],\n [587, 262, 104, -290, -192, -153, -354, -381, -271, -485]]\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[[575, 66, -18, -197, -12, -338, -918, 151, 640, 997],\n [430, -96, -444, 408, 239, -273, 503, 156, -484, -634],\n [643, 577, -179, 441, -395, -90, -438, -396, 603, 440],\n [-54, -304, -161, -904, -54, 63, -744, -223, -284, 526],\n [519, -398, 79, -100, 384, -472, -66, 42, 199, -282],\n [185, -236, -560, 205, 69, -93, 40, 342, -274, 52],\n [904, 697, -88, 637, 253, -468, 210, 60, -78, -148],\n [444, -720, 110, -422, -6, -694, -180, 248, 482, -272],\n [289, -522, 385, -147, -87, -734, 531, 218, 364, -1032],\n [212, 306, -368, 709, -170, 201, -43, -119, 301, 253]]\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[[806, -790, 572, -320, -145, -675, -608, -896, 784, 211],\n [-153, -185, -424, -425, 258, -542, 404, -535, 181, 721],\n [229, 262, 9, 422, -547, 688, 559, 402, -622, 186],\n [753, -1064, 501, -186, -255, -1022, -615, -987, 786, 487],\n [363, 641, -370, -456, 201, 72, 1212, -452, 663, -236],\n [-199, -217, 106, 137, -289, 278, -543, 307, -423, -37],\n [-331, 174, -289, 30, 92, 786, 286, 634, -283, -280],\n [600, 713, 862, 165, 342, 614, -350, -7, 22, -617],\n [-634, -384, -626, -532, 216, 12, 62, 91, -353, 715],\n [394, 855, -79, -341, -65, -364, 733, -461, 158, 1]]\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 10x10 matrix:\n[[-301, -144, -713, 501, -129, 877, -230, 61, -165, -261],\n [-228, -243, 59, -1730, 967, -129, 1295, 585, -1422, -853],\n [-1014, -479, -935, -244, 331, 334, 518, -187, -708, -1134],\n [339, 554, -242, 87, -190, 244, 337, -74, -403, 78],\n [44, -108, -282, 219, -222, 805, -220, 281, -383, -213],\n [-41, 173, 437, 183, -385, -1158, -295, -73, 676, 192],\n [-470, -441, 82, -1250, 750, -322, 982, -18, -939, -878],\n [-115, 285, 175, -249, -177, -426, 299, 463, -500, -380],\n [50, -220, 140, -547, 317, 753, 337, 537, -954, -413],\n [-364, -147, 394, -155, 122, -515, 44, 203, 32, -225]]\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[[-395, 85, -3, -87, -476, -680, -958, -201, 35, -188],\n [-187, -133, 25, 83, 211, 10, 123, -391, -132, 457],\n [285, -646, 92, 636, -38, -261, -472, -279, 170, 90],\n [13, -574, 2, 772, -234, -148, 143, -599, -404, -112],\n [-555, 664, -123, -908, 26, 557, 610, 355, -171, 292],\n [-1115, 1325, -349, -1578, 244, 376, 333, 321, -176, 619],\n [1424, 70, 658, 615, 95, -76, 130, 156, 798, -720],\n [646, 411, 273, 334, -268, -436, -474, -386, 614, -307],\n [-177, -507, -65, 592, -790, 137, -143, -695, -61, 387],\n [-54, 506, 355, -770, 693, -123, -98, 404, 340, 235]]\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[[-433, -79, 282, -316, 505, -81, 569, -281, 212, -309],\n [229, 42, -261, 249, -312, 31, -298, -169, -188, 438],\n [-481, -263, 89, -280, -101, -248, 77, -539, 354, -161],\n [81, 34, -24, 67, -40, 38, -67, 105, -54, 27],\n [368, 335, -92, 397, 403, 315, 261, 112, -514, 459],\n [-483, -171, 152, 166, -243, -51, -133, -207, 156, -135],\n [-557, -327, 258, -336, -247, -257, -115, -37, 524, -617],\n [604, 267, -246, 255, 37, 205, -112, 308, -402, 404],\n [-795, -350, 290, -427, 66, -304, 286, -603, 530, -442],\n [-572, -232, 263, -474, 280, -235, 425, -442, 418, -405]]\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[[-210, 667, 428, 253, -5, -299, 165, -505, 431, -209],\n [50, -518, -477, 345, -217, 238, 309, 518, -106, 111],\n [-529, -127, 619, -516, -566, 915, 384, 124, -44, 774],\n [-104, -437, -166, -87, -490, 594, 132, 395, -223, 294],\n [-52, 406, 187, 159, 62, -271, 4, -322, 232, -214],\n [104, 46, -95, 55, 109, -174, -117, -52, -4, -155],\n [-356, 374, 463, 39, -356, 219, 274, -254, 264, 128],\n [-544, 544, 778, -70, -438, 340, 398, -388, 372, 282],\n [210, -295, -345, 138, 292, -187, 16, 247, -93, -40],\n [-59, 273, 96, 273, 69, -237, 161, -180, 244, -143]]\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[[507, 119, 215, -440, -369, 560, -511, -1206, -380, 1203],\n [750, 82, -361, -550, 886, 262, 626, -609, -487, 746],\n [-173, -453, -102, 384, 608, -793, -255, 962, -42, -331],\n [-320, -399, -258, 335, -125, 252, -759, -208, -392, 612],\n [-1127, 668, -660, -288, -502, 317, 647, 332, 565, 59],\n [876, 263, 992, -279, -540, -214, 287, 154, 921, -706],\n [-266, 547, 96, -12, 312, -428, 200, 296, -173, -152],\n [7, -30, -557, -113, 713, -3, 924, 291, 61, -516],\n [-989, -38, -1234, -815, 104, -5, 231, 885, 924, 867],\n [-583, 637, -22, 226, -397, 417, -28, -524, -494, 268]]\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[[-676, 127, 337, -76, -299, -430, 837, -405, 614, -502],\n [486, 205, -250, 327, -13, 169, 176, -350, -797, 154],\n [637, 484, -78, -26, 492, 169, 34, -540, -758, 352],\n [-94, 512, 525, -76, 218, -277, 299, -123, 85, -653],\n [178, 287, 215, 184, -25, 53, -57, 127, -208, -151],\n [330, 194, 107, -270, 688, -35, -371, 103, -283, -341],\n [-342, -508, -36, -321, 168, 43, -450, 480, 462, -224],\n [84, 179, 35, -444, 865, -678, 263, -311, -156, -1126],\n [-948, -114, 287, -147, -240, -300, 1005, -537, 551, -885],\n [-639, -440, 28, 390, -1020, 699, 148, 134, 376, 626]]\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 10x10 matrix:\n[[320, -48, -48, 80, -144, 144, 320, 352, -48, -16],\n [60, -9, -9, 15, -27, 27, 60, 66, -9, -3],\n [-160, 24, 24, -40, 72, -72, -160, -176, 24, 8],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n [200, -30, -30, 50, -90, 90, 200, 220, -30, -10],\n [120, -18, -18, 30, -54, 54, 120, 132, -18, -6],\n [380, -57, -57, 95, -171, 171, 380, 418, -57, -19],\n [180, -27, -27, 45, -81, 81, 180, 198, -27, -9],\n [60, -9, -9, 15, -27, 27, 60, 66, -9, -3],\n [200, -30, -30, 50, -90, 90, 200, 220, -30, -10]]\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 10x10 matrix:\n[[-252, 1018, 250, 113, 718, 128, 531, -137, -62, -458],\n [-998, 1254, -40, -704, -286, 818, -663, 7, 720, 128],\n [255, -192, 9, 262, 235, -270, 128, 457, -344, -320],\n [1069, -303, -172, 715, -303, -368, 58, 167, 303, -190],\n [1051, -1445, -266, 442, -292, -334, -94, 174, 382, -240],\n [120, -934, -960, -238, 319, -348, -640, -34, -114, -335],\n [60, 626, 1, 479, 386, 149, 582, 109, -92, -78],\n [13, -49, -692, -753, 837, 137, -699, -796, -174, -780],\n [739, -229, 181, 94, 1084, 313, 363, -80, -44, -1318],\n [-1158, 1141, 661, -479, 243, 246, 352, -103, -734, 436]]\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[[94, 710, 439, 755, -38, 167, -2, 515, -859, 528],\n [-469, -614, 35, -504, -33, 219, -308, -245, 42, -262],\n [38, -417, 400, -722, 334, 270, -67, -116, 581, -762],\n [209, 129, 143, -247, 337, -34, 136, 250, -616, 173],\n [-1152, 288, 576, 190, -227, -219, 9, 874, -1390, 770],\n [-366, 14, 444, -416, -58, 926, -395, -644, -560, -127],\n [1, -293, 181, -197, 101, 632, -371, -690, -628, -154],\n [-396, -482, -90, -303, -455, 371, -246, -349, -207, -172],\n [782, -305, -125, 487, 560, 353, -408, -393, -484, -187],\n [745, -341, -206, -127, 771, -175, -6, -639, 309, -353]]\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 10x10 matrix:\n[[18, 27, 3, -30, -9, -24, -57, 33, 15, -63],\n [42, 63, 7, -70, -21, -56, -133, 77, 35, -147],\n [12, 18, 2, -20, -6, -16, -38, 22, 10, -42],\n [132, 198, 22, -220, -66, -176, -418, 242, 110, -462],\n [-42, -63, -7, 70, 21, 56, 133, -77, -35, 147],\n [96, 144, 16, -160, -48, -128, -304, 176, 80, -336],\n [132, 198, 22, -220, -66, -176, -418, 242, 110, -462],\n [-54, -81, -9, 90, 27, 72, 171, -99, -45, 189],\n [-36, -54, -6, 60, 18, 48, 114, -66, -30, 126],\n [-66, -99, -11, 110, 33, 88, 209, -121, -55, 231]]\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[[42, 11, 83, 208, 154, -195, -135, -51, -55, 173],\n [108, 39, -33, 12, 6, -15, -45, -69, -75, 27],\n [180, 55, 175, 508, 374, -479, -357, -173, -187, 435],\n [207, 81, -207, -282, -216, 255, 90, -96, -105, -192],\n [-195, -65, -65, -286, -208, 273, 234, 156, 169, -260],\n [-168, -74, 358, 632, 476, -582, -306, 30, 34, 478],\n [-522, -196, 332, 308, 244, -268, 6, 290, 316, 162],\n [-159, -57, 39, -38, -24, 41, 78, 104, 113, -56],\n [18, 19, -293, -608, -454, 565, 345, 61, 65, -483],\n [-336, -113, -89, -444, -322, 425, 375, 263, 285, -409]]\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 10x10 matrix:\n[[129, -66, 38, -23, 63, -126, 103, -64, -41, 155],\n [-56, 36, -16, 16, -32, 56, -60, 24, 16, -84],\n [337, 105, 118, 167, -11, -280, -308, -310, -175, -226],\n [275, -126, 82, -37, 125, -266, 189, -144, -91, 297],\n [139, -174, 34, -109, 133, -154, 325, -16, -19, 401],\n [46, 72, 20, 70, -38, -28, -162, -72, -38, -162],\n [-78, -153, -36, -144, 84, 42, 339, 138, 72, 345],\n [-104, -204, -48, -192, 112, 56, 452, 184, 96, 460],\n [-203, 12, -66, -39, -41, 182, 29, 148, 87, -35],\n [-239, -168, -90, -195, 67, 182, 413, 268, 147, 373]]\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[[43, -131, -462, 154, -60, 257, -316, 235, -291, -40],\n [388, -411, -208, -47, -95, 87, -384, 343, -199, 53],\n [249, -288, -258, 15, -75, 126, -324, 276, -204, 21],\n [373, -341, 78, -146, -60, -73, -196, 205, -21, 80],\n [340, -320, 24, -116, -60, -40, -208, 208, -48, 68],\n [207, -149, 250, -156, -10, -157, 20, 21, 115, 66],\n [350, -335, -4, -109, -65, -25, -232, 227, -67, 67],\n [-51, 67, 94, -18, 20, -49, 92, -75, 67, 0],\n [-501, 457, -110, 198, 80, 101, 260, -273, 25, -108],\n [150, -225, -420, 105, -75, 225, -360, 285, -285, -15]]\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[[480, -209, 595, -916, -883, -444, 306, 37, 71, 236],\n [-532, 33, -164, 383, 800, 666, -467, -710, 112, -475],\n [93, 5, -568, -302, -497, -448, 213, 96, 538, 242],\n [273, -195, 868, -102, -108, -49, 335, 376, 64, 18],\n [175, 340, -289, 368, 374, 144, -693, -405, 161, -53],\n [-149, 118, -93, -352, -207, 154, -251, -398, 240, -63],\n [300, -856, -26, -228, -37, -625, 944, -92, 90, -553],\n [613, -268, 596, 149, 323, -134, -44, -252, -208, -432],\n [-153, -238, -525, 430, 555, 52, 129, -358, 254, -809],\n [244, -60, -256, -195, -79, -252, -198, -393, -232, 141]]\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 10x10 matrix:\n[[-62, 217, -274, -473, 246, -332, -315, -188, 5, -319],\n [168, 433, -188, -795, 530, -646, 139, 206, 47, -475],\n [210, 7, -125, 462, 170, 341, -47, 62, -136, 116],\n [11, -10, 42, 329, -351, 251, -110, -453, 53, -28],\n [54, -134, 344, 389, -455, 255, 349, -78, 99, 167],\n [-193, 184, -247, -648, 155, -448, -376, -259, 52, -349],\n [8, 166, -63, -453, 212, -355, 52, 106, 39, -209],\n [70, 8, 348, -52, -276, -100, 498, 94, 152, -6],\n [-94, 260, -87, -509, -142, -381, -190, -520, 163, -447],\n [421, 586, -238, -5, 39, -71, -66, -707, 95, -640]]\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 10x10 matrix:\n[[28, -64, -4, 8, 0, -60, 60, 64, 84, -28],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n [-140, 320, 20, -40, 0, 300, -300, -320, -420, 140],\n [-84, 192, 12, -24, 0, 180, -180, -192, -252, 84],\n [-119, 272, 17, -34, 0, 255, -255, -272, -357, 119],\n [-133, 304, 19, -38, 0, 285, -285, -304, -399, 133],\n [126, -288, -18, 36, 0, -270, 270, 288, 378, -126],\n [-126, 288, 18, -36, 0, 270, -270, -288, -378, 126],\n [105, -240, -15, 30, 0, -225, 225, 240, 315, -105],\n [84, -192, -12, 24, 0, -180, 180, 192, 252, -84]]\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[[-220, 220, -210, 30, 20, -140, 150, -40, -120, 170],\n [462, 183, 66, -93, -342, 114, -30, -216, 387, 183],\n [242, -371, 306, -27, 38, 190, -222, 104, 105, -295],\n [352, -94, 186, -60, -152, 152, -126, -56, 246, -56],\n [-176, 176, -168, 24, 16, -112, 120, -32, -96, 136],\n [-22, -838, 479, 43, 402, 226, -365, 396, -192, -703],\n [440, -182, 270, -72, -160, 208, -186, -40, 294, -124],\n [154, -799, 522, 9, 286, 278, -390, 328, -51, -659],\n [110, 148, -45, -27, -130, -2, 39, -100, 114, 131],\n [-66, 840, -513, -27, -354, -258, 387, -372, 126, 699]]?\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[[-1022, -205, -143, 542, 428, 575, -253, 235, -217, 428],\n [-1, 689, 557, 217, 238, 278, -15, -502, -659, 693],\n [-763, -560, -125, 227, 237, 447, -149, 227, -321, 131],\n [-800, 682, -116, 284, 990, 153, 62, -6, -283, -36],\n [334, -251, -594, -1107, -184, -228, 1004, -847, 516, 429],\n [-1290, 776, 237, 801, 525, 471, -203, -618, 296, 1251],\n [-435, -415, -508, -160, -110, -117, 456, -133, -3, 354],\n [245, 127, 101, -199, -46, -180, 249, 508, -1, 145],\n [-63, 680, 931, 440, -73, -103, -9, 99, 139, 376],\n [155, -161, -326, -740, 14, 19, 626, -980, -397, 452]]\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[[845, 1002, 117, 29, 117, 50, -398, 153, 514, -193],\n [-139, 85, 599, -72, -16, 320, -21, -345, -52, 591],\n [470, 168, 401, -143, -255, 282, -441, -434, 136, 147],\n [-76, 277, -605, -140, 290, -315, 259, 408, 180, -575],\n [-227, 501, -56, -141, -63, 678, -242, -345, -278, 312],\n [-11, -767, -697, 141, -274, -326, -40, 175, -241, -604],\n [248, -653, 153, 232, -598, 286, -524, -430, -364, 191],\n [36, 778, 734, -364, 636, -282, 498, 148, 708, 262],\n [347, 486, -382, 269, 148, -153, -95, 473, 159, -339],\n [183, -436, -171, 35, -97, -380, 28, 131, 94, -369]]\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[[-536, 813, -355, 139, 227, -26, -292, -1113, 304, -660],\n [-339, 802, -208, 340, -118, 0, 127, -756, -229, 179],\n [-271, -243, 509, -120, -245, -187, 140, 124, -174, -8],\n [-318, 687, -46, 604, -642, 515, -453, -100, -124, 230],\n [100, -1011, 405, -406, 109, -319, 208, 688, 552, -743],\n [55, 434, -300, 554, -346, 402, -238, -92, -58, 165],\n [106, -554, 562, -545, 20, -230, 287, 715, -362, 631],\n [112, -201, -73, -604, 603, -163, -116, 74, 232, -119],\n [-170, 1381, -824, 793, -246, 780, -785, -701, 78, 175],\n [94, -188, -96, -127, 230, 216, -754, -225, 51, -411]]\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[[-303, -422, 124, -192, -4, -604, 150, -183, 226, 358],\n [527, 107, -467, -7, -381, 529, 120, 343, 327, 229],\n [-702, -200, 176, 52, -267, 41, -594, -441, -72, 168],\n [27, -34, -394, -53, -394, 413, -327, -79, 388, 310],\n [371, 97, -141, 188, -97, 220, 433, 465, 185, 281],\n [-528, 3, 42, 214, 8, 126, -431, -281, 170, 268],\n [355, 130, -38, 225, -86, 231, 443, 489, 16, 166],\n [-608, -87, 386, -91, 64, -197, -574, -543, -506, -434],\n [-228, -402, 292, -320, -236, -468, 6, -210, -340, -136],\n [308, 226, -342, 80, 118, 284, 42, 148, 362, 114]]?\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[[141, 75, -87, -90, 72, -441, -231, 108, -117, -291],\n [-126, 306, -48, 214, 132, 193, 178, 449, 288, -4],\n [253, -16, -30, -144, 242, -604, -404, -168, -185, -289],\n [31, -235, 171, -10, 152, 187, -33, -542, -11, 291],\n [41, 10, -42, -50, -38, -151, -66, 53, -67, -111],\n [-209, -286, 14, -94, -642, 503, 358, -89, -141, 263],\n [264, 63, -107, -168, 170, -742, -427, 33, -218, -440],\n [6, -300, 196, -20, 92, 282, 12, -622, -26, 366],\n [128, -8, -46, -102, 44, -349, -204, -27, -134, -198],\n [-149, 287, -93, 168, -40, 182, 217, 537, 223, -55]]\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[[167, 384, 451, -205, 287, -362, -619, 498, -847, -453],\n [265, 166, -524, -411, 150, 193, 279, -836, -17, -356],\n [101, -99, -386, 430, -201, -231, -544, -127, -278, -120],\n [-75, 271, 791, -727, 30, 770, 985, 153, 517, 290],\n [-22, -38, -375, -481, 408, 53, 395, -214, 665, -192],\n [-84, -764, 1392, 282, 180, 1007, 223, 456, 370, -291],\n [12, -301, -109, -140, -224, 35, 68, -149, -14, 98],\n [-120, -3, 658, 1018, -36, 162, -266, 335, -230, 81],\n [145, 279, -838, 138, -48, -888, -541, -347, -754, -115],\n [-66, 258, -358, -629, 455, -434, 35, 258, 325, -123]]\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[[28, 188, -112, -294, -136, 350, -578, -96, -480, 18],\n [-26, -6, 24, 23, 32, -35, 51, 2, 50, -11],\n [652, -258, -408, 29, -574, 175, -102, 161, -295, 262],\n [-394, 136, 256, 12, 358, -140, 119, -87, 225, -159],\n [242, -280, -64, 284, -110, -252, 493, 155, 323, 91],\n [-258, 122, 152, -41, 216, -35, -17, -74, 70, -103],\n [138, -68, -80, 26, -114, 14, 17, 41, -31, 55],\n [64, -76, -16, 78, -28, -70, 136, 42, 90, 24],\n [410, -96, -288, -80, -398, 224, -255, 67, -341, 167],\n [90, 166, -152, -295, -192, 371, -595, -82, -514, 43]]\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 10x10 matrix:\n[[-779, -1121, -577, 387, 849, -667, -606, -736, 746, -31],\n [16, 45, -18, -364, -218, 165, 762, 140, -633, 704],\n [-251, -408, 609, 688, 784, -145, -384, -600, 776, 525],\n [392, 500, -384, 869, -165, 434, 535, -562, -165, 798],\n [467, 92, -37, -763, -222, -111, 413, 946, -404, -264],\n [575, 1136, 707, 148, -701, 716, 632, 204, -570, 299],\n [-196, -404, 199, 224, -19, -468, -304, -629, 100, -532],\n [303, -665, -511, -297, 467, -208, -828, 203, 494, 175],\n [243, 206, 92, -845, -26, 212, 513, 1172, -355, -9],\n [395, -331, -1065, 39, -507, 8, -791, -714, -232, -359]]\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[[252, 62, 360, -1, 135, 138, 315, -441, -271, 245],\n [-264, -74, -370, -8, -150, -136, -320, 462, 292, -250],\n [-132, -265, -5, -232, -291, 148, 92, 231, 350, 43],\n [-12, -145, 95, -142, -141, 128, 142, 21, 140, 93],\n [-120, -519, 215, -489, -528, 398, 391, 210, 567, 244],\n [156, -186, 400, -225, -129, 298, 443, -273, 33, 317],\n [48, 143, -35, 131, 150, -98, -85, -84, -169, -50],\n [48, 352, -200, 340, 348, -296, -316, -84, -356, -204],\n [96, 77, 95, 53, 102, 2, 61, -168, -151, 54],\n [-228, -570, 80, -513, -609, 362, 283, 399, 705, 157]]\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[[953, -94, 1032, 360, 885, 509, 160, 772, 280, -244],\n [648, -647, 306, -305, 75, 327, 427, 103, -275, -296],\n [936, -277, -575, -909, -764, 454, 277, -10, -813, 145],\n [-721, -196, 199, 539, 661, -368, 1142, -26, 391, -398],\n [696, 319, 28, 679, 600, 243, 138, 859, 395, 653],\n [-518, 175, -353, -321, -294, -362, -281, -904, 165, 116],\n [205, 230, -296, 491, 868, 176, 66, 437, 383, 1175],\n [-215, 1017, -991, -33, -841, 102, -766, -22, -231, 517],\n [322, -266, -71, -433, -53, 139, -362, 16, -195, 509],\n [-436, -591, -438, -109, -314, -163, 360, -38, -606, -104]]\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[[-156, -1969, 397, 62, 391, -1319, -87, -1411, -1105, -421],\n [194, -582, -62, 410, 74, -313, -579, -314, -699, 28],\n [156, 123, -88, 494, -529, -83, 879, 158, 125, 150],\n [-581, 60, -22, -261, -123, -232, 60, -561, 13, -496],\n [179, -812, -36, 684, 245, -584, 212, 758, -105, 931],\n [-324, 577, -375, 52, 782, -338, -145, 370, 634, 439],\n [-169, 952, -313, -112, 195, 782, -190, 417, 268, -145],\n [-75, -439, 46, 594, -122, -261, -187, 239, 297, 229],\n [787, -666, 264, 57, 651, -200, -1154, -133, -104, -213],\n [456, 1241, -129, 2, -394, 335, -448, 1057, 1162, 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[[579, -164, 263, -75, 183, -177, 231, -86, 293, 324],\n [-162, -330, 336, -196, -503, 390, -406, 210, -184, -526],\n [141, 124, -97, 83, 244, -159, 185, -74, 97, 254],\n [476, 14, 324, 126, 366, 220, 16, 286, -8, 212],\n [164, 92, 150, 144, 249, 244, -68, 268, -122, 62],\n [-334, -343, 204, -255, -648, 274, -392, 73, -158, -592],\n [397, 69, 133, 110, 364, -7, 151, 91, 89, 306],\n [-29, 160, -291, 49, 158, -337, 255, -250, 147, 254],\n [-13, -53, -281, -158, -118, -569, 329, -507, 339, 210],\n [-138, 250, -196, 176, 223, 30, 26, 70, -116, 86]]\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[[-200, 212, -60, 86, -10, 106, 40, -6, -83, -1],\n [347, -330, 39, -214, 115, -196, -88, 69, 102, 27],\n [155, -146, 15, -98, 55, -88, -40, 33, 44, 13],\n [-165, 242, -165, -44, 165, 66, 0, 99, -143, 44],\n [-418, 548, -306, 0, 250, 188, 32, 150, -290, 68],\n [134, -164, 78, -20, -50, -64, -16, -30, 80, -14],\n [-431, 502, -207, 108, 95, 214, 64, 57, -229, 28],\n [432, -536, 264, -52, -180, -204, -48, -108, 266, -50],\n [-45, 66, -45, -12, 45, 18, 0, 27, -39, 12],\n [145, -294, 285, 178, -355, -32, 40, -213, 216, -93]]\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[[-348, -312, 16, 43, 463, -678, 262, -408, 770, -116],\n [603, 652, 233, 552, -92, -394, -158, -192, -920, 375],\n [-129, -143, 964, -514, 505, -71, -221, -552, 514, 123],\n [-482, -770, 349, -861, -276, 878, -163, -459, 189, -512],\n [-196, -439, -6, -194, -376, 279, -96, -492, -260, -407],\n [606, 513, 504, 336, -332, -115, -512, -480, -1198, 253],\n [222, 377, 356, 33, 469, -257, -118, 320, 380, 377],\n [627, 861, -255, 995, 15, -817, 362, -26, -968, 516],\n [-329, -257, -211, -220, 262, -19, -36, 426, 908, -88],\n [383, 368, 195, 147, -178, 19, -662, 221, -396, 205]]\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[[648, -322, -568, 26, 256, -530, -116, 578, 194, 42],\n [-601, 371, 396, 6, 77, 290, 184, -366, -154, -298],\n [-175, -224, 152, 335, -177, 285, 62, -265, 211, -169],\n [404, -164, -255, -107, -46, -220, -139, 264, 24, 268],\n [-14, -255, -48, 337, 34, 55, 66, -39, 257, -267],\n [473, -410, -336, 145, -49, -205, -118, 273, 237, 121],\n [-148, -64, -45, 291, 278, -40, 151, 12, 188, -472],\n [333, -57, -430, 10, 475, -500, 18, 488, 100, -236],\n [-110, 373, -112, -179, 530, -325, 122, 245, -163, -319],\n [-806, 144, 576, 358, -122, 610, 252, -666, 62, -474]]?\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[[154, -33, -248, 453, -291, -130, 64, 601, -429, -10],\n [847, -863, 201, 666, 42, 108, 230, 301, -1067, -329],\n [-259, -725, -96, 310, 693, -188, 60, -300, -572, 332],\n [-388, 225, 142, -453, 241, 100, 15, -194, 535, -39],\n [-600, 209, 630, -494, 235, 146, -90, -1044, 802, 374],\n [60, -874, -65, 968, 696, 84, 296, 512, -1140, -16],\n [99, 313, 218, -394, -461, -486, 204, -364, 606, -327],\n [-508, 198, -81, -557, 765, 1077, -751, 519, 373, -105],\n [861, -842, 50, 734, 413, -201, 608, 199, -1064, -601],\n [-79, -625, 31, 271, -128, -313, -258, 544, -533, -25]]\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[[-229, -175, -23, 418, -296, -108, -234, -789, -541, 33],\n [181, 116, -378, 332, 351, 195, 554, 121, 48, 162],\n [-172, 62, -722, 646, -312, -481, -29, -473, -354, -450],\n [57, -631, 185, 558, 685, -306, 949, 117, 26, -156],\n [77, -322, 231, -527, 141, 81, -264, 90, -104, 470],\n [-294, 175, 869, 391, 948, -518, 1198, 616, 472, 88],\n [-249, -610, 14, 97, 73, -487, 176, -390, -338, -368],\n [169, 191, 339, 758, -506, 621, 65, -191, 312, -326],\n [155, -468, 92, -148, 56, 81, -235, 500, 164, -22],\n [876, -243, 183, 127, -85, -206, 617, -125, 527, -145]]\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[[-325, -460, 1164, -129, -940, -267, 40, 484, -272, 583],\n [78, 689, -682, 840, -37, -384, -212, -176, 688, -983],\n [-257, 568, 245, -982, -564, -946, 627, 271, 513, -102],\n [992, 246, -322, 558, 70, 350, -552, -88, -60, -189],\n [196, -400, -939, 147, 988, 328, -111, -507, 165, -669],\n [225, 706, 151, 977, 259, -182, 504, 87, 495, -582],\n [-328, 414, 322, 403, 940, -309, -23, -353, -82, -49],\n [-979, -21, 511, 55, 110, -228, 444, 48, -117, 262],\n [-1070, 808, -433, -517, 514, -529, 495, 133, 238, -54],\n [270, -452, 423, 483, -100, 486, 405, 151, -115, 98]]\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[[274, 398, 480, -346, 274, -364, 112, -46, 154, 122],\n [47, 121, 132, -155, 131, -56, 56, -83, -7, 43],\n [247, 409, 480, -403, 327, -322, 136, -113, 107, 131],\n [229, 359, 426, -337, 271, -301, 112, -76, 112, 113],\n [88, -176, -132, 440, -396, -154, -176, 418, 242, -88],\n [-250, -446, -516, 466, -382, 322, -160, 160, -88, -146],\n [305, 35, 150, 355, -345, -455, -160, 530, 430, -35],\n [34, -154, -132, 326, -290, -70, -128, 284, 148, -70],\n [-208, -100, -174, -104, 114, 301, 56, -253, -245, -8],\n [51, 113, 126, -135, 113, -63, 48, -64, 4, 39]]\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[[154, -198, 746, -329, 333, -545, 68, -282, 853, -381],\n [22, 759, -332, 29, 61, -28, 36, -533, -428, 444],\n [-101, 469, 412, 318, -127, -94, -487, -440, 113, -155],\n [-583, 557, -697, -440, -436, -421, 99, -47, -624, 237],\n [563, -593, -296, 154, 378, 603, 428, 292, -144, 282],\n [-252, 81, -52, -383, -72, -377, 121, 77, 95, -55],\n [-144, -363, 523, 9, -146, -207, -266, 150, 471, -508],\n [-99, 204, 120, -259, 95, -295, 82, -59, 226, -4],\n [-224, 532, -80, -500, 175, -411, 265, 26, 179, 225],\n [-307, 286, -910, -256, -232, 88, 302, 321, -739, 465]]\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 10x10 matrix:\n[[-170, -240, -75, 10, -245, 205, -85, 115, 160, -180],\n [289, 363, 45, -2, 364, -371, 167, -143, -122, 201],\n [85, 51, -89, 18, 42, -137, 77, 23, 150, -71],\n [-289, -429, -166, 24, -441, 338, -134, 220, 342, -355],\n [-374, -450, -22, -4, -448, 490, -226, 162, 92, -214],\n [-357, -429, -20, -4, -427, 468, -216, 154, 86, -203],\n [-170, -156, 79, -18, -147, 247, -127, 17, -120, 16],\n [153, 249, 128, -20, 259, -168, 60, -142, -254, 239],\n [68, 90, 19, -2, 91, -85, 37, -39, -44, 58],\n [17, -93, -207, 38, -112, -79, 67, 125, 374, -255]]\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[[270, 132, 204, -105, 237, -54, 624, -189, -138, 213],\n [-247, 372, -283, 363, -308, -446, -159, -127, 300, -668],\n [-346, 32, 8, 248, 138, -306, 12, -322, 314, -420],\n [246, 36, -52, -145, -163, 178, -32, 243, -210, 237],\n [-551, -276, 297, 221, 622, -282, 205, -629, 432, -322],\n [135, -88, -11, -138, -75, 208, -115, 204, -154, 233],\n [-171, -288, 203, -40, 341, 76, 43, -174, 78, 105],\n [-244, -184, -22, 62, 30, 30, -306, -4, 134, -108],\n [-160, 112, -246, 164, -312, -110, -394, 122, 130, -322],\n [-496, -240, 299, 204, 610, -281, 261, -619, 399, -293]]\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 10x10 matrix:\n[[-2, 0, 149, 60, 120, -192, -412, 261, -562, 121],\n [-347, -103, 151, 162, -267, -4, -146, 752, -597, 32],\n [-246, -211, 58, 110, -214, -96, -58, 294, -275, -105],\n [206, 339, -42, -10, 394, 76, -112, -214, 59, 365],\n [159, -501, -55, -179, -265, -285, 108, -586, 378, -699],\n [-265, 16, -33, 264, 35, -16, -164, 204, -334, 227],\n [-170, -513, 151, 87, -120, -535, -410, 35, -536, -287],\n [84, -177, 183, -130, 318, -472, -246, -245, -123, 130],\n [-249, -524, -6, 298, 221, -722, -548, -495, -454, -16],\n [235, 505, 264, -484, -249, 630, 543, 941, 253, 91]]\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[[648, -968, -738, 301, 339, -1107, -35, 223, 61, -532],\n [367, -708, -287, 258, 81, -705, 43, 324, 140, -385],\n [-649, 819, 746, -141, -303, 1011, 8, -144, 37, 436],\n [-70, -67, 27, 46, -140, 21, -39, 154, 51, 34],\n [-148, -46, 754, 486, 278, 84, 236, -30, 408, -396],\n [531, 1, -614, -252, 604, -450, 51, -573, -332, -164],\n [107, -158, 381, -387, -701, -60, 389, 594, -22, 56],\n [-698, -22, 788, 492, -576, 552, -114, 622, 496, 116],\n [-248, -5, 199, 284, -20, 171, -113, 88, 195, -8],\n [-918, -150, 420, 1034, -214, 546, -596, 468, 666, 84]]\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[[-423, 607, 16, -98, 273, 70, -299, -190, -482, -68],\n [458, -562, 34, 565, -409, 27, 52, -164, 217, -583],\n [679, -571, -552, 434, 221, 939, -320, 140, 266, -177],\n [332, 70, -438, -336, 332, 485, 105, -298, 228, 205],\n [645, -889, -112, 598, -329, 253, 12, 236, 430, -327],\n [-18, 163, -169, 58, 225, 329, -249, -70, -172, -76],\n [103, -255, -58, 333, 2, 233, -245, 274, -23, -115],\n [69, 486, -39, -492, -36, -234, 477, -1014, 66, -177],\n [-378, 184, 108, -283, 173, -161, -56, 484, -107, 515],\n [-248, 131, 53, -370, 149, -157, 83, 362, 28, 536]]\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[[481, -254, -594, -145, -140, 536, 218, 126, 186, -275],\n [38, -682, -125, 173, 10, -864, -1136, -203, -44, -1113],\n [-552, -541, -282, -392, 18, -380, -297, -1010, -557, -1190],\n [-259, 246, 367, 71, 411, -469, -748, 441, -340, 297],\n [-282, 310, -125, 352, 53, 325, 783, -229, 461, -89],\n [-200, 533, 566, -576, -660, -384, -731, -175, -560, 484],\n [-216, 928, 1171, 520, 675, -753, -748, 281, -767, 725],\n [550, 279, -41, -471, 234, -676, -793, 401, -304, -170],\n [370, -133, -1198, -309, 510, 159, 904, 798, 1239, -499],\n [286, 544, -584, -277, 309, -465, -688, 544, 308, -447]]?\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[[-405, -172, -467, -274, -834, 742, 340, 488, 101, 177],\n [628, -33, -19, 336, 127, 288, 518, 72, 314, -275],\n [-114, 177, 107, -482, -227, 76, 104, 174, -340, -649],\n [-371, -449, 324, -497, 45, -22, -47, 152, -395, -563],\n [366, -241, 445, -283, 171, -232, 373, 142, -608, -1064],\n [878, 674, -378, 614, -186, 0, 446, -58, 234, 250],\n [-235, -71, 47, -3, 95, -268, -311, -127, -113, 289],\n [746, 576, 263, 382, 620, -507, -45, -412, 71, -285],\n [316, -187, -97, 160, -179, 107, 409, 179, -91, -74],\n [106, 266, -381, -241, -674, 948, 645, 465, 338, -435]]\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[[-284, -543, 0, -69, -270, -167, -238, 124, -42, -496],\n [-49, -27, 0, -59, 25, 65, -81, 44, -8, -69],\n [-243, -459, 0, -63, -225, -135, -207, 108, -36, -423],\n [265, 612, 0, -10, 365, 304, 159, -80, 38, 489],\n [196, 285, 0, 111, 90, -11, 218, -116, 30, 320],\n [-231, -102, 0, -296, 145, 342, -397, 216, -38, -319],\n [6, -87, 0, 71, -100, -135, 64, -36, 2, -14],\n [-175, -147, 0, -175, 35, 161, -259, 140, -28, -259],\n [122, 414, 0, -98, 310, 326, -6, 8, 16, 258],\n [260, 360, 0, 160, 100, -40, 300, -160, 40, 420]]?\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[[-231, -125, 519, -231, 82, 460, -54, -501, -255, 259],\n [474, 191, 300, -83, 277, 614, 475, -481, -267, -23],\n [-414, 275, -225, 26, 96, 68, 242, 667, 18, 24],\n [690, 125, -379, 652, 398, -440, 188, 185, 428, -432],\n [-570, -97, 411, -150, 112, 351, -97, -136, -147, 289],\n [216, 318, -64, -81, 61, 698, 805, 252, -85, -130],\n [-84, 371, 198, -616, -36, 368, 86, -263, -720, 309],\n [181, -439, 38, 356, 51, -886, -849, -459, 296, -48],\n [122, -25, -85, 781, 597, -129, 218, 300, 578, -289],\n [419, 656, -364, 262, 495, 279, 836, 561, -25, -274]]\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[[-96, 108, 66, 24, 66, -78, 66, 30, -120, -66],\n [192, -216, -132, -48, -132, 156, -132, -60, 240, 132],\n [-352, 396, 242, 88, 242, -286, 242, 110, -440, -242],\n [208, -234, -143, -52, -143, 169, -143, -65, 260, 143],\n [-128, 144, 88, 32, 88, -104, 88, 40, -160, -88],\n [-64, 72, 44, 16, 44, -52, 44, 20, -80, -44],\n [304, -342, -209, -76, -209, 247, -209, -95, 380, 209],\n [-288, 324, 198, 72, 198, -234, 198, 90, -360, -198],\n [-64, 72, 44, 16, 44, -52, 44, 20, -80, -44],\n [320, -360, -220, -80, -220, 260, -220, -100, 400, 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[[54, -153, 8, -25, -3, -105, 6, 129, -73, -7],\n [172, -226, -226, -146, 230, -98, 2, 134, 48, -252],\n [-8, -130, 279, 122, -252, -214, 35, 168, -273, 251],\n [302, -89, 0, 79, 101, -369, 118, 41, -209, -111],\n [-218, -154, -156, -220, 36, 320, -142, 132, 246, -46],\n [-177, 18, -194, -173, 101, 341, -111, -31, 290, -102],\n [-29, 110, -211, -101, 179, 205, -40, -133, 231, -177],\n [-380, -157, 78, -139, -221, 345, -166, 199, 137, 219],\n [-452, -637, 459, -91, -619, 49, -181, 701, -260, 598],\n [-310, 232, -77, -82, -24, 466, -119, -180, 313, 41]]\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[[-551, -369, -121, 315, 272, 353, 97, -100, -431, 30],\n [-146, -670, -268, 394, 727, 349, 502, -352, -518, 39],\n [680, 256, 44, -291, -106, -333, 41, 11, 392, -69],\n [294, -134, 0, 44, 229, -83, 240, -138, -6, 135],\n [-69, 125, 167, -3, -169, -98, -105, 80, 63, 201],\n [297, 479, 209, -309, -469, -332, -279, 212, 429, 21],\n [43, -435, -549, 61, 533, 396, 295, -240, -281, -657],\n [-510, -42, -382, -49, -66, 425, -249, 95, -174, -717],\n [656, 240, 192, -208, -104, -408, 80, 0, 368, 216],\n [-14, -138, -164, 29, 161, 130, 85, -71, -98, -192]]?\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[[-50, 340, 496, -729, 895, -727, -111, -348, -378, -192],\n [188, -516, 267, -621, -676, 71, 456, -6, 38, -229],\n [258, -210, 258, -626, 687, -748, 162, -351, 150, -551],\n [-521, 847, -50, 70, 125, 545, -392, 151, -224, -96],\n [-407, -360, 435, -1555, 474, -1047, -54, -860, -586, -933],\n [413, 232, 99, 719, 497, 413, 47, -245, 1067, 93],\n [-711, -2, 106, 8, -15, 486, -335, -487, -265, 54],\n [461, -591, 266, -354, 39, -946, -211, -452, 547, -336],\n [-716, 546, 535, 61, 223, 625, -568, -109, -446, 1196],\n [-606, 385, 178, -61, -321, 1274, 64, -102, -43, -326]]?\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[[-27, -218, 202, -165, -651, -132, -268, -260, 7, -379],\n [-1612, 478, -472, 27, 317, 135, 646, 1550, 148, -46],\n [1193, 30, -713, 274, -349, 103, -1370, -1391, 283, 336],\n [-541, -335, 621, -383, -166, 260, 173, 303, -739, -662],\n [567, -40, -868, 431, 886, 319, -721, -414, 69, 381],\n [-376, -492, -707, 567, -114, -506, -628, 340, -808, 242],\n [-836, 10, 70, 385, 166, -443, 929, 651, -235, -192],\n [-448, 806, 416, 163, 367, 391, -228, 144, 363, -241],\n [248, -400, 64, -501, -327, 297, -1122, 78, -624, 51],\n [-317, 152, -297, -127, 426, 472, 1024, 207, -37, 150]]\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[[87, 52, -109, 187, -166, 195, 206, 264, -78, 134],\n [78, 108, -110, 272, 66, 316, 332, 740, 16, 292],\n [-117, -32, 139, -187, 356, -175, -186, -44, 158, -74],\n [204, 24, -236, 272, -732, 232, 248, -184, -320, 40],\n [162, 92, -202, 340, -326, 352, 372, 452, -152, 236],\n [27, -8, -29, 17, -136, 5, 6, -116, -58, -26],\n [-135, -110, 175, -340, 155, -370, -390, -650, 80, -290],\n [-153, -88, 191, -323, 304, -335, -354, -436, 142, -226],\n [-117, 8, 131, -119, 496, -83, -90, 284, 214, 38],\n [18, 8, -22, 34, -44, 34, 36, 32, -20, 20]]\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 10x10 matrix:\n[[-16, 556, -408, -180, -178, -74, -682, -776, 16, -952],\n [348, 120, 740, 180, -260, -444, 408, -120, -80, 28],\n [-384, -111, -512, -153, 113, 282, -219, 120, -4, 14],\n [260, -341, -292, 81, 543, 466, -97, 448, 260, 462],\n [-258, -177, 106, -9, -89, -38, 281, 244, -116, 280],\n [-197, -313, -311, -36, 259, 328, 14, 406, 56, 385],\n [-712, -374, -628, -198, 157, 417, -39, 468, -72, 364],\n [-268, -71, -412, -117, 103, 228, -201, 72, 12, -14],\n [488, -260, 80, 180, 430, 246, 78, 360, 240, 448],\n [-43, 97, 619, 72, -416, -467, 449, -98, -216, 7]]\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[[304, -95, 380, -380, 323, -152, -285, 152, 304, -380],\n [128, -40, 160, -160, 136, -64, -120, 64, 128, -160],\n [240, -75, 300, -300, 255, -120, -225, 120, 240, -300],\n [352, -110, 440, -440, 374, -176, -330, 176, 352, -440],\n [256, -80, 320, -320, 272, -128, -240, 128, 256, -320],\n [-128, 40, -160, 160, -136, 64, 120, -64, -128, 160],\n [80, -25, 100, -100, 85, -40, -75, 40, 80, -100],\n [176, -55, 220, -220, 187, -88, -165, 88, 176, -220],\n [-112, 35, -140, 140, -119, 56, 105, -56, -112, 140],\n [-160, 50, -200, 200, -170, 80, 150, -80, -160, 200]]\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[[-2, -837, 48, -270, -250, 67, -1, 64, -64, -49],\n [-524, 714, -43, -469, -54, 3, 256, 239, 377, 494],\n [231, -624, 575, 532, -475, -147, 390, 70, 672, -260],\n [-12, 1069, -474, 312, 311, -16, -266, 73, -398, -255],\n [-706, 110, 223, 117, 630, -467, 124, -611, -677, 283],\n [-443, 336, -136, 131, -233, -95, 414, 318, 370, 35],\n [-459, -7, 244, 855, -223, -859, 16, 265, -942, -1030],\n [-9, 525, -648, -688, -664, 303, -129, 1074, -161, -344],\n [-967, 506, 160, 481, 533, -641, 323, -540, -543, 312],\n [643, 759, -483, 143, -11, 772, -406, 14, 429, -241]]\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[[840, -177, -23, 134, -224, 903, 312, -27, 457, -426],\n [143, -453, -5, -493, -364, -461, 199, 236, -354, -106],\n [396, -59, 429, -140, -54, 233, -503, 395, -258, 492],\n [155, -379, -189, 147, -352, 581, 451, -415, 722, -969],\n [-874, 227, -289, 456, 45, 64, -263, -339, -74, 132],\n [-409, 333, 12, -4, 141, -751, 212, 177, -112, 165],\n [99, -444, -319, -260, -140, -75, 581, -417, 464, -960],\n [1081, 345, 503, 186, 230, 670, 142, 329, 525, 100],\n [921, -128, -166, -131, -747, 503, 365, 821, 109, -314],\n [218, 763, 637, 357, 600, 18, -171, 252, 350, 538]]\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[[-228, -252, -36, -96, 108, 228, -264, 180, 144, -192],\n [-418, -462, -66, -176, 198, 418, -484, 330, 264, -352],\n [399, 441, 63, 168, -189, -399, 462, -315, -252, 336],\n [-342, -378, -54, -144, 162, 342, -396, 270, 216, -288],\n [-418, -462, -66, -176, 198, 418, -484, 330, 264, -352],\n [-323, -357, -51, -136, 153, 323, -374, 255, 204, -272],\n [-19, -21, -3, -8, 9, 19, -22, 15, 12, -16],\n [-114, -126, -18, -48, 54, 114, -132, 90, 72, -96],\n [380, 420, 60, 160, -180, -380, 440, -300, -240, 320],\n [-418, -462, -66, -176, 198, 418, -484, 330, 264, -352]]\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[[540, -166, -258, 1024, 506, -1071, 901, 665, -279, 88],\n [374, -40, 602, 389, 545, -988, 584, -116, 85, -129],\n [178, 50, -509, -501, -434, 793, -481, 272, 150, -332],\n [605, -1011, 285, -58, -525, -224, 11, 11, 150, 624],\n [507, -460, -343, -48, -234, 131, -89, 145, 56, 224],\n [13, -128, 441, 264, 38, -547, 389, 73, -16, 18],\n [964, -200, -591, 165, 516, -178, -36, 107, 79, 100],\n [-815, 713, 234, -691, -63, 711, -338, -789, 154, -624],\n [-838, 73, -99, 1156, 306, -820, 1043, -46, -669, 521],\n [165, -148, 28, -412, -443, 360, -212, 71, 203, -241]]\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[[-338, -203, 39, -268, 438, -271, 160, -454, -112, 17],\n [226, -429, 367, -544, 195, -722, 351, -127, -313, -368],\n [-605, -7, 227, 265, 313, 210, -81, -267, -80, 411],\n [-16, 245, 648, 81, 268, -311, 445, 181, -539, 366],\n [-263, 138, -570, 457, -283, 357, -42, 77, 578, 278],\n [-107, -83, -8, 202, -144, -439, 537, -147, 236, 279],\n [-119, 186, -433, 47, 44, -288, 475, -335, 293, 256],\n [-336, 181, -73, 279, 57, 202, -104, -627, 162, 376],\n [-220, -126, -380, 99, -100, 46, -43, -394, 417, 52],\n [337, 678, 34, 541, -479, 301, -94, -319, 122, 438]]\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[[-8, 81, 263, -43, 310, 454, -551, 140, 381, 367],\n [-174, 3, -129, -399, -288, -495, 477, -276, -351, -96],\n [-641, -346, 169, -1023, -356, 219, -15, 151, 268, 33],\n [-35, 278, 85, -663, 224, -29, -202, -525, 43, 348],\n [-89, 127, 384, -330, 424, 634, -786, 81, 555, 561],\n [68, 435, 397, 159, 456, -1, -451, -6, 67, 828],\n [-308, -217, 115, -711, -46, 478, -310, 42, 418, 0],\n [-686, -162, 374, -866, -260, 30, -55, 248, 163, 449],\n [259, -187, -500, -294, -86, 195, 147, -491, 58, -813],\n [-293, -274, 49, -367, -210, 226, -25, 209, 200, -122]]\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 10x10 matrix:\n[[-147, -279, -239, -225, 1335, 82, 392, 454, 384, 367],\n [507, 78, -241, 434, -575, -485, 910, -244, -831, -116],\n [-295, -61, 502, 215, 90, -453, -45, -51, -230, 86],\n [-337, 323, -285, -211, -84, 426, -635, -86, 503, -313],\n [-300, 281, 32, -725, -438, 99, -172, 267, -200, 377],\n [456, -627, 173, 144, 861, 415, 187, 537, 332, 520],\n [-230, 101, 453, -505, -788, 224, -1058, -285, 352, -202],\n [462, -16, 146, 1506, -548, -416, 242, -629, -465, -700],\n [-235, 138, -247, 195, 439, 316, -182, 187, 317, -50],\n [-57, -106, -158, -318, 385, 406, -456, -34, 709, -175]]\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 10x10 matrix:\n[[598, 222, 875, 375, -1359, -935, -320, -397, 646, 438],\n [215, 91, 438, 419, -202, -373, 653, -218, 496, -492],\n [-168, -249, -720, -953, 542, 238, -610, -125, -525, -309],\n [44, -520, -166, -851, -147, -355, -896, -158, -264, -75],\n [221, 371, 403, 193, -1112, -423, -577, -245, 148, 953],\n [-51, 495, -179, -308, -190, 51, -962, -241, -201, 452],\n [396, -120, 156, -230, 30, -524, 235, -447, 464, -1054],\n [44, 163, -338, 17, 209, 448, -112, 247, -114, 334],\n [415, 410, 674, 475, -1127, -565, -351, -220, 481, 697],\n [40, -511, 23, -160, -34, -252, 325, -6, 100, -359]]\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[[-16, -395, -82, -280, -308, 363, 46, 50, -155, 139],\n [-74, 405, 300, 327, 476, -299, 180, -92, 235, -80],\n [-106, 278, 210, 439, 532, 100, 562, -174, 0, -153],\n [138, -457, -548, -275, -567, 455, -154, 75, -440, -32],\n [-136, -315, 438, -480, -203, -37, -144, 125, 320, 419],\n [96, 103, -246, 104, -42, -71, -130, -4, -115, -151],\n [-84, -47, 66, 182, 210, 355, 494, -112, -145, -55],\n [-156, -131, 354, -58, 147, 199, 344, -37, 110, 173],\n [112, -152, -96, -484, -511, -400, -790, 219, 195, 204],\n [-148, 96, 284, 282, 427, 236, 602, -147, 5, -34]]\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[[31, 89, 111, -14, 186, 370, 34, -152, -284, -222],\n [136, -44, 21, -108, -135, 212, 124, -91, -95, -42],\n [3, -147, 9, 504, 522, -630, -12, 108, 378, -18],\n [230, -34, 159, 75, 270, 412, 209, -248, -271, -318],\n [-246, 338, 99, -220, 93, 592, -204, -107, -507, -198],\n [-62, 18, 129, 494, 777, -240, -62, -27, 43, -258],\n [286, -194, -15, -81, -252, 68, 253, -82, 67, 30],\n [-242, 262, -51, -454, -435, 424, -202, 25, -309, 102],\n [-18, 286, 135, -470, -201, 1040, 6, -277, -723, -270],\n [-317, 217, -42, -102, -27, -10, -278, 119, -77, 84]]\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[[55, 436, 522, -802, 624, -1175, 801, 25, -152, -1003],\n [43, 397, -79, -442, 561, 234, 212, -230, 326, -190],\n [-118, 46, -156, 56, -283, 875, -465, 331, 757, 925],\n [-592, -278, -255, 383, -690, 221, -90, -5, -292, 492],\n [499, 387, 86, 183, 543, 703, -589, 136, 601, 563],\n [105, -28, -466, -65, 228, 866, -297, 34, 379, 487],\n [44, 153, -362, 575, -85, 430, -145, -357, -407, -128],\n [28, 524, -97, 938, -600, 886, -543, -124, 233, 368],\n [210, -96, 398, -760, 215, -687, 243, 687, 391, -127],\n [32, -169, -79, 476, -977, 821, -412, -327, 682, 189]]\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[[423, -382, -176, 572, 446, 54, -386, 47, 338, -25],\n [422, -248, -14, 588, 84, 226, -494, 178, -48, 260],\n [-34, 34, -17, 102, -408, 289, -119, 136, -306, 119],\n [-225, -110, -365, -16, -198, 211, 133, -29, 126, -412],\n [258, -264, -181, 496, -16, 289, -361, 138, 20, 31],\n [210, -147, -35, 287, 112, 77, -224, 63, 49, 77],\n [128, -310, -286, 134, 696, -262, 56, -190, 690, -434],\n [230, -315, -235, 335, 440, -35, -160, -45, 425, -215],\n [181, -103, -2, 253, 26, 102, -215, 80, -31, 119],\n [128, 400, 669, -164, -268, -109, -135, 148, -652, 795]]\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[[-545, -87, -248, 7, -146, -593, 682, 122, 214, 148],\n [-837, -150, 359, -149, 269, 14, -194, -216, -38, -962],\n [-160, 473, 675, -180, 189, -302, -501, -202, -235, 23],\n [-263, 337, -818, 130, -190, -309, 399, 489, 282, 789],\n [-37, -160, -185, 191, -101, 877, -254, 386, 475, -1039],\n [-41, 769, 675, -161, -450, -547, -262, 405, 522, -92],\n [-62, -378, 350, -56, -394, -351, 571, 52, 413, -561],\n [-408, -497, -290, 382, 283, 781, 189, 403, 258, -582],\n [-341, -610, -127, 138, 73, 371, 321, 160, 226, -616],\n [760, 525, -410, 598, 267, 645, -105, -44, -307, 464]]\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[[592, -276, -174, 204, -34, 326, 48, 562, -340, -490],\n [271, 179, 50, -121, 171, 21, 58, 508, -315, -236],\n [71, 304, -219, -446, 82, -496, 97, 146, -10, 168],\n [364, 174, -876, 378, 104, 608, -6, -56, -514, -856],\n [-188, 49, 980, -108, 239, -559, -27, -104, -63, 742],\n [62, -170, 492, -207, -59, -145, 40, 507, 142, 189],\n [-37, 194, -460, -353, -164, 356, 73, 635, 252, -547],\n [226, 189, 102, -181, 132, 176, 63, 738, -235, -366],\n [-458, 103, 314, -353, -36, -676, -3, -455, 431, 785],\n [450, -84, 126, -215, -3, 99, 102, 983, -164, -327]]\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[[-590, -176, -64, -179, -10, -5, -332, 83, -383, -69],\n [4, -62, 173, -207, -85, -162, 46, 108, -29, -228],\n [-182, -182, 329, -476, -175, -329, -14, 245, -182, -483],\n [-76, -70, 121, -179, -65, -122, -10, 92, -73, -180],\n [-142, 56, -284, 281, 130, 251, -148, -149, -43, 339],\n [154, 70, -49, 126, 35, 63, 70, -63, 112, 105],\n [-312, -156, 138, -302, -90, -164, -132, 152, -234, -264],\n [-750, -192, -168, -123, 30, 75, -444, 51, -471, 27],\n [8, -124, 346, -414, -170, -324, 92, 216, -58, -456],\n [-154, -148, 262, -383, -140, -263, -16, 197, -151, -387]]?\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[[64, 32, -288, 32, -32, -304, 0, 192, -160, 48],\n [28, 14, -126, 14, -14, -133, 0, 84, -70, 21],\n [-80, -40, 360, -40, 40, 380, 0, -240, 200, -60],\n [-32, -16, 144, -16, 16, 152, 0, -96, 80, -24],\n [-16, -8, 72, -8, 8, 76, 0, -48, 40, -12],\n [-40, -20, 180, -20, 20, 190, 0, -120, 100, -30],\n [-24, -12, 108, -12, 12, 114, 0, -72, 60, -18],\n [60, 30, -270, 30, -30, -285, 0, 180, -150, 45],\n [-40, -20, 180, -20, 20, 190, 0, -120, 100, -30],\n [-72, -36, 324, -36, 36, 342, 0, -216, 180, -54]]?\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[[-40, -111, 54, -179, -141, -414, -36, 128, 52, 58],\n [-964, -752, 367, -355, -756, -336, 434, -428, 393, 74],\n [115, 76, 485, -224, 89, -167, 275, 452, -30, 368],\n [714, 530, 72, 350, 681, 163, -438, 304, -387, 206],\n [-627, -474, 336, -43, -365, -75, 143, -440, 171, 118],\n [-26, -45, -536, -189, -265, -164, 42, 24, 160, -386],\n [-507, -388, -255, 60, -388, -8, -83, -588, 183, -278],\n [-188, -206, 637, -93, -39, -345, 26, 60, -20, 444],\n [-100, -115, -273, -74, -196, -185, -74, -100, 94, -202],\n [-146, -74, 296, -292, -152, -14, 474, 256, 126, 160]]\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[[-461, -374, -324, -210, 423, 250, 210, -395, -319, -60],\n [-116, -114, 951, 303, -131, -260, -458, -277, -226, -1007],\n [515, -250, 903, 304, -481, -859, -501, -85, -945, -1443],\n [-241, 228, -75, -620, 1072, 860, 335, 229, 931, 138],\n [260, -201, -294, -130, -10, -336, 254, -624, -973, 280],\n [202, 1030, -1074, -415, 305, 205, 285, 279, 867, 576],\n [627, 15, -289, -168, 521, -245, 381, 297, 490, 169],\n [-685, -159, 135, 30, 131, 756, 32, 143, 413, 500],\n [-565, -151, -691, -72, -1683, 132, -514, -151, -958, 638],\n [113, -613, -249, -302, -342, -100, -65, 96, -156, 32]]\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[[-187, -10, -132, -254, -101, -325, -311, -186, 158, -73],\n [161, -296, 389, 420, 44, 29, -220, 338, 45, 246],\n [163, 85, -108, -1, -447, -382, 495, -419, 216, -466],\n [160, 72, 344, 560, 210, 838, 329, 408, -387, 220],\n [-212, 101, -199, -253, 566, -346, -633, 0, -22, 338],\n [194, 331, -437, -315, 298, 70, 706, -172, -195, -124],\n [-73, 267, -412, -455, 655, 318, 104, 123, -339, 264],\n [-106, -90, 9, -82, -849, -448, 57, -472, 399, -563],\n [-105, -126, -138, -258, -88, -892, -514, -295, 388, -67],\n [-267, 382, -234, -222, 350, 642, 66, 37, -402, 111]]\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[[-102, 257, 475, -25, -122, -524, 600, -384, -644, -369],\n [501, 381, -57, 549, 374, 168, 508, -537, -324, -99],\n [-282, -153, 143, -280, -274, -181, 102, 339, 188, 158],\n [23, -350, -249, 28, -112, 286, -27, 361, 529, 477],\n [-575, -280, 385, -555, -480, -555, -175, 170, -225, -230],\n [202, -84, -60, 253, 156, -7, -356, -697, -622, -479],\n [917, 471, -523, 907, 786, 744, 172, -581, -12, 67],\n [185, 56, -236, 148, 176, 314, -56, 139, 320, 224],\n [-271, -377, 237, -185, -382, -356, 84, -101, -284, -105],\n [-399, -210, 101, -445, -212, -235, -653, 150, -79, -262]]\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[[-715, -598, -512, -422, -320, -153, 516, -247, -373, 577],\n [259, 319, -149, 569, 377, -69, -626, -60, 269, -220],\n [-384, -140, -692, 356, 256, -260, -316, -256, 8, 268],\n [-183, -162, 321, -292, -60, 90, 298, 108, -168, 163],\n [500, 413, -132, -35, -119, -63, 196, 388, 309, -569],\n [-899, -409, -240, 3, 447, -206, 102, 27, -252, 640],\n [419, 529, -148, 693, 525, -106, -698, 125, 424, -424],\n [-1026, -923, 87, -601, -287, 64, 522, -425, -690, 1003],\n [94, -41, -256, 133, -160, -12, -215, -317, 7, 9],\n [402, 418, -218, -22, -20, -128, 242, 482, 326, -548]]?\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[[58, 542, -188, 318, 133, -150, 30, -548, 59, -184],\n [457, 250, 325, -120, 603, 15, 358, 49, 226, 644],\n [421, -543, 529, -600, 202, 259, 248, 906, 392, 1065],\n [16, 355, -436, -274, -439, -349, -295, -241, 467, -125],\n [-438, -362, -291, -114, 65, -91, -301, -394, -133, -474],\n [-595, 484, -314, 1010, -120, 480, 39, -11, -295, -610],\n [28, -20, 121, 94, 765, 389, 251, 54, 420, 658],\n [-352, -291, 178, 140, -20, 895, 217, 1381, 237, 577],\n [60, -487, -137, -650, 212, -487, -311, -691, 164, -47],\n [297, 488, 348, 486, -542, 226, 343, 765, -332, 68]]\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[[-198, 57, -217, -39, 445, 349, 38, -43, 591, 184],\n [0, 126, 30, 90, -66, 6, -60, 102, -126, 96],\n [77, -154, 53, -79, -104, -142, 48, -90, -98, -172],\n [-242, 730, -108, 424, 198, 458, -268, 482, 62, 728],\n [-154, 287, -111, 143, 219, 283, -86, 163, 217, 328],\n [143, -229, 112, -106, -223, -261, 62, -121, -239, -276],\n [154, -560, 46, -338, -76, -296, 216, -384, 56, -536],\n [88, -86, 82, -26, -166, -158, 12, -30, -202, -128],\n [-209, 94, -221, -17, 452, 370, 24, -18, 590, 220],\n [22, 31, 33, 31, -69, -37, -22, 35, -103, 8]]\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 10x10 matrix:\n[[-760, 463, -819, -237, 224, -299, -401, 560, 414, 162],\n [-429, -1, -464, -445, -435, -1020, -645, -179, -34, -786],\n [540, -367, 115, -20, 8, 721, 431, 155, -376, 334],\n [603, -536, 631, -304, -271, 429, 590, -575, -416, 198],\n [-29, -284, -302, -610, -464, 357, 96, 207, -339, 250],\n [245, -523, -351, -216, -48, -474, 137, 194, 215, -568],\n [-446, 137, -486, -68, 47, -854, -390, 177, 489, -544],\n [136, -155, -30, 236, 107, -987, -267, -247, 245, -965],\n [280, -237, -137, 174, -254, 112, -144, 287, -312, -328],\n [-216, 350, -279, 150, 155, -53, -417, 160, -165, -8]]\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 10x10 matrix:\n[[-12, -650, -112, -125, -171, 813, -324, 422, 409, 161],\n [-300, -50, -352, 73, -165, 245, -374, 34, 481, 357],\n [102, -22, 48, 104, -101, -684, 349, -499, 764, 781],\n [654, -5, -439, 379, -6, 118, -553, 312, -661, -795],\n [566, -243, -288, -58, -14, 364, -260, 619, -232, -683],\n [-275, -441, 44, -177, 65, 1027, -230, 575, -333, -430],\n [203, 230, 268, -145, 161, -399, 302, -32, -215, -133],\n [-157, 391, 163, -111, 217, -165, 279, 19, -574, -491],\n [-486, -145, 79, -211, 179, 772, -40, 471, -400, -451],\n [-707, -310, -124, 191, 160, 630, -144, 155, 73, 156]]\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[[-138, -7, -248, -515, 391, -117, -311, -222, 535, -294],\n [-262, 319, -493, -165, 155, 76, 349, 682, -184, -136],\n [273, -148, 125, -525, 506, 73, 321, 97, 574, -401],\n [102, 191, -591, -182, 538, 282, 156, 92, 176, -357],\n [369, -310, 105, 19, -183, -16, 386, 347, -390, -52],\n [432, -408, -84, -460, 41, -65, 725, 850, -360, -409],\n [261, -371, -725, -1162, 738, -203, 74, 287, 560, -785],\n [595, -710, 1036, -124, 12, 17, -381, -1045, 273, -451],\n [255, -390, 319, 241, -646, -451, 177, 259, -134, 809],\n [-460, 680, -644, 620, 31, 73, -480, -410, 367, 830]]\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[[-188, -422, 732, -352, -176, -730, 338, 110, 510, 10],\n [138, 291, -468, 240, 138, 465, -219, -57, -333, 3],\n [218, 285, -94, 208, 300, 75, -75, 131, -141, 101],\n [52, 1, 225, -16, 103, -235, 86, 116, 114, 61],\n [-162, -201, 30, -144, -228, -15, 39, -111, 81, -81],\n [-226, -255, -52, -176, -330, 75, 15, -187, 57, -127],\n [258, 380, -269, 288, 335, 250, -155, 101, -261, 96],\n [-118, -219, 290, -176, -132, -285, 141, 11, 219, -19],\n [-70, -56, -101, -32, -113, 110, -31, -87, -33, -52],\n [294, 343, 26, 240, 424, -55, -37, 229, -99, 159]]\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 10x10 matrix:\n[[15, 70, -630, -122, 62, 499, -735, 72, -19, -452],\n [55, -235, 494, 143, 300, -90, 30, 274, -180, 338],\n [-523, -201, -356, 126, -380, -328, 183, -610, -350, -189],\n [-387, -609, 6, 291, 308, 14, -528, 38, -736, 36],\n [-292, -139, -56, 101, -206, -279, 237, -338, -203, -4],\n [18, 91, -618, -128, 34, 471, -678, 50, 7, -443],\n [-31, 133, 364, 16, -312, -510, 861, -286, 204, 271],\n [-148, -146, -254, 43, 52, 136, -357, -36, -224, -167],\n [-96, -122, 252, 100, -20, -246, 276, -76, -110, 190],\n [-192, -114, -270, 39, -52, 44, -213, -148, -196, -171]]\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[[325, -379, 317, 180, 237, -268, 33, -152, 415, -22],\n [12, -124, -68, 392, 1028, -382, 344, 158, 256, -550],\n [-645, -401, 817, -278, 511, 711, 39, 389, 385, 75],\n [638, -30, 118, 581, 214, -110, 160, 118, 28, 7],\n [66, -502, 278, 326, 1252, -472, 375, -6, 472, -343],\n [531, 187, 14, 481, -289, 74, -50, 218, 120, -199],\n [182, 398, -18, -54, -1068, 580, -291, 154, -372, 387],\n [175, -353, 296, 85, 249, -206, 27, -128, 380, -30],\n [-790, -246, 75, -872, -60, 95, -112, -357, -175, 466],\n [-853, 27, -397, -752, 73, -184, -50, -310, -217, -5]]\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 10x10 matrix:\n[[308, -49, 116, -43, -54, -213, -190, 165, 50, 25],\n [260, -202, 48, -114, -48, -334, -224, 250, -52, 98],\n [-126, 147, -8, 79, 24, 209, 128, -155, 54, -71],\n [-195, -447, -222, -204, 27, -324, -69, 225, -312, 213],\n [185, 332, 182, 149, -27, 219, 29, -150, 242, -158],\n [195, 48, 98, 11, -33, -59, -89, 50, 78, -22],\n [285, 285, 210, 120, -45, 120, -45, -75, 240, -135],\n [-64, 62, -8, 34, 12, 94, 60, -70, 20, -30],\n [-44, -107, -52, -49, 6, -79, -18, 55, -74, 51],\n [82, -254, -44, -128, -18, -288, -146, 210, -128, 122]]\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[[59, 229, 503, -112, -295, -694, 43, -216, 145, 711],\n [217, -325, 422, -253, -334, -364, 199, 101, 169, -685],\n [-245, 181, -656, 103, 266, 644, -127, 456, 497, 255],\n [-170, 191, -323, 475, 330, 210, -259, -758, -17, 1114],\n [-422, 168, -11, -75, -194, 242, 449, -218, -346, -567],\n [-158, 359, -501, 129, 386, 773, -198, 218, -28, -256],\n [-101, 292, -84, -85, -120, -8, 153, -242, 994, 414],\n [392, 119, 483, -85, 79, 60, -254, 15, -551, -1171],\n [89, -215, 62, -172, -101, -245, 16, 592, -150, -38],\n [681, -144, 727, -258, -246, -460, -228, 35, 824, -755]]\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[[-300, -29, 116, -203, 1054, -529, 46, 629, 169, -265],\n [618, 1388, 272, 252, 612, 308, 166, 1269, 191, -796],\n [332, 444, -67, 370, -1054, 707, 18, -324, -566, -462],\n [982, 223, -464, -313, 224, 784, 278, 213, -79, -610],\n [-330, -361, -762, 138, 426, 10, 592, -16, 482, -67],\n [335, 422, -507, 52, 52, 220, 645, 361, -73, 250],\n [-6, 767, -333, 598, 606, 344, 456, 783, 789, -928],\n [571, 532, 260, -136, -228, 142, -55, 256, -278, 345],\n [349, 82, -208, 154, -710, 577, 41, -401, -153, -122],\n [571, 87, 12, -7, -1160, 656, -171, -626, -658, 39]]?\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[[833, 878, -7, 52, 945, 157, -114, -228, -244, -73],\n [173, 696, 251, -493, -541, -429, 273, 656, 360, -15],\n [209, -243, -39, 359, 221, 789, -47, 202, -692, 105],\n [-330, 92, -63, 11, -330, -610, -46, -489, 473, 405],\n [619, 1076, -57, -554, 543, -653, 709, 671, 354, 835],\n [16, 61, -117, -72, 500, -200, 256, -139, -21, 399],\n [453, 607, 240, -84, 265, 781, 403, 157, 200, 7],\n [158, 32, 246, -701, 467, -532, 474, 687, 145, 619],\n [773, 301, -312, -417, 1620, -195, 936, 376, 265, 512],\n [-158, -80, -394, -8, -717, -649, -212, 407, 867, 75]]\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 10x10 matrix:\n[[86, -326, 230, -255, 493, -328, -462, -917, -191, -793],\n [-378, 288, -811, 881, 499, 463, -338, -241, 232, -773],\n [114, -445, -361, 164, 393, 298, -218, -151, -252, -490],\n [455, -240, 311, -339, -609, 186, 365, 755, -292, 915],\n [-681, 201, -48, -121, 16, 180, -597, -249, 613, 336],\n [-468, 485, -356, 168, 352, 240, -87, -241, 624, -191],\n [128, -425, 245, 90, -360, -541, -37, 145, -573, -27],\n [-474, 143, 17, -258, 329, 75, -471, -499, 506, 3],\n [-77, 104, 166, -286, -112, 268, -244, -70, 278, 407],\n [26, -477, 485, -658, -404, -321, -1, 227, -159, 669]]\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[[734, 534, 684, -976, 264, 434, 278, -236, 158, -168],\n [198, 560, 264, -138, 94, 282, 106, 58, -164, -108],\n [171, 635, 205, -96, 17, 214, 88, 92, -209, -91],\n [-295, -597, 275, 90, 501, -107, -210, 83, 163, 328],\n [-356, -410, 30, 406, 308, 46, -138, 118, -6, 126],\n [-117, -410, 307, -71, 430, -2, -114, 17, 160, 215],\n [-26, 214, -404, -160, -632, -808, -158, 70, -34, 266],\n [-115, -457, 375, -230, 441, -217, -190, 33, 223, 378],\n [203, 639, -154, -148, -424, -134, 77, 33, -181, -89],\n [-63, 72, -553, 273, -538, -175, 42, -28, -102, -170]]\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[[-336, -315, 399, -84, -441, -462, 399, 315, -210, 399],\n [-272, -255, 323, -68, -357, -374, 323, 255, -170, 323],\n [-48, -45, 57, -12, -63, -66, 57, 45, -30, 57],\n [-240, -225, 285, -60, -315, -330, 285, 225, -150, 285],\n [-192, -180, 228, -48, -252, -264, 228, 180, -120, 228],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n [304, 285, -361, 76, 399, 418, -361, -285, 190, -361],\n [-304, -285, 361, -76, -399, -418, 361, 285, -190, 361],\n [144, 135, -171, 36, 189, 198, -171, -135, 90, -171],\n [-256, -240, 304, -64, -336, -352, 304, 240, -160, 304]]?\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 10x10 matrix:\n[[-168, 0, 273, -462, -315, -420, -189, -126, 231, -357],\n [-8, 0, 13, -22, -15, -20, -9, -6, 11, -17],\n [-72, 0, 117, -198, -135, -180, -81, -54, 99, -153],\n [-56, 0, 91, -154, -105, -140, -63, -42, 77, -119],\n [136, 0, -221, 374, 255, 340, 153, 102, -187, 289],\n [-120, 0, 195, -330, -225, -300, -135, -90, 165, -255],\n [-80, 0, 130, -220, -150, -200, -90, -60, 110, -170],\n [-168, 0, 273, -462, -315, -420, -189, -126, 231, -357],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n [104, 0, -169, 286, 195, 260, 117, 78, -143, 221]]\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[[698, -604, 464, -719, -101, -523, -121, 773, -525, 645],\n [-572, 69, -128, -19, -888, -610, -335, -762, 303, -94],\n [591, -161, -615, 485, -7, -450, 255, 271, 149, -17],\n [799, -246, 231, -326, 800, -15, -178, 176, 38, -237],\n [-430, -46, 430, 31, 93, 184, -238, 312, -398, -660],\n [464, 725, 6, 613, 194, 776, 985, 866, -458, -847],\n [-756, -409, 46, -263, -378, -440, -960, -1000, 215, 321],\n [39, 233, 240, -37, -56, -3, 454, -295, -111, -148],\n [787, 57, 510, -410, 159, 244, 390, 1057, -479, -281],\n [60, 578, 269, -500, 288, 700, 1202, -141, 187, 1097]]\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[[736, 152, -717, 542, -212, -200, 120, 263, -110, 198],\n [392, 446, -515, 208, 55, -168, 100, 617, -331, 287],\n [556, 545, -787, -300, -166, 235, -166, 753, -625, 294],\n [907, -149, -990, 280, -202, 16, -420, 100, -303, 275],\n [454, 322, -661, -151, -430, 508, -134, 644, -283, 14],\n [-181, -298, -111, 201, -355, -163, -235, 17, 350, -183],\n [328, -68, -575, 645, -366, -652, -10, 178, 211, 84],\n [66, -240, -458, 446, 351, -840, -520, 170, -107, 399],\n [44, -107, -245, -415, 98, -55, -509, -39, -330, 193],\n [-81, 149, -90, -387, 242, 264, -313, 344, -362, 148]]?\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[[-436, -193, 272, -253, 251, -189, 98, 427, -31, -300],\n [-121, 130, 234, 64, 162, 4, 173, 160, 80, -167],\n [-196, -321, -80, -285, -5, -157, -142, 139, -127, -28],\n [286, 273, -52, 273, -91, 169, 52, -247, 91, 130],\n [-147, -609, -378, -483, -189, -231, -399, 21, -273, 147],\n [-129, -324, -150, -270, -60, -138, -183, 66, -138, 33],\n [-754, -318, 484, -426, 442, -322, 182, 742, -46, -526],\n [522, 409, -172, 433, -211, 281, 24, -471, 123, 278],\n [-146, 307, 412, 187, 271, 51, 328, 227, 169, -270],\n [-492, -425, 128, -437, 179, -277, -54, 435, -135, -244]]\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[[170, -216, -385, -573, 306, -184, -995, 714, -686, -161],\n [613, -721, -285, 485, 280, 209, 180, 64, 378, 263],\n [538, -186, 108, -799, -290, 340, 75, 198, -39, 443],\n [586, -867, -173, -97, 70, -179, -576, 524, 94, 30],\n [481, 74, -232, -63, -339, -254, 124, 259, 261, 10],\n [173, -221, -39, -959, -670, -51, -1060, 585, 198, 83],\n [-801, -51, 715, 509, 256, -201, 256, -575, -144, -337],\n [207, -129, 69, 417, 198, 469, 832, -451, 270, 365],\n [693, 181, -334, 980, 180, 535, 1739, -627, 666, 538],\n [-75, 558, 88, 555, -32, 330, 1231, -691, 347, 226]]\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 10x10 matrix:\n[[-47, 625, 226, -123, 59, 226, 431, -131, 467, 754],\n [-323, 295, 479, -275, 161, 146, 417, -168, 28, 296],\n [-349, 153, 109, -257, -135, 453, 516, -26, 133, 139],\n [-4, 358, 150, -422, -82, 117, 319, -310, -59, 95],\n [-678, -204, 293, -454, -15, 446, 557, -77, -194, -292],\n [163, 107, 343, -211, 297, -480, -217, -336, -338, -96],\n [528, -14, -504, 134, -241, -181, -372, -2, -10, -171],\n [-122, 360, 357, -190, 262, -12, 246, -211, 205, 450],\n [434, 194, -158, 22, 51, -309, -280, -168, 68, 119],\n [480, -436, -404, 672, 39, -504, -823, 342, -81, -260]]\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[[152, -396, -219, 704, 181, -118, -126, -278, -610, 323],\n [149, 617, 126, -499, -15, -652, 375, -279, 696, -574],\n [-155, -228, -152, 252, -12, 391, -293, 48, -292, 290],\n [-364, -437, 193, 375, -206, 257, -428, 219, -234, -37],\n [108, 235, -79, 3, -590, 69, 104, -189, -634, 547],\n [4, 694, -431, 9, -383, -215, -80, -803, -98, 212],\n [109, 45, -257, 50, 174, 103, 10, -139, -94, 227],\n [615, -185, 30, -48, -147, 87, 621, 276, -944, 847],\n [97, 511, -298, -161, -315, 4, 80, -412, -180, 347],\n [10, 140, 1, -62, 157, -266, 40, -148, 350, -315]]?\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[[-661, 457, -609, -673, -173, -937, -694, -410, -20, 532],\n [442, -976, 411, 90, -293, 440, 231, 456, -235, -516],\n [551, -420, 141, 927, 151, 611, 254, 182, 43, 13],\n [276, 433, 443, 161, 332, -277, 365, 77, 140, -22],\n [611, -134, 67, 725, 475, -281, -354, 5, 248, 889],\n [-125, 67, 248, -420, -445, 406, 842, 15, -380, -1227],\n [-543, 105, -345, -470, -158, -436, -506, -70, 33, 287],\n [130, -193, 136, 391, -255, 341, 554, 158, -204, -624],\n [329, 25, -95, 377, 125, 285, 129, -230, -31, 74],\n [-24, 355, -120, -125, -221, -73, 428, -347, -273, -480]]?\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 10x10 matrix:\n[[-7, 407, -278, -168, 410, 275, -391, 349, -107, -185],\n [421, 162, 270, -247, 122, -260, -188, -740, -668, 10],\n [239, -385, 120, 104, -230, -47, 453, -387, -255, 395],\n [432, 464, -385, -99, 584, 405, -396, 360, -476, 200],\n [53, -245, -185, 239, 5, 397, 397, 186, -139, 296],\n [452, 99, -626, 77, 320, 443, -31, 825, 19, 725],\n [638, 156, 20, 327, 336, 302, -19, -125, -810, 371],\n [-272, -246, 185, 543, -176, 221, 356, 92, 82, -148],\n [-228, -343, 298, 623, -56, 553, 635, -373, -599, -257],\n [392, -72, -735, -397, 118, 153, 44, 666, 292, 866]]\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[[114, -10, -542, -246, 114, 712, 90, 154, -430, -372],\n [-928, 50, -266, 72, -68, -176, -86, 86, 484, -282],\n [-960, 35, -325, 80, -100, -94, -67, 143, 448, -347],\n [-851, 45, -396, 3, -34, 21, -58, 122, 346, -366],\n [-374, 60, 163, 80, 13, -461, -107, -135, 417, 124],\n [-362, 270, 25, -316, 541, -653, -281, -609, 585, 286],\n [329, 110, -133, -325, 372, 113, -57, -279, -156, 97],\n [326, -70, 112, 66, -104, 130, 76, 92, -224, 48],\n [-638, 185, -173, -186, 308, -392, -199, -309, 528, -3],\n [399, -195, 81, 231, -375, 414, 201, 393, -447, -114]]\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[[-304, 76, -300, -201, 73, 168, -295, 399, -726, 317],\n [-839, 439, -224, 734, 45, -591, -323, 508, 123, -356],\n [-107, -485, 300, 322, -7, 234, -765, -401, -669, 332],\n [-1229, -7, 254, 536, -224, -613, -273, -421, 555, -480],\n [753, 53, -149, 191, -365, 395, 17, 499, -136, -94],\n [-91, 745, 175, -208, 130, -372, 1198, -155, 237, 7],\n [-630, -375, 184, 195, -22, 28, -840, -460, -526, 229],\n [1409, -310, 158, -375, -161, 693, 645, 104, -4, 165],\n [-706, 748, -381, 99, -140, -272, 84, 545, -354, -54],\n [697, -19, 119, -35, 383, 86, 85, -200, -128, 280]]?\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 10x10 matrix:\n[[516, -82, 325, -119, -284, 64, 169, 50, 179, 172],\n [-304, -87, -366, 289, 123, -176, 195, 343, -138, 219],\n [-317, 182, 205, -165, 130, 237, -323, -353, -142, -422],\n [632, -150, -63, -23, -216, -212, 201, 130, 315, 336],\n [9, 125, -294, -157, 209, -149, -405, -426, 159, -287],\n [77, -86, -32, 100, -72, -57, 190, 213, 5, 200],\n [-222, 51, 466, -37, -91, 342, 61, 35, -232, -123],\n [745, -71, -407, -148, -45, -425, -128, -218, 524, 155],\n [108, -280, -259, 399, -150, -248, 611, 736, -29, 658],\n [390, 86, 23, -285, -12, -50, -313, -440, 283, -212]]\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[[893, -345, -41, 257, -768, -222, -222, -77, -243, -119],\n [-45, -605, -721, -276, 817, 783, -533, 380, 447, -30],\n [-277, -473, -642, -229, 449, 600, -418, 255, 91, -21],\n [21, 74, -453, 21, 567, -65, 243, -740, -531, -402],\n [-643, 491, 790, 75, -309, -64, 298, 421, -315, 577],\n [414, -180, 156, 217, 387, 463, -77, 311, -606, 399],\n [-186, 96, -115, -192, -357, -410, 0, -198, 758, -362],\n [-726, 433, -23, -204, 381, -200, 342, -343, 214, -190],\n [-791, 486, 412, -97, 65, -100, 318, 106, 13, 235],\n [464, -136, 141, 48, -601, -252, -174, 148, 496, -66]]?\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[[678, -165, -1078, 155, 200, 1131, 760, 646, 278, -625],\n [601, 108, 45, 660, -122, 397, -349, -640, 750, 104],\n [298, -186, 444, -307, -238, -568, -976, -23, -259, 542],\n [-1009, 211, 281, 84, -37, -841, -94, -479, -31, 39],\n [-114, -115, 968, -78, 80, -129, -1037, -134, 241, 1018],\n [5, -76, 53, 362, -875, -670, -931, -496, 698, 264],\n [-296, 402, 745, -626, 256, 90, -240, 294, -593, 566],\n [273, -13, 531, -173, -966, -432, -726, 179, -348, -178],\n [44, -388, -17, -117, -869, -582, -918, 498, -77, -134],\n [-185, 257, 229, 73, -78, -385, 145, -23, -271, 495]]\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[[-501, 339, -727, 369, -502, -228, 746, 317, -21, -705],\n [30, 91, 914, -665, 718, -513, -647, -533, 156, 773],\n [290, -378, 35, 468, -321, 496, 50, 75, 254, 312],\n [157, -178, 584, -180, 316, 57, -479, -241, 199, 552],\n [104, 59, 323, -261, 272, -215, -243, -108, -142, 381],\n [166, -3, -832, 373, -540, 237, 639, 355, -344, -601],\n [218, -37, -118, -339, 157, -45, 17, -319, -4, -297],\n [-22, 179, -470, 79, -254, -201, 493, 87, -184, -331],\n [732, -137, -9, 137, -207, -54, 263, 40, -420, 757],\n [-77, -85, -134, -103, 132, 373, -290, 150, -131, -527]]\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[[653, -41, -260, 237, 249, -196, 498, -45, -441, -332],\n [45, -61, -118, 122, -116, -121, 201, -224, 109, -306],\n [261, 193, -230, 121, 104, -878, 1083, -301, 92, 189],\n [-10, 2, 215, -152, 175, 102, -148, 390, -271, 533],\n [-281, 53, -92, 31, -261, -148, 70, -367, 477, -252],\n [65, 433, -216, -80, 201, -105, -32, -166, 210, -13],\n [-222, 54, 143, -179, 30, 649, -899, 239, 3, -5],\n [207, 21, -104, 32, 126, 503, -541, 70, -189, -430],\n [-65, 671, -325, -126, 180, -329, 96, -390, 537, 14],\n [243, -393, -66, 270, -171, -45, 324, -120, -210, -483]]?\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[[114, 546, -231, 568, -456, -380, 571, 451, -89, 66],\n [-591, 859, -681, -652, 129, -562, -247, 56, -498, 519],\n [-169, -403, 273, 783, 714, -415, -625, 46, 358, 1380],\n [-556, -69, -43, -172, 679, -441, -943, -491, -160, 962],\n [52, -700, 527, 963, 420, -175, -317, -36, 413, 855],\n [169, -86, 157, 358, -89, -403, 411, -103, -31, 383],\n [-48, -85, 72, 531, 559, -428, -356, 156, 273, 1202],\n [241, -249, 219, 788, -229, 350, 257, 604, 410, -251],\n [-637, 799, -687, -200, 123, -300, -261, 731, -180, 552],\n [9, -327, 167, -159, -468, 685, 213, 58, -8, -1188]]?\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[[670, 15, 478, 68, 5, -22, -358, 244, -175, 155],\n [-36, -80, -12, 349, 15, 257, -274, 72, -75, 356],\n [-72, 184, 30, -278, -442, -724, 453, 173, -234, -619],\n [-1252, -52, -298, 4, 11, 1058, -757, -445, 573, 18],\n [-323, 1042, -342, -782, -802, 91, 889, 698, 251, -82],\n [-784, -629, 772, 233, 613, 160, -960, -532, -149, -614],\n [-787, -143, -59, -283, 245, 257, -105, -513, 294, -393],\n [-16, 519, -1072, -433, -702, 115, 589, 383, 794, -78],\n [-5, 386, 198, -434, -167, 336, 711, 888, 246, 482],\n [-23, 764, -284, -151, -568, -197, 147, -140, -403, -109]]?\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 10x10 matrix:\n[[498, -360, -89, -320, -130, -267, -797, 132, 408, -180],\n [538, -208, 835, -343, 104, -225, -146, -280, 841, 130],\n [25, 74, 12, 65, -398, 74, -290, 268, -129, -396],\n [371, -209, 146, 501, -399, 415, -350, 86, -447, -693],\n [251, -190, -105, 150, -214, 113, -400, 116, -172, -362],\n [323, -126, 483, 1, -32, 31, -71, -144, 263, -96],\n [-461, 568, 422, 9, -372, 78, 418, 216, -33, -122],\n [-115, 177, -141, -195, -423, -136, -381, 406, 45, -275],\n [-237, 294, 507, -213, 192, -129, 567, -192, 393, 408],\n [468, -290, -90, -470, -262, -376, -940, 268, 534, -226]]\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[[663, -403, 152, -653, -531, 294, -284, 639, -297, -196],\n [-274, -128, -505, 365, -536, -215, 76, -54, 425, 1273],\n [350, -985, -383, 34, -536, 57, -906, -453, 139, 304],\n [292, 243, -86, 25, 552, -673, 429, -540, -387, -287],\n [-231, -94, -316, 63, -150, 296, -295, 267, 211, 53],\n [530, 69, -550, 101, -672, -267, -595, 278, 487, 487],\n [626, 273, -209, 698, 133, -27, 336, 102, 21, -529],\n [-775, 1064, 605, 64, 255, -260, -142, 8, 450, 71],\n [460, -258, -77, 37, -694, 384, -1023, 315, 579, -64],\n [251, 557, -239, 151, -60, -261, -381, 210, 345, -200]]\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[[180, 20, -140, -140, -320, 160, 20, -20, 180, -120],\n [-240, 21, -732, -342, 54, -66, 606, 447, -669, 69],\n [6, -3, 66, 36, 18, -6, -48, -33, 39, 3],\n [1, 16, -307, -177, -126, 50, 211, 140, -142, -31],\n [-179, 18, -591, -281, 22, -42, 483, 354, -520, 47],\n [-103, -9, 33, 53, 164, -84, 21, 33, -125, 64],\n [225, -8, 461, 191, -142, 98, -413, -316, 522, -87],\n [-23, 6, -147, -77, -26, 6, 111, 78, -100, -1],\n [-39, 3, -111, -51, 12, -12, 93, 69, -105, 12],\n [190, 15, -30, -80, -290, 150, -60, -75, 245, -115]]\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 10x10 matrix:\n[[-719, 308, 527, -374, 660, 163, 178, -181, -255, -203],\n [837, -211, -707, 896, -446, -1158, -301, 1, -178, 160],\n [-166, 995, 417, 22, 552, 698, 535, 353, 461, 251],\n [81, 66, -245, 46, -103, -607, -294, 266, 763, -368],\n [-45, 72, -923, 688, -671, -369, -76, 590, -36, 188],\n [-232, 756, -261, 615, -219, 47, 500, 451, 245, 346],\n [166, -619, 74, -408, -33, -96, 482, -850, -4, 38],\n [435, -352, -127, 294, 275, -519, -753, 93, 857, -106],\n [271, -90, -1110, 839, -1110, -276, -92, 669, 362, 282],\n [-832, -318, 212, -530, 176, 598, 155, -253, 245, -298]]\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[[759, -281, -628, 198, 734, 68, 374, -329, -34, 586],\n [62, 578, 347, -33, 442, -1, -789, 278, 498, -209],\n [475, -254, -227, 1342, 278, 19, 784, 157, -806, 375],\n [-91, 230, 340, 673, -73, 326, 66, 368, -406, -21],\n [-670, 512, 452, 358, -129, 486, -833, 861, -56, -455],\n [-661, 307, 172, -30, -554, 885, -157, 631, -384, -700],\n [-51, -315, 130, 579, -463, -135, 757, -93, -631, 191],\n [-437, -315, 180, -547, -702, -437, 172, -340, 71, -12],\n [160, -5, 360, -253, -164, -360, 229, -468, 162, 258],\n [-148, -350, -162, 70, -324, -481, 299, -90, -148, -124]]\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[[167, 23, -90, 290, -10, 108, -280, -22, 5, -56],\n [-28, -208, -143, -176, -200, -79, 193, -7, -201, -57],\n [-250, 29, -127, -12, -6, -47, -726, 347, -29, 212],\n [-89, -281, -438, -46, -225, 162, -334, 66, -376, -85],\n [145, -380, -269, -242, -208, 257, 922, -471, -408, -404],\n [251, 32, 262, 2, -9, -154, 717, -244, 144, -112],\n [81, -183, -264, 94, -196, 54, -190, 12, -213, -88],\n [170, -115, -84, 52, -90, 84, 293, -194, -108, -171],\n [215, -535, -719, 26, -282, 671, 389, -527, -698, -573],\n [311, -541, -577, -22, -341, 487, 727, -577, -629, -582]]\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[[266, -120, -225, -81, -336, 174, -557, -56, 267, -156],\n [260, 128, 35, 9, -650, 278, -481, 144, 199, 116],\n [547, -333, -523, -267, -284, -86, 151, 370, -142, -114],\n [389, 47, -148, -72, -624, 32, -326, 170, 121, 66],\n [-147, 2, -133, -9, 454, -697, 223, -397, -32, -151],\n [-554, 344, 460, 237, 455, -297, 236, -363, -39, 143],\n [-40, -514, -359, -150, 579, 243, -55, -129, 42, -431],\n [228, -278, -514, -210, 316, -714, 402, -94, -174, -242],\n [538, -549, -812, -336, 2, -271, -234, -63, 112, -477],\n [381, 159, -213, -63, -566, -498, -299, -86, 156, 38]]\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[[242, -492, -269, 84, -358, 517, 141, -42, 69, 20],\n [187, -377, -39, 54, 2, 377, -229, 123, 124, -85],\n [-193, 289, 152, -144, 108, -236, 20, 6, -71, 12],\n [178, 2, -470, 372, -444, -190, 622, -390, -100, 210],\n [-178, 194, 136, -190, 40, -98, 32, 23, -60, 7],\n [179, -457, -19, -26, -38, 517, -249, 163, 136, -101],\n [225, -697, -148, -120, -340, 864, -56, 126, 131, -64],\n [147, -63, -414, 258, -456, -48, 570, -327, -87, 183],\n [481, -517, -730, 548, -696, 290, 638, -400, 9, 198],\n [397, -181, -588, 646, -372, -166, 480, -389, -11, 177]]\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[[-20, -20, -28, -72, 32, 56, -12, 0, 36, 76],\n [15, 15, 21, 54, -24, -42, 9, 0, -27, -57],\n [80, 80, 112, 288, -128, -224, 48, 0, -144, -304],\n [-85, -85, -119, -306, 136, 238, -51, 0, 153, 323],\n [-85, -85, -119, -306, 136, 238, -51, 0, 153, 323],\n [-35, -35, -49, -126, 56, 98, -21, 0, 63, 133],\n [75, 75, 105, 270, -120, -210, 45, 0, -135, -285],\n [105, 105, 147, 378, -168, -294, 63, 0, -189, -399],\n [45, 45, 63, 162, -72, -126, 27, 0, -81, -171],\n [65, 65, 91, 234, -104, -182, 39, 0, -117, -247]]\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 10x10 matrix:\n[[275, 520, 406, 6, 273, 19, 71, -334, 283, 16],\n [-393, -664, -732, 21, -538, -348, 17, 565, 74, 289],\n [341, -516, -438, 143, -1242, -18, 495, -157, -84, 389],\n [-241, -376, 247, 278, 402, -79, -304, -511, -1245, -774],\n [-95, -2, 202, -687, 561, -80, -254, 248, -447, -142],\n [-109, 383, 79, -297, 589, 463, -862, -263, 154, -1414],\n [-590, -229, 58, -663, 520, -532, -505, 265, -831, -537],\n [-388, -228, -229, -666, 661, -928, -39, -15, -1173, 142],\n [301, -492, 263, 577, -228, 383, -332, -564, -234, -899],\n [-8, -137, -719, -417, -594, 305, -17, 431, 411, 48]]\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[[234, 342, 204, -618, 264, -162, 276, 468, -396, -294],\n [-243, -363, -218, 639, -282, 173, -280, -484, 412, 313],\n [-144, -30, 16, 444, 18, -10, -322, -334, 226, 4],\n [-279, -396, -234, 741, -303, 186, -339, -561, 471, 339],\n [-18, 111, 92, 96, 117, -71, -137, -71, 17, -112],\n [-123, -66, -18, 365, -25, 16, -241, -275, 197, 43],\n [123, 66, 18, -365, 25, -16, 241, 275, -197, -43],\n [-51, -204, -146, 89, -187, 114, 49, -69, 99, 191],\n [189, 186, 94, -531, 123, -76, 299, 401, -311, -149],\n [-180, -165, -80, 510, -105, 65, -295, -385, 295, 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 10x10 matrix:\n[[56, -150, 158, 55, -14, -89, -50, -187, -64, -50],\n [-123, 475, -367, -266, 319, 518, -279, -63, 629, -482],\n [-343, 661, -71, 212, -45, 575, -229, -237, 309, -233],\n [354, -228, -412, -731, 652, 189, -352, 444, 474, -314],\n [588, -1292, 411, -95, -378, -929, 348, 113, -787, 722],\n [425, 84, 383, 235, -368, 188, -445, -176, 228, -143],\n [609, -1180, 431, -165, -28, -354, -325, -405, -352, 151],\n [715, -229, 144, -278, -275, 120, -418, 218, 393, -2],\n [826, -71, 181, -118, -115, 232, -691, 40, 571, -390],\n [-425, -313, 417, 327, 107, -351, 232, -413, -670, 166]]\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[[249, -177, 138, 261, -450, -315, 186, -135, -171, -168],\n [-388, 168, -78, -326, 78, 100, -244, 120, -304, -936],\n [119, 69, 361, 358, -87, -60, 486, -43, 117, 933],\n [216, 13, 245, 277, 85, -46, 381, -49, 365, 1269],\n [-610, 364, 95, -429, 213, 116, -138, 200, -308, -794],\n [-422, 256, -31, -427, 347, 128, -210, 164, -24, -334],\n [-67, 233, 583, 328, -95, -119, 648, 7, 15, 940],\n [-386, 377, 715, -1, -203, -385, 551, 73, -289, 76],\n [-67, 28, -90, 147, -12, 313, -5, 28, -178, -227],\n [114, 133, 567, 363, -91, -235, 663, -47, 207, 1298]]?\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[[-79, 21, -168, 33, -12, 930, 398, -167, -38, 127],\n [-247, 29, 120, 251, -194, 243, -67, -310, -280, -168],\n [-241, -162, -316, 17, 1066, 33, 423, 604, 53, 677],\n [-71, 181, -795, 281, -626, 49, 16, -957, 37, -692],\n [-501, 140, 279, 73, 907, -230, -286, -173, 72, 523],\n [136, 13, 397, -73, -139, 799, 85, -190, 185, 296],\n [148, -426, -484, 124, 337, 24, 616, 575, -246, 144],\n [710, -604, 266, -79, -308, 294, 528, 475, -487, -169],\n [-4, 153, 391, -39, -52, 487, -210, -1181, -108, -187],\n [164, -489, -1230, 490, -301, 483, 989, -6, -445, -436]]?\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[[-97, -543, -172, 326, -606, 49, 73, -260, -257, -688],\n [-762, 1006, 124, -114, -216, -510, 692, -176, 376, -68],\n [-396, 374, 299, 363, 323, 466, 196, 160, -243, 33],\n [-462, -253, 20, 24, -653, -317, 180, -78, -44, -807],\n [-406, 226, -72, 14, -492, -370, 388, -256, 140, -392],\n [-580, 503, 325, 437, 232, 443, 346, 106, -247, -76],\n [524, -39, -460, 53, -151, -89, 57, -486, 143, 335],\n [534, -292, -370, -45, -146, -94, -131, -300, 85, 190],\n [-105, 478, -356, -603, -645, -1136, 408, -458, 724, -25],\n [-73, -432, 122, -1, -109, 66, -208, 210, -178, -377]]\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[[-52, -286, 26, -182, 182, -156, -247, 26, 78, -13],\n [-28, -154, 14, -98, 98, -84, -133, 14, 42, -7],\n [20, 110, -10, 70, -70, 60, 95, -10, -30, 5],\n [-16, -88, 8, -56, 56, -48, -76, 8, 24, -4],\n [68, 374, -34, 238, -238, 204, 323, -34, -102, 17],\n [-68, -374, 34, -238, 238, -204, -323, 34, 102, -17],\n [-76, -418, 38, -266, 266, -228, -361, 38, 114, -19],\n [28, 154, -14, 98, -98, 84, 133, -14, -42, 7],\n [64, 352, -32, 224, -224, 192, 304, -32, -96, 16],\n [32, 176, -16, 112, -112, 96, 152, -16, -48, 8]]\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[[298, -880, -303, 106, -212, 163, -96, 179, -192, -246],\n [-174, 384, 634, -557, 483, 372, 117, -157, 201, -703],\n [-447, 269, -263, 107, -364, -708, -239, -74, 37, 415],\n [-472, 553, -155, 202, -696, -781, 352, -63, -86, 22],\n [-209, -277, -481, 54, 373, 529, -736, 294, -231, -426],\n [257, 648, 944, -266, -177, -185, 1194, -394, 276, -112],\n [-517, 186, -140, -161, -762, -712, 2, -212, 112, -651],\n [-76, 697, 624, 55, 109, -87, 1141, 246, -256, 179],\n [207, 397, 213, 42, 375, 766, -184, -929, 174, -228],\n [-102, -643, -245, -267, 9, -56, -356, 681, -58, -467]]\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 10x10 matrix:\n[[-354, 474, -501, 20, 30, -94, -140, 160, -89, 289],\n [-267, -119, 12, -55, -488, 593, -228, -131, -350, 240],\n [-681, 391, -618, -133, -140, 191, -210, 154, -326, 366],\n [-56, -288, 79, -214, 238, -120, 218, 43, 37, -307],\n [193, -411, 361, -77, -14, 101, 126, -112, 29, -249],\n [284, -128, 320, 168, -312, 272, -122, -183, -18, 88],\n [-387, 109, -327, -173, 106, -35, 16, 131, -121, 31],\n [161, -219, 221, -21, 26, 5, 86, -60, 57, -157],\n [-37, -201, 188, 7, -424, 495, -164, -169, -226, 136],\n [-272, 92, -182, -48, -180, 220, -130, 9, -192, 182]]\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[[-400, -160, 18, 352, 428, -170, 140, -182, -206, 430],\n [-604, -345, -560, 363, -331, 322, 752, -923, -509, 37],\n [-660, -14, -656, 113, 368, 723, 317, -171, -605, -341],\n [216, 413, -658, -408, 617, 575, -100, 543, -345, -511],\n [-160, 176, 256, -82, 66, 412, 470, -662, 0, -512],\n [144, -145, -14, -119, 509, -658, 213, -45, -915, -28],\n [-134, 109, 24, -272, -246, 641, 25, 150, 34, -519],\n [22, -123, 277, 225, 92, -707, 291, -166, -324, 410],\n [268, 423, 244, 140, 89, -492, -400, 550, 301, -62],\n [796, -150, 240, -651, -312, -32, -138, 285, 306, 235]]\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[[-945, 364, 7, -16, -213, -167, -1177, 153, 157, -263],\n [201, 1490, 699, -74, -330, 538, 20, 192, -789, -207],\n [133, -437, -476, 331, -302, 269, 73, -437, -291, 1062],\n [151, -552, 603, -384, 329, -1088, 12, 530, 306, -599],\n [314, -400, -266, -217, -454, -368, -174, 166, -566, 444],\n [-321, -278, -861, -580, 181, -149, 554, 80, 1205, -538],\n [1227, 534, 452, 486, -304, -20, -546, -865, -1565, 252],\n [-807, -159, -298, -183, -331, 520, 134, 1399, 602, -419],\n [483, 345, 139, 573, 541, 494, 722, -174, 258, 244],\n [-661, 199, -485, 459, -36, 1129, -87, 139, 329, -26]]\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[[66, 158, -244, -266, 320, -22, 316, -430, -418, 168],\n [-144, -162, 216, 189, -270, -72, -234, 270, 297, -117],\n [323, 87, -6, 168, -42, 343, -164, 405, 264, -115],\n [-162, 2, -76, -182, 128, -202, 196, -370, -286, 120],\n [163, 41, 2, 91, -28, 175, -90, 215, 143, -62],\n [-237, -7, -94, -245, 164, -289, 262, -505, -385, 162],\n [-625, -343, 314, 49, -328, -549, -118, -145, 77, -16],\n [-659, -331, 278, -14, -274, -599, -48, -265, -22, 25],\n [621, 305, -250, 28, 242, 569, 28, 275, 44, -33],\n [355, 123, -54, 126, 18, 359, -112, 345, 198, -89]]?\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[[-368, 100, 50, 328, 222, 166, 308, -196, 246, -160],\n [-208, -16, 106, 320, 156, 230, 184, -110, 204, -26],\n [29, 185, -365, -229, 89, -423, 366, -152, 202, -295],\n [222, -164, -50, 126, 69, 54, 182, -21, 279, 73],\n [-144, -128, 277, 360, 62, 403, -68, 9, 46, 155],\n [589, -357, 37, -65, -158, 75, -212, 215, 23, 348],\n [-466, 122, 130, 362, 208, 238, 224, -182, 158, -144],\n [-366, 150, -18, 246, 216, 66, 336, -210, 234, -216],\n [-338, 332, -210, -146, 101, -298, 246, -181, 7, -359],\n [-108, 222, -237, -216, 39, -327, 186, -108, 15, -258]]?\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 10x10 matrix:\n[[94, -382, -262, -235, -472, -320, -986, -441, -1102, 49],\n [767, 924, -124, -100, 63, -331, -48, 100, -935, 558],\n [-155, -170, 1005, 681, -170, 206, 508, -49, 710, -195],\n [279, 103, 372, 210, 394, -283, -11, 531, -132, -125],\n [-143, 95, 50, 393, 365, -705, -192, -943, 510, 563],\n [-375, 150, 209, -307, 939, 436, 564, 894, -26, -604],\n [-32, -321, 345, 275, 51, -259, -114, -97, -894, -307],\n [-162, -639, -46, 955, 233, 621, 753, -540, -103, 355],\n [207, -131, 82, 47, -802, 41, 712, 4, -342, -700],\n [-654, -684, 317, 714, -183, 12, 28, -1228, 1027, 307]]\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[[764, 280, -341, 53, -107, 226, -690, 742, 121, -373],\n [104, -69, -487, 359, -457, 59, 320, -388, 295, 922],\n [-32, 311, 431, -121, 35, -481, -784, 616, -413, -980],\n [437, -382, -82, -281, 341, -258, 2, -34, -171, -46],\n [-646, -169, 422, -100, 111, -280, 330, -550, -192, 134],\n [683, 685, 464, 971, -474, 852, 164, 472, -371, -390],\n [-266, -191, -420, 197, -4, 336, 1173, -95, 305, 362],\n [-746, 271, 396, -78, -207, -376, -554, -170, -58, -112],\n [203, 410, -16, -128, 55, 69, -731, 949, 10, -947],\n [41, 154, -327, 158, -241, 353, -23, 19, 358, 346]]?\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[[-203, 189, 675, -713, 11, -16, 857, 1119, 642, -1024],\n [-863, 33, -44, -1310, -697, -773, 549, 543, -629, -899],\n [109, 85, -828, 375, 160, 668, 292, -472, 771, -74],\n [351, 529, 106, 44, 312, -431, -499, 340, 202, 477],\n [-26, 508, -485, -155, -451, -402, -393, -228, -467, 279],\n [-139, -121, -477, -310, 191, 58, 0, 68, 249, 31],\n [0, 394, -261, -121, -499, 98, 308, -243, 247, -674],\n [2, -563, -253, 453, 1250, 607, 700, 305, 1650, 50],\n [153, 125, 1122, 118, -19, -543, 256, 924, 805, -84],\n [178, -227, -257, 243, 445, -379, -774, -871, -652, 665]]?\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[[386, 281, 457, 1184, -492, -899, 289, 955, -938, 50],\n [-346, 739, -579, 1000, -115, -186, -175, 410, 811, 205],\n [-326, 895, -119, 316, -92, -382, 40, 152, 708, 490],\n [207, -17, -602, 239, -219, -143, -340, 417, 430, -296],\n [204, -517, -798, -436, 734, -325, 37, -309, 532, -51],\n [-546, 52, 568, -336, 712, 842, -150, -579, 1094, -189],\n [356, 680, 800, -62, -738, -335, 208, -10, -741, 876],\n [312, -326, 649, -434, 2, -77, 112, 358, 557, 281],\n [-394, 614, -693, -186, -476, 696, -696, -380, 135, 280],\n [414, -218, -346, -476, -79, -21, -614, 108, -72, -79]]?\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[[81, -459, -49, -52, 271, 442, 387, -229, -318, 316],\n [-229, -173, -201, -206, -37, 194, -205, 153, 274, 388],\n [215, 129, 220, 149, 2, -64, 52, 9, -128, -92],\n [39, 0, 6, 48, 48, -51, 141, -126, -138, -174],\n [352, -199, 266, 145, 206, 299, 331, -121, -382, 210],\n [-346, 124, -312, -128, -124, -298, -142, -48, 220, -356],\n [26, 215, 50, 87, -70, -253, -21, -27, -14, -326],\n [-128, 350, -22, 4, -226, -358, -332, 182, 296, -252],\n [-275, -238, -293, -213, 27, 165, -44, -14, 152, 214],\n [535, -27, 477, 278, 165, 204, 299, -53, -430, 136]]?\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[[101, -326, -713, -606, 1244, 322, -445, 460, 848, 832],\n [-164, 529, 645, 443, -593, -341, 671, -1133, -540, -827],\n [570, -331, 18, -145, -541, -415, 100, 394, -648, -284],\n [-113, -260, 204, 334, 52, 636, -539, 557, 316, 124],\n [-360, 354, -577, -46, -145, -268, -305, -200, -246, -468],\n [681, -506, -138, -476, 435, 38, 87, 572, -82, 321],\n [-50, -95, -653, -330, 140, -213, -431, 282, 21, 18],\n [-272, -224, -219, 354, 240, 847, -1024, 666, 543, -43],\n [-292, 128, -577, -140, 204, 332, -521, 497, -398, -335],\n [-631, 619, 123, -118, 141, 530, 621, -599, -592, -527]]\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[[-44, 193, 108, -209, -461, -671, -113, -74, 20, -312],\n [-6, -273, -34, 207, 274, 529, 168, 4, -44, 132],\n [460, 298, -388, -362, 371, 224, -323, 236, -24, 654],\n [-191, 468, -45, 143, -260, -509, 424, 20, 476, -519],\n [-68, 178, 152, -130, 125, -183, -537, 43, -160, 280],\n [120, -260, -4, -8, 541, 651, -413, 79, -328, 656],\n [-631, -112, 559, 411, -26, -190, -158, -159, -76, -305],\n [-494, -327, 478, 421, 312, 317, -274, -106, -244, 80],\n [502, -145, -314, -361, 225, 404, -247, 111, -244, 572],\n [-451, -583, 535, 410, 481, 616, -475, -122, -480, 333]]\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[[811, 8, -184, 456, -15, 1303, -48, 133, -423, 131],\n [260, 311, -261, 382, -660, 1095, -487, 312, -249, 630],\n [256, -529, 353, -524, 1219, -126, 399, 1141, 196, 1516],\n [45, 77, 970, 354, -169, 1030, -641, -494, 275, 559],\n [159, -1043, -259, -370, 112, -359, 630, 803, 100, 274],\n [512, 606, -991, 726, -991, 588, -581, -574, -1186, -579],\n [191, -40, 247, 332, 189, 428, -160, -99, -32, 361],\n [-336, -331, -203, -364, -711, -44, -179, 833, 110, 1062],\n [-1011, 91, -583, -212, -653, -961, -131, 906, 113, 1031],\n [-63, -292, -343, -592, -86, -410, 414, 693, 458, -101]]?\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[[-326, -62, -98, -155, -103, -264, 324, -285, -39, 169],\n [-768, 174, -165, -492, -42, -384, 640, -716, -212, 466],\n [-825, -244, -528, -639, -66, 87, 777, -353, -293, 430],\n [267, 202, 177, 258, -213, -183, -365, -66, -90, -177],\n [-403, -173, -457, -440, -31, 457, 319, 8, -339, 185],\n [-1092, -90, -594, -958, 226, 316, 996, -450, -344, 658],\n [735, 348, 534, 619, -64, -253, -763, 149, 181, -392],\n [-275, 424, 250, -77, 14, -579, 163, -611, 1, 230],\n [-362, -466, -167, -261, 357, 28, 656, 133, 401, 249],\n [151, 691, 283, 108, -153, -185, -471, -396, -335, -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[[588, 49, 498, -94, -284, -86, -485, -231, -21, 104],\n [-785, 93, 393, -78, -124, -365, 1074, 172, 12, -161],\n [-654, -103, 185, -373, -691, -217, 588, -309, 410, 226],\n [-922, -329, -541, 42, 494, -351, 417, 456, -44, 307],\n [293, 384, -361, -366, 139, 441, -1092, -269, -411, 93],\n [-387, 1130, 782, -346, -188, 114, -127, 30, -856, -508],\n [-83, -653, -1251, 164, 862, 28, 257, 121, 102, 83],\n [-617, -739, -262, 251, -187, 44, 307, 208, 1097, -161],\n [71, -376, -262, 229, 435, -790, 624, 145, -520, 305],\n [314, 339, 171, 135, -72, -183, 304, -117, -598, -247]]\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[[117, -160, 392, -58, 98, 225, -312, 425, 223, -267],\n [43, -288, 138, -588, 103, 389, -1, -415, -386, 260],\n [250, -588, 494, -376, 36, 176, -70, -685, -60, 362],\n [446, -427, 402, -170, -121, 182, 209, -1048, 142, 537],\n [-385, 141, -54, -104, 52, -149, -32, 490, -208, -289],\n [49, -752, 326, -93, 111, -387, -327, -529, -125, 337],\n [127, -720, 708, -262, 114, -33, -360, -215, 61, 83],\n [-475, 256, -234, -218, 153, 15, -147, 795, -372, -410],\n [522, -103, 276, 234, -320, 4, 508, -1118, 461, 520],\n [370, -121, 114, -167, 110, 556, -218, -13, 102, 53]]\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[[258, -515, -139, -618, 22, 306, 126, 198, 88, -140],\n [-187, 670, 256, 326, 237, 30, -131, 111, 360, 374],\n [102, 133, 19, -30, 570, 132, -92, 574, 260, 296],\n [-77, 54, -264, -746, -735, 654, 193, -757, 392, 204],\n [34, 282, 88, 184, 42, 126, -274, 82, 184, 358],\n [120, -147, 200, 114, 160, -129, -90, 286, -68, -153],\n [-171, 724, 253, 144, 408, 183, -72, 270, 560, 470],\n [87, 32, -266, 1020, -385, -438, -716, -335, -730, 359],\n [-26, 55, -222, 1174, 499, -837, -394, 343, -814, 113],\n [-30, -337, -60, -360, -295, -3, 317, -287, -120, -422]]\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 10x10 matrix:\n[[-260, 469, 645, -62, 61, -95, 109, 41, 30, 28],\n [469, -21, 494, 243, -352, 305, 451, 415, 320, 578],\n [329, -300, 15, -272, -400, 464, 96, 426, 869, -140],\n [-370, 35, 150, -127, 408, -608, 96, -171, -705, -9],\n [563, -102, -481, 702, -411, 723, -39, 42, 246, 390],\n [-475, 87, -4, 618, -22, 292, -486, -41, 178, 32],\n [338, 10, -1149, 719, -145, 635, -327, -414, -250, -23],\n [-681, -265, 721, -314, 178, -237, 475, 603, -22, -205],\n [401, 438, -534, 814, 56, 107, -111, -612, -805, 517],\n [936, 331, 816, 139, -448, 142, 502, 241, 389, 947]]\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[[-150, 98, -139, 26, -151, 66, -208, -67, -239, -297],\n [322, 192, 350, 138, -54, -306, 160, -70, 354, 350],\n [182, 640, 266, 334, -530, -390, -288, -322, -10, -182],\n [-86, 46, -81, 10, -77, 42, -112, -33, -133, -163],\n [250, 346, 297, 202, -227, -318, -16, -159, 197, 131],\n [-102, -514, -169, -262, 443, 282, 272, 263, 67, 213],\n [-20, -318, -61, -156, 291, 144, 208, 167, 99, 197],\n [357, 80, 371, 89, 65, -285, 272, -7, 445, 483],\n [-315, -520, -385, -295, 365, 435, 80, 245, -215, -105],\n [287, 686, 378, 371, -532, -483, -224, -336, 112, -56]]\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[[-64, 586, -610, -12, -202, 412, -14, 22, 88, 162],\n [-162, -160, -160, 425, -89, 417, 190, -429, 103, 468],\n [636, 100, 22, 334, -128, 32, 232, -428, -92, 512],\n [-834, -2, -437, 55, -40, 540, -64, 42, 230, -12],\n [-354, -642, 504, -63, 235, -281, -68, 107, 1, -314],\n [-600, 82, -398, 40, -58, 444, -46, 30, 176, 18],\n [-772, -151, -144, -146, 80, 203, -155, 246, 157, -305],\n [350, -14, 248, -111, 51, -325, -16, 75, -115, -110],\n [-944, -114, -367, 34, 3, 509, -86, 77, 241, -84],\n [-250, -527, 389, 27, 168, -175, -13, 0, 5, -155]]\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[[-419, 571, 443, 526, -265, 601, 704, -200, -374, -516],\n [-511, 249, 204, 258, -419, 79, 74, 430, -508, -140],\n [-206, 819, 730, 31, 55, -372, -236, -298, -612, -586],\n [27, 211, 79, 298, 199, -1167, -372, -800, -566, 328],\n [439, 48, -117, -202, 326, 30, 208, -750, 192, 200],\n [23, -530, -407, 635, 245, -625, -144, -350, 182, 464],\n [221, -313, -225, -209, 23, 992, 228, 470, 854, -336],\n [-729, -8, 486, 674, 410, -608, -418, 320, -480, 10],\n [-331, -481, -325, 842, 327, 201, -542, 579, 691, -227],\n [-181, 159, 407, 141, 692, -456, -128, -468, -366, 262]]\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[[259, -259, 449, -157, 292, -114, -43, -83, -30, -489],\n [117, -262, -217, 277, 47, -338, -296, -2, 317, -12],\n [135, 166, -714, -277, -311, -133, -6, 113, 351, 527],\n [4, 90, 536, 99, -179, 276, -378, -825, 240, -406],\n [203, -269, -825, 2, 105, -580, 43, 686, 218, 443],\n [186, 8, 405, -16, -192, 123, -478, -857, 450, -407],\n [215, 148, -849, -372, -320, -212, 6, 185, 419, 596],\n [99, 147, -455, -139, -316, -50, -153, -159, 388, 325],\n [256, -354, 435, -56, 374, -205, -56, 15, -50, -513],\n [-72, -148, -128, 8, 324, -168, 388, 724, -428, 116]]\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[[158, -749, -210, -353, 635, 709, 356, -16, -96, -415],\n [-508, -670, -305, -1, -226, 24, 281, -422, 77, -293],\n [954, 1290, 289, 259, 840, -106, -260, 86, -517, 910],\n [168, 1242, -288, 147, -170, -1004, -555, -140, -580, 734],\n [-318, -455, -398, 137, -494, 61, 192, -261, 255, -288],\n [220, 197, -132, 116, 986, 117, -82, -603, -193, 613],\n [-454, -833, 48, -136, -783, 237, 206, 315, 547, -753],\n [138, -295, 414, -362, 96, -125, 77, 361, -223, -70],\n [337, 953, 133, 46, 823, -164, -461, -101, -305, 687],\n [98, 122, 451, -297, 132, 122, -334, 596, 231, -112]]?\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 10x10 matrix:\n[[-607, -129, -226, 933, -105, -513, 8, -5, 280, -260],\n [-208, -137, 15, 212, -77, 153, 213, -60, 54, -279],\n [-291, 688, 338, 75, -704, 610, 301, -445, 268, -142],\n [89, 48, 155, -687, 208, 262, 31, -57, -312, -17],\n [185, 361, 76, -339, 107, -435, -237, 80, -5, 307],\n [171, -255, -31, 9, 71, -101, 130, 49, 53, -165],\n [127, -19, 340, 425, 173, 364, 339, 969, 158, 186],\n [624, -267, -191, -326, 15, 304, -237, -93, -163, 318],\n [-376, -662, -383, 290, 84, 96, 7, -359, -189, -438],\n [-825, 603, 368, 13, -465, 210, 463, -549, 172, -620]]\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[[-416, 975, -249, -945, 221, 267, -634, 155, 341, -9],\n [100, 458, 265, -268, -71, 219, -360, -136, -70, -263],\n [351, 458, -602, 136, 85, -205, 390, 422, 525, -1375],\n [829, 412, -298, 1, 38, 30, -430, 671, -141, -196],\n [-124, -556, 352, 83, -321, 319, -53, -754, -108, 248],\n [-46, 140, -151, 62, -220, -136, 83, -45, 218, -419],\n [286, 32, -117, 239, -393, -203, 94, -217, -129, 249],\n [-682, -405, 817, -24, 398, 84, 141, -625, -419, 1033],\n [-90, 729, 424, 275, 494, -654, 185, -74, -418, 695],\n [187, -326, 484, 8, 355, 433, -58, -75, -247, -178]]?\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, -54, -396, -378, 342, 198, 108, -324, -378, -54],\n [-147, 63, 462, 441, -399, -231, -126, 378, 441, 63],\n [-91, 39, 286, 273, -247, -143, -78, 234, 273, 39],\n [-35, 15, 110, 105, -95, -55, -30, 90, 105, 15],\n [140, -60, -440, -420, 380, 220, 120, -360, -420, -60],\n [-112, 48, 352, 336, -304, -176, -96, 288, 336, 48],\n [105, -45, -330, -315, 285, 165, 90, -270, -315, -45],\n [56, -24, -176, -168, 152, 88, 48, -144, -168, -24],\n [-28, 12, 88, 84, -76, -44, -24, 72, 84, 12],\n [-91, 39, 286, 273, -247, -143, -78, 234, 273, 39]]\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[[299, -222, -397, -16, -199, 114, -510, 611, 501, 602],\n [378, -906, -267, 253, -163, -156, 469, 15, -226, 254],\n [149, -439, -113, 149, -169, 128, 233, 187, 28, 192],\n [-443, -479, 19, 106, -265, 296, 1112, -175, -399, -144],\n [-439, 446, -484, -864, -6, -278, -172, -480, -46, -136],\n [-161, 655, 721, 306, 431, 58, 136, -209, -235, -88],\n [67, 72, -345, 237, -18, 25, -774, 789, 569, 971],\n [-287, 153, 91, 611, 344, -741, -358, 15, -355, -81],\n [375, 178, 541, -99, 18, 488, 575, 157, -71, 85],\n [183, -38, -416, 356, 217, -574, -1259, 176, 395, 392]]?\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 10x10 matrix:\n[[0, -119, -56, -56, 119, 77, -63, 42, -49, 42],\n [0, 255, 120, 120, -255, -165, 135, -90, 105, -90],\n [0, -221, -104, -104, 221, 143, -117, 78, -91, 78],\n [0, -102, -48, -48, 102, 66, -54, 36, -42, 36],\n [0, 170, 80, 80, -170, -110, 90, -60, 70, -60],\n [0, -34, -16, -16, 34, 22, -18, 12, -14, 12],\n [0, 17, 8, 8, -17, -11, 9, -6, 7, -6],\n [0, -170, -80, -80, 170, 110, -90, 60, -70, 60],\n [0, -238, -112, -112, 238, 154, -126, 84, -98, 84],\n [0, 272, 128, 128, -272, -176, 144, -96, 112, -96]]\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[[-135, 179, -945, 278, 315, -62, 76, -463, -462, 290],\n [19, 596, -780, -34, -456, 164, 348, -465, -554, 2],\n [497, 387, -156, -817, -435, -387, -107, -890, -479, 30],\n [194, 0, 491, -555, -580, -234, -1, 18, 50, -478],\n [-152, -417, -14, -213, -6, -333, -727, 38, 201, 39],\n [212, -181, 152, 149, 380, 144, -71, 167, 86, 245],\n [-273, -777, 646, 172, 665, -411, -304, 472, 543, -182],\n [294, 39, 31, -960, -548, -641, -351, -697, -336, -379],\n [-290, 15, -63, -527, -299, -73, -868, -564, 20, 40],\n [-287, 603, -1003, 301, -54, 737, -83, -569, -485, 435]]?\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[[0, 336, 126, -105, -147, 378, -21, 336, -231, -399],\n [0, -144, -54, 45, 63, -162, 9, -144, 99, 171],\n [0, -48, -18, 15, 21, -54, 3, -48, 33, 57],\n [0, 320, 120, -100, -140, 360, -20, 320, -220, -380],\n [0, -288, -108, 90, 126, -324, 18, -288, 198, 342],\n [0, -304, -114, 95, 133, -342, 19, -304, 209, 361],\n [0, 160, 60, -50, -70, 180, -10, 160, -110, -190],\n [0, 32, 12, -10, -14, 36, -2, 32, -22, -38],\n [0, -352, -132, 110, 154, -396, 22, -352, 242, 418],\n [0, -224, -84, 70, 98, -252, 14, -224, 154, 266]]\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[[-18, 218, -551, -46, 278, -444, -426, 287, -500, 308],\n [435, 73, 532, -335, -348, 261, -55, -652, 13, 261],\n [-40, -276, 376, -44, -376, 400, 196, -360, 208, -44],\n [-260, 222, -597, 313, 341, -138, 179, 938, -131, 244],\n [191, 220, -162, -102, 460, -670, -471, -135, -122, -435],\n [-126, -612, 555, 65, -33, 868, 923, -180, 301, 214],\n [617, 545, 351, -107, 440, -174, 186, 10, 254, -108],\n [-65, -94, -358, -112, 286, -319, -350, -44, -475, 198],\n [364, 197, 215, -247, -72, -3, -150, -328, -117, 250],\n [30, -61, 135, -121, -332, 33, -226, -354, -9, -50]]?\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 10x10 matrix:\n[[-424, 606, 652, 338, -31, -308, 245, -684, 45, 102],\n [195, -83, -826, 302, 404, -595, -123, -68, 455, 643],\n [-206, -151, 180, 337, -197, 17, -67, 65, 34, -8],\n [157, -285, -626, -781, 463, -154, 328, 448, 158, 207],\n [-481, -293, 334, -289, 62, -25, 519, 309, 72, 206],\n [-511, -676, 526, -555, -309, 427, 312, 537, -408, -316],\n [401, -333, -206, 805, -415, 295, -704, 2, -85, 137],\n [18, 296, -164, -687, 329, -216, 595, 128, 292, 9],\n [269, -187, -1278, -476, 911, -863, -90, -305, 106, 802],\n [-431, 794, 1346, 133, -613, 424, 534, -99, 81, -805]]\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 10x10 matrix:\n[[63, -167, -165, 322, 544, -595, -681, 841, -90, 536],\n [-1272, 480, 743, -961, -259, -268, 370, -906, 354, -619],\n [-111, -549, 654, -453, 408, 513, -186, 310, 146, -388],\n [-62, -940, 538, 321, -291, 565, 132, 530, 13, -886],\n [-628, 1766, 62, -601, -172, -30, 388, 119, 361, -326],\n [-303, 98, 13, -337, -372, -456, -306, 1130, 866, -195],\n [357, 634, -1092, 1005, -689, -621, 640, 419, -133, 636],\n [-1092, 718, 753, -371, 291, -115, 22, -220, -542, -523],\n [641, -570, -798, 381, 64, -162, -602, 733, -337, 423],\n [-88, -370, 510, -1009, 1216, -104, -957, 23, 655, 403]]\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[[-130, 217, 9, -128, -169, -142, 100, 42, 128, 331],\n [64, 346, -503, -411, -657, -176, 1013, -652, 21, 785],\n [336, -179, 235, 18, 129, 188, 324, 76, 452, -195],\n [-595, 258, 543, -507, 295, -336, -122, 313, 400, 595],\n [-55, 0, 262, 50, 152, -5, -227, 301, 207, -74],\n [-323, -62, 362, -208, 420, -93, -277, 177, 69, 38],\n [356, -43, 44, 159, -128, 151, 247, 96, 335, -146],\n [-293, 318, -1, -263, -197, -250, 116, -1, 90, 539],\n [275, 187, -197, -138, -453, -6, 751, -249, 325, 373],\n [356, -373, -78, 389, 186, 304, -221, -4, -213, -692]]?\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[[531, 316, 155, 127, 192, -205, -115, 447, 291, 205],\n [249, 112, -565, 268, 718, -47, 245, 552, 151, -39],\n [-225, -64, 317, -98, -396, 181, -193, -454, -13, -11],\n [181, 236, -187, 325, 408, 269, -117, 109, 381, -13],\n [-45, -317, 603, -147, 301, -101, 258, -4, 456, 440],\n [143, 329, -93, 3, -585, -21, -388, -88, -354, -238],\n [-324, -38, -94, 58, -191, 367, -154, -456, -59, -201],\n [-214, -472, 14, -74, 690, -84, 574, 174, 268, 252],\n [-189, -285, -21, 36, 520, 104, 324, 15, 283, 137],\n [432, 170, 366, -30, 41, -301, -54, 352, 225, 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[[315, 1147, -568, -1096, -212, -698, -650, 85, -859, -446],\n [-520, -544, -84, 69, -259, -494, -149, 394, 1475, 163],\n [776, 102, 14, -744, -202, 368, -68, -370, 226, -250],\n [243, -703, 595, 848, 209, 857, 375, -689, -156, 497],\n [-123, 173, 16, 125, 6, -153, -175, -98, -532, 132],\n [-273, 391, 180, 284, 375, 125, -849, -345, -683, -46],\n [-487, 163, -494, 393, 200, -349, 905, 968, 554, -410],\n [14, -180, 358, -91, 16, 487, 376, 114, -665, -33],\n [-635, 372, -434, 422, -3, -868, 203, 547, -413, 113],\n [75, -386, 333, -244, -499, -192, -977, -718, 515, 537]]?\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[[95, -19, -19, 209, 114, 380, 361, -190, -304, -247],\n [45, -9, -9, 99, 54, 180, 171, -90, -144, -117],\n [110, -22, -22, 242, 132, 440, 418, -220, -352, -286],\n [-95, 19, 19, -209, -114, -380, -361, 190, 304, 247],\n [35, -7, -7, 77, 42, 140, 133, -70, -112, -91],\n [95, -19, -19, 209, 114, 380, 361, -190, -304, -247],\n [80, -16, -16, 176, 96, 320, 304, -160, -256, -208],\n [-90, 18, 18, -198, -108, -360, -342, 180, 288, 234],\n [-100, 20, 20, -220, -120, -400, -380, 200, 320, 260],\n [-5, 1, 1, -11, -6, -20, -19, 10, 16, 13]]?\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[[-193, -151, -614, -449, -239, -256, 508, 139, -12, -181],\n [-33, -438, -502, -548, -754, -368, 404, 224, 647, -145],\n [659, 177, 332, 373, -12, -169, 404, 279, -361, 394],\n [-6, -5, 680, 468, 178, 233, -609, -317, 147, -24],\n [-629, -79, -155, -121, 185, 12, -246, -324, 105, -487],\n [-553, -72, -45, -241, 255, 787, -1165, -477, 414, -55],\n [774, 289, 325, -76, -411, 246, 205, 970, 71, 939],\n [164, 463, 347, 291, 249, -171, 455, 515, -537, 175],\n [567, 201, 73, -7, 42, 501, -246, 238, -152, 726],\n [340, -140, 596, 171, -569, -101, 287, 486, 216, 282]]?\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[[-116, -28, 296, 216, 347, -70, 113, 41, -183, -296],\n [-224, 236, -220, -136, 71, -394, -387, 277, -211, 48],\n [608, 27, 441, 369, 258, 1, 368, -624, -193, -58],\n [-58, 42, -276, -206, -240, -8, -176, 112, 114, 192],\n [-77, 180, 75, 86, 282, -343, -160, 80, -300, -114],\n [-325, 187, -272, -189, 10, -326, -398, 370, -135, 44],\n [242, -453, 339, 189, -150, 727, 644, -348, 419, -118],\n [-283, -318, -129, -168, -321, 487, 143, 231, 437, -10],\n [-284, 126, -162, -114, 57, -244, -281, 303, -119, -20],\n [-211, 169, -476, -343, -278, -206, -430, 306, 47, 268]]?\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 10x10 matrix:\n[[-111, -352, -177, -400, 221, 25, -188, 191, 287, 57],\n [-24, -222, -192, -186, 72, 10, -140, 56, 158, -84],\n [-107, 207, 457, -55, 143, -4, 180, 183, -62, 503],\n [44, -60, -310, 160, -122, 32, -26, -232, -50, -440],\n [97, -420, -440, -286, -4, -35, -367, 85, 296, -241],\n [-90, 17, -303, 269, -61, 111, 153, -372, -156, -558],\n [158, 385, 440, 239, -172, -97, 124, 62, -209, 364],\n [-173, -109, -599, 313, -41, 190, 170, -563, -154, -943],\n [135, -358, 42, -580, 122, -143, -443, 527, 428, 513],\n [-146, -203, -8, -309, 228, 35, -60, 174, 187, 164]]\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[[632, 30, 882, -410, 45, 118, 122, 224, -138, 925],\n [-315, -431, -359, 313, -271, 130, -1186, -488, -689, -131],\n [-96, -408, -217, 91, 835, -641, 853, 734, 829, -1194],\n [14, -257, 35, -200, 472, -141, 558, 1029, 460, 124],\n [253, -187, -515, -52, -215, 353, 570, 679, 376, -907],\n [-229, 606, -489, 322, 24, 4, -1091, -608, 73, -547],\n [-49, -269, -689, -835, 297, 187, -281, 210, 844, -2037],\n [-395, 73, -1047, -195, 26, 110, -1265, -352, 73, -1206],\n [571, 16, 782, 177, -318, 398, 107, -378, -197, -226],\n [-641, -90, 149, 875, 378, -350, -30, -201, 309, -343]]\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 10x10 matrix:\n[[605, 542, 504, -170, -139, -489, 96, 136, -309, -374],\n [462, -586, -345, -118, 985, 933, 676, -76, -358, 1215],\n [125, 312, 359, -902, -55, -39, -18, 231, -505, 142],\n [145, 539, -586, -228, 3, -340, 47, 333, -96, -247],\n [678, -606, -362, -38, -116, 725, 146, -39, 704, 722],\n [-385, -762, 264, -60, 1177, 414, 619, -587, -256, 719],\n [-732, -97, 97, 188, 470, 193, -64, -89, -501, 59],\n [-154, 357, 214, 8, -175, -27, -491, 170, 164, -557],\n [-63, 978, 695, -304, -635, -509, -711, 448, -377, -988],\n [442, 1100, -558, 136, -141, -322, -262, 712, -328, -671]]\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[[85, -357, 323, -17, 204, 289, 85, 136, 340, 102],\n [-60, 252, -228, 12, -144, -204, -60, -96, -240, -72],\n [110, -462, 418, -22, 264, 374, 110, 176, 440, 132],\n [-60, 252, -228, 12, -144, -204, -60, -96, -240, -72],\n [100, -420, 380, -20, 240, 340, 100, 160, 400, 120],\n [-65, 273, -247, 13, -156, -221, -65, -104, -260, -78],\n [80, -336, 304, -16, 192, 272, 80, 128, 320, 96],\n [-30, 126, -114, 6, -72, -102, -30, -48, -120, -36],\n [40, -168, 152, -8, 96, 136, 40, 64, 160, 48],\n [60, -252, 228, -12, 144, 204, 60, 96, 240, 72]]\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, -334, 119, -979, 37, -236, 646, 1, -120, 47],\n [-337, 244, 67, -938, -271, -125, 194, -474, 105, 61],\n [30, -310, 118, -379, -673, 886, -482, -504, 586, 312],\n [187, 85, -181, 733, 319, -557, -38, -6, -671, -169],\n [-245, 531, -66, 177, -90, -135, -580, -963, -550, 134],\n [-391, 426, -112, -640, 63, -595, 308, 215, 1361, -148],\n [40, -26, 637, -191, 252, 703, -31, -400, -1044, 487],\n [-93, -781, 9, 169, -90, 610, -293, -19, -11, 243],\n [-44, -3, -482, 614, 348, -955, 147, 485, 346, -401],\n [458, -5, 148, 81, 96, -446, 242, -138, 134, 21]]\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[[302, 245, 205, -316, -870, 295, -318, 530, 690, -519],\n [274, -45, -343, -112, -213, 393, 104, 562, 813, -496],\n [379, -372, -520, 649, -112, -62, 689, -1172, -583, 168],\n [-72, 352, 560, -229, 793, -631, -307, -148, -667, 1053],\n [-261, -298, 458, -26, -562, 403, -657, 156, -25, -91],\n [400, -92, 122, -463, -8, 52, -506, 161, -22, 41],\n [84, -267, -333, 56, -606, 413, -15, 206, 398, -704],\n [842, 326, -566, -85, -370, -263, 338, 18, 314, -277],\n [340, -73, -500, 156, 126, 39, 253, -6, 334, -255],\n [-598, -127, 586, -713, 433, 45, -772, 680, -374, 316]]\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[[240, 45, -300, 15, 165, 165, -45, 105, 285, -45],\n [-160, -30, 200, -10, -110, -110, 30, -70, -190, 30],\n [-32, -6, 40, -2, -22, -22, 6, -14, -38, 6],\n [160, 30, -200, 10, 110, 110, -30, 70, 190, -30],\n [272, 51, -340, 17, 187, 187, -51, 119, 323, -51],\n [80, 15, -100, 5, 55, 55, -15, 35, 95, -15],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n [144, 27, -180, 9, 99, 99, -27, 63, 171, -27],\n [-288, -54, 360, -18, -198, -198, 54, -126, -342, 54],\n [48, 9, -60, 3, 33, 33, -9, 21, 57, -9]]\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[[569, -296, 456, -482, 35, 615, -1033, 297, -200, 167],\n [-228, 1250, -208, -11, -711, 132, 339, 416, 806, 7],\n [94, 75, 380, 569, 359, -273, 344, 97, 78, -311],\n [-323, 580, -358, -985, 304, 4, 120, 208, 388, -147],\n [-668, -77, -346, 433, -303, -584, 404, -289, -515, -723],\n [145, -237, -1444, -417, -797, 8, -107, 559, 152, 618],\n [94, 671, 142, 155, -205, -264, 840, 653, 515, 385],\n [-67, 61, 1128, 251, 553, 204, -313, -561, -222, -546],\n [-156, -273, 204, -22, 202, -276, 249, -120, -387, -74],\n [-767, -79, 322, 216, -156, -421, 6, -449, -901, -1099]]\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[[95, 99, -118, 37, 20, 107, 398, -245, 449, 197],\n [378, -703, -495, -678, -130, -481, -195, -353, 473, 218],\n [428, -679, -505, -669, 98, -654, -514, 163, 94, -161],\n [-29, 154, 283, -62, -294, 205, -140, -48, -433, -58],\n [-297, 43, 108, 338, 242, -45, -150, 325, -215, -146],\n [-272, 220, 256, 319, 12, 193, 13, 96, -241, -37],\n [-59, -183, -80, -6, 114, -181, -176, 123, -23, -50],\n [-291, -262, 141, -17, -366, 94, -5, -568, 118, 431],\n [102, -142, 102, -308, -214, -103, -457, 128, -513, -196],\n [147, -196, -267, -136, 122, -193, 70, -54, 349, 68]]?\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[[-299, 12, -267, 3, 782, -147, -397, -585, 261, 242],\n [-505, 80, -280, 49, -300, 175, 9, 560, 383, -178],\n [-528, -24, -297, -98, 243, 94, -346, -124, -61, -318],\n [143, -366, -79, -307, -331, 581, -1, -388, 414, -24],\n [-725, 276, -156, 397, 200, -233, -17, 702, -189, -386],\n [-1298, 307, -1003, -517, 944, -475, -1329, -297, -58, -13],\n [75, -77, 368, 478, -359, 124, 595, 732, -94, -155],\n [-312, 117, 7, 207, -385, 21, 210, 793, -123, -325],\n [-235, -381, -133, -64, -96, 266, -50, 341, 531, 543],\n [382, 175, 63, 49, -733, 175, 483, 372, 667, 141]]\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[[-203, -121, 146, 442, -404, -25, -170, -364, 93, -344],\n [108, -648, -523, -624, -526, -65, 580, -84, -676, 231],\n [-552, 638, 870, 659, -575, 881, -715, -621, 482, -603],\n [-311, 917, 224, 613, 438, 119, -284, 297, 553, -45],\n [393, -406, 397, -168, -315, 609, -431, -462, -165, -296],\n [144, -168, -22, 304, 313, -513, -210, 87, -145, -87],\n [286, 47, -506, -480, 92, -30, 500, 378, 254, 819],\n [-131, -138, 213, 494, 66, -966, -443, -151, 36, 207],\n [-797, 677, -847, 585, -538, -380, 768, 351, 185, 546],\n [-23, -500, -557, -139, -649, 173, 619, -167, -313, -199]]\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[[-613, 662, 538, -935, -217, 1050, -520, -718, -208, -16],\n [-401, 167, 1010, 430, 199, 29, 718, 301, -509, -210],\n [-73, -599, 768, -313, 116, 842, 268, -1020, 140, 131],\n [-30, -27, -26, 226, 489, -4, 116, 313, -1005, -214],\n [-813, 610, 1336, -54, -225, 738, 36, -237, -481, 230],\n [-123, 703, 687, 281, -91, -120, 51, 87, -9, 124],\n [494, 624, -108, 489, 605, -497, 115, 433, -585, -223],\n [-408, -306, 535, -464, 328, 609, 198, -471, -739, -416],\n [-87, -125, 264, 121, 509, -243, 678, 331, -609, -699],\n [241, 664, 533, 816, 769, -423, 412, 558, -1142, -226]]\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[[588, -458, 182, -149, 35, -620, 63, 29, 150, -190],\n [-188, -32, -64, -142, -78, 92, -238, 26, 84, 40],\n [-40, -80, -16, -108, -44, -24, -140, 20, 72, 0],\n [-280, 300, -84, 158, 14, 344, 70, -30, -132, 100],\n [-286, 116, -92, -41, -57, 238, -161, 7, 6, 80],\n [200, -460, 52, -374, -102, -392, -350, 70, 276, -100],\n [-209, -31, -71, -153, -85, 105, -259, 28, 90, 45],\n [-306, 76, -100, -95, -79, 226, -231, 17, 42, 80],\n [-132, 252, -36, 192, 48, 228, 168, -36, -144, 60],\n [-333, -107, -115, -305, -157, 133, -483, 56, 186, 65]]?\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 10x10 matrix:\n[[39, 182, -195, 260, 273, 65, 0, 52, 208, -156],\n [-66, -308, 330, -440, -462, -110, 0, -88, -352, 264],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n [-27, -126, 135, -180, -189, -45, 0, -36, -144, 108],\n [-24, -112, 120, -160, -168, -40, 0, -32, -128, 96],\n [12, 56, -60, 80, 84, 20, 0, 16, 64, -48],\n [24, 112, -120, 160, 168, 40, 0, 32, 128, -96],\n [-30, -140, 150, -200, -210, -50, 0, -40, -160, 120],\n [18, 84, -90, 120, 126, 30, 0, 24, 96, -72],\n [-39, -182, 195, -260, -273, -65, 0, -52, -208, 156]]\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[[-66, -3, -42, -18, -24, -66, -48, 33, -21, 57],\n [-66, -3, -42, -18, -24, -66, -48, 33, -21, 57],\n [-88, -4, -56, -24, -32, -88, -64, 44, -28, 76],\n [396, 18, 252, 108, 144, 396, 288, -198, 126, -342],\n [-154, -7, -98, -42, -56, -154, -112, 77, -49, 133],\n [330, 15, 210, 90, 120, 330, 240, -165, 105, -285],\n [-44, -2, -28, -12, -16, -44, -32, 22, -14, 38],\n [132, 6, 84, 36, 48, 132, 96, -66, 42, -114],\n [462, 21, 294, 126, 168, 462, 336, -231, 147, -399],\n [330, 15, 210, 90, 120, 330, 240, -165, 105, -285]]\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[[-88, -368, -420, -43, 178, -372, 496, -276, 117, 55],\n [-478, 331, -201, -723, 372, -214, 96, -88, -555, -653],\n [183, -846, -546, 457, 102, -429, 720, -466, 489, 569],\n [573, -717, -174, 656, -190, -244, 191, -122, 426, 827],\n [304, -251, 252, 807, -396, 423, 19, 36, 793, 546],\n [-570, 217, -87, -201, 396, 250, 236, -392, -169, -451],\n [-167, 152, -216, -595, 18, -431, 132, 218, -171, -411],\n [509, -511, -93, 461, -232, -229, 70, 34, 329, 635],\n [-120, 262, -129, -713, 234, -395, -187, 132, -739, -416],\n [132, 263, 249, -102, -290, 66, -310, 416, 46, -84]]\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[[-32, 224, 128, 352, 192, 64, 0, 144, -96, -192],\n [24, -168, -96, -264, -144, -48, 0, -108, 72, 144],\n [-38, 266, 152, 418, 228, 76, 0, 171, -114, -228],\n [24, -168, -96, -264, -144, -48, 0, -108, 72, 144],\n [10, -70, -40, -110, -60, -20, 0, -45, 30, 60],\n [22, -154, -88, -242, -132, -44, 0, -99, 66, 132],\n [14, -98, -56, -154, -84, -28, 0, -63, 42, 84],\n [-8, 56, 32, 88, 48, 16, 0, 36, -24, -48],\n [-26, 182, 104, 286, 156, 52, 0, 117, -78, -156],\n [12, -84, -48, -132, -72, -24, 0, -54, 36, 72]]\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[[-201, 399, 554, 371, 192, -44, 154, -398, 196, -145],\n [276, -253, 19, -18, -270, -354, 357, 360, -608, 204],\n [-338, 282, -716, 410, -60, 668, -92, -340, -28, 402],\n [-294, 193, 475, -330, 80, 336, -193, 118, -2, 246],\n [-212, 55, 586, -636, 186, 232, -399, 217, 276, -5],\n [180, -238, 170, -346, -34, -230, -36, 302, -62, -88],\n [-272, 60, 358, -603, 71, 421, -373, 281, 51, 262],\n [270, -262, 384, -350, 52, -460, -12, 256, 100, -338],\n [-32, -1, 29, -166, 198, 38, -287, -118, 492, -318],\n [-201, 289, 337, 161, 180, 94, -32, -287, 264, -112]]\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 10x10 matrix:\n[[374, -242, 264, 352, 352, 198, 352, -198, 462, -484],\n [51, -33, 36, 48, 48, 27, 48, -27, 63, -66],\n [-68, 44, -48, -64, -64, -36, -64, 36, -84, 88],\n [323, -209, 228, 304, 304, 171, 304, -171, 399, -418],\n [-170, 110, -120, -160, -160, -90, -160, 90, -210, 220],\n [-221, 143, -156, -208, -208, -117, -208, 117, -273, 286],\n [-153, 99, -108, -144, -144, -81, -144, 81, -189, 198],\n [-238, 154, -168, -224, -224, -126, -224, 126, -294, 308],\n [-204, 132, -144, -192, -192, -108, -192, 108, -252, 264],\n [-340, 220, -240, -320, -320, -180, -320, 180, -420, 440]]\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[[132, -10, -142, 348, 280, 198, 150, -536, -448, 500],\n [776, -10, -184, 24, 118, -390, 12, -854, 144, 970],\n [-93, 40, -233, 173, 201, 200, -206, -23, -252, 40],\n [107, -55, 131, 213, 82, 87, 408, -440, -276, 355],\n [212, 16, -236, 236, 252, 80, -56, -452, -272, 480],\n [113, -49, 326, -305, -321, -317, 227, 131, 436, -140],\n [-182, 27, -228, 358, 311, 385, -64, -155, -528, 115],\n [-113, -117, 564, 17, -227, 23, 775, -103, -68, -80],\n [-363, -2, 31, 187, 91, 334, 92, 171, -340, -260],\n [-318, 42, -75, -66, -21, 132, -267, 477, 24, -465]]\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[[-395, 484, -323, -27, -286, -190, 187, 205, 187, -568],\n [-297, 210, -393, 33, -162, -168, -24, 204, 6, -405],\n [127, -214, -28, 36, 348, 74, 131, 210, -228, 355],\n [242, -312, 129, 27, 350, 130, 51, 64, -212, 468],\n [390, -396, 402, -2, 244, 200, -108, -240, -108, 542],\n [-29, -38, -122, 26, 88, -18, 25, 130, -92, 27],\n [-470, 754, -314, -84, -76, -166, 763, 541, 217, -475],\n [-264, 194, -376, 30, -40, -138, 101, 295, -41, -287],\n [404, -358, 413, -15, 406, 232, 128, -79, -151, 673],\n [287, -426, 282, 34, -144, 90, -621, -536, -14, 161]]?\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 10x10 matrix:\n[[354, -66, -288, 120, 189, -276, 18, 387, -192, 27],\n [66, 91, -263, 167, 161, -82, 33, 365, -87, 23],\n [404, -126, -226, 66, 154, -300, 6, 298, -194, 22],\n [54, 64, -194, 122, 119, -64, 24, 269, -66, 17],\n [-94, -154, 424, -272, -259, 124, -54, -589, 136, -37],\n [520, -325, 39, -143, 0, -338, -39, -78, -169, 0],\n [178, -2, -208, 104, 133, -148, 18, 283, -112, 19],\n [-426, 134, 236, -68, -161, 316, -6, -311, 204, -23],\n [92, -138, 170, -138, -98, -36, -30, -242, 10, -14],\n [84, 74, -250, 154, 154, -92, 30, 346, -90, 22]]\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[[-236, 613, -284, 22, -465, 805, -608, 60, -737, 99],\n [-364, 524, -535, -292, -107, 225, -380, 34, -179, 79],\n [654, -157, -30, 186, 53, -187, 538, 18, 175, 1],\n [97, 455, 62, -82, -166, 139, -191, 17, -209, 348],\n [605, 72, -89, 172, -86, 29, 353, 35, -37, 86],\n [-215, 621, -388, -280, -140, 195, -355, 33, -199, 240],\n [-237, -27, -9, 261, -324, 684, -375, 27, -573, -249],\n [87, -435, 39, -231, 540, -924, 549, -57, 855, -45],\n [408, -1075, 612, 405, 336, -513, 714, -62, 504, -385],\n [-360, -95, 349, 160, -194, 410, -416, -14, -386, -94]]?\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[[211, -491, 183, 159, -380, 76, -164, 246, 48, 5],\n [121, 575, 58, 26, -22, 182, 400, 35, -112, 614],\n [-109, 622, -195, 224, -109, 354, -177, -237, 687, -133],\n [181, -329, 33, -242, -82, -267, -227, 310, -30, -486],\n [187, 531, -159, -277, -68, 20, -70, 240, 348, -411],\n [-224, -641, 172, 53, 319, -334, 141, -221, -693, 342],\n [-109, -431, -32, 20, 19, -54, -186, -54, 13, -291],\n [179, 768, 95, -253, 224, -879, -538, 50, 204, -505],\n [227, -692, 108, -26, -351, -23, -274, 364, 59, -385],\n [-43, 131, 85, -224, 383, -485, 149, -59, -497, 165]]\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 10x10 matrix:\n[[606, -73, -432, 94, -166, -432, -85, 100, 296, 108],\n [-34, -4, 67, 219, 182, 185, -286, 277, -167, -245],\n [232, 0, -213, -34, -155, -258, 0, 46, 212, -12],\n [110, -19, -64, 64, 12, -38, -67, 62, 14, -10],\n [270, 30, -330, -333, -435, -543, 336, -243, 483, 201],\n [264, -101, -127, -185, -132, -221, 433, -533, 123, 677],\n [-484, 189, 120, -419, -307, -99, 243, -67, 235, -315],\n [-488, 72, 334, -48, 134, 344, 0, 8, -228, -188],\n [102, 25, -163, -266, -285, -320, 289, -236, 294, 182],\n [56, -183, 248, 363, 499, 487, -93, -161, -543, 455]]\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[[130, -470, 530, 50, 520, -320, -10, 60, 160, -200],\n [-142, -28, -14, 16, -41, 54, 126, 111, 109, 72],\n [156, 264, -228, -48, -182, 68, -188, -198, -242, -16],\n [148, 70, -28, -22, 3, -34, -140, -129, -135, -64],\n [172, -176, 236, 8, 254, -180, -108, -66, -22, -144],\n [-446, -362, 242, 86, 138, 20, 454, 438, 486, 152],\n [-85, -457, 451, 67, 404, -208, 169, 210, 296, -76],\n [-369, 315, -441, -9, -484, 352, 245, 162, 80, 292],\n [-92, -368, 356, 56, 314, -156, 156, 186, 254, -48],\n [460, 184, -52, -64, 42, -124, -428, -390, -402, -208]]\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[[33, -542, 8, -113, 184, -203, 162, -214, 152, -129],\n [22, -568, 449, -1, 68, 118, 330, -84, 406, 51],\n [-347, -4, 51, -59, 132, -71, -41, -104, -233, 206],\n [225, 178, -454, 19, -148, -143, -228, -738, 104, -145],\n [-229, -966, 416, 19, 128, -33, 420, 58, 94, 169],\n [-239, 591, -240, -21, 25, -54, -277, 401, -550, 92],\n [-239, -23, -198, -54, 93, -194, -108, -175, -302, 85],\n [-331, 603, 192, -11, 29, 194, -167, 131, -211, 295],\n [-21, 460, -327, -252, 266, -251, -284, -228, -124, -184],\n [127, 20, -492, 11, -98, -231, -194, -582, -67, -128]]\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[[18, 234, -72, -180, 180, -72, 162, -144, -216, 0],\n [16, 208, -64, -160, 160, -64, 144, -128, -192, 0],\n [-1, -13, 4, 10, -10, 4, -9, 8, 12, 0],\n [10, 130, -40, -100, 100, -40, 90, -80, -120, 0],\n [18, 234, -72, -180, 180, -72, 162, -144, -216, 0],\n [19, 247, -76, -190, 190, -76, 171, -152, -228, 0],\n [-5, -65, 20, 50, -50, 20, -45, 40, 60, 0],\n [-9, -117, 36, 90, -90, 36, -81, 72, 108, 0],\n [5, 65, -20, -50, 50, -20, 45, -40, -60, 0],\n [-12, -156, 48, 120, -120, 48, -108, 96, 144, 0]]\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[[-598, -159, 39, 488, -388, 338, 102, -91, 309, 108],\n [-253, -523, 548, -58, -327, 306, 1032, -597, 104, -285],\n [-328, 138, 197, 120, -339, -74, -75, -60, 67, 108],\n [1120, 298, -20, -585, 58, 686, -475, 398, -684, 553],\n [436, -275, 276, 62, 563, -3, 306, -544, -22, -275],\n [258, -188, -383, 111, 481, -345, -1, 787, -803, -220],\n [1149, 58, -312, -812, -58, 777, -210, 299, -844, 704],\n [-62, 182, 80, -201, 84, -554, -77, -516, 292, -63],\n [307, -37, 587, -198, 6, 257, 300, -626, 163, -74],\n [-546, -253, -514, -157, -531, -126, 300, -123, -35, 298]]?\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[[167, -78, -201, -290, 460, -253, 574, 159, -502, -3],\n [-49, 7, 92, 163, -205, 178, -525, 76, 193, -54],\n [-192, 27, 260, 61, 50, -235, 493, -46, 21, 75],\n [115, 105, -346, -39, -239, 312, -159, -514, 415, 60],\n [-329, 244, 11, 383, -135, 366, -59, -629, 1194, 78],\n [143, 50, -443, -141, 361, 146, 213, -219, 184, -6],\n [88, 13, -49, 60, -490, 268, -654, -129, 137, -12],\n [293, -76, -321, -211, 29, 110, -297, 115, -330, -66],\n [-141, 126, -43, 97, 11, 80, 295, -403, 504, 84],\n [-139, -50, 332, 110, -11, -169, -22, 294, -162, -27]]\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[[96, 680, -51, -426, -521, 170, -52, -180, -306, -357],\n [-89, -233, 116, 655, 515, -632, 364, -17, -153, -40],\n [-178, 394, 244, 287, 196, -413, 429, -341, 126, -334],\n [-426, -34, 536, -618, 178, 628, -154, 310, 662, 88],\n [-332, -508, 442, -131, 526, 181, -88, 605, 104, 216],\n [-107, 245, 100, -404, -211, 427, -96, -168, 557, -10],\n [54, -470, -9, 132, 249, -152, -127, 550, -672, 149],\n [261, -107, -441, 258, -222, -23, -34, -440, 399, 203],\n [-361, -25, 479, -631, 120, 594, -194, 387, 409, 61],\n [-368, 0, 521, -389, 267, 279, -30, 397, 126, -55]]\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 10x10 matrix:\n[[524, -534, 790, -663, -211, -169, -310, 646, -716, -723],\n [68, 370, -17, 193, 143, -301, -35, 388, -426, -224],\n [342, -616, 869, -668, -455, 438, -61, 351, -513, -514],\n [116, -149, -265, -76, 58, -259, 0, -80, 523, -50],\n [84, -69, 96, 8, 300, -367, -477, 238, -605, 159],\n [210, -274, 534, -346, -13, -188, -352, 305, -688, -276],\n [208, -223, 268, -213, -553, 888, 519, 294, 210, -331],\n [252, -456, 39, -275, -29, -15, -157, 120, 172, -22],\n [190, -156, 416, -130, 5, 104, -276, 481, -811, -67],\n [468, -104, 415, -169, 137, -339, -425, 954, -1053, -407]]\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 10x10 matrix:\n[[239, 252, -156, 161, 262, -282, 296, 206, -201, -275],\n [-166, -64, 167, 78, -2, 92, -262, -71, 209, 114],\n [156, 344, -7, 412, 462, -352, 102, 251, -19, -304],\n [-160, -480, -60, -640, -680, 480, -40, -340, -60, 400],\n [-393, -404, 262, -247, -414, 454, -492, -332, 337, 445],\n [78, -200, -200, -430, -372, 172, 240, -116, -242, 106],\n [111, 364, 58, 497, 522, -362, 12, 256, 61, -299],\n [-221, -12, 261, 229, 116, 54, -386, -47, 324, 101],\n [393, 404, -262, 247, 414, -454, 492, 332, -337, -445],\n [-144, -432, -54, -576, -612, 432, -36, -306, -54, 360]]\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[[-63, 98, 84, -98, 119, -49, -119, 56, -49, 35],\n [126, -196, -168, 196, -238, 98, 238, -112, 98, -70],\n [-63, 98, 84, -98, 119, -49, -119, 56, -49, 35],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n [27, -42, -36, 42, -51, 21, 51, -24, 21, -15],\n [-63, 98, 84, -98, 119, -49, -119, 56, -49, 35],\n [36, -56, -48, 56, -68, 28, 68, -32, 28, -20],\n [162, -252, -216, 252, -306, 126, 306, -144, 126, -90],\n [63, -98, -84, 98, -119, 49, 119, -56, 49, -35],\n [90, -140, -120, 140, -170, 70, 170, -80, 70, -50]]\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[[344, 96, 218, -27, 1100, -24, 344, -191, -813, 383],\n [-476, -234, -535, -222, 323, 126, 461, 38, 13, 170],\n [-754, -69, -808, 148, -82, 281, 740, 473, -146, 279],\n [-775, -808, -299, -512, -682, -490, -152, 781, 734, -799],\n [259, 142, -61, 325, 986, 135, 1069, 301, -1700, 406],\n [368, -289, -312, -1166, 145, -1390, -573, -837, 568, -396],\n [216, 706, 446, 758, 197, 413, 261, 1, -688, -64],\n [-65, -296, -299, 211, -838, -663, -164, -231, 430, -737],\n [-349, 159, -164, -203, -9, 91, -275, -618, 885, -188],\n [281, -446, -251, -913, 247, -1008, -515, -452, 515, 81]]?\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, -632, -173, -31, 523, -194, -465, -22, -830, -590],\n [141, -29, 148, 579, 258, -304, 783, -317, 575, -229],\n [-510, -288, -245, -423, -134, -37, -172, -301, -108, 246],\n [86, 366, 417, 339, 591, -358, -5, 338, -379, -40],\n [293, -201, -62, -263, -16, 251, -638, 409, -648, -189],\n [535, 524, 356, 553, 780, -589, 86, 314, -131, -153],\n [-128, 490, 98, 35, 220, -367, 16, 58, 162, 357],\n [103, -279, 21, 547, 335, -471, 874, -491, 684, -252],\n [-203, -313, -409, -839, -468, 119, -682, 462, 74, 542],\n [-253, 145, 70, 212, -96, -200, 634, -175, 804, 266]]\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[[-925, -796, -634, -521, -105, 503, 155, -158, -202, -176],\n [3, 65, -24, 247, 377, 2, 168, -388, -1268, 59],\n [-790, -143, -22, 35, 19, -492, 178, -122, 48, 308],\n [-1145, 626, 376, -436, 168, -435, 73, 16, 624, 186],\n [106, -356, 430, -7, 782, -712, 565, -1024, -1169, 16],\n [-973, -548, 80, -395, -297, -3, 189, -203, 342, 112],\n [639, -349, 442, 1187, -585, 607, -254, -331, -557, 118],\n [-165, 323, -938, -709, 828, -235, -156, -273, -95, -8],\n [-68, 36, -1019, -255, -69, 26, 1032, 157, 472, 876],\n [-759, 318, 431, -557, 627, -958, 341, -421, 834, 72]]\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[[-105, 462, 462, -168, 462, 147, 189, 357, 84, 84],\n [35, -154, -154, 56, -154, -49, -63, -119, -28, -28],\n [35, -154, -154, 56, -154, -49, -63, -119, -28, -28],\n [-25, 110, 110, -40, 110, 35, 45, 85, 20, 20],\n [15, -66, -66, 24, -66, -21, -27, -51, -12, -12],\n [-60, 264, 264, -96, 264, 84, 108, 204, 48, 48],\n [70, -308, -308, 112, -308, -98, -126, -238, -56, -56],\n [-85, 374, 374, -136, 374, 119, 153, 289, 68, 68],\n [65, -286, -286, 104, -286, -91, -117, -221, -52, -52],\n [-110, 484, 484, -176, 484, 154, 198, 374, 88, 88]]?\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[[-544, -546, -8, 735, -1109, -187, 117, 117, -604, 191],\n [293, -13, 221, -603, 1178, 438, -122, 673, 13, 301],\n [597, 250, -669, -659, -800, -557, -897, 106, 195, -1309],\n [3, 132, -485, 4, 9, -385, -393, -161, 822, 150],\n [273, -223, 487, 270, -1022, -889, -556, 241, 225, -367],\n [355, -639, 5, 24, 57, -476, -257, 338, -211, 101],\n [499, -712, 311, 238, 228, -534, 443, -242, -515, 111],\n [353, 326, -589, -210, 347, 160, -149, -569, 182, -483],\n [-128, -398, -402, -309, -2, -206, 294, -52, -476, 85],\n [-119, -754, 301, 658, 54, 9, 303, 404, -523, 672]]\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[[-194, -814, -376, -622, 157, 235, 122, 105, 24, 35],\n [203, -283, -381, 568, -1009, -13, 552, -400, 530, 355],\n [127, 353, 11, 606, -782, -45, 405, -405, 384, 260],\n [-345, -278, -497, 243, 694, 75, 564, -283, 418, -414],\n [-81, -544, -763, 930, -63, 226, 630, -924, 587, -250],\n [294, 437, 452, 440, -280, -248, -283, -410, 77, 153],\n [-355, -400, -66, -403, 412, -24, -98, -18, 74, 35],\n [-800, -348, -782, -373, 565, 337, 842, 471, 199, -304],\n [-25, -298, -297, 499, 569, -421, -215, 140, 82, -275],\n [-682, -505, -682, -519, 1360, -80, 625, 738, 246, -558]]\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[[280, 846, 1398, -1337, 245, -411, -494, 842, 120, -312],\n [-442, 715, 257, 98, 314, 706, 313, -706, -686, -220],\n [1232, 381, -346, -7, -423, -629, 563, 35, -224, 607],\n [55, -556, -1042, 796, -889, 842, -41, 77, -457, 920],\n [163, -2, 494, -434, 215, -554, -440, -31, -77, 212],\n [-448, -290, 88, 384, -206, 305, -788, 526, -26, 946],\n [310, 993, 541, 229, 413, 200, 110, -670, -536, -20],\n [336, 336, 694, 31, 699, -413, 279, -257, 312, -335],\n [141, -712, -509, 148, -283, -46, 93, 75, 185, 102],\n [-178, 314, 634, 642, 673, -277, -556, -237, 182, 378]]\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[[317, 360, -618, 1084, 817, 252, -824, 145, -77, -826],\n [-26, -159, -124, -89, -30, 651, -410, 179, -116, -986],\n [-1336, 135, 843, 55, -189, 815, -323, 442, 252, -124],\n [-1112, 262, 1147, -627, -715, -336, 1008, -49, 570, 927],\n [-327, -711, 580, -347, -407, -471, -650, 628, 4, 494],\n [1298, 32, -742, 138, 319, -1070, 284, -455, -115, 515],\n [-873, -122, 802, 137, -511, -92, -95, 755, -15, 69],\n [355, -168, -362, 312, 575, -498, -728, -55, 176, 200],\n [-292, -490, 93, -144, -88, 34, -535, 352, 21, -473],\n [670, -184, -617, 352, 674, -230, -751, -174, -108, 369]]\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[[606, 517, -73, -289, -1078, 139, 113, 138, 452, -61],\n [-876, -627, -100, 318, 351, -135, -687, 217, -170, -538],\n [486, 748, -338, -341, -216, 351, 228, 215, 360, 659],\n [110, 614, -215, 611, 387, 721, 703, -613, 673, 530],\n [-101, 343, 239, 590, -241, 333, -165, -258, 12, -561],\n [-364, 692, -552, -317, 488, -75, 310, -92, 305, 576],\n [460, 868, -382, 434, 578, 586, 502, -417, 471, -389],\n [380, -149, -267, 990, 634, 192, -189, 10, 399, -497],\n [456, -624, 700, 124, -406, -53, 199, -104, -277, 887],\n [-141, -218, -656, -614, 54, -362, -949, 1184, 5, 585]]\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[[-868, -1079, 379, 41, -398, 547, -214, -707, -94, 60],\n [402, 646, -531, 54, 126, -183, 0, 655, 474, -78],\n [-928, 280, 194, -463, -308, -307, -167, -306, 0, 591],\n [-395, -293, -497, 63, -865, -197, 702, -361, 1382, -11],\n [583, 910, -211, -237, 498, -183, -195, 490, -146, -101],\n [300, -756, 715, 493, 523, 51, -184, -156, -843, -391],\n [-561, 289, -1091, -65, -846, 174, -640, -76, 288, 697],\n [-186, -65, 275, -69, 64, -190, -319, -458, -1258, 489],\n [-300, 241, 1626, -499, 587, -402, -206, -418, -417, -135],\n [-856, -52, -596, -493, -1042, 126, 459, -249, 453, 798]]?\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[[630, 377, -302, 383, 353, -541, 51, 423, -24, 138],\n [676, 586, 709, -19, 650, 164, 232, -268, 492, -934],\n [578, 16, 5, 48, 212, -532, -809, 485, -697, 173],\n [1451, 494, 427, 838, 845, 154, 14, -56, 73, -937],\n [1083, 312, 344, -271, 926, -814, 80, -112, -562, 118],\n [-1041, -743, -152, -1308, -756, -724, 211, 26, -86, 491],\n [42, 279, -45, 38, 520, 68, 375, -460, -337, 803],\n [-273, -687, 302, -271, -602, -13, -1496, 556, -799, -78],\n [-789, -171, -695, -394, -620, 92, 676, -375, -2, 854],\n [-200, 14, -54, 709, -116, 697, 830, -211, 1065, -726]]?\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[[172, 178, -363, -197, -119, -775, -741, 460, 44, 239],\n [162, -301, -243, 220, 539, -74, 527, 200, -129, 335],\n [-194, 397, 435, -477, -617, 364, -136, -118, 486, -66],\n [166, 25, -232, 2, -126, -365, -309, 262, 60, -15],\n [352, -358, -211, 742, 401, -215, 116, 72, -545, -416],\n [82, -176, -191, -85, 202, 82, 562, 229, 271, 407],\n [556, -442, -860, 188, 86, -494, 444, 796, 438, 284],\n [14, 342, 586, 156, 73, -29, -431, -147, -477, -254],\n [-122, 560, 662, -299, -721, 253, -544, -183, 214, -419],\n [376, -437, -141, 665, 482, 91, 695, 145, -283, -188]]\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[[-217, -524, -292, 57, -564, -80, -365, 5, -779, 661],\n [148, 797, 43, -405, 375, -133, 506, -95, 764, -562],\n [10, 163, -193, -131, -299, -617, 176, 43, -98, -10],\n [70, -121, 215, 227, 234, 202, -52, 50, 123, -152],\n [-23, 27, -133, -118, -401, -75, -133, 30, -171, 195],\n [-308, 353, -444, -590, 735, -282, 716, -444, 106, 15],\n [185, -90, 479, 340, 336, 723, -245, 106, 387, -292],\n [146, -385, 262, 398, -631, 416, -674, 284, -244, 205],\n [-177, -620, -90, 249, -155, 137, -321, -2, -606, 473],\n [150, 55, 334, 140, 142, 631, -222, 71, 349, -197]]\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[[237, 299, -201, 149, 288, -106, 18, -41, 339, -116],\n [-696, 15, -57, 518, 47, -80, -62, -27, -494, -611],\n [-720, -249, -93, 199, -375, -377, 204, 362, -274, 11],\n [58, 111, 215, -473, -281, 103, -144, 34, -184, 315],\n [-29, -525, 171, -119, 398, 380, -426, -631, -15, 158],\n [-338, -61, -8, 487, 610, 277, -412, -608, -270, -647],\n [-201, -513, 424, -181, 313, 672, -642, -799, -517, -72],\n [-79, -41, 77, 71, 718, 394, -658, -833, -69, -238],\n [36, -275, 278, -298, 758, 643, -918, -1116, -92, 98],\n [13, 256, 92, -343, -683, -214, 300, 594, -175, 269]]?\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[[-75, -67, -79, 4, -445, -236, 213, 139, 76, -66],\n [-18, -108, 372, -132, 540, 438, -186, -72, 48, 240],\n [572, 341, -619, 679, -129, -405, -218, -690, -764, -627],\n [197, 355, -671, 112, -86, -463, -210, -195, -210, -353],\n [287, 306, -2, 220, 952, 445, -463, -406, -356, -4],\n [-278, 291, 73, 28, 206, 300, 279, 553, 262, 257],\n [196, 134, 246, 516, 350, 438, 64, -186, -368, -8],\n [89, 143, 119, -103, 865, 428, -421, -194, -60, 161],\n [-331, 137, -239, -404, -143, -210, 103, 511, 464, 144],\n [628, -7, -107, 445, 389, 17, -532, -984, -760, -399]]?\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[[540, -73, -177, 85, 470, 511, -208, -140, 509, 459],\n [-888, 534, 200, -357, 10, -33, -87, -45, -340, -233],\n [-136, 230, 267, -278, 340, 463, -57, 33, -176, -262],\n [-396, -271, 93, 391, -94, -86, 260, 226, 242, -111],\n [166, 649, 179, -514, 194, -398, -60, 285, -925, 395],\n [-232, -95, -31, -186, -418, -137, 48, -1017, -256, -237],\n [311, 116, -48, -68, 20, -149, -84, 279, -103, 139],\n [-391, 80, 473, -78, -188, -39, 167, -190, -252, -579],\n [81, -144, 61, -101, -70, 358, -62, 155, 80, -670],\n [978, 31, 268, 385, 422, -184, 63, 351, 271, 841]]\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[[-19, 3, -11, 11, 7, -19, 18, -21, -12, -21],\n [247, -39, 143, -143, -91, 247, -234, 273, 156, 273],\n [399, -63, 231, -231, -147, 399, -378, 441, 252, 441],\n [-95, 15, -55, 55, 35, -95, 90, -105, -60, -105],\n [323, -51, 187, -187, -119, 323, -306, 357, 204, 357],\n [38, -6, 22, -22, -14, 38, -36, 42, 24, 42],\n [152, -24, 88, -88, -56, 152, -144, 168, 96, 168],\n [228, -36, 132, -132, -84, 228, -216, 252, 144, 252],\n [57, -9, 33, -33, -21, 57, -54, 63, 36, 63],\n [-361, 57, -209, 209, 133, -361, 342, -399, -228, -399]]?\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[[-559, 313, -942, 356, -532, 415, -459, 271, 425, -233],\n [-88, -151, 253, -247, 550, -439, 1250, -642, -186, -417],\n [-299, 80, -739, 570, -267, -229, -110, 41, 229, -154],\n [-141, 488, -273, 253, -153, 433, -405, 60, 300, 337],\n [-399, -1, 249, -277, -395, 547, -171, 214, 233, -585],\n [178, -214, 44, -37, -29, -82, -140, -221, 141, -196],\n [348, 215, -373, 298, 8, 72, -614, -126, 218, 574],\n [-157, -599, -328, -399, 338, -682, 1129, -125, -535, -640],\n [-80, -77, 154, -676, 8, 488, 68, 150, -129, -212],\n [-88, -386, 162, -965, 118, 238, 417, 399, -561, -331]]\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[[-469, -19, -497, -320, 732, -213, -1092, -389, 890, 626],\n [-652, 60, -13, -372, 953, -229, -855, -139, 299, 270],\n [-949, 384, -589, -747, -48, -563, -454, -432, 107, -582],\n [-852, 117, -1117, 198, 2, -100, -118, -271, -192, -75],\n [420, -132, 144, -667, 200, 490, 410, -54, -109, 462],\n [3, 365, -40, -661, 60, -88, -413, -475, 508, -171],\n [93, 255, -562, -238, 204, 300, -243, -234, 471, 389],\n [59, 619, 377, -617, -382, -307, -282, -729, -57, -184],\n [-393, -73, -279, 399, -140, -322, -177, 77, 10, -213],\n [386, -571, -828, 555, -694, 546, 1104, 355, -99, -266]]\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[[25, -154, -553, -1, -138, -254, 491, 133, 408, 238],\n [-128, -263, -369, 202, -212, -692, 257, -272, 1024, 676],\n [498, -149, 750, -584, -426, 12, -284, 501, 265, 625],\n [-636, 161, -507, 278, -309, 337, 37, -823, -159, -859],\n [347, -323, 866, -741, -302, -67, -315, 462, 213, 504],\n [-274, -203, 456, -300, -273, 86, -336, -458, 55, -187],\n [168, 126, -93, 140, -5, -241, 22, 429, 284, 331],\n [107, 257, -258, 319, -38, -155, 40, 291, 237, 205],\n [-106, -73, 498, -164, 216, 139, -337, -160, -362, -243],\n [3, -229, 271, -145, 531, -67, -22, -6, -338, -43]]\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[[-243, -12, -12, -210, 219, -257, -283, 124, 198, -397],\n [31, -196, 190, -31, -1081, -687, 699, -753, -517, 62],\n [-20, -55, 369, -159, -367, 210, 429, -55, -52, 386],\n [-424, -147, -465, -32, -4, -304, -418, -246, 71, -446],\n [240, 210, 79, 111, 400, 306, -76, 490, 111, 149],\n [333, -182, 332, -85, -365, -164, 273, -423, -182, 158],\n [513, -257, 3, 106, -425, -313, -77, -484, -253, 81],\n [-229, -143, -673, 222, 327, 454, -595, -170, 152, -21],\n [-285, 240, -75, 24, 501, 175, 37, 283, 148, -179],\n [0, 5, -239, 82, -19, -116, -301, 176, 25, -93]]\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 10x10 matrix:\n[[-777, -171, -388, -11, 207, -202, 129, 166, 255, 211],\n [256, -5, 6, -234, -217, 434, -606, -44, 375, -194],\n [-430, -180, -468, 468, -148, -464, -281, -34, 257, 136],\n [418, -110, 176, -110, -70, 16, 216, 728, -228, -70],\n [-131, -406, -313, 117, -123, -124, -355, 756, 376, -137],\n [-171, 49, -191, -571, -144, 350, -80, 410, 256, 295],\n [72, -276, 277, 790, 424, -437, 79, -396, -198, -655],\n [-32, 175, -180, -302, -283, 262, -316, -132, 241, 262],\n [-398, 31, -709, -342, -588, 46, -467, 480, 516, 674],\n [385, -89, 55, 89, -212, 214, -618, -78, 272, -345]]\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 10x10 matrix:\n[[105, -90, 75, -10, 90, -110, 105, -95, -75, -80],\n [42, -36, 30, -4, 36, -44, 42, -38, -30, -32],\n [147, -126, 105, -14, 126, -154, 147, -133, -105, -112],\n [420, -360, 300, -40, 360, -440, 420, -380, -300, -320],\n [462, -396, 330, -44, 396, -484, 462, -418, -330, -352],\n [210, -180, 150, -20, 180, -220, 210, -190, -150, -160],\n [-189, 162, -135, 18, -162, 198, -189, 171, 135, 144],\n [231, -198, 165, -22, 198, -242, 231, -209, -165, -176],\n [-168, 144, -120, 16, -144, 176, -168, 152, 120, 128],\n [-378, 324, -270, 36, -324, 396, -378, 342, 270, 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[[-168, -235, -308, -123, 350, 74, -72, -255, -112, 314],\n [95, -204, -348, -153, -234, -171, -235, -210, 203, -226],\n [302, 224, 219, 6, 829, 381, 360, -94, -811, 80],\n [305, -67, 28, -14, 188, 25, -69, -313, -111, -124],\n [-44, 438, 844, 402, -302, 32, 255, 532, 168, 18],\n [-51, 416, 936, 425, 406, 307, 411, 318, -275, 410],\n [-301, 166, -278, -163, 216, 171, 299, 408, -427, 126],\n [-339, -117, 52, 124, -752, -311, -261, 189, 781, 48],\n [-121, -82, -1020, -543, 148, 45, 96, 134, -517, -256],\n [-402, 300, -258, -158, 30, 152, 394, 692, -412, 52]]\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[[-429, 80, 222, 228, 172, 84, 241, 430, 354, -206],\n [731, 12, -1158, -1034, 982, 62, -493, -568, 74, 784],\n [-236, -157, 712, 642, -770, 3, 305, 155, -327, -512],\n [154, 178, -174, -179, -179, -115, -489, -371, 116, 71],\n [263, -299, 44, 105, -196, 258, 34, -293, -303, -283],\n [343, -515, -68, 75, 125, 540, 237, -264, -321, -391],\n [206, 61, -410, -297, 256, 228, -497, -435, 363, -87],\n [-501, 108, 722, 670, -748, 14, -3, 166, 206, -684],\n [180, -347, 332, 268, -416, -49, 473, 63, -757, -22],\n [-566, 477, 360, 270, -367, -279, -290, 240, 573, -182]]?\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 10x10 matrix:\n[[-584, 191, -225, -196, 181, -356, 295, -30, -380, 168],\n [-938, 115, -814, -683, 201, -899, 857, -172, -4, 107],\n [201, 241, -482, -52, 75, -207, 984, -966, 263, -318],\n [1232, -443, 412, 143, -153, 540, 338, -813, 665, -443],\n [939, -929, -336, -588, -221, 627, 302, -270, 609, -726],\n [286, 118, -535, 104, 76, 114, 675, -487, 203, -409],\n [401, 229, -15, -88, -147, 165, 181, -702, 324, -266],\n [1275, -177, 727, 1098, -166, 983, -683, -38, 105, -446],\n [-257, 563, -328, -80, 12, -142, 95, -243, 525, -268],\n [-86, 114, -426, -367, 89, -190, 800, -399, 131, 113]]\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[[25, 136, -142, -180, 65, 223, 73, 86, -32, 133],\n [-320, 49, 418, 422, 350, -277, -383, -184, 424, 220],\n [-33, -199, 496, 486, 233, -212, 144, 134, 108, -13],\n [145, 172, -42, -1, 150, 13, 121, 191, 305, -138],\n [-299, 219, 285, 168, 541, 212, -128, 49, 226, 591],\n [-435, 9, 667, 614, 559, -246, -354, -135, 424, 437],\n [-456, -82, 302, 239, 129, -140, -486, -385, -23, 433],\n [-261, 352, -142, -36, 91, -283, -717, -410, 648, 7],\n [-146, -56, 642, 540, 586, 26, 214, 278, 180, 362],\n [-189, -135, -30, 94, -347, -512, -588, -528, 124, -265]]?\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[[-1378, -406, 383, -581, 132, 529, 21, 160, 532, 568],\n [441, -232, 109, 151, -147, -293, -508, -106, -142, -80],\n [-945, 62, 506, -106, 323, 325, 111, -56, 321, 486],\n [751, 674, -865, 291, 512, 273, 348, -825, 105, -319],\n [409, -136, -494, 2, -374, 292, 323, -173, -60, -518],\n [-771, -110, 580, 121, 437, -130, -184, -157, 721, 581],\n [-164, -117, 462, 141, 244, -84, -484, -319, 521, 140],\n [-224, -6, -24, 183, -298, -70, 565, 530, -330, 154],\n [510, -181, 414, 485, -92, -225, -568, -489, 50, -172],\n [-442, -701, -72, 79, -566, 508, -596, 923, 203, 316]]?\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[[360, -380, -80, 80, 320, 20, 280, 40, 120, 160],\n [-324, 342, 72, -72, -288, -18, -252, -36, -108, -144],\n [54, -57, -12, 12, 48, 3, 42, 6, 18, 24],\n [-378, 399, 84, -84, -336, -21, -294, -42, -126, -168],\n [180, -190, -40, 40, 160, 10, 140, 20, 60, 80],\n [252, -266, -56, 56, 224, 14, 196, 28, 84, 112],\n [36, -38, -8, 8, 32, 2, 28, 4, 12, 16],\n [36, -38, -8, 8, 32, 2, 28, 4, 12, 16],\n [288, -304, -64, 64, 256, 16, 224, 32, 96, 128],\n [126, -133, -28, 28, 112, 7, 98, 14, 42, 56]]\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[[-661, 186, 669, -287, 371, -167, 496, -814, 174, -4],\n [72, -24, -601, 574, -504, 326, -199, 393, -371, -57],\n [-8, -34, 495, -198, 240, -254, 445, -485, 251, -399],\n [-327, -401, 367, -319, 275, -615, 354, -341, -1, 71],\n [-611, 166, 566, -449, 110, -121, 837, -580, -103, 351],\n [48, 54, 87, -64, 329, -40, -469, -46, 307, -61],\n [-316, -237, 503, -186, 646, -550, -186, -577, 425, -295],\n [-379, -149, -617, 677, -489, 189, -186, 227, -537, 87],\n [114, 454, 317, -110, 216, 302, -18, -282, 378, -236],\n [458, 223, 43, 208, -182, 292, 240, -61, 155, -609]]\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[[-341, -586, -384, 347, 158, -57, 27, 680, -325, 116],\n [-35, -107, -281, 360, -329, -520, 61, 131, 243, 412],\n [-959, -251, 175, -406, 373, 618, -353, -131, -367, -796],\n [-649, -288, 255, -477, 40, 629, -755, -185, -555, -393],\n [14, 95, 16, 376, 280, -224, 744, -11, 448, -298],\n [174, 435, -657, 140, -46, -54, -807, 285, -328, -147],\n [-382, -322, -632, 459, 289, -341, -62, 794, 153, -266],\n [590, 243, -234, 229, -691, -419, -646, -72, -14, 685],\n [42, -472, 510, -338, 90, 244, -57, 91, 106, 22],\n [384, 378, -437, 369, -73, -549, 491, 147, 342, 312]]\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 10x10 matrix:\n[[-95, 246, -272, 72, -221, -419, 317, -164, -168, 108],\n [551, -316, 528, 534, -408, -116, -344, 592, -125, -429],\n [-413, 283, -124, -354, 257, -460, 170, -93, -78, -161],\n [-78, 213, 357, -479, 536, -89, -661, 961, 189, -737],\n [-316, 430, 92, -524, 434, 484, -388, -322, 818, 72],\n [683, -98, 313, 475, -417, 262, -525, 766, 128, -221],\n [-31, 338, -41, -237, 158, -59, -270, 452, 163, -214],\n [211, 6, -397, 615, -772, -47, 608, -828, -115, 716],\n [-161, -428, -208, 170, -90, -29, 624, -760, -408, 426],\n [77, -852, 641, 119, 245, 367, -147, -160, -121, -214]]\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[[470, -262, -305, 413, -24, 228, -204, -569, 491, -127],\n [-569, 323, -1124, -62, -463, 659, 514, -467, -468, 284],\n [-65, -293, -213, -50, 172, 132, -323, -291, 126, -248],\n [643, -685, -490, -514, 639, 587, -120, -603, 164, 374],\n [-337, -75, 277, 299, -197, -48, -20, -46, 597, 472],\n [-310, 96, -975, -390, 8, 73, 530, 323, -504, 222],\n [-111, -5, 738, 17, 115, -493, -258, 463, 120, -202],\n [142, -50, -780, 123, -99, 420, -29, -573, -116, -306],\n [-440, 324, -66, 34, -459, 771, 159, -787, -208, 389],\n [-105, 61, 190, 908, -517, -98, -158, -309, 832, 23]]?\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 10x10 matrix:\n[[114, -24, 87, 775, 895, -123, -341, 485, -587, 572],\n [-164, 509, 850, -275, -209, -566, 1541, -1246, -211, 19],\n [-906, -397, 54, -10, -641, -194, -697, 159, 383, -329],\n [-347, -1522, -234, -499, 49, -246, -152, 481, -74, -99],\n [-768, 166, 410, -168, -530, -698, -430, 207, -332, -805],\n [-491, -1035, 257, -31, 22, -634, 385, -92, -214, -111],\n [-450, 390, 428, 9, -447, -311, 341, -614, 256, -304],\n [-177, -446, -300, -617, -351, 782, -836, 503, 704, 225],\n [-193, 445, 744, -247, -261, -62, 769, -631, -505, 433],\n [-146, 325, 253, 609, 98, -865, 431, -387, -58, -554]]\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[[-40, -2, 552, -136, -92, -162, -474, -180, 485, -84],\n [243, -378, 381, -514, 278, 164, -24, 9, 408, -584],\n [443, 131, 22, -37, -207, 65, -2, 68, -527, -571],\n [274, -624, -24, -82, 547, 415, -488, 680, -272, -439],\n [-263, -443, -42, -17, 528, 330, -172, 424, 163, -16],\n [-439, -484, 86, 434, 406, -121, 181, -394, 509, -211],\n [-482, 313, -478, 619, -143, -114, 164, -8, -312, 685],\n [-90, 242, -364, 380, -239, -275, 59, -140, -222, 670],\n [537, 263, 815, -1615, -105, 620, 149, 349, 350, -1118],\n [309, 505, 247, -11, -650, -459, -344, -355, -46, 302]]?\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[[1003, -712, -63, -560, 78, 134, -892, 1176, -870, -835],\n [481, -572, 217, 200, -332, 224, 77, -36, 747, -247],\n [-341, 458, 391, 211, 300, 76, 136, 18, -37, 585],\n [157, 175, -424, -242, -206, 372, -248, 190, -421, -72],\n [46, -376, 1618, 636, -115, 349, -825, -55, 493, 385],\n [-92, 454, -165, 1018, 121, 343, 85, -427, 465, 611],\n [-236, -689, -416, 521, 112, -235, -153, -472, -126, 59],\n [698, -837, -188, -351, 807, 801, 991, 277, 231, -476],\n [-106, 415, -536, -1267, 426, -28, 779, 414, -1010, -174],\n [26, -44, 310, 198, -553, 292, -1258, 437, -240, 140]]\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[[600, 47, -4, 46, -456, 11, 267, -145, -278, -88],\n [-1003, 517, 381, -260, -182, -312, -116, -513, 892, 644],\n [-95, -400, -317, 25, -309, -201, -527, 470, -565, 80],\n [-509, 559, 68, 22, -591, -636, -508, -590, -192, 457],\n [-474, 189, 108, -280, 140, -69, 198, -513, 475, 282],\n [-252, 134, -79, 39, -649, 221, 108, 173, 500, 251],\n [66, -270, 291, -389, 559, -633, -225, -399, -535, 75],\n [-181, 267, 164, -65, -168, -506, -304, -432, -241, 235],\n [-483, -245, -363, 55, 273, 158, -304, 379, -7, -22],\n [158, -39, -135, -114, -872, -80, 115, -88, -109, 263]]?\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[[488, 301, 256, 283, -49, -3, -521, 340, -234, 192],\n [-343, -556, -252, -655, 414, -376, 892, -486, -215, -179],\n [-276, -207, 394, -80, -138, -64, -388, -7, -174, -192],\n [-387, -490, -291, -244, 650, 131, 882, -652, 134, -108],\n [-299, 264, -243, 281, 549, 242, 230, -328, 237, 388],\n [-355, 33, 192, 39, 118, -30, -239, -110, -82, 85],\n [393, -187, 395, 357, 143, 414, -352, 39, -55, -148],\n [219, 568, 94, 223, -622, -124, -697, 567, 18, 179],\n [116, 254, -198, 221, -179, 199, -24, 132, 303, 82],\n [263, 57, 360, 474, -21, 433, -550, 139, 72, -35]]\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[[13, 275, -672, -392, -401, 166, 565, 329, 234, -295],\n [-218, 94, 386, 160, -228, -314, -28, 168, -192, 12],\n [-138, 506, 471, 192, -361, -76, -47, 235, -470, 61],\n [-156, -90, 786, 207, 127, -367, -278, -148, -117, 256],\n [208, 292, 408, -51, 235, -25, -136, -346, -97, 284],\n [-276, -137, 263, 138, -183, -18, -47, 261, -47, -26],\n [-238, -373, -424, 347, -225, 370, -146, 462, -194, -309],\n [11, -152, 319, -12, 224, -392, -84, -272, 129, 153],\n [-173, 242, 65, 136, -388, -299, 104, 280, -271, -135],\n [212, 34, -314, -422, 184, 662, 198, -94, 404, 64]]\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[[-233, -135, 190, 117, -19, -89, 167, 19, -27, 166],\n [-161, -95, 132, 81, -15, -65, 115, 11, -15, 118],\n [-519, -305, 425, 261, -47, -207, 371, 37, -51, 378],\n [315, 125, -233, -153, -37, 3, -239, -97, 159, -114],\n [7, -135, 52, 9, -151, -281, -37, -173, 297, 262],\n [499, 205, -372, -243, -51, 19, -377, -145, 237, -194],\n [273, 135, -213, -135, -3, 57, -201, -51, 81, -150],\n [-94, -130, 108, 54, -90, -190, 50, -86, 150, 212],\n [281, 95, -201, -135, -51, -31, -217, -107, 177, -70],\n [-231, -145, 193, 117, -31, -111, 163, 5, -3, 186]]\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[[-351, -167, -43, -194, -139, -373, -525, 204, -208, -328],\n [-472, -84, -355, -639, 869, 317, 810, 636, -403, -105],\n [241, 502, -374, 503, -284, 95, 404, 13, -156, 52],\n [22, -64, 92, -70, 962, 889, -351, -440, 437, 979],\n [25, 658, -181, 691, 289, 505, -441, -196, 142, 466],\n [156, -69, 277, -192, -283, -158, 51, 92, 236, -164],\n [-147, 191, -46, -5, -76, -198, 334, 396, -205, -453],\n [-69, 13, 269, -491, -149, -197, 177, 545, 176, -432],\n [191, 383, 114, 207, -76, -29, 1070, 332, -56, -448],\n [-84, 37, 691, -97, 369, 255, -889, -95, 685, 205]]\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[[58, -497, 420, -625, -98, 674, -651, -114, 269, 81],\n [-600, 403, -2, 110, -8, -401, 384, -326, 203, -81],\n [1145, -322, -382, -212, 19, 378, -86, 126, -184, -332],\n [132, 102, -502, -400, 73, -83, -97, -66, 368, -212],\n [-473, 312, 243, 234, 677, -771, -751, -279, -582, 270],\n [-650, 535, 81, -86, -43, -538, 303, -252, 719, 37],\n [-538, 732, -812, 215, 204, -440, 238, -495, -71, -67],\n [269, -588, 372, -496, -212, 237, -219, 488, 823, -171],\n [1039, -256, -834, -126, -409, 496, 433, 600, 94, -15],\n [-517, 171, -154, -142, -141, 347, 126, 419, -270, 311]]\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[[134, -335, -449, -267, 252, -265, -182, 172, -228, -96],\n [277, 344, 42, 1, 511, -433, 297, 10, 203, -118],\n [144, -742, -583, -533, 549, -151, -175, 124, -599, -215],\n [206, 663, 120, 307, 42, -389, 250, 57, 500, 142],\n [164, -622, -523, -412, 516, -54, -14, 71, -566, -40],\n [-342, -116, 346, 137, -513, 625, -67, -189, -87, 113],\n [-429, 12, 490, 193, -701, 571, -211, -168, 99, -16],\n [-28, 296, 8, 146, -330, -294, -262, 162, 386, -70],\n [-211, 131, 87, 138, -599, -38, -423, 122, 301, -86],\n [-461, -114, 424, 231, -785, 813, -131, -216, -65, 208]]\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[[248, 834, -454, 572, 82, -208, 56, 166, 98, 134],\n [396, 64, -139, 298, 1147, -182, -729, 258, -36, -271],\n [-301, -643, 422, -837, 402, 270, 518, 647, -59, 506],\n [-817, -341, -317, 143, -258, 13, 405, -138, 222, -403],\n [1072, 852, 470, 36, -301, -364, -668, -666, -462, -554],\n [310, 40, 177, -7, -13, -62, 565, -53, -363, 208],\n [-953, -578, 82, -453, 97, 298, 1067, 680, 782, 570],\n [601, -433, 162, -688, -76, 464, 176, 130, -1048, 285],\n [-3, -298, -542, 172, 782, 188, 348, 847, -555, 988],\n [525, -746, -179, -152, -508, 691, 94, -584, -492, -380]]\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 10x10 matrix:\n[[617, 180, 78, 351, -412, -533, 141, -814, 578, -494],\n [-451, 104, 1123, 741, -260, -1239, -38, -782, 214, -250],\n [210, -999, 285, -126, -548, -181, 901, 233, 383, -663],\n [963, -158, 184, 221, -1296, -111, 365, -446, 1123, -752],\n [-346, 220, 569, 453, 296, 285, -177, -27, 582, 286],\n [7, 962, -444, 131, -796, 122, -901, -281, 202, 498],\n [186, -331, 196, 581, -358, 212, 340, -92, 525, 57],\n [-256, -308, -625, -621, -558, -142, 289, 329, -381, 101],\n [631, 110, -525, -567, -336, 980, 97, 35, 644, -204],\n [1625, -1380, 1105, 1278, -406, -434, 854, -280, 652, -1643]]\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[[-510, 257, 478, -1, 609, 156, 457, 14, -300, 275],\n [407, -80, 195, 338, 392, -416, 131, -211, -641, 196],\n [164, -306, 212, 294, 551, -834, 166, 377, -507, 95],\n [889, -245, -382, 152, -65, -556, -73, -21, -317, -36],\n [-507, 70, 255, -78, -219, 406, -239, -362, 224, -85],\n [-883, 145, 765, 293, 560, 134, 208, 186, -158, 242],\n [568, -180, 182, 614, 277, -526, -54, -119, -631, 187],\n [-383, -130, 103, -330, 34, -122, -31, -59, 91, -160],\n [-315, 164, 2, -215, 351, 49, 438, 529, 101, 106],\n [363, -75, -359, -61, -639, 198, -432, -353, 287, -215]]\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[[51, 391, 199, -117, 165, -462, -12, -215, -631, 174],\n [417, 34, -374, -30, 270, 0, 501, -245, 2, 276],\n [445, 723, -21, -609, 232, -223, -63, -203, -664, 473],\n [-179, -369, 225, 332, -410, 167, -78, 45, 402, -79],\n [-588, -758, -8, 697, -75, 87, 102, 230, 565, -639],\n [360, -35, -175, 287, 247, -342, 699, -488, -201, 342],\n [-144, 244, 520, 118, -132, -528, -150, -232, -572, 132],\n [545, 670, 142, -554, -67, -125, -96, -287, -523, 667],\n [137, 44, -672, -294, 588, 220, 225, 203, 104, -212],\n [272, -56, -790, -179, 630, 226, 477, 80, 194, -116]]\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[[-6, 4, -145, -182, -173, -56, -37, 115, -205, -107],\n [295, 50, -167, -196, -26, 466, -500, -233, -137, 166],\n [223, -72, -141, -200, -148, -8, -130, -289, -659, 82],\n [-261, -226, -693, -163, -478, -698, 54, 558, -555, -211],\n [-47, 275, 738, 25, 265, 307, 367, -100, 578, -181],\n [81, -4, 240, 293, 311, 184, -21, -285, 306, 236],\n [47, -219, -171, 308, 118, -223, -50, -218, -199, 299],\n [136, 36, -68, -228, -124, 132, -140, -92, -284, -28],\n [170, -110, -90, 75, 50, 10, -140, -305, -310, 225],\n [63, 364, 363, -388, -20, 604, -82, 111, 445, -294]]\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[[276, -100, 138, -170, 272, -339, 54, 462, -507, -18],\n [10, -150, 6, -76, 228, -209, 66, 228, -251, -349],\n [46, 306, -208, 462, -688, -126, -612, 94, 268, -321],\n [-190, 90, -176, 246, -308, 84, -216, -178, 326, -321],\n [-232, 100, -94, 118, -228, 355, -6, -458, 467, 158],\n [-525, -288, -187, -11, 275, 161, 258, -341, 255, -761],\n [267, 60, 83, -17, -25, -226, -120, 325, -276, 121],\n [89, 266, -81, 269, -493, 20, -372, -21, 224, 118],\n [164, 98, -36, 146, -202, -247, -282, 294, -133, -191],\n [-484, -296, -106, -122, 372, 253, 390, -410, 233, -460]]\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 10x10 matrix:\n[[-340, -20, 280, 60, 360, 60, 40, 420, 40, -380],\n [-51, -3, 42, 9, 54, 9, 6, 63, 6, -57],\n [357, 21, -294, -63, -378, -63, -42, -441, -42, 399],\n [-238, -14, 196, 42, 252, 42, 28, 294, 28, -266],\n [-323, -19, 266, 57, 342, 57, 38, 399, 38, -361],\n [34, 2, -28, -6, -36, -6, -4, -42, -4, 38],\n [-374, -22, 308, 66, 396, 66, 44, 462, 44, -418],\n [272, 16, -224, -48, -288, -48, -32, -336, -32, 304],\n [-187, -11, 154, 33, 198, 33, 22, 231, 22, -209],\n [289, 17, -238, -51, -306, -51, -34, -357, -34, 323]]\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[[-66, -34, 243, 364, 316, -550, -86, 53, 439, -137],\n [205, 154, 253, 328, 289, -635, 79, 407, 503, 171],\n [301, 78, -32, 686, 248, -1035, -316, 502, 777, 247],\n [250, -2, -406, 318, -147, -370, -383, 252, 239, 261],\n [-502, -434, -286, 126, -99, 190, -543, -732, -169, -563],\n [-76, 44, -67, -694, -331, 980, 359, -239, -746, 12],\n [-429, -158, 540, 170, 452, -245, 80, -362, 239, -535],\n [-13, 32, 44, -172, -43, 215, 137, -32, -158, 6],\n [517, 430, 229, -140, 55, -155, 517, 731, 137, 585],\n [-484, -132, 741, 138, 573, -260, 223, -375, 270, -604]]\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[[15, 3, 16, 22, -2, -3, 14, 0, -17, 21],\n [-225, -45, -240, -330, 30, 45, -210, 0, 255, -315],\n [-135, -27, -144, -198, 18, 27, -126, 0, 153, -189],\n [-300, -60, -320, -440, 40, 60, -280, 0, 340, -420],\n [195, 39, 208, 286, -26, -39, 182, 0, -221, 273],\n [-135, -27, -144, -198, 18, 27, -126, 0, 153, -189],\n [-300, -60, -320, -440, 40, 60, -280, 0, 340, -420],\n [285, 57, 304, 418, -38, -57, 266, 0, -323, 399],\n [-90, -18, -96, -132, 12, 18, -84, 0, 102, -126],\n [-330, -66, -352, -484, 44, 66, -308, 0, 374, -462]]\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[[219, 323, 312, -511, -15, 181, 172, 131, 64, -216],\n [908, -294, -188, -9, 135, 286, 17, 661, -459, 249],\n [3, 160, 161, -328, -12, -164, -988, -746, 36, -330],\n [-187, 171, -472, 318, -184, -113, -57, -465, 349, 175],\n [9, 112, -382, 600, 218, 277, -1005, -906, 614, 518],\n [-114, 76, -1178, 944, -112, -310, -968, -1241, 266, 555],\n [-1186, -348, 1311, -886, -388, -359, 837, 519, -99, -930],\n [-1256, -107, 231, -123, -647, -339, 438, -489, 543, -194],\n [-685, -331, -971, -540, -189, 1095, -1417, -1449, 212, 588],\n [827, 65, -166, 138, 162, -5, 481, 492, -211, 542]]\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[[-119, -101, -127, -40, 50, -289, 2, 22, 34, 221],\n [210, -240, -370, -472, -67, -356, 50, -82, 61, 308],\n [-157, 57, 385, 430, 9, 137, -36, -78, 7, -97],\n [96, 44, -204, -228, 4, 44, 16, 92, -32, -52],\n [-218, 318, -204, 6, 181, 210, -26, 400, -125, -262],\n [698, -243, 293, -235, -374, 289, 58, -545, 87, -87],\n [200, -125, 39, -111, -110, -17, 22, -177, 43, 59],\n [366, -236, -34, -292, -185, -88, 46, -282, 75, 144],\n [-205, 330, -156, 39, 170, 258, -28, 383, -127, -296],\n [46, -301, 55, -17, -84, -377, 18, -263, 115, 359]]?\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[[-133, -89, -526, -280, 372, 316, 2, -384, -283, 248],\n [-171, -141, -198, -298, 93, -320, -427, 113, 48, 651],\n [134, 112, 128, 230, -51, 292, 359, -123, -61, -529],\n [7, -1, 130, 28, -102, -172, -92, 150, 103, 58],\n [-85, -77, 26, -132, -54, -348, -324, 214, 131, 410],\n [144, 108, 360, 276, -234, -24, 186, 150, 126, -414],\n [-144, -120, -144, -248, 60, -304, -380, 124, 60, 564],\n [67, 35, 442, 164, -330, -428, -160, 418, 295, -2],\n [-75, -45, -390, -170, 285, 320, 85, -335, -240, 75],\n [13, 11, 10, 22, -3, 32, 37, -15, -8, -53]]\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[[1062, -49, -151, 70, -129, -164, -530, -202, 91, 123],\n [36, 188, 15, -1046, -34, -173, -391, -699, -121, 101],\n [-532, 351, -157, -553, 346, 204, 136, -122, -289, -468],\n [-16, -357, 293, 103, -49, 110, -117, -59, -81, 279],\n [-142, -316, 261, -195, 252, 191, -124, -306, -15, 101],\n [-416, 109, -3, 433, -169, 308, 257, 675, -637, -191],\n [-138, -494, 333, 397, 157, 261, 41, 77, 13, 180],\n [106, -73, -153, 500, 474, 230, 193, 203, 237, -380],\n [210, -120, 98, -395, 204, 268, -417, -331, -410, -62],\n [206, 140, -212, -155, 170, -386, 107, -337, 802, -34]]?\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[[173, -55, -807, -507, 203, -902, -964, -118, 311, -379],\n [193, -239, -361, -69, -438, -792, -425, -578, 129, -779],\n [458, -37, -676, -538, -682, -699, -72, -727, 197, -596],\n [794, -318, -437, -458, 300, 360, 984, 361, -297, 539],\n [-166, 173, 588, 425, -857, 169, 183, -294, -10, 55],\n [-32, -609, -42, 140, 332, -144, 86, 478, -253, 188],\n [-105, 110, -729, -869, -440, -185, 52, 194, 714, 311],\n [800, 215, 689, 636, -756, 360, -226, -728, -232, -679],\n [138, 521, 605, 638, -271, 127, 77, -739, -96, -449],\n [-19, -273, -593, -565, 109, 75, 39, 937, 821, 585]]?\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[[-684, -812, -342, -250, 512, 32, 588, -431, -962, 118],\n [-225, -825, -395, -555, -329, -177, -76, -275, -279, 308],\n [-319, 52, 13, -280, 236, -359, 215, -794, 67, -387],\n [-684, -911, -428, -369, 520, -33, 496, -561, -997, 163],\n [88, -142, 108, 232, -1182, 277, -857, 579, 595, -41],\n [74, -493, -152, -475, -622, -225, -482, -178, 357, 45],\n [-323, -158, -27, 300, 280, 311, 347, 214, -547, 61],\n [-539, 144, -135, 42, -546, -105, 233, -280, -131, 51],\n [-435, 130, 41, 248, -598, 91, -193, -96, 117, -209],\n [-78, 270, 160, 332, -771, 169, -213, 380, 365, -70]]\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[[80, 5, 15, -60, 95, 15, -60, -50, 10, -110],\n [-320, -20, -60, 240, -380, -60, 240, 200, -40, 440],\n [-144, -9, -27, 108, -171, -27, 108, 90, -18, 198],\n [-176, -11, -33, 132, -209, -33, 132, 110, -22, 242],\n [48, 3, 9, -36, 57, 9, -36, -30, 6, -66],\n [-320, -20, -60, 240, -380, -60, 240, 200, -40, 440],\n [336, 21, 63, -252, 399, 63, -252, -210, 42, -462],\n [304, 19, 57, -228, 361, 57, -228, -190, 38, -418],\n [-352, -22, -66, 264, -418, -66, 264, 220, -44, 484],\n [-240, -15, -45, 180, -285, -45, 180, 150, -30, 330]]\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[[-162, 268, 204, -174, 624, -465, -234, 93, 838, -463],\n [-186, 84, 99, 310, 480, -163, -213, -656, 501, -159],\n [570, 876, -726, 478, -325, 764, -179, 926, 435, 761],\n [-580, 91, -587, 224, -294, 262, -597, -568, -700, 290],\n [125, -46, 137, -43, 43, 173, 58, -91, 359, 1160],\n [-264, -92, -283, -303, 50, 318, -222, 482, -215, 581],\n [-128, -161, -177, -540, 71, 593, 1, 412, 745, 119],\n [0, 69, -45, -151, -80, 79, -185, -554, 335, 698],\n [334, 808, -251, -310, -297, 90, -233, 181, 1341, -59],\n [328, 47, -289, -68, -440, 273, 188, 692, -606, -220]]\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[[-276, 183, -30, 222, 513, 9, -120, 333, -183, 258],\n [-111, 121, -370, 246, 631, 289, -56, 458, -32, 67],\n [358, -215, -130, -214, -465, 123, 152, -279, 257, -352],\n [321, -142, -500, -24, 38, 416, 128, 97, 275, -355],\n [-245, 196, -280, 308, 756, 210, -112, 525, -133, 203],\n [341, -151, -530, -26, 39, 441, 136, 102, 292, -377],\n [-267, 201, -210, 294, 711, 153, -120, 486, -156, 231],\n [-324, 234, -180, 324, 774, 126, -144, 522, -198, 288],\n [-260, 166, 20, 188, 426, -30, -112, 270, -178, 248],\n [179, -132, 120, -188, -452, -86, 80, -307, 107, -157]]?\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[[-277, -249, 40, 570, 235, -249, 147, 291, 115, 271],\n [58, 117, -797, 254, -418, 288, 240, -630, -452, -216],\n [-281, 383, -172, 159, -442, 302, -170, 163, 224, -610],\n [-235, -468, -451, -151, 520, 403, 151, -619, 183, 305],\n [-40, 1128, -74, -375, -591, 566, -230, -108, 163, -506],\n [265, 485, -387, 126, -396, -77, 547, -297, -552, 371],\n [134, 27, 273, 746, 121, -521, 344, 382, -36, 628],\n [565, 128, -28, 232, -266, 88, 798, 229, 325, 338],\n [675, 293, 241, 113, -552, -270, 643, 783, -172, -57],\n [145, -213, 105, 335, -277, -617, 51, 289, -499, -27]]\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[[-48, -24, -42, 21, 63, 60, 15, 21, -45, 36],\n [80, 40, 70, -35, -105, -100, -25, -35, 75, -60],\n [304, 152, 266, -133, -399, -380, -95, -133, 285, -228],\n [-336, -168, -294, 147, 441, 420, 105, 147, -315, 252],\n [-288, -144, -252, 126, 378, 360, 90, 126, -270, 216],\n [128, 64, 112, -56, -168, -160, -40, -56, 120, -96],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n [-288, -144, -252, 126, 378, 360, 90, 126, -270, 216],\n [272, 136, 238, -119, -357, -340, -85, -119, 255, -204],\n [-320, -160, -280, 140, 420, 400, 100, 140, -300, 240]]\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 10x10 matrix:\n[[-326, 106, -76, -20, -237, 134, -121, -47, -13, 165],\n [-153, -411, 84, -327, 9, 555, -207, -321, 75, 300],\n [-85, 102, -290, 127, 79, -232, 340, 78, -39, 137],\n [425, -456, 194, -197, 384, 174, 37, -147, 74, -68],\n [-216, 63, 490, -192, -499, 499, -828, -126, 41, -166],\n [66, 655, -122, 458, -153, -721, 192, 442, -113, -380],\n [-114, 222, -352, 210, 46, -358, 402, 150, -62, 112],\n [-309, -140, 202, -253, -297, 542, -486, -236, 49, 163],\n [-71, 233, -352, 231, 73, -405, 431, 173, -65, 80],\n [-104, -164, 688, -356, -446, 748, -1018, -254, 90, -194]]\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[[678, -708, 241, 204, 605, 482, 172, 323, -247, -290],\n [26, 200, -507, -224, -53, -499, -107, 508, 40, 571],\n [148, -295, -173, 86, 455, 428, 388, 570, -238, -98],\n [362, 130, 37, 124, 558, -286, 19, 717, -565, 535],\n [-424, -63, 515, 242, 314, -173, 892, 447, -127, -272],\n [-126, -201, 630, 61, -372, -220, 3, -728, 428, -480],\n [-138, 205, 354, 169, 259, -332, 304, 318, -294, 151],\n [374, 35, 190, 93, 375, -451, -55, 467, -347, 428],\n [-362, -189, 708, 229, -249, 546, 220, -948, 236, -917],\n [-166, -50, -55, 192, 562, 434, 671, 713, -433, -97]]\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[[-328, -368, -188, -224, 800, -551, -105, 35, 336, -193],\n [-238, 132, 572, 505, -49, -476, -321, 432, 280, -75],\n [-244, 372, 381, 314, 2, -539, -454, 480, 121, 120],\n [-7, 230, -27, -12, -18, -136, -136, 126, -83, 120],\n [112, 48, -772, -588, 556, -268, 92, -144, -196, 60],\n [647, 278, -420, 66, -240, -100, 443, -45, -332, -159],\n [-372, 8, 628, 351, -147, -54, -363, 256, 256, 67],\n [118, 364, 24, 160, -124, -291, -103, 241, -108, 61],\n [187, -298, -158, -95, -59, 359, 349, -308, -30, -155],\n [223, 338, -459, -245, 111, -227, 24, 41, -275, 122]]\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[[-260, 219, -1015, -416, -914, -388, -115, -61, -249, 533],\n [-444, -176, -490, 145, 886, -15, -34, 1129, -501, -1085],\n [-321, 680, -516, -765, -764, -23, 576, -171, -552, -311],\n [319, 222, 293, -197, 880, -450, -444, 316, 322, -725],\n [458, -51, 857, -172, -243, 869, 328, -190, 24, -125],\n [509, -74, -154, -82, -163, -138, 187, -1328, 377, 472],\n [55, -421, 1325, 594, 684, 333, -60, 327, -34, -452],\n [330, -135, -769, -920, -739, -263, 497, -1244, 335, 19],\n [316, 103, 54, -601, -229, 426, 172, 353, 359, -657],\n [-450, 71, -787, -39, 193, -616, 178, -187, -220, -185]]?\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 10x10 matrix:\n[[-29, -19, -212, 69, -117, 144, 128, -67, 294, 248],\n [117, 215, -291, -390, 43, 643, 154, 237, -173, -417],\n [50, -169, 280, -90, -25, -250, -157, -188, -235, -164],\n [431, 5, -503, -540, 161, 95, 374, -365, -25, -17],\n [3, 185, 407, 84, 426, -503, -241, 313, -524, -320],\n [-452, -294, 725, 591, -364, -349, -496, 26, 71, 131],\n [-273, -213, -101, 360, -490, 249, 27, -155, 636, 514],\n [-198, -63, 286, 228, -125, -60, -205, 104, -9, -16],\n [-211, 71, -143, 246, -185, 335, 46, 197, 347, 215],\n [-241, -319, 504, 219, -370, -124, -341, -149, -13, -35]]\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[[135, 973, -85, 284, -297, 136, -268, -187, 726, -222],\n [-163, -850, -688, -69, 54, 40, 489, 263, 148, 374],\n [275, -26, -149, -221, -101, -275, -456, 264, 108, 275],\n [351, 355, 76, -284, -266, -157, -359, -122, 482, 189],\n [179, -86, -753, 606, -240, -294, -353, 239, 573, 354],\n [268, 696, -147, -233, -240, 13, -245, -377, 621, 229],\n [-158, -1480, -268, -495, -29, -308, 568, 702, -215, 172],\n [-761, -441, 8, -541, 339, 241, 1189, -136, -886, -411],\n [-69, -702, 29, 513, 405, 666, 351, -155, 36, 280],\n [-629, -167, 135, -877, -202, -443, 985, 98, -652, -723]]?\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[[572, 552, -49, -16, -360, 89, -23, 157, 110, -236],\n [779, 851, -458, 44, -210, -215, 589, 470, -267, -747],\n [-769, -253, 362, -199, -273, -36, -426, -610, 644, 145],\n [142, -26, -131, 902, -239, -286, 372, -142, -26, -680],\n [-525, -128, -532, -45, 336, 716, -307, 623, -23, -143],\n [-57, -31, -389, -743, 289, -247, -783, 335, 200, 1377],\n [30, -959, -20, 904, -363, 145, 150, -231, 282, -373],\n [162, 338, 702, -98, -557, 133, 887, -362, -87, -955],\n [20, -226, 284, -1612, 209, 809, 561, 594, -405, 371],\n [-217, 894, -176, 535, -584, -20, 343, 513, -35, -457]]\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[[-57, 113, -403, -81, -350, 365, -130, -698, 808, 171],\n [859, -220, 184, 831, -170, -188, -537, -133, -338, 652],\n [-15, 580, 10, -345, -273, 67, 392, 565, 158, -673],\n [15, 152, 184, 46, 651, 316, -111, 101, 246, -28],\n [-223, -791, -540, -13, -708, 15, 260, 495, 354, -6],\n [-804, -318, -41, -346, 475, 113, 550, 555, -88, -62],\n [119, 713, 44, -211, -436, 31, 663, 1271, -36, -802],\n [-596, 224, -260, -917, -890, 53, 705, 36, 644, -609],\n [641, 688, 487, 207, 63, -127, -89, 334, -346, -240],\n [-39, -402, 330, 184, 783, -256, -196, 282, -714, 54]]\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 10x10 matrix:\n[[-10, -22, 36, 10, 34, -38, 0, -10, -36, 20],\n [-70, -154, 252, 70, 238, -266, 0, -70, -252, 140],\n [30, 66, -108, -30, -102, 114, 0, 30, 108, -60],\n [-40, -88, 144, 40, 136, -152, 0, -40, -144, 80],\n [50, 110, -180, -50, -170, 190, 0, 50, 180, -100],\n [70, 154, -252, -70, -238, 266, 0, 70, 252, -140],\n [65, 143, -234, -65, -221, 247, 0, 65, 234, -130],\n [25, 55, -90, -25, -85, 95, 0, 25, 90, -50],\n [-65, -143, 234, 65, 221, -247, 0, -65, -234, 130],\n [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": "Determine the rank of the following matrix:\n[[-170, 330, 102, 172, 160, 64, 36, -362, -92, 98],\n [35, -315, 504, -56, 420, -147, -378, -49, 266, 371],\n [235, -675, 324, -256, 180, -207, -378, 391, 346, 211],\n [255, -711, 306, -276, 156, -213, -378, 435, 354, 195],\n [-25, -111, 354, 12, 316, -77, -234, -133, 146, 267],\n [-100, 228, -12, 104, 32, 56, 72, -196, -88, 4],\n [-100, 156, 141, 98, 164, 17, -36, -232, -16, 118],\n [0, 240, -510, 20, -440, 130, 360, 120, -240, -380],\n [-95, 375, -348, 112, -260, 139, 306, -107, -242, -247],\n [135, -63, -504, -120, -492, 57, 270, 387, -126, -393]]\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[[-226, -61, -224, 170, 515, 670, -65, 19, 33, 69],\n [-722, -87, -278, 158, 297, -68, -279, 219, 119, 265],\n [343, 73, -78, -90, 88, 544, 223, -168, 99, -78],\n [-324, -493, 142, 500, 371, 204, -427, 303, -343, -347],\n [327, 2, 8, 14, 169, 560, 146, -131, -34, -143],\n [-327, 247, -286, -231, -109, -300, 66, -18, 331, 410],\n [-254, -239, -51, 377, 626, 667, -228, 114, -213, -102],\n [53, 535, -32, -365, -187, -454, 252, -240, 107, 520],\n [778, 13, 112, -372, -765, -174, 379, -167, 267, -381],\n [-84, 563, -495, -468, 17, 187, 387, -280, 551, 634]]\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[[-348, 57, -144, 18, -327, 30, 294, -114, 3, 81],\n [-247, 160, -136, -179, -219, -184, 0, 72, 60, -95],\n [140, -101, 80, 118, 123, 122, 18, -54, -39, 67],\n [232, 245, 16, -466, 249, -506, -690, 438, 135, -415],\n [77, -98, 56, 133, 63, 140, 84, -84, -42, 91],\n [-82, 233, -96, -348, -53, -370, -314, 254, 107, -261],\n [-305, 28, -120, 51, -289, 64, 296, -128, -8, 99],\n [-629, 286, -312, -261, -571, -260, 212, 28, 94, -87],\n [-510, 186, -240, -138, -468, -132, 252, -36, 54, -12],\n [384, -180, 192, 168, 348, 168, -120, -24, -60, 60]]\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[[399, -314, 296, -493, 459, 72, 358, 381, 139, 30],\n [133, -9, -461, 293, 260, 143, 832, 42, -213, -321],\n [296, -620, 270, -124, -346, 240, -278, 296, -78, 564],\n [11, -214, 202, 3, -183, -136, -276, -23, 93, 234],\n [447, -499, 360, -423, 403, -37, 363, 368, 184, 129],\n [-303, -5, -545, 853, -840, 193, -265, -325, -427, 206],\n [-187, -22, -291, 503, -530, 94, -215, -201, -238, 156],\n [-565, 607, -302, 441, -427, -121, -522, -489, -94, -158],\n [-86, -19, 25, 218, 179, -525, 226, -253, 234, -181],\n [-107, 116, -126, 157, -57, -40, 11, -116, -37, -79]]\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[[395, -14, -338, -239, -104, -701, -586, 28, 265, 393],\n [-177, 170, 641, -167, -7, 95, -164, 914, -78, 165],\n [-375, -475, -1019, 421, -46, 625, 572, -636, 713, -601],\n [364, -341, 402, 13, 93, -700, -813, -13, -185, -524],\n [887, -529, -416, -48, 587, -891, 58, 451, 1028, 363],\n [-215, 910, 941, -255, 507, -967, -847, 0, -559, 214],\n [-556, 130, 621, 217, -56, 17, -189, 1091, 10, 471],\n [402, 602, 366, -797, -187, -470, -146, -630, -673, 637],\n [405, -647, 270, 684, -19, 348, -330, 348, -194, -649],\n [-641, 289, 424, -152, 23, 77, -524, 869, 148, -317]]\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[[40, -88, -320, -152, -290, 504, -94, -212, -324, -660],\n [-260, -267, 311, -129, 116, -124, 196, 375, 44, 437],\n [164, 65, -81, 13, 42, 146, -96, -101, -142, -181],\n [-216, -65, 139, 8, -23, -259, 134, 149, 233, 314],\n [-136, -367, 309, -240, 207, 187, 138, 411, -273, 254],\n [-84, 29, -415, -46, -478, 257, -59, -331, -21, -626],\n [112, 414, 80, 367, 164, -669, -35, -128, 541, 473],\n [92, 253, -457, 115, -388, 104, -152, -473, 88, -591],\n [200, 413, -93, 315, 57, -404, -117, -267, 354, 119],\n [-492, -603, 249, -402, -120, 261, 291, 489, -213, 150]]\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[[-661, -5, -504, 156, 78, -97, -97, 84, -671, 115],\n [59, -87, 990, -875, -614, -333, -988, 69, 133, -477],\n [-183, -170, 832, -66, -237, 265, 132, 54, -355, 427],\n [160, 565, 191, -433, -718, -536, -591, 380, -498, -778],\n [-62, 214, -304, 224, 101, 279, 277, -84, -406, 2],\n [-31, 495, -394, 161, 13, 335, 361, -365, -186, -126],\n [-20, 46, 79, 481, 158, 353, 697, 121, -915, 412],\n [-553, 272, 558, -121, -535, 443, 141, -233, -25, 373],\n [-199, -369, 19, -101, 82, -30, -294, 61, 456, 159],\n [220, -359, -306, 414, 805, 468, 627, -429, 151, 402]]?\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[[-27, -154, -31, -26, -122, 545, 584, -398, -94, -673],\n [-339, -131, -165, 428, -471, -246, 547, -351, -797, -378],\n [-127, 437, -40, -118, -31, 484, 708, -1008, -53, 82],\n [-538, 64, -571, -486, -42, 452, 113, 162, -22, 388],\n [-153, -404, 196, 881, 94, -777, -659, 443, -145, 268],\n [263, 738, 210, -474, -117, 692, -104, -506, 700, 721],\n [566, -127, -446, 289, -1207, 367, 124, -333, -164, -527],\n [308, 201, -137, 196, -1081, 333, -587, -1, 237, 527],\n [-574, -53, -475, -256, 593, -129, 330, 72, -227, 188],\n [397, 90, 567, 187, -67, -128, -709, 217, 441, 331]]\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[[-285, -133, -418, -152, 19, -152, -323, -399, -342, 304],\n [-240, -112, -352, -128, 16, -128, -272, -336, -288, 256],\n [195, 91, 286, 104, -13, 104, 221, 273, 234, -208],\n [-315, -147, -462, -168, 21, -168, -357, -441, -378, 336],\n [-300, -140, -440, -160, 20, -160, -340, -420, -360, 320],\n [-270, -126, -396, -144, 18, -144, -306, -378, -324, 288],\n [-105, -49, -154, -56, 7, -56, -119, -147, -126, 112],\n [270, 126, 396, 144, -18, 144, 306, 378, 324, -288],\n [285, 133, 418, 152, -19, 152, 323, 399, 342, -304],\n [-330, -154, -484, -176, 22, -176, -374, -462, -396, 352]]\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[[-352, 137, -317, 110, -435, -365, 431, 284, 136, 15],\n [-94, 17, -267, 40, 105, -83, 307, -90, -56, 197],\n [366, 85, 604, -81, -236, 390, -683, 94, -30, -491],\n [-526, 40, -710, 440, 370, 45, 589, -471, 36, 274],\n [572, 121, 91, -260, 459, 512, -234, -411, -538, 119],\n [-886, 253, -102, 305, -568, -17, -686, 223, 379, -691],\n [112, 101, -84, 247, 142, 362, 197, -328, -106, -29],\n [-823, -218, -211, 709, 38, -69, 122, -159, 667, -199],\n [-74, 140, -27, 217, -611, -198, 483, 331, 191, -150],\n [254, 106, 7, -3, -1, 174, 163, -95, -179, 28]]\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[[-212, -539, 462, -1054, -160, 619, -70, 211, -57, -1228],\n [509, 472, -268, 110, 28, -925, 466, 1, 277, 84],\n [164, -107, 289, -318, 553, 126, -509, -91, -328, -622],\n [63, -265, 343, 190, 1030, 988, -1056, -517, -464, -232],\n [86, -124, 62, -555, -239, -128, 379, 337, 122, -670],\n [-124, 86, 305, -229, -588, -97, 13, 114, 148, 19],\n [-812, 231, 596, 559, 777, 46, 495, 137, -432, 206],\n [-254, -341, 356, -951, 274, 1007, -417, -275, 128, -1127],\n [32, 593, -285, 32, 750, -311, 354, -427, 387, -120],\n [-11, 636, -442, 1055, -85, -517, 391, -283, 347, 1378]]\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[[-340, 118, -529, -97, -390, 36, 257, 46, 129, -135],\n [-376, 6, -492, -226, -90, 36, -329, -134, 353, -118],\n [567, -273, 405, -473, 1, -291, -108, -18, -440, -512],\n [-229, 24, 105, 574, 359, 219, -119, -92, 352, 655],\n [141, 297, 390, 338, 299, 147, 18, 174, -148, 311],\n [-278, 484, -316, 282, -372, 186, 671, 318, -95, 128],\n [-133, -484, -56, 307, -1, -33, 147, -272, 312, 342],\n [-675, 72, -1017, -198, -669, 45, 336, -30, 369, -219],\n [267, -235, 355, 199, 73, -75, 230, -30, -156, 144],\n [-424, -702, -249, 343, 246, 24, -387, -562, 805, 557]]\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[[281, 6, 112, -143, 414, -103, 66, 187, -235, 175],\n [368, 228, 121, 309, 376, 362, -58, -86, -158, -122],\n [-467, -192, -129, -95, -546, -236, 25, -175, 136, -16],\n [116, -252, -165, -427, -12, -568, 212, 190, 152, 124],\n [-329, -65, -221, 17, -543, -1, -49, -72, 469, -190],\n [-4, 416, 260, 402, 292, 850, -342, 168, -86, -38],\n [-459, -150, 34, 101, -426, -153, 28, -453, -285, 9],\n [11, -105, 76, 68, 17, -217, 127, -362, -411, 34],\n [-92, -49, 66, 57, -43, -72, 35, -209, -250, 35],\n [53, 40, 264, 293, 224, 63, 42, -475, -729, 55]]?\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 10x10 matrix:\n[[118, 199, -223, 385, -112, -86, -105, 235, -221, 132],\n [-229, -389, -103, -217, 21, -439, -1, 18, -62, 58],\n [2, 4, 116, -112, 42, 134, 44, -102, 106, -68],\n [-21, -34, 310, -336, 119, 321, 122, -281, 287, -182],\n [98, 166, -46, 182, -42, 86, -34, 72, -56, 28],\n [-135, -231, -381, 189, -105, -621, -123, 294, -330, 222],\n [-14, -26, -430, 406, -154, -506, -162, 376, -392, 252],\n [-199, -337, 109, -385, 91, -157, 75, -160, 128, -66],\n [-23, -37, 385, -413, 147, 403, 151, -348, 356, -226],\n [4, 8, 232, -224, 84, 268, 88, -204, 212, -136]]\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[[465, -32, -98, 91, -5, 188, 223, 164, -149, 559],\n [532, -369, -72, 183, 251, 366, 260, 158, -90, 407],\n [-106, 198, -58, 93, -111, 72, 42, -181, -280, 170],\n [388, 24, 330, -291, -77, -6, 532, -81, 206, 532],\n [468, 219, -410, 348, -155, 297, 88, 203, -596, 836],\n [456, 54, 348, -402, -131, -147, 484, 74, 376, 511],\n [-38, -191, -540, 625, 224, 431, -358, 98, -612, -68],\n [264, -235, -136, 23, 126, -41, -180, 426, 222, -102],\n [26, -464, 322, 181, 417, 620, 630, -691, -268, 180],\n [12, 305, 568, -661, -306, -461, 408, -162, 570, 158]]\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[[-141, -481, 46, 298, -635, -1084, 495, -517, 124, 90],\n [-313, -147, -98, -179, 87, -550, -500, -486, -19, -10],\n [-47, -1, -709, -7, -56, -572, 77, -46, -48, -557],\n [-492, 232, -730, -660, 794, -88, -1270, -168, -230, -482],\n [295, 110, -171, 329, -503, -289, 657, -9, 123, -33],\n [129, 90, -52, -108, 344, -305, -694, -565, 26, -272],\n [182, -85, 598, 118, 33, 487, 142, 143, 45, 296],\n [-86, 179, -286, -224, 317, 139, -408, 57, -85, -204],\n [511, 4, 492, 332, -150, -21, 192, -319, 174, 96],\n [-172, -307, 453, -79, 170, -51, -331, -249, -8, 193]]\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[[-15, -1, -7, 3, 30, -23, -20, -21, -9, -9],\n [495, -324, -308, 342, -430, 248, 275, 406, 164, -186],\n [213, -47, 7, 33, -330, 239, 218, 249, 105, 45],\n [-204, 119, 105, -123, 200, -123, -129, -179, -73, 57],\n [-387, 372, 420, -414, 150, -24, -87, -222, -84, 306],\n [-162, 183, 217, -207, 20, 29, -7, -71, -25, 165],\n [-468, 336, 336, -360, 360, -192, -228, -360, -144, 216],\n [3, -112, -168, 138, 170, -156, -117, -86, -40, -150],\n [-375, 281, 287, -303, 270, -137, -170, -279, -111, 189],\n [147, -184, -224, 210, 10, -52, -13, 50, 16, -174]]\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[[350, 322, -207, 158, 184, 17, 158, 35, -184, -226],\n [-463, -458, -297, -448, 61, 77, -160, -184, 182, -4],\n [-71, -100, 60, -62, -61, 10, -506, 337, -278, -326],\n [-354, -307, 82, -186, -108, -7, 193, -312, 402, 437],\n [-417, -431, -504, -508, 179, 113, -193, -173, 92, -185],\n [-399, -380, 85, -248, -131, 9, -226, -34, 154, 130],\n [-142, -146, -299, -218, 132, 57, 50, -165, 88, -46],\n [-412, -380, -165, -334, 10, 41, 140, -349, 368, 284],\n [-244, -237, 387, -36, -268, -42, -477, 283, -78, 7],\n [-402, -382, -173, -342, 12, 47, -2, -243, 264, 158]]\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[[94, 99, -499, -110, 42, -741, -90, 212, 26, 826],\n [73, 94, 302, 101, -4, 620, 104, 532, -423, -151],\n [-140, -78, -300, -3, 1, -553, -221, -654, 416, 28],\n [-223, 115, -343, -10, -67, 326, -451, -166, 245, -187],\n [-78, -470, 345, 287, 458, 132, 633, 65, -20, -476],\n [-1, 255, -476, -257, -223, -246, -428, -49, 205, 445],\n [139, 365, -294, 50, -134, -347, -347, 419, -407, 773],\n [208, -159, 442, 235, 186, -355, 509, 225, -442, 158],\n [-32, -255, 443, 386, 256, 66, 350, -83, -244, -406],\n [-148, 68, -542, 20, 6, -510, -404, -342, 288, 312]]?\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[[137, 375, -69, -158, -187, 132, 319, -254, 336, 48],\n [-117, 436, -94, 26, 78, 80, 576, -554, 595, 3],\n [460, 242, -26, -384, -518, 184, -70, 184, -58, 102],\n [-172, -260, 44, 168, 212, -112, -164, 104, -176, -48],\n [-84, 276, -60, 24, 60, 48, 372, -360, 384, 0],\n [-372, -67, -5, 292, 405, -116, 201, -280, 197, -75],\n [311, 319, -49, -282, -367, 164, 127, -34, 142, 78],\n [-201, -371, 65, 206, 255, -148, -267, 190, -284, -60],\n [-128, 8, -8, 96, 136, -32, 104, -128, 104, -24],\n [218, 212, -32, -196, -256, 112, 76, -12, 86, 54]]?\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[[81, 823, 491, -304, 214, -182, -156, -139, 249, 95],\n [473, -41, 201, -243, 86, 16, 319, -334, 103, -670],\n [-583, -625, -561, 420, -468, 342, -46, 711, -327, 519],\n [52, -297, -179, 544, -49, 94, -275, 206, -540, 158],\n [-12, -702, -506, 834, -610, 728, 356, 282, 312, -58],\n [83, -258, -85, -79, 391, -456, -307, -228, -609, -12],\n [217, 241, 207, -135, -195, 302, 430, -125, 651, -380],\n [52, -290, -95, -141, -367, 398, 561, 108, 384, -427],\n [368, 540, 386, -125, -210, 398, 543, -291, 1066, -487],\n [640, 177, 233, 890, -4, 296, -286, -41, -340, -170]]?\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 10x10 matrix:\n[[-290, 237, -486, -47, 618, -106, 774, 300, -924, 197],\n [159, -400, 193, -358, -174, -161, -146, -344, 5, 34],\n [466, 148, -90, -7, -155, -497, -138, -159, -152, 243],\n [-461, -127, 234, -104, 333, 283, 14, -206, 141, -111],\n [-427, -771, 821, 64, 67, 576, -402, -257, 467, -108],\n [-343, -636, 120, -762, 376, -52, 374, -467, -533, 45],\n [240, -113, -163, -140, -127, -220, 148, 62, -328, 109],\n [562, 74, -532, -587, -161, -785, 342, -195, -704, 237],\n [-432, -34, 238, 574, 207, 612, -12, 432, 204, -96],\n [498, 98, -273, 226, -600, -63, -60, 473, 74, -55]]\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[[302, -142, -190, 765, -576, 194, -381, -256, 508, 443],\n [272, -186, 493, -231, 587, 104, 132, -304, -454, 293],\n [492, 72, 125, -501, 236, -128, 599, -991, -874, 33],\n [306, -200, -720, 195, -419, -807, -78, -952, -52, 470],\n [106, 517, -34, -93, 349, 57, 726, 268, -133, -778],\n [-670, 694, -103, 412, -771, -19, -501, -374, -262, 165],\n [-937, 490, -678, 177, -805, 18, -17, -441, 366, -722],\n [-18, -663, -828, 69, -885, -25, 397, -111, 763, -197],\n [-83, -644, -454, -700, -137, 456, 348, -105, 576, -629],\n [593, -522, 20, -653, 588, -691, -515, -96, -155, 388]]?\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[[-294, -78, 336, 214, -727, -357, -433, -444, 2, -263],\n [507, -389, 187, 162, 1260, -782, -141, 384, -847, 110],\n [217, -670, 296, 374, 191, -482, -489, -378, -350, -46],\n [-259, 33, 283, -263, 389, -183, -203, -276, -308, 385],\n [157, 765, 21, -571, -98, -103, -220, 484, -125, 1022],\n [-37, -942, 517, 23, 907, -213, -689, -711, -455, 139],\n [-227, -750, 1027, 150, 122, -611, -421, -447, -7, -43],\n [274, -464, 581, 417, 1, -657, -523, 41, -442, 68],\n [-91, 67, -209, -259, 164, 334, -346, -367, -193, 383],\n [554, 180, -304, 429, 232, -456, -307, 450, -991, 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[[-76, -152, 285, -57, -19, -304, -171, -361, -266, 304],\n [32, 64, -120, 24, 8, 128, 72, 152, 112, -128],\n [-68, -136, 255, -51, -17, -272, -153, -323, -238, 272],\n [-80, -160, 300, -60, -20, -320, -180, -380, -280, 320],\n [80, 160, -300, 60, 20, 320, 180, 380, 280, -320],\n [32, 64, -120, 24, 8, 128, 72, 152, 112, -128],\n [-88, -176, 330, -66, -22, -352, -198, -418, -308, 352],\n [-32, -64, 120, -24, -8, -128, -72, -152, -112, 128],\n [48, 96, -180, 36, 12, 192, 108, 228, 168, -192],\n [-64, -128, 240, -48, -16, -256, -144, -304, -224, 256]]?\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 10x10 matrix:\n[[-45, -137, 50, -110, -180, -41, 524, 13, -418, 316],\n [150, -743, 391, 320, -341, 201, -273, 348, -175, -31],\n [34, 859, 29, -681, -151, 422, 192, 327, -94, 58],\n [-547, 12, -87, 325, -9, 231, -388, -286, 291, -198],\n [213, -167, 60, -189, -8, -234, -263, -180, -7, -87],\n [775, -422, -172, 165, 637, -208, 185, 324, 184, 237],\n [401, -836, 58, 276, 153, -536, -199, -207, -25, -7],\n [49, 737, 159, -1006, -314, 706, -69, 299, -179, 117],\n [241, -112, 198, -153, 21, 1095, -450, 742, 219, 114],\n [-346, -164, 576, 468, -870, -264, -720, 20, -87, -768]]\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[[199, -326, -372, 560, 433, 636, -137, -359, 132, -870],\n [-274, 478, 226, -366, -332, -181, 226, 9, -259, 749],\n [291, -148, 365, -447, -309, -1021, -596, 883, 462, 118],\n [78, 98, 288, -384, -670, 350, 518, -96, -508, 252],\n [-18, -545, 278, -350, -44, -1223, -248, 857, 502, 250],\n [-324, -640, -129, 231, 490, -593, -221, 292, 622, -204],\n [10, 340, 415, -533, -653, -315, -137, 350, -30, 443],\n [-579, -101, 10, -50, -104, 345, 893, -440, -434, 479],\n [636, 725, -18, -70, -2, -39, -526, 103, -164, 36],\n [178, -292, 14, -2, 224, -688, -464, 504, 454, -152]]\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[[394, 366, -433, 406, -520, -103, -407, -164, 545, -118],\n [270, 81, -135, -180, 207, 234, -225, -45, -171, -531],\n [-56, -147, 152, -314, 389, 185, 88, 61, -382, -235],\n [-86, -30, 47, 46, -52, -67, 73, 16, 41, 158],\n [474, 243, -333, -44, 29, 230, -427, -119, 23, -665],\n [-322, -231, 289, -148, 199, -38, 311, 107, -227, 277],\n [-88, -123, 136, -202, 253, 97, 104, 53, -254, -83],\n [210, 63, -105, -140, 161, 182, -175, -35, -133, -413],\n [-154, -105, 133, -56, 77, -28, 147, 49, -91, 147],\n [-266, -210, 257, -174, 228, 3, 263, 96, -249, 178]]\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[[285, -105, -105, -180, -285, 150, -210, 180, 60, 75],\n [190, -70, -70, -120, -190, 100, -140, 120, 40, 50],\n [38, -14, -14, -24, -38, 20, -28, 24, 8, 10],\n [-228, 84, 84, 144, 228, -120, 168, -144, -48, -60],\n [342, -126, -126, -216, -342, 180, -252, 216, 72, 90],\n [285, -105, -105, -180, -285, 150, -210, 180, 60, 75],\n [399, -147, -147, -252, -399, 210, -294, 252, 84, 105],\n [-19, 7, 7, 12, 19, -10, 14, -12, -4, -5],\n [-361, 133, 133, 228, 361, -190, 266, -228, -76, -95],\n [133, -49, -49, -84, -133, 70, -98, 84, 28, 35]]\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[[-6, 72, -42, -102, -72, -126, -132, -60, -78, 12],\n [-12, 144, -84, -204, -144, -252, -264, -120, -156, 24],\n [-8, 96, -56, -136, -96, -168, -176, -80, -104, 16],\n [-15, 180, -105, -255, -180, -315, -330, -150, -195, 30],\n [21, -252, 147, 357, 252, 441, 462, 210, 273, -42],\n [6, -72, 42, 102, 72, 126, 132, 60, 78, -12],\n [-6, 72, -42, -102, -72, -126, -132, -60, -78, 12],\n [3, -36, 21, 51, 36, 63, 66, 30, 39, -6],\n [-18, 216, -126, -306, -216, -378, -396, -180, -234, 36],\n [-19, 228, -133, -323, -228, -399, -418, -190, -247, 38]]\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 10x10 matrix:\n[[-71, -150, -701, 6, -282, 734, -513, -716, 52, -813],\n [240, -35, 904, 195, -540, 374, 165, 237, 231, 614],\n [-646, -532, 246, -603, 318, 367, 287, 349, 503, 1479],\n [524, 358, 426, 324, -531, 191, -16, 85, -91, -3],\n [279, -157, -158, 301, -430, 752, -69, -474, 68, 17],\n [-408, 45, -1183, 651, 583, 148, 54, -26, -411, -89],\n [378, -319, -1106, -423, -367, 338, -442, -852, 36, -621],\n [657, 552, 648, 355, -263, -1041, 309, 142, -298, -750],\n [54, -334, 1048, 37, -310, 242, 180, 563, 308, 1112],\n [891, -571, -291, 639, 596, -538, 405, -626, -485, -31]]\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[[388, -1094, -111, 160, 241, -214, -1045, -74, -739, -1095],\n [776, 273, 563, 429, -428, 133, -48, 320, -222, -499],\n [-482, 117, 389, 733, -424, 695, 405, 970, 287, 220],\n [337, -575, -437, 1, 348, -498, -1056, -312, -239, 38],\n [-442, -10, 350, -552, 626, 52, 689, 80, -377, -131],\n [-924, -342, 9, 193, 279, -25, -589, 78, -225, 4],\n [-55, 715, 115, 752, -862, 605, 26, -280, 37, 505],\n [-307, 108, 73, -9, 65, -213, -5, 537, 543, 182],\n [489, -675, -275, -547, 684, -490, 26, 295, 25, -120],\n [-341, -859, -396, 268, -111, 319, -432, -162, -305, -551]]\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 10x10 matrix:\n[[-240, -428, -41, 83, 408, 483, 6, -625, 94, -822],\n [52, 169, -285, -20, -249, 51, -284, 382, -119, 298],\n [40, 118, -129, -23, -158, -13, -126, 225, -64, 202],\n [-168, 213, 123, -339, -394, 43, 424, -233, -16, -174],\n [252, -241, 20, 415, 521, -224, -374, 257, 61, 288],\n [-304, -228, -365, -65, 24, 687, -178, -389, -42, -718],\n [-140, -331, -212, 141, 315, 432, -242, -285, 23, -512],\n [-56, 201, 131, -223, -294, -93, 304, -61, -12, 34],\n [120, -10, 215, 85, 142, -277, 98, 45, 60, 186],\n [184, 13, 135, 145, 142, -313, -48, 219, 32, 346]]\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[[-740, -15, 790, 636, 96, 672, 528, -807, 258, 201],\n [683, -222, -736, 196, -121, -241, -944, 693, -310, -327],\n [-624, -346, 84, 414, 539, 547, 224, -447, -263, 486],\n [-580, 187, 480, -75, -173, -193, 861, -270, 448, -270],\n [-877, -612, -48, 294, 294, 1008, 794, -714, -271, 1251],\n [701, 257, -103, 199, -275, 114, -1047, 99, 108, -210],\n [-797, -91, -54, 356, -113, 425, -117, -685, 319, 35],\n [-601, -418, 234, 281, 297, 661, 520, -510, -288, 689],\n [99, -314, -243, -33, 399, 279, 483, 185, -400, 806],\n [895, 602, 516, -903, -317, -253, -1200, -156, -136, -343]]?\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[[-162, -344, 224, -57, -16, 199, 144, 254, 349, 140],\n [400, 484, -115, -55, 19, -208, -171, -245, -556, -204],\n [-400, 104, -590, 370, 14, -248, -126, -370, 64, -24],\n [372, 456, -114, -48, 18, -198, -162, -234, -522, -192],\n [-368, 80, -524, 332, 12, -216, -108, -324, 72, -16],\n [48, -232, 334, -162, -14, 200, 126, 274, 176, 88],\n [422, 492, -99, -68, 19, -205, -171, -239, -571, -208],\n [-22, -204, 219, -92, -11, 149, 99, 199, 179, 80],\n [234, -200, 512, -291, -16, 253, 144, 362, 79, 68],\n [-466, -508, 67, 94, -19, 199, 171, 227, 601, 216]]?\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[[1038, -56, 236, -137, -407, -352, 363, -15, 583, -1003],\n [1066, 618, 867, -619, -299, -446, 550, -395, 691, -681],\n [299, -202, 902, -1, -201, 8, 184, -392, 323, 106],\n [-345, 372, -656, 26, 434, -24, -481, 87, -684, 789],\n [-217, 173, -314, 60, 151, -6, -456, -120, -510, 882],\n [-391, 472, -12, -483, -319, 308, 587, -336, 573, -530],\n [187, 298, -230, 8, 516, 64, 160, -142, -87, -156],\n [-293, -596, -108, 534, 400, 228, -174, 233, -300, 155],\n [-304, -4, 61, 82, 412, 190, 140, 70, -62, -68],\n [-420, -480, -69, 753, 981, 298, -587, -49, -917, 1241]]?\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[[-460, 70, -110, -56, 228, -436, -736, -170, 88, -335],\n [187, -527, 39, 470, 260, -101, -468, -3, -738, 473],\n [-20, -588, 378, 544, 164, -351, -173, -233, -835, 520],\n [-5, -525, -211, 141, 491, -277, -328, -68, -365, 274],\n [1083, -870, -26, 130, 275, 190, 540, -101, -474, 893],\n [-598, 134, 714, 55, -614, 299, -133, -110, -15, -379],\n [-159, 162, 80, -352, -454, 890, 342, 327, 443, -365],\n [415, 259, 265, 591, -302, 8, -157, 101, -561, 359],\n [763, -823, 337, 19, -7, 270, 813, -231, -328, 697],\n [-463, -14, 150, 90, -18, -119, -695, -90, -114, -264]]\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[[-323, -17, 153, -85, 425, 357, 85, -408, 340, 595],\n [221, 95, -119, 75, -359, -295, -103, 296, -284, -453],\n [335, -295, -105, 25, -185, -180, 80, 360, -160, -445],\n [-235, 71, 97, -45, 241, 209, 17, -280, 196, 387],\n [-33, -231, 55, -55, 231, 176, 132, -88, 176, 187],\n [-36, 144, -8, 20, -72, -49, -69, -16, -52, -14],\n [207, -531, -5, -55, 171, 101, 237, 152, 116, -83],\n [354, -294, -114, 30, -210, -201, 75, 384, -180, -480],\n [-282, 798, -6, 90, -294, -183, -363, -192, -204, 72],\n [122, -598, 46, -90, 334, 233, 293, 32, 244, 108]]\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[[-170, 72, -46, 184, 549, 573, 42, 711, -438, -850],\n [-332, 214, 955, 157, 777, -371, -399, 144, 417, 285],\n [330, -367, 87, -642, -258, 307, 137, 26, 286, 77],\n [335, 99, -349, -148, -933, -308, 205, -938, 113, 736],\n [-248, 327, -58, 603, 356, -46, -263, 593, -338, -550],\n [-500, -1139, -32, -1011, 118, 27, -276, 233, -486, 273],\n [-156, 1208, 199, 729, 69, 258, -104, -100, -799, -246],\n [-269, -35, -721, 762, 256, -336, 366, -359, -69, -175],\n [-581, -738, -1182, 300, -10, -459, 191, -291, -624, -25],\n [58, 765, 441, 374, 152, 246, -304, 520, -230, -414]]?\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[[523, -263, -606, -226, 423, 490, 384, -431, 383, 178],\n [684, 390, 148, -583, 250, -211, 678, -119, -360, -432],\n [-719, -256, 169, 391, -219, -619, -558, 373, 441, -170],\n [-245, -155, 423, 445, -639, 651, -484, -501, -241, -39],\n [625, -417, -729, 458, 789, 190, 228, 185, 339, 79],\n [208, -673, -199, 535, -20, -202, 322, 351, 879, 335],\n [-121, 127, -516, 241, 567, 595, -650, 41, -550, 218],\n [-289, -244, 182, 1143, 191, 360, -668, 526, -35, 555],\n [195, 170, -252, 192, 289, 20, -244, 237, -708, -338],\n [156, 326, 88, -203, -252, 703, 60, -879, -545, -342]]\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 10x10 matrix:\n[[-326, 398, 571, 123, 293, 214, -32, 172, 52, -623],\n [-616, 100, -181, 69, -24, 32, 448, 1300, 624, -197],\n [428, 435, 426, 618, 300, -677, 236, -233, -42, -285],\n [-686, -554, 193, -215, 163, 554, -200, -82, -678, -97],\n [-169, -624, 545, 104, -43, -119, -681, -373, -369, -228],\n [-611, 639, 234, -521, 538, 615, 82, -39, 195, -487],\n [-22, 972, 345, -263, 551, 161, 155, -308, 357, -472],\n [667, -337, -186, 91, -397, -1, -392, -846, -532, 419],\n [-997, -53, -441, -686, 165, 1038, 277, 513, -109, 37],\n [-947, -239, 104, -985, 456, 518, -101, 224, 239, -78]]\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[[-228, -48, 72, -36, 192, -144, 96, 84, 24, 72],\n [-171, -36, 54, -27, 144, -108, 72, 63, 18, 54],\n [-190, -40, 60, -30, 160, -120, 80, 70, 20, 60],\n [19, 4, -6, 3, -16, 12, -8, -7, -2, -6],\n [-133, -28, 42, -21, 112, -84, 56, 49, 14, 42],\n [95, 20, -30, 15, -80, 60, -40, -35, -10, -30],\n [133, 28, -42, 21, -112, 84, -56, -49, -14, -42],\n [399, 84, -126, 63, -336, 252, -168, -147, -42, -126],\n [342, 72, -108, 54, -288, 216, -144, -126, -36, -108],\n [304, 64, -96, 48, -256, 192, -128, -112, -32, -96]]?\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[[-364, -50, 344, 503, -194, -222, -99, -297, 43, 350],\n [-282, -18, 132, 177, -180, -84, -3, -213, 93, 126],\n [57, 6, -42, -60, 33, 27, 9, 45, -12, -42],\n [90, 64, -420, -654, -26, 274, 208, 116, 138, -448],\n [-90, 10, -60, -105, -80, 40, 55, -55, 75, -70],\n [-330, 12, -60, -132, -258, 42, 114, -222, 204, -84],\n [-650, -10, 100, 85, -460, -60, 105, -465, 305, 70],\n [-454, 34, -196, -361, -380, 132, 219, -291, 331, -238],\n [-36, 4, -24, -42, -32, 16, 22, -22, 30, -28],\n [517, -4, -2, 55, 383, -3, -126, 360, -277, 28]]\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[[148, -241, -2, 495, -66, -277, -447, 597, -118, -307],\n [-190, 236, -434, -594, -280, 569, 309, -254, -201, -48],\n [-245, 70, 26, 870, -260, -49, -408, 620, 71, 374],\n [334, -194, 398, -452, 510, -380, 302, -584, 180, -168],\n [-54, -264, -86, 234, 172, -192, -776, -120, -344, 198],\n [-144, -750, 538, -118, 59, -691, -52, -827, -184, 388],\n [-96, -533, 611, 146, 102, -659, 28, -529, 62, 416],\n [-310, 56, -493, 39, -927, 485, 253, 667, -266, -303],\n [110, 44, 18, 378, 76, -95, -247, 406, 75, -92],\n [-102, 107, 62, -153, 164, 66, 52, -415, 61, 339]]\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[[-501, -214, 361, 119, 284, -434, 328, 537, 298, 293],\n [-411, -238, 391, 17, 380, -458, 292, 435, 250, 287],\n [102, -43, 58, -136, 146, -53, -35, -117, -53, 5],\n [-33, -165, 253, -187, 374, -275, 77, 22, 33, 132],\n [90, 55, -90, 0, -90, 105, -65, -95, -55, -65],\n [-93, 88, -127, 187, -248, 128, 14, 111, 44, -41],\n [-396, -242, 396, 0, 396, -462, 286, 418, 242, 286],\n [-78, -311, 478, -340, 698, -521, 153, 59, 71, 253],\n [459, 4, -39, -357, 192, 84, -230, -509, -256, -125],\n [-279, 106, -141, 357, -372, 126, 100, 319, 146, -5]]?\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[[332, 207, -454, -70, 257, 443, -23, 120, -634, 362],\n [-67, 1031, 741, -992, 413, 770, 372, 477, -73, 754],\n [378, 544, -654, 358, 158, -354, -122, 282, 282, 9],\n [-419, -275, -169, -113, 434, -590, 294, -841, 28, -602],\n [-810, -525, 1480, 631, 340, 16, -342, 38, 366, -747],\n [-303, -39, 280, -375, 146, 200, 521, -183, -119, 40],\n [-12, -15, -41, -689, 1331, 142, 441, -1002, -308, 489],\n [-1111, -962, 508, 719, -586, -3, -10, -215, 492, 96],\n [-264, 154, -32, -97, 13, -454, 620, -164, -231, 372],\n [568, 1186, 130, -140, -289, 195, -231, 1172, 164, 369]]\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[[249, 105, 1387, -19, -1237, 124, 1056, 512, -972, 525],\n [-268, -363, 721, 789, -503, 1101, -633, 657, -944, -776],\n [-773, -806, 131, 15, 563, -132, 178, 307, 1048, 11],\n [-216, -93, 1222, 687, -1035, 340, 1113, 1626, -280, -675],\n [520, -327, 809, 383, -484, -162, 950, 783, -456, 259],\n [297, -1184, 370, 562, -42, 259, 255, 115, 740, -91],\n [-120, -702, -173, -451, 274, -6, -892, -963, 188, 505],\n [-600, 235, 21, 26, 243, 240, -276, 156, -59, -6],\n [-288, -178, 281, 326, -189, 51, 52, 787, 125, -277],\n [364, 1013, -298, -838, -20, -773, -38, -349, -785, 814]]?\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[[-397, 360, 379, -183, -11, -597, 418, -270, 509, -118],\n [42, -765, 378, -432, -85, -319, 107, 369, -506, 43],\n [-693, -552, 1074, -122, -407, -72, 329, 150, -699, 104],\n [864, 415, -1598, -114, 491, -688, 89, 80, 97, -163],\n [-501, -218, 856, 460, -296, 660, -541, -127, -402, -288],\n [559, 88, -514, -74, 352, -409, 306, 31, 398, 561],\n [260, 71, -511, 149, -246, 319, 9, -306, 169, 314],\n [516, -155, -616, 112, 21, -768, 507, -222, -185, 633],\n [-438, 175, 407, -45, -456, 416, 420, -338, 461, 489],\n [-99, -56, 252, 286, 19, -140, -44, -85, -252, 17]]\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 10x10 matrix:\n[[76, -2, -241, 106, -190, 52, -50, -112, 164, 61],\n [206, -186, 55, 26, 312, -158, 160, 354, -196, 39],\n [-273, 196, 68, 332, -715, 529, 45, -689, 268, 247],\n [255, -338, 357, 126, 641, -115, 401, 575, -488, 256],\n [-67, 24, -298, -44, 311, 131, -287, -107, 68, 363],\n [-517, 302, 235, -80, -145, 401, -218, -557, 76, 182],\n [-312, 186, 351, -332, 128, -72, -119, -36, -120, -279],\n [309, -56, -848, -118, 103, -273, -400, 129, 328, -41],\n [-62, 222, -437, 50, -764, 94, -244, -490, 508, -225],\n [-20, 10, -379, -66, 330, 76, -318, -64, 92, 331]]\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 10x10 matrix:\n[[-110, -3, 75, -357, 437, 269, 665, -190, 3, -74],\n [662, -146, 515, -120, -76, -253, 437, 163, -197, -379],\n [593, -673, 213, 195, 71, 221, 266, 385, 470, -541],\n [-546, -659, -414, 223, -277, 515, -579, -54, 249, 377],\n [-480, 243, 494, 387, 393, -47, 123, -511, -376, 610],\n [-191, 79, 519, 607, 287, -109, -36, -262, -167, 388],\n [-1184, -425, -424, 386, -187, 294, -797, -104, -109, 448],\n [-194, -502, 33, -42, 376, 687, 427, -312, 314, 284],\n [425, -316, -57, -138, -14, 270, 211, 107, 363, -170],\n [1010, -326, 386, 330, -226, 58, -16, 53, 393, 113]]\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[[-712, 355, 299, 62, -695, -14, -616, -335, 18, -160],\n [-551, -195, 499, -5, -303, -277, -799, -37, 277, -20],\n [-815, 1, 795, -201, -92, 75, -1000, -137, 55, -449],\n [-900, 15, 62, -520, 355, 74, -722, 319, 438, 517],\n [327, 215, 27, 625, 557, 35, 327, -62, 55, -47],\n [-756, 227, 64, 25, -208, 263, -757, -316, -1, -389],\n [-951, 136, -131, -644, 316, 505, -1315, -5, 367, -258],\n [-275, 519, -233, 490, -165, -37, -399, -209, 295, 194],\n [-362, -208, -625, -985, 550, 508, -390, 265, 388, 81],\n [440, -569, 91, -253, 218, 121, 413, 242, -999, -404]]?\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[[-198, 45, -81, 189, -162, -180, 27, -54, -180, -27],\n [88, -20, 36, -84, 72, 80, -12, 24, 80, 12],\n [-418, 95, -171, 399, -342, -380, 57, -114, -380, -57],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n [330, -75, 135, -315, 270, 300, -45, 90, 300, 45],\n [-396, 90, -162, 378, -324, -360, 54, -108, -360, -54],\n [88, -20, 36, -84, 72, 80, -12, 24, 80, 12],\n [440, -100, 180, -420, 360, 400, -60, 120, 400, 60],\n [-198, 45, -81, 189, -162, -180, 27, -54, -180, -27],\n [-352, 80, -144, 336, -288, -320, 48, -96, -320, -48]]\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 10x10 matrix:\n[[-327, -60, -888, -604, 168, 59, 159, 1033, 408, -242],\n [-101, 24, -72, -279, -401, -129, 111, -49, -872, -51],\n [-16, 394, 160, 249, 169, 564, -392, -26, 630, 129],\n [584, 108, -582, -198, 134, -921, 768, 379, -430, 573],\n [24, 316, 126, 28, -198, 386, -260, -108, 214, 212],\n [280, 690, -381, -176, -119, -198, 274, 237, -877, 503],\n [105, -153, -154, -374, -503, -329, 262, -13, -455, 170],\n [-214, -34, 467, 189, -156, 804, -646, -299, 1099, -96],\n [-345, -629, -754, -842, -311, -699, 604, 637, -995, -490],\n [374, 145, -1109, -549, 235, -842, 837, 995, -262, 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[[236, -187, -216, -17, 178, -391, 364, 275, 184, 325],\n [668, -21, -13, -91, 197, 153, 416, -585, -193, 671],\n [204, -312, 57, 80, 149, -149, 353, 21, 248, 224],\n [-508, 106, -272, -14, -116, -411, -293, 775, 133, -434],\n [-264, 62, -452, -70, 8, -622, -52, 854, 152, -130],\n [396, 368, -206, -212, 34, 171, 7, -415, -461, 412],\n [44, -631, 468, 283, 118, 65, 376, -133, 520, -23],\n [-136, -350, 394, 206, -10, 170, 68, -122, 302, -214],\n [-52, -242, -89, 66, 87, -353, 195, 409, 300, 6],\n [588, 247, -235, -207, 135, 77, 228, -437, -387, 627]]\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[[-206, 518, -703, 111, -228, -287, 1083, 190, 768, 1000],\n [447, -135, 211, -60, 458, 245, -510, 242, -21, -222],\n [-628, 69, 823, -287, -503, -269, 411, 667, 319, -145],\n [-1, 280, -209, 230, 56, 295, 272, 168, 86, 437],\n [-230, 293, -317, 647, -345, 491, 831, -77, 259, 799],\n [248, 580, -979, 797, 265, 229, 208, 280, -88, -199],\n [-30, 1103, 27, 828, -151, 452, 834, 1164, 910, 355],\n [-361, 359, -323, 358, -333, 99, 895, 254, 339, 621],\n [-103, 214, -375, 275, -198, 162, 585, -217, 289, 737],\n [37, 370, -682, 324, 318, 5, 389, 768, 429, -78]]?\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[[-8, 180, -60, -97, 119, 80, 16, 33, 110, -178],\n [-154, 84, 84, -77, 91, -14, 140, -105, 28, -98],\n [-396, 216, 216, -198, 234, -36, 360, -270, 72, -252],\n [-457, 220, 260, -213, 251, -55, 414, -318, 65, -262],\n [-275, -172, 268, 33, -47, -173, 234, -258, -149, 142],\n [465, 244, -436, -31, 49, 271, -398, 426, 223, -194],\n [-462, 252, 252, -231, 273, -42, 420, -315, 84, -294],\n [-156, 612, -108, -357, 435, 228, 168, 9, 354, -618],\n [-530, 172, 332, -203, 237, -102, 476, -387, 24, -222],\n [-534, -60, 420, -81, 87, -210, 468, -441, -120, 6]]\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, 189, 57, -237, 21, -37, 27, 162, -143, -175],\n [-40, -54, -110, -318, -140, 158, -150, -32, -86, 85],\n [-386, 155, -261, -134, 266, -205, 331, -413, -608, 457],\n [-85, 333, 87, 441, 588, -608, 623, -99, -365, 45],\n [193, 144, 106, 255, 64, -61, 134, 4, 27, -111],\n [326, 66, 390, 585, 219, -316, 152, 411, 441, -494],\n [-178, -292, 168, 619, 17, -62, -58, 91, 567, -104],\n [505, 451, 209, 98, 267, -296, 339, 196, -228, -323],\n [-658, -417, -401, -186, -344, 447, -309, -533, -24, 626],\n [293, -131, 331, 539, -82, 14, -129, 345, 665, -438]]\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 10x10 matrix:\n[[414, 380, -232, -6, -18, 260, -276, 530, -390, -358],\n [-15, -171, 49, -55, 53, 85, 192, -48, 156, 233],\n [-107, 457, -164, 195, 44, -76, -651, 303, -179, -557],\n [-188, 307, -448, 71, -94, -437, -176, 144, -638, -412],\n [318, -35, 34, -226, 183, 567, 122, 336, 97, 297],\n [438, 333, -94, -379, 162, 596, -141, 520, -415, 21],\n [470, -300, 347, -304, 117, 687, 401, 53, 379, 580],\n [-130, 84, 84, 481, -149, -318, -398, -106, 319, -473],\n [-430, 277, -72, 487, -76, -511, -648, -70, 116, -646],\n [-29, -171, 529, -496, -110, -49, 318, -754, -143, 410]]\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 10x10 matrix:\n[[-11, -5, 13, 19, -10, 6, 12, 16, 6, -5],\n [209, 95, -247, -361, 190, -114, -228, -304, -114, 95],\n [22, 10, -26, -38, 20, -12, -24, -32, -12, 10],\n [220, 100, -260, -380, 200, -120, -240, -320, -120, 100],\n [66, 30, -78, -114, 60, -36, -72, -96, -36, 30],\n [242, 110, -286, -418, 220, -132, -264, -352, -132, 110],\n [77, 35, -91, -133, 70, -42, -84, -112, -42, 35],\n [77, 35, -91, -133, 70, -42, -84, -112, -42, 35],\n [231, 105, -273, -399, 210, -126, -252, -336, -126, 105],\n [88, 40, -104, -152, 80, -48, -96, -128, -48, 40]]\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[[-176, 235, 37, 692, 56, 31, -1001, -662, 81, -156],\n [837, 56, 980, 138, 9, 542, 303, -535, -459, 536],\n [-163, -438, 315, 120, 434, 398, -1031, -566, 19, 516],\n [364, 476, 306, 794, 158, 54, -699, -199, -346, 5],\n [-1057, -727, -484, -503, -610, -420, -540, 14, 510, 316],\n [168, -85, -505, 86, 385, 16, -334, -523, 196, -302],\n [-122, 560, -926, 439, 114, -453, -8, -88, 380, -1150],\n [-153, -295, 430, -143, -694, 60, -118, -478, -26, 590],\n [-498, 227, 60, 62, -272, -60, 205, 71, 220, -325],\n [-179, -165, -565, 311, 21, -553, -981, 222, 87, -4]]\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[[267, -344, -231, 140, -20, -248, -175, 64, -364, 409],\n [266, -115, -180, -90, -160, -428, -203, -123, -346, 570],\n [490, -209, -175, 188, 533, 5, 94, -152, 36, 304],\n [37, 438, 190, -294, 115, 3, 138, -391, 314, 37],\n [-140, -252, -332, 129, -314, -252, -108, 536, -259, -53],\n [-652, 355, 549, -392, -845, 51, -286, -214, -192, -190],\n [723, -187, -405, 19, 374, -484, -32, -235, -185, 812],\n [39, -588, -341, 604, 386, 318, 139, 674, 4, -427],\n [-82, 462, -257, -280, -15, -303, 263, 191, 408, -162],\n [393, 11, -307, -134, 44, -500, -52, -125, -142, 579]]\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[[24, 336, 282, 534, -578, 585, 608, -170, -113, -56],\n [254, 475, 419, 739, -997, 367, 965, -343, -154, 400],\n [290, -212, 186, -428, -414, -470, -296, -165, 106, 369],\n [86, 533, 272, 636, -460, 716, 594, -78, 6, 126],\n [-384, -212, 673, -486, 1365, -19, -441, 501, -296, -595],\n [222, -638, -29, 356, -342, 195, -140, 870, -372, -526],\n [136, 146, 21, 152, -1036, -308, 388, 101, -193, 121],\n [721, -88, 405, 301, -132, 729, -13, -447, 80, 455],\n [582, -874, -1053, 387, -569, -347, -28, 370, -599, -342],\n [445, -236, 373, 596, -800, 457, 376, 318, -413, -152]]\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[[-317, -45, 26, -580, 130, 123, 44, -595, -78, 231],\n [-77, 353, -368, 31, 44, 214, -36, -316, -57, 37],\n [5, -359, 330, -370, 10, -41, 68, -67, 68, 133],\n [-323, 169, -94, 42, 78, -129, -40, -83, -176, -75],\n [-263, -405, 436, -463, 73, -215, 63, -95, -53, 103],\n [-352, 390, -358, -89, 119, 122, -45, -460, -181, 38],\n [382, -114, 76, 272, -122, 4, 6, 388, 160, -74],\n [266, 422, -456, 462, -72, 232, -64, 76, 54, -98],\n [-264, -146, 222, -65, 50, -273, 0, 107, -119, -66],\n [-114, 302, -260, 248, 22, -4, -58, -4, -104, -106]]?\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 10x10 matrix:\n[[212, -60, -88, 618, 532, 662, -330, -106, 180, -168],\n [281, 129, -241, 12, -554, -116, 237, 289, -199, 191],\n [-288, 96, 49, -282, 4, 0, 112, -107, 35, -221],\n [175, -227, 175, -353, 109, -350, 177, -345, 37, 176],\n [432, 28, -223, 621, 196, 595, -159, 72, 73, -35],\n [-136, 88, -12, 181, -236, -139, -170, 407, -108, 141],\n [-494, 74, 183, 525, 362, 221, -635, 388, 111, -103],\n [-145, 751, 511, -337, 56, 253, 388, 466, 447, -263],\n [612, -474, -757, 324, -349, 97, 53, -408, -433, 174],\n [-132, 726, 489, 80, 3, 225, 67, 826, 373, -58]]\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[[136, -314, 176, -591, -488, 154, -464, -229, -157, 21],\n [-842, -119, 466, 41, -160, -58, 611, 587, -678, -24],\n [82, 47, -447, 148, 79, -76, -239, -458, 436, -224],\n [175, 257, -393, 285, 242, -291, 68, -199, 406, -337],\n [162, -37, -252, -61, -56, 16, -315, -375, 275, -100],\n [407, 140, -466, 127, 243, -703, 211, -39, 409, -779],\n [311, 572, -238, 343, 199, 385, -389, -551, 525, 441],\n [376, 736, -247, 134, -55, 20, -346, -648, 527, -47],\n [103, 299, -221, 239, 178, -255, 150, -73, 248, -261],\n [115, 329, -265, 176, 20, 221, -366, -554, 414, 150]]?\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[[917, 660, 504, 24, -299, 608, -153, -367, 277, 280],\n [-371, 1319, 108, -739, -254, 705, 460, -299, -162, -37],\n [88, 21, 93, -30, 214, -31, 7, -286, -187, 464],\n [-313, 779, 94, -1017, -656, 296, 211, -178, -132, -142],\n [-123, -333, -591, 423, -116, -521, -539, -291, 678, -36],\n [-486, 15, -688, 198, -582, -287, 248, -51, -167, -487],\n [983, -1154, -88, -246, -44, -891, -658, -270, -158, 1077],\n [498, -898, -785, -948, -424, -977, -452, 165, -434, 424],\n [1005, 51, 1662, 37, 237, 607, -22, -533, -515, 897],\n [813, 84, -312, -227, 173, 34, -252, 64, -62, 372]]?\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[[382, -383, -109, 144, 154, 98, -109, 41, 57, -140],\n [-292, 361, 49, -206, -178, -72, 25, -105, 13, 184],\n [-497, 214, 80, -512, 90, -726, 311, -123, 136, 174],\n [-408, 424, 297, -197, -194, 69, 96, -666, 4, 134],\n [-589, 249, 373, -116, 72, -332, 418, -314, -113, -38],\n [-376, 339, 491, -85, -151, 262, 130, -1110, -17, 15],\n [523, -802, -65, 172, 473, -153, 44, -50, 116, -339],\n [-596, 376, 124, -449, -15, -602, 305, -85, 56, 201],\n [-509, 857, 266, 52, -559, 563, -79, -319, -221, 243],\n [-278, 376, 429, 459, -254, 697, 62, -384, -352, -134]]?\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[[-712, -36, 628, 210, 1323, 604, -115, 973, 644, -1306],\n [779, -449, -1135, -355, 0, -599, 327, 454, -850, -300],\n [-136, -274, 68, 150, 39, 355, 78, -819, -557, 862],\n [-1120, -845, 1072, 579, 1045, 1300, -33, 181, 8, -128],\n [-373, 304, 82, -521, -587, -586, -578, 0, 257, 368],\n [-1272, -469, 1329, 32, 840, 889, 30, 784, 273, -868],\n [575, 467, -445, -1, -399, -636, 521, -589, 379, 234],\n [746, 239, -1054, -93, 413, -92, 283, -413, -996, 298],\n [-521, 54, 849, -233, -642, -119, 203, -167, -134, 288],\n [-395, -610, 459, 738, 1481, 1106, 147, 875, 666, -1279]]\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[[360, -204, -180, 35, -14, -278, 346, -318, 130, 325],\n [62, -32, 169, 1131, -8, 221, 584, 4, -48, 450],\n [317, -916, -240, 368, -646, -385, 328, -49, 687, 90],\n [-440, -30, -143, -119, -24, 253, -578, 484, 38, -344],\n [-527, -122, -238, -204, 443, 27, -449, 418, 321, 565],\n [-256, -340, -950, 448, 50, 493, -512, 702, 309, 313],\n [-298, -62, 72, -1097, 317, -233, -499, 53, 301, -421],\n [-232, -387, 397, 809, -22, -16, 423, 135, 402, 272],\n [-5, 524, 378, -39, -108, 123, -14, -65, -471, 45],\n [-213, 90, 543, -295, 264, -112, 68, -113, 67, -374]]\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[[-886, -285, -266, 212, 86, 450, -86, 675, -321, -262],\n [54, -461, -138, 172, 579, -256, 195, -700, 199, 344],\n [109, 421, 203, -254, -1228, 322, 685, -398, -580, -277],\n [401, 536, -675, 829, -474, 613, 577, -620, 211, 367],\n [22, -97, -450, -509, 157, -720, 734, -759, -437, -99],\n [-1057, 268, -731, -221, -560, -315, 446, 459, 18, 101],\n [-535, -621, -1125, -73, 497, 108, 493, -505, -343, -290],\n [-429, -162, -453, -257, -770, -312, 918, -381, -674, 46],\n [686, 540, 136, 225, -1441, 1341, 898, -331, -1099, -342],\n [-138, -59, 362, -235, 386, -1073, -35, -156, 601, 686]]\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[[324, 152, 14, -296, 22, 64, -24, -162, 0, 160],\n [-84, -22, 11, 16, -137, -134, 144, 27, 30, -20],\n [-305, -81, 39, 62, -489, -479, 514, 99, 107, -74],\n [484, 176, -22, -264, 418, 440, -440, -198, -88, 176],\n [616, 318, 51, -664, -177, -74, 184, -333, 50, 340],\n [7, 41, 32, -138, -284, -253, 298, -36, 65, 50],\n [232, 110, 11, -216, 7, 38, -8, -117, 2, 116],\n [104, -22, -55, 152, 541, 498, -568, 9, -122, -36],\n [-260, -180, -60, 440, 420, 340, -440, 180, -100, -200],\n [199, 145, 52, -362, -376, -309, 394, -144, 89, 162]]\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[[-211, -362, 564, -426, 101, -6, 106, 44, 494, -552],\n [238, -162, -59, -43, -1, 333, -214, -498, 15, -149],\n [-540, 110, 228, -936, 171, 642, 383, 317, -262, -362],\n [-846, -47, 94, -717, 126, 97, 86, 108, 9, -338],\n [780, 885, 205, 408, -325, 946, -658, -454, -1050, 649],\n [-567, -579, 340, -517, -310, -400, 576, -173, 840, -108],\n [804, 291, -49, 392, -48, 394, 2, 17, -389, 278],\n [540, 421, -463, 552, 490, 99, -283, 570, -638, -37],\n [-444, -352, -270, -58, 93, -238, 94, 265, 233, 93],\n [610, -404, -272, 608, -2, -456, 52, -173, 464, 35]]\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[[111, 995, 345, 671, -2, 505, -218, -872, -47, -218],\n [281, 655, 871, -125, 851, 340, 243, 183, 744, -1294],\n [919, 139, -351, 260, 461, -148, 1008, 490, -137, 105],\n [-72, 449, -575, -584, 709, -693, 652, -536, -359, -468],\n [436, 461, -633, 75, 379, 1142, -598, -139, 98, -405],\n [-169, -596, -434, -7, -590, -763, -134, 175, -437, 778],\n [357, -21, -266, 85, 328, -884, 419, 365, -156, -135],\n [22, 414, -295, -340, 48, 307, 136, -531, -203, -85],\n [399, -170, -372, -28, 605, 377, 138, 555, 227, -263],\n [38, -105, -492, -573, 58, -530, 321, 178, 288, -5]]\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[[-64, -352, 336, 352, 112, -320, -16, -208, 192, -48],\n [-80, -440, 420, 440, 140, -400, -20, -260, 240, -60],\n [8, 44, -42, -44, -14, 40, 2, 26, -24, 6],\n [-56, -308, 294, 308, 98, -280, -14, -182, 168, -42],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n [12, 66, -63, -66, -21, 60, 3, 39, -36, 9],\n [68, 374, -357, -374, -119, 340, 17, 221, -204, 51],\n [-20, -110, 105, 110, 35, -100, -5, -65, 60, -15],\n [4, 22, -21, -22, -7, 20, 1, 13, -12, 3]]\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 10x10 matrix:\n[[214, 25, 732, -440, -1126, 145, -632, -373, 22, 85],\n [212, -674, 156, -140, 22, 8, 202, 14, -826, -1018],\n [386, -139, 712, -132, -634, 317, -748, -321, -386, -339],\n [-362, 339, 117, 328, -76, 312, -229, -402, 607, 831],\n [376, -475, 247, -86, -776, 128, -309, 140, -375, -653],\n [-460, -410, 568, -640, -1108, -10, 352, -686, 100, 126],\n [412, -380, 78, -258, 51, -155, 31, 244, -725, -898],\n [-58, 21, 829, -416, -949, 224, -468, -691, 70, 270],\n [-36, -113, -42, 486, -299, 357, -275, 4, 243, 136],\n [71, -71, -241, 619, 82, 306, -244, 215, 135, 0]]\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[[61, 233, -427, 470, 460, 26, -442, -48, -333, 332],\n [-694, -502, -66, -279, -740, -792, 561, -425, 425, -1064],\n [22, 389, -173, -218, 992, -137, 45, 699, -486, 38],\n [144, 274, 650, -739, -412, -336, -49, 327, 85, -134],\n [-494, 89, -363, 510, 89, 463, 282, -485, 1178, 41],\n [-273, 292, -48, -500, 718, -613, 166, 220, -888, -431],\n [241, 75, 386, -652, 204, -236, -50, 1242, -225, 404],\n [-319, -260, -944, 79, 601, 247, -196, 423, 187, 168],\n [-410, -494, -111, -61, -830, -416, 41, -353, 401, -364],\n [94, 120, 245, 108, -538, 367, 333, -890, 758, -685]]\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 10x10 matrix:\n[[585, -302, -846, 281, 481, 74, 188, 294, -431, -557],\n [729, -456, -320, -51, 97, 68, 293, 346, -676, -637],\n [581, -465, -753, 276, 24, 388, 148, -54, -883, -609],\n [767, -457, -404, 433, 137, -61, 59, 591, -114, 62],\n [355, -901, -253, 764, -68, -146, -207, 412, 99, -461],\n [-1022, 257, 318, -876, 126, -549, -109, 10, -510, -83],\n [607, 286, 621, 203, 714, -240, 393, -806, 546, 326],\n [-155, 179, -1290, 65, -16, 418, -244, 773, -1353, -727],\n [460, -377, 281, 264, -157, 21, 142, -82, 1047, 438],\n [762, -383, -362, -209, 515, -69, 491, -102, -845, -600]]\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[[312, -603, 195, -276, -429, 518, 35, 1231, 410, -558],\n [172, 355, -384, -95, 25, 1383, 320, 456, 557, -204],\n [-211, -459, -679, -333, 185, -270, 289, -743, 399, -246],\n [450, 383, -1301, -12, 721, 684, 1088, -1060, 339, -17],\n [346, 142, 55, -548, 190, 723, 336, 685, 290, -152],\n [1017, -662, -249, -682, -160, -678, 40, 668, 355, -571],\n [321, -450, 495, 966, 123, 519, 628, -630, -625, 576],\n [-238, 1370, -1222, 231, 602, 158, 623, -236, -407, 220],\n [24, -103, -1128, -585, 625, 242, 1159, -182, 330, -457],\n [-545, -623, 870, -471, -512, -790, -864, 759, -122, 4]]\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 10x10 matrix:\n[[-74, 141, -139, -829, 189, 151, 48, -8, 398, 712],\n [-34, 110, 438, -69, -255, 148, 49, -189, -349, -42],\n [289, 112, 144, -64, 198, -79, 250, 304, 447, -172],\n [-205, 256, -467, -785, 222, 212, -225, -212, -151, 1026],\n [-465, 679, -920, 625, -113, 68, 149, 641, -1149, -403],\n [158, -1059, 959, 172, -153, -306, -672, -1117, 672, -95],\n [192, 195, 591, -47, 45, -138, 340, 308, 580, -542],\n [74, -873, 402, 700, -235, -327, -89, -174, 650, -806],\n [-246, 480, -799, -62, 112, 126, 201, 535, -394, 169],\n [122, -148, 12, 113, 329, -303, -423, -293, 339, 32]]\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[[-415, 45, 539, -223, 407, 23, 475, -478, -215, 59],\n [-463, -578, -1061, 730, 195, -174, -63, 54, 418, -343],\n [534, 598, -173, -458, 208, -466, -324, -185, 365, 562],\n [133, 429, -554, 655, 294, 133, 217, -609, 413, -259],\n [-425, -957, -242, 529, -555, 471, -230, 523, -315, -746],\n [-763, -1114, 238, 61, 761, 1036, 143, -910, 534, -1120],\n [215, 228, -345, -141, 181, -588, -232, 105, 488, 677],\n [83, 30, 430, -873, 51, 15, -560, 53, -517, 378],\n [-158, 393, -259, 498, 11, 681, 175, -140, -763, -809],\n [6, -185, 388, -300, -134, -333, 262, 20, 113, 122]]?\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[[-690, 776, -104, 878, 371, 144, -410, -79, 428, -247],\n [588, 12, -246, -423, 211, -950, 359, -438, 19, -201],\n [84, -93, 200, -574, -4, 299, 702, 271, 265, -164],\n [-105, -320, 470, 1163, -42, 435, 75, -701, 677, 359],\n [-306, 197, 275, 1269, 194, -398, -704, 255, -404, 172],\n [-922, 292, 119, 737, 525, 279, -560, -685, -228, 259],\n [676, -1081, 852, 237, -369, 346, 696, 159, 98, 503],\n [-287, 158, 653, 96, 517, -43, 260, -1048, -207, 724],\n [-509, 419, 7, 491, -368, 663, -318, 481, 452, -71],\n [597, -1235, 191, -174, -499, 401, 653, 509, 224, -198]]\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[[-36, 145, 223, -185, 271, 17, 601, -99, 1, 75],\n [-338, -84, 553, 135, 595, -156, 522, -73, -155, 107],\n [310, 314, -118, -652, -24, 530, -154, -718, -342, -472],\n [430, 271, -287, 24, -249, 174, 1, -104, 223, -175],\n [309, 140, -190, 674, -205, -281, 404, 525, 680, 237],\n [-256, -259, 16, 391, -76, -410, 89, 615, 270, 418],\n [277, 9, -425, -4, -448, 195, -765, -107, -21, -268],\n [-425, -255, 459, 111, 466, -110, -51, -130, -353, -4],\n [-144, -79, 183, -73, 203, 69, -151, -231, -271, -129],\n [77, -40, 16, 606, 9, -203, 8, 245, 278, 55]]\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[[-509, 279, -658, -58, -659, -53, 271, 90, -413, 375],\n [13, 529, -243, 90, -7, -200, 583, 233, 406, 812],\n [37, -163, -25, -770, -83, -164, -101, 323, -488, -76],\n [921, -380, 174, -1186, 749, -570, -380, 37, 287, 271],\n [73, 205, -497, 1010, 248, -307, -151, -427, 265, 112],\n [218, 305, -131, 28, 214, 53, -275, 360, 436, -540],\n [166, -830, 181, -664, -20, -31, 337, 134, 1057, -13],\n [118, 140, -26, -236, 90, 45, -207, 419, 101, -493],\n [-280, -139, -746, 196, -261, -504, -84, -74, -663, 86],\n [-601, 568, 251, -520, -863, 977, 418, 582, 89, -214]]\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[[146, -13, -339, -195, -345, 373, 6, 185, -175, -71],\n [264, -420, -519, 63, 388, -553, -723, 46, 586, -103],\n [-161, -429, -475, 120, 427, -720, -504, -81, 851, -330],\n [59, -347, -339, 497, 163, -102, -504, -604, 819, -506],\n [377, -628, -309, -214, 417, -701, -205, 371, -177, 316],\n [-344, -504, -184, 232, 469, -32, -126, 208, -455, -714],\n [-741, 65, 185, 57, 54, 9, 506, 253, -348, -370],\n [74, -640, 18, 237, 254, -215, 250, -204, -317, -112],\n [-934, 508, 627, -188, 134, -35, 681, 505, -622, -87],\n [91, 587, 19, 315, -161, 596, -594, -34, 200, -214]]\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[[430, 159, -307, 535, 67, -114, 381, 508, 115, 318],\n [-54, 245, -623, 255, 97, -328, -91, 4, 741, 406],\n [-339, -458, 220, -308, -242, -103, -380, -518, 626, 248],\n [-585, 3, 10, -144, -106, 175, -795, -471, 36, -405],\n [-20, -543, 38, -158, -279, 278, -626, -11, -1, 90],\n [-114, 335, 509, -248, 377, 294, 59, -44, -874, -356],\n [-261, -295, 133, -334, -197, 280, -583, -237, -248, -338],\n [2, 64, -998, 149, -339, -619, 261, -75, 1048, 5],\n [-103, -202, 453, -1079, 348, 213, -189, -281, -500, 202],\n [394, 107, -939, -342, -141, -274, 513, 348, -90, -362]]?\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[[731, 146, -305, -123, 329, 390, -256, 395, 469, 793],\n [0, -637, -530, 278, -24, -95, -59, -877, -1194, -673],\n [-229, -246, -928, 215, -317, -64, 352, -42, 1284, -237],\n [-901, 631, 856, -126, -380, 209, 245, 537, 527, 163],\n [324, 310, 321, -590, 326, -323, -421, 631, 941, 255],\n [-317, -17, 630, -720, 675, -723, -386, 434, 654, -354],\n [-369, -13, -51, 227, -5, -1118, 15, -652, -1015, -1054],\n [-222, 341, 253, -91, -292, 681, 14, 397, 423, 519],\n [-259, -369, -510, 83, 522, -276, 300, 96, 921, -113],\n [-347, 839, 1025, -811, 276, -260, -670, 809, 450, 219]]?\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[[-20, 75, -65, -264, -126, -106, 44, 138, -17, -91],\n [-398, -483, -263, -192, -729, 65, -82, -132, -206, -136],\n [138, 350, -72, -314, 133, -107, 40, 286, -19, -161],\n [110, 168, 95, -87, 144, -125, 85, 102, 101, 40],\n [-18, 11, 167, -344, -191, -369, 234, 116, 214, 120],\n [236, 513, 116, -567, 177, -422, 247, 438, 197, -50],\n [-176, -285, 49, -66, -342, -112, 74, -114, 61, 101],\n [-32, -100, 338, -278, -218, -488, 334, 24, 364, 298],\n [48, -138, 753, -267, -141, -852, 615, -36, 750, 669],\n [208, 55, 623, 116, 308, -472, 380, -74, 561, 539]]?\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[[-98, 21, 126, -14, -7, 70, 70, -126, -14, 28],\n [-210, 45, 270, -30, -15, 150, 150, -270, -30, 60],\n [252, -54, -324, 36, 18, -180, -180, 324, 36, -72],\n [-308, 66, 396, -44, -22, 220, 220, -396, -44, 88],\n [182, -39, -234, 26, 13, -130, -130, 234, 26, -52],\n [238, -51, -306, 34, 17, -170, -170, 306, 34, -68],\n [266, -57, -342, 38, 19, -190, -190, 342, 38, -76],\n [266, -57, -342, 38, 19, -190, -190, 342, 38, -76],\n [224, -48, -288, 32, 16, -160, -160, 288, 32, -64],\n [-140, 30, 180, -20, -10, 100, 100, -180, -20, 40]]\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 10x10 matrix:\n[[84, 109, -1132, -1102, -514, -749, 1564, -544, 219, -334],\n [176, -148, -450, 443, -40, 484, 169, 298, 486, 10],\n [448, 51, -259, -1070, -277, -422, 967, -391, 366, 120],\n [76, -194, 45, 324, -201, -262, -453, 46, 367, -337],\n [-385, -405, 189, 129, 93, -53, 432, -24, 671, -415],\n [-547, -274, 340, 627, 11, 157, -310, -95, -890, 122],\n [-349, 111, 1135, 396, 852, 142, -269, -21, -54, 645],\n [701, 216, 469, 252, -717, 390, -705, 838, 396, 613],\n [-559, 49, 171, 351, 546, -437, -443, -86, -696, -138],\n [166, -8, -827, -380, -483, 245, 575, 102, -79, -204]]\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[[-1036, -329, -326, -636, 683, 537, -1052, 982, -149, 308],\n [360, 502, -270, -211, -59, 529, 173, 116, 40, 46],\n [46, 350, -276, 60, 132, 40, -98, 780, 24, 800],\n [530, -66, 657, 323, -715, -456, -137, 115, 418, 54],\n [-236, -997, 718, -74, -319, -921, -318, -692, 225, -209],\n [-207, -152, 32, 330, 119, -479, -6, 256, -40, 409],\n [-99, -342, 204, -53, -98, -144, 148, -614, 49, -520],\n [-12, 800, -698, 466, 668, 312, -85, 1032, -649, 822],\n [279, 575, -109, 748, 174, -9, -140, 693, -473, 344],\n [-326, -119, 49, -33, -202, 71, 260, 411, 630, -25]]\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[[-56, 642, 323, 166, 102, 730, 287, -14, -274, -380],\n [-59, -748, -73, -360, -389, -795, 881, -77, 309, 734],\n [-295, 101, -168, 423, 549, 175, 853, -789, -273, 285],\n [461, -439, -540, -49, 183, -763, -502, -173, -159, 284],\n [86, -160, -100, -889, -572, -672, -1191, 308, 298, 281],\n [97, -94, 45, -653, -878, 299, 118, 450, 365, -323],\n [-346, 113, 1044, -145, -170, 48, 504, 326, 164, 530],\n [387, 24, 112, -122, -304, -447, -1, 720, -161, -255],\n [438, 453, 762, -509, -278, -303, 42, 89, -178, 550],\n [508, -298, -576, -808, -1165, -159, 444, 594, 197, -612]]\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[[-635, -15, -426, 159, 274, -694, -20, -961, 505, -536],\n [-637, -128, -1036, -218, -248, -522, -12, -182, 538, -90],\n [-582, -565, -530, 149, 361, 725, 226, -503, 780, -202],\n [-516, 13, 267, 395, 740, -271, -40, -364, -281, -339],\n [148, -54, 101, 474, 409, 183, -80, -171, 3, 1045],\n [-481, 12, -402, 73, -309, 392, -232, -304, 338, -408],\n [19, -94, -492, -384, 14, -150, -96, -859, 402, 191],\n [212, 516, 548, 589, 345, -197, -345, -76, -989, 754],\n [621, 71, 467, 16, -311, 7, 503, 757, -826, 42],\n [-812, -89, 112, 346, 505, -1507, 199, -11, -560, -302]]?\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[[0, 10, -5, 100, -80, -85, 65, -5, 60, 50],\n [0, -28, 14, -280, 224, 238, -182, 14, -168, -140],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n [0, -32, 16, -320, 256, 272, -208, 16, -192, -160],\n [0, 2, -1, 20, -16, -17, 13, -1, 12, 10],\n [0, 40, -20, 400, -320, -340, 260, -20, 240, 200],\n [0, 28, -14, 280, -224, -238, 182, -14, 168, 140],\n [0, -28, 14, -280, 224, 238, -182, 14, -168, -140],\n [0, 30, -15, 300, -240, -255, 195, -15, 180, 150],\n [0, -32, 16, -320, 256, 272, -208, 16, -192, -160]]\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[[517, 269, -28, 481, 872, -461, 949, -670, 197, 704],\n [52, 59, 338, 168, -263, 288, -868, -231, -96, -666],\n [141, 334, 514, 492, 445, -850, 349, -232, -139, 760],\n [27, -346, 42, -115, -329, -451, 339, 675, -235, 499],\n [-419, 461, -1031, -918, -293, 274, 299, 518, 542, -130],\n [-910, 24, 557, 200, 27, -14, -56, 235, -195, 215],\n [112, -505, 7, -242, -885, 84, -551, 663, -293, -65],\n [-336, -1190, -262, -227, 373, 943, 435, 0, -220, -299],\n [357, 1080, -872, -307, -287, -225, 219, -81, 713, 623],\n [-449, 343, 22, 10, -190, 666, -785, -355, 171, -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[[-49, 274, -106, -291, -83, 43, -147, 318, -281, 323],\n [-14, 88, -32, -79, -24, 4, -49, 89, -88, 88],\n [10, 384, -56, 247, 4, -384, -287, -149, -292, -260],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n [27, -534, 126, -3, 57, 303, 357, -102, 459, -9],\n [-57, 62, -78, -448, -89, 269, 14, 419, -123, 489],\n [45, -686, 174, 82, 89, 331, 448, -209, 603, -105],\n [-22, -56, -16, -207, -32, 172, 63, 177, 16, 224],\n [6, 108, -12, 96, 6, -126, -84, -66, -78, -102],\n [-18, -256, 24, -259, -20, 320, 203, 185, 180, 276]]?\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[[253, -207, -263, -542, 312, 245, 34, 53, -40, -351],\n [77, -12, -149, -175, 204, -66, 161, 214, -322, -67],\n [-102, -341, -355, 295, -80, -415, 549, 40, 169, -198],\n [-25, 326, 476, 134, -118, 434, -719, -442, 289, 231],\n [140, 462, 42, 160, -93, 17, 292, -161, 18, -271],\n [-339, -125, 129, 699, -569, -358, 154, -217, 570, 204],\n [-311, 375, 399, 967, -327, -168, -258, -465, 264, 366],\n [195, 265, 107, -374, -473, 164, 354, 52, 364, -312],\n [117, -350, -358, -100, 454, 86, -29, -158, 1, -295],\n [148, 255, 263, -369, -318, 347, -121, -60, 301, -90]]\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[[-370, 543, -18, -82, -85, -160, 100, -12, -254, -293],\n [-520, -385, -17, -603, -551, -363, 397, -281, -69, 52],\n [-70, 421, 329, -692, 280, 36, 171, -559, 152, -41],\n [140, -342, 438, 419, -1167, -598, -230, -409, 490, 561],\n [-122, -282, -444, 257, -1, 89, -138, 591, -265, -81],\n [348, 369, 186, -483, 298, 109, -227, -847, 482, -137],\n [-114, -694, -75, -15, -284, -87, 206, 103, -100, 164],\n [-370, 397, -902, -119, -104, -292, 719, 84, -31, -763],\n [-568, 124, -249, -266, 1115, 724, -218, 826, -1265, -544],\n [248, 496, -399, 116, 489, 268, -332, 385, 191, -143]]\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 10x10 matrix:\n[[-46, -333, 545, 1195, 714, 759, -4, 553, -273, -630],\n [862, -227, -360, -568, -1046, 272, -548, 219, 1053, 58],\n [600, 229, 743, 507, 286, 77, -657, 586, -597, -62],\n [470, -576, 302, 295, -732, 794, -620, 503, 662, -634],\n [158, 327, -416, -419, -230, 48, 235, -151, 80, 248],\n [-56, -9, 115, 854, 414, 941, 318, 366, -304, -472],\n [186, -97, 145, -320, -478, 521, 2, 30, 461, -490],\n [-340, 568, 279, 663, 928, 79, 411, 79, -1233, 70],\n [178, 536, 54, -90, 556, 512, 646, 10, -201, -222],\n [-216, -141, -689, -698, -758, -749, -149, -463, 399, 626]]\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[[380, -441, -819, 929, -50, 103, 245, 225, -652, -34],\n [293, 419, 12, 128, 276, -223, -442, -419, 145, 690],\n [-513, -101, 290, -155, 138, 79, 409, -263, -462, -363],\n [-385, -780, -793, 740, 782, 292, -236, -714, 556, -687],\n [-879, 112, -53, 60, 652, 462, 21, -463, 201, -558],\n [505, 0, -455, 541, 520, -526, -321, -6, 517, 628],\n [-351, 68, 65, -669, -43, -579, 585, 24, -695, 492],\n [820, 496, -156, 418, -644, 380, -388, 530, -221, 409],\n [-419, -941, -504, -153, -273, 228, 452, 504, 206, -993],\n [190, 78, -443, 521, -117, 584, -379, -131, -58, -104]]\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 10x10 matrix:\n[[-39, 17, -464, -3, 177, -492, 13, 564, 112, -109],\n [-411, -554, -906, 366, 479, -19, 314, 385, -699, 151],\n [-39, 850, 395, 703, 900, 838, 692, -772, -273, 765],\n [38, -392, -762, -38, -529, -231, 234, 825, -512, 154],\n [643, -752, -1608, 802, -532, -744, 240, 728, 95, -27],\n [22, -395, 121, -435, -859, -73, -434, 128, 181, -326],\n [-582, -581, -1044, 147, -35, -200, 15, 487, -581, 38],\n [-1154, -45, 516, -390, -38, 602, 184, -339, 109, -354],\n [161, -171, -903, 556, 202, 50, 608, 171, -1164, 735],\n [-529, -296, -226, -190, -549, -84, -541, -327, 7, -219]]\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 10x10 matrix:\n[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n [-70, 154, -182, -140, 126, -210, -224, -84, 252, 56],\n [-75, 165, -195, -150, 135, -225, -240, -90, 270, 60],\n [-110, 242, -286, -220, 198, -330, -352, -132, 396, 88],\n [-75, 165, -195, -150, 135, -225, -240, -90, 270, 60],\n [50, -110, 130, 100, -90, 150, 160, 60, -180, -40],\n [40, -88, 104, 80, -72, 120, 128, 48, -144, -32],\n [105, -231, 273, 210, -189, 315, 336, 126, -378, -84],\n [60, -132, 156, 120, -108, 180, 192, 72, -216, -48],\n [35, -77, 91, 70, -63, 105, 112, 42, -126, -28]]\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[[225, -171, -72, -255, -288, 102, 180, 126, 207, 390],\n [-18, 294, -96, 238, 288, -76, -360, -300, -126, -268],\n [-78, 252, -45, 238, 282, -82, -300, -243, -147, -298],\n [-294, 276, 75, 374, 426, -146, -300, -219, -291, -554],\n [139, 163, -142, 51, 76, -2, -220, -200, 23, 14],\n [32, 110, -59, 68, 86, -18, -140, -121, -23, -58],\n [-300, 228, 96, 340, 384, -136, -240, -168, -276, -520],\n [56, -136, 16, -136, -160, 48, 160, 128, 88, 176],\n [406, 328, -361, 34, 82, 30, -460, -431, 125, 166],\n [393, -141, -183, -323, -354, 140, 120, 57, 300, 548]]\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[[398, 691, 793, 359, -348, -297, 331, -652, -512, 484],\n [-25, 565, 437, 507, -112, -381, -146, -464, -228, -317],\n [214, -249, -348, -537, 529, 381, 156, -32, -183, 478],\n [-164, 476, -330, -84, 449, 149, 489, 630, 744, -145],\n [273, 794, 807, 397, -272, -275, 146, -754, -528, 450],\n [235, -465, 413, 378, -931, -460, -8, -82, -279, -260],\n [-297, 75, -255, -97, 84, 187, 78, 540, 596, -67],\n [-389, 361, -115, 183, 184, -21, -170, 216, 432, -405],\n [415, -80, 751, 468, -1030, -511, 231, -314, -437, 98],\n [-137, -38, -519, -285, 717, 238, -85, 140, 158, -197]]\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[[478, -32, -266, 98, 14, -260, 196, 70, -218, 292],\n [-218, 408, -76, 28, -434, 322, 56, 312, 334, -146],\n [83, 16, -57, 21, -21, -34, 42, 31, -25, 50],\n [181, -516, 152, -56, 553, -359, -112, -414, -383, 127],\n [571, 48, -361, 133, -77, -266, 266, 159, -209, 346],\n [-417, 36, 228, -84, -21, 231, -168, -54, 195, -255],\n [-575, 184, 247, -91, -175, 388, -182, 43, 349, -356],\n [47, 172, -114, 42, -189, 65, 84, 160, 83, 23],\n [143, 400, -285, 105, -441, 134, 210, 379, 179, 74],\n [268, -88, -114, 42, 84, -182, 84, -22, -164, 166]]?\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[[-147, -191, -33, -47, 247, -381, -156, -242, 132, 94],\n [0, 143, -297, 242, 473, -132, 66, -484, 33, 209],\n [-273, -494, 228, -323, -2, -579, -354, 22, 213, -29],\n [105, 233, -177, 197, 143, 183, 156, -154, -72, 74],\n [63, 210, -252, 237, 318, 45, 126, -330, -27, 147],\n [14, 272, -524, 434, 816, -198, 132, -836, 46, 362],\n [84, 332, -444, 404, 596, 12, 192, -616, -24, 272],\n [-168, -404, 348, -368, -332, -264, -264, 352, 108, -164],\n [-175, -293, 97, -167, 77, -393, -216, -66, 142, 16],\n [-42, -114, 114, -114, -126, -54, -72, 132, 24, -60]]\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, -505, -366, -2, 28, -207, -205, 119, 59, -524],\n [182, 135, -508, 265, 666, -382, -426, -269, -317, -327],\n [-132, -440, -831, 238, -424, 357, -130, -442, -63, 203],\n [-159, 481, 1088, 351, -412, -576, -505, -336, -107, -495],\n [-10, 331, -497, 502, 372, -10, -820, -129, -1010, 712],\n [-654, -1374, -1124, 440, -90, 374, 444, -349, -42, -271],\n [-119, 330, 67, 125, 390, -523, -73, 12, -25, -584],\n [391, -104, 251, 244, 388, 809, 555, -227, 91, 923],\n [-75, 875, 1246, -542, -241, -397, 389, 729, 729, -456],\n [-254, 12, -697, 25, -350, 542, 163, 179, 154, 557]]\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[[-662, 728, -85, 72, 260, 23, -265, 123, -469, -318],\n [-656, 866, -432, 67, 595, 6, -477, 177, -353, -426],\n [-459, 128, -6, 292, 172, 157, -233, -81, -377, -314],\n [-600, 308, -112, 276, 368, 267, -288, -54, -406, -407],\n [674, -215, -112, -387, -72, -166, 400, 211, 719, 464],\n [-210, 497, -410, -91, 576, 77, 38, 363, 279, -53],\n [-149, -41, 150, 271, -292, -368, -149, 42, -282, -47],\n [-741, 473, 92, 132, 413, 528, 246, 195, -199, -221],\n [-11, -26, 213, -76, -154, 112, 182, -40, -44, 74],\n [114, -511, 175, 348, -375, -265, -190, -195, -205, -38]]\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[[-17, -11, 6, -15, 7, -11, -6, 5, 12, 11],\n [289, 187, -102, 255, -119, 187, 102, -85, -204, -187],\n [-34, -22, 12, -30, 14, -22, -12, 10, 24, 22],\n [51, 33, -18, 45, -21, 33, 18, -15, -36, -33],\n [-323, -209, 114, -285, 133, -209, -114, 95, 228, 209],\n [-272, -176, 96, -240, 112, -176, -96, 80, 192, 176],\n [-221, -143, 78, -195, 91, -143, -78, 65, 156, 143],\n [-136, -88, 48, -120, 56, -88, -48, 40, 96, 88],\n [51, 33, -18, 45, -21, 33, 18, -15, -36, -33],\n [-119, -77, 42, -105, 49, -77, -42, 35, 84, 77]]\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[[224, -210, 266, -56, -266, 56, -140, 210, -28, 42],\n [-336, 315, -399, 84, 399, -84, 210, -315, 42, -63],\n [-80, 75, -95, 20, 95, -20, 50, -75, 10, -15],\n [240, -225, 285, -60, -285, 60, -150, 225, -30, 45],\n [160, -150, 190, -40, -190, 40, -100, 150, -20, 30],\n [-224, 210, -266, 56, 266, -56, 140, -210, 28, -42],\n [-128, 120, -152, 32, 152, -32, 80, -120, 16, -24],\n [80, -75, 95, -20, -95, 20, -50, 75, -10, 15],\n [-240, 225, -285, 60, 285, -60, 150, -225, 30, -45],\n [208, -195, 247, -52, -247, 52, -130, 195, -26, 39]]\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[[-712, -374, -76, -359, -501, -308, 693, -334, -323, -379],\n [-53, -14, 247, -256, 260, -407, -21, -757, -735, 50],\n [118, 106, 577, 11, 92, -1001, -258, -865, -160, -33],\n [-285, -679, -2, 204, -697, -41, 701, -62, -131, 22],\n [-721, -54, -459, -453, -55, 344, 448, 260, -241, -406],\n [179, 48, 187, -504, 24, -226, 19, -730, -538, 111],\n [-349, -179, 105, -323, 253, -242, 177, -373, -437, -477],\n [-593, -785, -176, 98, 138, 377, 667, 35, -871, -260],\n [-462, -457, -277, 376, 452, 561, 260, 515, -473, -205],\n [856, -150, 312, 207, 129, 159, -251, -347, -298, 596]]\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[[358, -34, -195, 681, -242, -475, 71, 113, -521, 527],\n [-18, 88, 363, 1166, -345, -379, 75, 196, -978, 11],\n [118, -113, 113, -494, -194, -123, -49, -462, 428, -472],\n [-344, -188, 328, 268, 136, 552, 657, 125, -53, -44],\n [714, -1220, 462, -499, 665, 116, 327, -385, 791, -115],\n [1307, -688, -106, 74, 15, -738, -1307, 246, 406, 536],\n [57, -574, 1, -710, 78, 427, 323, -1050, 1192, -772],\n [481, -331, 387, -135, -464, -463, 32, -257, 125, -236],\n [-614, 649, -360, -308, 35, 99, 790, -12, -417, 180],\n [196, -287, 203, 223, 155, 42, 11, 286, -79, 238]]\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 10x10 matrix:\n[[-315, -353, -339, -539, -312, -176, -144, -827, -307, -399],\n [85, -430, -216, -173, -346, -311, 107, -329, -405, -580],\n [-228, 266, -226, -544, 460, 94, -762, -532, 388, 626],\n [-12, 362, 307, 345, 204, 275, 127, 501, 296, 377],\n [-432, 456, 2, -29, 428, 586, -227, 34, 457, 939],\n [-256, -10, 93, 111, -212, 177, 313, 15, -88, -101],\n [461, -277, 132, 586, -280, -145, 629, 676, -345, -460],\n [-365, 35, -102, 62, -12, 411, 189, -16, 1, 342],\n [19, 497, 447, 287, 264, 180, -12, 479, 427, 339],\n [-48, 50, -170, -301, 200, -30, -393, -304, 127, 229]]\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 10x10 matrix:\n[[-129, -594, -113, -713, 255, 593, -171, 383, -358, 80],\n [170, -946, -503, -437, 614, 421, 158, 551, -597, -71],\n [927, -381, -698, 227, 832, -414, -455, 998, 235, 378],\n [292, -331, -181, -565, -18, 804, 634, 517, -177, 3],\n [-32, 256, 4, 316, -405, -354, 284, -360, 29, -182],\n [-94, -903, -700, 302, 652, -780, -541, -185, -808, -180],\n [747, 308, -78, 378, 477, 215, 396, 419, 415, 359],\n [-199, -362, -307, 127, -266, -375, 187, -195, -422, -615],\n [-652, -351, 334, -477, 241, 610, -290, -90, -336, -269],\n [252, 94, 54, -243, 136, 525, 396, -82, -74, 684]]\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[[-181, 229, 214, 112, 152, 0, -279, -160, 32, 246],\n [115, -356, -200, -331, 136, -5, 699, -317, -394, -123],\n [87, 111, 217, -515, -138, -85, -123, -67, -58, 235],\n [-178, 102, 120, 112, 248, 16, -30, -280, -96, 180],\n [-356, 298, 398, -36, 484, -12, -144, -672, -248, 544],\n [-2, 76, 24, 94, -80, 2, -186, 146, 132, -10],\n [-50, -18, 15, -13, 118, 5, 102, -161, -102, 51],\n [-338, 245, 122, 629, 328, 75, -324, -149, 118, 147],\n [228, -309, -224, -317, -132, -19, 462, 41, -166, -227],\n [-167, 121, 108, 172, 196, 20, -105, -184, -24, 146]]\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[[222, 1, -160, -304, 575, 727, -398, 348, 671, 699],\n [35, -121, -66, -48, 521, 624, 33, 615, 672, 457],\n [225, 134, -154, -260, -92, -51, -433, -301, -185, 202],\n [-50, -154, -116, 200, -138, -144, 418, 526, -100, -62],\n [-315, -146, 254, 332, 116, 49, 523, 255, 227, -318],\n [32, 19, -108, 76, -489, -545, 116, -134, -599, -267],\n [2, 93, 104, -100, 85, 79, -230, -348, 65, -5],\n [-336, -141, 212, 438, -282, -409, 678, 136, -252, -601],\n [-168, -12, 160, 174, -159, -236, 222, -166, -171, -350],\n [224, 224, -32, -378, 89, 136, -690, -622, -3, 254]]\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 10x10 matrix:\n[[58, -73, -92, 235, 407, -755, 586, 676, -510, 811],\n [-200, -529, 57, -448, 133, -414, 998, 255, -143, -12],\n [-346, 347, -300, -523, -60, 37, -874, 108, 416, 231],\n [-493, -105, 653, -214, 180, 872, 40, -953, 531, -787],\n [-338, -263, 787, -107, 966, 66, 297, 15, 790, -336],\n [-261, 369, 160, 498, -304, 673, -225, -954, -159, 334],\n [-313, 162, -34, -360, -120, 283, -582, -240, 583, -59],\n [-401, -191, 294, -5, -48, 277, 186, -258, 302, -722],\n [19, -213, -279, -634, 321, -732, 62, 979, 121, 11],\n [-23, -129, -382, -50, -645, -159, 245, 20, -235, 66]]\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[[-5, 143, 310, -386, -437, -23, -341, -601, -133, -181],\n [-210, 77, -595, -259, 557, 453, -304, 626, 103, 221],\n [245, -204, 303, -236, -135, -372, 288, -239, 19, -344],\n [182, 166, 39, 838, 192, 170, 219, 273, -187, 359],\n [111, 122, 207, 525, -132, 4, 111, -113, -154, 158],\n [206, 102, 641, -6, -628, -262, -31, -805, -225, -227],\n [361, 74, 631, 99, -428, -256, 127, -613, -256, -212],\n [319, 229, 160, 805, 190, 197, 196, 195, -290, 325],\n [-606, 25, -262, -306, -370, 75, -466, -249, 219, 56],\n [-464, -191, 10, -502, -584, -317, -200, -525, 283, -262]]?\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[[32, 207, 107, -87, 495, 300, 72, -454, 395, -578],\n [-629, -470, -135, 741, -381, 304, 502, -469, 456, -338],\n [437, 412, 17, -752, 325, -130, -598, 561, -480, 467],\n [-39, -81, -148, -133, -304, -130, -262, 519, -413, 607],\n [-83, -107, -66, 69, -198, -50, -14, 143, -111, 199],\n [-569, -276, -265, 241, -251, 412, -2, 19, 102, 136],\n [-61, 83, -214, -433, -58, 106, -530, 625, -449, 669],\n [109, 132, -47, -312, 69, -18, -294, 313, -248, 299],\n [-561, -180, -265, 119, -79, 536, -82, -21, 154, 58],\n [-535, -465, -76, 777, -396, 186, 570, -505, 455, -383]]\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[[129, -764, 414, -90, 371, -63, 160, 332, -226, 175],\n [1023, 642, 534, 1265, -764, -90, -504, 790, -624, -324],\n [266, 865, -192, 563, -577, -40, -39, -64, 181, -352],\n [-95, -435, -498, -138, 385, 246, -43, -265, -31, 399],\n [-1060, -690, -53, -1059, 741, -55, -72, -319, 308, 475],\n [-371, -41, -278, 79, 450, 435, -1249, 515, -17, 764],\n [1064, -345, -113, 211, -234, -193, -680, 225, -155, 750],\n [-789, -455, 49, -572, 795, 59, 687, -22, 464, -96],\n [847, -182, 226, 409, -331, -630, 55, 123, 161, 234],\n [-79, 464, -237, -158, -220, 18, 436, -410, 146, -413]]\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[[330, -749, -606, 414, -379, -717, 216, -412, -229, 155],\n [-969, 737, 586, -544, 612, 830, 45, 759, -104, 51],\n [315, -866, -186, 492, -305, -1165, -807, -292, 22, 834],\n [336, -247, 151, 460, -485, -953, -730, -235, 121, 476],\n [-471, 433, 234, -427, -29, 408, 879, 77, 446, 241],\n [0, -523, 123, -278, 411, -501, -716, 146, 30, 134],\n [196, -688, 315, -389, -303, -728, -156, -880, 1473, 621],\n [485, -904, 467, 396, -440, -1010, -622, 7, -335, 460],\n [178, -615, -629, -233, 663, 794, 887, 529, -826, -3],\n [-145, -246, -477, 150, -276, -580, -226, -836, 1028, 768]]\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[[340, 17, -306, 85, -340, -85, -323, 289, 323, 153],\n [-260, -13, 234, -65, 260, 65, 247, -221, -247, -117],\n [260, 13, -234, 65, -260, -65, -247, 221, 247, 117],\n [160, 8, -144, 40, -160, -40, -152, 136, 152, 72],\n [160, 8, -144, 40, -160, -40, -152, 136, 152, 72],\n [-360, -18, 324, -90, 360, 90, 342, -306, -342, -162],\n [-100, -5, 90, -25, 100, 25, 95, -85, -95, -45],\n [-340, -17, 306, -85, 340, 85, 323, -289, -323, -153],\n [380, 19, -342, 95, -380, -95, -361, 323, 361, 171],\n [100, 5, -90, 25, -100, -25, -95, 85, 95, 45]]?\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 10x10 matrix:\n[[165, -219, 280, 288, -90, 109, 266, -689, 61, 168],\n [129, 154, -206, 268, -399, 23, 567, -949, 6, 112],\n [-297, -737, 492, 199, -68, 511, -371, 113, 151, -176],\n [291, -198, 334, 111, 486, -41, -262, 205, -23, -207],\n [10, -47, -434, -519, -196, 276, 520, -356, -2, 601],\n [134, 46, 216, 33, 387, -214, -331, 452, -41, -195],\n [597, -135, 68, -65, 544, 13, 165, -245, -75, 44],\n [-447, -29, 12, 173, -187, 54, -510, 604, 35, -549],\n [-332, 297, -426, -265, -319, -47, 31, 281, -20, 60],\n [6, -67, 2, -25, 41, 58, -36, 48, 1, -34]]\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[[67, -618, 440, 77, 24, 423, -666, 386, -138, 344],\n [163, 320, -33, -370, -217, -18, 379, -370, -84, -223],\n [128, -19, 275, 376, 68, 180, -377, -26, 192, 610],\n [166, -269, 209, -694, -300, 290, 57, -10, -420, -418],\n [-231, 451, -561, -9, 84, -511, 621, -156, 114, -486],\n [-470, 137, -671, 212, 286, -592, 413, 242, 120, -544],\n [-235, -29, -220, 376, 239, -224, -56, 220, 168, 43],\n [206, -240, 319, -395, -219, 339, -147, -20, -258, -41],\n [488, 463, 330, -407, -389, 267, 236, -686, -42, 211],\n [398, 375, 231, -500, -374, 208, 299, -578, -120, -8]]\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[[-705, -478, -485, -434, 754, -638, -84, 342, -298, 362],\n [-114, -68, 4, -25, 89, -149, -637, 55, 329, 380],\n [-337, -290, -146, -89, 572, -75, -133, 453, 265, 349],\n [-554, 87, 298, -255, 48, -237, 316, 369, 178, 229],\n [139, 330, -509, -335, 8, 311, 275, -827, -62, 146],\n [186, 109, 435, -139, -114, 569, -548, 281, 646, 331],\n [-1001, -478, -211, -396, 1060, -371, -443, 972, 527, 832],\n [96, 538, 343, -160, -621, 519, -1029, -970, 709, 573],\n [-221, -99, -57, -155, 665, 497, -224, 587, 850, 612],\n [308, -167, 149, 222, -60, -293, -238, 562, 70, -82]]\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[[-94, 254, -314, -62, 44, -475, 170, -95, -432, -125],\n [492, 136, 55, 66, 21, -121, 383, 380, -745, -319],\n [634, 74, 227, 284, 51, -104, 391, 137, -617, -310],\n [255, 342, 446, -555, -619, -158, -495, 27, -321, 554],\n [-307, 430, 70, -89, -267, -760, -613, -914, 326, 787],\n [713, 320, 588, -71, -407, -264, -119, -63, -599, 262],\n [-424, -280, -280, 260, 450, 362, -60, 441, 769, 121],\n [214, -193, 96, -123, -20, 475, 176, 580, -190, -271],\n [-73, 233, 122, -600, -579, -255, -273, -542, -354, 112],\n [-187, -345, 34, -258, -113, 598, -45, 103, 286, -207]]?\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[[-67, -229, -585, 12, -253, 310, 140, -585, 1098, 421],\n [-836, 31, 531, -105, 106, 202, 119, -509, -120, 151],\n [-41, -113, 168, -301, 284, -340, -475, 301, -349, -224],\n [-160, -192, -5, -386, -54, 82, -244, -354, 639, 1093],\n [-436, 300, 448, 165, -53, 128, 245, -108, -496, -248],\n [-650, -444, 274, -587, 424, -118, -493, -384, 262, 396],\n [-210, 71, 257, 267, 160, 74, 339, -9, -494, -663],\n [396, -45, -354, -15, -102, -96, -141, 189, 243, 48],\n [-998, 270, 361, 39, -223, 338, 201, -668, 63, -13],\n [267, -510, -272, -115, 388, -118, -85, 30, 276, -124]]?\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[[-199, 59, -784, -726, -280, -204, 368, -708, -376, -258],\n [-173, -130, -262, -742, -311, 381, -93, -154, -594, -253],\n [-306, -48, -238, -621, -193, 131, -60, -98, -428, -59],\n [121, -388, -31, -520, -282, 482, -11, -162, -548, -491],\n [-271, 448, -734, -714, -429, 443, -261, -236, -484, -17],\n [639, -77, 431, 1102, 352, -322, 276, 29, 751, -48],\n [-145, -681, -114, -475, -118, -252, 448, -481, -395, -505],\n [-855, 132, -169, -272, -62, -126, -351, 256, -166, 421],\n [-559, 102, -395, -859, -129, -173, 37, -158, -426, 160],\n [94, 301, 128, 17, 41, 239, -253, 297, 51, 232]]\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[[286, -494, -126, 231, -1064, -3, -73, -204, -23, 326],\n [-514, -251, 305, 291, -478, 248, -327, -715, 588, -276],\n [440, -268, -363, -748, 82, -181, 331, 224, 327, 807],\n [0, 582, 417, -321, 970, 788, -402, -109, -189, -587],\n [-277, 535, 50, 356, 203, -285, -294, 782, -283, -286],\n [-536, 111, 1190, 1036, -426, 178, -613, -442, 389, -1121],\n [-423, 577, -83, 312, -43, -464, -261, 435, -75, -65],\n [-167, 16, 375, 138, 663, -301, 192, 630, 204, -366],\n [88, -732, -28, 82, -686, 129, -127, 185, 349, 219],\n [29, 196, -943, -129, -363, 125, -173, 165, -721, 462]]?\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[[-252, 44, -98, 198, -98, -22, 198, 194, 76, 108],\n [342, -114, 3, -213, 183, -63, -213, -219, -6, -78],\n [-375, 146, 47, 212, -220, 105, 212, 223, -31, 59],\n [-333, 88, -58, 231, -157, 22, 231, 232, 47, 105],\n [24, 32, 96, -56, -24, 64, -56, -48, -72, -56],\n [-342, 152, 88, 174, -218, 128, 174, 188, -62, 30],\n [294, -140, -98, -140, 196, -126, -140, -154, 70, -14],\n [-207, 180, 264, 15, -213, 228, 15, 42, -195, -93],\n [216, -206, -319, 3, 239, -269, 3, -29, 236, 120],\n [402, -72, 152, -314, 158, 32, -314, -308, -118, -170]]\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 10x10 matrix:\n[[-630, -1084, 225, 168, -215, 429, -194, -192, -173, -75],\n [-535, -47, -31, 824, 10, 769, -2, -233, -342, -21],\n [8, 514, -178, 20, -152, -273, -471, 800, 1, -87],\n [-489, -410, 540, 741, -334, 627, -607, -27, -214, -312],\n [-282, 441, -103, -389, -282, -582, 410, 365, 568, -448],\n [120, -282, -158, 698, 349, 897, 360, -793, -789, 488],\n [-832, -572, 628, 436, -608, 255, -464, -231, -423, -530],\n [24, 82, -342, -408, 126, -275, 779, -216, 203, 67],\n [188, 834, -468, 332, 385, 167, 415, -378, -523, 335],\n [8, -990, 669, -380, -250, -136, -668, 73, 374, -197]]\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 10x10 matrix:\n[[266, -243, -258, -627, 50, -18, -441, 573, 125, 904],\n [-205, -168, 47, -363, -97, -379, 3, -313, -106, -373],\n [-154, -223, -421, -638, -137, 483, 98, -900, 254, -913],\n [141, 226, -254, 343, 124, 526, 321, -72, -230, -651],\n [570, -632, -507, 405, -345, 383, 253, 253, 327, 515],\n [-20, 323, 50, 193, 269, 889, -56, -358, 167, -384],\n [474, -874, -723, -973, -84, 755, -365, -139, 358, 218],\n [473, -491, -145, -828, 414, 572, -803, 505, -91, 683],\n [18, -98, -540, 611, -864, -577, 812, 43, 638, 490],\n [59, 169, 93, 77, 87, -439, -53, 590, -292, 406]]\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[[-39, 587, 642, 2, 408, -120, 835, -483, 506, -715],\n [-91, 105, -654, 280, -342, 318, -333, 321, -160, 103],\n [-65, -296, 521, -316, 313, -221, 249, -42, 271, 195],\n [59, 317, -170, 498, -246, -254, 387, -405, 180, 121],\n [-59, 224, -41, 104, -1, -115, 261, -24, 553, 211],\n [280, 80, 495, 253, 19, -537, 526, -876, -289, -245],\n [-242, 85, -68, -235, 177, 399, -101, 489, 279, -160],\n [-50, -145, 199, -144, 127, -195, 156, 27, 399, 354],\n [27, 112, -480, 429, -377, -43, -49, -63, -61, 278],\n [-142, -154, -470, -26, -173, 227, -390, 519, 141, 444]]\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[[54, 0, -36, -63, 72, -63, 27, -180, 0, -126],\n [-72, 0, 48, 84, -96, 84, -36, 240, 0, 168],\n [-126, 0, 84, 147, -168, 147, -63, 420, 0, 294],\n [54, 0, -36, -63, 72, -63, 27, -180, 0, -126],\n [-108, 0, 72, 126, -144, 126, -54, 360, 0, 252],\n [48, 0, -32, -56, 64, -56, 24, -160, 0, -112],\n [-60, 0, 40, 70, -80, 70, -30, 200, 0, 140],\n [-6, 0, 4, 7, -8, 7, -3, 20, 0, 14],\n [72, 0, -48, -84, 96, -84, 36, -240, 0, -168],\n [-24, 0, 16, 28, -32, 28, -12, 80, 0, 56]]?\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[[117, 13, -60, -158, -193, -246, 6, 421, -272, 100],\n [155, -485, -504, -203, 1349, 451, -342, -428, 198, 109],\n [308, 738, 376, 209, -1268, -567, 370, 711, -934, 429],\n [-374, -549, -30, 120, 816, 247, 173, 89, 317, 262],\n [-80, 560, -456, -364, 136, -56, -244, -38, -770, -558],\n [-98, 534, 554, 205, -1537, -559, 388, 584, -298, -32],\n [-393, -719, -290, -228, 972, 162, -46, 215, 369, -24],\n [-649, -145, -642, -847, 328, -97, -500, 42, 171, -1379],\n [-369, 240, 252, 78, -656, -109, 111, -65, 195, -479],\n [35, 142, 546, 697, -231, 220, 409, -315, 167, 583]]\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 10x10 matrix:\n[[-49, -14, -98, 14, 91, 140, -63, -42, 35, 154],\n [-56, -16, -112, 16, 104, 160, -72, -48, 40, 176],\n [133, 38, 266, -38, -247, -380, 171, 114, -95, -418],\n [35, 10, 70, -10, -65, -100, 45, 30, -25, -110],\n [21, 6, 42, -6, -39, -60, 27, 18, -15, -66],\n [-119, -34, -238, 34, 221, 340, -153, -102, 85, 374],\n [-119, -34, -238, 34, 221, 340, -153, -102, 85, 374],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n [-105, -30, -210, 30, 195, 300, -135, -90, 75, 330],\n [98, 28, 196, -28, -182, -280, 126, 84, -70, -308]]\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[[-670, -31, -1031, 621, 162, -326, -728, -120, -307, -534],\n [74, 1101, 313, -447, -175, -87, 182, -793, -38, 153],\n [842, -424, -143, 363, -51, 278, 336, 576, 237, -627],\n [-1460, -169, -923, 290, 563, 32, -653, -491, -653, 227],\n [643, -32, 770, 6, -300, -506, -410, 798, 429, -202],\n [358, -136, -321, 824, -713, -915, -458, 465, -184, -801],\n [140, -316, 848, -448, 74, 268, 654, 190, 69, 744],\n [-736, 483, -158, -263, 820, 48, 465, -319, 165, -74],\n [531, 491, -203, 232, 331, -344, -108, 218, 699, -277],\n [830, -45, -162, 45, 291, 239, 362, 241, 771, 123]]\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 10x10 matrix:\n[[-71, 221, -404, -351, -185, 147, -416, 171, 98, -167],\n [-127, 173, 408, -219, 12, 230, -14, -428, -230, -5],\n [-245, -441, 304, 775, -230, 104, 794, -294, -238, 233],\n [443, 37, 87, -937, 366, -362, -783, 3, 274, 100],\n [-28, 230, 820, 230, 382, 93, 446, -458, -359, -15],\n [-434, -38, 247, 668, -308, 407, 693, -331, -373, -8],\n [-323, -255, -75, 659, -381, 222, 571, -74, -163, 65],\n [-176, 574, 114, 54, 105, 310, 62, -37, -223, -331],\n [-322, 78, 433, 228, -158, 373, 387, -487, -365, 6],\n [60, -54, 641, 304, 314, -82, 449, -315, -210, 115]]\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[[152, -47, 72, -101, -178, -392, 17, 201, 826, 524],\n [279, -89, -118, -361, 48, -578, -200, 430, 201, 94],\n [-210, -277, -15, -312, -454, -45, -203, 344, 595, 386],\n [-121, 10, -238, 46, -289, -264, 41, -47, 238, -265],\n [297, 6, -4, -256, 519, 4, -191, 285, -591, 3],\n [144, 305, -193, 282, -26, -76, 312, -371, 465, -70],\n [-306, 119, 211, 648, -492, -86, 434, -645, 527, -148],\n [-71, -165, 247, 52, -146, -388, -31, 152, 173, 182],\n [493, -69, 42, -459, 446, -453, -285, 483, -346, 56],\n [125, -73, 478, 255, -142, -842, 118, -156, -7, -264]]\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 10x10 matrix:\n[[42, 321, -825, -99, -173, 177, 336, 29, -19, 76],\n [-614, -444, 265, -120, -393, 438, 34, -397, -153, 629],\n [213, 127, 76, 114, 69, -516, 126, 297, 22, -306],\n [154, -127, 516, 27, 276, -243, -218, 62, 8, -145],\n [-106, 122, 90, 492, -461, -726, 277, 463, 147, -523],\n [-416, -494, 285, -456, 17, 690, -106, -595, -273, 889],\n [-98, -64, -93, -108, 27, 450, -152, -241, -1, 209],\n [216, 150, 206, 378, 110, -222, -316, 242, 270, -628],\n [-77, -471, 1007, -48, 298, -24, -436, -186, -57, 135],\n [-621, -717, 662, -396, -109, 606, -136, -637, -306, 980]]\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[[527, -38, 430, 364, -904, -532, -26, 352, -269, 212],\n [-70, -609, 229, -642, 527, -233, -196, 204, 583, 99],\n [-295, 344, -572, -65, 414, 584, 294, -520, -181, -454],\n [-852, 125, 306, 247, 616, 116, -193, 274, 22, 540],\n [-178, 745, -926, 310, 145, 748, -153, -586, -26, -174],\n [-385, 299, -275, -50, 126, -61, -294, 32, 92, 227],\n [-606, 120, 21, -178, 277, -297, -299, 266, 115, 389],\n [-3, -103, 294, -165, -426, -834, -455, 554, 173, 526],\n [188, -25, 88, -185, -484, -494, 215, 114, -304, -174],\n [-126, -40, -249, 11, 728, 925, 519, -582, -81, -583]]\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[[-380, 6, 344, -322, 496, 128, 446, -48, 258, 248],\n [-354, -17, 224, -325, 354, 140, 341, -38, 81, 148],\n [-150, 53, 352, -71, 438, 4, 343, -34, 459, 284],\n [2, -90, -386, -98, -433, 82, -299, 27, -636, -332],\n [328, 40, -104, 328, -212, -152, -236, 28, 96, -48],\n [-306, -31, 124, -299, 228, 136, 241, -28, -45, 68],\n [-260, 8, 252, -216, 358, 84, 318, -34, 204, 184],\n [-264, -34, 76, -266, 162, 124, 184, -22, -90, 32],\n [12, -59, -262, -55, -297, 50, -208, 19, -423, -224],\n [356, 38, -136, 350, -256, -160, -274, 32, 66, -72]]\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[[-618, -74, -146, 458, 746, -84, 218, -864, 309, 442],\n [256, 317, -64, 348, 296, -174, 324, 428, 283, 211],\n [428, 473, -226, 354, 282, -185, 269, 203, -124, -231],\n [182, 399, -451, 277, 38, -302, 408, 290, -235, -186],\n [190, 257, -383, 19, -476, -244, 368, 858, -84, -30],\n [194, 99, -1, -43, -78, -115, 93, 349, -87, -66],\n [657, 514, -464, 3, -626, -131, 203, 864, -436, -584],\n [554, 118, 246, -146, -246, 236, -286, 356, 1, -278],\n [113, -163, 348, -129, 74, 471, -585, -684, -5, -275],\n [162, 101, -17, -43, -78, -235, 225, 553, -49, 52]]?\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 10x10 matrix:\n[[110, 374, 396, -418, 110, 220, 66, -330, 44, 418],\n [-30, -102, -108, 114, -30, -60, -18, 90, -12, -114],\n [-110, -374, -396, 418, -110, -220, -66, 330, -44, -418],\n [-75, -255, -270, 285, -75, -150, -45, 225, -30, -285],\n [-75, -255, -270, 285, -75, -150, -45, 225, -30, -285],\n [10, 34, 36, -38, 10, 20, 6, -30, 4, 38],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n [90, 306, 324, -342, 90, 180, 54, -270, 36, 342],\n [-35, -119, -126, 133, -35, -70, -21, 105, -14, -133],\n [-85, -289, -306, 323, -85, -170, -51, 255, -34, -323]]\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[[36, 490, 35, 134, -152, 67, -629, -398, -790, -235],\n [-434, -1006, -143, 62, 238, 297, 446, 435, 269, -48],\n [1012, 2, 12, -602, -127, -339, 839, 88, 508, 576],\n [-720, -940, -248, 438, 377, 478, -282, 371, -526, -605],\n [477, 286, 185, -528, -86, -303, 668, 27, 844, 551],\n [-905, 1, 96, 896, 19, 443, -608, -55, -145, -113],\n [565, 1232, 246, 316, -421, -49, -693, -682, -677, 267],\n [571, -146, -600, 772, -255, -449, -640, 17, -844, -458],\n [-380, -779, -193, -446, 118, -4, 388, 219, 135, -275],\n [446, -373, -20, -300, -540, -98, 836, -206, 387, 761]]\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[[-170, -138, 192, -242, -208, 4, 362, 398, 216, -100],\n [35, -551, -266, -459, -316, -42, 449, 321, 482, 300],\n [286, -236, -506, -4, 60, -40, -186, -344, 62, 394],\n [-38, 238, 148, 182, 120, 20, -162, -98, -196, -152],\n [-46, 257, 167, 193, 126, 22, -168, -97, -209, -169],\n [-71, 538, 313, 422, 282, 44, -387, -248, -451, -329],\n [0, 197, 77, 173, 122, 14, -178, -137, -179, -95],\n [-46, 60, 90, 20, 4, 8, 10, 40, -30, -74],\n [-69, -304, -19, -316, -238, -16, 371, 334, 313, 79],\n [-182, 383, 413, 207, 106, 42, -92, 57, -251, -363]]\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[[107, 49, -207, 1080, 494, -335, -423, 414, -373, 23],\n [206, -309, -117, 537, 313, -355, -290, 481, -3, -362],\n [731, 85, 408, -593, -241, 572, 229, 417, 206, -438],\n [150, 216, 143, 229, 31, 202, 115, 193, -216, 1],\n [-378, 538, 181, 745, 799, 655, -384, -205, -1311, -33],\n [-355, -227, -14, -131, -219, -401, 586, 101, 401, -100],\n [840, -101, 273, -769, -860, 166, 526, 389, 818, -66],\n [724, -102, 235, 154, 255, 250, -192, 731, -71, -670],\n [-209, -125, 328, -710, -610, 199, 842, -135, 296, -113],\n [-240, 424, -399, 1327, 1064, -203, -921, 33, -861, 273]]?\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[[-52, -20, -55, -249, -63, -120, -87, 56, -203, -247],\n [402, 222, -91, 388, -100, 298, 54, -326, 536, 307],\n [148, 346, -118, -497, -537, 114, -71, -94, 31, -442],\n [228, 0, 2, 562, 194, 184, 90, -200, 410, 478],\n [192, -34, -154, 93, 73, -58, -113, -138, 33, -18],\n [10, -186, -222, -307, 99, -354, -271, 30, -429, -420],\n [422, 420, -36, 286, -348, 468, 136, -348, 684, 282],\n [110, 216, -84, -296, -330, 72, -50, -72, 30, -270],\n [-205, -410, -120, -205, 370, -490, -240, 190, -610, -305],\n [-504, -94, 454, 175, 147, 138, 349, 346, 11, 406]]\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 10x10 matrix:\n[[8, -252, -113, 551, -55, -594, 84, -21, 117, -108],\n [9, 426, 321, 399, 454, 114, -487, -134, 292, -288],\n [526, 592, 89, 285, 57, 530, -134, -565, 17, -548],\n [433, -82, -364, -304, -573, 292, 553, -295, -385, -70],\n [375, 514, 150, 437, 183, 302, -243, -447, 132, -503],\n [300, 176, -60, 133, -108, 178, 78, -288, -57, -247],\n [-284, 76, 269, 342, 435, -268, -422, 173, 314, -11],\n [146, -72, -137, 38, -189, -36, 188, -107, -92, -57],\n [-151, 26, 157, 399, 282, -302, -271, 70, 244, -76],\n [432, 452, 27, 19, -43, 550, -20, -433, -79, -364]]\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 10x10 matrix:\n[[404, -30, -31, 56, -482, 68, -8, -127, -330, 34],\n [491, -83, 168, -49, -384, -36, -81, -370, -359, -564],\n [-762, 770, 29, -234, -90, -373, 561, 366, 273, 160],\n [390, -674, 12, -123, -19, -442, -379, -484, -405, -696],\n [-296, 679, 196, -135, 477, 485, -23, 706, 492, 651],\n [549, 247, 183, -152, 199, 798, 94, 131, 562, -448],\n [90, -252, -90, 143, 183, 182, -263, 88, -31, 394],\n [390, -100, 308, -443, 936, 444, -476, 259, 599, -576],\n [-2, 509, 277, 296, 543, 1134, -120, 449, 534, 649],\n [252, 813, 314, -73, 125, 1011, 389, 314, 732, -223]]\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[[-349, 307, -320, -563, 15, 493, 65, 467, 77, 266],\n [352, 50, -611, 34, -131, -316, -24, -585, -494, 10],\n [581, -1011, -104, -656, -1132, -590, -129, -659, 142, -126],\n [380, 264, -193, -978, -363, 1298, -36, 473, 74, 362],\n [-287, -53, -540, -575, -19, -121, 89, 725, 21, 626],\n [447, -133, 459, -388, -559, 178, 38, 406, 134, 18],\n [408, -57, -201, -743, -26, -34, 37, 77, -61, 415],\n [-823, 57, -25, 831, 286, -267, 182, 133, -72, -57],\n [-162, -511, -63, 284, -814, -3, 77, -280, 112, -74],\n [63, 1010, 230, 44, 217, 415, 437, 901, -439, 380]]\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[[-29, -540, -185, -191, -203, 111, -527, -562, 62, 278],\n [171, -78, -83, 57, -33, 275, -91, -58, 20, 134],\n [61, -180, -102, -17, 13, 424, -310, -372, 105, 306],\n [-317, 453, 257, 1, 214, -472, 414, 340, -38, -338],\n [278, 263, 20, 210, 25, 101, 341, 470, -80, -140],\n [459, -103, -158, 169, -172, 283, 53, 246, -79, 38],\n [71, 37, -30, 61, 108, 423, -119, -178, 93, 222],\n [437, -173, -198, 151, -96, 621, -173, -70, 27, 282],\n [-97, -629, -198, -251, -222, 81, -629, -694, 81, 318],\n [-359, 147, 168, -125, 64, -569, 173, 102, -39, -270]]\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[[729, -26, 301, -52, -247, -416, -418, 130, -61, -439],\n [-33, 431, -512, -489, -224, 179, -24, 416, 278, 454],\n [420, 287, -54, -54, 130, -265, -305, 436, -461, -107],\n [1048, 36, 153, -171, -284, -264, -474, 176, 395, -369],\n [-391, -139, 81, -293, -1237, -794, -28, 56, -125, -841],\n [-416, 137, 892, 374, -1, 395, -114, -314, -360, 376],\n [-334, -286, 330, 597, -100, -402, 196, -515, -209, -540],\n [-560, -356, 145, 131, -982, -626, 294, -384, -53, -593],\n [124, 45, -513, 721, 873, 535, 534, -344, 383, 607],\n [-118, -275, 940, -812, -717, -379, -614, 366, -938, -280]]\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[[336, 424, 241, 159, 533, 239, 288, -180, -22, -369],\n [-22, 399, 532, 243, -136, -68, 185, -348, 277, 125],\n [-27, 368, -62, 138, 337, -146, -57, 297, -293, -137],\n [433, 218, -251, -135, -152, 73, 189, -319, -71, 308],\n [-185, -25, -237, -422, -205, -36, -151, 378, 287, 8],\n [428, 246, 160, 574, 334, 99, -388, -10, -165, -232],\n [-188, 62, 96, -352, -191, -41, 731, -427, 71, 285],\n [-68, -412, -413, -489, -260, 67, 69, 65, 64, 146],\n [-330, -274, -42, -42, -145, -107, -413, 421, 149, -87],\n [-419, 251, 466, -247, -1, -67, 834, -357, 227, 50]]\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[[-261, 689, 445, 336, 467, 152, 36, 174, -321, 304],\n [-151, -508, -91, 251, -143, 569, -10, -236, -244, 546],\n [361, 607, 188, 290, 254, -490, 70, -842, -766, 606],\n [-36, -868, -403, -459, -509, -112, -311, 235, 489, -644],\n [329, -600, 128, 226, 377, -296, 385, -300, 368, -721],\n [200, -406, 791, -39, -99, 126, 147, 609, 1108, -2100],\n [113, -885, -124, -825, -496, -475, -253, 617, 1112, -1584],\n [-844, 44, -268, 166, 54, -74, 379, -510, -1052, 1496],\n [370, 278, 286, 396, 81, 112, 532, -743, -391, 461],\n [-272, -770, -429, -539, 16, -955, -281, 40, 142, -403]]\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[[175, -624, 172, -268, -187, -176, 484, -71, 167, 285],\n [-10, 41, -253, -218, -122, -391, 74, 599, -133, 10],\n [59, 133, 375, 170, -7, 417, -338, -534, 184, -55],\n [-19, -32, 218, 268, 181, 422, -52, -643, 111, -25],\n [79, 285, 205, -70, -205, 55, -434, 88, 86, -75],\n [-45, -742, -368, -128, 175, -368, 968, 121, -121, 265],\n [-180, 261, -57, 438, 384, 429, -150, -507, -75, -180],\n [191, -406, 312, -208, -229, -24, 184, -171, 219, 205],\n [2, -163, -126, -106, -19, -192, 226, 192, -48, 70],\n [-165, -335, -386, 154, 364, -80, 614, -89, -183, 65]]\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 10x10 matrix:\n[[-288, -229, -276, -225, 116, -42, -1035, -275, -12, 756],\n [95, -671, 50, -276, -826, 221, 312, -166, 797, -583],\n [337, 301, -318, 708, -412, 522, 7, 538, -597, 20],\n [271, -463, 189, -458, 1057, -833, -710, 1022, -336, 767],\n [233, 568, -310, 331, -82, -275, 342, 232, -449, -58],\n [273, 42, 94, -105, 412, -565, -162, -167, -311, 294],\n [-102, -226, -465, -614, 27, -852, -256, 98, 395, 522],\n [544, 535, 5, 545, -5, -51, 911, 466, -519, -282],\n [-31, 208, 536, 149, -4, 335, 881, -477, 189, -767],\n [349, -243, 541, -234, 1005, -556, -322, -65, -381, 539]]\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[[215, -724, -167, -93, -66, -61, -148, 373, 315, 176],\n [335, -205, 18, -553, 322, 451, -375, -50, 204, -571],\n [-543, 747, 462, 663, -456, 188, 817, 156, -307, -179],\n [255, 73, 235, 5, 177, 230, 620, 423, 54, 78],\n [439, -605, -480, -880, 359, -186, -791, -317, 190, 441],\n [60, -144, -208, 18, 240, -106, -496, -490, 2, -556],\n [60, 590, -167, 296, 706, -313, 115, -1247, -499, -737],\n [-460, 734, -111, 345, -194, -638, -127, -390, -414, 779],\n [-70, -508, 61, -478, -389, 529, -127, 191, 234, -293],\n [-1269, 164, 342, 431, -1654, 296, 279, 330, -150, 171]]\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[[-260, -170, 222, -611, 127, 102, -214, 564, 301, -109],\n [410, 502, 839, -51, 537, -252, 902, -114, -109, 1],\n [-256, -641, -919, -8, -767, -626, -186, -152, -288, -236],\n [-727, 150, -1017, -345, -659, 518, 261, 378, -230, 248],\n [411, 787, 52, -153, 316, 720, 777, 469, 131, 400],\n [283, 697, 787, -56, 625, 826, 357, 652, 95, -89],\n [-470, -319, -381, -325, -650, -594, -930, 298, 297, -595],\n [346, -499, -340, 408, -105, -158, 206, -263, -439, -53],\n [510, -755, 837, 570, 709, -330, -108, -743, -263, -24],\n [653, -196, -77, 318, 316, 664, 51, 336, -75, 80]]\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 10x10 matrix:\n[[119, -175, 435, 407, 85, -133, 120, 34, -182, -106],\n [-128, 457, -468, -308, -142, -59, -363, -232, -424, 8],\n [127, -105, 357, -617, 324, 507, -218, 284, -520, -256],\n [662, 428, -576, -126, 187, 366, 434, -180, -510, -240],\n [326, 34, -72, 584, -31, -50, 478, -188, 268, -38],\n [-463, -236, 21, -801, 62, -16, -447, 405, -90, 183],\n [110, 4, -146, -788, 278, 314, -108, 302, -582, -96],\n [40, -208, -334, 518, -173, -260, 618, -32, 1020, 306],\n [-437, -343, -95, -497, 1, -263, -162, 407, 186, 319],\n [136, 222, -294, -738, 138, 602, -142, 45, -138, -137]]\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[[-192, -27, 377, -158, -92, -45, 33, -146, 315, -350],\n [66, -198, 241, 92, 107, -129, -93, -88, 99, -244],\n [-144, 120, 32, -144, -120, 64, 80, -16, 96, -16],\n [-90, 207, -216, -114, -123, 132, 102, 78, -72, 222],\n [216, -279, 129, 234, 216, -165, -159, -42, -45, -150],\n [-42, -174, 383, -4, 41, -127, -59, -144, 237, -372],\n [192, 27, -377, 158, 92, 45, -33, 146, -315, 350],\n [510, -579, 162, 538, 481, -334, -344, -46, -186, -214],\n [312, -348, 88, 328, 292, -200, -208, -24, -120, -120],\n [216, -114, -166, 204, 156, -50, -94, 68, -210, 140]]?\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, -117, 102, -380, -284, 144, -624, -489, 310, 120],\n [97, 303, -52, 322, 19, 216, 850, 667, -653, -669],\n [457, 72, -228, 355, 397, -580, 86, -76, -368, 573],\n [186, -207, 219, -124, -20, 241, 244, 326, -162, -303],\n [-69, 668, -141, 511, -321, 375, 664, 633, -296, -484],\n [-171, 376, -18, 150, 9, -48, -13, -26, -104, 208],\n [-735, 828, 451, 120, -47, 473, 159, 475, 550, 161],\n [-558, 305, 322, -236, 84, 20, -487, -305, 343, 539],\n [444, 198, -570, 688, 194, -402, 610, 295, -254, -92],\n [-49, 136, 19, 195, -145, 351, 466, 547, 314, -458]]\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[[46, -378, -234, -249, -250, -1198, 618, 80, 95, 382],\n [469, -169, -546, -553, -736, -883, -111, 596, -346, 867],\n [67, 340, -1, 389, -683, -520, -407, -454, 604, 270],\n [-289, -701, -793, -691, -577, -365, 446, 597, -687, 626],\n [-619, -362, -207, 265, -206, 262, -189, 163, 58, -207],\n [-239, -423, -320, -221, -172, -148, 223, 317, -174, 123],\n [874, 699, 402, -78, 202, 200, -521, -38, 125, 74],\n [345, 189, -236, 370, 219, 133, 612, -382, 271, -234],\n [742, 406, 439, -587, 355, -294, 23, 19, -294, 317],\n [277, 295, 181, -246, -186, 80, -319, -84, 154, 207]]\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[[-90, 355, -231, -243, 116, -152, -488, -6, -234, -117],\n [-130, 239, -147, -239, 68, -176, -344, 10, -226, -57],\n [200, -256, 150, 322, -64, 253, 382, -23, 302, 42],\n [-140, -10, 24, -148, -24, -147, -18, 29, -134, 48],\n [70, 511, -357, -133, 196, -7, -658, -49, -140, -231],\n [140, -166, 96, 220, -40, 175, 250, -17, 206, 24],\n [-190, -199, 159, -125, -100, -170, 220, 52, -106, 141],\n [-300, 142, -60, -384, 8, -341, -254, 51, -354, 36],\n [300, 166, -150, 258, 104, 292, -152, -72, 228, -162],\n [480, 248, -228, 420, 160, 470, -220, -114, 372, -252]]\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[[555, -308, -570, -469, -612, 830, -260, -201, 211, 169],\n [-73, 252, -466, -520, -845, 360, -286, 495, 299, -174],\n [-142, -812, -56, -245, 774, 420, 894, 194, 887, 957],\n [-894, 548, 445, -683, -298, 75, 35, 286, 849, -141],\n [879, 278, -742, 32, -389, -237, -168, -192, -1056, -509],\n [-986, 515, 1027, 43, 106, -266, -53, 276, 585, -136],\n [222, -478, -270, -368, 807, 319, 19, -456, 346, -52],\n [36, 16, 772, 372, 748, 58, 408, 478, 346, 130],\n [442, 110, 479, 867, 443, -395, 767, 887, -365, 432],\n [384, -597, -287, 33, -36, 476, 105, -119, 174, 591]]\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[[606, 66, 1163, 891, 528, -326, -140, 91, -229, -961],\n [312, -679, 701, 108, 49, -182, 313, -28, -625, -1134],\n [-106, -25, -108, 140, 146, 460, -1237, -386, 642, 188],\n [-596, -593, -750, -824, -189, 398, 494, 423, 679, 100],\n [-39, 283, -475, 32, 501, 432, -204, 365, -85, 65],\n [-563, -67, -197, 267, -54, -350, -255, 196, 692, 76],\n [363, 39, 1125, -118, -14, -419, 820, 29, 4, -758],\n [533, 855, -380, 267, 19, 472, 577, 107, -693, 40],\n [102, 19, 624, -738, -458, -167, 495, 122, 11, 259],\n [-230, 631, -1055, 90, 343, 390, -31, 435, -65, 606]]\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[[-98, -74, -284, 88, 295, -63, -19, -343, -224, -88],\n [-41, 167, 372, -199, -110, 329, -153, 304, 87, 44],\n [-693, 170, -85, -7, 244, 417, -434, 196, -521, -310],\n [451, 204, 436, -44, -499, 54, 190, 166, 556, 343],\n [-2, 582, 243, 23, 138, 692, -215, -547, 33, 249],\n [177, -336, -416, 100, 303, -438, 214, -446, -100, -51],\n [200, -348, 169, -325, 102, -182, 69, 287, 77, -57],\n [194, -244, 460, -508, 64, 70, -46, 490, 140, -22],\n [176, -173, -196, 179, -216, -426, 252, 15, 149, 33],\n [157, -567, -435, 94, 52, -755, 314, 31, -38, -157]]\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[[245, -84, -118, -277, -528, 318, 200, 908, -356, 1107],\n [-171, 967, 39, -549, -327, -175, 296, -108, 646, 832],\n [-163, -443, 853, -217, -693, 646, -546, 383, 359, -207],\n [54, 1027, -532, -199, -362, -327, 785, -143, 900, 1161],\n [23, -56, -525, 611, 648, -376, -166, -815, -465, -648],\n [-574, -150, 150, 449, 446, -260, 225, 201, -636, -117],\n [-398, -298, 554, -160, 3, 89, -259, 55, 226, -475],\n [-167, 777, 49, -572, -98, 67, 12, 241, -533, 721],\n [-307, -768, 796, 305, 331, 18, -543, -391, 330, -1502],\n [-631, 519, 232, 229, 35, -51, 204, 34, -306, 192]]\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, 130, 194, -333, 64, -69, -10, 250, 434, -287],\n [-43, -433, -533, 716, 168, -671, -610, -1217, -1123, 990],\n [66, -286, 407, -1037, 889, -156, -732, 112, 482, -886],\n [-406, -1205, 73, 256, 209, -127, -120, 10, 314, -350],\n [145, -17, 168, -286, 137, 458, 297, 671, -53, -360],\n [-125, 865, 263, -504, -547, 526, -452, 49, -181, -419],\n [-124, 20, -440, 532, 49, -1079, -631, -1412, -216, 938],\n [75, 377, 359, -1163, 894, -62, -163, 774, 66, -575],\n [-584, -32, 200, 172, -733, -169, -109, 105, 79, 99],\n [-24, -553, -411, 474, 368, -826, -820, -1291, -745, 750]]\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, 16, 44, -203, -221, 127, 355, 204, -551, 228],\n [-46, 34, -35, -34, -45, -28, 9, -6, -29, 49],\n [89, -122, 273, 441, 524, -117, -46, -90, 136, -445],\n [-290, 308, -230, -286, -376, -262, 260, 12, -532, 450],\n [630, -400, 47, -293, -262, 798, -180, 270, 429, -6],\n [130, 64, 100, 2, 2, -86, 330, 96, -526, 80],\n [573, -432, 81, -162, -111, 753, -297, 198, 624, -150],\n [767, -418, 32, -440, -422, 929, -78, 372, 277, 121],\n [573, -278, 110, -206, -178, 563, 58, 264, 21, 23],\n [5, -188, 35, 166, 211, 157, -395, -102, 682, -300]]\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[[-252, -270, 378, 18, -234, 342, 396, -180, -18, 324],\n [-224, -240, 336, 16, -208, 304, 352, -160, -16, 288],\n [-56, -60, 84, 4, -52, 76, 88, -40, -4, 72],\n [280, 300, -420, -20, 260, -380, -440, 200, 20, -360],\n [-238, -255, 357, 17, -221, 323, 374, -170, -17, 306],\n [28, 30, -42, -2, 26, -38, -44, 20, 2, -36],\n [-196, -210, 294, 14, -182, 266, 308, -140, -14, 252],\n [-42, -45, 63, 3, -39, 57, 66, -30, -3, 54],\n [28, 30, -42, -2, 26, -38, -44, 20, 2, -36],\n [-210, -225, 315, 15, -195, 285, 330, -150, -15, 270]]\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[[533, 34, -185, -319, -170, 79, -57, -670, -133, 13],\n [-77, 184, -553, -546, -96, -63, -245, -169, -362, 496],\n [93, 536, 67, 1236, 238, -41, -335, -72, -840, 294],\n [379, -376, 385, 67, 558, 913, -89, 12, 544, 417],\n [-277, 280, -499, -700, -350, -764, 20, 149, 89, -194],\n [-89, 284, -31, 113, 346, -44, -393, 366, 69, 545],\n [294, -1496, 360, 464, 572, 778, 508, -144, 310, -390],\n [9, -1468, -55, -909, 124, 418, 310, -176, 413, -167],\n [-564, 468, 189, 542, 341, -247, -398, 844, -13, 292],\n [178, -518, 72, 161, -166, 357, 225, -516, -490, 51]]\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[[145, -332, -335, -233, -139, -255, -335, -28, -61, -49],\n [-1, -10, -25, 23, 31, 12, 8, -41, 25, -47],\n [-225, 558, 615, 287, 111, 360, 500, 187, 9, 241],\n [-193, 500, 575, 209, 43, 291, 419, 232, -35, 289],\n [-198, 396, 330, 418, 330, 396, 484, -154, 198, -154],\n [-18, 90, 150, -56, -102, -9, 19, 167, -90, 194],\n [78, -192, -210, -102, -42, -126, -174, -60, -6, -78],\n [94, -302, -410, 0, 122, -93, -177, -309, 134, -366],\n [-8, 28, 40, -4, -16, 6, 14, 34, -16, 40],\n [-13, -76, -205, 205, 271, 111, 79, -352, 217, -403]]\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[[276, -758, 264, 80, 581, 892, 913, 132, 70, -350],\n [-235, -167, 231, -331, 348, 617, 224, 161, 19, 504],\n [606, -2, -710, -780, -98, 354, 365, -438, -237, 344],\n [-284, 553, -786, -1108, -483, -249, -449, 616, -143, 1165],\n [352, 208, -334, -1014, 754, 21, 230, 124, -924, 396],\n [-122, -288, 547, -457, 436, 1250, 839, -39, 248, 197],\n [721, -1050, -195, 818, 544, 868, 670, 677, 374, 751],\n [94, -560, 1386, 1121, 274, 121, 200, -86, 580, -957],\n [-32, 440, 499, 492, -264, -840, -832, -269, 81, 26],\n [337, 512, -555, 382, -734, -496, -522, -759, 198, 233]]\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[[243, -35, 332, -412, -134, 618, 491, 579, 265, 317],\n [100, 199, -287, 723, -5, -830, -595, -819, -246, -373],\n [-487, -473, -169, -205, -1181, 622, -285, 827, -1123, -244],\n [514, 556, 15, 618, -352, -925, -741, -1247, -441, -639],\n [-517, 53, 709, 137, -95, -104, 621, 211, -453, 966],\n [72, -306, 183, -18, 684, -538, 499, -86, -141, 837],\n [978, 101, -557, 146, 9, -520, -821, -661, 278, -1148],\n [766, 13, 217, -103, 602, -384, 394, -349, 299, 480],\n [-1271, -522, -513, -180, -1067, 670, -620, 906, -1031, -685],\n [981, -521, -555, -228, 80, 126, -114, 255, 114, -198]]?\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 10x10 matrix:\n[[-167, -597, 762, 305, 154, -229, 119, -136, 120, -603],\n [-655, -510, 474, 69, -584, 91, -171, -348, -303, -361],\n [244, -283, -298, -579, 297, 632, 123, -79, 662, 321],\n [-273, -31, -512, 284, -203, -219, -162, -211, -265, 350],\n [279, -286, -651, -565, 134, 674, 149, 39, 609, 600],\n [165, 290, -879, -229, -112, 287, 119, 54, -129, 549],\n [681, 673, -362, 39, 540, -267, 79, 487, 233, 341],\n [162, 80, -637, -107, 207, 203, 321, -171, -98, 190],\n [-602, 4, 602, 785, 229, -988, -645, -562, -186, -319],\n [-76, 194, 132, -53, -199, 20, -67, 44, -206, -107]]\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 10x10 matrix:\n[[-799, -307, -110, -217, -333, 296, 541, -428, -263, -262],\n [792, -448, 624, -389, -765, -757, -416, -320, 135, 314],\n [26, -603, 800, -133, -434, 927, 880, 403, -370, -711],\n [690, -468, 352, 299, -196, 187, -310, 604, -29, -233],\n [33, 66, 125, -77, 166, 471, 399, 209, -285, -252],\n [-9, -564, -621, -116, -460, -463, -1292, 586, -19, 406],\n [659, 248, -26, -230, 110, -646, -775, 46, -358, 749],\n [-204, -84, -350, 174, -8, -308, -586, 0, -208, 412],\n [486, 362, -183, 428, 601, 213, -64, 324, 203, -244],\n [136, 137, 217, 146, 263, 160, -122, 388, -527, 323]]\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[[109, -267, 262, -248, 286, 293, -229, 341, 447, 232],\n [424, -284, 648, -316, 92, -32, -196, -120, 452, 172],\n [-50, 93, 230, 407, -369, -164, 7, -135, 259, -631],\n [-125, 240, -260, 235, -245, -235, 200, -265, -390, -215],\n [163, -70, -136, -435, 285, 9, 38, -83, -344, 631],\n [76, -8, 40, -72, 4, -60, 16, -98, -60, 80],\n [-90, -30, -356, -260, 320, 206, 14, 226, -266, 484],\n [-104, 180, -300, 90, -100, -144, 168, -173, -406, -6],\n [-401, 76, -196, 439, -93, 257, -60, 449, 298, -507],\n [-243, -22, -128, 167, 71, 271, -90, 407, 244, -171]]?\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[[52, 194, -237, -30, 166, -115, -123, 159, 304, -182],\n [4, -214, -54, -360, 442, 170, -360, 234, -134, -386],\n [-12, -286, 17, -370, 414, 215, -341, 197, -236, -350],\n [6, 223, 4, 310, -357, -170, 293, -176, 173, 305],\n [122, 641, -527, 220, 41, -415, -4, 193, 841, -125],\n [54, 343, -224, 190, -93, -230, 89, 28, 413, 41],\n [100, 442, -445, 50, 190, -275, -131, 239, 632, -238],\n [34, -91, -189, -360, 517, 95, -414, 315, 49, -473],\n [94, 571, -394, 290, -113, -380, 115, 74, 701, 29],\n [-126, -651, 546, -210, -63, 420, 21, -210, -861, 147]]?\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[[-85, 135, 116, -517, 868, -472, -482, 229, 720, 907],\n [347, -179, -190, -781, 124, 341, -428, 305, 316, -365],\n [-668, 606, 324, 442, -20, -322, 488, -202, 72, 172],\n [-167, -270, -286, 230, -909, 64, 346, -380, -69, -142],\n [-319, 212, -417, -74, 117, 134, 213, -923, 207, -118],\n [-90, -591, -475, 590, -1103, -141, 527, -997, -408, -413],\n [-519, 696, 267, -372, 45, 211, 131, 212, 254, -596],\n [284, -95, 209, -278, 199, -388, -95, 356, 411, 21],\n [66, 330, 360, -591, 683, 242, -590, 971, 178, 173],\n [197, -361, 237, 398, -165, -725, 167, -7, -88, 66]]\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, 26, -10, -6, -4, -6, -34, -28, 40, 12],\n [60, 65, -25, -15, -10, -15, -85, -70, 100, 30],\n [-132, -143, 55, 33, 22, 33, 187, 154, -220, -66],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n [-72, -78, 30, 18, 12, 18, 102, 84, -120, -36],\n [216, 234, -90, -54, -36, -54, -306, -252, 360, 108],\n [168, 182, -70, -42, -28, -42, -238, -196, 280, 84],\n [-60, -65, 25, 15, 10, 15, 85, 70, -100, -30],\n [-168, -182, 70, 42, 28, 42, 238, 196, -280, -84],\n [264, 286, -110, -66, -44, -66, -374, -308, 440, 132]]\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[[299, 379, 261, -199, -406, -264, -115, -175, -273, -41],\n [528, 849, 734, -447, -493, -318, -170, -116, -266, 168],\n [110, 283, 431, -967, 196, -320, 361, 310, 279, 805],\n [-282, -641, -677, -171, -108, -359, 309, -164, -125, -81],\n [100, 54, -59, -524, -479, -592, 203, -240, -303, 77],\n [-182, -279, -151, 619, 584, 648, -193, 258, 337, -133],\n [668, 292, 211, 110, 33, 188, -603, 72, -153, -113],\n [-66, -303, -328, 309, 65, 126, -104, -50, -44, -246],\n [277, 181, -100, 133, -803, -403, -230, -519, -634, -532],\n [-169, -302, -250, 194, 232, 171, 24, 75, 124, -56]]?\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[[-161, 23, -177, 0, 325, -203, 565, -244, 974, 837],\n [44, -128, -1575, -1034, -1138, -467, -234, 811, 136, 956],\n [-55, -87, -743, -507, -351, -273, -142, 550, -359, 115],\n [-1006, 458, -135, -388, 60, -819, -602, 131, -618, 0],\n [-315, 32, -408, -436, -425, 124, 18, 13, -54, -229],\n [169, -552, 594, 199, 464, 376, 583, -249, 649, 177],\n [26, 324, -903, -389, -1229, 235, -502, 128, 14, -68],\n [1105, 20, -265, -337, 168, -548, 601, 214, -198, 815],\n [726, -477, -120, 96, -20, 348, 382, 249, 139, 76],\n [622, 327, -195, -100, 59, -138, 484, -148, -258, 30]]\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[[70, 0, 290, 9, -159, 293, -537, -34, -165, -453],\n [299, 163, 194, -56, 118, 231, -158, 245, -223, -238],\n [-36, 424, 241, -547, -601, 120, 79, -93, 570, -487],\n [286, 238, 944, -70, 66, -488, -14, -118, -192, -18],\n [357, -356, -229, 715, 610, 141, -762, -83, -1134, 336],\n [-26, 36, 81, 340, 96, -617, 623, 59, 201, 647],\n [-514, 233, -308, -914, -391, -334, 1111, -123, 1155, 79],\n [-132, -26, 149, -34, 56, -275, 430, 113, 269, 156],\n [401, 255, 1002, -253, 201, -196, -153, 77, -328, -317],\n [197, 265, 308, -524, 86, 75, 156, 161, 45, -308]]\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 10x10 matrix:\n[[486, -375, -828, 401, -261, 102, 514, -1307, 76, -414],\n [-124, 248, -190, 696, 662, 768, 308, -158, -266, -120],\n [621, -486, -754, -34, 99, -710, 747, -930, 388, 426],\n [252, -436, -165, -245, -784, -181, -148, -388, -45, -427],\n [316, 198, 166, 380, -48, -91, 467, -487, -26, 479],\n [265, 513, 1038, 240, -915, 36, -504, 11, -114, -136],\n [464, -351, 247, -326, -579, -634, 9, -26, 11, 274],\n [51, 506, 559, 300, -1006, 245, -280, -574, -57, -333],\n [336, 127, 255, 160, 91, -258, 109, -16, 107, 330],\n [-703, -107, -859, -557, 631, -176, 183, 44, 425, 124]]\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[[74, -143, -224, 334, -829, 658, -128, 110, -42, -167],\n [314, 77, 900, 750, -99, -243, 179, 268, -424, 580],\n [102, 29, -188, -138, 421, -207, 279, 78, 206, -243],\n [-286, 277, 531, 386, -354, -237, 72, 189, -130, -301],\n [160, -243, 93, 100, 293, -49, 159, 65, 110, 299],\n [-436, -298, 367, 180, -337, 120, -117, -51, 102, 407],\n [-524, 82, -152, -426, 94, -161, -207, -180, 210, -433],\n [470, -310, -1102, -345, 176, 536, 336, 15, 438, -197],\n [1048, 593, -346, 59, -119, 128, 470, 27, -636, 628],\n [-490, -261, -5, 0, -292, 232, -577, -31, 192, -678]]\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[[289, -739, -340, 337, 607, -671, 27, 809, -438, -524],\n [923, -725, 238, -753, 455, 433, 91, -361, 102, 32],\n [-53, 574, 473, 98, 224, 591, 155, -466, 31, 393],\n [-514, 1064, 385, 133, -463, 704, -27, -652, 408, 556],\n [-201, 425, -176, 461, -827, 43, -818, 49, 472, -151],\n [-597, 280, -323, -233, -786, 90, 362, -158, 909, 604],\n [143, 389, -362, 224, -131, 850, -152, -387, 986, 443],\n [208, -179, 543, -1032, 373, 496, 894, -704, 9, 621],\n [842, -616, 113, -655, 539, -68, 333, -500, -541, 175],\n [193, -126, 647, -839, -30, 33, 493, -635, -292, 466]]\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[[1296, 299, -275, -58, 331, -251, 247, 360, 258, 1190],\n [-312, 165, 172, 134, 227, 45, -162, -73, 83, -238],\n [261, -62, -214, 60, -400, -283, -191, -150, 266, 208],\n [384, -192, -147, -441, -18, 282, 612, 177, -576, 270],\n [450, 309, -141, -54, 81, -111, -9, -204, 114, 402],\n [507, -474, -278, -531, -328, 243, 724, 284, -657, 338],\n [-351, -224, 99, 27, -80, 89, 5, 113, -100, -318],\n [-472, -356, -22, -310, -400, 296, 252, -210, -552, -516],\n [61, 341, 246, 653, 557, -392, -582, 385, 874, 220],\n [206, -399, -188, -485, -301, 291, 605, 113, -660, 76]]\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, -562, -199, 195, 438, 155, 263, 94, -1, -558],\n [-183, 644, 407, -276, -506, 251, 415, -550, 117, -130],\n [-389, -269, 289, -91, 544, -209, 260, 573, 740, -195],\n [-546, -61, 694, -533, -20, 163, -202, -156, 49, 771],\n [144, 25, 130, 24, -221, -275, -310, -478, -78, 931],\n [25, 99, -270, 201, 195, 97, -146, 443, 27, -612],\n [-509, 86, 661, 17, 502, -357, -445, 142, 852, 524],\n [-234, -416, 375, -242, 180, 93, 797, -22, 256, 40],\n [-333, -550, -118, 78, 899, 122, -64, 1552, 198, -531],\n [-833, -465, 794, -785, 439, 339, 244, 739, -47, 162]]\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 10x10 matrix:\n[[511, 166, 405, -577, -229, -24, -206, 612, 110, -52],\n [321, 331, -63, -377, 295, -127, -312, 112, -199, -307],\n [291, -367, 821, -72, -417, 16, 240, 462, -429, 364],\n [-368, -344, 58, 286, -332, 78, 292, 14, 660, 428],\n [-359, 180, -693, 358, -305, 421, 46, -448, 252, -345],\n [-482, 38, -642, 481, 156, 135, 84, -624, 70, -163],\n [305, -79, 460, -207, -657, 243, 86, 485, -7, 70],\n [235, 339, -208, -175, -391, 355, -158, 75, -133, -468],\n [89, -54, 128, 143, -39, 88, 84, -117, -700, -103],\n [-171, -196, 4, 434, -221, 227, 260, -297, -562, -10]]\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[[51, 374, 153, -34, -102, 102, 102, -17, -68, -153],\n [42, 308, 126, -28, -84, 84, 84, -14, -56, -126],\n [-12, -88, -36, 8, 24, -24, -24, 4, 16, 36],\n [-24, -176, -72, 16, 48, -48, -48, 8, 32, 72],\n [-3, -22, -9, 2, 6, -6, -6, 1, 4, 9],\n [-9, -66, -27, 6, 18, -18, -18, 3, 12, 27],\n [60, 440, 180, -40, -120, 120, 120, -20, -80, -180],\n [-30, -220, -90, 20, 60, -60, -60, 10, 40, 90],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n [24, 176, 72, -16, -48, 48, 48, -8, -32, -72]]\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[[107, -182, 705, 461, 451, -205, -345, -151, -307, -585],\n [376, -69, 825, 871, 504, -183, -125, -541, -235, -917],\n [239, -752, 278, 321, -397, 225, -222, 456, 687, 102],\n [-11, -199, 55, -64, -31, 354, -281, 202, -71, 335],\n [-630, -370, -789, -614, -274, 48, -495, 317, 0, 523],\n [123, 241, 60, -70, 53, 332, 46, -10, -202, 278],\n [-141, -105, -164, -512, -655, -66, -528, 866, 424, 425],\n [-104, 108, -228, -20, -16, -260, 128, -188, 36, -210],\n [97, -71, 264, 380, -121, -342, -532, -65, 123, -640],\n [-395, 301, -432, -511, -134, 232, -955, 141, -557, 369]]\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 10x10 matrix:\n[[62, -311, 841, 674, 201, -72, 526, 23, 71, 110],\n [163, 279, -440, -259, 111, 39, -199, -305, -131, -369],\n [60, 335, -765, -580, -85, 0, -460, 5, -45, -170],\n [533, 204, 7, 115, 392, -423, 39, 490, 230, -105],\n [-468, -20, -452, -476, -460, 312, -340, -196, -144, 152],\n [400, 137, 169, 280, 413, -132, 208, -213, -35, -386],\n [-761, -297, -113, -307, -663, 426, -193, -149, -128, 450],\n [483, 49, 357, 385, 427, -378, 259, 385, 210, -70],\n [-158, -302, 427, 210, -164, -159, 144, 662, 265, 569],\n [296, -159, 726, 652, 379, -195, 494, 63, 98, -57]]\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[[-391, -727, -108, -172, 520, -339, 336, -141, 391, 475],\n [405, 220, 648, -408, 156, 206, -15, -447, -243, -710],\n [669, 523, 146, -309, -54, 46, 142, 160, -133, -991],\n [-345, -538, -480, -42, 174, -422, 207, 75, 405, 530],\n [96, 551, -146, 287, -760, 232, -577, -23, -332, 45],\n [39, 323, 188, 225, -261, 306, -275, -17, -280, -24],\n [28, -555, -198, -412, 705, -487, 708, 205, 509, -172],\n [-315, -374, -688, 106, -38, -418, 133, 281, 383, 558],\n [342, 197, 572, -251, 259, 226, 118, -178, -193, -632],\n [-152, -673, -230, -339, 652, -490, 599, 91, 516, 109]]\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[[-907, 81, -82, -396, -270, -4, 28, 857, 721, -238],\n [1109, -174, -441, 1412, 522, 509, 0, -444, -537, -157],\n [-784, 281, 1445, 382, -408, 181, -50, 1156, 1151, -979],\n [556, 385, -696, 141, 538, -182, -48, -321, -509, -14],\n [-15, 886, 513, 527, 248, 118, -485, 147, 1115, -555],\n [-277, 369, -779, -379, -481, -281, -237, -87, -730, 455],\n [419, 249, -693, 43, -608, 334, 48, 639, -989, 77],\n [17, 118, -382, 614, 50, -292, -218, 267, -1346, 252],\n [-30, 113, -1123, -23, -471, 55, 167, -69, 409, 14],\n [633, 123, -231, 1174, 799, 629, -578, 404, 277, 333]]\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[[494, -157, 304, -106, 184, -425, 57, -167, -3, 40],\n [-328, -678, -360, -271, 138, -243, 340, 493, -326, -248],\n [319, -236, -304, -410, 220, -296, -218, 29, 248, -486],\n [-471, -235, 583, 138, 87, -99, 888, 156, -923, 871],\n [-585, 161, -587, -291, 3, 438, -120, 207, 25, -227],\n [-624, -642, 281, -170, 245, -278, 1035, 438, -1068, 627],\n [104, -52, 386, 622, -306, -14, 98, -14, -32, 246],\n [332, -96, 253, 562, -295, -108, -123, -44, 218, -33],\n [354, 1001, 479, 206, -89, 371, -402, -699, 349, 421],\n [350, 851, 158, 10, -34, 327, -537, -575, 489, 82]]\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[[84, 123, 374, -88, -202, 95, 319, -298, 28, -336],\n [-350, 431, -526, -48, -293, 44, -87, -445, 409, 273],\n [-9, 58, -333, -209, -424, 187, 144, -981, -329, -113],\n [-365, 97, -557, -395, -222, -52, -614, -397, 846, 319],\n [199, -8, 88, 7, 383, 222, 191, 601, -140, -20],\n [17, 294, -1113, 118, 650, -21, -301, 292, 316, 380],\n [199, -289, 544, -160, -309, 13, 198, -504, -354, -443],\n [-616, 325, -337, -317, -330, 651, -72, 594, 276, 855],\n [60, -26, -160, 66, 489, -423, -482, 357, 751, -17],\n [268, 274, -623, 292, 343, -95, 232, -392, -284, -177]]\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[[32, 144, -88, 80, -80, -168, -160, -96, -144, -168],\n [-24, -108, 66, -60, 60, 126, 120, 72, 108, 126],\n [-28, -126, 77, -70, 70, 147, 140, 84, 126, 147],\n [-52, -234, 143, -130, 130, 273, 260, 156, 234, 273],\n [48, 216, -132, 120, -120, -252, -240, -144, -216, -252],\n [40, 180, -110, 100, -100, -210, -200, -120, -180, -210],\n [60, 270, -165, 150, -150, -315, -300, -180, -270, -315],\n [48, 216, -132, 120, -120, -252, -240, -144, -216, -252],\n [16, 72, -44, 40, -40, -84, -80, -48, -72, -84],\n [-64, -288, 176, -160, 160, 336, 320, 192, 288, 336]]\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[[173, -117, 176, -201, -212, -254, 299, -219, 162, 10],\n [333, 215, -37, 441, 415, 3, -267, -51, -422, -62],\n [-119, 156, 142, -27, 56, -103, -77, 102, 24, 50],\n [298, 121, -202, 476, 400, 177, -294, -27, -442, -92],\n [416, -137, -576, 610, 378, 519, -288, -105, -550, -192],\n [21, 65, 62, 23, 46, -62, -25, 3, -26, 10],\n [27, -146, -137, -15, -79, 120, 63, -48, 20, -34],\n [198, -75, -462, 456, 300, 453, -282, 9, -402, -132],\n [219, 253, 118, 277, 314, -136, -191, -21, -274, -10],\n [-203, 32, 42, -111, -60, 5, -17, 114, 112, 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[[-859, 491, 506, 150, 982, -201, -953, -43, -135, -63],\n [73, -8, -97, 294, -530, 171, 228, -471, 270, -542],\n [673, -70, -219, 182, -871, -712, 693, 957, 620, -635],\n [274, 486, 264, -544, -204, -460, 201, -187, 28, -1],\n [-97, 642, 615, 423, 779, -35, -38, 183, -239, -180],\n [-176, 226, 357, -618, -182, -388, -283, -1052, -633, -199],\n [632, -172, -241, 108, -4, 486, 848, 263, -275, 336],\n [-13, 107, 251, 9, -64, 947, 243, 310, 108, 538],\n [166, 608, -507, -137, 722, 222, -271, 97, 70, 84],\n [604, -667, -298, -391, -538, -1115, 514, -97, -457, -132]]\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[[-73, 74, -126, -11, 102, -112, -78, -94, 299, -212],\n [-79, 19, 133, 2, -499, 49, 95, -107, -237, 589],\n [61, -94, 450, -221, 466, 156, -590, 30, -23, -384],\n [144, -148, 396, -140, 374, 208, -352, 154, -252, -232],\n [522, -372, 96, 174, 357, 378, 510, 711, -984, -42],\n [172, -106, -158, 190, -218, 94, 550, 262, -472, 334],\n [-6, -24, 112, 18, -336, 76, 120, -8, -278, 436],\n [175, -167, 439, -190, 645, 215, -519, 185, -151, -525],\n [143, -133, 217, -8, 18, 183, 33, 180, -417, 143],\n [-254, 183, -59, -81, -169, -189, -241, -345, 488, 11]]\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[[76, 64, -52, 12, -52, 68, -40, -8, 44, 84],\n [399, 336, -273, 63, -273, 357, -210, -42, 231, 441],\n [342, 288, -234, 54, -234, 306, -180, -36, 198, 378],\n [-342, -288, 234, -54, 234, -306, 180, 36, -198, -378],\n [-152, -128, 104, -24, 104, -136, 80, 16, -88, -168],\n [-399, -336, 273, -63, 273, -357, 210, 42, -231, -441],\n [-152, -128, 104, -24, 104, -136, 80, 16, -88, -168],\n [152, 128, -104, 24, -104, 136, -80, -16, 88, 168],\n [-57, -48, 39, -9, 39, -51, 30, 6, -33, -63],\n [-380, -320, 260, -60, 260, -340, 200, 40, -220, -420]]\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[[-117, 9, 162, -45, -135, 180, -90, -63, -81, -126],\n [182, -14, -252, 70, 210, -280, 140, 98, 126, 196],\n [-91, 7, 126, -35, -105, 140, -70, -49, -63, -98],\n [286, -22, -396, 110, 330, -440, 220, 154, 198, 308],\n [143, -11, -198, 55, 165, -220, 110, 77, 99, 154],\n [-273, 21, 378, -105, -315, 420, -210, -147, -189, -294],\n [-156, 12, 216, -60, -180, 240, -120, -84, -108, -168],\n [-13, 1, 18, -5, -15, 20, -10, -7, -9, -14],\n [-221, 17, 306, -85, -255, 340, -170, -119, -153, -238],\n [-286, 22, 396, -110, -330, 440, -220, -154, -198, -308]]\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 10x10 matrix:\n[[-194, -230, 472, -498, 284, 568, 42, 182, 12, 796],\n [414, 251, -248, 275, 193, 4, -209, -71, -638, 62],\n [-639, -76, 143, -337, 131, -241, 88, 555, 33, 216],\n [300, 301, -535, 532, -335, -533, 85, -268, -159, -884],\n [-284, -20, 81, -273, -224, 18, 570, 51, 55, -177],\n [15, 137, -191, 74, -278, -176, 403, -122, -95, -481],\n [30, -103, 10, 71, -269, -29, 91, -245, 472, -331],\n [-855, -367, 580, -865, -248, 310, 877, 283, 598, 212],\n [4, 134, -186, 112, -98, -219, 128, 10, -166, -283],\n [-397, -280, 261, -255, -211, 3, 168, 33, 731, -78]]\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[[45, -231, 301, -394, -241, 790, 271, -709, -201, 27],\n [-525, 346, 354, 499, 669, 217, -180, -418, -965, 730],\n [-229, -62, 19, 653, 141, -546, 115, 377, -641, -15],\n [-641, 631, 765, 17, 155, -495, 38, 128, 220, 433],\n [368, -341, -64, -683, -490, 19, 21, 261, 658, -203],\n [-454, 521, 581, -94, 148, 186, 138, -730, 77, 205],\n [-166, 127, 328, 87, -28, 779, 311, -487, -278, 71],\n [-101, -53, 284, -155, -77, -22, 5, 279, -38, 278],\n [-630, 658, 565, 420, 316, 9, 217, -566, -251, 177],\n [-548, 771, 347, 346, 698, 289, -233, -576, -300, 612]]\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[[352, -327, 230, 9, 284, -72, 26, -43, 113, -24],\n [417, -103, 219, -215, 425, 181, -79, -38, -87, 98],\n [48, -304, -192, 52, 248, 148, -52, -68, -24, -148],\n [348, -110, 316, -87, 210, -61, 17, -9, 60, 85],\n [298, 111, 380, -153, 86, -78, 20, 29, 23, 180],\n [142, -12, 194, -21, 20, -99, 35, 11, 62, 57],\n [-62, -189, 204, 307, -338, -510, 204, 33, 347, -84],\n [350, -52, 98, -253, 452, 301, -125, -45, -170, 89],\n [237, 194, 429, -122, -55, -179, 59, 55, 66, 206],\n [-107, 381, 67, -118, -201, 6, -8, 61, -85, 153]]\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[[195, -210, 15, 180, -180, 210, 120, 60, -210, 255],\n [91, -98, 7, 84, -84, 98, 56, 28, -98, 119],\n [156, -168, 12, 144, -144, 168, 96, 48, -168, 204],\n [286, -308, 22, 264, -264, 308, 176, 88, -308, 374],\n [13, -14, 1, 12, -12, 14, 8, 4, -14, 17],\n [65, -70, 5, 60, -60, 70, 40, 20, -70, 85],\n [-169, 182, -13, -156, 156, -182, -104, -52, 182, -221],\n [156, -168, 12, 144, -144, 168, 96, 48, -168, 204],\n [39, -42, 3, 36, -36, 42, 24, 12, -42, 51],\n [169, -182, 13, 156, -156, 182, 104, 52, -182, 221]]\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 10x10 matrix:\n[[428, 1323, -475, 181, 964, -242, -277, -209, 55, -97],\n [-248, -29, -270, -286, 274, 501, -510, -14, 166, 407],\n [-648, 534, 316, 654, 81, 158, 125, -614, -541, 580],\n [-653, 223, 119, 141, 33, -700, 412, -568, -304, 707],\n [388, 1121, 205, 360, 380, -157, -288, -379, 863, -315],\n [489, 134, -569, -418, 634, -426, 147, 514, 307, -343],\n [830, -326, -464, -372, -194, -38, 329, 825, -331, -963],\n [-396, -177, 172, 13, 113, -530, 411, -110, 213, 354],\n [-249, 646, -763, -267, 1338, -363, -135, -37, 16, 690],\n [204, 327, 10, 186, 397, -9, -597, -298, 29, 165]]\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[[69, 540, -336, 301, 29, 287, 192, -268, 81, -251],\n [-32, -258, 147, -148, -29, -131, -113, 110, -30, 108],\n [-32, -168, 252, -48, 156, -156, 172, 280, -120, 208],\n [37, 318, -147, 193, 74, 146, 193, -90, 15, -103],\n [13, 84, -84, 37, -31, 59, -20, -84, 33, -67],\n [-10, -12, 126, 30, 132, -60, 182, 164, -78, 110],\n [-31, -120, 294, 1, 239, -163, 302, 352, -159, 249],\n [-24, -18, 315, 84, 339, -147, 471, 414, -198, 276],\n [-1, 114, 147, 131, 250, -38, 383, 234, -123, 139],\n [4, -96, -168, -124, -260, 52, -392, -256, 132, -156]]\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[[-19, -411, -454, -95, -694, -129, -549, -412, -100, -345],\n [-172, 90, -518, -88, -331, -547, -62, -28, 311, 263],\n [-453, -451, 1079, -891, 687, -509, 743, 296, 32, 88],\n [-184, 237, -811, 594, -551, 14, -403, -58, -23, 60],\n [-1092, -862, -77, 122, -66, -272, -160, 346, -36, -741],\n [687, 365, 78, 207, 28, 341, -305, 107, 193, 215],\n [-243, 280, 23, 101, 938, -588, 1240, 633, -44, 228],\n [530, 195, -124, 35, 73, 40, 177, -128, -174, 40],\n [-9, -36, 489, -195, 257, -106, 558, 101, 100, 204],\n [-360, 65, 412, 22, 794, -19, 295, 633, 185, -12]]?\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 10x10 matrix:\n[[-171, 476, 913, -269, -48, -73, -328, 411, 16, 143],\n [400, -281, -172, 392, -123, -350, 402, -312, -117, 155],\n [146, -643, 342, -181, -343, -816, -235, 219, -193, 395],\n [880, -24, 162, -509, -235, -150, 1120, 304, -1104, -205],\n [-105, -784, -505, -47, -20, 497, 326, 357, -730, -379],\n [-906, -706, -253, -70, -291, -127, -908, 313, 469, -78],\n [-389, -99, 329, -419, -611, 17, 152, 763, -347, -494],\n [17, -292, -217, -195, -676, -215, 608, 329, -350, -499],\n [26, -280, -359, -698, -83, 339, 321, 461, -632, -464],\n [535, 630, 4, 525, 321, -12, 397, -686, 260, 245]]\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[[-67, -486, -178, 447, 238, 102, -340, -296, -5, -424],\n [-30, 491, 132, -482, -161, -69, 230, 235, -14, 507],\n [-49, -154, -70, 133, 98, 42, -140, -112, -7, -112],\n [234, 219, 180, -138, -273, -117, 390, 267, 42, 27],\n [-92, -358, -152, 316, 210, 90, -300, -246, -12, -278],\n [-76, 312, 56, -324, -56, -24, 80, 112, -20, 368],\n [-2, 338, 100, -326, -126, -54, 180, 174, -6, 334],\n [-22, 344, 92, -338, -112, -48, 160, 164, -10, 356],\n [5, -122, -34, 119, 42, 18, -60, -60, 3, -124],\n [99, -343, -54, 361, 49, 21, -70, -113, 25, -417]]?\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[[172, 361, 855, 491, -169, 353, 25, 406, -481, 26],\n [-297, 1319, 97, -69, 680, 849, 244, -667, 281, -164],\n [494, -352, -539, 325, 797, 204, 29, -458, 22, -877],\n [691, -735, -582, -1457, -98, 266, -371, 75, 703, 617],\n [-546, 32, 688, 923, 60, -407, 15, 470, -31, -609],\n [-400, -333, -513, 616, -173, -670, -691, 547, -233, -363],\n [210, 848, 99, 12, 366, 751, 195, -368, -61, 26],\n [326, -682, -114, -28, -667, -385, -35, 208, -462, 302],\n [430, 56, -227, 5, -254, 328, -741, 752, 273, -81],\n [-333, -78, -35, 1436, 129, -329, -526, 805, -414, -871]]\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 10x10 matrix:\n[[0, -238, -238, 187, -238, 34, 170, -340, -170, -357],\n [0, -252, -252, 198, -252, 36, 180, -360, -180, -378],\n [0, -154, -154, 121, -154, 22, 110, -220, -110, -231],\n [0, -266, -266, 209, -266, 38, 190, -380, -190, -399],\n [0, 14, 14, -11, 14, -2, -10, 20, 10, 21],\n [0, 28, 28, -22, 28, -4, -20, 40, 20, 42],\n [0, 42, 42, -33, 42, -6, -30, 60, 30, 63],\n [0, 280, 280, -220, 280, -40, -200, 400, 200, 420],\n [0, 140, 140, -110, 140, -20, -100, 200, 100, 210],\n [0, -28, -28, 22, -28, 4, 20, -40, -20, -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[[117, -122, -367, 1119, -662, 244, -120, 131, 559, -216],\n [254, -237, 206, -706, -425, 202, 561, 703, 183, -464],\n [-328, 665, -430, 668, 629, -544, -519, -925, -215, 412],\n [-177, 241, 44, -1227, 733, -437, 306, -70, -551, 222],\n [-246, 124, -697, 166, -18, -245, 141, -168, 85, 240],\n [-16, 42, -168, -560, 214, -200, 334, 250, -138, -20],\n [-272, 406, 125, -508, 1204, -535, -321, -598, -765, 536],\n [-9, 266, -486, 1049, -279, -93, -209, -215, 381, -111],\n [-7, -54, 65, 591, -384, 226, -264, -247, 243, -2],\n [-68, -62, -454, -800, 208, -264, 596, 468, -140, 38]]?\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[[260, -208, -91, -13, 65, 117, -208, -13, 260, -273],\n [-300, 240, 105, 15, -75, -135, 240, 15, -300, 315],\n [20, -16, -7, -1, 5, 9, -16, -1, 20, -21],\n [220, -176, -77, -11, 55, 99, -176, -11, 220, -231],\n [-160, 128, 56, 8, -40, -72, 128, 8, -160, 168],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n [80, -64, -28, -4, 20, 36, -64, -4, 80, -84],\n [-180, 144, 63, 9, -45, -81, 144, 9, -180, 189],\n [-420, 336, 147, 21, -105, -189, 336, 21, -420, 441],\n [240, -192, -84, -12, 60, 108, -192, -12, 240, -252]]\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[[-462, -572, 57, -288, 450, -161, -121, -281, -1237, -604],\n [-260, -327, -557, 626, 276, -173, 1074, -1038, -643, -800],\n [-394, -788, -722, 199, 117, -446, -83, 279, -555, -301],\n [-17, 295, -252, 570, -242, -154, 722, -412, 557, -211],\n [-21, -107, -912, -184, -53, 348, 293, -993, 56, -698],\n [-816, 3, -342, -79, -173, -284, -671, -491, -259, -753],\n [-195, 163, -73, -361, 54, -339, -177, 531, -330, -421],\n [301, -281, 297, -112, 148, -240, 150, 1078, -173, 453],\n [219, 240, 79, -265, -74, 431, -314, 62, 1393, 639],\n [872, 183, -609, 210, -626, 820, 44, -480, 1016, 686]]?\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[[146, 615, 540, -23, -343, 743, 147, 87, 88, -431],\n [314, 145, -684, -394, -240, 205, 283, -101, -54, 133],\n [169, 709, -610, -1320, -295, 237, 748, 215, 613, 141],\n [654, 144, -79, 160, 83, 514, 72, 607, 276, -224],\n [320, -1, -518, 56, 79, 228, 346, -977, -667, 46],\n [179, 649, -335, -614, -420, 399, 598, 506, 534, -329],\n [325, 265, -602, -727, -532, 251, 70, 461, 352, 365],\n [162, 898, 485, 91, -511, 603, 693, -311, 125, -465],\n [-279, 732, 461, -270, -184, 220, 653, -29, 362, -560],\n [-599, 95, 368, 495, -281, -218, 155, -429, -277, -460]]\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, 782, -91, 823, 166, -74, 762, -271, 684, -839],\n [-261, -55, -268, -320, 77, 231, -1152, -279, 4, -324],\n [393, -1648, 550, -536, 334, 70, -582, -698, -1759, 258],\n [168, 32, -56, -346, 89, 680, 620, 877, -326, 154],\n [277, -281, 424, -534, -448, 143, -1103, 131, -4, 878],\n [397, -65, 844, -812, -441, -7, -640, 463, 102, 1578],\n [-241, -187, 324, 434, -93, 137, -520, -296, -862, -245],\n [353, -1042, 847, 13, 559, -296, -247, -1167, -1528, -43],\n [-321, -242, 167, -193, -203, -598, -564, -300, 10, 561],\n [520, -671, 514, -512, 242, 81, -667, -330, -973, 529]]?\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[[158, -293, 463, -307, -6, 146, -38, -21, 217, 13],\n [-24, -131, 147, -99, 98, 172, -48, 107, 153, 63],\n [-275, 95, -292, 190, 240, 205, -61, 282, 62, 131],\n [-226, -39, -95, 59, 262, 298, -86, 301, 175, 151],\n [234, -309, 531, -351, -78, 78, -18, -105, 189, -27],\n [86, -216, 322, -214, 28, 142, -38, 22, 178, 28],\n [165, 225, -174, 120, -300, -435, 123, -336, -336, -183],\n [-156, 206, -354, 234, 52, -52, 12, 70, -126, 18],\n [-319, 129, -362, 236, 268, 217, -65, 316, 52, 145],\n [-266, -179, 53, -41, 382, 498, -142, 433, 347, 227]]\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 10x10 matrix:\n[[-141, -9, -216, 422, -223, 1, 222, 473, -254, -449],\n [-283, -317, -51, -668, 60, -714, 505, -80, -47, -322],\n [-8, 115, 458, -530, -8, -271, 63, -289, -24, 1],\n [-353, -282, -370, -166, 1, 245, -431, -217, -162, -69],\n [-266, -36, -478, -52, -340, 553, -865, 11, -668, 1024],\n [-57, -164, -262, -64, 109, 232, -393, -254, 86, 318],\n [-338, -589, -790, -94, 187, 60, -327, -274, 162, 14],\n [183, 135, -178, 910, -53, 292, 231, 578, 66, -411],\n [-13, -36, -228, 196, 56, 441, -361, -13, -38, 211],\n [-159, -99, -225, -302, -159, -58, -241, -48, -315, 606]]\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[[-601, -206, 20, -444, -222, 345, -25, -738, 24, 447],\n [-861, 147, -462, 162, 81, 18, -78, -720, 498, 477],\n [489, 365, -104, 198, 99, 171, 414, 528, 352, -543],\n [-404, -378, 320, -892, -446, 696, 134, -748, -184, 356],\n [39, 218, -60, -268, -134, 609, 511, -82, 424, -241],\n [-250, -107, -30, 22, 11, -147, -203, -218, -90, 244],\n [-405, 67, -274, 306, 153, -288, -222, -240, 158, 273],\n [-272, 624, -652, 560, 280, 66, 344, -16, 932, -172],\n [-463, 59, -230, 66, 33, 12, -52, -396, 242, 267],\n [680, -213, 454, -230, -115, -3, 13, 526, -518, -326]]\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[[-110, -180, -416, -516, 292, -68, 282, -48, -234, -488],\n [-119, -186, -410, -500, 344, -108, 357, -84, -295, -568],\n [226, 319, 319, 399, 101, -401, 399, -402, -334, 59],\n [138, 161, -60, -88, 238, -356, 465, -348, -391, -197],\n [366, 461, 297, 313, -117, -343, 165, -366, -150, 489],\n [229, 350, 526, 668, -40, -316, 225, -324, -187, 248],\n [380, 465, 119, 99, 197, -613, 627, -618, -534, 77],\n [-299, -388, -437, -483, 465, -23, 399, 18, -320, -900],\n [17, -3, -220, -278, 264, -218, 378, -204, -316, -339],\n [60, 37, -225, -309, 133, -141, 207, -138, -178, -119]]\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[[-419, -220, -826, 892, 460, -455, 663, -51, -307, 295],\n [-761, -140, 342, -223, -907, -135, -650, 634, -647, -472],\n [168, 417, 1103, -27, -843, -86, -303, -1308, -689, -947],\n [-387, -393, 92, 197, -517, -232, -633, 962, -629, 396],\n [-203, -201, -1134, 138, -337, -256, -13, 1120, -460, 1271],\n [-179, 809, 1220, 58, -1115, 13, -206, -963, -666, -837],\n [-272, 3, 100, -83, -145, 487, -9, 923, 400, -506],\n [568, 283, 224, -4, 911, 688, -327, 250, 829, -338],\n [150, -446, -1091, 521, 840, -459, 261, -97, -48, 697],\n [-42, 565, 818, -516, -466, 1161, 549, 488, -407, -578]]\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 10x10 matrix:\n[[425, 569, -440, -49, -28, -80, -126, 260, 463, -816],\n [-790, -278, 864, -6, -276, -500, -95, -314, -129, 789],\n [424, -600, 47, -712, 270, 132, -402, -334, 969, 25],\n [-216, 12, -190, 12, -89, 400, -105, 514, -74, 121],\n [-466, -1355, -57, -431, 784, 585, -144, -905, -359, 351],\n [-448, -891, 316, -357, 391, -169, -91, -695, -4, 407],\n [-671, 355, -118, 97, -457, -74, -310, 382, 350, -498],\n [561, 190, -203, -582, 119, 471, -711, -133, 948, -622],\n [739, -486, -502, 57, 77, 321, 515, 331, 201, 114],\n [-156, -700, -697, -299, 142, 606, -110, 482, 515, -210]]\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[[554, 498, -511, -376, -335, 195, 360, 677, 134, -769],\n [-294, -476, -157, -582, 227, -316, -39, -573, -319, 60],\n [598, -146, -1139, 286, -125, 293, 104, 245, -578, -301],\n [-474, -433, -848, 1186, -350, -686, -240, -2, -186, 710],\n [-628, -308, 149, -188, 465, 990, -1, -479, 1055, 58],\n [842, 504, -144, -1216, -460, 800, 311, 181, 14, -752],\n [-134, 57, 75, 1113, 344, 137, -414, 364, 1280, 543],\n [-21, 90, -885, -757, -50, 778, 167, -864, 50, -39],\n [-100, -1084, -309, 82, -345, -799, 97, 68, -902, 293],\n [-396, -622, -32, -689, -21, -278, 22, -365, -540, -236]]\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 10x10 matrix:\n[[132, -194, 355, -239, -322, -159, -416, 45, -79, 608],\n [1, 538, -104, -444, 415, 390, 263, 12, -228, 309],\n [312, -54, -698, 652, 671, 890, 732, 398, -84, -449],\n [-296, 506, -285, -2, 768, -119, -48, -98, -218, -339],\n [496, -14, -423, 309, 526, 367, 704, -283, -311, 118],\n [365, 190, -11, -137, 1074, 71, -34, -405, -388, 553],\n [792, -411, 310, 241, 266, 439, 386, -81, 232, -283],\n [482, -298, -18, -125, -98, -130, 578, -251, 257, 241],\n [-361, 717, -238, 85, 461, 174, 82, -204, -465, -541],\n [-198, 670, 483, -623, 499, -301, -482, -469, -305, 135]]\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[[-321, -142, 585, 781, -428, 263, 382, 131, -48, 473],\n [-121, 35, -7, -551, -353, -690, -173, 227, -97, -57],\n [14, -139, -167, -632, -381, -14, -526, 145, 166, -266],\n [-657, 85, 426, 232, 592, -481, 740, 277, -703, -458],\n [-287, -121, 114, -232, -493, 267, -94, -15, 316, -134],\n [97, -182, -496, -570, 872, 436, -320, 349, -509, -877],\n [519, 191, -618, -337, -289, 437, -140, -651, 842, 492],\n [545, 745, -1050, -614, -22, 255, -26, -528, 1119, 407],\n [109, -274, 144, 104, -297, -168, 113, -24, -298, 523],\n [-557, 428, -189, -95, 422, 211, 938, 62, 22, -146]]\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 10x10 matrix:\n[[236, -43, 303, 272, -195, -60, -200, 397, 143, 160],\n [161, -88, 153, 17, 195, -150, 85, -158, -52, 205],\n [-136, 103, -103, 68, -325, 180, -180, 343, 117, -220],\n [-129, 93, -102, 51, -282, 162, -153, 291, 99, -201],\n [116, -44, 128, 68, 32, -72, -12, 28, 12, 116],\n [-224, 107, -227, -68, -185, 180, -60, 107, 33, -260],\n [157, -62, 171, 85, 57, -102, -7, 20, 10, 161],\n [-321, 63, -408, -357, 240, 90, 255, -507, -183, -225],\n [-534, 205, -587, -306, -161, 336, 46, -111, -49, -538],\n [-109, -37, -192, -289, 408, -78, 307, -599, -211, 19]]\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[[-21, -261, -115, 437, 413, -288, -284, 487, -225, 11],\n [7, 138, 140, -556, -138, 278, 159, -270, 283, 145],\n [96, 136, -155, 598, -458, -227, 109, -242, -270, -366],\n [173, -160, -424, 362, 228, -240, -31, 516, 437, -405],\n [-125, 33, 346, -779, 146, 356, -2, -176, 100, 489],\n [406, 0, -473, 214, -152, -259, 123, 208, 694, -472],\n [579, 101, -42, -231, -441, -307, -17, -347, 339, 205],\n [-103, -398, -220, 416, 764, -244, -337, 856, -25, -57],\n [425, 56, -63, -528, -165, -54, 51, -133, 650, 165],\n [422, -145, -224, -263, 191, -225, -114, 313, 680, 86]]?\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[[-940, 156, -27, 1039, -569, -219, -397, -799, 957, 152],\n [-339, 104, -390, 654, -234, -88, 279, 100, 319, -712],\n [403, -327, -267, 136, 141, -138, 642, 1315, -595, -622],\n [449, -198, 466, 617, 505, -761, -320, -203, 128, 389],\n [1033, -419, 0, -75, 1022, 145, 541, 1070, -986, -658],\n [-79, 232, -343, -47, 174, 117, 697, 359, -4, -48],\n [-601, -561, 564, 585, -137, -152, -1220, -504, 26, 519],\n [321, -252, 519, -630, -242, 163, -616, -280, -170, 719],\n [838, -409, 786, -61, 171, 26, -876, 70, -446, 54],\n [466, 88, -598, -298, 304, 194, 1098, 1318, -652, -1016]]\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[[132, 85, -715, 113, 4, 276, -7, -163, 29, 460],\n [118, -168, 514, 469, -310, 63, -312, -48, 122, 574],\n [-466, 205, 43, -109, 38, -226, 440, 354, 525, -311],\n [-547, 478, -332, 35, -312, -238, 206, 152, -97, 345],\n [-415, 496, 25, -77, -283, -570, 446, 278, 231, 543],\n [-236, -46, 409, 317, -114, 42, -507, -92, -168, 442],\n [-314, 669, 29, 371, 8, 117, 251, 248, 902, -614],\n [239, -120, -14, 48, 225, 91, -290, -212, 32, 550],\n [-544, 15, 137, 338, -139, 169, -131, 167, 260, -91],\n [188, -527, 128, -188, -135, -257, 1, -43, -307, 900]]\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[[928, -664, 57, 1019, 100, 443, 19, 863, 415, -518],\n [729, 152, -666, 501, 178, 538, -391, 699, -126, -453],\n [167, -465, 329, -486, -54, 876, -116, -260, -443, -413],\n [-85, 843, -766, -448, 198, -631, -606, -71, -260, 118],\n [584, 176, -331, 654, 366, 654, -333, 569, 78, -304],\n [-203, 176, 306, -280, 389, 12, -392, -605, -109, -63],\n [-62, -28, -147, -558, -91, -1043, -63, 103, 57, 229],\n [314, 352, -431, -399, 256, -402, -655, 314, -368, 42],\n [-176, 73, 60, -305, 246, 248, -9, -216, -104, -43],\n [240, -259, -123, 587, -989, -330, -119, -626, 731, -635]]?\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[[-480, 414, -613, -243, 203, 465, -463, -273, -486, -473],\n [104, -1091, 367, 343, -29, -785, 105, 467, -679, 439],\n [648, 94, 593, 254, -587, -107, 635, 55, 157, 343],\n [-638, -575, -410, -13, 513, -476, 855, -352, 48, 986],\n [324, -300, 390, 282, -591, 660, -811, 56, -164, -184],\n [95, -131, 470, -169, 441, 222, -162, -181, -484, 850],\n [278, -580, 503, 136, 212, -730, 541, 422, 365, 753],\n [16, 298, -244, -69, 17, 77, -400, 507, 700, -651],\n [819, 13, 819, 225, -483, 82, -9, 435, 486, 180],\n [550, 669, 734, -220, -53, 224, 295, -716, -513, 270]]\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[[-184, -501, 139, -187, -443, -225, 274, 118, -350, -481],\n [122, 440, 236, -396, 270, -306, -912, -290, 80, -404],\n [658, 436, 462, -494, 175, -487, -728, -134, -786, 158],\n [-473, -44, -149, 421, -577, 228, 706, -65, 71, -428],\n [-453, -83, -71, 220, 385, -259, 46, -263, -13, -231],\n [509, 247, 17, 16, -56, 166, -38, 235, 229, 741],\n [147, 120, -205, -111, 563, 348, -446, 3, 367, 248],\n [188, 511, 196, -315, 295, -252, -892, -235, 298, -172],\n [363, 267, 331, -226, -778, -194, -122, 169, 187, -39],\n [430, 558, 304, -327, 221, -341, -796, -174, -55, 98]]?\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[[-1025, -1030, -555, 520, 516, -177, -357, 600, -256, 502],\n [-989, -1250, -223, 273, 151, -712, -398, 326, -58, -115],\n [-118, 348, -113, 114, 377, 9, -875, -548, 117, -113],\n [-287, -1406, -2, 396, -282, -507, 266, 1030, -424, 229],\n [370, 280, 157, 365, 115, 471, 110, -6, 152, 506],\n [85, 292, 106, -340, 68, 96, 576, 57, 212, 49],\n [-193, -774, -157, 649, -48, -115, -516, 362, -365, 259],\n [42, -246, 62, 290, 34, 265, 529, 438, 46, 546],\n [-350, -1236, -215, 251, -383, -557, -110, 790, -652, -104],\n [368, 420, 415, -493, -110, -282, 114, -368, 341, -480]]\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[[392, -490, -123, 628, -384, -242, -461, -69, 568, 63],\n [875, -159, 330, 534, 438, 313, 31, -302, 806, -183],\n [-558, 441, -208, -177, 88, 324, 558, -41, -538, 145],\n [83, 824, -221, 554, 317, 331, 716, -154, -141, 415],\n [296, 199, -206, 185, 590, 768, 395, 0, -41, 170],\n [-929, -742, -451, -656, -480, 521, -117, 71, -526, -145],\n [285, -31, 209, 227, -36, -21, 14, -237, 389, -107],\n [-444, 738, -237, 130, -285, -238, 413, -25, -458, 386],\n [841, -219, 800, 114, 420, -915, -622, 139, 717, -430],\n [-253, -490, -321, -260, -278, -353, -624, 486, -305, 86]]\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[[-199, -627, -4, 125, 173, 141, -44, 371, -193, 795],\n [-238, 142, 82, -249, -542, 537, 1166, 56, 332, -609],\n [-322, -178, 163, 145, 644, -128, 973, -597, -665, -196],\n [-229, -608, -137, 784, 258, -203, -198, 467, 28, -810],\n [-418, -744, -50, 151, 169, 86, 1291, 404, -395, 356],\n [517, 886, -37, 151, 315, -801, 1100, -1194, -574, -70],\n [191, -64, -153, 519, -369, 316, 325, 98, 378, 498],\n [444, 262, -313, -125, -197, -668, -781, 175, -32, 591],\n [273, 555, 247, 406, -509, 349, 127, -316, 643, -1047],\n [374, 524, -239, -268, -754, 811, -131, 485, 1149, -23]]\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[[90, 98, 132, 262, 117, 74, -184, 78, 245, -368],\n [270, 102, 108, 338, -97, 126, 24, 202, 95, -432],\n [-90, -122, -168, -318, -173, -86, 256, -82, -325, 452],\n [54, -36, -63, -64, -151, -3, 174, 31, -169, 111],\n [-396, -124, -120, -436, 202, -172, -112, -292, -54, 544],\n [144, -94, -165, -166, -398, -7, 458, 83, -444, 289],\n [234, 124, 147, 376, -1, 127, -86, 181, 201, -499],\n [72, -104, -168, -216, -332, -32, 400, 32, -412, 344],\n [-54, -102, -144, -258, -171, -66, 240, -54, -291, 372],\n [108, -66, -117, -114, -288, -3, 330, 63, -318, 201]]\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[[78, -102, -242, -291, -390, 145, -414, 406, 4, 250],\n [-104, -227, -275, -349, -481, -32, -526, 368, -64, 147],\n [154, 220, 216, 281, 392, 99, 434, -254, 76, -64],\n [-556, -334, -22, -80, -146, -562, -200, -236, -200, -378],\n [260, 23, -209, -233, -299, 322, -302, 444, 72, 353],\n [714, 399, -21, 42, 105, 735, 168, 378, 252, 525],\n [280, 139, -37, -19, -7, 296, 14, 192, 96, 229],\n [496, 283, -5, 41, 89, 508, 134, 248, 176, 357],\n [650, 404, 48, 121, 208, 651, 274, 242, 236, 424],\n [-600, -312, 56, 12, -24, -628, -72, -376, -208, -472]]?\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[[374, -517, 36, -143, 325, -127, -343, -66, 424, -317],\n [4, 27, -210, 31, -171, 201, 39, 148, 2, 177],\n [423, -552, -171, -129, 192, 60, -345, 75, 477, -177],\n [561, -737, -195, -176, 281, 49, -464, 77, 633, -262],\n [20, 58, -552, 78, -442, 526, 94, 388, 16, 458],\n [-32, 92, -312, 60, -284, 308, 92, 224, -40, 292],\n [-495, 682, -33, 187, -418, 154, 451, 77, -561, 407],\n [-597, 802, 93, 205, -394, 58, 517, -1, -675, 377],\n [-145, 234, -231, 89, -306, 258, 177, 179, -167, 309],\n [419, -579, 39, -160, 363, -141, -384, -73, 475, -354]]\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 10x10 matrix:\n[[150, -119, -88, -191, 176, -208, 29, 224, -83, -122],\n [334, -72, -185, -372, 194, -468, -27, 412, -254, -154],\n [-37, 459, 39, 200, -567, 99, -263, -306, -104, 291],\n [-138, -113, 105, -63, 496, -106, 348, 192, 3, -18],\n [194, -632, -173, -224, 342, 8, 29, 244, 198, -454],\n [-71, -309, -47, 318, -505, 669, -339, -494, 454, -175],\n [-425, -172, 246, 277, 323, 391, 347, -198, 311, 39],\n [224, -85, -142, -183, -18, -182, -117, 164, -91, -128],\n [-108, 292, 64, 248, -468, 236, -200, -344, 32, 212],\n [-486, 488, 347, 376, -18, 208, 269, -316, -2, 466]]\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 10x10 matrix:\n[[126, 420, 210, -63, -147, 294, 294, 399, 378, 21],\n [132, 440, 220, -66, -154, 308, 308, 418, 396, 22],\n [-54, -180, -90, 27, 63, -126, -126, -171, -162, -9],\n [6, 20, 10, -3, -7, 14, 14, 19, 18, 1],\n [120, 400, 200, -60, -140, 280, 280, 380, 360, 20],\n [-126, -420, -210, 63, 147, -294, -294, -399, -378, -21],\n [66, 220, 110, -33, -77, 154, 154, 209, 198, 11],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n [-90, -300, -150, 45, 105, -210, -210, -285, -270, -15],\n [-108, -360, -180, 54, 126, -252, -252, -342, -324, -18]]\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 10x10 matrix:\n[[-455, -274, 327, -578, -213, 79, 1140, -603, 548, 97],\n [151, -779, 339, 300, -463, 226, 423, -211, -215, 118],\n [112, 508, 88, 513, 441, -469, -165, 811, 206, 903],\n [-31, 1274, -239, 657, -410, -8, 119, 696, -547, 232],\n [-174, -391, -396, -183, 276, 372, 141, -36, -58, 744],\n [503, -636, -387, 385, -48, 280, -891, 522, -351, -782],\n [-68, 111, 113, 63, 747, -635, 138, 398, 233, 940],\n [-141, 1116, 453, -240, 866, -1307, -1074, 267, 680, 856],\n [380, -312, -38, 700, -437, 104, -217, 685, -466, -406],\n [-671, 1275, 389, -695, 600, -1456, 380, -417, -482, 447]]\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[[63, 44, 447, -141, -260, -70, -230, 348, 86, 186],\n [482, -158, -28, 608, 121, 29, -538, 172, -281, 203],\n [82, 89, 178, 145, 48, -253, 91, -135, -348, -26],\n [507, 96, 79, 183, 111, -279, 231, -430, -19, -553],\n [797, -318, -221, 315, -228, 18, -5, -222, -124, -542],\n [509, -576, -677, -145, -510, 628, 43, -88, 508, -604],\n [-683, 520, 333, -426, 261, 406, 242, -478, 724, 9],\n [222, -297, 146, -237, -574, 63, -295, 619, 118, 128],\n [-701, 226, -335, -672, 137, 438, 692, -606, 776, -409],\n [-501, -110, -55, -68, -25, -600, -22, 734, -846, 705]]\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[[594, -140, -322, -805, 274, 669, -488, -240, 86, 166],\n [-12, 328, -74, -144, 358, 333, 117, 832, 584, 341],\n [348, 321, -373, -815, 394, 225, -112, 178, 35, 66],\n [-188, -359, 546, 160, -306, 207, 242, 246, -733, -277],\n [-355, -142, 545, 227, -294, -263, -397, 139, -633, 546],\n [-370, 181, -569, 961, 688, -352, 881, -316, 181, 253],\n [-333, -543, 299, 1079, -260, -516, -637, -963, -454, 1071],\n [225, 207, -209, -170, 318, 174, -240, 250, 492, 589],\n [15, -89, 245, -75, -268, 447, 180, 534, 490, -589],\n [474, -186, 210, -650, -321, 258, -1226, -158, 144, 616]]\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[[402, 241, -111, 747, -15, 48, -1199, -101, -529, 540],\n [-118, -166, -110, 516, 437, -233, 56, 118, -35, 159],\n [713, 55, -830, -333, -42, 84, -340, 16, 248, -162],\n [627, -564, -1038, 1086, 293, -287, -463, 282, 262, 581],\n [500, -245, -261, -144, -85, 52, 83, -142, 230, -167],\n [-604, 700, 461, -541, -20, -269, 428, -880, 36, -280],\n [82, -472, 318, -52, 200, 387, 293, -97, 399, -44],\n [357, -88, 68, 52, 574, -94, 71, -240, -181, -352],\n [168, -269, -38, 242, 151, -237, 275, -129, 21, -88],\n [-734, -8, 389, 51, -122, -78, 363, 527, -189, 92]]\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 10x10 matrix:\n[[-589, 174, -43, -43, -173, -681, -507, -513, -73, -303],\n [-91, 234, -410, -304, 133, 582, 82, -211, -16, -171],\n [382, 152, -115, -229, 258, 634, 356, 11, 185, -327],\n [-545, 145, -468, -237, 40, 440, -179, -314, -363, 135],\n [-412, -271, 9, -298, 167, 364, -73, -68, -388, 579],\n [-405, 98, -190, -468, 303, 560, -52, -439, -280, -127],\n [272, -168, 253, 227, -132, -359, 56, 302, 178, 173],\n [-206, 58, 370, 372, -168, -948, -359, -238, -61, -457],\n [800, 69, 57, -414, 451, 918, 662, 170, 441, -378],\n [-395, -305, 485, -348, 140, -449, -272, -294, -80, 175]]\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[[-310, 122, -61, -213, -340, 189, -492, -228, -151, 187],\n [122, -276, 619, -360, 163, -293, -122, 475, 307, -499],\n [-179, 153, -316, -43, -252, 465, -152, -334, -180, 424],\n [-102, 79, -169, -128, -151, 197, -236, -267, -2, 288],\n [147, -272, -14, -59, 4, 405, -68, -286, 205, 339],\n [-111, 356, 55, -185, 73, -636, -52, 343, -12, -386],\n [-250, 151, 142, -209, -187, -74, -254, 181, -163, -197],\n [149, -22, 40, -369, 135, -148, -191, -75, 404, 113],\n [-120, -72, -154, -199, -246, 263, -565, -562, 127, 486],\n [-486, 232, 320, -332, -348, -488, -702, 224, -224, -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 10x10 matrix:\n[[161, 383, 293, -102, 95, 207, 14, -354, 529, -176],\n [-367, -244, -235, 228, -70, -57, 410, 108, -65, -176],\n [112, 133, 112, -70, 35, 56, -84, -98, 126, 0],\n [104, -16, 8, -64, 0, -40, -176, 64, -136, 128],\n [-110, -26, -38, 68, -10, 14, 156, -20, 66, -96],\n [-104, -263, -200, 66, -65, -144, -20, 246, -370, 128],\n [-380, -242, -236, 236, -70, -52, 432, 100, -48, -192],\n [-438, -276, -270, 272, -80, -58, 500, 112, -50, -224],\n [-353, -332, -293, 220, -90, -119, 326, 212, -239, -80],\n [-443, -404, -359, 276, -110, -141, 418, 252, -277, -112]]\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[[13, 710, -383, -213, -186, -842, -199, -66, 339, 23],\n [335, 602, -91, -142, -161, -332, 12, 157, 126, -458],\n [-1126, -300, -431, 524, -636, -20, -113, 134, -337, 185],\n [320, -169, -84, 96, 67, -754, -105, -749, 427, 4],\n [269, -250, -186, 161, 351, 501, 972, 651, 285, -289],\n [-51, -235, 220, 11, -117, 924, -489, 189, -472, 431],\n [-1048, -410, -69, 431, -371, -91, -244, -30, -314, 440],\n [39, -110, 1148, 802, -178, -284, 74, 738, -270, 280],\n [-290, 376, 316, 365, -131, -834, -159, -379, -469, -641],\n [671, 108, 13, -264, 218, 348, 522, 882, 557, 636]]\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[[89, 211, -530, -1, -149, 7, -227, 292, -723, -314],\n [-8, -221, -329, -406, 93, 240, -157, -190, -180, -429],\n [-313, -269, -64, -411, -385, 153, -263, 192, -261, -112],\n [502, 382, -837, 148, 419, 37, -67, -96, -660, -622],\n [-155, 167, 415, 345, -338, -252, 74, 372, 99, 532],\n [11, -177, -392, -383, 75, 229, -179, -144, -273, -456],\n [-20, -136, 3, -154, 81, 91, -1, -152, 114, -90],\n [419, 340, -649, 171, 344, 3, -32, -66, -513, -463],\n [-28, -223, 168, -172, 184, 107, 88, -306, 390, -17],\n [-370, -345, 113, -424, -383, 150, -209, 134, -54, 1]]?\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, -153, 132, 92, 166, -271, 189, -559, -234, 417],\n [-126, -410, -22, 23, -33, 626, -78, 298, 78, -97],\n [62, 182, 142, 460, -182, -484, 294, -332, -358, 270],\n [-96, 204, -36, 303, -195, -318, 216, -198, -252, -3],\n [-365, -257, -248, 435, -314, 327, 303, -127, -360, -237],\n [680, 200, 770, -286, 362, -350, -456, 478, 502, 736],\n [-360, -248, -135, 725, -443, 221, 432, -173, -525, -92],\n [-27, 415, 25, -7, -79, -382, -39, 100, 57, -69],\n [-495, -433, -282, 914, -544, 363, 621, -385, -748, -167],\n [-496, -368, -320, 1100, -612, 120, 816, -696, -976, -100]]\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 10x10 matrix:\n[[1070, 263, 462, -281, 100, 1037, 207, -517, -195, 558],\n [-16, 138, 73, 307, 230, 302, -49, -73, -204, 171],\n [-407, -925, 113, 285, -324, -535, -137, 159, 153, -212],\n [284, 116, 293, 46, -277, 176, 269, -184, 176, 241],\n [-539, -197, 192, 18, 245, 86, -826, -845, -165, 614],\n [-555, -186, -426, -207, 70, -238, -365, -299, -595, 160],\n [-1016, -457, -161, 750, 20, -449, -302, 40, -341, 33],\n [1359, 72, 329, -15, -317, 554, 1066, 659, 260, -358],\n [-103, 378, 14, -370, -337, -90, 19, -566, 60, 445],\n [-343, 208, -668, 299, 487, -213, 107, 878, -394, -690]]\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[[-544, -791, 211, 189, 415, -957, -1027, -568, -367, -74],\n [-26, -487, 271, 158, 120, -6, -43, -643, 181, -745],\n [67, 298, -39, 24, 134, 232, 524, 260, 466, 4],\n [-436, -686, -303, -190, 183, -393, -445, -468, -116, 475],\n [381, 738, -552, -326, -422, 303, 282, 686, 119, 608],\n [-299, -496, -322, -144, 628, 81, 456, -402, 757, 492],\n [354, 427, -894, -491, -586, 86, 26, 294, 389, 365],\n [-293, 138, 294, 178, -448, -469, -536, 314, -655, -494],\n [397, 751, 144, 39, -845, 106, -203, 622, -602, -484],\n [-53, -228, 636, 392, 367, 224, 455, -370, 355, -919]]\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 10x10 matrix:\n[[-217, -977, 556, -207, 641, 237, -540, 390, 553, -178],\n [586, 206, -228, 205, 19, -817, 197, -70, -245, 482],\n [201, 85, -299, -378, -123, -95, -148, 0, -13, 29],\n [-144, 377, -780, -227, -821, -174, -285, -431, -195, -104],\n [-88, -206, 266, -440, 234, 484, -178, 202, 186, -394],\n [-90, -452, 353, 289, 316, -160, -128, 94, 166, 35],\n [-253, -135, -82, -667, -125, 567, -414, 54, 195, -508],\n [15, -368, 566, -461, 659, 681, -16, 496, 337, -234],\n [-657, -897, 153, 795, 20, -378, -515, -124, 378, 255],\n [-131, 454, -222, 452, -448, -179, 273, -347, -314, 44]]\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[[192, -116, 123, 58, -160, 145, -88, 240, 435, 524],\n [98, 203, 79, -171, 159, 212, 12, -81, -109, -106],\n [153, 7, 104, 59, 34, 95, -26, -8, 111, 213],\n [-106, -103, 469, -101, -159, 165, -32, -357, 39, 196],\n [223, 408, -146, -420, 219, 412, -6, 325, 13, -177],\n [159, 150, 167, -168, 77, 288, -26, -11, 68, 113],\n [379, 78, 585, -208, -67, 621, -126, -13, 476, 723],\n [318, 328, -249, -74, 338, 175, 20, 234, -63, -130],\n [358, 374, -447, 300, 672, -170, 120, -82, -503, -460],\n [421, 487, 13, 69, 698, 196, 94, -404, -516, -327]]?\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 10x10 matrix:\n[[-305, -168, -1, -377, -364, 440, -480, -432, 51, -40],\n [172, -1016, 715, -932, 235, 799, 451, -821, 514, -492],\n [-426, 128, -212, 351, -176, -49, 428, 425, -28, 604],\n [-268, 512, 758, 768, -1206, -524, 610, -438, -1110, -562],\n [-237, 712, -204, 488, -521, -754, 64, 939, -462, -392],\n [-635, -212, -448, 90, -3, -495, -485, 404, -10, -173],\n [-1010, -823, 74, -147, 973, 319, 80, 731, -325, 1376],\n [-1028, 146, -650, 878, 242, -430, 25, 858, -471, 1180],\n [-107, -352, 543, 141, 356, 99, 1000, 73, -303, 501],\n [-372, -330, -292, -205, 188, 334, -210, -152, 187, 332]]\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[[884, 377, -655, 278, 115, -1659, -702, -925, -560, 408],\n [6, -663, 534, 307, -213, 528, -60, -38, 105, -38],\n [-2, 701, -222, -375, 441, 161, 723, 519, -426, 619],\n [-743, -1543, 1464, -356, 66, 806, 285, -273, -610, -60],\n [-705, -648, 124, -407, -627, 506, 104, -29, 149, -177],\n [231, -274, -111, 263, 602, 299, -521, 197, 474, -989],\n [-787, -80, 914, -263, -166, 715, 487, 150, 113, 535],\n [393, -178, -322, 281, -78, -765, -869, -261, 384, -618],\n [-73, -240, 184, 297, 498, 129, -612, -21, -527, -57],\n [-534, -181, 81, -780, -211, 236, 514, 166, 19, 418]]\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[[-251, 19, -755, 60, 634, -388, -374, 563, 271, -120],\n [727, 236, -571, -99, -193, -84, 488, 50, -436, 62],\n [386, 458, 234, 180, -160, -616, -788, -334, 306, 296],\n [284, 452, -378, -450, -412, -754, -596, 146, 486, 146],\n [604, -522, -3, 474, 557, 493, 842, 63, -1125, -417],\n [174, -547, 418, 384, 258, 826, 934, -185, -905, -276],\n [182, -144, -89, 78, 509, -705, -818, 381, 121, -339],\n [-164, -393, 559, -672, -493, -124, -224, 166, 190, -406],\n [280, -168, 88, 102, 74, 137, 268, -26, -390, -145],\n [694, 100, -560, -147, -257, 230, 904, 44, -646, 6]]\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[[513, 225, -272, 169, -176, -44, 243, -294, 487, -336],\n [-195, -138, 187, -137, 139, 31, -84, 39, -275, 216],\n [-377, 210, -442, 359, -26, -189, -97, 491, 22, -191],\n [504, 88, -10, 20, -362, 116, 114, -220, 522, -306],\n [33, 190, -301, 251, -221, -61, 0, 203, 309, -300],\n [-101, 161, -354, 183, 414, -266, 179, -108, -227, 76],\n [-167, 228, -464, 301, 240, -265, 107, 107, -78, -77],\n [-442, -46, -57, 12, 407, -154, -53, 146, -501, 287],\n [-647, -82, -18, 33, 270, -107, -211, 429, -506, 259],\n [486, 225, -256, 194, -352, 11, 162, -147, 605, -429]]\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[[-892, -823, 31, 279, -1138, 93, 59, 14, -115, -721],\n [531, 792, 344, -341, 476, -72, -209, 54, 314, 458],\n [84, -515, -253, 189, -38, 110, 515, -251, -306, -49],\n [148, -318, -168, 76, -64, 6, 440, -52, -10, 87],\n [126, 28, -424, 216, 146, -305, -276, 563, 583, -17],\n [-205, -287, 41, 8, -398, 21, 224, 4, 15, -84],\n [-468, -837, -352, 66, -419, 45, 701, -37, -337, 0],\n [-609, -581, 22, 325, -969, -4, -132, 160, 188, -686],\n [-242, -275, 325, -349, -416, 189, 697, -328, -363, 269],\n [-321, -828, -145, 286, -677, 121, 495, -172, -203, -387]]\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[[850, -756, -341, 102, -88, 499, -166, 8, -356, 346],\n [621, -467, -151, 478, 335, 28, -177, -106, 70, -42],\n [-16, 626, -210, -453, -258, 467, -398, -85, -22, 338],\n [414, -404, 158, 694, 708, 252, 112, 4, 116, -156],\n [-718, 291, 839, -164, 244, 382, -66, -163, 83, -205],\n [-468, 234, 301, -603, -503, 154, -163, -291, -183, 209],\n [400, 246, 6, 981, 911, 83, 301, -356, 374, 44],\n [-494, -237, 256, -452, -555, -451, 95, -49, -186, -106],\n [306, 311, -335, -668, -789, 664, -345, -623, -430, 964],\n [-329, 103, 162, -157, -138, -64, 222, 6, -70, 14]]\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[[38, 119, -51, 223, -35, -46, 77, -142, -247, 276],\n [145, 126, 375, -84, 33, 299, -274, 321, -189, -84],\n [-100, -205, -194, -149, 48, -111, 179, -62, 434, -211],\n [-76, 36, -440, 396, -64, -340, 412, -508, -120, 464],\n [-187, -34, -106, -80, -154, -248, -256, -105, -190, -47],\n [-186, -258, -397, -90, 13, -289, 300, -248, 483, -143],\n [247, 294, 500, 84, 16, 394, -328, 337, -504, 133],\n [23, 191, -349, 577, -73, -260, 407, -519, -397, 691],\n [45, 195, 81, 201, -87, -6, -141, -57, -471, 279],\n [-87, 34, -44, 20, -104, -138, -160, -81, -224, 59]]\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[[-331, -9, -140, -138, -99, 108, 428, -185, -225, -665],\n [53, 244, -53, 340, -32, -901, 338, -99, 110, -302],\n [-448, 341, -168, -222, 214, 774, -438, 560, -412, 776],\n [216, 789, 474, 653, -277, -202, 119, 106, -258, 8],\n [-182, 190, 188, 125, -64, 213, 598, -567, -67, 282],\n [549, -761, 80, -533, 125, 109, 152, -651, 556, -396],\n [45, -135, -236, 60, -410, -69, -185, 91, 200, -194],\n [730, -868, 270, -21, -47, -294, -397, -135, 514, -404],\n [663, -207, 176, 344, -430, -443, -391, 73, 436, -252],\n [974, -455, 353, 165, -322, -305, -381, -186, 635, -249]]\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[[27, -141, 69, 183, -348, -9, 36, -228, 9, 222],\n [397, 219, 438, -190, 297, 26, 180, -38, 190, 96],\n [574, 304, 655, -255, 407, 33, 260, -78, 269, 178],\n [12, 76, -116, -116, 128, 28, 8, 128, 40, -224],\n [-247, -271, -251, 285, -508, -23, -90, -168, -118, 112],\n [341, 187, 298, -178, 221, 38, 164, -14, 186, -8],\n [399, 167, 411, -133, 156, 31, 194, -104, 202, 120],\n [178, 258, 40, -310, 464, 46, 70, 244, 123, -314],\n [348, 382, 241, -425, 671, 55, 140, 266, 199, -290],\n [527, 207, 651, -137, 216, 19, 246, -184, 236, 300]]\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 10x10 matrix:\n[[230, -380, 95, -225, 260, -65, 205, 75, 0, 65],\n [-124, 232, 72, -228, -52, 156, -236, -28, -104, -208],\n [-207, 330, -140, 357, -273, 5, -129, -73, 46, 18],\n [328, -568, 17, 15, 286, -209, 413, 95, 100, 259],\n [-14, -4, -129, 363, -104, -117, 113, -17, 104, 169],\n [-59, 122, 87, -258, 13, 126, -166, -8, -94, -173],\n [-166, 316, 121, -375, -52, 233, -341, -35, -160, -313],\n [-81, 126, -69, 180, -117, -12, -36, -30, 30, 27],\n [-231, 402, -3, -36, -195, 156, -300, -66, -78, -195],\n [-60, 120, 70, -210, 0, 110, -150, -10, -80, -150]]\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[[-221, 71, -21, 59, 86, 142, 105, 224, -216, 30],\n [-180, -563, -223, -280, 21, 601, 438, -10, -557, -78],\n [-214, -246, 218, -380, 264, -348, 204, -410, 342, 324],\n [-278, -380, 260, -590, 14, -154, 130, -468, 86, 56],\n [160, -289, -109, -156, -222, 266, 9, -138, -199, -231],\n [487, 760, -36, 714, -86, -404, -527, 323, 456, -19],\n [369, -55, -99, 69, -177, 3, -148, -128, 116, -137],\n [281, 225, -207, 366, -253, 269, -219, 327, -233, -291],\n [-265, -209, 35, -247, -7, 201, 162, -22, -274, -51],\n [69, 18, 14, 54, 197, -233, 64, -103, 298, 236]]?\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[[-136, -113, 424, -221, -407, -330, -20, -95, 536, -510],\n [147, -687, 510, 675, 420, -167, -79, -528, -474, -888],\n [69, 442, -408, -6, 170, 369, -407, 479, -232, 982],\n [-320, 311, -718, -565, -206, 107, 239, 404, 238, 835],\n [-291, -114, -169, -232, -178, -209, 254, 119, 234, -85],\n [-61, -259, 271, 42, -18, -172, 232, -269, 110, -416],\n [-26, -386, 361, 440, 243, -356, 138, -206, -152, -816],\n [-6, -490, 90, 208, 216, 307, -226, -207, -372, 288],\n [328, 423, 203, 185, 144, 317, -837, 172, -132, 623],\n [265, 600, 77, 0, -49, 587, -278, 543, -76, 933]]?\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[[96, 561, -398, -142, 208, -92, -736, -410, -336, -12],\n [328, -501, -8, 87, 257, 63, 668, 443, 108, -280],\n [685, -46, -457, 370, 190, 161, 416, 360, -179, 268],\n [231, -623, -369, -360, 28, 233, 458, 235, -16, -1026],\n [41, -688, -271, -275, -128, 328, 1001, 688, 419, -385],\n [-113, 232, 70, 94, -532, -15, -515, -382, -160, 177],\n [343, 126, 55, 185, 629, -200, -256, -211, -371, -236],\n [-196, 53, 964, 57, -327, -787, -1014, -507, 154, 42],\n [175, 237, -77, -19, 282, -124, -685, -572, -541, -539],\n [505, -89, -574, -207, 373, 38, -105, -19, -312, -705]]\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[[494, 422, -465, 256, 216, 325, -247, 326, 947, 279],\n [280, 298, -454, 447, 22, 427, 3, -5, 568, -368],\n [448, -158, 494, -271, 364, 109, 444, -747, 45, -248],\n [552, -365, -85, -206, -68, -62, 211, -269, 484, -274],\n [-368, 242, 264, 147, 336, -246, -176, 469, -465, 59],\n [-218, -446, 197, -134, -338, -48, 233, -383, -634, -421],\n [-86, 557, -404, 177, 44, 82, -106, 98, 730, 445],\n [-106, -110, -61, -510, -218, -451, -129, 111, 344, 872],\n [-34, -243, -398, 24, -406, -107, -450, 718, -24, 228],\n [432, 127, 61, 111, 470, 36, -284, 564, 206, 99]]\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 10x10 matrix:\n[[-336, -781, 1132, 467, 122, 458, -556, -114, -458, 548],\n [205, 93, 547, -412, 244, 1023, -396, -544, 389, -45],\n [66, -435, 402, 1028, -700, 108, -278, -307, -13, 251],\n [-338, 233, -541, -671, 316, 57, 0, 497, 220, -98],\n [-127, -88, 613, 330, -51, 191, -719, 242, -232, 314],\n [532, 221, -342, 169, -328, 758, 130, -960, 1026, -574],\n [-146, 152, -64, -365, 211, 91, -157, 275, 17, 24],\n [590, 1131, -1102, -540, -317, -511, 449, 129, 437, -528],\n [144, -242, 210, 685, -408, -237, 46, -212, -179, 110],\n [359, 329, -561, -137, -301, -57, 465, -334, 394, -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[[377, 633, -37, -78, 496, -145, 147, 163, 388, -552],\n [-65, -200, 35, 0, -160, 95, 5, 25, -100, 155],\n [22, -135, 52, -30, -112, 124, 66, 110, -40, 81],\n [19, 99, -23, 6, 80, -59, -15, -31, 44, -72],\n [-262, -644, 90, 24, -512, 258, -34, 6, -344, 518],\n [273, 840, -147, 0, 672, -399, -21, -105, 420, -651],\n [132, -283, 146, -102, -240, 338, 220, 352, -48, 139],\n [-207, 336, -195, 144, 288, -447, -309, -489, 36, -147],\n [465, 93, 171, -198, 48, 351, 411, 603, 228, -228],\n [-164, 144, -116, 96, 128, -260, -204, -316, -16, -36]]\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[[-230, 258, 747, 620, -125, -607, -151, 294, 185, -324],\n [-138, -114, 564, 9, -213, -411, 216, -174, 564, -321],\n [163, -30, -51, -276, -106, 79, 346, -54, 77, 195],\n [35, 112, -28, 98, 21, 14, -35, 140, -154, 91],\n [168, -448, -641, -787, 62, 542, 249, -536, 125, 155],\n [-422, -376, 478, 90, -34, -388, -264, -464, 694, -748],\n [261, 418, -100, 173, -22, 81, 161, 506, -506, 496],\n [-152, 12, 267, 219, -16, -224, -143, 12, 137, -231],\n [31, 32, 106, -12, -67, -70, 123, 28, 64, 29],\n [-253, -286, -65, 2, 138, 19, -376, -326, 195, -403]]\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[[102, 36, 78, 126, -60, -120, -12, -90, 132, 42],\n [-204, -72, -156, -252, 120, 240, 24, 180, -264, -84],\n [34, 12, 26, 42, -20, -40, -4, -30, 44, 14],\n [238, 84, 182, 294, -140, -280, -28, -210, 308, 98],\n [102, 36, 78, 126, -60, -120, -12, -90, 132, 42],\n [-153, -54, -117, -189, 90, 180, 18, 135, -198, -63],\n [-255, -90, -195, -315, 150, 300, 30, 225, -330, -105],\n [-85, -30, -65, -105, 50, 100, 10, 75, -110, -35],\n [85, 30, 65, 105, -50, -100, -10, -75, 110, 35],\n [289, 102, 221, 357, -170, -340, -34, -255, 374, 119]]\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[[-322, 377, 89, -327, -265, -197, 2, 181, 322, 179],\n [27, -306, -278, 653, 502, 95, 41, 65, -827, -572],\n [-387, -346, 225, 847, 218, -970, 135, -184, -159, 90],\n [488, -239, 201, -471, -781, 381, 242, 284, 565, 255],\n [-417, -270, -392, 755, 578, 1, 83, 8, -654, -472],\n [-88, -6, -318, -254, 150, 642, -76, -248, 290, 110],\n [30, -117, -328, 241, -69, 420, 250, 733, -743, -747],\n [62, -664, 28, 316, -216, 82, 280, -157, 399, 264],\n [-182, -178, -151, 412, 614, -87, -162, -571, -116, 64],\n [84, -108, 212, 490, 279, -620, -61, -131, -438, -117]]?\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[[311, -160, 530, 15, 658, -1110, 38, 126, -92, 222],\n [-900, 246, -493, -127, 370, -334, 34, -602, 139, -421],\n [1325, 766, -27, -792, -95, -146, 268, 988, 235, 575],\n [-496, 326, -908, -765, 804, 93, -235, -794, 117, -118],\n [670, 936, 468, -332, 450, -1196, 1173, 367, -293, 163],\n [-408, -158, 555, 422, -116, 335, -22, -134, -213, 264],\n [-77, -434, -77, 114, 582, 284, -468, -391, -495, 355],\n [-486, -134, 154, 527, -330, -591, 523, -199, 49, -798],\n [-139, -168, 172, 577, 28, 450, 151, -188, -807, 207],\n [488, 98, 673, -211, -203, -430, 461, 258, 390, -62]]?\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[[-355, 488, 906, 828, 154, -396, 815, -698, -833, -106],\n [-92, 238, -56, -1019, -374, 724, -295, -1032, 232, -934],\n [-609, -84, -524, 85, 349, -588, 40, 557, -344, -380],\n [-23, -498, -83, 676, 258, 526, 89, 530, 951, 749],\n [-368, -278, -379, -61, 138, 535, -238, 225, 550, 169],\n [597, -1020, -1062, -598, -366, 406, -627, 358, 715, 290],\n [-827, -304, -113, 784, 855, 2, -20, 499, 360, 314],\n [-712, 280, 547, 928, -14, 454, 1382, 35, 519, -151],\n [-25, 404, 681, 329, 77, 24, 308, -390, -139, 21],\n [1112, -284, -386, -964, -3, -597, -1558, -124, -587, 293]]?\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, 480, 10, -131, 28, 325, 72, -253, -448, -83],\n [78, 328, 29, 231, -384, -297, 293, -405, -171, -232],\n [194, 316, 221, 310, 196, 308, 189, -456, -429, 294],\n [351, -231, 217, 373, 151, -181, -310, 94, -678, -367],\n [404, 18, 31, 549, -150, -349, 487, -479, 95, 252],\n [-97, -9, -36, -202, 23, -5, -360, 286, -480, -538],\n [-303, 337, -154, -336, -249, 22, 27, -17, -71, -324],\n [-646, 170, -424, -724, -676, -341, 55, 295, 747, -485],\n [-209, 39, -328, -320, -203, -136, 165, 101, 393, -75],\n [-435, 779, -87, -265, -517, 128, 525, -555, 367, 129]]\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[[261, -225, 217, -38, 994, 57, 372, 667, -367, -558],\n [-436, 1205, -556, -551, 618, 1673, -1251, -634, -388, -100],\n [315, -387, 119, -377, 347, 905, -532, -335, -828, 458],\n [128, 621, -266, -524, 552, 714, -709, 88, -544, 256],\n [-872, 883, -1350, -853, 523, 710, -912, -572, 217, -185],\n [-1065, 683, -949, -455, 12, 532, -621, -416, -127, 267],\n [198, -583, 544, 447, 104, -820, 756, 919, 32, 145],\n [-80, 42, 20, -597, 382, 309, 122, -151, -88, -716],\n [131, -43, 11, -302, 149, 301, -38, -62, -646, 656],\n [-745, -375, -683, -194, 498, 1010, -762, -730, 119, 64]]\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[[853, 4, 107, -81, -272, 214, 772, -46, 437, 290],\n [-257, 57, -417, -466, 878, 183, -950, 248, -343, 444],\n [-758, -57, 366, -143, 458, -315, -728, -290, -585, -49],\n [-283, 210, -331, 41, 641, 398, -615, 353, 299, 291],\n [771, 184, 926, 306, -482, -779, 750, -77, 244, -62],\n [-347, 225, -181, 924, 38, -83, -392, 1212, 582, -447],\n [-96, -55, -868, -693, -450, -851, -390, -468, -1338, -426],\n [287, 90, -408, 272, -472, -294, 188, 489, 72, -359],\n [441, -309, 114, -349, -582, -653, 400, -185, -767, -268],\n [240, -314, -379, -917, 440, 1072, 162, -681, -78, 776]]?\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[[29, 60, -98, -129, -56, -36, 4, 84, 131, 79],\n [-75, 156, -18, -441, -312, 444, -156, 756, -21, 279],\n [-9, -64, 70, 153, 84, -40, 20, -168, -87, -95],\n [95, 122, -256, -237, -74, -202, 48, 42, 353, 143],\n [-96, -9, 159, -45, -93, 333, -102, 315, -240, 33],\n [58, -209, 91, 561, 371, -443, 162, -861, -74, -353],\n [113, 156, -314, -309, -104, -228, 52, 84, 431, 187],\n [-53, -121, 189, 264, 119, 53, -2, -189, -251, -162],\n [-54, -8, 92, -18, -48, 184, -56, 168, -138, 14],\n [117, 80, -254, -117, 12, -328, 92, -168, 363, 67]]\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 10x10 matrix:\n[[-606, 1663, 777, 313, -334, 567, 603, -406, 509, 637],\n [-288, 594, -370, -663, -507, -680, 279, -21, 677, 470],\n [318, -207, 951, -749, -44, 196, -764, 51, -389, -64],\n [369, -524, -581, -64, 469, 17, 517, 566, -399, -298],\n [-342, -393, -275, -366, -143, -635, -43, 513, 113, 173],\n [619, 111, 201, 39, -41, 414, 190, -311, 789, 182],\n [-625, 472, -296, -380, -383, -557, -7, -19, -34, 339],\n [-86, 593, 268, 63, 186, 731, 1157, 687, 36, 904],\n [-74, 86, 742, 579, 111, 478, 258, 343, 142, 340],\n [325, -599, -270, -141, -113, -621, -646, -87, -309, -264]]\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[[-73, 285, 148, 75, -69, -97, 199, 65, -65, -137],\n [-395, -355, 116, 217, 419, -231, -85, -125, 787, -465],\n [-195, 83, -82, 275, 185, 147, -309, -405, 493, 431],\n [-494, 134, -657, -459, -496, -345, -550, -809, 486, -129],\n [231, 49, 357, 224, -95, 26, 375, 716, -441, -154],\n [756, -306, -210, -333, -594, 330, -21, 778, -1156, 397],\n [-454, 20, 403, 670, 938, 47, 1, -473, 1082, 50],\n [458, -302, 112, -130, -194, 90, 238, 746, -706, -126],\n [-9, -17, 13, -305, -125, -250, 228, 108, -209, -513],\n [412, -450, 46, -152, 246, 226, 86, 272, -370, 90]]\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[[-106, 96, -133, -50, 479, -255, -239, 225, 239, -450],\n [-406, -23, -324, 219, 2, 4, 164, 181, 41, -251],\n [-290, 53, -226, 115, 246, -172, -16, 191, 189, -351],\n [-864, 139, -514, -23, 433, 31, 411, -43, 112, -329],\n [410, -116, -5, 2, 102, -44, -530, 465, -60, -388],\n [445, 45, 351, -321, 93, 9, -204, -216, -54, 250],\n [560, -120, 219, 186, -201, -183, -465, 341, 51, -116],\n [608, 229, 1035, 285, -508, -788, 98, -726, 689, 981],\n [284, -18, 376, 194, -485, -117, 113, -254, 79, 500],\n [-854, -4, -783, -138, 484, 374, 268, 251, -230, -604]]?\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[[228, -57, -323, -323, -114, -76, -114, -380, 209, -361],\n [-144, 36, 204, 204, 72, 48, 72, 240, -132, 228],\n [-36, 9, 51, 51, 18, 12, 18, 60, -33, 57],\n [-156, 39, 221, 221, 78, 52, 78, 260, -143, 247],\n [-24, 6, 34, 34, 12, 8, 12, 40, -22, 38],\n [60, -15, -85, -85, -30, -20, -30, -100, 55, -95],\n [60, -15, -85, -85, -30, -20, -30, -100, 55, -95],\n [48, -12, -68, -68, -24, -16, -24, -80, 44, -76],\n [120, -30, -170, -170, -60, -40, -60, -200, 110, -190],\n [-228, 57, 323, 323, 114, 76, 114, 380, -209, 361]]\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[[-6, -29, 191, -73, -47, -207, 95, -97, -100, -123],\n [-15, -920, 1012, -79, -527, -191, 589, 12, -234, 46],\n [-34, -628, 852, -55, -463, -251, 205, 250, 45, 9],\n [46, -856, 381, 111, -271, 394, 719, -210, -350, 299],\n [-85, 562, -529, -335, 311, 56, -407, 186, 37, 56],\n [-215, -113, 428, -849, -141, -260, -93, 493, -192, 142],\n [-41, 263, 111, 142, -144, -216, -774, 707, 740, -55],\n [36, 108, -412, 140, 164, 332, -20, -76, 12, 136],\n [-134, 176, 7, -362, -36, -37, -518, 652, 301, 160],\n [72, 187, -566, 242, 250, 385, 34, -243, -36, 100]]\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[[-124, -7, -2, 97, 63, 15, -87, -85, 92, -81],\n [508, 162, -160, -178, -302, -549, 534, 5, -707, 295],\n [-178, 71, -41, 150, 24, 4, -90, -66, 108, -112],\n [-607, 646, -377, 600, -104, -191, -42, -21, 253, -503],\n [-89, -316, 224, -143, 293, 454, -273, 94, 425, -86],\n [-47, 256, -199, 116, 72, -222, 234, 50, -6, -274],\n [780, -11, 12, -729, 5, 60, 663, 738, -241, 136],\n [67, -157, 149, -149, -79, 241, -147, 97, 44, 205],\n [444, -879, 495, -514, 324, 298, -198, -220, -66, 430],\n [362, 176, -182, -32, -264, -594, 444, -142, -658, 222]]\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[[577, 328, 1, 212, -526, 231, -195, -161, 134, 804],\n [-184, 786, 176, 20, -416, 17, -303, 51, 76, 187],\n [167, -318, -31, -98, 4, 56, -470, 566, -430, -219],\n [10, -124, 468, -602, 556, -447, 781, -455, 260, 9],\n [267, 232, -254, 411, -399, 263, -471, 479, 124, 526],\n [-2, -443, -854, 919, -253, 534, -368, 252, -30, -43],\n [363, 469, 243, -135, -367, 15, -517, 519, -52, 521],\n [-181, -268, 88, -186, 413, -199, 661, -574, 166, -241],\n [-144, -203, -235, 182, 100, 64, -142, 348, -32, -193],\n [-805, -294, 276, -592, 841, -514, 398, 215, -122, -1060]]\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[[-26, 296, -731, -380, 991, -743, -12, -340, -921, 65],\n [-572, 180, -422, 52, 597, -864, -612, 281, -292, 81],\n [615, 117, 486, 784, -208, 517, 215, -153, 195, -33],\n [181, -323, 553, 628, -585, 650, 317, 137, 706, -146],\n [463, 436, 114, 365, 161, 227, -69, -94, -189, 291],\n [-576, 140, -420, -433, 323, -501, -497, 258, -158, 305],\n [264, 364, 50, -258, -196, 396, 42, 448, -106, 232],\n [-476, -318, -506, -434, 339, -579, 273, 365, -277, -462],\n [-284, -347, 313, 19, -456, 306, -281, -539, 702, 342],\n [-177, 135, 297, 563, -220, 221, -444, 399, 516, 369]]\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[[-25, 80, -65, 40, -50, 90, -30, 30, -110, -20],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n [-85, 272, -221, 136, -170, 306, -102, 102, -374, -68],\n [100, -320, 260, -160, 200, -360, 120, -120, 440, 80],\n [10, -32, 26, -16, 20, -36, 12, -12, 44, 8],\n [-20, 64, -52, 32, -40, 72, -24, 24, -88, -16],\n [-75, 240, -195, 120, -150, 270, -90, 90, -330, -60],\n [70, -224, 182, -112, 140, -252, 84, -84, 308, 56],\n [15, -48, 39, -24, 30, -54, 18, -18, 66, 12],\n [30, -96, 78, -48, 60, -108, 36, -36, 132, 24]]?\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[[247, 82, -760, 40, -5, -798, 228, -276, -181, -63],\n [104, -277, -166, -117, 294, -302, -260, -32, 243, -46],\n [-82, 500, 327, 889, 130, -305, 34, 608, 86, -751],\n [92, 756, -709, 682, -431, -689, 489, 265, -367, -231],\n [-89, -212, 420, -282, 425, 193, -348, -117, 292, -56],\n [164, 619, -1001, 404, 220, -440, 448, 323, 566, -18],\n [-86, 524, -398, 154, -240, -651, 92, 651, -403, 299],\n [210, -341, 153, 59, 330, 20, 222, -654, 149, -526],\n [-25, 286, -261, 29, -102, -353, 15, 114, -189, 92],\n [-174, 634, -723, -921, 452, -68, 13, -43, 421, 993]]\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[[-358, -563, -265, -305, 309, -558, 237, -189, 367, -36],\n [115, 107, 445, -317, 228, 57, -39, 406, -254, -11],\n [132, -109, 133, -470, 332, -314, 98, 35, 66, -182],\n [577, 552, 72, 151, -248, 317, -167, -131, -160, -187],\n [-147, -460, -8, -606, 497, -605, 230, -27, 257, -151],\n [-256, -438, 114, -521, 461, -458, 185, 162, 129, -28],\n [355, -31, -761, 83, -168, -411, 129, -972, 578, -399],\n [197, 205, 155, -23, -24, 135, -69, 90, -134, -45],\n [-40, 37, -157, 242, -180, 102, -30, -127, 38, 50],\n [497, 259, -379, 101, -204, -81, -9, -604, 242, -325]]?\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[[-38, 540, -1006, -45, -278, -248, 347, 47, 425, 361],\n [-204, 56, -1354, 101, 567, -287, -179, -602, 154, 126],\n [396, 592, -694, -603, 665, 440, -699, -669, 205, -306],\n [159, 811, 292, -1036, -604, -706, -37, -809, -566, 1241],\n [89, -185, 659, -361, -68, -185, 110, 141, -365, 128],\n [-280, -204, -647, 777, -255, -556, 809, 503, 144, 214],\n [108, 607, 56, -974, -227, -163, -59, -34, 80, 444],\n [-132, -1529, 276, 687, 409, -23, -152, -33, -420, -442],\n [31, 916, -515, -784, -559, -417, 318, -259, 70, 884],\n [88, -23, -813, 787, -511, -917, 513, 275, 234, 497]]\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 10x10 matrix:\n[[702, 237, 50, 93, -22, -428, 242, -146, -387, 382],\n [94, 639, 282, 340, -222, 173, 147, -676, 318, 320],\n [-268, -125, -96, 293, -96, -37, -532, -78, -167, -637],\n [41, 1259, -888, -660, -9, 106, 346, -784, -192, 517],\n [-511, -264, 326, 488, 299, 97, -569, -403, 74, 549],\n [357, 169, 771, 29, 309, -334, -305, -539, 221, 809],\n [0, -1187, 317, 746, 537, -154, 291, 397, 132, 93],\n [431, 835, -112, -153, -33, -139, 567, -574, 179, 399],\n [-804, 153, -259, 224, -877, 384, -869, -198, 42, -169],\n [245, 984, -89, -672, -11, -240, 129, -837, 648, 212]]\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[[269, 226, -239, 82, 162, 529, 196, -144, 105, 105],\n [-385, 135, 462, 481, 226, 41, -233, 369, -145, -69],\n [-601, -526, 446, -839, -311, -632, -422, 67, 418, 192],\n [17, 347, -220, -336, -519, -620, 529, 107, -264, 296],\n [304, -77, -171, -321, -22, 108, 201, -361, 196, 116],\n [238, 102, 63, 233, 417, 537, -334, -235, 475, -153],\n [-746, -18, 115, 244, -16, -98, -1162, 737, 339, -391],\n [105, -476, -629, 150, -161, 130, 67, 120, -601, -326],\n [416, 626, -1203, -46, -524, -28, 174, 199, -74, -96],\n [171, 842, -391, 165, -111, 232, 332, 194, 25, 239]]\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[[733, 43, -420, -649, 750, -533, -1454, 732, 254, -497],\n [-291, 413, 337, 120, -267, 283, 270, -235, -104, -160],\n [-297, 248, 580, 773, -145, 145, 524, -536, 101, -240],\n [-136, 463, 379, 740, -261, -179, 121, -432, -15, -732],\n [-99, -554, -856, 48, -494, -159, 426, 263, 30, 621],\n [226, -181, 344, -511, 540, 49, -138, 90, 49, 324],\n [157, -221, 203, -624, 214, 53, 219, 228, -129, 614],\n [-230, -182, -231, 573, -789, -225, 920, -178, -273, 221],\n [527, 226, -398, -272, 132, -57, -604, 1083, -322, -117],\n [326, 8, -424, 191, 58, 141, -266, 854, -247, 40]]\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[[82, 360, 681, 299, -504, -90, -113, -613, -700, -282],\n [-48, 276, 549, -36, -894, -76, 24, -430, -791, -408],\n [757, -908, -17, 355, 246, -203, 244, -186, 436, -530],\n [-309, 496, 749, 343, -307, 135, -50, -470, -291, 87],\n [-132, 590, 779, 67, -405, -349, -294, -523, -320, 227],\n [44, -733, -331, -601, -231, -780, 13, 220, 293, -364],\n [-465, -577, -257, -95, -218, 123, 366, 265, 11, -547],\n [-978, 726, 261, 285, 430, -41, -260, 239, 73, 848],\n [-166, 616, 1216, 285, -1092, -151, -62, -849, -954, -302],\n [-468, -54, -55, 259, -249, -172, 241, 549, -469, -7]]\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[[-721, 141, 95, 109, 303, -653, -758, 241, 5, -233],\n [154, 284, -331, -423, -232, 242, 416, -304, 550, -261],\n [-35, 559, 307, -254, -296, 30, -95, 139, 190, -234],\n [-395, -465, 206, 410, 92, -1110, -826, 474, -984, 89],\n [64, -141, -145, -593, -146, 135, -238, 228, 205, -957],\n [-377, 55, -491, -875, 118, 380, -170, -300, 816, -787],\n [-2, 395, 737, -532, -1197, 594, -156, -82, 135, -484],\n [61, 594, -345, -738, 626, 357, 374, -286, 566, 572],\n [-527, -257, -583, -210, -279, -137, -90, -612, 180, -409],\n [103, 86, 634, -145, -840, 511, -44, -96, -294, 18]]\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 10x10 matrix:\n[[-144, 454, 84, -410, 367, 221, 258, 713, -110, 170],\n [-252, -333, 177, -193, 80, 433, 304, 427, -164, 81],\n [34, 543, -317, -223, 58, 18, -337, 110, 30, -17],\n [138, -358, 70, 146, 32, -699, -99, -859, 452, 126],\n [-347, -424, -362, -33, -182, 33, 69, -76, -95, -123],\n [706, 352, 299, -319, -106, -95, 24, -238, 415, 601],\n [361, 324, 301, -740, -40, 701, 354, 685, 44, 674],\n [-235, -848, 23, 130, -63, -334, 188, -552, 184, 18],\n [217, -291, 150, 894, -283, -423, -152, -654, -67, -439],\n [28, -480, -1203, -45, -970, -169, -792, -1162, 253, -139]]\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 10x10 matrix:\n[[-235, 60, 598, 300, -459, -366, -362, -309, -247, -234],\n [401, 292, 290, 844, 229, 776, 332, 813, 595, -612],\n [-108, 340, 6, -403, -297, -421, -36, -425, -35, 183],\n [102, 282, -289, -194, 140, -369, -82, -119, 239, 726],\n [-337, 322, -217, -125, 97, 587, -341, 395, -315, -755],\n [-879, -226, 46, -836, 115, -40, -666, -947, -673, -564],\n [-351, 628, -547, -1006, 263, -482, -676, -564, -356, 378],\n [-609, -289, -25, -373, 89, 325, -234, -360, -264, -488],\n [-528, -743, 311, -923, -115, -165, -27, -1197, -751, -726],\n [5, 479, 999, 465, -372, -667, -181, -730, 474, 82]]\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[[759, 707, 180, -272, -554, 533, 321, 746, 621, 160],\n [-242, 499, -196, 364, -248, -423, 631, 523, -13, -234],\n [269, 564, -902, -92, -426, -202, 951, 186, 713, -46],\n [417, 226, -585, -104, -239, -383, 358, 127, 439, 20],\n [-284, 6, -565, 323, -150, 25, 252, -165, 484, 496],\n [144, 15, 425, 392, -151, 1147, -629, -570, 186, 1064],\n [56, -467, -655, -631, 75, -326, -348, 62, 1040, -37],\n [-11, 431, 587, 435, -76, 797, -181, -562, -517, 184],\n [-506, -360, -17, -310, 306, 287, 528, -123, -317, -275],\n [-339, -105, 313, -188, 113, -105, 264, 662, -213, -394]]?\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[[63, -57, 131, 112, 924, 207, -136, -50, -150, -399],\n [-674, 144, 163, -906, 741, 421, -261, 18, 197, 347],\n [-603, -495, -733, -438, 72, -602, 190, -425, 137, -317],\n [236, 36, 94, 378, -597, 117, 143, 114, -3, 278],\n [321, 395, -216, 48, 0, -679, 230, -298, -236, -562],\n [-203, -571, -730, -492, -240, -1216, -282, -145, 133, -792],\n [-85, 81, 479, -86, 102, 727, -252, 346, 122, 567],\n [-72, 244, 20, -186, 477, -1, 61, -162, -89, -148],\n [-120, 687, 282, -143, 132, 500, 375, -155, -68, 545],\n [-448, 114, -181, -106, -243, 285, 543, -304, 87, 575]]\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[[-130, 39, 38, -176, 280, 200, 348, -121, 254, -482],\n [-176, -388, 465, 390, -339, -106, 186, 387, 432, 27],\n [-195, -687, 194, 689, -225, -155, 163, 387, -262, 459],\n [178, 274, -562, -434, -1390, 113, -454, 605, -658, 1170],\n [712, 293, -756, -382, -1066, -385, -130, 160, 148, 348],\n [564, -11, -807, -154, -1129, 306, 162, 236, 185, -209],\n [431, 725, -485, -724, 287, -765, 155, -402, 326, -40],\n [-376, 254, 464, 170, 114, 374, -414, 176, -97, 118],\n [549, 288, -675, 364, -547, -178, -393, 122, -226, 320],\n [647, 554, -1005, -287, -746, -198, -259, 62, -282, 416]]\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[[185, 47, -95, 438, 79, -199, 343, 302, -116, -455],\n [-22, -65, 297, 301, 622, 133, 197, 433, -595, -51],\n [151, -142, -118, 691, -170, -258, 601, 343, 3, -820],\n [-69, -14, -50, -232, -92, 154, -132, -143, -163, 189],\n [276, 252, 58, -449, -211, 252, -353, 33, 54, 413],\n [69, -333, 387, -23, -856, 269, 46, 79, 802, -182],\n [-265, -491, 971, -341, -148, 635, -285, 90, 514, 512],\n [-44, -186, 760, -282, 57, 582, -286, 273, 120, 490],\n [-307, -228, 148, 456, -24, 96, 190, 159, -9, -363],\n [181, 571, -1037, -356, -418, -543, -281, -667, 222, 39]]\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[[175, 393, 225, -746, 163, 481, 288, -236, 273, 430],\n [-694, 405, -496, 104, 23, 26, 659, -144, 87, -388],\n [146, -67, 428, 658, 32, -209, -407, 490, -240, 301],\n [350, -437, 154, -689, -1005, 88, 561, -230, -551, -282],\n [82, -391, -219, 464, 759, -200, -111, -264, -144, 1359],\n [-479, -43, -675, 587, 688, 290, -212, -214, 34, 829],\n [-346, 602, -350, 161, -17, -336, 501, 195, 293, -829],\n [-80, -310, 43, 486, -13, -39, 190, -174, 175, 627],\n [-39, -315, -124, 679, -726, -491, 1159, -49, -317, 394],\n [-537, -333, -686, 533, 50, 68, 951, -614, -72, 1045]]\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[[147, -77, 18, 159, 114, -115, 57, 54, 88, -200],\n [165, -233, -81, 225, 114, -157, 57, 99, 250, -278],\n [171, 219, 234, 87, 162, -75, 81, -18, -216, -120],\n [54, 162, 138, -2, 60, -6, 30, -30, -164, -4],\n [423, -201, 66, 451, 330, -327, 165, 150, 232, -568],\n [339, -103, 93, 343, 270, -251, 135, 105, 126, -434],\n [-312, 184, -24, -344, -240, 248, -120, -120, -208, 432],\n [39, -149, -84, 83, 18, -55, 9, 48, 156, -100],\n [18, -282, -186, 106, -12, -66, -6, 78, 292, -124],\n [-276, 250, 39, -332, -204, 236, -102, -129, -274, 414]]?\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[[23, 186, -214, -377, 295, 84, -76, 274, -349, -89],\n [301, 357, -63, 126, 175, 98, -217, -217, -168, 7],\n [-85, 135, -293, -610, 369, 86, -27, 493, -452, -135],\n [-346, -297, -77, -421, 0, -58, 207, 457, -47, -72],\n [-426, -537, 131, -101, -304, -154, 319, 249, 305, 8],\n [-259, -153, -149, -484, 123, -10, 129, 469, -182, -93],\n [-95, 105, -267, -570, 331, 74, -13, 467, -408, -125],\n [-360, -300, -92, -460, 16, -56, 212, 492, -68, -80],\n [106, 162, -70, -44, 126, 52, -90, -10, -136, -18],\n [-253, -291, 41, -128, -131, -78, 179, 199, 122, -11]]\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 10x10 matrix:\n[[43, 8, -268, 253, -195, 40, 173, -146, -54, 381],\n [317, -97, -311, -613, -242, -197, 72, 448, -853, 87],\n [-242, -126, -86, 655, 440, 231, 126, -616, 951, 85],\n [-717, 213, 110, 733, 332, -64, -464, 195, 482, -407],\n [-158, -400, 124, 438, 324, -23, -121, 60, 207, 62],\n [-273, 213, 309, 418, -271, -154, -245, 85, 171, 2],\n [-115, -60, -324, 451, 638, 687, -481, -553, 1018, -811],\n [7, -495, 167, -12, -31, -538, -251, 401, -79, 8],\n [-43, -34, 489, 428, 192, 275, -11, -766, 1148, -112],\n [-446, -197, 976, 401, -247, -916, 50, 471, -4, 567]]\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 10x10 matrix:\n[[-18, 298, 723, 754, 264, 239, -83, -477, -123, -245],\n [82, 196, 610, 621, 662, -129, 158, -736, -103, -134],\n [248, 170, -17, 18, 2, -51, -287, -210, -611, 210],\n [-142, 359, 702, 497, 374, 205, -103, -137, -473, -283],\n [-46, -288, -607, -594, 421, -282, 558, -110, 501, 163],\n [281, -153, -806, -524, -802, 423, -580, 409, -294, 411],\n [362, 121, -220, 377, -678, 532, -323, 60, 46, 61],\n [-17, 331, 54, 45, 370, -356, 566, -42, -39, -134],\n [-624, -231, -906, -1620, 106, 5, 189, 558, -33, 301],\n [494, 584, 528, 1019, -602, 434, -684, -611, -624, 76]]\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[[183, 239, -254, -193, -11, -55, 283, 424, -209, 22],\n [9, 87, -32, -29, 97, -195, 39, 32, -27, -194],\n [117, 78, -143, -104, -104, 156, 156, 260, -117, 208],\n [-213, -214, 279, 208, 96, -100, -308, -484, 229, -192],\n [102, -31, -99, -65, -219, 389, 103, 212, -80, 438],\n [84, -97, -63, -35, -273, 503, 61, 164, -50, 546],\n [69, -152, -33, -10, -318, 598, 26, 124, -25, 636],\n [9, 33, -18, -15, 27, -57, 21, 24, -15, -54],\n [-84, -254, 154, 126, -182, 394, -178, -216, 128, 364],\n [42, -8, -42, -28, -84, 148, 44, 88, -34, 168]]?\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[[-177, -112, 333, -436, -316, -579, -259, -252, 263, -130],\n [-17, 224, -252, -58, -644, -106, 318, -366, 372, -27],\n [-209, -285, -75, 41, 178, 7, 348, -33, 139, -552],\n [146, 93, -284, 87, -276, 97, 322, -298, -62, 174],\n [134, 18, -122, 16, 116, 71, -69, -117, -310, 474],\n [420, 94, 59, 574, -78, 579, 477, 416, -153, -661],\n [10, -16, -45, -72, -38, -75, -15, -148, -61, 173],\n [881, 227, 366, 439, -438, 384, 145, 211, -586, -109],\n [-123, 10, 112, -194, -58, -222, -220, -38, 134, 75],\n [-448, -124, -4, -616, -256, -710, -246, -550, 396, 248]]\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[[-263, 67, -173, -347, -467, 55, 119, 957, -291, -17],\n [-225, -12, -299, 229, -6, 87, 62, -106, 59, 169],\n [46, 292, 452, -235, -181, -301, 4, 315, -277, -384],\n [-175, -752, -553, -27, 124, 287, -58, 0, 643, 571],\n [240, -1041, -282, -411, 244, 331, -201, 94, 789, 538],\n [-52, 16, 108, 199, 148, -163, -29, -397, 153, -40],\n [26, 673, 436, -10, -214, -282, 84, 179, -592, -500],\n [417, 88, 279, -514, -164, 114, -37, 585, -358, -209],\n [-142, 358, 12, 412, 71, -120, 67, -444, -144, -108],\n [-368, 191, -448, 310, -153, 146, 153, 63, -164, 160]]\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[[-354, 357, 115, -235, -162, -546, -332, 170, -129, -21],\n [374, -680, -76, 882, -198, -180, 412, 194, 428, -30],\n [-21, 35, 42, 83, -175, -241, -163, 155, 85, -61],\n [272, -230, -34, 294, -120, 132, 16, 80, 230, -78],\n [78, -115, -103, -153, 398, 572, 394, -354, -173, 137],\n [-5, 175, 93, 36, -367, -346, -480, 301, 167, -166],\n [-525, 413, 77, -480, 161, -376, -50, -87, -395, 134],\n [-54, 283, 141, 19, -518, -542, -692, 430, 209, -227],\n [-232, 189, 104, 14, -268, -613, -291, 262, 21, -58],\n [227, -98, -88, -105, 237, 642, 166, -247, -28, 27]]\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[[-659, 471, 30, -1158, 497, -426, 566, -588, -823, 323],\n [-461, 541, 63, -441, -682, -532, 174, -439, -866, 179],\n [461, -38, -894, 413, -504, -382, -111, -512, 237, -7],\n [336, -540, 365, -323, 534, -202, 279, 241, 747, -298],\n [-144, 123, 291, 239, -346, -262, -14, -105, -307, -1036],\n [-635, -373, 207, 590, -1281, -252, -683, -276, -1188, 519],\n [161, -254, 152, 757, -445, -90, -590, -361, 214, 320],\n [-986, -75, 451, -982, 486, 32, 354, 129, -1176, 237],\n [616, 702, -545, -508, 370, -288, 548, -400, 674, -235],\n [-131, -510, 734, 377, -1139, -558, -332, -259, -334, 89]]\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 10x10 matrix:\n[[219, -59, -593, -528, -258, -453, 93, -16, 491, 39],\n [78, 700, -308, -182, 693, -277, 446, -435, 458, 685],\n [-711, 146, -512, 1377, 535, -70, -700, -797, -1022, -969],\n [599, -156, -65, -177, 1108, 764, 148, 736, 219, 258],\n [-396, -311, -424, -436, -1316, -521, -199, -530, 191, -430],\n [639, -165, -54, -578, 94, -897, -519, -37, -161, -777],\n [-740, 83, -1039, 275, 659, 241, -759, -380, -250, -713],\n [-619, 339, 242, 300, -73, -236, -639, -223, -890, 125],\n [-973, 185, 824, 659, -1341, 1, 175, -747, -198, 7],\n [44, 197, -264, -720, 724, 574, -17, -473, 830, -6]]\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[[-126, -627, -92, 237, -156, 39, -126, -397, -560, 477],\n [-203, -360, -128, -104, -420, 620, -390, -21, 265, -38],\n [-320, -417, 482, 99, -91, 79, -35, -143, -767, 395],\n [-158, 311, 554, -241, 16, 115, 96, 337, 14, -265],\n [-170, -196, 332, 96, 35, -76, 47, -88, -555, 280],\n [-67, -332, -304, 448, 185, -172, -213, -299, -466, 694],\n [247, 449, 198, -487, -128, -23, 390, 270, 579, -853],\n [-311, 159, 14, 239, 226, 243, -472, 246, 3, 453],\n [-208, -122, -199, 658, 500, -277, -351, -152, -655, 1042],\n [228, 125, -111, -207, -102, -68, 217, 7, 341, -427]]\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[[112, 120, -650, 86, 554, 70, 425, -378, 360, -238],\n [-511, -332, 465, 261, -276, 298, 3, 557, -170, 481],\n [262, -568, -503, 143, 36, 90, 8, 10, 60, -59],\n [727, -164, 796, -693, -609, -50, -113, 194, -41, -180],\n [-385, 128, -560, 417, 361, -83, -64, -185, -28, 70],\n [53, -458, 757, 79, -530, 280, 152, 0, -420, 73],\n [-76, -708, 347, 71, -294, 421, 183, 653, 57, 381],\n [689, 264, 427, -851, -370, -508, -603, 391, 170, -81],\n [-382, -880, -234, 624, 188, 347, 234, 565, 115, 668],\n [-857, 456, -508, 337, 341, 132, -39, 172, 111, 128]]\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[[-488, -123, -27, -331, -135, 250, 228, 257, 130, -291],\n [85, 3, -807, 503, -468, 719, -342, 86, -376, 53],\n [288, -493, -21, 990, -206, -21, -248, 140, 106, 144],\n [-235, 162, 44, -18, -205, -91, -269, -35, 152, -57],\n [589, -616, 526, 174, 695, -377, 714, 85, 26, 156],\n [-255, -258, -260, 283, -344, 376, -64, 264, 46, -151],\n [643, -547, 95, 427, 438, -25, 476, 88, -180, 203],\n [-433, -45, -171, -224, -225, 328, 84, 211, 52, -242],\n [74, 142, -246, 271, -223, 109, -346, -85, -96, 91],\n [-536, 654, 350, -698, -106, -452, -344, -250, 316, -138]]\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[[-128, 524, -420, 4, 204, -492, -448, -24, 124, 116],\n [45, 401, -252, 54, -88, 45, 202, -473, 174, -125],\n [347, -200, 303, 206, -177, 321, 286, -408, 56, -119],\n [-220, 126, -192, -109, 200, -363, -400, 373, -49, 155],\n [-36, -145, 81, 0, 173, -270, -416, 373, -90, 172],\n [-261, 172, -243, -135, 205, -378, -394, 383, -45, 152],\n [-195, 435, -390, -114, -26, -39, 154, -187, 106, -85],\n [-606, 498, -630, -381, 162, -333, -132, 405, -21, 57],\n [430, 186, 78, 355, 6, -129, -204, -555, 195, 5],\n [-271, -228, 27, -259, -101, 288, 370, 311, -149, -78]]\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[[-86, 152, 54, 182, 98, 434, 122, 32, 252, -296],\n [-967, 80, 188, -450, 1117, 10, -357, 542, 419, -209],\n [283, 2, 203, 13, -353, 215, 141, 131, -113, 192],\n [-514, 25, 202, -337, 583, 10, -208, 415, 181, 2],\n [-224, -267, 63, -70, 243, -403, 90, 138, 157, 121],\n [14, 57, -165, 238, 1, 97, 88, -228, 129, -261],\n [-653, 509, -197, -684, 818, 107, -981, 128, -254, -194],\n [19, -288, 118, 144, -51, -226, 331, 81, 194, 109],\n [-502, -39, -482, -541, 647, -950, -768, -231, -337, 94],\n [-496, 296, -109, -363, 610, 97, -540, 101, -22, -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[[-280, 252, 106, -542, 522, -150, -160, 296, 272, 58],\n [-180, 138, -146, -93, 148, 0, 70, -111, -62, 177],\n [-198, 168, -448, -105, 257, 117, 308, -465, -289, 408],\n [-120, 76, 458, -166, 26, -230, -400, 608, 416, -286],\n [192, -212, 328, 494, -608, -56, -212, 254, 88, -346],\n [-58, 116, 168, -625, 575, -109, -152, 327, 313, -58],\n [666, -428, 25, -43, 4, 196, 154, -136, -59, -244],\n [362, -202, -241, -142, 202, 206, 288, -357, -195, 65],\n [714, -448, 336, -245, 105, 77, -84, 259, 231, -476],\n [-278, 196, 359, -251, 150, -242, -362, 546, 385, -152]]\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[[15, 317, 179, -314, -40, 101, 323, 282, 293, 332],\n [-237, 452, 171, -270, -274, 33, 147, 181, 32, 38],\n [-120, 80, 41, -5, -160, -127, -103, -87, -97, -175],\n [-328, 762, 307, -503, -396, 99, 339, 373, 159, 191],\n [283, 262, 400, -495, -14, -250, 440, 228, 709, 503],\n [-267, 230, -46, -11, -154, 188, -22, 90, -235, -109],\n [-267, 507, 251, -320, -384, -127, 107, 116, 57, -42],\n [286, -456, -107, 225, 252, -151, -139, -215, 57, -29],\n [66, 341, 348, -414, -178, -252, 276, 145, 443, 248],\n [-370, 563, 209, -291, -430, -47, 73, 132, -64, -107]]?\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 10x10 matrix:\n[[93, -181, 105, -49, -328, -175, 414, -524, 134, 256],\n [-347, -992, 63, -577, 450, 286, 265, -1, 416, 622],\n [370, 377, 16, -185, -523, 716, -92, -56, -213, -421],\n [-621, 82, -337, -10, 597, -552, 1085, -410, -537, 529],\n [212, 75, -446, -354, 427, -966, 942, -302, -269, 631],\n [481, -501, 482, -62, -331, 350, -724, -80, 208, -61],\n [62, 260, 182, 275, -44, -524, -673, 277, 248, -538],\n [228, -112, -157, -113, 208, -409, 207, -242, 29, 410],\n [1265, 23, 64, -106, -376, -559, -508, -30, 151, 86],\n [-263, 714, 1, 184, 567, 296, -987, 578, -627, -955]]\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 10x10 matrix:\n[[-601, 210, 302, 169, -434, -570, -536, 250, -680, 204],\n [328, 155, 429, 288, -214, -8, 378, 423, -302, -459],\n [-254, -338, 872, 170, -512, 198, 338, 252, -50, 168],\n [-265, -134, -800, -591, 255, 558, -635, 23, 116, 2],\n [-86, 517, 226, -148, 147, -901, -335, -486, 578, 124],\n [183, -310, -377, -821, 900, -478, 433, 23, 498, 467],\n [672, 890, 446, -513, 712, 640, 769, 191, 290, -357],\n [-442, -219, -558, 1, -12, 48, -436, 59, -562, 387],\n [-63, 412, -602, 270, -39, 794, -600, 608, -74, -191],\n [-1062, -751, 622, 68, -1155, -165, -919, -32, 268, 226]]\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[[-144, -309, -495, 279, -388, 277, 902, -277, 495, 301],\n [172, -451, -429, -329, -564, -571, 128, -537, 627, 273],\n [-843, -461, -236, 123, 471, 121, 414, 350, 412, 84],\n [623, 800, 605, -57, 247, -206, -320, 388, -462, -190],\n [-15, -19, 368, -408, 587, -338, 159, 337, 4, 58],\n [-779, -368, -1, -658, 218, -427, 187, -380, 557, -303],\n [-198, 187, -91, 372, -55, 295, -72, 111, -53, -151],\n [-426, 359, 1, 171, -15, 183, 434, -64, 266, -346],\n [-885, -332, -289, -64, 185, 71, 1231, -123, 846, 0],\n [-253, -99, 56, -531, -114, -357, -152, -505, 230, -304]]\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[[-230, 187, 12, -169, -72, -38, 236, -10, -224, -195],\n [-480, 154, -166, -130, -122, 36, 306, -74, -394, -208],\n [257, -81, 452, -168, -290, -10, 130, 221, 295, -40],\n [-102, 236, 403, -398, -319, -84, 447, 167, -83, -329],\n [-57, 91, -62, -18, 76, -34, 12, -43, -93, -44],\n [533, -525, -203, 544, 277, 130, -701, -48, 524, 571],\n [278, -608, 244, 194, -424, 248, -128, 210, 522, 322],\n [112, 67, 435, -271, -291, -50, 263, 197, 133, -168],\n [79, -663, -172, 416, -214, 314, -298, 27, 337, 440],\n [-371, 13, -126, -58, -168, 82, 224, -37, -251, -108]]?\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[[330, -135, 285, 165, 245, 365, 30, 495, -95, -100],\n [-60, 161, -247, 27, -219, -113, -78, -299, -133, -120],\n [-42, 10, -26, -24, -22, -44, 0, -52, 20, 20],\n [-207, -199, 227, -222, 209, -132, 132, 124, 372, 350],\n [-138, -159, 189, -159, 173, -79, 102, 123, 277, 260],\n [99, -238, 368, -33, 326, 177, 114, 451, 189, 170],\n [-51, -270, 372, -147, 334, 43, 150, 369, 335, 310],\n [-18, 72, -108, 18, -96, -42, -36, -126, -66, -60],\n [96, -226, 350, -30, 310, 170, 108, 430, 178, 160],\n [-357, -231, 231, -336, 217, -266, 168, 42, 518, 490]]?\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[[-436, 91, 297, -186, -90, -26, 118, -354, 345, 325],\n [-1413, 263, 850, -812, -298, -51, -16, -916, 844, 619],\n [406, 192, -454, -623, -163, -121, 912, 42, 969, -158],\n [-310, 204, 411, -300, -127, -171, 655, 97, 570, 26],\n [-532, -644, 368, -651, -765, -622, 755, -124, -28, 1034],\n [535, 184, -359, 199, 468, 163, -572, 778, -380, -1014],\n [404, -624, -380, 132, 502, -406, -970, 1520, -1138, -1012],\n [-192, -356, 611, 255, -196, -485, 421, 429, -53, 500],\n [-357, 552, 560, 44, 7, 344, -381, -317, -69, 384],\n [586, 250, -314, 622, 302, 384, 387, 122, -751, -138]]\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 10x10 matrix:\n[[-109, -980, -30, 300, 510, -628, 306, -731, -438, -355],\n [357, -82, 249, -189, 234, -208, -97, 150, -136, -107],\n [-567, -262, 576, -636, -12, 341, 488, 135, 398, 4],\n [302, 358, -700, -26, -668, 285, -448, -18, -710, 267],\n [136, 625, -28, 29, -389, -46, 454, 382, 86, 298],\n [339, -336, -361, 53, 211, 128, -1099, -301, -477, -235],\n [220, 33, -94, 399, 241, -313, -104, -76, 24, -93],\n [-46, 263, 397, 46, 149, -179, 489, 309, 514, 41],\n [126, -769, 292, -227, 662, -84, -622, -273, -145, -436],\n [-162, -320, 380, 428, 754, -372, 76, -156, 634, -326]]\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[[-78, 65, -65, 78, -169, -182, 143, -39, 104, -260],\n [-126, 105, -105, 126, -273, -294, 231, -63, 168, -420],\n [-48, 40, -40, 48, -104, -112, 88, -24, 64, -160],\n [90, -75, 75, -90, 195, 210, -165, 45, -120, 300],\n [-12, 10, -10, 12, -26, -28, 22, -6, 16, -40],\n [18, -15, 15, -18, 39, 42, -33, 9, -24, 60],\n [72, -60, 60, -72, 156, 168, -132, 36, -96, 240],\n [-102, 85, -85, 102, -221, -238, 187, -51, 136, -340],\n [132, -110, 110, -132, 286, 308, -242, 66, -176, 440],\n [12, -10, 10, -12, 26, 28, -22, 6, -16, 40]]\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[[144, 256, -590, 145, 102, 756, -514, -256, 43, 405],\n [-129, -160, -976, -141, 36, 840, -166, -317, -212, 168],\n [41, 100, 247, -590, 175, 40, -167, -533, 846, -52],\n [56, -905, -380, -212, -459, -54, 47, -177, 146, -503],\n [-542, 72, 434, -1356, -482, 169, -287, -1120, 558, 490],\n [-40, 453, -106, -602, -594, 779, 437, -345, 191, 986],\n [-398, 544, -120, -1100, -222, 704, -480, -438, -238, 780],\n [-291, 1062, 899, -585, -567, -202, 7, -598, 134, 550],\n [72, 902, -216, 1112, 1045, -185, -734, 210, -129, -39],\n [384, 92, 1182, -423, -771, -245, 494, -276, 514, -208]]\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[[-446, 418, -283, -773, 385, 70, 142, 282, -5, 315],\n [-142, -34, -22, 319, -91, 174, -422, -348, -96, -114],\n [-146, 721, -319, -665, 616, 9, 84, 15, 394, -12],\n [730, -255, -77, -459, 196, -507, 502, 257, -54, 96],\n [-131, -4, 263, 261, -447, 132, 283, 176, 3, -147],\n [407, 312, -64, -183, 513, -244, 169, 30, 568, -108],\n [345, -494, 96, -25, -216, -248, 266, 217, -303, 147],\n [209, -554, 186, 373, -295, -106, -39, 38, -242, 90],\n [77, -222, -125, -221, 571, -234, -179, 200, 139, 489],\n [-836, -42, 117, 94, -17, 316, -197, 365, -10, 486]]?\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[[-415, 92, -499, 34, 288, 584, 209, -365, 212, -915],\n [376, 166, -206, -622, -188, 153, -494, 562, -333, -92],\n [-315, 529, -885, 19, 1063, 94, 1131, -1288, 674, -396],\n [-248, 366, 145, -497, 174, 192, 220, -22, -487, 621],\n [745, -335, -579, 343, 1103, -56, 770, -494, -280, 70],\n [-139, 20, 288, -613, -183, 500, -404, -55, -209, -137],\n [-753, -25, 110, 304, -471, -564, -663, 267, -272, -287],\n [281, -422, -605, 452, -322, -776, -820, 645, -226, -457],\n [-531, 229, 268, -460, -162, 696, -6, -424, 329, -309],\n [-387, 61, -164, 428, -213, -442, -328, 737, -568, -225]]\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[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n [-120, 440, -160, 400, -320, -120, -80, 80, 340, -120],\n [-18, 66, -24, 60, -48, -18, -12, 12, 51, -18],\n [-114, 418, -152, 380, -304, -114, -76, 76, 323, -114],\n [-90, 330, -120, 300, -240, -90, -60, 60, 255, -90],\n [-96, 352, -128, 320, -256, -96, -64, 64, 272, -96],\n [126, -462, 168, -420, 336, 126, 84, -84, -357, 126],\n [-18, 66, -24, 60, -48, -18, -12, 12, 51, -18],\n [30, -110, 40, -100, 80, 30, 20, -20, -85, 30],\n [-24, 88, -32, 80, -64, -24, -16, 16, 68, -24]]\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[[-211, -446, 629, 370, 233, 170, 66, -555, -477, 141],\n [-181, -18, 188, 149, 262, 39, 21, -78, -210, 1],\n [-334, -220, 999, 49, 106, -389, -258, -364, -1142, 668],\n [-466, -275, 356, 422, 80, 120, 638, -724, -171, 801],\n [-154, 363, 182, -627, -650, -857, -41, 207, -421, 1332],\n [465, 295, -693, -636, -929, -354, 8, 395, 654, 356],\n [86, -202, 378, -139, -209, -175, -240, -96, -343, 207],\n [-137, 66, 20, -401, -345, -295, 176, 185, 221, 825],\n [411, 529, -470, -748, -337, -452, -607, 968, 218, -303],\n [505, 524, -552, -1004, -801, -650, -509, 960, 381, 184]]\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 10x10 matrix:\n[[36, -180, -144, -225, -63, 27, 216, 243, 63, 243],\n [-76, 218, 52, 34, -20, 186, -96, -180, -52, -36],\n [122, -241, 86, 242, 135, -462, -88, 65, 29, -263],\n [78, -183, 10, 76, 59, -252, 8, 101, 33, -83],\n [-140, 286, -84, -252, -146, 516, 80, -94, -38, 274],\n [68, -88, 120, 261, 119, -327, -152, -59, -7, -283],\n [172, -446, -44, 52, 90, -492, 112, 310, 94, -58],\n [12, -114, -132, -222, -72, 90, 192, 192, 48, 240],\n [30, -69, 6, 33, 24, -99, 0, 36, 12, -36],\n [176, -430, -4, 125, 117, -543, 56, 263, 83, -137]]\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[[333, -108, 668, -77, 1083, -673, 34, 881, 1014, 906],\n [-381, -69, 941, -493, 609, -610, -84, -630, 222, 307],\n [-995, 1027, -26, 407, 545, -94, 353, 828, 29, 442],\n [-420, -946, 576, 60, 545, -686, -105, 309, 804, -232],\n [229, -499, 1395, -835, 765, -1121, -514, -819, 939, -220],\n [283, -504, -83, 82, -185, 453, -570, -505, 47, -568],\n [253, 437, 1021, -312, 111, -1184, -142, 672, -240, 205],\n [-303, -698, 488, -45, 630, -771, 160, 1271, 996, -578],\n [-1022, 451, -568, 863, -189, 481, 618, 834, -539, -152],\n [427, 380, 249, 72, 509, 211, -613, -1259, 539, 597]]?\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 10x10 matrix:\n[[814, -146, -452, -370, -424, 57, -1275, -377, -600, 35],\n [415, -172, -371, -260, 163, 63, -850, -501, -54, 120],\n [267, -46, -846, -658, 469, -135, -537, -339, 695, 587],\n [499, -169, 526, 630, 199, -1703, -607, 172, 209, -217],\n [155, 424, 157, -35, -202, 610, 712, 253, -50, 454],\n [-449, -338, -414, -227, 401, 90, -15, -7, 211, -600],\n [917, 811, -19, 33, 84, -417, 106, 277, 468, 1125],\n [540, 495, -446, -414, 156, 74, -113, -103, 404, 946],\n [-1128, 703, 355, 552, 127, 1060, 1045, 47, -221, -183],\n [1124, -339, -715, -554, -419, -153, -1271, -300, 149, 767]]\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[[587, -871, 177, -407, -401, -13, -519, 236, -459, -307],\n [-247, -468, 361, -180, -45, 175, 703, -811, -270, -235],\n [438, -959, 588, -931, 59, 141, -288, 563, 198, -304],\n [248, 309, -325, -154, 69, -137, 86, -155, -375, 554],\n [-38, -102, 334, 59, 723, 120, -395, 1065, 701, 41],\n [219, 265, -205, -317, -351, -688, 353, -650, -366, 667],\n [-226, 209, -107, 402, -170, -162, -104, -191, -238, -32],\n [194, -268, -138, 611, -54, 134, -403, 384, -441, -162],\n [79, -911, 326, -486, -62, 295, 241, 103, 119, -234],\n [-164, 150, -295, 30, -73, 343, -655, 210, 390, -346]]\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 10x10 matrix:\n[[-22, 183, -1, 105, -304, -35, -604, -245, -267, -104],\n [345, -719, 167, 107, 215, -337, 668, 244, 28, 145],\n [-782, 680, 244, 968, 27, 770, 520, -27, 768, -491],\n [-137, 408, 250, 505, 318, 572, 340, -606, 74, -177],\n [-292, 555, -16, -104, 212, 409, 420, 270, -159, 131],\n [332, -85, 332, -458, 687, -41, 492, 206, -394, -64],\n [-14, -292, 828, 514, 451, 3, 394, -454, 133, 97],\n [-466, 499, 155, -118, 498, 438, 262, -33, 680, -185],\n [-188, 310, 333, -633, 627, 90, -188, -423, 117, 438],\n [-212, 611, 218, 1013, 61, 403, 36, -695, -268, -481]]\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[[78, 88, -412, 65, -103, 387, -455, -95, 15, 60],\n [-843, 575, 601, 342, 393, -215, 353, 74, 284, -138],\n [41, -312, 288, -323, -72, 14, 125, -43, -132, -17],\n [220, 78, -446, -151, -13, 627, -247, 193, 345, 314],\n [233, -171, 17, -138, -15, -122, 214, 122, 17, 73],\n [266, 154, -236, 77, 149, -86, 320, 381, 374, 241],\n [-728, 607, 427, 129, 437, 258, 325, 293, 617, 134],\n [319, -354, 90, -527, -34, 284, 247, 241, 176, 263],\n [584, -278, -398, -203, -149, 101, -25, 141, 19, 196],\n [-216, 342, -160, 95, 129, 422, -166, 111, 338, 147]]\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 10x10 matrix:\n[[881, 323, -317, -10, -222, -85, 492, -269, -108, 938],\n [637, -838, -1816, -354, 85, -489, 1255, -339, -212, -52],\n [-272, 597, 566, 346, 184, -144, 212, -303, 24, 146],\n [-143, 329, 862, -284, 337, 812, -713, -652, 442, -170],\n [70, -1181, -1852, -890, -47, -556, 460, -811, -200, -141],\n [36, -480, -612, -301, -1047, -259, -539, -202, -627, 613],\n [-353, -556, -592, -212, 458, -482, 172, -361, -272, -576],\n [547, -268, -391, -516, -270, 552, -84, -424, 258, 192],\n [485, -132, -393, -405, -768, 246, 239, -541, 259, 410],\n [146, 451, 515, -103, 31, 567, -762, -398, -65, 666]]\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[[-69, 231, 135, -87, -120, -99, 180, -153, 69, 21],\n [-243, 499, -29, -97, -234, 72, 200, -397, -33, -9],\n [-261, -35, -339, 61, 446, 678, -400, 545, 313, 241],\n [-172, 369, -7, -75, -182, 33, 160, -302, -26, -10],\n [515, -761, 167, 139, 102, -450, -120, 273, -187, -147],\n [167, -190, -134, 106, -164, -147, -40, -265, -401, -217],\n [28, 234, 474, -184, -146, -399, 380, -82, 264, 80],\n [-576, 730, -406, -66, -56, 672, -40, -280, 68, 116],\n [242, -200, -24, 86, -254, -327, 60, -360, -446, -262],\n [274, -570, -346, 244, 54, 27, -340, 20, -482, -234]]\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[[-337, 476, -704, 70, -667, -235, -291, -471, 408, -277],\n [162, 683, -732, -823, -341, 391, 734, -321, -388, -385],\n [53, 395, -107, -116, 353, 209, -448, 344, -708, 289],\n [-472, 418, -142, 344, 162, -301, -547, 262, -134, 229],\n [158, 642, 23, 214, -208, -208, -204, -1071, -462, 620],\n [31, -897, -425, -351, -345, 370, 146, 387, -105, 309],\n [-150, 1013, 8, 76, 776, -67, -640, 18, -900, 529],\n [-104, 432, -310, 478, -900, -422, -568, -1088, 546, -48],\n [-655, 619, 626, 286, 424, -362, 629, 270, 166, -54],\n [77, -134, -128, -585, 833, 265, 359, 73, -162, -23]]\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[[-720, 108, 580, 44, -307, 358, 91, 102, -134, -248],\n [-698, 151, 244, 188, -343, 1084, 39, 291, 369, 333],\n [-264, 448, -508, -208, 119, 104, 660, 150, -205, 845],\n [-22, -898, -60, -438, -1068, 582, -215, 162, -455, 307],\n [499, -174, -418, -279, 780, -937, 327, -156, 100, -104],\n [-134, 262, -380, -92, 583, -533, 715, -276, 87, -171],\n [-375, -243, 582, -285, -300, 2, -65, 279, -426, -25],\n [264, 220, -588, 198, 747, 327, 152, 144, 956, 581],\n [-930, 1012, 248, 270, -369, 556, 417, 78, -408, 338],\n [23, 194, 150, -287, 373, -903, 285, 0, -553, -82]]\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[[-232, 48, 273, -396, 149, 288, 373, 460, -6, 64],\n [-614, 66, 569, 58, -486, 1063, 850, -150, -706, -93],\n [100, 79, 518, -97, -553, 99, 722, 35, 291, 223],\n [620, -29, -73, -638, -66, -503, 93, 776, 88, -69],\n [663, 131, 352, 8, 5, 71, 124, 93, 566, -213],\n [-582, 315, -168, 909, -431, -405, 134, -871, -266, 546],\n [430, 130, -273, -454, 873, -409, -448, 703, 824, -21],\n [-394, -683, -52, -630, 584, -314, -493, 219, -799, -249],\n [281, -285, 39, 125, -431, -216, 82, 855, 352, 516],\n [669, 455, 101, -678, 566, 29, 35, 444, 1284, -180]]\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[[60, 60, -36, -80, 80, 88, 48, -44, -8, -12],\n [195, 195, -117, -260, 260, 286, 156, -143, -26, -39],\n [-255, -255, 153, 340, -340, -374, -204, 187, 34, 51],\n [-255, -255, 153, 340, -340, -374, -204, 187, 34, 51],\n [-120, -120, 72, 160, -160, -176, -96, 88, 16, 24],\n [15, 15, -9, -20, 20, 22, 12, -11, -2, -3],\n [-150, -150, 90, 200, -200, -220, -120, 110, 20, 30],\n [-240, -240, 144, 320, -320, -352, -192, 176, 32, 48],\n [330, 330, -198, -440, 440, 484, 264, -242, -44, -66],\n [-30, -30, 18, 40, -40, -44, -24, 22, 4, 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[[-129, 253, 173, -1189, -352, -78, -1165, -587, 187, -396],\n [116, 62, 495, -484, 173, 30, -119, -367, -789, 91],\n [-323, 405, -790, -488, -492, 211, 346, 32, 740, -106],\n [656, -476, 189, -47, -406, -655, -492, -21, -43, 170],\n [-18, 234, 38, -828, 1179, 780, 87, -811, -592, 10],\n [-128, -59, -173, 1143, -926, -302, 866, 803, 942, 133],\n [405, -1103, -681, 297, -277, -928, -16, 218, -9, 296],\n [47, 183, 598, 245, 383, 228, -132, -68, -486, 19],\n [-100, 229, -532, -303, 132, 323, 799, 84, 52, 76],\n [548, -299, 254, 940, -583, -425, 773, 393, 35, 538]]?\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 10x10 matrix:\n[[-29, 786, -501, 769, -264, 510, 624, 344, -57, -269],\n [-254, 359, -10, 253, 227, 207, 555, 497, -232, -135],\n [771, -258, 37, 165, -1158, 99, 354, -380, 656, -40],\n [326, -538, -97, -371, -448, -378, 186, -45, 561, 5],\n [-450, -202, 383, -592, 1528, 100, -50, 823, -716, -678],\n [-249, -550, 721, -1081, 179, -470, -1023, 95, -346, 856],\n [-797, -25, -232, 201, 498, 134, 380, 475, -616, 105],\n [-296, -345, -707, -534, 6, 841, 185, 206, -401, -885],\n [-31, 287, 216, 601, 457, 437, 79, 36, -434, -339],\n [240, 23, -76, 856, -461, 153, 929, -417, 574, -373]]\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[[-25, -117, -58, -56, -15, 44, 101, 115, 77, -93],\n [121, -149, -562, -516, 72, -485, 544, 543, 359, 78],\n [-366, -488, -256, -220, 223, 79, -173, 12, -62, -381],\n [240, 193, -121, -118, -74, -269, 316, 222, 181, 240],\n [-97, -230, -633, -562, 291, -559, 161, 269, 120, 27],\n [58, 244, 148, 140, 11, -57, -201, -236, -154, 183],\n [-159, 137, 154, 160, 173, -10, -559, -495, -373, 75],\n [464, 654, 746, 652, -480, 374, 116, -164, 14, 348],\n [-180, -417, -447, -402, 168, -165, 186, 306, 159, -234],\n [72, 430, 718, 652, -186, 444, -486, -584, -350, 138]]\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[[-272, -583, 94, 401, 559, -58, -407, -24, -206, -344],\n [-666, -562, 21, 101, 380, -62, -487, 204, 111, -80],\n [-122, 68, 292, -188, -328, 253, -221, -304, -379, 185],\n [126, 1171, 222, -387, -551, 193, 18, 646, 282, 569],\n [623, 433, -535, -561, -670, -17, -235, 202, 89, 767],\n [77, 318, -187, 267, 573, -337, 968, 782, 903, -317],\n [354, 24, 99, -79, -138, 158, 117, -260, -383, 148],\n [-221, 357, 166, -84, -76, 92, -431, 450, 89, 250],\n [62, 440, -76, -153, -698, -15, -63, -528, 11, -125],\n [315, 166, -117, -522, -365, 170, 141, 166, -70, 712]]\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[[-706, 344, -303, 117, 918, -705, 36, -201, 429, 883],\n [410, -243, -111, -288, 49, 52, 148, 90, -192, 81],\n [-648, 226, 449, 256, -323, -219, -224, -399, 35, 386],\n [494, -236, 184, -14, -42, 62, 58, 228, -186, -258],\n [475, 423, 140, -210, -297, 67, 170, 603, -157, -1043],\n [656, -833, -76, -469, 194, -118, 232, -417, -17, 687],\n [-152, 143, 94, 497, 605, -165, 410, -302, 571, 893],\n [599, -1000, -176, -196, -318, 579, -315, 65, -577, -235],\n [-866, 656, 58, 294, -56, -228, -169, -221, 421, -50],\n [218, -83, 409, 316, -337, 214, -122, 178, -118, -519]]?\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 10x10 matrix:\n[[-93, -192, -252, 639, -524, -22, -279, 67, 309, 27],\n [-649, 2, 341, -100, -112, -449, -616, 239, 435, -82],\n [-248, -80, 262, -273, -257, -446, -583, 141, 430, -48],\n [-6, -41, -157, -15, 250, -146, -201, 107, 197, -20],\n [-457, -77, -497, 690, 261, -2, -405, 233, 167, -141],\n [464, -56, 133, -343, 139, -139, 294, -9, 283, 225],\n [521, -472, -628, 343, 229, 250, 227, 124, -10, -10],\n [238, -233, 223, -397, -197, -306, -145, 90, 384, 81],\n [110, -323, -616, 59, -129, 5, -740, 50, -197, -388],\n [606, -37, -213, 131, 635, 440, 1078, -58, -212, 274]]\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[[55, -35, -60, -40, 75, 35, 20, -35, -110, 10],\n [66, -42, -72, -48, 90, 42, 24, -42, -132, 12],\n [22, -14, -24, -16, 30, 14, 8, -14, -44, 4],\n [143, -91, -156, -104, 195, 91, 52, -91, -286, 26],\n [44, -28, -48, -32, 60, 28, 16, -28, -88, 8],\n [121, -77, -132, -88, 165, 77, 44, -77, -242, 22],\n [121, -77, -132, -88, 165, 77, 44, -77, -242, 22],\n [99, -63, -108, -72, 135, 63, 36, -63, -198, 18],\n [231, -147, -252, -168, 315, 147, 84, -147, -462, 42],\n [-209, 133, 228, 152, -285, -133, -76, 133, 418, -38]]\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[[-300, 65, 70, 185, -510, 55, -85, 175, -275, 150],\n [-400, 118, 203, -51, -116, 136, 106, 108, -69, -129],\n [-200, 88, 203, -301, 464, 126, 256, -62, 241, -369],\n [20, 9, 42, -139, 274, 23, 99, -65, 145, -150],\n [420, -127, -224, 83, 66, -149, -133, -101, 43, 168],\n [-220, 67, 119, -48, -26, 79, 73, 51, -18, -93],\n [-140, 61, 140, -205, 314, 87, 175, -41, 163, -252],\n [120, 0, 63, -321, 672, 30, 216, -174, 357, -333],\n [-80, 64, 182, -394, 704, 108, 304, -140, 370, -450],\n [260, -89, -175, 150, -146, -113, -155, -21, -72, 213]]\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 10x10 matrix:\n[[-133, 20, 72, -210, 191, -9, 93, -67, 145, 141],\n [41, -114, -27, 274, -187, 172, -26, -37, -152, 27],\n [288, -180, -162, 720, -576, 234, -198, 72, -450, -216],\n [319, -212, -180, 822, -653, 279, -219, 73, -511, -231],\n [-195, -118, 99, -22, 105, 218, 140, -177, 66, 303],\n [-307, 154, 171, -694, 569, -190, 212, -97, 442, 255],\n [-114, 46, 63, -236, 198, -53, 79, -42, 153, 102],\n [129, 134, -63, -94, -3, -232, -94, 147, 12, -237],\n [-154, 172, 90, -532, 398, -244, 104, 2, 316, 66],\n [-107, 130, 63, -390, 289, -186, 72, 7, 230, 39]]\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[[-406, 358, 262, 534, 546, -34, -268, -347, 147, -60],\n [341, -446, 406, -120, 366, -349, 830, 601, -406, 799],\n [236, 189, 154, 149, 314, -53, -534, 366, -296, 11],\n [-84, -113, -94, -146, -119, 410, 451, 79, 254, -446],\n [-3, -666, 160, -55, 186, -448, 790, -205, -187, 915],\n [-143, 220, 328, 310, 11, 4, 132, -175, 36, 229],\n [-182, -218, -146, -509, -95, -78, 1056, 243, 68, 226],\n [299, -172, 116, -83, -483, -8, 171, 40, -182, 386],\n [423, -222, -267, -192, 164, -100, -537, 367, -63, -421],\n [-127, -783, -562, -556, -605, 122, 526, -518, -76, 360]]\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 10x10 matrix:\n[[-8, -80, 332, -229, 157, 236, -152, -41, -199, 136],\n [158, 422, 265, 135, 327, 155, 355, 139, 122, -406],\n [342, 349, -35, 324, 158, 156, 422, -332, -219, 137],\n [-20, 99, 399, -93, 481, 348, 74, -249, -186, -109],\n [-359, -544, -18, -12, -835, -85, -276, 546, 129, 462],\n [283, -15, -299, -835, 542, -429, -776, -333, -125, -253],\n [-722, -589, 416, 154, -440, 363, -21, 294, 76, 279],\n [550, 83, -299, -388, 66, -232, -376, -312, -371, 375],\n [373, 375, -350, 242, -49, -244, 275, 0, 95, -115],\n [-361, -90, 70, 732, -325, 307, 614, -50, 67, 184]]\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[[348, -90, -408, -556, -374, -458, -96, 184, 674, 562],\n [12, 699, 342, -112, -215, 55, 174, 88, 479, 361],\n [198, 374, -2, -334, -318, -210, 26, 156, 712, 526],\n [-189, 21, 279, 496, 296, 284, -87, -94, -125, -322],\n [56, 171, -90, -429, -254, -118, 250, 36, -200, 186],\n [72, -327, -258, -120, -9, -135, -66, 0, -123, -33],\n [-79, 758, 451, -13, -146, 170, 237, 42, 269, 232],\n [-384, 127, 494, 689, 440, 524, 58, -196, -618, -608],\n [49, -223, -35, 293, 161, -17, -305, 18, 426, -29],\n [158, 211, -64, -303, -250, -186, 32, 112, 446, 378]]\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 10x10 matrix:\n[[179, 233, 207, 91, -122, -236, -125, 159, -80, 230],\n [-272, -289, -306, 17, 136, 323, 85, -357, 0, -255],\n [-314, -385, -360, -103, 196, 401, 181, -321, 96, -369],\n [74, -7, 72, -209, 28, -41, 115, 249, 160, -55],\n [-262, -227, -288, 139, 92, 283, -1, -435, -96, -171],\n [-72, -145, -90, -159, 88, 123, 133, 27, 128, -167],\n [-60, -98, -72, -78, 56, 90, 74, -18, 64, -106],\n [197, 235, 225, 49, -118, -248, -103, 213, -48, 222],\n [336, 357, 378, -21, -168, -399, -105, 441, 0, 315],\n [-223, -177, -243, 157, 66, 232, -27, -399, -112, -122]]\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[[223, -251, 107, -677, -72, -553, -205, -129, 410, -81],\n [334, -281, 34, -281, -237, 72, 425, -365, 152, -28],\n [105, -147, 90, 495, -132, 285, -48, -63, 3, 54],\n [154, -104, -18, 324, -178, 478, 460, -228, -136, 42],\n [-126, 150, -71, 714, -6, 602, 249, 44, -357, 85],\n [563, -598, 224, -372, -371, -219, 35, -446, 523, -46],\n [252, -354, 216, -98, -146, -336, -458, -82, 420, -20],\n [293, -256, 43, 118, -253, 319, 414, -326, 40, 17],\n [313, -356, 156, -262, -191, -245, -129, -212, 365, -34],\n [-485, 532, -216, -50, 363, -47, -31, 380, -373, -2]]\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[[247, -218, -16, -385, -9, -406, 349, -228, -420, -71],\n [-211, -46, -530, 20, -35, -68, -61, -91, 312, -322],\n [235, -28, 405, 429, 335, -285, -96, 114, -524, 504],\n [2, -133, -209, 130, 164, -327, -10, -128, -168, -51],\n [-734, 644, 234, 711, -354, 246, -1156, 277, -94, 433],\n [-226, 290, 133, 227, -200, 109, -412, 188, -45, 251],\n [20, -129, 65, 136, 278, 215, 78, -76, 224, -151],\n [-372, 431, -289, -321, -748, 285, -289, 246, 379, -55],\n [4, -73, 183, -19, 106, 61, 28, -139, -90, -68],\n [-320, 188, -57, 141, -184, -1, -391, -13, -52, 14]]?\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 10x10 matrix:\n[[-312, -84, 71, -135, 250, 221, -166, -70, 195, -401],\n [-491, -411, 50, -52, 355, -166, 353, -667, -316, 71],\n [-213, -1, -13, -113, 107, 49, -55, -131, 15, -214],\n [448, 12, 23, 233, -230, -103, 110, 278, -31, 443],\n [12, -572, 318, 266, 344, 178, 168, 40, 186, 242],\n [321, 453, -222, -36, -429, -192, -69, 195, -141, 117],\n [429, 321, -120, 78, -381, -114, -57, 327, -33, 219],\n [-310, 422, -360, -340, -206, -358, 60, -496, -467, -192],\n [-604, 228, -281, -407, 50, -257, 64, -692, -416, -383],\n [282, 10, -28, 152, -186, -180, 170, 66, -156, 390]]\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[[-198, 396, 66, -594, 660, 242, 748, -528, -814, 286],\n [161, -338, -39, 518, -583, -222, -660, 467, 719, -266],\n [-302, 380, 306, -416, 358, 16, 416, -278, -442, -32],\n [-111, 30, 213, 87, -186, -167, -202, 156, 229, -241],\n [458, -500, -534, 464, -322, 96, -384, 242, 398, 208],\n [-74, 116, 54, -152, 154, 40, 176, -122, -190, 40],\n [-210, 372, 114, -525, 561, 181, 638, -447, -692, 203],\n [-198, 108, 330, 36, -174, -212, -184, 150, 214, -316],\n [220, -88, -396, -110, 286, 286, 308, -242, -352, 418],\n [132, -168, -132, 186, -162, -10, -188, 126, 200, 10]]\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[[-824, -130, 395, 1449, -262, 1127, -734, 136, 57, 721],\n [1139, -279, -256, -685, -673, -257, -228, -561, -351, -701],\n [326, -244, -470, -136, -35, -657, 73, -169, 22, -241],\n [224, -444, -193, -426, -95, 152, 35, 728, -1336, 1060],\n [129, 266, -702, -265, 74, -912, 474, 582, -566, 725],\n [-212, 573, 72, 58, 147, -452, -145, 405, 488, 635],\n [84, 193, 478, 107, 228, -565, -253, 87, 1101, -520],\n [-298, 603, -667, 665, 23, -198, 481, -674, 297, -168],\n [-197, 425, -173, -165, 150, 191, 544, -419, -7, -19],\n [-485, -359, -876, 991, -501, -11, -34, -294, -275, 368]]?\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[[-410, 262, 193, -541, -1215, 1078, 218, -147, -230, -116],\n [528, -276, 479, -809, 35, -281, -481, -764, 216, -887],\n [-71, 153, -745, 71, 126, 290, -208, 105, -636, 693],\n [-6, 693, -618, 473, -508, 359, 149, -102, -74, 369],\n [18, -498, -178, 140, 383, -244, 66, 434, -393, 98],\n [364, -496, 140, -196, -99, -360, -44, -162, -9, -880],\n [193, -616, 415, 101, 685, -525, 230, 478, -86, 84],\n [469, -305, -215, 354, 682, -739, -72, 99, -45, -80],\n [-955, 64, 287, -51, -766, 758, 375, 433, 131, 5],\n [-67, -299, -178, -429, -339, 311, -158, -62, -459, -286]]\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[[678, -686, -93, 996, 125, 492, -1128, 251, 540, 519],\n [20, -375, 407, 495, 389, 515, -80, 397, 1178, 674],\n [257, -435, -457, 652, 33, 35, -1084, -62, -567, 135],\n [81, 872, -506, 107, 244, 805, 718, -931, -469, -500],\n [-427, 819, -458, 801, -1008, -494, -408, -608, 205, -560],\n [-477, 471, -361, 252, -343, -1049, -10, 390, -14, -40],\n [-16, 210, 35, -386, 400, 354, 657, 314, 371, 490],\n [37, 401, -437, 613, -623, -124, -434, -349, 527, -119],\n [-158, 482, -154, 245, -22, -375, 498, 237, 670, -260],\n [233, 87, -580, 419, 535, 696, 37, -381, 158, -120]]\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 10x10 matrix:\n[[78, -75, 422, 531, 389, -454, -124, -217, -168, 311],\n [-333, 322, -430, 617, -376, 858, -77, 265, 751, -35],\n [127, 168, -79, -945, 475, -129, 344, -701, -316, -236],\n [458, -596, -593, -1614, -120, -45, 291, 276, -757, -675],\n [156, -253, -310, -421, -11, 491, 156, 140, 17, -358],\n [-284, 932, -570, 65, -211, 264, -579, -393, 179, 411],\n [356, -393, -449, 168, -601, 101, -528, 896, -304, 245],\n [-121, -813, 473, 16, 457, -638, 487, 109, -247, -692],\n [-141, 591, -845, -352, -754, 361, -288, 268, 124, 157],\n [-546, -354, 586, -95, 892, -960, 193, -649, -309, -781]]\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[[119, 103, -495, -1319, -200, 575, 308, 555, -516, -379],\n [-330, -12, 366, 1222, -78, -437, -104, -373, 338, 318],\n [-93, -229, -678, -574, -671, -459, 557, 653, 154, 470],\n [315, -77, -106, -443, -385, -245, 63, 140, 316, 335],\n [152, -113, -467, -845, -780, -386, 119, 559, 206, 532],\n [-586, 200, 88, 654, -228, 359, 446, -19, -310, -298],\n [133, 1, -171, -528, 97, -177, -396, 121, -71, 126],\n [-11, 355, -52, -721, -258, 7, -605, 83, -289, 79],\n [-666, 272, -260, 157, -828, 666, 1344, 361, -428, -431],\n [-522, 658, -35, -450, -95, 770, -47, 33, -928, -660]]\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[[-881, -309, 507, -581, -309, 225, 329, -381, 215, -169],\n [817, 64, -105, 685, 281, 192, -552, 450, 175, 378],\n [-311, -496, 312, 243, 564, 725, -559, -196, 566, 80],\n [-115, -82, -419, 225, 534, -164, 312, 4, -157, -174],\n [413, -210, 254, -767, -1117, 628, 688, -182, -374, -532],\n [17, -27, -63, 141, 425, 231, -215, -341, 7, -214],\n [142, 221, 947, 326, -151, 363, -253, -231, 473, 285],\n [321, -326, 183, 711, 552, 599, 211, 140, 305, 56],\n [-15, 598, 575, 123, -133, -277, 25, -426, 41, 53],\n [-224, 51, -441, 694, 956, -548, -766, 469, 341, 604]]\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[[-100, -36, -160, 120, -112, -176, 200, 208, 260, 284],\n [-146, -139, 145, -130, 263, -14, -305, 97, 640, 565],\n [-209, -113, 90, -205, -7, 52, 5, -316, -285, -302],\n [-84, -59, -1, -10, 49, -58, -35, 87, 278, 261],\n [-419, -191, -68, -170, -204, -108, 310, -312, -341, -323],\n [630, 415, -191, 375, -282, 126, 260, 95, -842, -726],\n [958, 566, -242, 635, -145, 88, 85, 592, -224, -113],\n [742, 392, -26, 380, 110, 148, -230, 454, 118, 148],\n [167, 128, -107, 135, -160, 10, 180, 11, -359, -307],\n [-272, -220, 152, -170, 306, -72, -330, 140, 884, 790]]\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[[-117, 333, -341, 225, -248, -314, 132, -187, -81, 340],\n [850, -248, 96, -689, 28, 304, 644, 602, -562, -393],\n [-568, -268, 416, 262, -339, -62, -904, -71, 974, 267],\n [294, -975, -88, -116, 242, -378, 22, 44, 274, -571],\n [519, 79, 386, -414, 28, 516, 120, 660, -166, 129],\n [8, -10, -431, 470, 394, -769, 344, -363, -121, 246],\n [600, -42, 191, -504, 101, 11, 816, 262, -693, -265],\n [125, -962, -370, 373, 102, -1055, -122, -130, 674, 9],\n [24, -12, -430, 195, 174, 262, -392, 130, 220, 37],\n [-118, 215, 634, 128, 274, 18, -86, 70, 108, 439]]?\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[[-52, 157, 353, -194, 332, -263, 361, -388, -61, -315],\n [25, 534, 399, -139, 238, -400, 153, -140, 213, -88],\n [303, 737, 256, -203, 567, 25, 87, -124, 121, 518],\n [-75, 380, 445, -260, 420, -170, 405, -340, -80, -250],\n [-300, -127, 153, -275, 328, 593, 509, -252, -614, -317],\n [253, -116, -159, 65, 87, -68, -124, -96, 92, 269],\n [-189, -40, 239, -288, 434, 338, 525, -388, -482, -304],\n [-286, -701, -251, 114, -378, 223, 23, 52, -289, -419],\n [-71, -424, -247, 35, -78, 394, 15, 12, -287, -14],\n [-294, -507, -141, 147, -474, -51, -51, 132, -78, -471]]\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[[754, 74, 454, -54, 226, 192, -30, 552, 360, 376],\n [286, -116, 695, -454, -30, 327, -328, 151, -121, 49],\n [-28, 52, 175, -80, 78, 77, -204, 43, -123, -37],\n [156, 462, -234, 516, 546, -150, -102, 432, 186, 174],\n [815, 291, 215, 267, 467, 62, 23, 734, 506, 470],\n [423, 298, -39, 339, 402, -50, 16, 481, 322, 282],\n [-363, -450, -136, -323, -596, -19, 288, -584, -159, -237],\n [394, 333, -53, 366, 439, -59, -17, 490, 301, 271],\n [375, 190, 80, 175, 280, 15, -20, 380, 235, 225],\n [548, 220, 355, 64, 366, 137, -180, 535, 225, 287]]\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[[-42, -273, 0, 441, 441, -336, 315, -378, -84, 210],\n [11, -131, 0, -258, -468, 238, -120, 9, -8, -340],\n [-8, -214, 0, -30, -198, 56, 30, -144, -40, -188],\n [38, 463, 0, -247, -23, 144, -245, 438, 108, 114],\n [19, 272, 0, -95, 59, 42, -115, 237, 60, 114],\n [-19, 25, 0, 304, 458, -262, 170, -105, -16, 304],\n [11, 301, 0, 46, 284, -82, -40, 201, 56, 268],\n [10, 11, 0, -143, -199, 120, -85, 66, 12, -126],\n [10, 362, 0, 104, 412, -140, -20, 222, 64, 368],\n [-17, 65, 0, 302, 484, -266, 160, -75, -8, 332]]\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 10x10 matrix:\n[[-208, -268, -378, -330, 90, 388, -24, 378, 226, 228],\n [-188, -290, -531, -435, 171, 566, -84, 567, 215, 186],\n [-309, -288, -125, -175, -73, 80, 108, 42, 311, 385],\n [24, -54, -293, -205, 149, 338, -108, 357, -7, -62],\n [-576, -498, -79, -215, -209, -26, 252, -105, 571, 734],\n [192, 120, -156, -60, 156, 216, -144, 252, -180, -264],\n [-242, -134, 265, 125, -229, -350, 204, -399, 223, 340],\n [-57, -96, -193, -155, 67, 208, -36, 210, 67, 53],\n [3, -162, -652, -470, 310, 742, -216, 777, 34, -73],\n [337, 340, 239, 265, 31, -204, -84, -168, -345, -409]]\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 10x10 matrix:\n[[-610, 709, -495, 125, -493, 337, -364, 350, -593, -629],\n [-394, 119, 128, -411, 685, 59, 28, 526, 51, 402],\n [150, 915, 19, 268, -438, -184, -223, 745, 271, -63],\n [-355, -275, -892, 22, -119, 329, 1306, -370, -1921, -242],\n [109, -60, -9, 171, 1303, -695, 630, 504, 409, 686],\n [-10, -179, -226, -484, 121, 484, -64, -284, 303, 232],\n [-228, -212, 620, -269, 401, -439, -1037, 105, 958, 517],\n [-137, -523, -86, 115, 1577, -1205, 595, 195, -21, 878],\n [-542, 286, -659, -2, 812, -112, -110, 250, -255, -295],\n [532, 226, 174, -392, 172, 775, -1283, -213, 975, 459]]\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[[16, 88, -136, -112, -96, 8, -176, -104, 120, -32],\n [36, 198, -306, -252, -216, 18, -396, -234, 270, -72],\n [-2, -11, 17, 14, 12, -1, 22, 13, -15, 4],\n [42, 231, -357, -294, -252, 21, -462, -273, 315, -84],\n [-26, -143, 221, 182, 156, -13, 286, 169, -195, 52],\n [-44, -242, 374, 308, 264, -22, 484, 286, -330, 88],\n [-16, -88, 136, 112, 96, -8, 176, 104, -120, 32],\n [-14, -77, 119, 98, 84, -7, 154, 91, -105, 28],\n [22, 121, -187, -154, -132, 11, -242, -143, 165, -44],\n [-28, -154, 238, 196, 168, -14, 308, 182, -210, 56]]\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 10x10 matrix:\n[[-42, -115, 335, -403, 143, -282, 94, -355, 130, -60],\n [-200, 331, -116, 614, -473, 502, 624, 57, -56, -175],\n [454, 365, 575, -180, 248, 73, 197, -281, -501, 164],\n [20, 261, 114, 242, -165, 260, 374, -65, -158, -47],\n [0, 360, -240, 666, -354, 546, 330, 276, -234, -24],\n [494, 509, 571, -5, 165, 240, 328, -239, -616, 168],\n [52, 149, -254, 378, -141, 284, -18, 287, -150, 49],\n [-538, -514, -201, -281, -104, -404, -70, -136, 686, -253],\n [-314, -173, 103, -175, -107, -182, 246, -273, 346, -202],\n [-276, -10, -370, 404, -328, 222, 142, 218, 178, -132]]\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[[-151, 164, -637, -317, -100, -113, 575, -492, 123, 359],\n [-121, 69, 85, 68, -25, 188, 122, 141, 376, -416],\n [-31, 358, -1144, -171, 97, -131, 973, -606, 156, 374],\n [-116, -510, 398, -42, 409, 336, -553, 491, -39, -262],\n [10, -785, -74, -149, 314, 377, -390, -304, -892, 665],\n [-259, -115, -7, 2, -44, 71, 272, 367, 246, -155],\n [252, 782, -53, 496, -468, -417, 538, 72, 317, -300],\n [-515, -251, -128, -524, 299, 297, 46, 153, 689, -332],\n [206, 42, 895, 756, -435, -176, -306, 786, -213, -345],\n [-186, -164, -387, -464, 12, 192, 165, -631, -60, 363]]\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[[-103, -346, 782, -107, 21, 100, -363, -422, -102, -15],\n [-254, -154, 106, 13, -102, 19, -55, -353, 92, -215],\n [51, -66, 42, -15, 27, -6, 81, 12, -162, 81],\n [-369, -174, 269, 5, -140, 55, -261, -511, 282, -342],\n [91, 138, 177, -31, 52, 43, -305, 125, 226, 26],\n [-336, -86, 87, 29, -141, 32, -181, -400, 308, -332],\n [-105, 214, -357, 71, -78, -25, -7, 65, 338, -182],\n [202, 274, -387, 37, 55, -48, 135, 412, 48, 126],\n [319, 184, 401, -90, 170, 70, -444, 336, 138, 237],\n [463, -162, 509, -137, 248, 29, 13, 295, -614, 536]]\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[[446, 254, -124, -396, 251, 18, -394, 333, 271, -348],\n [-387, -373, 148, 168, -149, 293, 286, -723, -16, -123],\n [400, 88, 31, -741, -117, 157, -602, 270, -121, -511],\n [44, -160, 62, -306, 11, 342, -154, -405, 157, -504],\n [110, -30, 85, -399, -247, 69, -302, 138, -289, -179],\n [223, 33, -40, -300, 179, 203, -226, -111, 286, -441],\n [-285, -39, -3, 501, -25, -194, 390, -36, -84, 476],\n [-246, -110, 2, 378, 73, 8, 338, -303, 121, 170],\n [-65, -51, 23, 39, -35, 24, 50, -84, -26, 14],\n [-634, -370, 113, 693, -100, 81, 680, -729, -20, 351]]?\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, 21, 105, 21, -441, 168, -231, -462, -42, 126],\n [-72, -12, -60, -12, 252, -96, 132, 264, 24, -72],\n [-24, -4, -20, -4, 84, -32, 44, 88, 8, -24],\n [-90, -15, -75, -15, 315, -120, 165, 330, 30, -90],\n [24, 4, 20, 4, -84, 32, -44, -88, -8, 24],\n [-96, -16, -80, -16, 336, -128, 176, 352, 32, -96],\n [-12, -2, -10, -2, 42, -16, 22, 44, 4, -12],\n [24, 4, 20, 4, -84, 32, -44, -88, -8, 24],\n [-54, -9, -45, -9, 189, -72, 99, 198, 18, -54],\n [54, 9, 45, 9, -189, 72, -99, -198, -18, 54]]?\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[[211, 71, 179, -838, -370, -439, -221, 545, -1114, -277],\n [-307, -99, 175, 779, 190, 422, -567, -195, 537, 362],\n [-415, 62, 320, -179, -407, -209, -236, 375, -588, 91],\n [-157, -789, -475, -239, 254, -492, -89, 195, -649, -106],\n [-54, 634, 734, -217, -372, -6, -58, 162, -125, -279],\n [-662, -706, 151, 138, 415, -155, -225, 73, -409, 195],\n [-253, -601, -528, 314, 312, -140, 96, -149, 171, 99],\n [771, -43, -369, -639, 226, -294, 365, -35, -215, -586],\n [67, -147, -103, 114, 312, 3, 157, -211, 284, -163],\n [-484, -654, -777, 734, 111, 188, -79, -153, 369, 801]]\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 10x10 matrix:\n[[-520, 17, -440, -773, 13, -81, 124, -565, 496, 188],\n [-19, -421, 525, 191, 307, 128, 645, 606, -122, -663],\n [-552, -845, 572, 257, 220, 356, 88, -602, -392, -1031],\n [-102, -464, 120, 320, -265, 94, 181, 803, -98, -524],\n [-614, 23, 12, -498, 745, -164, 616, -79, 40, -269],\n [694, -640, -773, -239, 219, 857, 333, -363, 383, -512],\n [657, -87, 306, 65, 241, 1060, -109, -919, -978, 285],\n [-934, -206, -369, -661, 773, -21, 793, 405, -323, -546],\n [881, 493, -129, 46, -22, 525, 33, 328, -370, 878],\n [-384, -154, 256, 300, -528, -762, -138, 647, 527, -387]]\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[[-656, 741, -144, 382, -351, 227, 231, 45, -750, 11],\n [-130, -201, -298, -290, -222, -306, -728, -381, 304, -251],\n [402, 150, 211, -90, 301, 233, -304, 260, 66, -552],\n [213, 127, 230, 172, 239, 266, 470, 340, -140, 103],\n [474, -344, 275, 294, 252, 296, 163, 620, 464, -222],\n [-536, 119, 310, 610, -372, 18, 392, 97, -464, 17],\n [209, -370, -72, -490, 86, -371, -437, -429, 340, -4],\n [213, -119, 421, 510, 131, 330, 413, 612, 74, -165],\n [155, -608, 158, 46, -38, -211, -151, -1, 486, -70],\n [245, 535, -171, -40, 316, 472, 269, 384, -193, 45]]?\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 10x10 matrix:\n[[232, 289, -31, 287, 17, 690, 137, 401, -150, -273],\n [698, 361, 105, 389, 63, 998, 801, 153, -596, -535],\n [20, 490, -197, -603, -373, -33, -128, 53, 583, -576],\n [207, 513, -261, -249, -300, 499, 12, 311, 170, -621],\n [10, 97, -1, 458, 137, 559, -118, 499, -121, 48],\n [-128, -138, 416, 358, 336, -144, 20, -12, 172, 372],\n [240, 114, -177, -219, -189, 139, 240, -127, -217, -324],\n [-104, -127, 558, 736, 522, 155, 45, 224, 91, 487],\n [137, 117, -425, -586, -414, -96, 43, -213, -109, -426],\n [160, 226, 368, 548, 296, 554, 218, 348, 58, -18]]\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[[188, -360, 42, -269, -140, -79, 140, -190, -173, -162],\n [253, 236, -222, -158, -314, 89, -191, 147, -175, 203],\n [-171, -204, 42, 133, 343, 149, 1, -217, 111, -228],\n [3, 455, 42, 61, -230, -214, 95, 405, 57, 428],\n [258, -402, -130, -303, -228, 61, -214, -292, -275, -366],\n [-758, -354, 444, 594, 828, -120, 146, -282, 518, -540],\n [201, 492, -364, -4, 95, 518, -59, 177, -38, 534],\n [896, -305, -106, -944, -842, -192, 528, 6, -631, 391],\n [73, 350, -68, 15, 78, 152, 253, 221, 52, 503],\n [-66, 62, -172, 134, 272, 356, -202, -110, 58, -52]]\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[[-81, 22, 217, -433, -190, 490, -209, -162, -282, 95],\n [-249, -28, -102, -95, 133, -377, 149, -66, 86, -293],\n [528, -372, 161, -178, 600, -334, -378, 161, 813, -32],\n [-221, 150, 309, -55, -53, 73, 39, 92, 120, 47],\n [-39, -238, 75, 256, -223, -95, 53, 244, 252, 15],\n [475, -254, -557, -486, 959, -1354, -272, -243, 964, -85],\n [115, -328, -768, -461, 17, -760, 473, -612, 176, 55],\n [-62, 112, -275, 1031, -395, 606, -17, 448, -791, -154],\n [214, -738, -681, -489, 807, -364, -428, 49, 655, -516],\n [172, 2, 165, 274, -560, -147, 519, -152, 5, 434]]\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 10x10 matrix:\n[[299, -64, -89, 472, 52, -276, -234, -199, -214, 116],\n [349, -453, 606, 242, -288, 46, 648, 136, -590, 668],\n [-24, -21, -391, 85, 577, 651, 34, 435, 287, -562],\n [141, 411, -664, -366, 464, -447, -68, -414, -217, -793],\n [-409, 301, 440, -614, -662, 215, 328, 412, 315, 233],\n [-108, 60, 418, 377, -650, -425, -630, -313, 194, 816],\n [342, -20, -162, 191, 296, -336, -58, -433, -415, -9],\n [-426, -407, -665, -267, 495, 164, -60, 213, 410, -1099],\n [-220, -47, -375, 547, 291, -131, -1141, -406, 576, -41],\n [-113, 365, 30, -803, -94, 242, 722, 367, -75, -365]]\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[[405, -604, -159, -370, -220, -214, 24, -152, -233, -217],\n [-816, -761, 664, -63, -551, -733, 58, -919, -199, -725],\n [3, -512, 415, 101, -144, 611, 350, -383, -390, 318],\n [-232, 694, -158, 321, 263, -182, -375, 267, 40, -44],\n [551, 498, -33, -390, 470, -115, -229, 483, 24, 6],\n [1378, -91, -549, -300, -157, 204, -135, 554, 277, 386],\n [758, 624, -173, -287, 345, -154, 135, 653, 647, 375],\n [-348, 496, -494, 50, 263, -416, 112, 318, 436, -91],\n [414, -673, -68, 234, -590, 568, -609, -328, -258, 188],\n [-768, 4, -664, 186, -69, -126, 217, 113, -100, -499]]?\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[[679, 298, -246, -771, -626, -589, -562, -339, -595, -1129],\n [-73, 159, 197, 41, -22, 56, 13, 133, 95, 263],\n [-456, -50, 495, 918, 325, 424, 320, 652, 51, 444],\n [172, -54, -43, 192, 139, 187, 313, 73, -50, 75],\n [-329, 74, 380, 562, 301, 344, 296, 389, 93, 489],\n [-442, -179, 361, 810, 190, 259, 115, 570, -2, 150],\n [159, 189, 248, 256, -114, 36, 22, 328, -309, -242],\n [-242, 499, 490, 247, 178, 13, -116, 189, -568, -383],\n [572, -221, -448, -489, -438, -209, -66, -215, 218, -79],\n [-240, -473, -124, 281, -30, 22, -57, 154, 283, 100]]?\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 10x10 matrix:\n[[396, 525, 795, -73, 208, 39, -377, -320, 87, 112],\n [-566, -797, -307, 1176, -226, 849, 1327, 866, 41, -163],\n [95, 379, 8, -46, -131, -481, -471, -285, -354, 318],\n [-360, -17, 185, 118, 535, 339, -1105, -534, -23, 139],\n [311, 22, 615, 482, -126, 656, -746, -794, -562, 870],\n [-137, 493, 162, -108, 436, -1020, -286, -475, -351, 866],\n [0, 739, 759, 235, 697, 394, -347, -287, 556, -14],\n [298, -533, 75, 556, -305, 1408, 203, 132, -159, 157],\n [-719, 462, -293, 280, 744, -448, -693, -215, -12, 295],\n [388, -525, 353, -55, -128, 242, -9, -219, -426, 385]]\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[[-120, 102, -433, 503, -1212, -673, 114, -101, -686, -145],\n [135, -1059, 661, 306, -210, 399, -461, 359, -609, 644],\n [-193, 316, -484, 10, -101, -404, 305, -96, 267, -129],\n [127, 292, 504, -206, -212, 143, -811, -459, 373, 341],\n [388, -361, 403, 303, 255, 330, 65, -293, -246, -83],\n [-75, -847, 658, 33, -305, 916, 28, 803, -973, -434],\n [145, 420, 33, -46, 1144, 415, 656, 462, 1223, -832],\n [582, -139, 830, -192, 379, 421, -1072, 349, -406, 675],\n [21, 436, -65, -672, 669, 260, 27, -480, 29, -169],\n [103, -531, 546, 647, -274, 634, 386, 1243, -95, -876]]\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 10x10 matrix:\n[[48, 422, -162, -464, -148, 389, -219, 96, 61, -124],\n [329, -120, 103, -140, 366, -621, 200, 354, 208, -325],\n [102, 602, 32, -704, 286, -577, 245, 346, 375, -640],\n [-343, 60, 23, 124, -116, -101, 208, -256, -150, -11],\n [93, 4, 261, 392, 250, 255, -394, -30, 532, 611],\n [4, -236, -114, 244, -265, 607, -301, -157, -232, 377],\n [77, -222, -241, -176, -236, 26, 137, 56, -479, -303],\n [502, 110, 38, -180, 230, 347, -509, 366, 483, 216],\n [-252, -128, -186, 140, -416, 466, -48, -300, -466, 148],\n [108, 38, 76, -260, 294, -815, 435, 254, 91, -546]]\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[[50, -351, -111, 145, 207, 150, -465, 56, -406, -72],\n [611, -145, -61, 428, 640, 637, 16, 771, -131, -302],\n [106, 181, 92, 19, 215, 162, 323, 311, 267, -213],\n [-246, 51, -1, -177, -375, -322, -39, -416, 14, 236],\n [185, 8, 38, 125, 379, 295, 115, 417, 73, -284],\n [-539, 263, 140, -408, -398, -473, 214, -478, 330, 67],\n [-659, 205, 125, -464, -484, -573, 92, -631, 255, 114],\n [41, 180, 48, -35, -81, -33, 255, 23, 203, 42],\n [-710, -285, 32, -319, -3, -310, -543, -439, -243, -223],\n [37, 277, 121, -56, 92, 59, 428, 213, 371, -154]]\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[[168, -252, -228, 168, -252, 216, 0, -228, -132, -180],\n [-280, 420, 380, -280, 420, -360, 0, 380, 220, 300],\n [238, -357, -323, 238, -357, 306, 0, -323, -187, -255],\n [-42, 63, 57, -42, 63, -54, 0, 57, 33, 45],\n [98, -147, -133, 98, -147, 126, 0, -133, -77, -105],\n [-210, 315, 285, -210, 315, -270, 0, 285, 165, 225],\n [196, -294, -266, 196, -294, 252, 0, -266, -154, -210],\n [70, -105, -95, 70, -105, 90, 0, -95, -55, -75],\n [-140, 210, 190, -140, 210, -180, 0, 190, 110, 150],\n [56, -84, -76, 56, -84, 72, 0, -76, -44, -60]]?\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 10x10 matrix:\n[[-396, -125, 116, -235, 26, 685, 74, -472, 295, 332],\n [-316, 103, 803, -985, -341, 249, 120, -1012, 104, -95],\n [263, 66, 179, -280, -571, 624, 206, -428, 647, -292],\n [12, -521, 514, -197, 188, -541, -52, -352, 630, -585],\n [406, -72, 395, -517, -314, 35, -201, -800, 312, -467],\n [206, 33, -208, -430, 337, -262, -197, -104, 234, -498],\n [500, -441, 514, 297, -390, -382, -93, -286, 406, -464],\n [-57, -112, 380, 226, -174, -699, 471, 602, 350, -498],\n [-146, -70, -283, 2, 463, 73, -355, -146, -354, 365],\n [-819, -263, 456, -127, -28, 585, 458, -252, 507, 387]]\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 10x10 matrix:\n[[-139, -255, 195, -180, -59, 132, 252, -230, 87, 240],\n [190, 345, -159, 261, 206, -132, -306, 251, -240, -447],\n [2, 0, 108, 18, 130, 48, 36, -62, -126, -126],\n [-4, -5, -65, -15, -84, -28, -18, 35, 82, 85],\n [-37, -70, 116, -39, 59, 64, 90, -99, -49, -7],\n [-151, -280, 302, -183, 41, 184, 306, -303, -7, 161],\n [161, 300, -366, 189, -95, -216, -342, 349, 57, -123],\n [-44, -85, 191, -39, 132, 100, 126, -149, -118, -67],\n [-105, -200, 370, -105, 215, 200, 270, -305, -185, -65],\n [46, 100, -536, -6, -530, -256, -252, 354, 502, 442]]\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[[-229, 217, 169, 71, -18, 103, -172, -120, -226, 317],\n [-319, -323, -301, 191, 332, 53, 418, 240, 304, -153],\n [52, -247, -208, 13, 117, -52, 247, 156, 247, -260],\n [-164, -382, -340, 130, 294, -4, 442, 264, 370, -284],\n [183, 582, 513, -168, -417, 27, -657, -396, -567, 465],\n [124, -202, -164, -26, 58, -68, 182, 120, 206, -252],\n [100, -88, -68, -32, 4, -44, 68, 48, 92, -132],\n [-255, 147, 107, 93, 34, 101, -92, -72, -158, 263],\n [-223, -5, -21, 101, 106, 69, 60, 24, -6, 103],\n [-65, 212, 177, -2, -91, 51, -207, -132, -213, 233]]\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[[-224, 94, 188, 152, -194, -273, 14, -228, -368, -142],\n [-196, 98, 124, 88, -118, -213, 46, -204, -232, -86],\n [-546, 356, 132, 8, -56, -457, 306, -592, -172, -38],\n [-154, 132, -44, -88, 88, -77, 154, -176, 132, 66],\n [-294, 210, 24, -48, 30, -216, 204, -324, 12, 24],\n [483, -351, -24, 96, -69, 345, -348, 534, -54, -54],\n [21, 87, -264, -288, 333, 183, 204, -6, 582, 246],\n [203, -209, 148, 216, -231, 44, -278, 242, -374, -172],\n [616, -416, -112, 32, 16, 492, -376, 672, 112, 8],\n [-343, 231, 64, -16, -11, -275, 208, -374, -66, -6]]\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[[-891, -585, 161, 331, -316, 480, -311, 113, -150, -637],\n [57, 525, -118, -21, -135, -87, -113, 571, -711, -16],\n [319, -280, -39, 193, 388, -236, 72, -428, 33, -20],\n [-837, -580, -146, 207, -154, 603, -14, 66, 175, -562],\n [371, 417, -379, -133, 223, -148, 273, 241, -131, 254],\n [416, 830, -317, -586, -74, -23, 360, 344, 220, 512],\n [171, 278, 479, 171, -215, -422, -477, 252, -739, 99],\n [-254, 339, -454, -544, -243, 680, 257, -9, 132, -538],\n [-710, 111, -442, -496, -437, 1030, 152, -1, 107, -946],\n [-669, -382, -305, -333, -193, 828, 358, -228, 1000, -325]]?\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[[437, 683, 301, 392, -189, 349, 506, -703, -673, -701],\n [31, -280, 371, -217, 594, -71, -13, 524, 596, -157],\n [-896, -263, -176, 27, 19, 61, -46, 350, 519, 437],\n [-114, 376, -539, -437, -443, 565, 118, -900, -275, 94],\n [117, 71, -178, 134, 271, -452, 125, -214, 59, 237],\n [49, 308, -505, 163, -219, -495, 258, 739, -387, 663],\n [-724, 679, -506, -678, -1024, -873, 704, -175, -526, -309],\n [92, 731, -684, 54, -377, -82, 394, -779, -697, 455],\n [-589, 107, -588, 279, -271, -1048, 236, -212, 71, 336],\n [871, -272, 677, 371, 672, -401, -607, 108, -58, -63]]\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[[62, -286, 584, 92, 505, -531, 548, 821, 299, -140],\n [29, 373, -252, -148, 161, 448, 609, -36, 1059, -142],\n [-41, 390, -333, -262, -317, 823, 133, -379, 770, 371],\n [-334, -928, 630, 172, -296, -282, -568, 152, -1476, 405],\n [-25, 137, -360, -362, -2, -468, -1153, -289, -297, 174],\n [313, 95, -572, -66, -13, 197, 113, -128, 426, -107],\n [218, 295, -502, -61, -75, 613, 311, -304, 556, 206],\n [-485, -3, 494, -110, 470, -287, 195, 233, 210, -240],\n [316, 359, -814, 483, 9, 510, 441, -806, -459, -418],\n [-490, 284, -260, -176, 343, -429, -508, -477, -173, -786]]\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[[-193, -669, 48, -99, 33, 297, 310, 89, -614, 277],\n [-191, 313, -557, -162, 464, -10, -212, 113, -13, 70],\n [-30, -597, -46, -418, 705, 528, -649, 262, -412, 75],\n [268, -137, 599, 127, -470, -29, 71, -181, 176, -120],\n [126, 111, 458, 386, -867, -324, 695, -290, 200, -33],\n [219, -676, 386, -459, 560, 599, -899, 151, -236, -46],\n [89, 592, -65, -186, 29, -106, -279, -246, 346, 15],\n [-384, 637, -682, -152, 55, -194, 423, -206, -114, 397],\n [179, 285, -133, 488, 72, -372, -234, 351, 579, -590],\n [-300, 492, -798, 348, 180, -414, 336, 279, 141, -114]]?\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[[755, 9, 278, 115, -438, -13, -793, -49, 281, 219],\n [1619, -254, 838, 372, -416, 95, 163, -479, 293, 275],\n [176, -862, 126, -146, -384, -65, 212, -513, 930, -75],\n [1097, -917, 464, 539, -185, 288, 590, -678, 445, 195],\n [-389, -237, -422, 363, 29, -454, 70, 60, -153, -17],\n [-520, 187, -521, 111, 772, 680, 832, -596, -646, 173],\n [-778, 588, -429, -318, 147, -284, -205, 220, -316, -86],\n [-732, -137, -193, -35, -55, -966, 523, 462, -22, -401],\n [-31, 648, 547, -418, -390, -545, -1013, 1473, -27, -385],\n [355, 395, 620, -121, -81, -19, -290, 889, -191, -201]]\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[[-319, -329, 233, 205, 601, 267, -111, 431, 335, 311],\n [529, 234, 398, -86, 424, -643, 437, -275, 6, -22],\n [-316, -331, 100, 160, -73, 164, -566, 723, 313, 94],\n [460, 442, -746, 323, -529, 492, 451, -1022, 213, -382],\n [408, 612, 183, 653, -853, -166, 291, -83, 209, -214],\n [-185, -101, 171, 310, 112, 339, 106, 355, 237, 83],\n [850, 507, -73, 637, -300, 296, 771, -644, 414, -536],\n [391, -157, -477, -1104, 128, -144, 112, -766, -894, -558],\n [613, 710, 129, 812, -745, -65, 402, -430, 275, -265],\n [-239, 19, -16, -50, 338, -24, 588, 161, 319, 282]]\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 10x10 matrix:\n[[-239, -85, -550, -125, -112, -520, -145, 617, -319, 131],\n [-235, -412, 29, 552, -223, 922, 7, -311, 617, 611],\n [210, 284, -30, -392, 152, 378, 255, 56, -473, -659],\n [-184, -341, 707, 199, -515, 100, -658, -50, -394, 96],\n [745, 118, 616, 435, -59, 114, -539, 951, -297, 6],\n [698, 28, 79, -324, -43, 568, 460, -190, -456, -829],\n [902, -641, 723, -561, -578, 467, -103, 867, -1218, -398],\n [772, -205, 589, -43, -433, 283, -374, 711, -960, -506],\n [481, 210, 860, -464, -101, 44, -141, -239, -878, -973],\n [-554, -865, -327, -203, -828, 326, 18, -532, -461, -19]]\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[[104, -12, -43, 87, 94, 229, -222, -57, 251, -19],\n [-227, -550, -876, -218, -376, 272, -220, -699, -88, 396],\n [-37, -509, -33, 827, 332, -410, 663, -253, 1048, 85],\n [-183, -228, -621, -871, -504, 685, -870, -428, -497, 283],\n [-236, 596, -294, -618, 128, 138, -598, 526, -216, -572],\n [-183, -23, -738, -302, -254, 561, -546, -678, 282, -50],\n [244, -278, 587, 361, -156, 135, 297, -549, 430, 334],\n [-211, -346, -302, -148, -266, -8, 85, -427, 13, 230],\n [526, 273, 385, -24, -115, 420, -349, 174, -813, 222],\n [-63, -201, -214, 315, 169, -211, 239, -22, 330, 2]]\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[[156, 220, -48, -154, -639, 304, 219, -202, 169, -494],\n [513, -198, 107, -254, 229, 593, 20, 421, 216, -595],\n [173, 113, 134, -1013, -736, 539, -243, -847, 852, 130],\n [-162, -1167, 223, 27, 383, 184, -165, 209, -382, -815],\n [-144, 68, 433, 617, -127, -431, 540, 164, -261, -278],\n [-88, -185, -97, -155, -54, 114, -602, -819, -407, 39],\n [-345, -122, -170, 380, -244, -716, 198, -27, 63, 169],\n [416, 248, -964, -164, -456, -24, -530, -568, 262, -18],\n [38, -151, -618, 161, 210, -197, -111, 416, 21, 11],\n [-119, -260, -1224, -182, 222, -158, -1077, -537, -294, 522]]\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[[1276, 465, -866, -849, 1199, -741, 164, -233, 439, -647],\n [-665, -66, 539, 515, -102, 89, 432, -175, -166, 350],\n [-287, 458, 156, -267, -181, -508, 381, 452, 463, 265],\n [256, -413, -617, 495, -403, -198, -817, 157, 142, -279],\n [275, -196, -541, -410, 235, -733, 171, 88, 161, -424],\n [-148, 343, 90, -356, -618, 9, -295, 680, 340, 223],\n [-390, -713, -152, 316, -385, -231, -7, 3, -250, -152],\n [94, 183, -68, -592, -390, 73, -275, 513, 164, 7],\n [548, -396, -935, 103, -391, -443, -634, 249, 294, -328],\n [-154, 200, 369, -79, -98, 389, 352, -67, -82, 401]]\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[[-200, -140, 220, -300, 160, 100, -320, 220, 200, -380],\n [130, 91, -143, 195, -104, -65, 208, -143, -130, 247],\n [-40, -28, 44, -60, 32, 20, -64, 44, 40, -76],\n [80, 56, -88, 120, -64, -40, 128, -88, -80, 152],\n [-220, -154, 242, -330, 176, 110, -352, 242, 220, -418],\n [-190, -133, 209, -285, 152, 95, -304, 209, 190, -361],\n [140, 98, -154, 210, -112, -70, 224, -154, -140, 266],\n [160, 112, -176, 240, -128, -80, 256, -176, -160, 304],\n [130, 91, -143, 195, -104, -65, 208, -143, -130, 247],\n [-180, -126, 198, -270, 144, 90, -288, 198, 180, -342]]\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[[0, -288, 120, 123, -15, -90, -336, 150, 114, -69],\n [-132, 258, -366, 39, -177, 60, 444, -144, -54, -9],\n [-158, -481, -109, 384, -253, -175, -390, 239, 248, -200],\n [246, -75, 513, -246, 351, 15, -354, 57, -60, 114],\n [-34, -95, -27, 79, -54, -35, -74, 47, 50, -41],\n [4, 158, -58, -72, 14, 50, 180, -82, -64, 40],\n [-102, -189, -121, 196, -157, -75, -110, 91, 112, -100],\n [-24, 204, -132, -60, -24, 60, 264, -108, -72, 36],\n [-2, 17, -11, -5, -2, 5, 22, -9, -6, 3],\n [66, 495, -77, -286, 121, 165, 506, -253, -220, 154]]\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[[210, 131, 133, 305, 214, 101, 393, -420, -419, -56],\n [103, 135, -127, -57, 13, 87, 76, 139, 86, 120],\n [403, 419, -285, -169, 377, 215, 346, 439, -138, 394],\n [-64, -3, -123, -145, -152, 3, -153, 218, 285, 62],\n [-291, -303, 180, 39, -213, -177, -291, -183, 90, -237],\n [-195, -168, 151, 316, -461, 0, -58, -585, 241, -311],\n [534, 570, -356, -74, 346, 342, 530, 342, -104, 442],\n [-178, -337, 366, -21, 406, -313, -170, -64, -615, -181],\n [-214, -243, 187, 87, -130, -141, -181, -232, -17, -216],\n [186, 312, -243, 234, -438, 330, 291, -282, 486, 51]]\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[[19, 10, 9, 14, -5, -15, 11, -5, 10, 2],\n [285, 150, 135, 210, -75, -225, 165, -75, 150, 30],\n [38, 20, 18, 28, -10, -30, 22, -10, 20, 4],\n [152, 80, 72, 112, -40, -120, 88, -40, 80, 16],\n [361, 190, 171, 266, -95, -285, 209, -95, 190, 38],\n [-361, -190, -171, -266, 95, 285, -209, 95, -190, -38],\n [342, 180, 162, 252, -90, -270, 198, -90, 180, 36],\n [-247, -130, -117, -182, 65, 195, -143, 65, -130, -26],\n [399, 210, 189, 294, -105, -315, 231, -105, 210, 42],\n [285, 150, 135, 210, -75, -225, 165, -75, 150, 30]]\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[[-545, -23, -25, 610, 461, 997, 1025, 182, -349, 753],\n [-50, 15, 278, 44, -43, 243, -52, 454, -107, -775],\n [-503, 1324, -438, 1366, -321, 278, -51, 22, 197, 690],\n [751, -1256, 215, -986, 269, -649, -281, 299, -615, -924],\n [185, -483, 18, -663, 694, -509, -158, -165, 288, -205],\n [861, -389, -601, 324, 394, -1143, -1109, 26, -368, -345],\n [-1134, -155, 729, -457, 59, 442, 749, 96, -176, -275],\n [-253, -311, 170, -740, -403, 423, 636, -298, 265, 556],\n [-815, 333, -31, -181, -188, 122, 486, -306, 403, 755],\n [71, -528, -232, -565, 180, -723, -310, -418, 144, 240]]\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[[-1234, 795, 157, -720, 723, -280, -373, -23, -3, -608],\n [-93, 1323, -45, -305, 61, -635, 907, 511, -284, -685],\n [-661, 341, -436, -156, 35, -355, -338, 248, -190, 637],\n [116, -319, -100, -97, 388, 865, -1224, 304, -445, -335],\n [-660, 461, 54, 241, -5, -648, 32, -537, 863, 160],\n [-896, 192, -450, -1132, 285, 57, -824, 763, -943, 464],\n [367, -1028, 136, 381, 205, 682, -160, -571, 88, 19],\n [-720, 80, -166, -538, -14, -308, 32, 396, -380, 304],\n [-731, 408, 248, 209, 268, -331, -240, 25, 206, -275],\n [145, -642, -330, -319, 58, 703, -1238, 171, -398, 618]]?\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[[-14, 56, -140, -210, -294, -56, 14, -252, -210, -42],\n [-3, 12, -30, -45, -63, -12, 3, -54, -45, -9],\n [20, -80, 200, 300, 420, 80, -20, 360, 300, 60],\n [5, -20, 50, 75, 105, 20, -5, 90, 75, 15],\n [22, -88, 220, 330, 462, 88, -22, 396, 330, 66],\n [4, -16, 40, 60, 84, 16, -4, 72, 60, 12],\n [10, -40, 100, 150, 210, 40, -10, 180, 150, 30],\n [-20, 80, -200, -300, -420, -80, 20, -360, -300, -60],\n [-10, 40, -100, -150, -210, -40, 10, -180, -150, -30],\n [-7, 28, -70, -105, -147, -28, 7, -126, -105, -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[[72, -228, -36, 12, -264, 24, -108, 144, -24, 156],\n [-126, 399, 63, -21, 462, -42, 189, -252, 42, -273],\n [-102, 323, 51, -17, 374, -34, 153, -204, 34, -221],\n [-42, 133, 21, -7, 154, -14, 63, -84, 14, -91],\n [78, -247, -39, 13, -286, 26, -117, 156, -26, 169],\n [-126, 399, 63, -21, 462, -42, 189, -252, 42, -273],\n [-54, 171, 27, -9, 198, -18, 81, -108, 18, -117],\n [90, -285, -45, 15, -330, 30, -135, 180, -30, 195],\n [18, -57, -9, 3, -66, 6, -27, 36, -6, 39],\n [-18, 57, 9, -3, 66, -6, 27, -36, 6, -39]]\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[[87, 130, -50, 122, -41, 96, 15, 43, 60, -28],\n [-283, -258, 298, 10, -408, -334, 183, -77, -113, 359],\n [361, 379, -360, -32, 415, -566, -597, 561, -487, -660],\n [-216, 24, -431, -438, -7, -241, 260, 255, 112, 73],\n [307, 47, 587, 666, -130, -65, -451, -128, -377, -143],\n [103, -119, 68, -212, 444, -684, -641, 213, -646, -465],\n [-144, -80, 190, 176, -385, 232, 342, -200, 241, 375],\n [-655, -548, 345, -204, -663, 127, 791, -448, 395, 896],\n [14, 421, -630, -78, -165, 316, 482, 284, 512, 95],\n [-31, 265, -568, -228, 13, 302, 387, 185, 445, 46]]\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 10x10 matrix:\n[[-142, -736, -14, 852, -200, -286, 560, 114, -77, -360],\n [267, -182, -279, -353, -507, -350, 7, 322, -53, 301],\n [-700, 10, -28, -88, 683, 316, -846, 384, 325, -167],\n [344, -821, -85, 907, 296, -83, 116, -77, -40, 166],\n [425, 755, -292, -13, 476, 420, 573, -152, -452, 263],\n [312, -390, -462, -154, -1341, -597, 1001, -56, 118, 140],\n [-151, 1118, 381, -554, 30, 42, 228, -27, 290, -16],\n [201, -1063, -87, 142, 126, 158, -800, -252, -225, -62],\n [468, 23, 505, 288, -659, -828, 522, 216, -425, 1561],\n [-8, -931, -28, 60, 798, 755, -472, -191, -997, -539]]\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[[971, 265, -305, -317, -116, -73, -107, -133, -805, 935],\n [-204, -149, -193, -361, -372, 708, -200, -137, -166, -28],\n [603, 149, -468, 798, 902, -152, 619, 617, -278, -574],\n [10, 179, -693, -575, -97, -910, -450, 354, -567, 45],\n [-81, -196, -226, 1289, 448, 790, 905, -140, 453, -1569],\n [-863, -896, 2, 243, -567, -524, 464, 193, 440, 58],\n [102, 73, 316, 13, -372, 736, 241, -941, 167, 96],\n [376, 16, 842, -348, -1246, 228, -108, -1012, 102, 515],\n [-685, 403, 324, 147, 336, 823, 931, -976, -531, 240],\n [-1350, 23, -94, 375, 1087, 610, 416, -542, 490, 36]]?\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[[-95, -24, -251, 217, -364, 287, 571, 208, -409, 104],\n [-305, 246, 139, -203, 266, -13, -449, 178, 191, -76],\n [-410, 288, 62, -154, 168, 106, -302, 304, 58, -48],\n [-304, 165, -96, 21, -91, 219, 119, 299, -183, 26],\n [-82, 39, -42, 21, -49, 75, 71, 89, -75, 14],\n [110, 18, 262, -224, 378, -304, -592, -226, 428, -108],\n [-326, 180, -94, 14, -84, 226, 106, 316, -182, 24],\n [555, -315, 135, 0, 105, -360, -120, -525, 270, -30],\n [193, -102, 69, -21, 70, -147, -95, -194, 129, -20],\n [-19, 51, 113, -112, 175, -104, -280, -43, 178, -50]]\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[[1022, -50, 350, -122, -453, -130, 181, -316, -11, 270],\n [829, 185, 405, 40, -437, -182, 233, -201, 56, 395],\n [-360, -526, -181, -512, 388, 51, -304, 183, -450, -354],\n [-421, 375, 182, -24, 150, -187, -468, 270, -95, 889],\n [-518, -208, -306, -14, 286, 154, 20, 126, -46, -568],\n [388, -275, -74, -95, -121, 95, 116, -226, 18, -313],\n [538, 347, 275, 423, -417, -96, 730, -109, 268, -231],\n [-124, -394, 628, -1142, 426, -534, -540, 684, -1252, 578],\n [50, -609, 456, -1211, 389, -397, -678, 460, -1166, 509],\n [-159, 350, 52, 249, -43, -42, -52, 44, 189, 374]]\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[[273, 169, -364, 260, -143, -208, -143, 208, -182, -78],\n [-9, 107, -44, 184, -217, -176, -229, -76, 110, -6],\n [236, -4, -240, -32, 172, 64, 188, 272, -296, -56],\n [-137, -188, 234, -307, 275, 272, 286, -41, -4, 47],\n [457, 236, -586, 355, -147, -272, -142, 377, -348, -127],\n [-200, -227, 318, -367, 308, 320, 319, -89, 38, 65],\n [410, -37, -402, -107, 358, 160, 389, 491, -542, -95],\n [295, -5, -300, -40, 215, 80, 235, 340, -370, -70],\n [-224, 124, 168, 236, -400, -256, -428, -332, 392, 44],\n [-410, -160, 500, -230, 30, 160, 20, -370, 360, 110]]\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[[-510, -539, 67, -256, 130, 260, 416, -489, 69, 385],\n [717, 340, 510, 318, -72, 46, -22, -303, -1053, -395],\n [-478, -275, -155, -157, -22, -89, 18, 137, 567, 335],\n [-108, -55, 197, 10, -103, -434, 211, 807, 282, 89],\n [321, 410, -42, 270, -221, -218, -619, 129, -16, -159],\n [7, 38, 122, 31, -70, -329, 130, 655, 179, -13],\n [285, 207, -299, -28, 195, 416, -85, -486, -275, -316],\n [425, 270, 314, 268, -155, -108, -229, -91, -526, -187],\n [212, 266, -340, 70, 29, 286, -479, -532, -89, -184],\n [253, 259, -247, -44, 151, -32, 151, 550, 117, -360]]?\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[[-134, -200, 495, -220, -39, 240, 478, 1086, 61, -119],\n [209, -96, 681, -5, -13, -576, 113, 303, 707, -79],\n [-406, 416, -194, -106, 582, 584, -235, 191, 556, -974],\n [-506, 108, 62, 183, -121, 71, -782, -310, 611, -771],\n [59, 425, -707, 44, 267, 355, 750, -49, -962, 173],\n [-295, 309, -228, 134, -18, 153, -741, -354, 621, -852],\n [-155, 384, 446, -249, -79, -137, 193, 520, 738, -204],\n [-87, 87, 285, -237, -243, -139, 313, 45, 30, 616],\n [-432, -309, 449, -126, 852, 516, 385, 1088, -94, -484],\n [-437, 843, -489, -94, -125, 471, 153, -166, 142, -475]]\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[[214, -237, -298, 71, 301, 56, -75, 150, 158, 125],\n [-238, -219, 34, -407, -205, 448, -93, -126, -374, -365],\n [373, 136, -181, 497, 377, -483, 70, 215, 501, 475],\n [-225, 28, 177, -225, -257, 175, -2, -139, -257, -235],\n [190, -31, -154, 185, 219, -140, -1, 118, 214, 195],\n [-356, 518, 572, -34, -534, -224, 170, -260, -212, -150],\n [157, -327, -313, -52, 262, 203, -111, 123, 53, 20],\n [190, -31, -154, 185, 219, -140, -1, 118, 214, 195],\n [-156, 346, 324, 66, -266, -224, 118, -124, -44, -10],\n [134, 229, 46, 301, 87, -364, 91, 62, 254, 255]]?\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[[-473, 43, 551, 107, 1116, 13, -260, -182, 686, 831],\n [126, 10, 12, 431, -545, 143, 1302, 187, 3, -135],\n [-76, -64, 177, 79, -369, 409, 584, -1517, 420, 85],\n [538, 31, -289, 397, -487, 50, 960, -1217, 809, -501],\n [-860, -65, 7, 168, 139, 480, -660, -427, -708, -94],\n [24, 241, 25, -187, 961, -474, -722, -375, 225, 223],\n [193, -117, 139, -567, -746, 115, -51, 260, -691, -48],\n [205, 661, 175, 11, 640, -200, 93, -609, 578, 259],\n [-645, -334, -23, 43, -609, 423, 213, 81, -4, 388],\n [574, -26, -153, 344, 58, -437, 953, 613, 470, -92]]\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 10x10 matrix:\n[[-118, -423, 1251, 503, 408, 159, 245, -539, -64, -560],\n [473, -365, -769, 351, 261, 319, -97, 127, 183, -40],\n [-45, 303, -589, -928, -529, 130, 12, 506, 2, 510],\n [-508, 34, 727, -762, -405, -369, 67, -617, -627, 296],\n [-505, 624, 89, -899, -1048, 94, -223, 495, -128, 724],\n [-293, 484, -392, 394, 85, -314, -101, 221, 1140, -222],\n [-385, 1125, 65, -868, -936, -24, 334, 1484, 76, 340],\n [-608, 342, 48, -17, -612, 358, 127, 342, 938, -306],\n [84, -1095, -329, -474, 107, 248, 346, -1063, 58, 91],\n [-232, -1254, -94, -139, 1, 548, 298, -1288, 498, -367]]\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[[-285, 454, 281, -223, -347, -11, 218, -270, 3, -319],\n [418, -305, -30, -149, -180, 102, -135, 228, -530, -273],\n [-474, 423, -81, 76, 356, -114, 141, -173, 549, 458],\n [361, -511, -283, -189, 292, 157, -325, 474, -2, 176],\n [-535, 730, 190, -146, -97, -101, 314, -365, 222, 0],\n [-472, 424, -38, -80, 282, -60, 120, -134, 568, 354],\n [-417, 241, 149, 503, 30, -193, 211, -432, 494, 176],\n [-48, 149, -272, -614, 383, 146, -137, 378, 141, 301],\n [-11, -176, -468, -65, 758, 37, -232, 387, 447, 738],\n [288, -256, 538, 328, -942, -20, 128, -366, -584, -950]]\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[[749, -258, -2, 602, 548, 679, -593, 473, 74, -138],\n [-462, 246, -440, -551, -294, -1, -327, 189, 379, 678],\n [838, -824, -577, 524, 638, 183, 142, 603, 567, 176],\n [4, -778, 227, 180, -585, -305, 180, 314, 326, 130],\n [-1036, 282, 87, -693, -1076, -512, 101, -346, 164, 146],\n [466, -648, -724, 231, 247, 267, -233, 684, 828, 396],\n [-220, -132, -190, -60, -599, 424, -894, 465, 647, 200],\n [-565, 599, -381, -610, -201, 42, -312, -102, 159, 399],\n [474, 128, 432, 155, 572, 365, -431, 403, -599, 640],\n [-154, 151, -162, -355, 31, -37, -140, 219, 13, 735]]?\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 10x10 matrix:\n[[196, -28, 210, 126, -224, -126, -112, 0, -294, 308],\n [-98, 14, -105, -63, 112, 63, 56, 0, 147, -154],\n [-266, 38, -285, -171, 304, 171, 152, 0, 399, -418],\n [-280, 40, -300, -180, 320, 180, 160, 0, 420, -440],\n [-210, 30, -225, -135, 240, 135, 120, 0, 315, -330],\n [-56, 8, -60, -36, 64, 36, 32, 0, 84, -88],\n [252, -36, 270, 162, -288, -162, -144, 0, -378, 396],\n [252, -36, 270, 162, -288, -162, -144, 0, -378, 396],\n [-238, 34, -255, -153, 272, 153, 136, 0, 357, -374],\n [112, -16, 120, 72, -128, -72, -64, 0, -168, 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[[-558, -839, -285, -64, -78, -102, -84, 270, 116, 144],\n [478, 842, -144, 150, -29, 56, -66, -33, 299, 338],\n [-346, -313, -175, 570, -25, -552, -17, -115, -235, 325],\n [622, 530, 199, 61, 253, 807, 380, -291, 19, -408],\n [-425, -211, 207, 63, 32, -568, -259, 77, -330, 248],\n [362, 836, -347, 427, 13, -31, -62, -141, 335, 540],\n [613, -89, 78, -554, -11, 1145, 326, 404, 457, -477],\n [56, 242, 177, 5, -98, -419, -37, -244, -272, -183],\n [-11, 188, 292, 237, 1, -516, 33, -396, -515, -210],\n [-581, -341, -363, 72, 96, -115, -142, -122, 110, 218]]\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[[-526, -661, 817, -335, 300, 74, 738, -79, 811, 0],\n [324, -646, 170, -490, 738, 590, -88, 85, 26, 829],\n [-868, -297, 877, -229, -190, 222, 530, 508, 966, -404],\n [77, -1011, 241, -493, 680, -210, -107, 797, 61, 23],\n [-457, -974, 151, -112, -92, -558, 141, -282, 381, -333],\n [-400, 994, 519, 580, -871, 287, 273, 112, 556, -380],\n [185, 139, 622, -323, 253, 175, 786, 360, 460, -485],\n [48, -544, -919, 26, 517, -1077, -293, -765, -906, 249],\n [-464, -567, -260, -371, 283, -325, 5, -112, -111, -59],\n [-653, 276, 207, 82, -240, -384, 475, 6, 275, -578]]\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 10x10 matrix:\n[[-18, -74, -55, 200, -42, -100, 64, -142, 64, 78],\n [-204, -148, -130, 244, 116, -344, -64, -80, 232, 144],\n [522, 214, 215, -142, -438, 692, 352, -160, -476, -192],\n [-12, 30, 20, -99, 40, 24, -48, 81, -14, -33],\n [18, -66, -45, 210, -78, -60, 96, -168, 36, 72],\n [-72, 54, 30, -225, 132, 0, -144, 207, 6, -63],\n [-480, -200, -200, 140, 400, -640, -320, 140, 440, 180],\n [-174, -48, -55, -21, 166, -204, -144, 105, 142, 39],\n [342, 174, 165, -192, -258, 492, 192, -30, -336, -162],\n [498, 204, 205, -135, -418, 660, 336, -153, -454, -183]]\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[[503, 264, 127, -358, -331, 141, 327, -338, -154, 37],\n [-142, 449, 294, 205, -250, -193, 88, -65, -24, -479],\n [-517, -541, -43, 324, 509, 188, -236, 626, 268, 119],\n [448, 84, 356, -823, -267, 376, 407, -211, 18, 720],\n [206, 153, 50, -63, 285, 332, 69, 317, 257, 437],\n [89, 87, 617, 193, 425, 129, -35, 798, 220, 347],\n [414, 401, 838, -965, -895, -276, 443, -701, -383, 303],\n [712, -69, -512, -342, 8, 368, 190, -332, -99, 315],\n [237, 64, 891, -502, -193, 785, 688, 347, 191, 279],\n [32, 12, 376, 20, 134, 861, 492, 523, 344, -59]]\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 10x10 matrix:\n[[390, -1394, -1006, 368, -193, 1206, -480, -286, -444, 233],\n [220, 419, 1059, 23, -169, -569, -413, -435, 276, -315],\n [433, -143, 173, -161, -16, -19, -19, 537, -102, 322],\n [282, 449, -248, 926, 687, -597, 688, -325, -425, -517],\n [13, -132, -656, -568, -187, 782, 87, 853, 56, 414],\n [-127, 563, 91, -619, -71, 162, 77, 261, 256, -194],\n [-7, -628, 142, 50, 79, 1166, -468, 613, 780, 153],\n [586, 202, -84, 210, 248, 30, -20, -542, -592, -654],\n [-133, -208, -53, -25, -399, 670, -568, -128, 199, 54],\n [159, 34, 719, -1494, -176, -235, 391, 641, 136, 516]]\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 10x10 matrix:\n[[-579, -152, 297, 141, 202, 283, 447, 680, 444, 750],\n [1274, 391, 1206, 221, 1380, 954, 364, -181, 928, 152],\n [227, -575, -821, -478, -421, -960, 224, -55, -440, -648],\n [-197, 616, 106, 1320, 422, 194, 303, 567, 338, 99],\n [-568, 112, 200, 272, -90, 608, -687, -86, 265, -101],\n [-312, -371, -151, -142, -435, -967, -191, 346, -627, -111],\n [-163, 435, 241, 335, -277, 721, -235, -338, -367, 258],\n [-174, -274, -192, -194, -410, 294, 492, -105, -230, 536],\n [988, 639, 1307, 802, 1671, 533, 19, 493, 1291, 233],\n [-696, 27, -58, -473, -387, 357, 132, 62, -209, 531]]\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[[-43, 318, 156, -188, 948, -227, 477, -288, -676, -364],\n [634, -4, 197, 296, -969, -552, 276, 425, 325, 647],\n [1092, 242, 1131, -576, -215, 241, -453, -1, 534, 753],\n [-209, -183, 173, 148, 510, -725, 776, 215, -25, -81],\n [-1054, -901, 485, 963, 21, 991, -35, -732, -590, -34],\n [-95, -253, 1113, -151, 313, -576, 394, 4, 17, 181],\n [-545, -556, -298, 829, -436, -227, 899, 164, -593, 905],\n [-651, -650, 28, 681, -370, 870, 32, -602, 59, -119],\n [142, 15, -331, -150, -238, 515, -204, -69, -762, 414],\n [-773, -893, 738, 1207, -312, 531, 69, -157, -59, 1077]]\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[[863, 335, 510, 542, -580, 393, -207, -213, -834, -31],\n [-381, 611, 77, 294, -106, 745, 279, -24, 178, -49],\n [-648, 578, -488, -514, 109, 346, 167, -580, 330, -59],\n [668, -322, 171, -404, 218, -781, 404, -110, 400, -107],\n [-1027, 269, -742, 114, -62, -132, -45, -422, -66, 614],\n [30, 93, -10, 377, 30, -456, 176, -246, -75, 507],\n [494, -121, -68, -702, 124, -481, -60, 12, 194, -147],\n [95, -168, -262, -107, -631, -300, 660, -360, 123, -134],\n [-774, 678, -68, 103, 364, 679, 280, -188, 475, 34],\n [-78, 259, -101, -207, -692, 548, 876, -93, 479, -581]]?\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[[-182, -238, 126, -56, -42, 42, -168, 168, -42, -168],\n [91, 119, -63, 28, 21, -21, 84, -84, 21, 84],\n [78, 102, -54, 24, 18, -18, 72, -72, 18, 72],\n [195, 255, -135, 60, 45, -45, 180, -180, 45, 180],\n [247, 323, -171, 76, 57, -57, 228, -228, 57, 228],\n [143, 187, -99, 44, 33, -33, 132, -132, 33, 132],\n [39, 51, -27, 12, 9, -9, 36, -36, 9, 36],\n [-273, -357, 189, -84, -63, 63, -252, 252, -63, -252],\n [169, 221, -117, 52, 39, -39, 156, -156, 39, 156],\n [-208, -272, 144, -64, -48, 48, -192, 192, -48, -192]]?\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[[53, -352, 306, -928, 235, 685, -528, -467, -323, -484],\n [683, -283, 233, 86, 20, -485, 561, 145, 743, -843],\n [367, -184, -169, 793, -453, -699, 895, 311, 583, 398],\n [-820, 597, -77, 290, 847, -48, -25, 278, 192, 449],\n [-163, -83, -453, 278, -14, -426, -19, -131, 57, -76],\n [-158, 602, 340, 533, 336, -668, 296, 609, 1142, 288],\n [-498, 448, 534, -498, 1164, 397, -299, 138, 358, -309],\n [-310, 338, -20, 448, 224, -159, 316, 336, 226, 559],\n [74, 338, 666, -619, 152, 251, -668, 59, 318, -375],\n [177, 504, 11, 819, -117, -722, 540, 643, 601, 77]]\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[[-286, 198, -286, -88, 440, -286, 374, -88, 22, 22],\n [273, -189, 273, 84, -420, 273, -357, 84, -21, -21],\n [-91, 63, -91, -28, 140, -91, 119, -28, 7, 7],\n [182, -126, 182, 56, -280, 182, -238, 56, -14, -14],\n [-26, 18, -26, -8, 40, -26, 34, -8, 2, 2],\n [-117, 81, -117, -36, 180, -117, 153, -36, 9, 9],\n [260, -180, 260, 80, -400, 260, -340, 80, -20, -20],\n [-78, 54, -78, -24, 120, -78, 102, -24, 6, 6],\n [-104, 72, -104, -32, 160, -104, 136, -32, 8, 8],\n [104, -72, 104, 32, -160, 104, -136, 32, -8, -8]]\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[[-418, 80, 297, 273, 126, -214, -113, -292, 266, -189],\n [228, 400, -40, 84, -224, 28, -260, 248, -256, -152],\n [-95, 540, 211, 336, -154, -153, -404, 38, -70, -343],\n [-152, -440, -21, -147, 210, 16, 299, -200, 214, 201],\n [-19, -740, -191, -378, 266, 139, 534, -162, 198, 419],\n [38, 520, 118, 252, -196, -86, -372, 132, -156, -286],\n [-190, 40, 136, 126, 56, -98, -54, -132, 120, -88],\n [76, 440, 71, 189, -182, -52, -309, 144, -162, -227],\n [-399, -340, 169, 42, 266, -121, 194, -362, 358, 59],\n [-323, 260, 284, 315, 28, -205, -231, -186, 156, -260]]\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[[-393, 122, 16, 215, 66, -465, 52, -866, -704, 44],\n [-309, -242, 22, 25, 370, -255, -28, -352, -330, 440],\n [193, 494, -157, -268, -541, -125, 361, 304, -10, -539],\n [-155, 14, 98, -286, -25, -95, 370, -80, -55, 325],\n [69, -22, -49, 183, 36, 45, -225, 4, 9, -166],\n [328, 46, -358, -125, -42, -35, -187, 821, 184, -428],\n [403, 348, -213, -343, -469, 100, 226, 819, 350, -541],\n [-216, -316, 84, -532, 310, -90, 406, 250, 86, 810],\n [-312, 324, 279, -304, -352, -180, 727, -630, -273, 272],\n [-339, -66, 233, 183, 130, -105, 63, -786, -323, 340]]\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[[-616, -268, 497, 538, -154, 268, -251, -39, -438, -354],\n [-29, -325, 26, 197, -59, -344, 125, 854, -212, -184],\n [-189, -691, -148, 322, 347, -140, 236, 410, 200, 166],\n [-155, 333, 15, -495, -266, 413, -335, -634, 119, -185],\n [67, 1080, -103, -250, -916, -383, -506, 297, -194, -537],\n [-235, 111, 94, -469, 414, 723, -498, -379, -171, 531],\n [108, 266, -6, 127, -210, -260, -15, 216, -108, -118],\n [815, 393, -626, -241, 241, -588, 407, 183, 502, 543],\n [540, -282, -803, -696, -105, -615, 536, 549, 861, -122],\n [339, 866, 276, -91, -158, 123, -212, -448, -422, 101]]\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[[32, 48, -104, -120, -112, -96, -8, 136, 24, 112],\n [40, 60, -130, -150, -140, -120, -10, 170, 30, 140],\n [-72, -108, 234, 270, 252, 216, 18, -306, -54, -252],\n [-52, -78, 169, 195, 182, 156, 13, -221, -39, -182],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n [-64, -96, 208, 240, 224, 192, 16, -272, -48, -224],\n [20, 30, -65, -75, -70, -60, -5, 85, 15, 70],\n [-8, -12, 26, 30, 28, 24, 2, -34, -6, -28],\n [32, 48, -104, -120, -112, -96, -8, 136, 24, 112],\n [72, 108, -234, -270, -252, -216, -18, 306, 54, 252]]\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[[207, -665, 636, -154, 28, 165, 189, 885, -216, -265],\n [34, -77, 111, 142, -314, 433, 5, 402, -1422, -344],\n [-898, 378, 27, 291, 143, -372, 52, 454, -656, 528],\n [1011, -1124, 417, -232, -483, 756, -422, 243, -448, -444],\n [608, -789, 57, -737, -91, -381, -150, 49, 865, -261],\n [-641, 608, 449, 716, -14, -325, 898, 86, -30, -244],\n [-284, 735, -433, 117, 689, -39, 339, -381, 268, 175],\n [-464, -156, -16, -188, 820, -284, -476, -40, 1593, 948],\n [415, -534, 546, 320, -406, 243, -13, -752, 49, -418],\n [344, 25, -744, -308, -153, 560, -356, 1074, 12, -53]]\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[[-243, -21, 117, 63, -48, -114, 120, -33, -534, 54],\n [-404, -726, 518, -136, -136, 394, 492, 596, 516, -328],\n [342, 320, -348, 18, 284, -206, -290, -248, 212, 0],\n [-278, -298, 164, -12, 322, -150, 257, 177, 50, -310],\n [-47, 325, -133, 127, 24, -304, -116, -317, -770, 206],\n [-134, -165, 113, -16, 56, 7, 132, 116, 42, -112],\n [245, 312, -230, 35, -26, -69, -245, -230, -78, 172],\n [-127, -284, 196, -63, -76, 189, 178, 243, 268, -122],\n [668, 783, -683, 82, 280, -355, -636, -602, 18, 244],\n [-424, -657, 493, -106, -128, 321, 472, 526, 330, -284]]?\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[[589, 284, 170, -72, -104, -590, -196, 105, 565, -408],\n [-438, -7, -549, -89, -284, 388, 206, -132, -483, 651],\n [469, 93, -364, 35, 104, -840, 313, 152, 490, -739],\n [-31, -562, 904, -956, 543, 260, 145, -424, -487, 190],\n [-140, -19, -22, -270, -153, 411, -22, 57, -403, 122],\n [-500, -355, -507, -113, 378, 125, 454, 11, -375, -153],\n [-38, -394, -233, 159, 313, -134, 564, -78, -278, -302],\n [-721, -3, -505, 1095, -264, 1257, 110, 682, -700, -131],\n [-285, -117, -197, 358, -94, 605, 319, 324, -486, -218],\n [-70, 338, 797, 606, -58, 640, -961, 409, 364, 27]]\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[[331, -529, -505, -206, 20, -80, -703, 372, -151, 114],\n [182, -505, -107, -328, 110, 12, -382, 52, -56, -166],\n [-60, 433, -177, 372, -170, -68, 124, 172, -6, 350],\n [5, 98, -97, 211, 285, -208, -131, 104, -307, -223],\n [233, -392, -345, -51, 375, -240, -619, 272, -411, -297],\n [-227, 617, 139, 500, 190, -184, 363, -52, -209, -132],\n [-67, -128, 289, -181, 145, 56, 133, -240, 25, -315],\n [-78, 137, 100, 263, 615, -320, -56, -36, -512, -647],\n [95, -130, -155, -199, -505, 240, -25, 88, 391, 563],\n [-274, 808, 117, 675, 225, -252, 428, -16, -282, -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[[231, -56, 81, 262, -657, 645, 83, 577, -85, -704],\n [-820, 551, -905, -216, 329, 460, -738, -914, 239, -125],\n [777, -207, -809, 521, -957, 389, -152, 633, -653, -718],\n [1040, 312, 28, 163, -656, -654, -738, -32, -951, 229],\n [34, -98, 562, -92, -207, 253, 836, 196, 557, -185],\n [433, 317, 347, -129, -482, 143, 456, 673, 245, -248],\n [-620, -339, 317, 206, 341, 375, -228, -237, 76, -139],\n [-65, 293, -491, -362, 134, -147, -134, 48, 0, -4],\n [457, 725, 407, -524, 7, -665, 670, -79, 608, 707],\n [-170, -540, -189, 25, 72, 14, 884, -969, 551, 85]]\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[[-8, -455, -161, 348, 46, -32, -697, 513, 612, -196],\n [57, -143, -55, 103, -153, -56, -150, 384, 100, -99],\n [41, 223, 93, -199, -181, -4, 186, -270, -406, 67],\n [-561, 683, -32, -354, 56, -268, 482, 167, -125, -73],\n [631, -595, 879, 351, 326, -406, 165, -719, 194, -552],\n [41, 259, -180, -232, -277, 234, 275, -36, -505, 328],\n [202, 336, -475, -359, -649, 576, 408, 139, -957, 714],\n [433, -215, 175, 57, -251, 40, 134, -90, -306, 5],\n [58, 142, -539, -140, 93, 732, 488, -97, -331, 817],\n [-98, -2, -650, -25, -469, 378, -467, 739, -92, 360]]\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[[176, 352, 0, 256, 144, -288, -336, -272, 256, 144],\n [-66, -132, 0, -96, -54, 108, 126, 102, -96, -54],\n [-143, -286, 0, -208, -117, 234, 273, 221, -208, -117],\n [-132, -264, 0, -192, -108, 216, 252, 204, -192, -108],\n [-99, -198, 0, -144, -81, 162, 189, 153, -144, -81],\n [-209, -418, 0, -304, -171, 342, 399, 323, -304, -171],\n [132, 264, 0, 192, 108, -216, -252, -204, 192, 108],\n [-110, -220, 0, -160, -90, 180, 210, 170, -160, -90],\n [-198, -396, 0, -288, -162, 324, 378, 306, -288, -162],\n [66, 132, 0, 96, 54, -108, -126, -102, 96, 54]]\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[[-132, -22, -209, 22, 198, 132, 132, 132, 176, 110],\n [252, 42, 399, -42, -378, -252, -252, -252, -336, -210],\n [36, 6, 57, -6, -54, -36, -36, -36, -48, -30],\n [72, 12, 114, -12, -108, -72, -72, -72, -96, -60],\n [156, 26, 247, -26, -234, -156, -156, -156, -208, -130],\n [216, 36, 342, -36, -324, -216, -216, -216, -288, -180],\n [-120, -20, -190, 20, 180, 120, 120, 120, 160, 100],\n [-168, -28, -266, 28, 252, 168, 168, 168, 224, 140],\n [-156, -26, -247, 26, 234, 156, 156, 156, 208, 130],\n [-252, -42, -399, 42, 378, 252, 252, 252, 336, 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 10x10 matrix:\n[[237, 270, 938, -48, -328, 814, 514, -205, -364, -30],\n [-131, 152, -331, -938, 87, -388, -345, -344, 325, 140],\n [-343, -31, -70, -721, -58, -132, -458, -1116, -753, -120],\n [-429, -7, -458, -351, 122, -456, -716, -784, -575, 70],\n [205, 0, -106, 749, 2, 14, 259, 726, -47, 35],\n [288, 508, -537, 333, 71, -388, 49, 1085, 165, 482],\n [628, 466, 155, -554, -353, 222, 785, 653, -155, 30],\n [296, 246, -30, 839, 32, 64, 295, 1053, 271, 281],\n [568, 248, 120, 751, -70, 228, 721, 1429, 539, 185],\n [124, 19, -495, -139, 237, -454, -18, 779, 1151, 199]]\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 10x10 matrix:\n[[176, 569, 567, -572, -155, -109, 61, -248, -95, 40],\n [-95, 258, 478, -37, 458, -423, -363, -418, 346, -83],\n [-329, 678, 240, -473, 273, 49, -128, -391, -567, -19],\n [-1114, 601, 768, -360, 1063, -707, 7, -1110, 208, 386],\n [275, 452, 255, -335, 457, 333, -114, -11, -504, -343],\n [198, -307, -344, 452, -99, -295, -130, 332, -172, 103],\n [-401, 1000, 136, -733, -34, 232, -796, -653, -369, -440],\n [-1174, 887, 224, -872, 417, -89, 130, -922, -546, 307],\n [-409, 151, 302, 213, 304, 172, 154, -197, -228, 168],\n [28, 879, 128, -410, -145, 255, -1090, -394, -320, -647]]\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[[396, 267, 86, -619, -833, -466, 138, 254, -433, -225],\n [257, 253, 604, 63, -195, -180, 285, -47, -349, -828],\n [-34, 410, 52, 241, 606, 407, 131, -46, -344, -241],\n [380, -235, 280, 320, -435, -5, 152, -102, -148, 97],\n [-78, 348, 28, -299, -24, -250, 381, -283, -517, -571],\n [463, 447, 182, -1051, 82, -27, 554, 37, -742, -729],\n [471, 21, 2, 149, -479, -688, -431, 599, -129, 552],\n [-336, -535, 272, -150, 1, -289, 309, -280, 973, -547],\n [-912, -411, -410, 879, 857, 54, -152, -780, 339, 346],\n [-331, 160, 734, 669, -86, -868, 335, 2, 756, -1201]]\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[[-13, -17, -20, 15, -13, -20, 11, -5, 21, 9],\n [-286, -374, -440, 330, -286, -440, 242, -110, 462, 198],\n [-247, -323, -380, 285, -247, -380, 209, -95, 399, 171],\n [-13, -17, -20, 15, -13, -20, 11, -5, 21, 9],\n [13, 17, 20, -15, 13, 20, -11, 5, -21, -9],\n [117, 153, 180, -135, 117, 180, -99, 45, -189, -81],\n [-273, -357, -420, 315, -273, -420, 231, -105, 441, 189],\n [169, 221, 260, -195, 169, 260, -143, 65, -273, -117],\n [-234, -306, -360, 270, -234, -360, 198, -90, 378, 162],\n [-208, -272, -320, 240, -208, -320, 176, -80, 336, 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[[150, 84, -235, -293, -184, 64, 190, -251, -343, 243],\n [-813, -378, -28, 73, 431, 7, -305, -398, -55, -39],\n [-173, 109, -14, -173, -223, -625, 226, -383, -409, 225],\n [34, 493, -91, -1315, -569, -264, 349, -1099, -579, 416],\n [477, 112, 132, 326, -137, -259, 173, 479, 162, -16],\n [-190, -719, -237, 347, 732, 228, -109, -126, 33, 367],\n [-367, 140, 310, -414, -3, -163, -171, -375, 198, -174],\n [-210, -418, -273, -29, 431, 460, -134, -260, -69, 214],\n [-98, 380, 381, -419, -270, -288, -50, -183, 207, -241],\n [660, 510, 104, -851, -468, 128, 256, -243, 61, 129]]\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[[-234, 36, 306, -324, -18, -324, -252, -216, 378, -324],\n [-221, 34, 289, -306, -17, -306, -238, -204, 357, -306],\n [-52, 8, 68, -72, -4, -72, -56, -48, 84, -72],\n [-273, 42, 357, -378, -21, -378, -294, -252, 441, -378],\n [-273, 42, 357, -378, -21, -378, -294, -252, 441, -378],\n [169, -26, -221, 234, 13, 234, 182, 156, -273, 234],\n [182, -28, -238, 252, 14, 252, 196, 168, -294, 252],\n [273, -42, -357, 378, 21, 378, 294, 252, -441, 378],\n [26, -4, -34, 36, 2, 36, 28, 24, -42, 36],\n [156, -24, -204, 216, 12, 216, 168, 144, -252, 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[[308, -92, 139, 310, -109, 364, -536, 8, 578, -239],\n [45, -7, 222, 23, -257, 56, -615, -718, 271, 487],\n [335, -563, 118, 28, 390, 435, -374, -253, -101, 647],\n [142, -678, 277, -1102, 116, 528, 339, -287, -772, 1058],\n [360, -708, 328, -1170, 42, 854, 454, 102, -488, 560],\n [-165, 73, -383, 386, 586, -423, 467, 362, -397, -151],\n [-228, 240, -180, 586, -6, -418, -254, 118, 76, -208],\n [-82, 446, 217, 84, -775, -60, -520, -302, 700, -381],\n [-156, 650, 123, 441, -732, -307, -665, -438, 867, -484],\n [112, -94, 62, 453, -62, 109, -642, -55, 329, 16]]\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[[656, 616, 370, 76, 18, -566, 404, 94, -162, 600],\n [420, 202, 143, 263, 258, 854, -226, -20, 48, -322],\n [-393, -308, -260, 79, -361, -11, -548, -718, 59, -510],\n [-155, -30, 243, -533, 450, 882, -272, 531, 295, -316],\n [-208, -48, -88, 153, 56, 257, -75, 927, 385, 829],\n [320, 405, 332, -52, -32, -10, -422, -32, 173, 347],\n [455, 885, 253, 569, -125, 946, 7, 81, 458, -258],\n [178, 718, 556, -402, 174, 358, -40, 764, 513, 432],\n [141, -388, -297, 327, -31, -408, 211, -497, -507, -131],\n [197, 90, 22, 265, -18, 667, -477, -520, 58, -615]]?\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[[-212, 761, -26, -234, 615, 285, -692, 195, 120, 214],\n [451, -196, 207, -165, -663, -78, -146, 465, -679, 401],\n [274, -744, -870, -344, 40, 303, 391, 185, -512, 691],\n [410, -359, 262, 144, -1033, -169, -434, 237, -1064, -218],\n [-547, 824, 111, 143, 967, -326, -595, -644, 713, -457],\n [342, 31, -303, 437, -21, -421, 362, -30, -426, -161],\n [-1062, 327, 496, -199, 705, 469, -178, -102, 569, 281],\n [-468, 374, 174, 64, 576, -376, -508, -476, 102, -78],\n [38, -483, -184, -206, -366, 282, -305, -7, -348, -51],\n [534, -420, -142, 544, -646, -516, 565, -7, -690, -326]]?\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[[312, -307, 183, 38, 173, -431, -328, 173, -489, 484],\n [-694, 39, -1313, 253, 235, 899, 1247, 474, 1118, -809],\n [142, -103, 72, -323, -704, -240, -521, -319, -569, 595],\n [66, 281, 355, -948, 444, -589, -617, -950, -70, 162],\n [89, 123, 222, 47, 351, -213, -105, -126, 152, -359],\n [-124, -353, 418, 11, -416, 374, 140, 159, -404, 927],\n [294, 32, 495, 92, 221, -490, -459, -88, -260, -114],\n [-419, -107, -59, -647, 169, -86, -7, -578, 155, 205],\n [510, -275, 682, 436, -14, 230, 140, 326, -268, 750],\n [-762, 24, -812, 116, 233, 1056, 1265, 295, 1053, -464]]\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[[381, 171, 469, -194, -1, 170, -260, -276, -578, -240],\n [288, 336, 416, -444, -194, 210, -440, -614, -544, 128],\n [-136, 43, -17, -207, -32, 55, -155, -302, -77, 179],\n [-366, -129, -313, 1, 37, -70, 75, -13, 293, 217],\n [112, 119, -69, 85, -188, -65, 81, 158, 231, 151],\n [-238, 10, -410, 114, -191, -155, 184, 193, 592, 404],\n [-114, -330, 42, 178, 405, 5, 128, 193, -192, -484],\n [-412, -329, -533, 399, 145, -230, 433, 553, 667, 35],\n [31, 182, 48, -215, -179, 55, -177, -286, -57, 253],\n [128, 4, 332, -190, 153, 155, -224, -301, -532, -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[[-754, 633, 169, 597, -235, 79, -19, -231, 510, 825],\n [47, -1036, -596, 435, 19, 171, -523, -1232, 356, 396],\n [-1028, 413, -169, -252, -258, 2, -228, -88, 1139, -1],\n [978, 604, -344, -970, 288, -1197, -185, 62, 1016, -344],\n [-899, -506, -387, 287, -141, 707, -255, -50, -79, -447],\n [275, 257, -709, -440, 352, -203, -716, 362, 152, -666],\n [1108, 310, 264, 134, -470, -219, 368, 181, -808, 99],\n [359, -358, -31, -35, 169, -201, -215, -389, 228, 195],\n [716, 169, -456, 42, -32, -317, -36, -17, -204, -273],\n [141, 383, -226, -59, -413, -525, 333, -356, 730, 24]]\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[[69, -152, -436, -329, -158, 216, -180, 153, -41, 42],\n [-253, 114, 77, 474, -24, 249, 272, -198, 140, -201],\n [688, 189, -550, -883, 350, -29, -258, 477, -216, -188],\n [836, 363, 35, -573, -226, -501, -507, 415, 638, -233],\n [-172, 53, 1214, 58, -113, -147, -126, -309, 117, -66],\n [43, 753, 152, 702, 167, 1101, -237, -110, -984, 552],\n [-278, -88, 195, 151, -206, 500, 32, -206, 181, -55],\n [-27, -408, -631, 166, -468, -429, 124, 143, 714, -143],\n [208, 3, 308, 733, 140, -347, 166, 79, -559, -406],\n [455, 127, 400, -214, 100, -731, -638, -61, 43, 57]]\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[[-114, -75, -120, 213, 114, 222, -129, 75, -135, -123],\n [-322, -158, -476, 104, 260, 56, -118, 220, 38, 222],\n [-122, -49, -208, -61, 86, -94, 5, 85, 99, 199],\n [-25, -59, 82, 440, 74, 500, -223, 10, -361, -477],\n [-277, -131, -422, 44, 218, -4, -79, 190, 71, 243],\n [-148, -47, -284, -189, 90, -246, 63, 105, 217, 373],\n [171, 129, 138, -472, -190, -508, 269, -110, 331, 359],\n [-296, -160, -400, 232, 256, 208, -176, 200, -80, 48],\n [308, 154, 448, -126, -252, -84, 126, -210, -14, -182],\n [-203, -124, -238, 291, 192, 294, -186, 135, -166, -118]]?\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[[176, 137, 141, -220, -137, 110, 12, -274, -97, 39],\n [-251, -32, -120, 296, 32, -148, 20, 277, 146, -77],\n [-185, 475, 159, 164, -475, -82, 128, -143, 131, -122],\n [249, -462, -126, -240, 462, 120, -132, 69, -168, 141],\n [-145, 230, 54, 144, -230, -72, 68, -13, 96, -77],\n [453, 111, 243, -540, -111, 270, -24, -537, -261, 132],\n [-285, 75, -81, 324, -75, -162, 48, 237, 171, -102],\n [142, -566, -222, -104, 566, 52, -144, 250, -110, 120],\n [358, -269, 15, -388, 269, 194, -100, -176, -223, 151],\n [216, 297, 237, -284, -297, 142, 44, -426, -113, 31]]?\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 10x10 matrix:\n[[-318, 622, -214, 20, 410, 220, -314, 964, 64, 624],\n [30, -220, 190, 10, -20, 20, 50, -220, 140, -210],\n [113, -310, 209, -49, -118, -22, 119, -442, 22, -299],\n [-220, 309, -40, 47, 289, 166, -200, 584, 172, 315],\n [95, 94, -545, 361, -294, -406, 89, 162, 14, 27],\n [85, -423, 465, -156, -19, 124, 103, -562, 90, -386],\n [-232, 261, 204, -165, 391, 344, -220, 436, 78, 299],\n [52, -420, 36, 432, -178, -242, 124, -172, 582, -452],\n [57, -210, 201, -69, -36, 36, 63, -294, 24, -195],\n [-34, 203, -422, 307, -85, -230, -26, 396, 116, 155]]\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[[266, 470, -648, -4, -46, -374, -2, -248, -358, 286],\n [-548, -796, 174, 4, 63, 301, -427, 196, 148, -28],\n [-516, -310, 655, -189, -108, 75, 95, 207, 8, -86],\n [153, 561, 275, -111, -64, -105, 381, 287, 145, -365],\n [-465, -1221, 261, 285, 271, 560, -670, 355, 363, -223],\n [243, 627, -339, -189, -186, -345, 309, -420, -318, 357],\n [-284, -216, -130, -182, -90, 124, -144, -137, 65, 180],\n [110, -174, -184, 194, 90, -90, -158, -154, -234, 196],\n [66, -178, -128, 225, 130, -88, -200, 64, -175, 21],\n [33, -301, 248, 369, 220, -102, -172, 355, -191, -218]]\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[[-340, 36, -431, -350, 445, 238, -196, -273, 278, 453],\n [100, 10, 170, 210, -170, -70, 70, 70, -90, -160],\n [-110, 59, -40, 133, 54, 77, -35, -112, 71, 85],\n [-360, 124, -276, 76, 308, 252, -156, -332, 260, 368],\n [-150, 75, -66, 153, 84, 105, -51, -150, 99, 123],\n [90, 59, 258, 449, -248, -63, 93, 38, -101, -209],\n [-300, 50, -342, -214, 358, 210, -162, -250, 238, 376],\n [-260, 64, -253, -78, 271, 182, -128, -227, 198, 299],\n [-80, -18, -157, -220, 155, 56, -62, -51, 76, 141],\n [410, -79, 445, 237, -469, -287, 215, 347, -321, -500]]\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[[-375, 212, -542, 532, -132, 226, -501, 215, -131, 67],\n [-114, 322, -303, -240, 193, 554, -55, 260, 243, -143],\n [354, 524, -202, 130, -158, 184, -437, -11, 319, -445],\n [425, -47, 305, -774, 705, 231, 420, -162, 14, 45],\n [39, 608, -437, 498, 3, 206, -533, 236, 209, 9],\n [-402, 458, -926, 756, -780, 242, -734, 236, 104, -516],\n [250, -365, 585, -112, 51, -735, 667, -194, -33, 386],\n [156, 487, -356, 602, 296, 105, -659, 73, -107, 262],\n [-126, -46, -50, 554, -638, -426, -203, -31, 1, -105],\n [303, 143, -570, -56, -689, -99, -20, -329, 61, -967]]\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[[-50, -472, 470, 40, 593, -256, -594, 524, 501, -208],\n [-746, -688, 343, 833, -616, -131, 540, -129, 385, 287],\n [-172, 308, 170, -348, 51, 630, -675, 453, 129, 245],\n [-61, 159, -500, -83, 48, 83, 411, -295, -65, -126],\n [163, 65, -269, 35, -46, -299, 576, -417, -179, -301],\n [235, -65, -168, 202, -243, -182, 165, -221, -351, 301],\n [404, 202, -531, 59, -345, 89, 45, -284, -684, 670],\n [257, -155, -53, -291, 899, -297, -390, 281, 284, -491],\n [-110, -420, 593, 253, 23, -157, -435, 384, 270, 144],\n [-7, -195, -62, 175, 96, -571, 789, -427, 133, -678]]?\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[[-413, 346, 95, -126, -560, -523, -536, -496, -336, -227],\n [98, -752, -537, -422, 348, -217, -157, -218, -104, 83],\n [-870, 58, -114, -443, -669, -151, 396, -179, 395, 532],\n [604, -252, -580, -634, -242, -411, 544, 106, -11, 831],\n [494, 1078, 222, 677, -229, -149, 124, 675, -345, -96],\n [557, -588, 216, 254, -79, 91, -326, 123, -419, -297],\n [497, -368, -498, -562, -75, -681, 484, -181, -351, 885],\n [-80, -184, -293, -26, 751, -73, 336, -38, 7, 288],\n [-87, -116, 311, 447, -26, -625, -951, -508, -1063, -661],\n [668, 68, 68, -73, -89, -361, -480, -306, -506, -225]]\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[[265, -361, 383, 1243, -85, 464, -642, -880, -188, -548],\n [-461, 226, -171, -50, 722, -490, 259, -6, 238, 445],\n [-222, -21, 39, -297, -454, 67, -48, -86, 397, 19],\n [142, -345, -619, -554, -757, 277, 500, 5, -306, -323],\n [-911, 73, -454, 604, 1106, -622, 100, -203, 632, -455],\n [557, -511, 2, -209, -674, 457, 283, -11, -638, -378],\n [199, 218, 268, 1181, 133, 398, -527, -147, 154, -596],\n [-136, 838, 292, 720, 501, -53, -422, 778, 515, -262],\n [-184, 265, 429, -383, 280, -401, -334, 128, 239, 747],\n [-498, -14, 769, -442, -11, -499, -866, 143, 683, 153]]\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[[735, 402, 91, 693, -579, 618, -83, -218, -199, 181],\n [-470, 299, 42, -320, -683, 735, -619, -713, 195, 286],\n [-396, -295, 126, -280, -85, 606, -328, -541, 178, 478],\n [79, -162, 431, 787, -14, -430, -42, 54, 301, -28],\n [138, -1221, 702, -398, 34, -106, -130, 70, -48, -119],\n [17, 135, 247, 481, 333, -876, 188, 638, -674, -1092],\n [-180, 622, -323, -25, 314, -552, -62, 123, -357, -955],\n [-556, 391, 172, 134, 57, 226, -692, -724, 422, -164],\n [397, -401, -236, 60, -419, 159, 418, 148, -307, 535],\n [91, 0, -191, -369, -563, 938, -166, -535, 497, 1027]]\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 10x10 matrix:\n[[351, -603, 28, -139, 220, -274, 654, 6, -220, 472],\n [20, -88, -670, -196, -172, 394, -130, 60, -586, -754],\n [-222, -138, -88, -1148, -565, 432, 96, 286, -136, -499],\n [11, -347, -38, -1074, -254, -96, 727, -150, -103, 79],\n [-254, 385, -240, 63, -449, -408, 436, -871, -171, 144],\n [-298, 710, 48, -175, -402, 946, -909, -132, -103, -1181],\n [-309, 102, 379, -989, -506, 431, -142, 311, 267, -303],\n [593, -707, -41, 37, 720, -329, 627, 8, -161, 477],\n [334, -413, 271, 659, 423, -588, 456, -7, 66, 945],\n [162, 212, -24, 725, 478, -196, -165, -310, 97, 115]]\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[[50, 176, -151, -95, 101, 394, 635, 547, -859, -129],\n [-274, -365, -71, -347, -230, -1024, -723, -1039, 735, 351],\n [738, 264, -111, 261, -328, -329, -88, -735, 853, -181],\n [-170, -51, -169, -107, -568, -756, -96, -506, -85, -119],\n [-359, -687, 430, -270, 5, -200, -11, 666, -548, -371],\n [-543, 65, 103, -379, 675, 38, 361, 703, -623, 21],\n [-5, 6, 358, -118, -619, 198, 683, 1149, -604, -487],\n [158, -820, 174, -542, 608, -466, -868, -840, 1106, 574],\n [-418, 495, -401, 175, -65, 421, 252, 109, -699, 271],\n [-955, -527, 163, -595, -93, -216, -591, 31, 133, 791]]\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[[14, -38, 36, -38, 2, -40, -28, -24, 18, 40],\n [98, -266, 252, -266, 14, -280, -196, -168, 126, 280],\n [154, -418, 396, -418, 22, -440, -308, -264, 198, 440],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n [-77, 209, -198, 209, -11, 220, 154, 132, -99, -220],\n [-98, 266, -252, 266, -14, 280, 196, 168, -126, -280],\n [98, -266, 252, -266, 14, -280, -196, -168, 126, 280],\n [-42, 114, -108, 114, -6, 120, 84, 72, -54, -120],\n [84, -228, 216, -228, 12, -240, -168, -144, 108, 240],\n [126, -342, 324, -342, 18, -360, -252, -216, 162, 360]]\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, 142, 192, -385, -15, -270, 67, 462, -209, -8],\n [-318, -650, 698, -192, -594, 612, 413, -505, -1285, -769],\n [-87, -289, 362, -85, -450, 440, 554, -189, -690, -397],\n [33, 387, 197, -101, 390, 272, 96, -27, -63, -321],\n [-331, 118, 42, 984, 718, 188, -96, -394, 850, 631],\n [-384, 242, -666, -119, -354, -390, 835, 535, 41, -34],\n [-106, -439, 383, -124, -349, 278, -5, -325, -666, -353],\n [-407, 211, -121, -687, -791, 104, -318, -168, -391, -328],\n [138, 374, -523, 79, 136, 162, -130, -246, 433, -134],\n [91, 404, -563, 114, 79, 716, -72, -821, 171, -695]]\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[[-13, 51, -722, -366, 269, -30, 134, -12, 939, -164],\n [963, 444, 628, -243, -809, 405, 771, 1887, 496, 520],\n [1169, 389, 453, -22, -32, -147, -307, 909, -26, 596],\n [258, 17, -470, -336, 601, -703, -393, -77, 581, 749],\n [1097, -287, 186, -459, 510, -234, 43, 667, 90, 902],\n [-381, 393, -539, -535, -153, 342, 386, 438, 1011, -436],\n [697, -96, 528, 296, -879, 61, 691, 1009, 69, 666],\n [789, -404, 1112, -43, 119, 410, 207, 537, -405, 505],\n [170, 368, 417, -225, 409, -83, -98, 690, 71, 369],\n [-522, -716, 161, 151, 762, -91, -730, -1314, -1162, -18]]\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[[-50, -90, -10, 95, 10, 95, -40, 40, 95, 95],\n [-50, -90, -10, 95, 10, 95, -40, 40, 95, 95],\n [-90, -162, -18, 171, 18, 171, -72, 72, 171, 171],\n [90, 162, 18, -171, -18, -171, 72, -72, -171, -171],\n [-110, -198, -22, 209, 22, 209, -88, 88, 209, 209],\n [190, 342, 38, -361, -38, -361, 152, -152, -361, -361],\n [-210, -378, -42, 399, 42, 399, -168, 168, 399, 399],\n [30, 54, 6, -57, -6, -57, 24, -24, -57, -57],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n [120, 216, 24, -228, -24, -228, 96, -96, -228, -228]]\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[[100, -243, 969, -507, -134, -1159, 103, 660, 588, 355],\n [556, -70, 413, -904, -141, -343, 168, 349, 565, -4],\n [448, 102, -88, -675, -114, -35, -153, -941, 310, 422],\n [491, 716, 481, -465, 375, 883, 746, 473, -227, 650],\n [40, 51, -538, 164, 513, 198, 270, -190, -150, -282],\n [-845, 20, -217, 571, -914, 584, -403, 503, -570, -670],\n [-917, -307, -617, -32, 227, 1199, -382, -860, -483, -243],\n [-1427, -492, 376, 1, -130, 492, -471, 10, -377, -343],\n [-353, 114, 29, 289, 808, 156, 80, -795, -325, -177],\n [973, 413, 62, 63, 23, -507, 393, 338, 256, 90]]\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[[-66, -470, -10, -491, -67, 335, 99, -313, 526, -6],\n [76, -140, -308, -498, -186, 238, 406, -26, 496, 220],\n [-218, -142, 446, 381, 269, -141, -529, -205, -374, -398],\n [124, -568, 448, -133, -103, 432, -420, -410, 327, 82],\n [-90, 102, 142, 280, 138, -177, -199, 25, -305, -174],\n [-66, 518, -546, -38, 16, -329, 553, 405, -143, 30],\n [-502, -270, -42, -228, 314, -113, 63, -267, 65, -556],\n [4, 528, -150, 390, 82, -385, 78, 363, -482, -23],\n [20, 484, -112, 382, 70, -348, 42, 332, -456, -10],\n [156, -492, 322, -197, -147, 423, -280, -335, 373, 153]]\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[[434, 0, -676, 528, -522, -570, -254, -36, 500, -138],\n [401, 508, -38, 214, 311, 355, 203, -306, 118, 121],\n [-66, 99, -272, -106, 1, -169, -108, 164, 90, 146],\n [363, 313, 113, 45, -67, 212, -160, -316, 307, 524],\n [-83, -195, 774, -337, -166, 348, -218, -238, -28, 540],\n [373, 217, -259, 481, 115, 42, 262, -192, 71, -402],\n [155, 385, -559, 266, 363, -50, 303, 88, -9, -359],\n [764, 314, -441, 682, -317, -156, -92, -394, 551, -6],\n [147, -654, -164, 246, -1115, -761, -679, 6, 508, 115],\n [-869, -27, 764, -900, 880, 676, 415, 318, -850, 67]]\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[[-383, 141, -8, 17, -76, -355, 97, 67, -434, -244],\n [101, -337, 197, -106, 19, -172, -223, -320, -244, 365],\n [81, 400, 440, 536, -617, 213, -1018, 22, -941, 164],\n [3, 630, 49, 633, -196, 562, -150, 91, 327, -471],\n [1020, -29, 221, 788, 176, -103, -485, -145, -248, 526],\n [-291, 49, -30, 42, -156, 230, 86, 73, 114, -376],\n [-276, 246, 21, -599, 199, 55, 132, -403, 562, 305],\n [397, 170, -266, 234, 341, 421, 434, 116, 1017, -210],\n [352, -671, -80, -25, 211, 38, 217, -59, 289, 86],\n [99, -296, -470, -450, 288, -117, 644, 494, 404, -95]]?\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 10x10 matrix:\n[[252, -252, 306, -342, -90, -396, 234, -396, 360, 198],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n [196, -196, 238, -266, -70, -308, 182, -308, 280, 154],\n [224, -224, 272, -304, -80, -352, 208, -352, 320, 176],\n [266, -266, 323, -361, -95, -418, 247, -418, 380, 209],\n [56, -56, 68, -76, -20, -88, 52, -88, 80, 44],\n [210, -210, 255, -285, -75, -330, 195, -330, 300, 165],\n [-112, 112, -136, 152, 40, 176, -104, 176, -160, -88],\n [126, -126, 153, -171, -45, -198, 117, -198, 180, 99],\n [-84, 84, -102, 114, 30, 132, -78, 132, -120, -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[[68, 545, -203, -236, -204, -121, -353, 129, 536, 399],\n [394, -227, 236, 543, 742, -190, 403, -3, -245, -91],\n [56, -259, 3, -262, -284, 89, -29, 297, -506, -213],\n [-124, 443, -141, -51, -79, -54, -219, -162, 619, 320],\n [-250, 47, 64, 357, 302, 22, 161, -501, 401, 43],\n [366, 591, -156, -100, 65, -271, -287, 288, 486, 472],\n [314, 206, 7, 141, 290, -197, 2, 138, 149, 196],\n [-472, 5, -173, -506, -744, 269, -293, -51, 26, -81],\n [612, 180, -34, -123, 111, -259, -116, 609, -205, 181],\n [-198, -9, -110, -363, -480, 142, -199, 93, -83, -55]]?\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[[15, -725, 491, -102, -293, -653, 190, -554, 689, -213],\n [41, 56, 173, 310, 509, 648, 105, 523, -171, 556],\n [-333, -340, -191, -175, -376, -778, -240, -373, 392, -508],\n [116, -736, 439, -136, 499, -581, -70, 24, 643, -204],\n [81, -613, 66, -236, 300, -204, -19, 210, 487, -157],\n [-237, -313, 66, 250, 678, -202, 67, 284, 327, 151],\n [88, 658, -78, 300, 508, 350, 227, 192, -477, 320],\n [573, -34, 175, -365, 62, 470, -68, 275, -150, 4],\n [207, 183, -533, -332, -487, 427, 546, -110, -99, -61],\n [381, -342, -2, -336, 804, -197, 150, 335, 347, -218]]\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[[-146, 673, -465, -195, 668, -1441, -237, 392, -38, -423],\n [-616, 253, -166, -375, -35, -1007, -466, 429, 487, -792],\n [381, -380, -200, -9, 205, 864, 138, -314, 327, 376],\n [481, 67, 75, 165, -215, 191, -362, 189, 136, -362],\n [-314, 250, 284, 79, -984, -111, -63, -34, -865, 597],\n [568, 582, -189, -42, -443, -634, -162, 44, -383, 219],\n [-219, -351, -276, 25, 664, -271, -130, 195, 281, -903],\n [183, 64, -233, 45, -96, -387, 40, -200, -579, 249],\n [32, -183, -700, -20, 409, -522, -308, -96, -336, -213],\n [1, 501, 200, 224, -248, -1274, -10, 317, -853, -570]]\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 10x10 matrix:\n[[54, -300, -348, 396, 318, 282, 216, 96, 54, -192],\n [-289, -174, -336, 212, 17, 565, 300, 38, -107, 288],\n [-472, 115, 17, -97, 22, -117, 252, 564, -68, 70],\n [209, -112, -62, 146, 159, -43, -36, -50, 79, -220],\n [-263, 153, 77, -217, -295, 166, 16, -78, -133, 406],\n [-352, 412, 369, -551, -543, -98, -136, -83, -179, 552],\n [288, 277, 420, -394, -341, -345, -436, -439, 9, 90],\n [137, -616, -685, 835, 764, 399, 452, 359, 160, -572],\n [-541, -41, -186, 124, 234, 4, 440, 769, -44, -54],\n [-86, 106, 121, -115, -11, -222, -8, 187, 5, -52]]\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, -508, 434, -67, 574, 137, -496, 533, -177, -430],\n [-142, 813, -782, 636, -1007, -200, 349, -554, 460, 545],\n [16, -380, 120, -593, 632, 193, 593, -746, -571, -528],\n [241, -540, 124, -476, 884, 513, 308, -709, -531, -769],\n [-308, 218, 592, 102, -240, 225, -975, 1444, 565, 733],\n [534, -487, -534, -245, 621, 209, 900, -1674, -663, -1195],\n [-379, 121, -112, -171, -21, -482, 837, -642, -476, 78],\n [-59, 263, -329, 18, -199, 256, 406, -708, 37, -38],\n [-472, -194, 391, 222, 590, -603, 110, 354, -688, 168],\n [-132, 441, 105, 374, -517, 641, -760, 661, 740, 381]]?\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[[-761, -326, 174, 636, 908, -100, -594, -576, -156, 743],\n [-428, 292, 1056, 212, -5, 85, 706, 98, 402, -147],\n [75, 47, -180, -372, 178, -425, -195, 203, -419, -65],\n [-378, -269, 10, 654, 211, 686, -224, -271, 636, 653],\n [862, 190, -160, -884, -467, -932, 225, 402, -838, -757],\n [443, 259, 676, -268, -952, -387, 501, 83, -307, -983],\n [111, -33, -108, -120, -280, 127, -232, 228, 72, -24],\n [-465, -502, -646, 586, 179, 136, -1405, -877, -504, 277],\n [-728, 24, -276, 538, 21, 917, -356, -435, 496, 50],\n [-372, -144, 116, 482, -299, 372, -490, -446, 65, -87]]\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[[255, 987, 315, 420, 194, 24, -153, -560, 562, -64],\n [-264, 468, 624, -189, -139, 909, -345, 7, 652, 368],\n [-410, -513, 195, -297, -152, 421, 189, 612, -424, -172],\n [-17, 336, 242, 285, 128, -36, 275, 49, -231, -557],\n [-96, 287, 181, -76, -211, 221, 15, 58, 183, -113],\n [206, 14, -534, -130, -402, -576, 110, -104, 46, -118],\n [-326, -23, 347, -92, -135, 383, 255, 448, -287, -427],\n [-84, 497, 389, 95, -24, 333, -5, -32, 228, -164],\n [-29, 180, 358, 87, 294, 446, -323, -193, 349, 423],\n [-6, 127, -171, -116, -389, -211, 217, 120, -53, -353]]\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[[54, 360, 324, 360, -306, 306, 144, 306, 0, -126],\n [-30, -200, -180, -200, 170, -170, -80, -170, 0, 70],\n [-18, -120, -108, -120, 102, -102, -48, -102, 0, 42],\n [60, 400, 360, 400, -340, 340, 160, 340, 0, -140],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n [39, 260, 234, 260, -221, 221, 104, 221, 0, -91],\n [-27, -180, -162, -180, 153, -153, -72, -153, 0, 63],\n [-12, -80, -72, -80, 68, -68, -32, -68, 0, 28],\n [-39, -260, -234, -260, 221, -221, -104, -221, 0, 91],\n [-3, -20, -18, -20, 17, -17, -8, -17, 0, 7]]\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 10x10 matrix:\n[[480, 178, 466, -22, 224, 284, -116, -394, 816, -336],\n [388, 540, 253, -367, 66, -108, -1290, 1057, -174, 910],\n [471, 450, -737, 484, -713, -122, -764, 773, -284, 193],\n [-213, 601, -110, -274, 115, 781, 362, -818, 446, 227],\n [-26, -288, -174, -38, -268, -556, -110, 467, -717, -25],\n [1016, 566, 459, 287, -472, -482, -964, 1340, -62, -243],\n [-162, -726, 524, -384, 910, -572, -490, -132, 37, 390],\n [412, -53, -214, 562, -530, 239, 25, 377, 468, -640],\n [-251, -234, 1, -175, 139, 832, 695, -905, 398, 8],\n [-416, -483, 25, -190, 221, -338, -635, 1164, -295, 591]]\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 10x10 matrix:\n[[99, 1003, -380, 122, -297, -319, 935, -111, -546, 189],\n [87, -130, -226, 576, -1640, -82, 267, 1684, -217, 15],\n [593, -25, 400, 241, 164, 286, 489, -338, -283, -870],\n [387, -434, 838, -441, -35, -546, 696, 245, -734, -564],\n [-211, -750, 432, -7, -475, -157, -385, 508, -327, -95],\n [293, 293, 98, 414, -201, 594, 476, -21, 222, 111],\n [87, 78, 411, -834, 628, -446, 63, -462, -105, 105],\n [267, -406, 439, 64, -470, 42, 255, 625, -116, -232],\n [-317, -459, 86, -93, -442, 150, -571, 718, 525, 688],\n [0, 257, -253, -441, 418, 93, -749, -295, 659, 244]]\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[[-57, 252, 315, -219, -183, -450, -216, 111, 330, 201],\n [-5, 276, 255, -131, -143, -462, -72, 167, 226, 101],\n [-101, -428, -225, -3, 113, 658, -200, -345, -94, 69],\n [-1, 216, 195, -97, -109, -360, -48, 133, 170, 73],\n [-115, -218, -15, -122, -6, 301, -284, -226, 102, 167],\n [65, 30, -75, 110, 50, -15, 180, 70, -130, -125],\n [-15, -378, -315, 138, 174, 621, 36, -246, -258, -93],\n [-2, -104, -90, 42, 50, 172, 16, -66, -76, -30],\n [-34, -160, -90, 6, 46, 248, -64, -126, -44, 18],\n [-104, -316, -120, -58, 54, 470, -232, -278, 0, 112]]\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[[205, -52, -8, 669, 52, 673, -188, 74, -279, 237],\n [995, -548, 164, 435, 112, 489, 310, -290, 252, 1048],\n [35, -215, 132, -917, -222, -506, 404, -657, 226, -5],\n [-669, 636, -358, 236, 73, 245, -532, 679, -193, -813],\n [-610, -351, 212, -286, 14, -205, -326, -217, -172, -393],\n [-167, -513, 372, 403, 24, 126, -224, -271, -478, 175],\n [-727, 57, 116, 322, -41, 80, -470, 89, -660, -526],\n [-238, -182, 184, 612, 18, 374, -342, -16, -575, -13],\n [253, -523, 324, -412, -67, -444, 354, -555, 146, 414],\n [589, -359, 104, -238, 47, -142, 376, -271, 451, 581]]?\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 10x10 matrix:\n[[-246, 84, 57, -153, 262, -129, -156, 178, 144, 0],\n [-669, 243, 432, -306, 532, -816, -43, 720, -147, 186],\n [237, -291, -300, -120, -386, 432, -159, -410, 153, 66],\n [79, 302, 379, 2, -71, -228, 277, 351, -238, 401],\n [-141, 285, 100, 152, 458, -70, -23, 194, 163, -240],\n [-143, 608, 376, -211, 447, -3, -121, 513, 374, 359],\n [-13, -593, -202, 37, -475, -288, 164, -285, -536, -116],\n [-215, 269, 109, 380, 605, -273, 108, 219, -10, -526],\n [105, -186, -450, 93, 97, 549, -321, -473, 456, -459],\n [-111, -309, -249, -219, -100, 105, -257, -216, 135, -54]]\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[[151, 218, -951, -76, 433, -34, -1043, -115, 174, -200],\n [-205, -46, 209, 24, -127, -106, -223, -159, 250, 68],\n [407, 422, 627, -180, -221, -1106, 468, -7, -187, -34],\n [182, -296, -128, -294, 60, 660, 690, 384, -520, 376],\n [121, 280, -596, -235, 278, -112, -698, -107, 136, -43],\n [-241, -531, 626, 712, -334, -183, 171, -55, 128, -201],\n [345, 237, -600, -464, 320, 317, 135, 233, -368, 137],\n [166, -271, 271, 184, -153, -555, -91, 6, -53, 31],\n [-83, 64, 142, 237, -72, -400, -323, -185, 249, -207],\n [210, -175, -497, -390, 219, 565, 126, 276, -364, 345]]?\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[[-124, -480, 414, 148, 52, 428, -450, 4, -232, 278],\n [439, -316, 170, 497, -602, 76, 336, 22, -224, 129],\n [306, -656, 531, 431, -327, 419, -294, 44, -406, 339],\n [-138, 642, -811, -585, 19, -139, 336, 110, 490, -199],\n [-114, 234, -19, -289, 443, -211, -264, -26, 74, -151],\n [-25, -506, 489, 365, -82, 292, -237, -46, -292, 230],\n [448, 4, -60, 268, -448, -168, 408, 28, -72, -44],\n [-30, 149, 146, 2, 321, -351, -66, -101, -32, -190],\n [-321, 325, 49, 65, 401, -549, 243, -213, 100, -332],\n [-321, 236, -526, -601, 120, 354, -174, 154, 340, 89]]\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[[-86, 80, -246, -103, 263, -101, -27, 156, 24, 114],\n [-73, -32, 327, 460, -413, 50, 324, -285, 222, -33],\n [124, 260, -116, -483, -137, -61, -647, -214, -596, 24],\n [246, -422, 126, -138, 265, 234, 102, 376, 116, -264],\n [421, -408, 53, -551, 334, 273, -307, 419, -242, -339],\n [-131, 42, 213, 428, -330, -14, 300, -257, 218, 39],\n [103, 194, -193, -479, 45, -63, -547, -53, -478, 33],\n [115, 92, -269, -519, 262, -43, -467, 149, -374, 15],\n [-264, 360, 88, 403, -493, -179, 103, -514, 28, 216],\n [-130, 460, -114, -95, -335, -205, -387, -444, -384, 210]]\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[[-19, 306, -242, -115, 590, -429, 455, -265, -373, -509],\n [201, -77, -552, 53, -143, 603, -227, 247, -137, 373],\n [88, 407, 248, 289, -470, -163, -536, 545, 1150, 563],\n [-366, 410, 311, 497, -131, 206, -505, 521, 376, -325],\n [-1083, 297, -150, 1094, -657, 377, 56, -7, -384, -87],\n [-300, 817, -48, 117, 97, -138, -279, 693, 496, 314],\n [676, -462, -290, -198, 41, -279, 309, -482, 230, -217],\n [-455, -186, -246, 182, 289, -323, 987, -786, -926, -547],\n [360, 38, -368, -247, 344, -88, -54, -135, -96, -811],\n [-707, 911, 487, 130, 27, -100, -452, 955, 542, 456]]\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[[-25, -238, 224, 473, -450, 159, 334, 457, 356, -186],\n [-299, -299, -415, -332, -387, -314, -9, -444, 244, -156],\n [367, 1084, -422, -83, -77, -134, 770, -173, 842, -1025],\n [-535, -576, -86, -491, 7, 243, -474, -3, -263, 527],\n [-291, -47, 165, 102, -678, 87, 501, 161, 265, -116],\n [585, 89, -293, 288, -22, 369, 669, 4, 385, -742],\n [564, 83, -432, 318, 82, 82, 238, -542, 469, -798],\n [26, 646, 622, -153, 209, -1103, -20, -67, -695, 375],\n [-800, 102, 573, -106, -195, 173, -461, 596, -140, 834],\n [-19, 345, 564, 296, 466, -97, -588, 384, -262, 486]]\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[[-221, 394, -716, 420, -112, -449, -499, -101, 231, 490],\n [219, -463, 119, -859, 1042, 796, 239, -116, 330, 472],\n [389, -205, 578, -331, 72, 8, -89, -244, -205, 32],\n [-186, 88, -325, 26, 186, 571, 449, 158, 233, 140],\n [46, 333, 532, -25, -450, -538, -83, -725, 284, -88],\n [-145, 198, 192, 482, -714, 286, 794, 201, -131, -536],\n [135, 215, 888, -906, 387, -100, -524, -573, -38, -335],\n [-8, -89, -390, -234, 501, -567, -813, -248, 294, 535],\n [-343, 182, -138, -27, 31, 222, 489, -150, 555, -79],\n [52, -472, -42, -36, 188, 587, 751, 296, 114, 12]]\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 10x10 matrix:\n[[-390, 210, -164, 12, -356, -42, -394, 42, 252, -148],\n [-254, 342, -340, 172, -76, 94, -466, 138, 364, -188],\n [468, -114, 40, 96, 532, 132, 332, 24, -168, 116],\n [217, -246, 238, -110, 100, -53, 351, -93, -266, 140],\n [-333, 174, -134, 6, -308, -39, -331, 33, 210, -124],\n [340, -15, -48, 124, 438, 136, 172, 54, -56, 54],\n [-264, -33, 88, -132, -374, -132, -88, -66, 0, -22],\n [-180, -195, 256, -228, -386, -192, 116, -138, -168, 62],\n [-150, 240, -244, 132, -16, 78, -314, 102, 252, -128],\n [43, -9, 2, 10, 50, 13, 29, 3, -14, 10]]\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[[432, -222, -24, 302, 150, 269, 393, -219, -342, 174],\n [-275, -865, -174, -153, -170, 169, -76, 230, 164, -418],\n [-928, -535, 35, -19, 417, -394, 399, -428, -872, 251],\n [160, 348, 59, -260, -180, 347, 368, 721, 244, -93],\n [40, 50, 494, -10, -199, 91, -81, 432, 133, -433],\n [0, -423, -823, -446, 377, 528, 1110, 614, -239, 5],\n [-255, 72, 330, -144, -83, -9, 127, 213, 69, -313],\n [-528, 273, 608, 265, 84, -114, 403, 74, -1064, 208],\n [792, -280, -82, 184, 157, 429, 184, 951, 150, 40],\n [-672, -347, 364, -103, 207, -689, -320, -527, -139, 189]]\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[[223, -123, -11, -261, 95, -516, -387, 105, -75, 299],\n [-124, 229, -165, -276, 262, -135, -16, 445, 430, -499],\n [64, 50, 375, -73, 183, -152, 91, -700, -655, 453],\n [-164, -159, 362, 194, 332, -104, 17, -597, -839, 553],\n [-405, 233, 165, 274, 198, 521, 483, -347, -219, -282],\n [209, -70, 260, -544, 300, -677, 36, -68, -141, 236],\n [168, 276, -142, -224, -48, -94, -242, 48, 206, -140],\n [-350, 15, -59, 126, 334, 66, 15, 233, 6, -238],\n [-45, -132, 445, 226, 82, 86, 245, -828, -836, 586],\n [181, 117, 86, -546, 176, -453, 95, 133, 226, -133]]\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[[350, -188, -176, -119, 289, -253, 265, 188, -266, -43],\n [-5, -60, -210, 75, -185, -210, 65, -300, -115, 345],\n [-120, 436, 212, 79, -273, 339, -421, 52, 244, -201],\n [-91, 220, 2, 97, -283, 78, -213, -164, 83, 99],\n [98, 178, 20, 1, -55, 63, -129, 88, 8, -105],\n [-167, -406, -18, -37, 207, -124, 307, -96, -27, 143],\n [-418, -364, 248, -37, 243, 157, 187, 4, 214, -65],\n [-379, 142, 162, 124, -288, 229, -232, -228, 261, 88],\n [109, -321, -80, -99, 305, -182, 310, 98, -150, 4],\n [108, 73, 90, -62, 130, 94, -41, 234, 17, -239]]\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[[-368, 108, -629, -64, 277, 662, -303, 407, 87, 521],\n [330, 269, -614, 1095, -1144, 957, -81, 603, 1134, 477],\n [349, -299, 26, -111, 1006, 528, -335, -30, -687, -812],\n [-284, -643, -420, -542, 46, -143, 577, 301, 437, 756],\n [-128, -783, -82, 254, 417, -579, 23, -267, -188, 434],\n [227, -846, -267, -132, 421, -838, 194, -87, -573, 232],\n [60, -51, 266, 1389, -280, -4, -163, 122, -187, -519],\n [-393, 441, 305, -67, 583, -489, -335, -107, -967, -416],\n [255, -415, -366, 1016, 677, 255, -722, 142, -1172, -536],\n [245, -695, 663, -493, 235, -225, 840, -672, 639, -296]]\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[[215, -255, -10, 485, 525, -290, -225, 140, 410, 355],\n [87, 176, -167, -10, -28, 106, 138, -63, -111, -270],\n [256, 118, -258, 266, 262, -8, 78, -14, 70, -202],\n [120, -205, 31, 317, 347, -212, -177, 105, 291, 291],\n [42, 161, -125, -61, -79, 112, 129, -63, -129, -243],\n [179, 272, -291, 46, 20, 146, 210, -91, -139, -422],\n [19, -108, 49, 106, 120, -94, -90, 49, 121, 158],\n [48, -131, 41, 163, 181, -124, -111, 63, 165, 189],\n [150, 50, -140, 170, 170, -20, 30, 0, 60, -90],\n [-58, 46, 16, -114, -122, 60, 42, -28, -88, -62]]\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[[-336, -966, 273, -198, 375, 117, 288, -162, 42, 171],\n [-189, -644, 132, -97, 290, -42, 622, -48, 268, 89],\n [-136, -326, 103, -178, 195, 127, -112, 28, -148, 161],\n [-205, -376, 163, -355, 278, 323, -642, 89, -509, 320],\n [-36, -160, 75, 226, -170, -75, 104, -321, 161, -221],\n [254, 628, -239, 120, -156, -193, 284, 227, 213, -93],\n [-89, -366, 53, -19, 167, -89, 566, -20, 280, 20],\n [80, 102, -41, 278, -215, -189, 352, -198, 318, -259],\n [104, 344, -107, -78, -10, 27, -192, 213, -133, 81],\n [87, 340, -45, 65, -196, 63, -506, -33, -227, -64]]\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[[286, 15, 191, -167, 73, 50, 408, 348, -427, 46],\n [-260, 568, 284, 605, 213, -266, -439, -287, 600, 455],\n [-980, 57, 477, -5, -348, 99, -422, 122, 331, 223],\n [-713, -247, -374, 250, 269, 285, -647, -573, 485, -787],\n [203, 88, -764, 780, -133, 12, -493, -410, -18, -293],\n [194, 427, -471, 653, -644, 16, -442, -364, 510, -107],\n [-164, 50, -126, 10, 191, 159, -157, -205, 668, -1016],\n [721, 560, 120, -299, 371, -431, 705, 518, 628, -196],\n [-674, -176, -441, 336, -71, 94, -789, -480, 656, -795],\n [-280, 239, 235, 645, 844, -288, -526, -160, 502, -953]]\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 10x10 matrix:\n[[115, 867, -39, 108, 352, -753, 384, 758, -569, 345],\n [-115, -1005, 355, 130, -79, 640, -455, -840, 184, -551],\n [-141, -465, -825, 467, 488, -648, -82, 458, -150, -602],\n [25, -255, -739, -469, -450, -194, 166, 692, -232, -38],\n [-395, -200, 778, 142, -293, 166, -331, -17, -644, 525],\n [-119, -694, 855, 301, -411, 1189, -617, -1061, 468, 295],\n [-51, 49, 508, 446, 167, -174, -115, 272, -753, 328],\n [-324, -325, 69, 72, -233, -102, -208, 312, -496, 223],\n [-253, 311, 169, -601, -361, -31, 119, -16, 15, 224],\n [348, 200, -571, -499, -249, -430, 463, 970, -633, 24]]\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[[-247, -156, -8, 143, 483, -177, -430, -206, -193, 53],\n [268, 812, -216, 331, -17, -419, 28, -563, 41, 386],\n [-488, -1133, 308, -205, 570, 197, -364, 393, -148, -546],\n [-192, -509, -315, -202, 323, -469, -235, 26, -591, -180],\n [365, 692, -114, 61, -468, -133, 430, -195, 238, 165],\n [290, 280, -690, 10, -158, -382, -72, -167, -639, 501],\n [-72, 535, 302, 289, -427, 947, 66, -547, 1190, 279],\n [17, 65, -104, -344, -416, -70, 284, 356, -198, -79],\n [72, 16, -350, -177, -565, 417, 168, -116, 194, 191],\n [332, 605, 305, 160, -356, 245, 367, 157, 382, 154]]?\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[[124, 332, 431, -245, -194, 18, 651, 191, -269, 665],\n [191, -609, -938, 1142, 1360, -15, -150, 753, -61, 502],\n [75, 178, 221, -604, -11, 1179, -81, 354, -29, -762],\n [-396, -333, 84, 310, 406, 21, 463, -129, 416, -419],\n [34, -322, -876, -466, 185, -1182, -646, -700, 627, 299],\n [84, 172, -66, -156, -752, -660, -399, -542, -213, 321],\n [-81, 317, 688, -829, -760, 1086, -761, -248, 207, -1536],\n [-323, -131, 997, -1319, -900, 523, 134, -392, 455, -830],\n [-35, -78, 34, 522, 385, 560, 96, -24, 111, -591],\n [-459, -476, 111, -166, -759, -1132, 128, -1199, 459, -113]]\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[[194, -37, 38, 155, 268, -341, 346, 152, 109, -51],\n [-28, -78, -236, 6, -216, 90, -112, -428, 174, 18],\n [-264, 124, 152, -236, -208, 428, -416, 152, -316, 60],\n [178, -95, -134, 163, 116, -283, 272, -158, 239, -39],\n [-22, -21, -74, -9, -84, 51, -58, -140, 45, 9],\n [-232, 5, -154, -172, -404, 427, -443, -373, -41, 66],\n [234, -174, -312, 231, 48, -348, 321, -447, 426, -45],\n [208, -186, -364, 216, -24, -294, 262, -550, 450, -36],\n [122, -110, -216, 127, -16, -172, 153, -327, 266, -21],\n [228, 4, 176, 166, 416, -424, 442, 410, 20, -66]]\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[[-399, -310, 191, -486, -303, 781, -629, -282, -231, -221],\n [-453, 63, -669, -150, 41, -164, 32, 493, -558, 339],\n [89, -46, 138, -136, 625, -479, 227, 654, 38, 460],\n [203, -24, 10, 146, -145, -177, 205, -194, 77, -104],\n [-4, -51, 213, 10, -132, 367, -520, -865, 284, -515],\n [-28, -333, 330, -356, 236, 21, -288, -175, 53, -40],\n [103, 212, 60, 216, 437, -193, -260, -408, 424, -180],\n [-34, -11, -187, 122, -266, 61, -278, -833, 68, -455],\n [305, 429, -117, 592, 219, -358, 34, -551, 527, -289],\n [-354, 222, -155, -116, 596, 44, -409, 320, 6, 225]]?\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 10x10 matrix:\n[[379, 517, 162, 307, 834, 422, 469, 63, -142, 135],\n [-197, -7, -269, -458, -315, -360, 540, 155, 117, -9],\n [1317, 78, 41, -789, 190, 730, 101, -151, 794, -118],\n [123, 363, 198, 578, 413, 492, -445, -532, -99, -111],\n [-39, 257, -109, 261, 269, 191, 216, -186, -121, -275],\n [374, 356, -562, 246, -125, 567, -83, -734, 430, -533],\n [-131, 461, -441, 1025, 40, 430, 154, -847, -137, -222],\n [858, -143, 103, -283, 574, 315, 431, 152, 264, -97],\n [172, 704, 331, 256, 887, 541, 4, -413, -152, -293],\n [465, -69, -174, 67, -131, 671, 447, -867, 113, -701]]\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[[889, -247, 266, -338, 902, -574, -419, -240, 725, 118],\n [791, -144, 374, -547, 548, -353, 19, -365, 478, 109],\n [410, 527, 216, 101, -432, 183, 125, -247, 207, 528],\n [683, 317, -446, -312, 1024, -590, -460, -798, 445, 299],\n [-348, -320, 730, -228, -108, 121, -477, 319, 165, -562],\n [78, 338, -728, -14, 312, -51, 358, -424, -269, 252],\n [-110, 432, -388, -330, -134, 70, 420, -7, -298, 397],\n [143, 869, -292, 874, 356, 452, -611, 5, 403, 383],\n [-541, -254, -856, 416, -342, 60, 739, 326, -782, 21],\n [126, -1119, 171, 202, 536, -676, -595, 54, 292, -663]]?\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[[-295, -107, -164, -3, -290, -119, -224, -267, -525, 388],\n [35, -393, -76, -113, 106, -141, 128, -201, -63, -52],\n [10, 286, 72, 79, -40, 112, -63, 171, 105, -9],\n [275, -57, 116, -41, 298, 51, 248, 159, 441, -364],\n [-210, 114, -72, 51, -240, -12, -207, -81, -315, 279],\n [-45, 175, 20, 53, -78, 55, -82, 69, -21, 62],\n [-70, 242, 24, 74, -116, 74, -120, 90, -42, 96],\n [455, -9, 212, -44, 478, 117, 389, 312, 756, -601],\n [200, 76, 112, 3, 196, 82, 151, 183, 357, -263],\n [-25, 271, 52, 78, -74, 97, -89, 138, 42, 37]]\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[[127, -155, -231, -118, 207, 652, 557, 333, -297, 360],\n [113, -1032, -291, -570, -566, -561, 430, -147, -145, -279],\n [385, -331, 181, 721, 367, 402, -670, 25, 612, -629],\n [203, 142, 347, 357, 132, 111, -465, -659, 578, -768],\n [-406, 433, 168, 538, -47, 21, -504, 133, 240, -116],\n [94, 87, -253, -989, -75, -185, 953, -74, -726, 743],\n [506, -704, -526, -1034, 87, -642, 675, 342, -591, 864],\n [231, 36, 334, 390, 115, 201, -432, -761, 675, -926],\n [-40, 235, -105, -561, -67, -287, 427, -256, -262, 351],\n [-140, -42, -204, -436, -224, -1298, -283, -401, 316, 87]]\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[[-197, -580, -99, 517, 218, 851, 97, -528, -527, 737],\n [690, -551, 310, 77, -256, -911, 122, -52, 839, -453],\n [-1201, 285, -316, 1305, 543, -44, 250, 187, 190, 195],\n [-729, -303, -771, 411, -324, 333, -199, -81, -633, 395],\n [418, -627, 622, -284, -862, -52, -629, -488, -759, 926],\n [-985, 369, -175, 284, 160, 814, -60, -143, -605, 262],\n [-490, 845, -140, -102, 111, -272, -650, 710, -255, -49],\n [277, -419, 211, 294, 655, 556, -735, -11, -136, 132],\n [432, 506, 601, -201, -121, -942, -361, 429, 171, 194],\n [189, -341, 32, -49, -510, 93, -1625, -73, -1028, 511]]?\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[[509, -1081, -302, 109, -682, 745, 84, 48, 824, 1201],\n [182, -905, 18, 387, 403, 184, 219, 317, 362, 867],\n [-633, 2, 23, 315, 1113, -518, 701, 858, -399, -794],\n [-859, -509, -267, 145, -368, -222, 946, 506, 81, 276],\n [-35, 480, 359, -445, -746, -38, -327, -294, 163, -440],\n [175, -98, 83, -842, -856, -420, -190, 663, 139, -2],\n [86, 186, -60, -240, -904, -161, 190, -776, -300, 46],\n [-250, -393, -122, 308, 435, -123, 446, 883, 94, -98],\n [758, 471, -711, -49, 67, -180, 195, 36, -941, -805],\n [794, 482, -91, -322, 279, -82, -722, -205, -439, -206]]\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 10x10 matrix:\n[[42, -726, 162, 572, 44, -24, -306, -192, -268, -62],\n [328, -181, -286, -17, -351, -349, 28, 305, 320, -390],\n [103, -517, 168, 502, 368, -81, -242, 154, -282, -314],\n [422, -374, -100, 328, 316, -418, -112, 720, 28, -832],\n [233, -62, -240, -85, -317, -252, 56, 209, 282, -250],\n [-22, 205, -67, -189, -105, 14, 95, -9, 108, 75],\n [-176, -502, 400, 578, 518, 214, -308, -234, -544, 88],\n [210, 534, -260, -432, 44, -230, 264, 584, 340, -392],\n [177, -315, -68, 194, -80, -179, -90, 134, 42, -250],\n [199, 137, -430, -404, -858, -241, 196, -40, 566, 36]]\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[[15, -68, 262, 76, -83, -125, 383, -18, -174, -228],\n [-645, 626, -154, -618, -516, -107, 244, -349, -753, -480],\n [707, -732, 172, 673, 504, 155, -162, 326, 683, 413],\n [53, -126, -530, -100, -8, 439, -420, -149, -115, 86],\n [-18, -60, 534, 115, -167, -298, 741, -22, -315, -429],\n [-492, 546, -348, -524, -281, 14, -207, -217, -339, -102],\n [-271, 102, -320, -345, -409, 267, 195, -387, -790, -487],\n [-410, 374, 34, -361, -372, -136, 346, -231, -566, -419],\n [-43, 28, 542, 102, -103, -367, 623, 46, -148, -298],\n [136, -138, -256, 54, 127, 222, -339, 21, 169, 208]]\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 10x10 matrix:\n[[105, -373, -496, 87, 429, -222, 370, 216, -137, 272],\n [8, -120, 362, 296, -2, 369, -575, -578, 389, -783],\n [-50, -130, 340, 348, 453, 399, -299, -170, 379, -855],\n [359, -242, 83, 90, 241, -461, 150, 6, 102, 258],\n [-31, -295, -104, -277, -79, 532, 950, -208, -471, 150],\n [350, -1005, -884, 182, -209, -305, 238, -730, -151, 751],\n [-256, 192, -269, -5, -356, 347, -27, -114, -53, 18],\n [127, -497, -104, 3, 251, -44, 306, -64, -126, 146],\n [-186, 761, 297, -89, -32, 318, -271, 118, 49, -763],\n [119, 296, 937, -142, 346, -656, -219, 810, 228, 225]]\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[[68, 88, -84, 72, -24, 72, -72, 12, -40, 44],\n [-374, -484, 462, -396, 132, -396, 396, -66, 220, -242],\n [323, 418, -399, 342, -114, 342, -342, 57, -190, 209],\n [102, 132, -126, 108, -36, 108, -108, 18, -60, 66],\n [374, 484, -462, 396, -132, 396, -396, 66, -220, 242],\n [289, 374, -357, 306, -102, 306, -306, 51, -170, 187],\n [-17, -22, 21, -18, 6, -18, 18, -3, 10, -11],\n [272, 352, -336, 288, -96, 288, -288, 48, -160, 176],\n [-51, -66, 63, -54, 18, -54, 54, -9, 30, -33],\n [357, 462, -441, 378, -126, 378, -378, 63, -210, 231]]\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[[-672, 876, -74, -583, -126, -516, -331, 170, 349, 631],\n [10, 533, -234, -633, 260, -418, -222, -225, 378, 129],\n [-150, 518, 722, 639, -209, -243, 691, -77, 746, -890],\n [845, 461, -4, -636, -366, 203, -282, -627, 367, -125],\n [930, 154, -383, -632, 172, 440, -511, 243, -610, -495],\n [-316, 42, -837, -818, -338, -700, -566, -47, -329, 1001],\n [-299, -348, 420, 1004, 1, 766, 224, 889, -434, -760],\n [-849, 292, -470, -207, 67, -1214, 61, 731, 117, -117],\n [665, 356, -367, -739, 285, 124, -722, -749, 844, 269],\n [-416, 328, -457, -416, -267, -392, -750, 56, 1330, 373]]\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[[-86, -162, 5, 84, 301, -600, 185, 144, -25, 112],\n [-578, -46, 277, -179, -286, 603, 50, 295, -294, -568],\n [-534, 8, -39, 8, 157, 327, 509, 103, -28, -870],\n [172, -134, -52, -203, -153, 87, -107, 36, -13, 220],\n [-354, 1312, 657, 817, 330, -160, 230, 12, 281, -570],\n [-628, -212, -21, 246, 431, -334, 437, 100, -155, -618],\n [46, 238, -199, -11, 134, 277, 406, -111, 276, -452],\n [12, 554, 225, 644, 369, -596, -59, -189, 157, 102],\n [-478, -366, -70, -17, 167, -51, 269, 125, -207, -446],\n [435, 737, 235, 393, 517, -1032, 290, 110, 482, 467]]\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[[101, 1, 56, -140, -81, -291, -274, 101, 229, 253],\n [-661, 273, -65, 703, 197, -118, 265, 158, -542, -34],\n [-259, 130, -193, 283, 255, 90, 62, -10, -284, -83],\n [387, -140, -38, -414, -35, 79, -221, -105, 309, 32],\n [342, -154, -187, -327, 134, 479, 23, -269, 75, -275],\n [-220, 79, 119, 223, -84, -195, 86, 129, -101, 82],\n [-151, 25, -154, 202, 195, 399, 308, -145, -329, -329],\n [-119, -58, 304, 152, -297, 75, 445, 27, -127, -172],\n [-207, 168, 9, 165, 27, -540, -342, 248, 66, 405],\n [319, -43, -317, -349, 273, 114, -419, -138, 218, 62]]\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[[94, -181, -299, -196, -401, -63, -308, 378, 156, 289],\n [-124, 34, -86, 356, -592, 324, -424, -202, -224, 298],\n [90, -231, -216, -609, -657, -360, -645, 602, -78, 451],\n [6, 1, 641, 290, 285, -111, 178, -466, -160, -325],\n [13, -108, 111, -1013, -455, -696, -655, 588, -442, 326],\n [-44, 117, -492, 523, 145, 582, 347, -142, 362, -21],\n [-66, 82, -52, 146, -21, 159, 16, -119, -52, 12],\n [-249, 242, 42, 122, -339, 219, -316, -278, -508, 176],\n [-144, 165, -341, 896, -153, 801, 132, -470, 140, 67],\n [-121, 154, -532, 676, -148, 738, 128, -245, 216, 130]]\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[[-65, -259, 12, -6, -600, -468, 286, -412, -193, -489],\n [-193, -1, 47, 208, -47, 35, -46, 24, 751, 323],\n [-736, 789, -505, 207, -62, -718, 1152, -114, 499, 418],\n [706, -549, -277, -656, -164, -1623, 394, -521, -464, 176],\n [263, -413, -312, -38, 463, -270, -609, 537, -83, -14],\n [-131, -241, 1260, 15, -11, 404, 248, -211, 301, 576],\n [-116, 733, -970, -13, 1157, 14, -161, 472, 276, 584],\n [127, 20, 127, 210, 754, 347, -484, 253, 79, 560],\n [-104, -224, 526, -197, -495, 437, 160, -299, -144, -1263],\n [-807, 818, -398, 740, -22, 530, 270, 881, 854, -14]]\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[[284, 426, -388, -206, -314, -162, -488, 116, -154, -460],\n [129, 222, -222, -121, -173, -97, -299, 27, -65, -244],\n [-265, -177, 8, -20, 58, -30, -143, -307, 182, 158],\n [-352, -297, 110, 33, 143, 11, -22, -352, 231, 286],\n [116, 231, -250, -139, -189, -113, -354, -4, -53, -258],\n [495, 411, -144, -40, -194, -10, 49, 501, -326, -394],\n [-278, -381, 322, 167, 269, 129, 380, -146, 157, 406],\n [-38, -285, 418, 247, 285, 209, 684, 190, -19, 342],\n [103, 240, -278, -157, -205, -129, -409, -35, -41, -272],\n [-247, -255, 152, 68, 150, 46, 111, -205, 154, 258]]\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 10x10 matrix:\n[[208, 260, -328, 414, 382, -140, 267, -22, 194, 184],\n [63, -197, -121, -263, -129, 304, 174, 154, 229, -400],\n [-343, -471, 605, -361, -271, -5, -792, 342, -291, -177],\n [176, 54, -364, -341, -401, 448, 775, -334, 241, -354],\n [-24, -24, 108, 150, -330, -81, 45, -222, -132, 87],\n [343, 489, -709, 96, 714, 122, 677, -28, 438, 56],\n [234, -122, -470, -436, -104, 586, 658, 104, 508, -642],\n [62, 186, -66, 408, 348, -278, -84, 28, -8, 302],\n [133, -65, -39, 746, 256, -342, -195, 256, 136, 152],\n [199, 39, -337, 63, 141, 158, 362, 74, 315, -190]]\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[[20, 428, -234, -33, -94, -382, 23, -219, 359, 213],\n [-314, 184, -165, 179, -94, -444, 49, -289, 137, 56],\n [-630, 756, -322, 19, -340, -218, -13, -581, 239, -97],\n [473, 12, 125, -173, 519, -98, -116, 204, -14, 2],\n [-332, 466, -257, 188, -700, -222, 287, -286, 401, 106],\n [-158, 586, -281, -430, -94, 354, -304, -330, 150, 71],\n [-286, 440, -141, -343, -222, 616, -217, -235, -33, -142],\n [223, 230, 214, -61, 157, 160, 92, 192, -56, -321],\n [-11, 563, -68, -101, -310, 156, 125, -79, 230, -118],\n [-101, -186, 122, 623, -39, -880, 441, 40, 93, -74]]\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 10x10 matrix:\n[[231, 147, 48, -90, 180, 114, 39, 266, -65, -49],\n [-678, -27, -536, 344, -38, -441, -64, -599, 18, -397],\n [567, 591, 719, 199, -79, 96, 238, 4, 439, 30],\n [-601, 287, -494, -154, -200, -458, -305, 10, -399, -545],\n [587, 74, 593, 27, -12, 202, 438, 22, 429, 203],\n [-278, -491, -206, -706, -437, -160, 12, 288, -374, 5],\n [-311, -382, 161, -592, -829, -178, -169, 100, -220, 248],\n [-464, -294, -219, -703, -705, -622, 439, -62, -122, -491],\n [337, 528, 338, 519, 290, 242, -196, -56, 228, 135],\n [-171, -135, -50, -175, -203, 0, -250, 102, -206, 136]]\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[[-791, -434, 632, 899, -215, 186, 962, -361, -507, -317],\n [232, 88, 175, -187, -47, 117, -588, -322, 224, -650],\n [839, -141, -572, -337, -321, 185, -142, -411, 184, 355],\n [95, 943, -429, -584, 4, -25, -1503, 107, 818, 941],\n [-1159, -109, 1044, 705, -753, 339, 401, 301, -328, -704],\n [-549, 154, 295, 554, 320, -294, 377, -715, -237, -204],\n [84, -42, -246, 142, -332, -134, 155, 99, 19, 109],\n [-587, -758, 634, 1074, 151, 140, 4, 99, 45, -78],\n [756, -605, -26, -108, -80, 48, 653, -13, -546, 448],\n [-20, -130, 62, 241, 595, -917, 648, 221, -475, 39]]\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[[-247, 1283, -558, 202, -963, -5, 690, 227, 209, -418],\n [-318, -842, 287, 394, 670, 629, 1261, -1172, -528, -83],\n [826, -618, -328, 148, 417, -622, -408, 141, 75, 819],\n [27, 163, -356, -29, -149, 64, -307, 290, 145, -292],\n [247, -476, 763, -228, 147, 115, 1086, -375, -709, 393],\n [293, -442, 270, -790, -175, 15, -1156, 960, -19, 798],\n [-50, 344, -38, 497, -496, -307, -169, 220, -19, -98],\n [527, -655, 265, -102, 34, -353, -204, 189, -394, 870],\n [-128, 687, -732, 284, -106, -5, -229, 194, 597, -750],\n [-208, 8, -235, 1559, -71, -534, 232, -653, -117, -358]]\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[[17, -134, -386, -301, -379, -6, 117, 296, 104, 207],\n [100, 68, 659, 564, 679, 148, -14, -544, -384, -309],\n [294, -204, 762, 629, 801, 205, -497, -524, -454, -228],\n [-397, 306, -761, -709, -838, -384, 23, 624, 740, 222],\n [-311, 246, -571, -537, -632, -302, -1, 472, 576, 162],\n [291, -410, 96, 74, 132, 121, -526, 36, -154, 135],\n [82, -296, -607, -477, -590, 7, 63, 492, 150, 363],\n [422, -592, -59, 42, 23, 320, 24, 48, -432, 231],\n [501, -566, 384, 418, 480, 419, -30, -308, -686, 33],\n [-119, 250, 362, 236, 328, -115, -308, -236, 86, -225]]\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 10x10 matrix:\n[[-586, -338, 639, 81, -1008, -395, 270, 174, 933, -639],\n [162, 333, -464, 80, 358, -16, 443, 64, -35, 221],\n [765, -118, -81, -16, 329, 2, 171, 117, -229, 592],\n [-109, 53, 51, 77, -116, 258, -184, -493, 51, -153],\n [-119, 19, 468, -22, -345, -61, -396, 90, 97, -185],\n [125, -26, -52, -163, 324, 88, -408, 142, -486, 158],\n [-187, 128, -4, -203, -260, -323, 389, 642, 523, -370],\n [-838, -63, 9, 358, -224, 379, -353, -1091, -74, -393],\n [229, -338, 424, -99, 5, 116, -708, -61, -447, 191],\n [-307, 146, 567, 45, 8, 432, -1535, -563, -820, -74]]\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[[-32, -80, -48, 20, -80, -20, -56, -32, 68, -60],\n [-16, -40, -24, 10, -40, -10, -28, -16, 34, -30],\n [-88, -220, -132, 55, -220, -55, -154, -88, 187, -165],\n [-32, -80, -48, 20, -80, -20, -56, -32, 68, -60],\n [-96, -240, -144, 60, -240, -60, -168, -96, 204, -180],\n [16, 40, 24, -10, 40, 10, 28, 16, -34, 30],\n [-128, -320, -192, 80, -320, -80, -224, -128, 272, -240],\n [160, 400, 240, -100, 400, 100, 280, 160, -340, 300],\n [-16, -40, -24, 10, -40, -10, -28, -16, 34, -30],\n [152, 380, 228, -95, 380, 95, 266, 152, -323, 285]]\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, 248, -45, -7, -195, 73, -357, -52, -2, -239],\n [340, 190, -50, 0, -135, 50, -315, -85, -10, -250],\n [414, 170, -65, 7, -102, 37, -336, -135, -20, -311],\n [14, 560, 35, -63, -567, 217, -441, 280, 70, 49],\n [-122, -410, -5, 39, 396, -151, 378, -145, -40, 53],\n [492, 12, -90, 30, 72, -30, -252, -258, -48, -390],\n [-352, -74, 60, -14, 15, -4, 231, 151, 26, 272],\n [-82, -2, 15, -5, -12, 5, 42, 43, 8, 65],\n [110, -666, -65, 83, 696, -267, 462, -401, -96, -159],\n [98, 344, 5, -33, -333, 127, -315, 124, 34, -41]]\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[[-71, -537, -306, 346, -394, -598, -671, -235, 46, 280],\n [-186, 728, -62, 652, 0, -803, 122, 506, -765, 9],\n [-184, -454, -499, -291, -392, 115, -676, -168, 608, 446],\n [325, 546, -717, -6, -342, -191, -578, 155, 283, 337],\n [461, 573, 329, 65, 424, -213, 181, -99, -382, -424],\n [-222, -483, 472, -591, 366, 536, 121, -372, 267, -201],\n [63, 698, -248, 707, -136, -899, -118, 393, -642, 66],\n [-40, 588, 7, -111, 228, -185, -90, 124, -184, -58],\n [17, 482, 126, 195, 121, 50, 540, 373, -337, -142],\n [374, 1119, 15, 316, 257, -441, 221, 346, -577, -244]]\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 10x10 matrix:\n[[210, -593, -187, 324, -277, -337, -955, 317, -287, 184],\n [-137, -139, -130, 838, 324, 46, -540, -215, 229, 550],\n [-431, 389, -5, -493, 41, -84, -107, 342, -263, 344],\n [-60, 170, -1358, 34, -749, 942, 513, -14, -793, -710],\n [174, 68, 110, 760, -307, -20, -690, 299, 3, 456],\n [433, -577, 36, 150, -16, -25, -235, 37, 64, 200],\n [743, -414, -170, 371, -542, 393, 183, 12, -36, -294],\n [264, -188, -134, 2, 697, -89, 229, -495, 184, -450],\n [373, -321, 712, 709, -458, -375, -721, 288, 337, 418],\n [521, -262, 447, -807, 866, -625, 182, -149, 164, -458]]\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[[-140, 294, -126, -196, 266, 210, -56, 266, -210, -70],\n [130, -273, 117, 182, -247, -195, 52, -247, 195, 65],\n [140, -294, 126, 196, -266, -210, 56, -266, 210, 70],\n [-100, 210, -90, -140, 190, 150, -40, 190, -150, -50],\n [100, -210, 90, 140, -190, -150, 40, -190, 150, 50],\n [30, -63, 27, 42, -57, -45, 12, -57, 45, 15],\n [-210, 441, -189, -294, 399, 315, -84, 399, -315, -105],\n [120, -252, 108, 168, -228, -180, 48, -228, 180, 60],\n [-180, 378, -162, -252, 342, 270, -72, 342, -270, -90],\n [-60, 126, -54, -84, 114, 90, -24, 114, -90, -30]]?\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[[-417, -127, -393, 2, 807, 299, -658, -57, -256, 488],\n [1036, -441, 500, 1167, -102, -364, 543, -718, 156, -254],\n [270, 30, 210, 651, -843, -28, 1094, -455, -249, -781],\n [814, -650, 596, 426, 233, 557, 60, -159, 441, -175],\n [-231, 142, 116, -378, 130, 189, 215, -836, -352, -280],\n [769, -246, 516, 470, 162, -86, 354, -157, 394, 22],\n [687, -418, 691, 559, -62, -119, 2, 106, 548, -67],\n [477, -294, 837, 654, -346, -70, 726, -844, 20, -639],\n [290, 641, 486, 34, 944, -279, 7, -348, 290, -690],\n [656, -360, 1292, 391, 52, 601, 113, 506, 953, -109]]\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[[153, 127, 649, -68, -814, -333, -35, -172, -85, -180],\n [668, 5, 155, -650, 96, 24, -189, -32, -194, 22],\n [857, 246, 519, -506, -516, -592, -525, 563, 313, 187],\n [-490, 35, -178, -92, 193, 527, -281, 205, -279, 636],\n [-411, 87, -389, 176, 468, 289, -175, 422, 113, 344],\n [157, -342, -192, 146, 92, -115, 494, -578, -9, -414],\n [149, -27, -8, 14, -81, -192, -51, 129, 176, 70],\n [698, 236, 228, -244, -78, -509, -276, 491, 416, -167],\n [110, -36, -164, -498, 431, 487, -197, -11, -377, 328],\n [375, -350, -63, 186, -90, -389, 581, -638, 129, -640]]?\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[[354, -161, -556, -26, -493, 80, -145, -180, -585, 493],\n [-517, 359, 745, 86, 472, -15, 363, 89, 597, -495],\n [-351, 274, 572, 168, 373, -93, 298, 236, 412, -341],\n [620, -317, -604, 278, -339, -90, -469, 348, -505, 395],\n [65, 13, -256, -170, -364, 307, -77, -544, -255, 212],\n [-372, 0, 164, -560, 184, 168, 108, -588, 372, -292],\n [174, -183, -235, -6, -36, -245, 2, 281, -218, 197],\n [-304, 308, 467, 116, 172, 188, 142, -141, 350, -305],\n [686, -443, -780, 38, -426, 173, -786, -80, -422, 306],\n [133, -163, -124, -126, 23, 270, -506, -288, 232, -235]]?\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[[222, 393, -284, -212, 713, 158, -191, -788, 567, -992],\n [-356, 68, 412, -333, 481, 420, -560, -512, 491, -313],\n [-67, 427, 525, -313, -220, 539, -256, -67, 105, 101],\n [-144, -690, -134, -343, 49, -440, 509, 477, -97, 45],\n [-97, -651, -61, 1074, 291, -847, -426, 457, 20, 208],\n [62, -93, 186, 868, -121, -386, -416, 431, -79, 344],\n [344, 846, 72, -437, -961, 700, 490, 44, -511, 431],\n [-373, -154, 543, -281, -253, 277, -150, 238, -66, 465],\n [135, 25, 135, -498, 285, -45, 121, 88, 380, -568],\n [218, -360, 398, 846, 26, -858, -350, 1042, 164, 74]]?\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[[476, -283, 497, 321, 114, 222, 351, -151, 14, 57],\n [-744, 488, -760, -551, -332, -210, -533, 224, -106, -23],\n [-292, 157, -311, -179, -14, -186, -221, 97, 22, -59],\n [80, 8, 104, -6, -168, 204, 78, -40, -100, 90],\n [336, -126, 378, 147, -168, 378, 273, -126, -126, 147],\n [-384, 334, -362, -373, -448, 138, -247, 94, -206, 107],\n [500, -311, 517, 352, 166, 192, 364, -155, 40, 40],\n [240, -90, 270, 105, -120, 270, 195, -90, -90, 105],\n [-152, 38, -178, -46, 140, -228, -130, 62, 92, -94],\n [-528, 312, -552, -354, -120, -252, -390, 168, -12, -66]]\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[[130, 428, 168, 95, 281, -518, -531, 829, -419, -229],\n [-126, 172, 112, -433, -215, -206, -27, 281, -295, 635],\n [1, 71, -14, -190, 271, -197, -546, 816, -213, 36],\n [-52, 316, 206, -176, -316, -274, 222, -87, -291, 444],\n [-164, -402, -152, -215, -315, 476, 495, -723, 351, 385],\n [122, 368, 178, 225, 59, -360, -99, 190, -254, -231],\n [-137, -87, -52, -458, -7, -1, -240, 461, -118, 488],\n [-190, 44, 54, -573, -267, -84, 15, 230, -226, 803],\n [82, 140, 40, 119, 193, -182, -267, 357, -123, -237],\n [-89, -309, -144, -125, -74, 323, 159, -284, 247, 141]]?\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[[521, -380, -769, 153, 662, 228, 107, 576, 408, 310],\n [-358, -166, 315, -143, 284, 1302, 659, 265, -263, -6],\n [634, 454, -836, 627, 11, 155, -570, 542, -132, 1343],\n [149, -290, -147, -259, 833, -426, -417, 7, 735, -447],\n [1027, 581, -691, 1089, 67, -549, -133, 570, 932, 763],\n [198, 245, 26, 902, -638, -329, 630, 25, 267, -240],\n [-459, 310, 877, 108, -36, 207, -405, -86, -206, -217],\n [86, -337, -371, -89, -258, -372, -466, 107, -639, 285],\n [-96, 211, 371, -351, 766, 38, -814, -1, 393, 13],\n [-97, -459, -15, -584, 103, -858, -19, -480, 314, -838]]?\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[[-261, 440, 520, 327, 124, 253, -122, 761, 456, -144],\n [-208, -685, -492, 1, -736, -298, 284, 725, 645, -351],\n [-102, -493, -211, -255, -160, -317, 25, 36, 498, -244],\n [-180, 1108, -625, 134, 335, 285, -404, -275, 1, 407],\n [-264, -153, 787, -164, -192, 402, -33, 978, 744, -333],\n [53, -408, -371, 6, -249, 305, -341, 80, -202, -246],\n [306, -758, -251, 37, -207, -350, 240, 137, 49, 22],\n [-3, 182, -645, -301, -184, 18, 648, 97, 320, 374],\n [471, -664, -199, 399, 69, -317, -198, 578, 359, 218],\n [76, 655, 37, -248, 561, 137, 315, -747, -373, 347]]\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 10x10 matrix:\n[[-149, 7, 41, 150, 380, 46, 577, -210, -10, -420],\n [-117, -517, 429, 318, -70, 839, -624, 34, -225, 31],\n [336, -175, 470, -50, -172, 347, -477, -334, -265, 42],\n [-251, -158, 24, 32, 542, 11, 624, 47, 9, -468],\n [-312, 359, 565, 381, 834, -537, 861, -102, 139, 351],\n [263, 954, -119, -352, -212, -560, 107, 118, 60, 31],\n [-34, -246, 1037, -98, 664, 96, -104, 277, -238, 220],\n [45, -1140, 197, 17, 328, -90, 41, -349, 0, 350],\n [-205, -159, -90, 75, 748, -962, 1117, -242, 322, 293],\n [112, 692, 109, -144, 17, -604, 137, 125, 108, 379]]\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[[546, -360, 106, -155, -159, -586, -114, 468, 308, -365],\n [98, -16, -238, 238, -348, -320, 334, 500, 698, -444],\n [511, -40, -137, 51, 140, -412, 41, 390, 367, -248],\n [161, 206, -411, 368, -69, -240, 415, 464, 733, -359],\n [-567, 263, -109, 181, -89, 463, 195, -299, -98, 187],\n [-567, 23, 3, 107, -455, 267, 195, -107, 66, -31],\n [203, 208, -125, 53, 454, 56, -35, -90, -105, 166],\n [-322, 304, -242, 266, 4, 272, 274, -84, 150, 52],\n [-630, 165, -216, 327, -552, 243, 450, 69, 423, -186],\n [434, 177, -8, -113, 788, 47, -278, -239, -429, 354]]\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[[-873, 277, -192, 895, 110, -749, 195, -240, 473, 518],\n [371, 206, -436, 240, -116, -196, 38, 136, -447, 25],\n [-209, 463, 486, 63, 760, 245, -231, 182, -113, -288],\n [-429, -271, 274, -520, -707, -551, 259, -909, -306, 539],\n [184, -103, 74, -711, -268, -443, 355, -538, -934, 391],\n [-341, 371, -192, 857, 735, 267, -531, 469, 526, -151],\n [99, 810, 429, 387, 71, 168, -234, 231, -324, -655],\n [105, 441, 958, -549, 175, 329, -41, -63, -520, -589],\n [-281, -590, -327, -1, 96, -4, 30, -36, 663, 428],\n [378, -167, 213, -814, -887, -197, 207, -589, -849, 67]]\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[[329, 16, -19, -467, -7, -344, -221, 68, 667, 604],\n [175, -176, -301, -507, 300, -352, -137, -354, 192, 484],\n [563, -572, -195, -364, -611, 201, -116, -150, -38, -287],\n [-733, 134, -22, 166, 120, 325, 968, -213, -464, -779],\n [-925, -14, -203, 97, 476, -314, 462, -342, -292, -353],\n [43, 284, -51, -275, 140, 19, 245, 121, 639, 216],\n [-198, -244, -421, 48, 482, 149, -111, -328, -296, -401],\n [-484, -162, -377, -370, 325, -102, 460, -307, 258, -400],\n [-282, 318, -188, 145, -256, -371, 538, -132, 22, 432],\n [-237, -414, -119, -590, 348, -598, -15, -505, -129, 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 10x10 matrix:\n[[213, -446, 299, -452, -276, 211, -557, 15, 249, -281],\n [146, 335, -9, 100, -1, -79, -75, -5, -783, 116],\n [-16, 426, -162, 795, 440, 26, 986, -119, -531, 279],\n [129, -133, -290, 592, 528, -288, 884, -120, -1201, 491],\n [-284, 287, 20, 320, 118, -260, 622, -128, -871, 451],\n [-418, 16, -544, 35, 227, -608, 251, 69, -52, 410],\n [537, 298, -143, 251, 129, -55, -417, 202, -625, -196],\n [7, -334, 278, -281, -191, 16, -166, -59, -222, 11],\n [67, -386, -236, 187, 343, 146, 672, -201, 38, 205],\n [-16, -364, 142, -230, -112, 178, -132, -12, 624, -186]]\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[[-310, 482, 96, 332, 371, -248, -1156, 503, -403, 108],\n [-424, -189, 82, -101, 256, -181, -902, -67, -63, 181],\n [-672, -26, -340, -560, 263, -504, 118, -601, 122, -759],\n [-310, -189, 321, 151, -278, 449, -475, 470, 906, 183],\n [755, -44, -114, 461, -216, 827, 310, -51, -610, -377],\n [-588, 377, 932, 59, -33, 418, -528, 136, 164, -971],\n [-276, 334, -11, 47, -14, -171, 1154, 433, -247, -728],\n [-536, 71, -191, 104, 658, -479, -415, -27, -800, -302],\n [841, -359, -147, -30, -209, 565, 955, -702, -414, -331],\n [-989, 414, 230, 246, 618, -694, -754, 841, 333, 210]]\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[[-430, -366, 105, -208, 644, -1045, 507, 745, 432, 258],\n [54, -72, 493, -250, 258, -423, 533, 201, 70, 592],\n [-279, 184, -114, 42, -677, 761, -377, -82, 32, -984],\n [86, 129, 480, 7, -146, -31, 472, -70, -125, 398],\n [-269, -73, -480, -86, -249, 139, -231, 151, -127, -655],\n [691, 468, 612, 632, -80, 543, -86, -893, -5, 763],\n [-326, -140, -320, -99, -73, -23, -163, 288, 71, -526],\n [-173, -163, 155, 228, -287, 568, -378, 165, 36, -103],\n [-95, 208, 581, -108, -10, -242, 559, 40, 291, 77],\n [-169, -399, -288, 302, 464, -365, -266, 368, 160, 278]]\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[[-1200, 679, -1096, 353, 337, 893, 893, -595, -62, -791],\n [314, -763, -489, 364, 217, -606, 358, 1085, 667, 742],\n [-457, 567, 158, -1109, 649, -334, 396, 619, -785, -1112],\n [1180, -583, 228, -322, -261, -132, -548, -125, 183, 272],\n [304, 232, -300, 185, 12, -329, 115, 432, 477, 670],\n [-261, 697, -275, -257, -148, 561, -202, -30, -72, -369],\n [554, -66, 343, -104, 396, 706, -629, 1573, 426, 125],\n [-339, -316, 698, 369, 75, 321, -188, -177, -259, -138],\n [159, 270, 46, -486, 160, -153, -238, -41, 465, 165],\n [-388, -29, -549, 307, -183, 76, 201, -499, 352, 165]]\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[[-98, 401, -547, 19, -296, -186, 45, -362, 863, 489],\n [266, 62, -123, -385, -545, -156, -418, 12, -258, 346],\n [154, 64, 92, 246, -4, 336, -188, 340, -322, -492],\n [498, 265, -220, -406, -485, 46, -559, 68, -21, 387],\n [-69, 89, -18, -385, 379, -38, -17, -59, -377, -36],\n [-494, -119, 71, 184, 168, -112, 229, 45, -623, -539],\n [649, -259, 367, -876, -338, -34, -729, 316, -1176, 247],\n [1254, -213, 389, -849, -776, 194, -1101, 483, -734, 578],\n [-282, 41, -125, -143, 26, -218, 85, -144, -235, -9],\n [-194, 430, -429, -47, -37, -20, -86, -89, -47, -133]]?\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[[103, -209, 311, 22, -209, -565, -574, -166, -117, 45],\n [181, 55, 11, 298, 274, -287, -388, -123, -241, 590],\n [432, 89, 286, 662, 110, 29, -228, -406, 29, 795],\n [300, -413, 378, 370, 284, 561, -262, -516, 279, 165],\n [131, -83, -47, 226, 480, -32, -373, -137, -195, 465],\n [84, 44, -292, 248, 768, 144, -220, -28, -276, 620],\n [145, 67, -91, 322, 397, 708, 317, -152, 175, 310],\n [-253, 199, -417, -254, 161, 422, 579, 326, 43, -270],\n [311, -654, 879, 156, -492, -296, -788, -615, 270, -235],\n [353, -227, 395, 454, 118, 73, -422, -463, 93, 430]]\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[[194, 168, -165, -26, 430, 593, 459, 103, -192, 148],\n [38, 212, -100, 174, 230, 390, 168, 142, -98, 206],\n [149, -74, -50, -223, 165, 145, 264, -59, -79, -87],\n [-197, -58, 125, 139, -345, -430, -417, -28, 157, -39],\n [106, 12, -60, -94, 170, 202, 216, 2, -78, 2],\n [71, -138, 15, -209, -5, -88, 81, -98, -3, -143],\n [136, -228, 15, -364, 20, -113, 171, -163, -18, -238],\n [-247, 342, 0, 589, -95, 95, -342, 247, 57, 361],\n [-79, -142, 95, -63, -235, -354, -219, -92, 103, -133],\n [-17, 222, -75, 239, 155, 310, 63, 152, -63, 221]]\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[[-265, 72, 387, -173, -180, 25, -762, 10, -94, -511],\n [-21, -64, -133, 103, -113, -215, 149, 210, 190, 180],\n [75, 73, 132, 509, 402, 74, 109, 99, 566, 426],\n [204, 140, 98, -102, 278, 448, 116, -504, -244, -162],\n [-272, -202, 231, 551, -253, -150, 182, -116, 514, 85],\n [-108, -372, -257, 48, 157, -147, 285, 223, -460, 453],\n [164, 58, 25, 393, 680, 162, 109, 184, 274, 590],\n [152, -15, 177, 484, 663, 451, 366, -389, 116, 410],\n [399, 221, 7, 248, 927, 472, 215, -101, 104, 519],\n [-464, -160, 643, 188, 555, 201, -1081, 239, -348, -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[[897, 73, 541, 674, -632, -189, -443, -486, 428, 524],\n [-310, -201, 75, -560, 355, 780, 553, 120, 169, -678],\n [120, 379, 95, -90, 625, -66, 515, -116, -59, -420],\n [151, -1090, 4, -569, -18, 1176, 117, -152, 735, -153],\n [394, 640, 963, 62, -120, -651, 164, -751, -178, -95],\n [-168, 824, 192, 460, -418, -438, -697, 412, -589, 517],\n [339, 557, 819, 396, -497, -482, -87, -494, 26, 116],\n [-102, 221, 244, 591, -980, -922, -580, -207, -145, 634],\n [63, 573, 421, -114, 378, 285, 309, 46, -116, -408],\n [-409, -258, 161, -576, 263, 850, 420, 103, 267, -493]]\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[[254, 114, -210, 248, 192, -264, -40, 242, -356, -60],\n [430, 553, 276, 175, 92, 264, 575, -17, -512, -182],\n [-51, -116, -111, 7, 18, -116, -155, 50, 52, 30],\n [-374, -347, -18, -235, -162, 16, -265, -129, 474, 132],\n [169, -193, -336, 171, 201, -304, -420, 161, -197, -57],\n [213, -477, 78, -211, 71, 488, -660, -575, 49, -275],\n [164, 108, 66, 46, 50, 104, 80, -48, -166, -86],\n [-85, 426, -60, 208, -19, -376, 545, 462, -133, 181],\n [206, -248, 219, -201, 15, 556, -330, -542, 11, -249],\n [183, -208, 45, -77, 68, 268, -325, -298, -54, -176]]\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[[-732, -30, -174, -69, 441, -78, -91, -407, -181, 19],\n [964, 245, -163, -640, -93, 276, 175, 1080, -213, 86],\n [95, 417, -861, -787, -255, 9, -311, 434, -203, 1018],\n [1167, 98, 1295, 816, -863, 48, 389, 401, 784, -859],\n [-193, -130, -100, 37, -115, -237, -498, 112, 203, 779],\n [15, -645, 264, 281, 534, -16, -5, 106, -145, -237],\n [-695, 213, -735, -536, 540, -61, 92, -221, -655, 299],\n [733, -258, 261, 377, -530, -90, -76, 342, 297, 242],\n [392, 191, 308, 64, -14, 65, 501, 228, -141, -551],\n [-199, 277, -134, -119, -294, 186, -131, -434, 284, -145]]\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[[92, -238, 88, -324, -42, 310, 20, -226, -300, -472],\n [96, 202, 208, 2, 104, -268, -220, -12, -18, 268],\n [146, 272, -12, 357, 279, -203, 80, 133, 347, 398],\n [124, 6, -68, 133, 163, 123, 188, 1, 147, -42],\n [-181, 70, 416, -488, -335, -430, -684, -119, -532, 148],\n [-473, -230, 4, -423, -606, -97, -356, 0, -445, -158],\n [-102, 200, -156, 361, 43, -239, 64, 241, 343, 422],\n [-185, -347, -384, 21, -189, 458, 394, 41, 55, -446],\n [113, 279, 224, 71, 149, -354, -242, 23, 45, 390],\n [344, 136, -292, 619, 547, 251, 624, 133, 653, 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[[513, -173, -331, 324, 74, -689, -157, 108, 655, 596],\n [-130, 146, -474, 64, 294, -262, -78, -480, -252, -240],\n [481, -118, 12, -352, 51, -353, 132, -624, 213, -406],\n [560, 305, 34, -686, 529, -893, -308, -696, 697, -287],\n [825, -927, 988, -389, 445, -511, 62, 1067, 176, 533],\n [81, 4, -408, 189, -150, 570, 303, 118, 622, 920],\n [135, -330, -23, 509, -125, 72, 309, -131, 244, -674],\n [-186, 495, -550, 264, -6, -925, -437, -225, 211, -623],\n [-205, -640, 34, -259, -123, 234, 933, 1363, -495, -1108],\n [-161, 576, 278, -770, -270, -303, -276, 680, 54, -295]]?\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[[367, -85, -46, 91, -538, -407, -546, -86, -164, 268],\n [-638, -463, 692, 197, -441, 697, -554, -113, 102, -166],\n [-1055, -305, 875, 501, 439, 512, -125, -240, 452, -661],\n [-258, -316, 677, -77, -487, 534, -195, -330, -379, -679],\n [-90, -314, 57, 529, -662, 598, -170, 90, -151, 125],\n [-476, -32, 177, -342, 6, -180, 41, -84, -442, -470],\n [392, -227, 745, 182, -632, 72, -875, -533, -162, -257],\n [-139, -998, 642, -225, -651, 395, -650, -690, 1104, 968],\n [-607, -204, -159, 247, -14, 30, 183, 110, -26, 161],\n [-232, -268, -40, -175, -771, 21, -214, 100, -566, -85]]\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[[374, 4, -406, 146, 119, -511, -58, -52, -109, 501],\n [200, 837, 788, -105, -427, -159, -514, -188, -711, 101],\n [-200, -324, -525, -193, 162, 73, 161, -253, 147, 306],\n [45, -599, -803, -478, 158, 635, 510, -175, 454, -381],\n [-405, -444, 686, 447, -299, 614, -358, -14, 556, -846],\n [435, -177, -186, 67, -498, 236, -37, -184, -371, 221],\n [571, -284, 90, -316, -463, 1108, -24, 103, -241, -476],\n [-16, 501, -793, -371, 1067, -402, 128, 532, 33, 289],\n [31, -367, -763, -222, 248, -82, 879, 198, 180, 116],\n [-506, -298, -431, 252, 349, -968, 242, -488, 616, 398]]\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[[-28, 74, 78, 38, -130, 18, -80, -88, -2, 88],\n [-25, 54, 53, 29, -89, 18, -51, -61, -7, 62],\n [-62, 188, 206, 94, -342, 36, -218, -230, 6, 228],\n [-280, 64, -152, 104, 216, 288, 344, 104, -312, -48],\n [320, -49, 207, -109, -301, -333, -434, -154, 367, 88],\n [-250, 371, 297, 221, -511, 207, -224, -364, -143, 388],\n [26, -117, -139, -55, 229, -9, 156, 152, -19, -148],\n [58, 64, 138, 10, -218, -72, -202, -134, 98, 116],\n [-287, 336, 217, 217, -385, 252, -105, -287, -203, 322],\n [400, -188, 84, -188, -92, -396, -328, -8, 404, -64]]?\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[[78, -606, -617, -131, 498, 657, -341, 416, 775, -652],\n [-1067, -147, -561, -25, 235, 346, -696, 702, 398, -816],\n [-81, 246, 277, 413, 716, 462, 385, 821, -177, 25],\n [1585, -257, 172, -1021, -334, -18, 448, -981, 167, 732],\n [-150, -342, 1119, -1378, -1125, -38, 257, -265, -239, 179],\n [746, 519, 764, 62, -319, -603, -72, -247, 336, 159],\n [-680, -325, -156, 330, 252, 176, -169, 144, -492, -215],\n [490, -600, -307, -1052, -444, 146, 145, -1034, 210, 540],\n [-562, -479, -331, 324, 460, 203, 542, -236, 561, 445],\n [398, -534, 191, -289, -370, 303, 874, 210, -401, -21]]?\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[[170, -413, 640, -397, 391, -270, 172, 618, 334, -440],\n [486, 193, -704, 1359, -581, 241, 331, -516, 209, -139],\n [-1414, -416, 57, -589, -516, 536, -410, -335, -846, 1095],\n [1194, 157, 170, 287, 181, -256, -198, 612, 352, -628],\n [-648, -338, 92, -260, -576, 482, -622, 16, -712, 796],\n [1368, 353, -12, 526, 382, -432, 192, 412, 673, -933],\n [-534, 11, 10, -417, 61, 46, -64, -176, -228, 312],\n [588, 335, -453, 758, -187, 18, 106, -231, 186, -221],\n [-206, -272, 374, -371, 323, -186, 280, 212, 217, -209],\n [312, 442, -887, 1196, -531, 247, 231, -743, 54, 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[[-367, -439, -772, -80, 358, 115, 143, -337, -380, 137],\n [366, -109, -40, 260, -429, -85, 46, 359, 657, 46],\n [-8, -104, -266, 67, -95, -232, 10, -126, -231, 246],\n [204, 29, -390, -440, 192, 398, 727, -383, -550, 297],\n [-240, -91, 116, 1071, -556, -935, -545, -244, 315, -302],\n [580, 505, 150, -433, -79, 364, 1004, -516, -630, 247],\n [-39, -35, -52, -276, -181, 242, -67, 820, 136, -118],\n [177, 65, 54, 604, -571, -561, 1, -181, 130, -8],\n [-310, -114, -240, 237, -419, -192, -127, 479, -84, -302],\n [-200, 285, 376, 13, -160, -112, -182, 220, -254, -304]]\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[[-13, -8, -7, -10, 21, 21, -22, 10, -15, -7],\n [-169, -104, -91, -130, 273, 273, -286, 130, -195, -91],\n [-156, -96, -84, -120, 252, 252, -264, 120, -180, -84],\n [-26, -16, -14, -20, 42, 42, -44, 20, -30, -14],\n [-208, -128, -112, -160, 336, 336, -352, 160, -240, -112],\n [26, 16, 14, 20, -42, -42, 44, -20, 30, 14],\n [104, 64, 56, 80, -168, -168, 176, -80, 120, 56],\n [-143, -88, -77, -110, 231, 231, -242, 110, -165, -77],\n [182, 112, 98, 140, -294, -294, 308, -140, 210, 98],\n [260, 160, 140, 200, -420, -420, 440, -200, 300, 140]]\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 10x10 matrix:\n[[-484, -940, -554, 14, 5, -356, 746, 858, 43, -724],\n [536, 140, -283, 421, 90, -157, -195, -503, 433, 295],\n [92, -359, 513, 990, 162, -119, 85, 163, 521, -419],\n [-684, -1212, 479, 543, -518, -147, -35, 859, -35, -1095],\n [-532, -404, 237, 159, -617, -692, -114, 486, -252, -428],\n [472, 516, 255, 183, 524, 92, -38, -360, 76, 394],\n [-484, 368, 57, -955, 174, -81, -263, 245, -553, 187],\n [-280, 661, -259, -312, 111, -191, 308, 171, 483, 459],\n [320, -621, -759, 898, -735, 197, 876, -47, 914, -235],\n [-108, 373, 333, 112, 821, -645, 160, 49, -11, -111]]\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[[390, 47, -484, 460, -27, 637, 564, 92, 35, 167],\n [-93, 1170, 790, 202, -326, 1120, 139, 22, 728, 314],\n [873, 477, 53, 601, -61, 908, 719, 398, 135, -782],\n [194, -839, -439, -191, 282, -1155, 1, -266, -630, -73],\n [-12, -229, -128, 114, 42, -431, -259, -355, 48, -65],\n [260, -1377, -1331, -183, 282, -1040, -383, 193, -1085, -1134],\n [30, 11, -30, -918, 69, 69, -789, 517, -647, -749],\n [-42, 191, -110, 684, -137, 622, 551, -34, 554, 408],\n [-256, 1064, 75, -272, -454, 1430, 193, 494, -99, 340],\n [28, -272, -327, 922, -57, -626, 745, -902, 348, 24]]\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[[-340, 85, 12, -123, -214, 197, -660, -41, 523, 357],\n [385, -296, -163, -622, 249, -106, 65, 27, 801, 356],\n [764, 65, -196, -374, 303, -241, 740, -862, 384, -373],\n [545, -162, -147, -216, -83, 415, 641, -503, -180, -954],\n [-256, 239, 235, 540, -165, 5, -88, -103, -469, 307],\n [556, -297, 74, -232, 973, -666, 101, 368, 397, 231],\n [561, -73, 129, -59, 301, 81, 93, 22, 101, -297],\n [-259, 111, -1, 686, -608, 472, -449, -216, -272, 181],\n [392, 341, -584, 100, -242, -251, 959, -299, 64, -107],\n [144, 397, 130, 252, 345, -73, 205, 88, 187, 273]]\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[[79, -141, 46, 22, -251, 102, -67, -64, -61, 36],\n [43, 141, 241, -38, -233, -48, -256, 290, 131, -216],\n [106, -78, 172, 4, -386, 84, -202, 80, 2, -72],\n [-13, 51, 20, -10, 29, -30, -17, 52, 31, -36],\n [12, -216, -186, 48, 48, 108, 186, -300, -156, 216],\n [102, -250, -8, 44, -294, 164, -18, -184, -130, 120],\n [136, -374, -51, 68, -374, 238, 17, -306, -204, 204],\n [-63, -147, -294, 42, 315, 42, 315, -336, -147, 252],\n [15, 35, 70, -10, -75, -10, -75, 80, 35, -60],\n [234, -308, 245, 40, -792, 250, -309, -26, -98, -12]]?\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[[110, -322, -52, 295, 250, -255, 322, 64, 268, -27],\n [-2, 108, -75, 205, 50, -23, -140, 83, -3, -22],\n [272, -622, -73, 94, 160, -288, 670, -143, 451, -129],\n [-174, -144, 177, 288, 420, -243, 132, 300, 18, 237],\n [64, 770, -273, -376, -740, 580, -810, -301, -371, -287],\n [84, 88, -258, 752, 280, -222, -176, 252, 176, -98],\n [184, -250, -59, -215, -150, 6, 294, -238, 172, -140],\n [18, 434, -88, -466, -540, 421, -430, -267, -275, -148],\n [-126, 666, -80, -163, -370, 383, -714, -24, -396, -45],\n [46, -430, 2, 567, 530, -439, 414, 254, 334, 79]]\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, -715, -222, 340, -16, 119, 168, 86, -718, -33],\n [116, 81, 253, -386, -477, 49, -413, -190, 187, 78],\n [-48, -840, -863, 1207, 88, 541, 362, 1297, -1038, 507],\n [70, -572, -198, 629, -127, 517, -293, 798, -534, 639],\n [217, -108, 172, -203, -507, -40, -172, -265, -155, -406],\n [865, 502, 558, -481, -966, -127, -600, -499, 398, -649],\n [-681, -343, -633, 425, 648, 160, 492, 571, -262, 730],\n [262, 288, 419, 395, 705, -47, -331, -299, 481, 484],\n [750, -28, 271, 854, 91, 239, -614, 77, 68, 574],\n [560, 480, -257, 296, -246, -234, 44, -367, 429, 121]]?\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[[-355, -351, 492, 298, 595, 145, -418, -98, -5, 179],\n [213, 248, -503, 418, -153, 764, -464, 194, 112, -463],\n [122, -50, 71, 190, -123, 633, 54, -259, -367, -378],\n [234, -447, -524, 323, 64, 38, -700, 216, 506, 386],\n [-15, 211, -674, -307, 108, 585, 590, -861, -763, -267],\n [-19, 300, 265, -44, 556, 563, -616, 23, 235, -468],\n [219, 428, -1149, -39, -839, -293, 590, 223, -58, 50],\n [726, -232, -27, -82, -289, 165, -602, 297, 607, -140],\n [-132, -282, -109, 783, -882, -691, 204, 791, 150, 518],\n [81, -28, -85, 761, -940, -218, 36, 813, 174, 45]]\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[[241, 513, -260, -299, 52, 224, 377, -14, -353, 455],\n [-1400, -482, -197, 941, -4, -68, -460, -94, 427, -569],\n [635, 283, 206, 220, 540, -254, -59, -37, -189, -230],\n [-279, 256, -1108, 213, 256, -78, 165, 112, 450, 428],\n [261, 567, 77, -11, 481, -20, 226, -185, -669, 157],\n [-62, 419, -420, -467, 15, -258, 455, -208, -265, 565],\n [668, -79, 219, 220, 512, -412, -522, -115, 160, -135],\n [674, 672, 725, 215, 591, 202, 235, -72, -1002, -385],\n [-378, 64, 708, 340, 304, -306, -350, -520, -611, -365],\n [-714, -904, -514, -42, -534, -64, -368, 194, 1006, 138]]\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[[-25, 361, 22, 788, -339, -285, 692, 167, 460, -443],\n [-817, -558, 504, 741, 603, 725, 12, -848, -97, -870],\n [-900, -769, 20, -136, 23, 211, -218, -941, -506, -507],\n [862, -179, 1101, -345, 310, 208, -397, 163, 272, 642],\n [-803, -578, -148, -111, 139, 608, -133, -527, -593, -623],\n [145, 845, -807, 88, 61, 41, 121, 577, 145, -401],\n [-688, 229, -1066, -288, -183, 1187, 1091, 379, -99, -1003],\n [-70, 292, -337, -367, 1009, 970, 16, 124, -74, -369],\n [160, 432, 56, 785, -476, -168, 542, 351, 850, -55],\n [-270, -435, 401, 207, 35, -459, 101, -480, -407, -183]]\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 10x10 matrix:\n[[388, 54, 310, -333, -49, -189, 14, 316, 262, -982],\n [33, -135, 267, -811, -27, -158, 94, 437, 301, -1013],\n [341, 536, -160, 308, 457, -244, 520, 113, -566, 360],\n [-258, -296, -398, 91, 3, 292, -64, -578, 187, 711],\n [766, 566, -166, -78, 248, -365, 564, -55, 115, -673],\n [-288, -52, 468, 147, -309, 97, -414, 308, -164, -226],\n [-968, 339, -183, 1119, -598, 384, -446, -588, -573, 1309],\n [586, 99, -463, -397, 986, -83, 914, -201, -170, 308],\n [1520, -921, 199, 261, 679, 270, -332, -318, 731, -110],\n [-205, -234, 4, -147, 277, 171, 68, 35, -210, 395]]\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[[94, -165, 610, -126, 138, -269, 544, 525, 627, 172],\n [19, 93, -374, -42, 15, 74, -510, -527, -393, 91],\n [174, 46, -82, 394, 4, -92, 236, -308, 46, -262],\n [-11, -34, 228, 280, 40, -237, 256, 37, 212, -178],\n [-137, 2, -69, 501, -100, -213, -110, -243, -134, -365],\n [-263, 179, -127, -692, 105, 476, -288, 276, -311, 322],\n [-80, -1, -415, 266, -289, 155, -300, -167, -373, -274],\n [430, -292, 83, 864, -125, -748, 72, -634, 336, -252],\n [265, -289, 288, -655, 60, -142, -160, 295, 375, 738],\n [-32, 162, 382, 105, 411, -294, 314, -208, 240, -23]]\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 10x10 matrix:\n[[-305, 1547, -235, 460, 115, 615, 735, -195, 241, 784],\n [-65, -40, -625, 261, 529, 196, 322, -429, -75, 51],\n [-628, -132, 93, 229, -267, -348, 355, -228, 103, -779],\n [522, 85, -552, -605, -230, -122, -888, 700, -571, -374],\n [597, -140, -59, -146, -577, 70, -726, 767, -399, -1095],\n [260, -966, -175, -568, 199, -461, -484, -92, -96, -440],\n [151, 880, 157, -127, -153, 232, -108, 47, 315, 625],\n [315, -849, 599, 44, -307, -59, -219, 389, -115, -656],\n [-23, -103, -819, -329, -285, -341, -727, 971, -1183, -416],\n [372, -822, 112, 465, 146, 341, 31, 352, -469, -215]]\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 10x10 matrix:\n[[519, -385, -285, 362, 366, -92, 192, -108, -356, -309],\n [325, 107, -918, 1038, 147, 421, 450, 218, -204, 518],\n [-261, -9, 1464, -128, -314, 94, 39, -199, 215, -588],\n [-724, -200, 560, -414, -130, 22, -528, 332, 112, -967],\n [-315, -244, 332, -419, -3, 298, -472, 417, 82, -889],\n [-411, -128, -102, 389, -207, -580, 118, -803, -366, 444],\n [-18, -74, 897, -31, -205, -504, -573, -1218, -854, -56],\n [-540, -28, 723, -9, -504, 189, -389, 214, 81, -276],\n [464, 76, -448, -305, 596, 723, 73, 454, 170, -541],\n [547, 381, 493, 358, -203, -59, -233, -811, -653, 710]]\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 10x10 matrix:\n[[-131, -689, 575, -138, -229, -74, 36, -88, 67, 68],\n [337, 35, -846, -125, -146, -164, 192, -142, -791, 105],\n [-237, 412, -39, 285, 273, 374, 379, 271, 276, -203],\n [187, -476, 829, -493, -55, 50, -333, 167, 290, -27],\n [-44, 39, -199, 216, -151, -454, -445, -419, -29, 196],\n [398, -362, 894, -135, 220, 452, 144, 540, 433, -618],\n [31, -187, -538, 342, -396, -842, -556, -794, -402, 341],\n [-45, 40, 511, 45, 269, 497, 335, 459, 434, -373],\n [168, 445, -511, 383, 49, -335, -391, -277, -48, -32],\n [-41, 5, 123, -404, 227, 788, 892, 684, -99, -202]]\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[[-95, -40, 419, 201, -5, 340, 44, -107, 264, 398],\n [-372, -420, 21, 234, 156, 234, 462, -498, -147, 9],\n [-174, -240, -258, 18, 102, -72, 264, -246, -264, -252],\n [318, 360, -12, -198, -134, -196, -396, 426, 130, -2],\n [-111, -120, 39, 81, 43, 92, 132, -147, -20, 34],\n [-50, 20, 473, 192, -30, 350, -22, -44, 323, 451],\n [110, 220, 583, 132, -110, 330, -242, 176, 473, 561],\n [-186, -180, 195, 180, 58, 242, 198, -240, 61, 181],\n [339, 360, -159, -261, -127, -308, -396, 447, 32, -142],\n [-79, -20, 430, 195, -13, 338, 22, -85, 279, 409]]\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[[315, -354, 102, 102, -153, -372, 369, 210, 30, -207],\n [-285, 347, -85, -136, 102, 322, -329, -190, -15, 214],\n [150, 31, 103, -278, -345, -286, 212, 100, 105, 101],\n [0, -165, -45, 270, 225, 90, -30, 0, -75, -165],\n [0, -132, -36, 216, 180, 72, -24, 0, -60, -132],\n [-75, 243, 19, -284, -180, 2, -59, -50, 65, 208],\n [225, -366, 42, 258, 45, -204, 243, 150, -30, -261],\n [-90, -122, -90, 336, 348, 228, -146, -60, -110, -164],\n [150, -420, -20, 460, 270, -40, 130, 100, -100, -350],\n [0, 110, 30, -180, -150, -60, 20, 0, 50, 110]]?\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[[242, -29, -375, -974, -722, 1188, -593, -996, 461, -373],\n [754, 15, -194, 372, 66, 455, -653, 600, 163, -277],\n [1053, -200, -550, -502, -509, 468, -463, -274, 136, 2],\n [425, 37, -198, -765, -160, 1323, -641, -569, 923, -345],\n [-403, -107, 331, 44, -258, -93, 199, -342, -5, 158],\n [281, -21, 96, 60, 279, 447, -127, -3, 630, -39],\n [487, 175, -478, -250, 25, 609, -624, 242, 79, -451],\n [-531, -99, 292, 232, -212, -480, 414, -241, -314, 208],\n [-477, 345, -48, -16, 850, -82, 273, 282, 155, -226],\n [1094, -408, 104, 416, -354, -116, -286, 384, 88, 444]]\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[[448, -229, 89, 339, -610, -215, -269, 577, 42, -134],\n [794, 861, -192, -171, 298, 202, -406, 47, 178, 198],\n [-682, -622, 507, -1019, -543, -44, 130, -287, 289, -408],\n [-86, 139, -450, -457, 503, -334, 159, 195, -314, -301],\n [-759, -82, 802, -1106, 263, 440, 167, -499, 670, 138],\n [-272, 305, -141, -163, -748, -180, 428, -1512, 41, -5],\n [111, -403, -191, -634, 186, 757, -675, 43, -421, -311],\n [-443, -505, 696, -723, -730, -419, 312, -464, 193, -16],\n [389, -372, -468, -225, 123, 995, -1439, -40, -932, -389],\n [243, -490, 207, -613, -200, -56, -322, 85, -269, -80]]\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[[-175, -229, 19, 201, 95, 168, 103, 435, -172, -156],\n [14, 158, 112, -84, -46, -174, 22, -132, 188, 0],\n [-100, 82, 194, -6, -58, -238, 92, 112, 190, -112],\n [-388, 358, 642, 202, 522, 290, 548, 244, 466, -384],\n [260, 256, -162, -146, 228, 422, -88, -662, 4, 264],\n [-175, -57, 97, 223, 375, 514, 219, 245, -96, -148],\n [-42, 361, 304, -88, 113, -98, 164, -229, 391, -60],\n [87, 159, 63, -183, -249, -450, -87, -207, 222, 60],\n [44, -138, -109, -49, -260, -299, -138, 89, -78, 36],\n [109, 219, 67, -191, -169, -340, -69, -305, 240, 84]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}