{"messages": [{"content": "Find the rank of the matrix:\n[[68, -22, 22, 100, 84, 150, -54, -20, -120],\n [-118, 53, -29, -86, -90, -129, 45, 34, 156],\n [72, -48, 8, -40, -4, -60, 24, -20, -40],\n [-256, 152, -40, 32, -56, 48, -24, 72, 208],\n [376, -239, 49, -140, 23, -210, 87, -105, -250],\n [-218, 157, -17, 190, 56, 285, -111, 60, 80],\n [-264, 183, -25, 188, 41, 282, -111, 73, 122],\n [268, -167, 37, -80, 29, -120, 51, -75, -190],\n [-202, 95, -47, -122, -138, -183, 63, 58, 252]]\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[[-221, -416, -36, -176, -316, -632, 54, -245, -317],\n [325, 294, -104, 199, 425, 779, 100, 409, 184],\n [-271, -356, -412, 210, -238, 402, 26, -127, 3],\n [-66, 718, 388, -58, -16, 197, -398, 276, -25],\n [29, 44, -70, 214, 108, 305, 29, -85, 472],\n [195, 144, 34, -47, 163, 129, -35, 3, -26],\n [-208, 72, 246, -30, -197, -450, -136, -245, 273],\n [-62, -606, -236, -42, -147, -420, 217, -401, -43],\n [-94, -412, -314, 271, -5, 181, 277, -64, 359]]\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[[86, -45, -359, 306, 266, -139, -183, 350, -211],\n [458, -21, 145, -366, 32, -271, 351, -148, 65],\n [163, -257, -2, -158, -33, 6, 321, -485, 333],\n [-444, -336, -512, 624, 118, 196, -274, -50, 28],\n [-611, -28, -52, 336, -159, 341, -306, -34, 4],\n [398, 9, 182, -338, 5, -521, 334, 20, -243],\n [244, -41, 99, -198, 0, -425, 245, 4, -223],\n [-692, -35, 128, 190, -314, 457, -205, -277, 163],\n [-531, 7, 52, 186, -202, 504, -232, -192, 235]]\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 9x9 matrix:\n[[154, 182, -306, -15, -272, -109, -293, -122, -185],\n [8, -227, 153, 33, 272, 46, 104, -58, 50],\n [-92, 52, 68, -14, -32, 30, 94, 108, 70],\n [-208, 71, 187, -25, -16, 78, 236, 234, 170],\n [-64, 388, -204, -60, -448, -56, -112, 152, -40],\n [-26, -125, 119, 16, 160, 39, 97, 0, 55],\n [314, -74, -306, 33, -16, -125, -373, -346, -265],\n [182, 42, -238, 7, -112, -91, -259, -182, -175],\n [-284, 145, 221, -41, -80, 96, 298, 330, 220]]\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 9x9 matrix:\n[[-17, -12, -25, 25, -8, 7, -31, 0, -20],\n [173, 93, 37, -37, -136, -376, 1, -66, -43],\n [229, 144, 205, -205, -24, -279, 227, -40, 120],\n [-168, -93, -56, 56, 112, 337, -30, 58, 19],\n [-28, -3, 84, -84, 112, 187, 130, 38, 109],\n [20, 15, 36, -36, 16, 1, 46, 2, 31],\n [-201, -141, -289, 289, -88, 92, -357, 2, -229],\n [-76, -66, -204, 204, -128, -98, -272, -28, -194],\n [-56, -21, 56, -56, 112, 217, 98, 42, 91]]\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[[179, 102, -56, 320, -33, 544, -28, 148, -159],\n [683, 512, 231, -411, -219, -87, 76, 73, -632],\n [-332, 462, -376, -30, -267, -196, 73, -33, -736],\n [-346, 234, 177, 485, -114, 317, -58, -375, -179],\n [435, 212, -95, -338, -180, 383, 212, 644, 7],\n [-257, 93, -77, -159, 13, -478, -86, -22, -172],\n [224, -157, 133, -102, 86, 288, 239, 524, 398],\n [274, 95, 505, 189, 121, 232, -63, 112, 32],\n [78, -56, 649, 47, 328, -844, -347, -654, -234]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[162, -63, -144, -162, 126, -81, 90, -54, -63],\n [234, -91, -208, -234, 182, -117, 130, -78, -91],\n [144, -56, -128, -144, 112, -72, 80, -48, -56],\n [18, -7, -16, -18, 14, -9, 10, -6, -7],\n [90, -35, -80, -90, 70, -45, 50, -30, -35],\n [-126, 49, 112, 126, -98, 63, -70, 42, 49],\n [288, -112, -256, -288, 224, -144, 160, -96, -112],\n [252, -98, -224, -252, 196, -126, 140, -84, -98],\n [252, -98, -224, -252, 196, -126, 140, -84, -98]]\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[[-229, 243, -44, 295, 134, 388, -45, 253, -144],\n [77, -98, 252, -361, 165, -122, 135, -290, 30],\n [-156, 79, 159, -49, 288, 252, 104, 2, -95],\n [-357, -113, 100, -139, 354, 100, -87, -69, -222],\n [153, 139, 363, -282, 215, 110, 279, -234, 63],\n [237, -265, 101, -338, -39, -310, 165, -246, 171],\n [371, 98, -74, 142, -279, 2, 216, 121, 261],\n [124, 96, 243, -179, 143, 94, 222, -139, 63],\n [-23, 335, 330, -139, 194, 172, 19, -207, -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 9x9 matrix:\n[[98, -70, -126, 0, 77, 126, -21, 14, 84],\n [140, -100, -180, 0, 110, 180, -30, 20, 120],\n [126, -90, -162, 0, 99, 162, -27, 18, 108],\n [28, -20, -36, 0, 22, 36, -6, 4, 24],\n [168, -120, -216, 0, 132, 216, -36, 24, 144],\n [84, -60, -108, 0, 66, 108, -18, 12, 72],\n [140, -100, -180, 0, 110, 180, -30, 20, 120],\n [-112, 80, 144, 0, -88, -144, 24, -16, -96],\n [238, -170, -306, 0, 187, 306, -51, 34, 204]]\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 9x9 matrix:\n[[-83, 288, 45, 83, 256, 45, -42, -466, 393],\n [47, -90, -201, 18, 238, -176, 17, -179, 394],\n [254, -234, -310, -369, -208, -280, 61, 103, -49],\n [-5, -26, -169, 30, 264, -187, 71, -143, 404],\n [-93, 392, 427, -44, -372, 416, -123, -59, -556],\n [186, -457, -194, -52, -149, -98, -59, 301, -188],\n [3, 63, -65, -65, 63, -95, 59, -81, 145],\n [-11, -367, -263, 319, 497, -203, -5, -33, 577],\n [66, -28, -90, -138, -66, -101, 46, 28, -8]]\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[[160, -105, 255, 114, -504, -261, -19, -317, 651],\n [-116, 244, -114, -5, -30, -117, -101, -17, -108],\n [-32, 59, -42, -36, 447, 353, -31, -5, -282],\n [-701, 54, -529, -189, 616, 237, 116, -32, -448],\n [30, 196, 72, -476, 391, -504, -279, 7, -210],\n [-161, -104, -333, 154, 161, 485, 671, 263, 42],\n [559, 178, 448, -243, -154, -534, -326, 12, 103],\n [-449, -41, -385, 380, -247, 296, 179, 31, -30],\n [25, -150, 91, -306, 459, 21, -26, -53, -109]]\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 9x9 matrix:\n[[-240, -100, 87, -458, -37, -217, 251, 583, -138],\n [-483, -322, 141, 209, -97, 233, -108, 137, -108],\n [397, 461, 276, -28, -13, -109, -36, -123, 449],\n [-200, 262, -480, 230, -260, -200, -220, -34, 251],\n [885, -706, 509, -220, 165, -113, 596, 185, -321],\n [38, -525, -681, 725, -508, -398, -46, -476, 191],\n [-519, -349, 286, -163, 51, 258, -314, -330, -443],\n [169, -624, 735, -49, 91, 216, 258, -446, -136],\n [-39, -404, -25, 507, -205, 456, 129, -170, 34]]\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[[95, -191, -156, 106, -43, 72, 361, -12, -49],\n [-44, -18, -332, -32, 232, -38, 464, 140, 120],\n [385, -427, 419, -340, -330, -485, -340, -294, 558],\n [12, 121, 340, 190, -172, -34, -139, -450, 16],\n [-113, -57, -516, 85, 150, 131, 308, 441, -279],\n [-138, -20, -504, 24, 186, 208, 208, 548, -330],\n [231, -154, 561, -85, -385, -465, -497, -543, 396],\n [-240, 181, -325, 461, -56, -375, 144, -191, -145],\n [214, -203, 274, -414, -24, 264, -289, 238, 76]]\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[[-92, 66, 30, 14, 176, 64, 156, -22, -18],\n [-60, 153, -79, -53, -136, -182, -308, 93, 167],\n [187, -249, 34, 33, -110, 91, 91, -69, -151],\n [-369, 234, -171, -64, 208, -185, -55, -182, -158],\n [267, -81, 90, 16, -271, 26, -176, 227, 263],\n [45, -99, -38, -5, -82, -27, -35, -71, -109],\n [-287, 39, -144, -29, 240, -73, 143, -309, -371],\n [302, -174, 144, 51, -175, 147, 29, 170, 160],\n [196, -105, 71, 22, -159, 55, -49, 115, 115]]?\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[[-172, 1, -91, -10, -46, -19, 487, 247, -708],\n [-65, -27, 393, 408, 82, 362, 423, -39, -448],\n [91, -566, -195, -193, 541, -180, 31, -192, 467],\n [-44, 299, 440, 296, -62, 249, -424, 277, 134],\n [137, -512, 400, 488, 162, 509, 744, -666, 174],\n [62, 230, -318, -225, -309, -328, -80, 56, -332],\n [-23, 163, -416, -434, 59, -451, -417, 244, -66],\n [164, -22, 420, 428, 4, 122, -72, 50, -128],\n [48, -58, -674, -718, 66, -563, -610, 26, 743]]\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[[-80, 96, 103, 60, -45, 246, -76, -64, -98],\n [-11, 179, -6, 115, 120, -240, 140, 28, -117],\n [-447, 591, 402, 435, -160, 408, 212, -156, -413],\n [94, -110, -118, -70, 54, -276, 80, 72, 110],\n [-440, 394, 347, 335, -279, 336, 290, -114, -217],\n [4, -174, -80, -75, -98, -234, 186, 74, 207],\n [-441, 439, 379, 350, -257, 456, 202, -146, -282],\n [-105, -65, 70, -10, -178, 174, 38, -26, 80],\n [-184, 334, 135, 245, 9, -84, 238, -22, -207]]\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[[519, 265, -196, 271, -5, -277, -52, 721, 214],\n [-159, 232, 214, -324, -346, -162, 19, 262, -26],\n [-48, 59, 48, 143, -122, -530, -325, 184, -115],\n [442, -63, -340, 444, 267, -49, 34, 207, 156],\n [-524, 49, 322, -469, -274, -42, 71, -117, -317],\n [293, 296, -222, -67, 4, 12, -236, -25, 110],\n [-52, -7, 230, 157, -119, -305, -653, -224, 196],\n [82, 163, -16, -71, -197, -171, 81, 303, 76],\n [-302, 221, 41, -498, 3, 150, -71, -244, -472]]\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[[150, 146, -168, -241, 101, 236, -123, -174, -57],\n [138, 174, -152, -271, 91, 244, -101, -146, -71],\n [12, -90, -20, 107, 13, -50, -41, -50, 43],\n [-66, -342, 56, 451, -31, -292, -31, -22, 155],\n [108, 244, -112, -346, 66, 264, -46, -76, -106],\n [-6, 200, 20, -246, -14, 130, 68, 80, -94],\n [-165, -80, 190, 165, -115, -205, 160, 220, 25],\n [252, -30, -300, -63, 183, 210, -291, -390, 33],\n [-168, 144, 208, -112, -128, -56, 232, 304, -80]]?\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[[-153, -61, 103, -163, -149, -173, 5, -209, 235],\n [-126, 138, 306, -186, 42, 234, 150, -318, -150],\n [-195, 25, 252, -236, -100, -15, 86, -346, 112],\n [-6, -62, -66, 10, -58, -126, -46, 38, 118],\n [81, 157, 92, 52, 188, 341, 94, 14, -352],\n [228, -84, -359, 291, 69, -92, -143, 447, -31],\n [-96, 48, 166, -126, -18, 64, 70, -198, -10],\n [-198, 74, 313, -253, -59, 82, 125, -389, 25],\n [-15, 45, 70, -30, 30, 85, 40, -60, -70]]\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 9x9 matrix:\n[[-214, -211, 121, -319, 16, 246, 298, -256, 96],\n [480, 52, -9, -138, -353, -186, -387, -40, -17],\n [-98, 73, -311, 293, 238, -209, -73, 37, 450],\n [45, -54, 600, -74, 30, 570, -537, -267, 195],\n [185, 193, 202, 142, 61, 72, -612, -237, 250],\n [-24, -61, 45, -112, -182, 20, 210, 70, -384],\n [269, 23, -365, -301, -74, -445, 408, 158, -105],\n [117, -70, -227, -11, 3, -162, 16, 121, 299],\n [-210, -103, 381, -269, 320, 450, 216, -140, 89]]\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[[161, -40, 117, -193, 182, 267, 195, 260, 333],\n [26, -28, 17, -23, 312, 354, -117, 147, 269],\n [-53, 182, 333, 2, 420, 284, -34, 494, 315],\n [487, -273, -117, -26, 112, 100, 36, 29, -34],\n [-215, 140, 94, -41, -162, -152, 165, 51, 96],\n [-169, 223, 327, -494, 36, 352, 112, -47, -186],\n [107, -26, -4, 60, -92, -179, -2, -49, -232],\n [-219, 112, 87, -126, 106, 234, 22, 80, 265],\n [-381, 3, -296, 128, -269, -156, -94, -350, 102]]\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 9x9 matrix:\n[[238, 330, -265, 383, 87, -64, -471, -124, 73],\n [-598, -352, -120, -463, -77, 22, -441, -10, -502],\n [-445, 19, 330, -258, 142, 130, 45, 109, -557],\n [34, 501, 190, -87, 102, 33, 11, -97, -586],\n [-573, -517, 391, -271, 189, 195, 484, 422, -144],\n [386, -506, 343, 149, -261, -138, 91, 221, 34],\n [-76, 108, -625, 118, 47, -403, 122, -442, -281],\n [-384, -41, -78, -577, -21, 111, 123, -46, -82],\n [256, -210, -736, -252, -501, -476, 144, -603, 42]]\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[[-264, 176, 225, -337, -27, 70, 27, -141, 43],\n [-216, 144, 270, -270, 270, 0, 234, -270, 18],\n [162, -108, -180, 204, -126, -15, -120, 162, -18],\n [24, -16, 75, 37, 327, -70, 233, -159, -23],\n [30, -20, -105, 33, -267, 45, -199, 159, 11],\n [-126, 84, 255, -151, 489, -65, 377, -333, -9],\n [-204, 136, 150, -262, -102, 70, -38, -66, 38],\n [108, -72, -90, 138, 18, -30, -6, 54, -18],\n [-84, 56, 150, -102, 258, -30, 202, -186, -2]]?\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 9x9 matrix:\n[[-112, -86, -44, 118, 224, -226, -256, 124, -342],\n [-1, -14, 40, 70, 119, -103, -97, 139, -267],\n [88, 54, 76, -22, -56, 74, 104, 44, -2],\n [100, 70, 60, -70, -140, 150, 180, -40, 170],\n [38, 38, -12, -86, -154, 144, 150, -134, 292],\n [-61, -18, -112, -86, -133, 97, 67, -233, 389],\n [-199, -126, -160, 70, 161, -197, -263, -59, -73],\n [-382, -237, -322, 109, 266, -341, -470, -164, -43],\n [-5, -13, 26, 53, 91, -80, -77, 101, -198]]\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 9x9 matrix:\n[[305, -65, 44, -205, 107, -46, 53, -36, -143],\n [-317, 354, -395, 340, 268, 155, 94, -15, 191],\n [210, 73, 45, 122, -231, -24, -103, -163, -244],\n [294, -402, 413, -418, -201, -181, 16, 78, 60],\n [-411, -203, 181, -10, -198, -34, -51, 191, 331],\n [-290, -420, 248, -430, -68, -202, -78, 295, 20],\n [-91, 243, -292, 99, 197, -70, 279, 1, 491],\n [573, -213, 300, -297, -129, -126, 105, -84, 45],\n [52, -238, 67, -542, -41, -519, 304, 190, 518]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 9x9 matrix:\n[[-368, -340, -580, -187, 592, -15, -8, -450, 465],\n [141, -242, -189, 172, -52, -319, 170, -51, -87],\n [-414, 261, 72, 196, 20, -29, -60, 219, 435],\n [-333, -460, -585, 61, 111, -258, -164, -647, 52],\n [165, -324, -292, 526, 81, -126, 408, 274, 117],\n [393, -247, -51, 195, -29, 227, 250, 136, -263],\n [-31, -302, -289, 445, 289, 485, 335, 212, 300],\n [-92, -335, -156, 52, 131, -167, 482, -249, 367],\n [-127, 288, 213, 250, -80, 460, -135, 398, 73]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-249, 688, -149, -101, -141, 182, -191, 13, 355],\n [-224, 282, -39, -78, -20, 227, -139, 42, -50],\n [68, -55, 284, -238, 278, 4, -20, 162, 0],\n [17, -33, -252, 121, 147, -317, -230, 565, -251],\n [-65, 89, 155, -143, 45, 178, 9, -93, 47],\n [3, -148, -382, 289, -25, -297, -156, 389, -337],\n [-16, 574, 13, -174, -44, -17, -71, -10, 602],\n [-68, 0, 21, -94, 240, -33, -191, 409, -261],\n [42, 58, -14, -66, 194, -184, -146, 381, -25]]\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[[-240, -32, 288, 160, 272, 288, 256, -192, 128],\n [-30, -4, 36, 20, 34, 36, 32, -24, 16],\n [150, 20, -180, -100, -170, -180, -160, 120, -80],\n [-135, -18, 162, 90, 153, 162, 144, -108, 72],\n [180, 24, -216, -120, -204, -216, -192, 144, -96],\n [45, 6, -54, -30, -51, -54, -48, 36, -24],\n [45, 6, -54, -30, -51, -54, -48, 36, -24],\n [-210, -28, 252, 140, 238, 252, 224, -168, 112],\n [225, 30, -270, -150, -255, -270, -240, 180, -120]]\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[[-125, -38, 213, -187, -221, 122, 334, -125, 397],\n [132, 26, 709, -386, -61, -148, -308, 454, -9],\n [277, -110, -40, 147, -82, -175, -104, 176, -261],\n [-228, 258, -77, 52, 40, 210, -106, 133, -108],\n [0, 242, -238, 196, -169, 122, 80, -221, -361],\n [306, -201, 240, -161, 331, -393, -431, 121, -164],\n [-166, 174, 251, -288, 189, 41, -140, -173, 62],\n [242, -342, -254, 168, 284, -290, -154, 36, -34],\n [-303, 106, -774, 437, 11, 323, 346, -357, 36]]\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[[-297, -382, -280, -127, -118, 301, -122, -330, -96],\n [-153, 141, 358, -278, -344, -43, 81, -292, -350],\n [-64, -133, -250, 21, 42, 128, -61, 26, 130],\n [95, -21, 504, 77, 3, -97, -9, -277, -414],\n [-40, -83, -120, -110, 76, -248, 156, -3, 24],\n [176, -78, 234, 99, 257, -402, 152, -49, -172],\n [-139, -4, -112, -125, -154, 135, -26, -52, 24],\n [-85, -59, -306, -52, 3, 71, -4, 96, 200],\n [80, -82, -82, 85, 185, -138, 46, 77, 72]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[319, -510, -4, -455, -49, 122, -492, 404, -119],\n [82, 347, -501, 178, 25, 17, 343, -544, 300],\n [661, -284, -581, -147, 183, 199, -144, -1, 140],\n [-509, 406, 403, 195, 77, 148, -2, 574, -133],\n [-352, 237, 517, -17, 21, -173, -148, 113, -238],\n [-182, 390, 262, 136, 205, -362, -400, -66, -88],\n [26, -537, -60, -248, -243, 196, -360, 728, -29],\n [-335, 233, -104, 416, -61, 14, 220, 52, 244],\n [-261, 189, 114, 192, 149, 117, -440, 643, 127]]\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[[45, -371, -65, -244, -337, -72, -67, 342, 169],\n [-183, -340, -45, -408, 131, 555, 32, -83, 342],\n [-7, 287, 186, -17, -189, -23, -118, 193, -582],\n [-252, -246, 14, -175, 376, 477, 139, -207, 394],\n [-552, -565, 77, -160, 169, 205, 177, -169, 196],\n [-351, -501, 513, 694, 166, -14, 286, 19, -103],\n [-120, -652, -310, -513, -726, 375, -21, 405, 58],\n [379, 239, -66, 26, -139, -370, -28, 250, 88],\n [-216, -21, 28, 620, 197, -248, -319, 69, -92]]\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[[-258, -23, -42, -299, -324, -144, -22, -46, 139],\n [-181, 116, -267, -233, 121, 203, -94, -121, -105],\n [-71, -214, -173, -7, 93, 105, 2, 91, 119],\n [-69, 63, 249, -120, -429, -327, 36, -33, 102],\n [-292, -312, -280, -234, -102, 48, -16, 90, 264],\n [88, 206, 336, 18, -292, -284, 36, -72, -50],\n [182, 101, -26, 189, 320, 184, -14, -18, -185],\n [-325, -335, -273, -267, -164, 11, -12, 96, 302],\n [7, -332, 97, 103, -183, -177, 90, 191, 283]]\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[[-244, 700, -7, 313, -527, -419, 171, -339, 1],\n [275, -99, -44, 470, -449, 283, -67, 142, -448],\n [357, -425, -540, -18, 27, 606, -252, 336, -64],\n [190, -216, -199, -17, -49, 503, -407, 107, 229],\n [-109, -90, -326, -138, 35, -171, -73, -211, -400],\n [-141, -468, 95, -596, 575, 123, -496, -193, 251],\n [17, 185, 173, 466, -485, -49, 30, -118, -405],\n [101, 73, 297, 292, -88, 44, 322, 241, -35],\n [-1, -173, 267, -73, 137, 70, -131, -12, 57]]\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[[84, 127, 153, 33, -153, -236, -86, 137, 180],\n [-433, 96, -189, 109, -215, 129, 120, -8, -145],\n [10, -173, -390, -147, 144, 89, -251, -119, -143],\n [293, -265, 292, -256, 26, 149, -68, -251, 5],\n [100, -109, -243, 45, 501, 24, -142, 261, 214],\n [-161, -9, -213, -28, -101, 32, -101, -41, -88],\n [-324, 42, 119, -24, -461, 125, 99, -160, -121],\n [-101, 152, 495, -1, -579, -39, 235, -185, -72],\n [381, -162, 214, -59, 405, 116, 162, -107, -26]]\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 9x9 matrix:\n[[-100, 90, -232, -109, -71, -81, -358, -329, 26],\n [-418, -186, -76, -268, -290, -273, -55, 4, -109],\n [-243, -102, -50, -122, -128, -124, -6, 47, -45],\n [37, 60, -82, -169, -177, -157, -314, -404, -53],\n [-235, -174, 78, -33, -55, -52, 257, 330, -46],\n [-72, 62, -176, -200, -190, -179, -393, -434, -37],\n [201, 102, -10, -118, -136, -110, -288, -437, -51],\n [-219, -52, -82, 119, 159, 123, 174, 348, 83],\n [-420, -72, -232, -61, -13, -44, -63, 133, 45]]\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[[27, 450, 462, 99, -357, 138, -408, 318, 189],\n [-213, -284, -538, -111, 517, 524, -304, 280, -465],\n [69, 275, 104, 142, -62, 109, -246, 115, -38],\n [384, 224, 244, 92, -236, -512, 280, -432, 236],\n [-15, -233, -642, 24, 584, 289, -98, -33, -516],\n [-189, -534, 38, -485, -57, -138, 316, -10, 253],\n [264, 52, 457, -309, -378, -387, 111, -148, 441],\n [-432, -180, -237, 209, 146, 263, 93, 180, -181],\n [-501, -20, -346, 389, 264, 543, -181, 372, -391]]\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[[188, -189, -222, 108, -359, 372, 89, -328, -391],\n [562, 147, 31, 530, -133, 42, 129, -246, -156],\n [-129, 244, 198, -146, 32, -27, -419, 113, 522],\n [27, -13, -445, 75, 169, 280, 171, -242, -35],\n [-343, -502, -264, -52, 545, -132, 111, 42, -248],\n [138, -16, 8, -14, -46, -378, 400, -18, -93],\n [111, -18, -140, 248, 93, -324, -52, -377, 400],\n [-269, -378, -185, 40, 52, 197, -114, -276, 287],\n [7, 279, -50, -249, 216, -119, 129, 167, 222]]?\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 9x9 matrix:\n[[59, 138, 301, 218, 126, 16, 515, -231, 11],\n [37, -29, 105, 240, 219, 82, 127, -64, -219],\n [-101, -39, -219, -470, -345, -95, -361, 174, 366],\n [-7, 194, 65, 380, 56, -71, 115, -99, -406],\n [-65, -122, 188, -68, 101, 100, 103, -15, 60],\n [-218, 481, 143, 384, 152, 50, 56, -337, 55],\n [19, -92, -190, -126, 26, 59, -259, 86, 142],\n [313, -302, -307, -18, 39, -22, -123, 230, -230],\n [268, 32, 133, 148, -39, -125, 554, -90, -120]]\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[[-294, -315, 325, 330, 257, 505, -160, -539, -125],\n [-67, 284, -233, -123, -201, -561, 160, 403, -233],\n [31, -151, 156, -41, 65, 174, -351, 31, 164],\n [-32, 98, -174, 334, -226, -105, 585, 325, 32],\n [-392, -76, 180, 88, 95, -90, -333, -71, -358],\n [299, 238, -265, -265, -232, -373, 127, 508, 201],\n [-435, -207, 298, 183, 272, 229, -307, -539, -398],\n [-3, 20, -29, 23, 74, 80, 186, -303, -97],\n [262, -99, 17, 14, -87, 193, -48, 289, 447]]\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[[-42, -12, -18, 33, -9, 45, 48, -30, -30],\n [238, 68, 102, -187, 51, -255, -272, 170, 170],\n [-84, -24, -36, 66, -18, 90, 96, -60, -60],\n [-168, -48, -72, 132, -36, 180, 192, -120, -120],\n [238, 68, 102, -187, 51, -255, -272, 170, 170],\n [-140, -40, -60, 110, -30, 150, 160, -100, -100],\n [182, 52, 78, -143, 39, -195, -208, 130, 130],\n [-112, -32, -48, 88, -24, 120, 128, -80, -80],\n [-154, -44, -66, 121, -33, 165, 176, -110, -110]]\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, -210, 195, 15, -120, -60, 195, 135, 45],\n [-150, -210, 195, 15, -120, -60, 195, 135, 45],\n [-90, -126, 117, 9, -72, -36, 117, 81, 27],\n [60, 84, -78, -6, 48, 24, -78, -54, -18],\n [40, 56, -52, -4, 32, 16, -52, -36, -12],\n [-40, -56, 52, 4, -32, -16, 52, 36, 12],\n [-70, -98, 91, 7, -56, -28, 91, 63, 21],\n [150, 210, -195, -15, 120, 60, -195, -135, -45],\n [-70, -98, 91, 7, -56, -28, 91, 63, 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[[-77, -199, -66, 178, 36, 3, -188, -70, -257],\n [127, -488, -344, 103, 1, 120, -315, -115, -337],\n [59, 175, -96, 36, 10, 313, -246, 338, 501],\n [-357, 62, 183, -45, 577, -663, 403, 255, -255],\n [138, 87, -106, 265, 28, 208, -191, -151, 206],\n [108, -96, -147, -211, 450, -227, 554, -130, -395],\n [57, -426, -265, -87, -16, 70, -165, 28, -322],\n [435, 187, -69, -459, 28, 277, 394, 257, 285],\n [-170, 11, 82, -107, -176, -22, -27, 54, 17]]\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[[-32, 59, 232, -67, -15, 72, -138, 158, 14],\n [-72, -198, 396, -198, -18, 288, 36, 72, 252],\n [16, 107, -64, 53, 1, -88, -74, 38, -98],\n [-10, 109, 107, -8, -9, -12, -138, 127, -56],\n [-44, -58, 266, -112, -14, 152, -44, 98, 112],\n [-40, -278, 156, -134, -2, 224, 196, -104, 252],\n [36, -27, -246, 81, 15, -96, 114, -144, -42],\n [-10, 235, 155, 10, -15, -60, -270, 235, -140],\n [-44, -184, 218, -130, -8, 200, 88, -10, 196]]\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[[561, 232, 647, 31, -336, 108, -113, 198, 461],\n [-279, 564, 8, -140, -183, -5, 476, -125, -128],\n [474, -622, 437, -418, 515, 491, -255, -201, 205],\n [394, -151, -71, -403, -5, -151, -12, -542, 643],\n [-131, -34, -360, -382, 275, 6, 317, -329, -71],\n [34, -107, -713, 176, -107, -347, 108, -502, 283],\n [-224, -387, 123, 282, 73, 61, -439, -31, -151],\n [-315, -45, 44, -23, 3, -167, -238, 239, -194],\n [-30, 288, -166, 568, -534, -373, -95, 150, 143]]\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[[-132, -781, -425, 96, -237, 498, 102, 70, -651],\n [315, 265, 84, -376, 173, -241, -276, -24, 155],\n [-61, -94, 93, -253, -98, 108, -467, 639, -288],\n [22, 12, -81, -213, 0, 244, -69, 392, 392],\n [-293, -162, -288, 87, -177, 361, 329, 333, 370],\n [-106, -469, -185, -124, 452, 517, 314, 140, -341],\n [-140, 321, -57, 259, -331, -310, -70, 249, 403],\n [-26, 361, 346, -296, 326, -228, -27, -38, -7],\n [-114, 202, -62, -158, 600, -84, 68, 298, -8]]?\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[[-212, 139, 195, -465, 790, -137, 130, 80, 304],\n [24, 438, 312, -439, 92, -158, -35, 242, -264],\n [-322, -347, -56, -361, 252, 686, 238, -510, 98],\n [258, -88, -65, 84, -45, -35, -59, -236, -208],\n [168, -3, 113, 643, -325, 208, -137, -307, 345],\n [-419, 307, 69, -231, 462, 437, 139, -377, 287],\n [164, -47, -87, 11, 683, 72, 689, -91, 106],\n [110, -490, -153, 146, -154, -58, -530, -355, 150],\n [567, 20, 39, 744, -510, -584, -271, 282, -43]]\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[[-394, -584, -155, 21, 474, -254, -317, -412, -398],\n [-43, 182, 110, -346, 390, -208, -767, -123, -592],\n [-96, -210, 155, 276, -145, -179, 210, -25, 283],\n [-30, -380, -496, 365, 217, -117, -51, 71, -189],\n [-40, -366, -626, 157, 175, 233, 235, -13, -121],\n [248, 184, -59, 161, -450, 112, 629, 184, 472],\n [165, 26, -145, 202, -87, -482, 63, -21, -40],\n [-43, 137, 116, -187, 279, 62, -602, 81, -355],\n [-42, -92, -79, 92, 265, -231, -456, 29, -327]]\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 9x9 matrix:\n[[74, 116, -336, 256, -116, -202, 32, -350, 534],\n [-116, 1, -346, 177, -45, -197, 30, -222, 520],\n [60, 6, 87, 139, -232, -227, 191, -177, 22],\n [-125, -153, 24, 341, -389, -616, 460, -241, 221],\n [334, 267, -124, 89, -39, 121, -140, -270, 170],\n [-145, -7, -119, -168, 141, 197, -183, 48, 95],\n [-27, 36, -224, -207, 481, 442, -390, 329, 3],\n [-154, -71, 11, -148, 97, 114, -77, 125, -60],\n [138, 172, 173, -352, 97, 498, -317, 19, -300]]\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 9x9 matrix:\n[[145, -477, -194, 157, -186, -172, 287, 212, 317],\n [207, -192, -70, 209, -184, -192, 295, 50, 106],\n [61, 273, 198, -148, 55, 99, -365, -44, -426],\n [-312, 165, 72, -169, 169, 145, -218, -162, -46],\n [-318, 291, 228, -310, 224, 274, -512, -150, -279],\n [-171, -104, 186, -256, 21, 107, -515, -10, -297],\n [-394, 413, 116, -97, 192, 69, -122, -424, -148],\n [-480, 37, 186, -147, 114, 136, -204, -292, 20],\n [-212, -155, -56, -20, 108, 198, 158, 106, 487]]\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 9x9 matrix:\n[[124, -237, -85, -443, 260, 331, -354, 128, -176],\n [123, 365, -17, 125, -269, 205, -118, 210, -64],\n [198, -649, 523, -123, -282, 380, -396, 159, 256],\n [216, 549, -42, 356, -74, -174, -150, 47, -22],\n [456, 240, 10, -312, 156, 244, -102, -61, -25],\n [150, -181, 54, -376, 190, -44, -347, -32, -98],\n [414, 485, 75, 226, -143, 99, 531, -146, 265],\n [-318, 360, -122, 365, -141, -160, 446, -164, 28],\n [507, 693, -200, -219, -48, 168, 248, 72, -95]]\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[[-197, -353, 362, 35, -472, -212, 365, -402, 196],\n [183, 10, 401, 222, 302, -186, 38, -239, -189],\n [-280, -518, 149, 95, -187, 114, 154, -724, 377],\n [-440, -363, 75, -44, 41, 243, -67, -538, 478],\n [-310, -76, 255, -208, -174, -98, 144, -174, 101],\n [-379, 18, 211, 47, 541, 168, -244, -647, -31],\n [245, 2, -378, -111, -121, -239, 198, 378, -91],\n [-66, 129, -84, -40, -135, -4, -19, 155, -64],\n [-126, 130, -98, -169, -479, 156, -77, 570, 248]]\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[[172, 202, -107, 223, 287, -158, 290, -251, 105],\n [-248, 89, 14, -3, -132, 342, 1, 211, -186],\n [-260, 334, -66, 291, -162, 533, -144, 411, -188],\n [217, 168, -83, 243, 282, -185, 443, -409, 164],\n [138, 377, -184, 325, 408, -102, 315, -173, 42],\n [176, 206, -161, 52, 549, -361, 376, -298, 25],\n [-301, 248, -36, 132, -107, 477, 17, 298, -235],\n [-175, 77, 16, 103, -275, 349, -336, 387, -101],\n [70, 187, -47, 313, -17, 119, 87, -51, 93]]\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[[-217, -223, 238, 331, 415, -143, -347, -135, 395],\n [145, 172, 77, -176, 72, 117, -266, -345, -464],\n [-97, 155, 209, -76, 187, 37, -448, -254, 326],\n [463, 222, 493, -90, 133, 934, 217, 323, -298],\n [519, 262, 221, -459, -301, 545, 337, 160, -272],\n [-198, 260, -150, 141, 600, -133, 144, -135, -72],\n [137, 622, -353, -311, -236, 731, 690, 267, -630],\n [-111, 69, -206, -176, -272, -170, -16, -101, 131],\n [350, -88, -111, -185, -598, -23, 285, 396, -95]]\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[[195, -15, -60, 195, -150, 270, -135, 15, -195],\n [52, -4, -16, 52, -40, 72, -36, 4, -52],\n [-182, 14, 56, -182, 140, -252, 126, -14, 182],\n [143, -11, -44, 143, -110, 198, -99, 11, -143],\n [-169, 13, 52, -169, 130, -234, 117, -13, 169],\n [-195, 15, 60, -195, 150, -270, 135, -15, 195],\n [130, -10, -40, 130, -100, 180, -90, 10, -130],\n [52, -4, -16, 52, -40, 72, -36, 4, -52],\n [-169, 13, 52, -169, 130, -234, 117, -13, 169]]\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[[-144, 232, 56, 132, -116, -142, -200, -260, -134],\n [-278, 138, 195, -377, -68, 173, 18, -78, 585],\n [-232, 130, 112, 0, -36, -64, 156, 10, 208],\n [-138, -40, 89, -175, 44, 89, 282, 188, 389],\n [-206, -27, 129, -227, 46, 107, 360, 225, 519],\n [-106, 28, 49, 3, 6, -28, 150, 70, 124],\n [-280, 278, 160, -112, -140, -16, -172, -274, 224],\n [-84, 67, 20, 132, -14, -112, 82, 7, -56],\n [-110, -37, 85, -227, 30, 129, 188, 131, 389]]\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 9x9 matrix:\n[[-127, 41, -12, -168, 209, 30, -295, -453, 216],\n [-198, -248, 55, -224, 214, -145, 703, 96, 196],\n [66, -239, 87, -40, 36, 264, -22, 200, -318],\n [-212, -156, -223, 136, 154, -278, 755, 498, -70],\n [-376, 25, -366, -175, 294, 276, -105, 114, -142],\n [-245, 41, 92, -262, 595, 183, -81, -168, 80],\n [-329, -134, -312, 188, 273, -551, 500, -71, 250],\n [6, 403, -326, -211, 204, 553, -367, 458, -398],\n [-360, -92, -113, -354, 465, 443, -142, -9, -133]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[197, -41, 99, -66, 223, -387, -52, -204, 126],\n [135, -27, 69, -42, 153, -261, -30, -138, 90],\n [-202, -2, -148, -62, -236, 228, -173, 137, -276],\n [-165, -15, -135, -90, -195, 135, -210, 90, -270],\n [101, -17, 55, -22, 115, -183, -6, -98, 78],\n [-40, -56, -88, -176, -56, -168, -320, -64, -240],\n [-29, -55, -79, -170, -43, -177, -306, -70, -222],\n [139, -43, 55, -88, 155, -327, -109, -167, 42],\n [18, -54, -44, -154, 12, -228, -263, -101, -156]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 9x9 matrix:\n[[-214, 23, 432, -212, 281, -174, 183, 29, 152],\n [203, -441, -729, 577, -94, 254, -486, 234, 433],\n [177, 127, -536, -137, -175, -444, -280, -141, 87],\n [240, 195, -96, -49, 507, -4, -83, 322, -141],\n [404, 54, -366, -227, -33, 250, -278, 226, -38],\n [92, 515, 54, -391, 19, -378, 160, -229, -496],\n [274, 302, -69, -88, 99, -162, 364, -87, -328],\n [-294, 100, 167, 322, 530, 64, -309, 191, -230],\n [-99, -265, -60, 401, 317, 198, -118, 176, 291]]\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 9x9 matrix:\n[[211, 218, 49, -325, -82, -225, -7, 281, -338],\n [-129, -247, -407, -4, 403, 120, -229, -164, 104],\n [83, -22, 243, -318, -313, -377, 226, -104, 142],\n [173, 28, -225, 636, 284, 494, -476, -241, -291],\n [-665, 91, -223, -6, 824, 122, -560, -82, -198],\n [320, 2, 445, -57, -575, -41, 116, 34, -184],\n [-171, 232, -323, 612, 500, 42, -64, -433, 347],\n [238, -263, -140, 437, -101, 626, -59, 146, -43],\n [-262, -56, 603, -65, -422, -121, 385, -57, 441]]\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 9x9 matrix:\n[[351, -220, -368, -8, 125, -31, -239, -165, -11],\n [217, -103, -314, 98, -97, 26, -49, 34, 152],\n [-313, 580, 281, 410, 37, 152, 83, 33, 163],\n [42, -348, -108, -436, 66, -127, -103, -304, -342],\n [59, 163, -353, 276, -15, -45, 81, 56, 366],\n [249, 113, 19, 312, 203, 79, -189, 116, 142],\n [168, -302, 14, -173, -241, 144, -108, 20, -210],\n [286, -372, -88, -177, 45, -115, -43, 178, -2],\n [-186, 423, -193, 295, 241, -140, 110, -115, 319]]\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[[-35, 63, -7, 63, 56, 91, -70, 91, 7],\n [25, -45, 5, -45, -40, -65, 50, -65, -5],\n [-85, 153, -17, 153, 136, 221, -170, 221, 17],\n [-20, 36, -4, 36, 32, 52, -40, 52, 4],\n [65, -117, 13, -117, -104, -169, 130, -169, -13],\n [70, -126, 14, -126, -112, -182, 140, -182, -14],\n [-30, 54, -6, 54, 48, 78, -60, 78, 6],\n [5, -9, 1, -9, -8, -13, 10, -13, -1],\n [30, -54, 6, -54, -48, -78, 60, -78, -6]]\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, 42, -388, 63, -493, -97, -95, 116, 534],\n [104, -26, 142, 239, 15, -126, -55, -224, -150],\n [153, -67, 29, 282, -104, -116, -109, -87, 20],\n [2, 158, -84, -7, -267, -162, 29, -322, 100],\n [89, -300, 206, 185, -210, 225, -224, 139, -217],\n [141, -27, -128, -10, -279, 99, -105, -17, -24],\n [148, -161, 35, 122, -57, 135, -140, 120, -139],\n [141, -225, 40, 241, 242, 71, -116, 379, 6],\n [-59, 194, -281, -145, 471, -162, 214, 265, 357]]\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[[129, 166, 216, 90, -122, -195, 63, 13, -159],\n [-81, 82, 258, -120, -262, -195, 7, 13, -243],\n [-105, 2, 114, -120, -150, -75, -17, 5, -123],\n [-207, 58, 339, -255, -394, -240, -20, 16, -342],\n [198, -44, -300, 240, 356, 210, 22, -14, 306],\n [75, 30, -15, 75, 50, 0, 20, 0, 30],\n [-30, -56, -87, -15, 60, 75, -19, -5, 69],\n [294, 276, 276, 240, -92, -270, 118, 18, -174],\n [237, 42, -159, 255, 254, 90, 50, -6, 192]]\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[[279, 32, 115, -445, 327, 425, 215, -570, -55],\n [150, 113, -6, -522, 443, -23, -117, -227, 197],\n [12, -311, 259, 112, -90, 203, 255, -149, 90],\n [-8, -74, -512, -173, 190, 160, -414, -1, -131],\n [218, 105, -373, -206, 142, -59, -297, -81, 410],\n [233, 524, 58, 224, -364, -342, 35, 121, 284],\n [-182, -421, 257, -60, 138, -22, -77, 97, 55],\n [-17, -65, -37, -263, 276, 2, -275, -5, -96],\n [-295, 177, -40, -126, 157, -355, -143, 336, -169]]\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, -261, -93, -407, 544, 299, 501, 248, 134],\n [-114, 262, -537, -678, 506, 122, 2, 165, -63],\n [863, 374, -580, -838, -434, -239, -231, 146, 331],\n [-37, -450, -72, 87, 118, -48, 293, -67, 382],\n [480, 290, 237, -241, -245, 227, 215, 54, -331],\n [-355, -285, 198, 132, 241, 322, 470, -120, -361],\n [99, -523, 457, 431, -114, 6, 731, -217, 57],\n [510, -161, -350, -364, 67, -269, 117, 131, 756],\n [107, 470, -104, -149, 59, -6, -270, -25, 17]]\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 9x9 matrix:\n[[-428, 287, 23, 112, 222, 119, 84, 184, 89],\n [-258, 458, 5, 310, -157, 139, -85, 53, 332],\n [2, -328, 183, -293, -15, -119, 406, 69, -584],\n [-126, 181, -120, -324, -159, 118, -7, 67, -3],\n [368, -359, 93, -165, -142, -75, -107, -199, -135],\n [315, -90, -165, -189, -156, 8, -282, -159, 160],\n [291, -265, 247, 61, -477, -212, 365, -94, -463],\n [183, 51, 433, -43, -719, 250, -433, -372, 217],\n [74, -156, 41, -173, 73, 39, -132, -74, -12]]\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 9x9 matrix:\n[[142, -143, -61, -261, -189, 83, -15, -518, 415],\n [33, 67, 41, 26, 24, -34, -37, 37, -47],\n [-361, -47, 177, 178, 290, 131, 78, 245, -99],\n [112, -4, -284, 44, -180, -140, 68, 272, -268],\n [-393, -59, 289, 134, 346, 197, 48, 81, 53],\n [228, 160, -32, -4, -92, -148, -96, 36, -112],\n [-228, 61, 355, 89, 313, 131, -57, -36, 95],\n [330, 0, -394, -90, -368, -201, 25, 68, -158],\n [43, 184, 62, 141, 81, -118, -63, 277, -266]]\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[[-24, -3, -150, -75, 141, 90, -81, -15, -156],\n [31, -28, 130, 65, -112, 24, -93, 13, 329],\n [30, -10, 160, 80, -146, -52, 16, 16, 250],\n [-8, -41, -130, -65, 135, 206, -275, -13, 108],\n [-47, -9, -300, -150, 283, 190, -178, -30, -293],\n [20, 15, 150, 75, -145, -130, 145, 15, 80],\n [-28, 19, -130, -65, 115, 6, 45, -13, -272],\n [-15, -20, -130, -65, 128, 136, -163, -13, -25],\n [-18, 4, -100, -50, 92, 40, -22, -10, -142]]\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[[72, 0, -70, 128, 278, -82, 48, 132, 24],\n [-303, 233, -121, -387, -146, 336, -67, 147, 156],\n [-188, -21, 106, 31, -156, 157, 77, 147, -231],\n [-129, -86, 206, 230, -103, 120, 194, 202, -463],\n [-77, 155, -391, -297, 342, -36, -233, 129, 660],\n [137, 151, 54, -209, -219, 93, 1, -301, -26],\n [-38, -127, 355, 425, -109, 116, 349, 207, -783],\n [-34, 205, 48, -67, 2, 251, 173, 117, -255],\n [177, 192, -81, -84, 186, 33, 60, -54, 45]]\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[[64, 58, 196, -12, 220, 112, -86, 204, -90],\n [-13, 318, 43, -134, 595, 360, 72, 248, -313],\n [-81, -296, 197, 404, -171, 38, 170, -204, 233],\n [-196, 30, -318, -222, 231, -48, -121, -133, -105],\n [19, 105, 76, 5, 343, 69, -300, 173, -157],\n [206, 6, 224, 472, -6, 310, -138, 22, 310],\n [-354, 196, -316, -294, 480, 134, 420, -104, -446],\n [37, -81, 68, 99, -240, 16, 232, -73, 140],\n [209, -178, 490, 210, -223, 9, 14, 199, 180]]\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 9x9 matrix:\n[[-45, -126, 9, -81, -117, 63, -72, 81, -117],\n [-65, -182, 13, -117, -169, 91, -104, 117, -169],\n [-10, -28, 2, -18, -26, 14, -16, 18, -26],\n [25, 70, -5, 45, 65, -35, 40, -45, 65],\n [-45, -126, 9, -81, -117, 63, -72, 81, -117],\n [-55, -154, 11, -99, -143, 77, -88, 99, -143],\n [10, 28, -2, 18, 26, -14, 16, -18, 26],\n [-65, -182, 13, -117, -169, 91, -104, 117, -169],\n [10, 28, -2, 18, 26, -14, 16, -18, 26]]\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[[-372, -192, 162, 357, 132, 414, 137, 63, -281],\n [-376, -15, -33, 661, 171, 246, 32, 3, -625],\n [372, -153, 791, 9, -280, 197, -79, -344, -359],\n [-17, 151, -48, 56, 93, 180, 109, -150, -105],\n [-517, 299, 188, 461, -129, 276, -10, -121, -154],\n [-586, -54, 183, 32, -68, 508, 163, -22, 35],\n [374, -157, -254, -443, 91, -320, -5, 177, 373],\n [-359, -199, 28, -349, -80, 319, 139, 18, 146],\n [291, -171, -110, -79, 9, -474, -168, 295, 259]]?\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[[270, 270, -108, -90, -144, -270, 252, -216, -198],\n [210, 210, -84, -70, -112, -210, 196, -168, -154],\n [135, 135, -54, -45, -72, -135, 126, -108, -99],\n [-150, -150, 60, 50, 80, 150, -140, 120, 110],\n [-105, -105, 42, 35, 56, 105, -98, 84, 77],\n [-210, -210, 84, 70, 112, 210, -196, 168, 154],\n [135, 135, -54, -45, -72, -135, 126, -108, -99],\n [240, 240, -96, -80, -128, -240, 224, -192, -176],\n [-210, -210, 84, 70, 112, 210, -196, 168, 154]]\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[[-149, -109, -126, -17, 5, -3, -14, 115, -40],\n [68, -133, -119, -44, -226, 7, -188, -73, -467],\n [304, 187, -395, -30, 57, -30, 206, -225, 44],\n [322, 284, -759, -56, -207, -131, -112, -721, -78],\n [-151, -118, 74, -138, -156, 142, -114, -333, 119],\n [-457, -322, 195, 62, 88, -102, 390, -104, 38],\n [452, 11, 11, -365, -305, 493, -396, -173, -116],\n [-498, 96, -87, 393, 266, -555, 232, 65, 231],\n [244, -343, 271, -446, -362, 628, -295, -60, -324]]\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, -360, -88, -104, 98, 109, -135, 194, -19],\n [36, 144, 110, 252, 24, -186, 276, 54, 226],\n [140, -616, -189, -314, 130, 182, -427, 385, -16],\n [-114, -220, 165, -242, -164, 428, -414, 377, -230],\n [246, -304, -130, 124, 238, -307, 111, 296, 437],\n [-280, 152, 450, -68, -356, 506, -250, 334, -298],\n [118, -236, -102, -16, 122, -65, -23, 134, 121],\n [98, 68, -229, 74, 156, -264, 226, -373, 62],\n [-40, -154, 195, -24, -88, 226, -150, 390, -15]]\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 9x9 matrix:\n[[-113, 103, 25, -71, 9, 277, -151, 1, 304],\n [-125, 115, 45, -110, -35, 300, -210, -5, 335],\n [-40, 70, 73, -182, -191, 108, -287, -42, 160],\n [147, 152, -13, -108, -167, -124, -58, 48, 91],\n [-326, -189, 445, -125, -417, 61, 60, 277, -149],\n [-91, 158, 225, -309, -433, 145, -319, 112, 294],\n [55, 25, 103, -122, -261, -152, -52, 73, -65],\n [-338, -235, 303, 76, -83, 132, 251, 229, -166],\n [318, 272, -372, -5, 240, -23, -195, -238, 275]]\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[[-207, 252, 255, -58, -30, 131, 235, 92, -132],\n [113, -128, -140, 67, -45, -29, -60, 17, -22],\n [-306, 360, 378, -132, 36, 138, 258, 48, -72],\n [300, -336, -372, 192, -144, -60, -132, 72, -96],\n [-98, 140, 119, 49, -147, 154, 259, 189, -266],\n [71, -68, -89, 88, -108, 37, 51, 98, -136],\n [87, -60, -111, 194, -282, 149, 229, 284, -396],\n [191, -224, -236, 85, -27, -83, -156, -25, 38],\n [-171, 216, 210, -19, -75, 143, 250, 131, -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[[406, -396, 198, 243, 82, -56, -643, -513, -369],\n [219, -706, -42, 31, 571, 78, -309, -76, 118],\n [91, 27, 69, -406, -618, -39, 71, 598, -359],\n [-184, 285, -181, 46, 98, -406, 234, -59, 38],\n [-642, -131, -166, 259, 61, -204, 323, 645, -187],\n [232, -96, 113, -326, 230, 57, 555, 409, 200],\n [328, -364, 117, -45, 115, 240, -519, -401, 161],\n [-190, -205, -307, 642, 714, -395, -69, -444, -459],\n [-376, -257, 60, 439, 517, -87, 240, -144, 116]]\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[[-102, 136, -116, 255, 34, -128, -228, -72, 83],\n [92, -62, 348, -510, -110, -74, 428, -88, -186],\n [-474, -69, 78, 84, 390, 12, -447, 186, -225],\n [-230, -73, -66, 154, 230, 104, -311, 170, -67],\n [184, -179, -106, -31, -32, 292, 115, 174, 50],\n [240, -187, -310, 198, -31, 401, -12, 240, 178],\n [-498, 6, 192, -15, 348, -138, -372, 72, -267],\n [-192, -86, 304, -337, 133, -47, 75, 38, -264],\n [398, -106, -368, 237, -184, 338, 104, 128, 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 9x9 matrix:\n[[265, 253, -2, -224, 173, -319, -492, -90, 74],\n [170, -147, 53, 504, 374, 359, -48, -495, -140],\n [15, 208, 395, 122, -439, 361, 232, -75, -163],\n [-151, -56, 394, 515, -300, 367, 328, -12, -73],\n [-235, -271, 257, 383, -463, 440, 616, 222, -83],\n [601, -551, 116, -377, 28, -354, -456, -88, 244],\n [683, 270, -126, -307, -121, -525, -409, -12, 262],\n [-561, -626, -731, -537, 632, -362, 163, 218, -12],\n [643, 544, 12, -100, 74, -92, -660, -279, 133]]\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[[-324, -140, 106, 92, 256, -40, -42, -50, -90],\n [314, 63, -32, 112, -174, 83, -118, 187, 56],\n [26, -86, -508, 39, -125, 241, -256, -304, -97],\n [-116, 58, 235, -153, 85, -171, 245, 27, 46],\n [-234, -161, 313, 299, 307, -46, -147, 226, -72],\n [88, 128, -279, -335, -217, 5, 195, -293, 46],\n [194, 175, 9, -247, -191, -80, 237, -10, 110],\n [-292, -94, 438, 134, 326, -168, 62, 204, -28],\n [-220, -84, 331, 133, 255, -115, 17, 169, -28]]\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[[478, 694, 471, 220, -9, 204, 275, -94, 103],\n [-348, 2, -786, -134, -534, -159, 68, -249, -225],\n [-210, -83, -716, -23, -308, -246, 20, -251, -184],\n [290, -249, 17, 148, 386, 16, 182, -216, -124],\n [-33, 65, -99, 618, 187, 65, 219, 15, 482],\n [-26, 682, -27, 674, -234, 305, 346, -238, 206],\n [-120, -67, 129, 416, 247, -60, -172, 134, 69],\n [-256, -54, -170, -321, -188, -193, -644, -51, 60],\n [-72, 100, -675, -147, -418, -50, 237, -312, 151]]\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[[-198, -375, 340, -127, 141, 261, -104, 383, -175],\n [76, 416, -314, 46, -130, -146, 36, -338, 250],\n [210, -58, -153, 49, -123, -24, 169, -41, -42],\n [-276, -348, 297, -135, 258, -60, -405, 324, -228],\n [-308, -307, 196, -331, -2, 608, -95, 466, 26],\n [158, 377, -397, 36, -205, -101, 115, -329, 247],\n [-284, 195, -295, -316, -58, 70, -408, 8, 264],\n [-250, 393, -438, -329, -181, 190, -281, -109, 438],\n [154, -25, 117, 156, -23, 56, 288, -37, -60]]\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[[-181, -200, -130, 17, -123, 53, -132, 47, -366],\n [-468, -356, 329, 78, -172, 116, 219, 28, -312],\n [-313, -380, 148, 165, -152, 202, 248, -510, 293],\n [273, 234, -210, 283, -115, 101, -302, 48, -76],\n [397, -59, -285, -242, 198, -263, -517, 33, -2],\n [195, 82, -1, 171, -273, 91, 159, 563, -344],\n [-862, -57, 469, 3, 37, -290, 247, -223, -164],\n [-456, -115, 192, 5, 218, 7, -208, -679, 209],\n [284, 325, -467, -181, 253, -218, -378, -189, 225]]\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 9x9 matrix:\n[[360, -345, 240, 382, -194, -164, 4, 397, -197],\n [-226, 257, -88, -204, 453, 275, -421, -227, 156],\n [-729, -79, 201, -533, -704, -563, 614, -145, 382],\n [-95, -669, 474, 132, 189, -140, 10, 232, 227],\n [-456, 378, 22, -464, -1175, -605, 497, 10, 53],\n [-147, -91, 13, -73, 126, -22, 76, 157, -58],\n [-607, -131, 25, -467, -197, -183, 489, -44, 231],\n [-148, 373, -308, 68, -99, 295, 5, 69, 178],\n [-634, -609, 196, -210, 554, 209, 136, 361, 313]]\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[[-259, 163, -84, -359, 157, 159, -453, -199, 443],\n [365, 162, -87, 79, 19, 687, 9, 440, 354],\n [-33, -275, 566, -221, -353, 136, 304, 176, -419],\n [-63, -492, 323, 150, -335, 86, -179, 132, -108],\n [-116, 303, -159, -75, -272, 45, 154, 199, 23],\n [57, 150, -466, -61, 570, 658, -565, -214, 1051],\n [-119, 162, -472, 33, 721, 98, -343, -323, 764],\n [-196, -213, 92, 283, 113, -674, -35, -240, -553],\n [-240, 81, 28, 131, -515, -24, 417, 246, -453]]\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[[-202, 274, 28, 83, -41, -238, 211, -4, -132],\n [42, 182, -118, 291, 153, -282, 293, -320, 170],\n [-140, 94, 70, -84, -82, -50, -4, 134, -158],\n [-96, -395, 57, 455, 51, 144, -415, -143, -169],\n [92, -369, -21, 319, 118, 137, -311, -195, 37],\n [-184, -404, 116, 380, -41, 233, -476, -6, -284],\n [206, -114, -58, -151, 25, 176, -21, 8, 190],\n [38, 33, 101, -506, 10, -208, -218, 263, -129],\n [138, 87, -187, 436, 180, -126, 338, -439, 315]]\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[[19, 251, 35, -127, -180, -17, 77, -231, 251],\n [17, 135, 18, -64, -86, -14, 35, -128, 135],\n [-6, -126, -18, 66, 96, 6, -42, 114, -126],\n [54, 98, 8, -20, 4, -40, -14, -116, 98],\n [-2, -338, -50, 186, 280, 6, -126, 298, -338],\n [18, 156, 21, -75, -102, -15, 42, -147, 156],\n [82, 94, 4, 0, 52, -60, -42, -128, 94],\n [16, 262, 37, -135, -194, -15, 84, -239, 262],\n [24, 356, 50, -182, -260, -22, 112, -326, 356]]\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 9x9 matrix:\n[[102, -17, -68, 221, -221, 272, 255, -238, -17],\n [42, -7, -28, 91, -91, 112, 105, -98, -7],\n [72, -12, -48, 156, -156, 192, 180, -168, -12],\n [-42, 7, 28, -91, 91, -112, -105, 98, 7],\n [-12, 2, 8, -26, 26, -32, -30, 28, 2],\n [-24, 4, 16, -52, 52, -64, -60, 56, 4],\n [-60, 10, 40, -130, 130, -160, -150, 140, 10],\n [-42, 7, 28, -91, 91, -112, -105, 98, 7],\n [78, -13, -52, 169, -169, 208, 195, -182, -13]]\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 9x9 matrix:\n[[-137, -145, 53, -236, -6, -30, 137, -259, -53],\n [-171, 223, -101, -130, -88, -64, -59, 121, -153],\n [187, -234, 145, 331, 163, 11, -72, 6, 178],\n [134, -446, 216, 232, 170, -86, -14, -224, 196],\n [167, -94, 59, 199, 81, 69, -16, 32, 124],\n [-243, -185, 129, 100, 95, -326, -209, -38, -74],\n [-318, 269, -10, -29, 67, -11, -115, 245, -237],\n [156, 502, -448, -318, -490, -54, -2, 178, -58],\n [-281, -154, 192, 107, 209, -144, -124, -10, -104]]\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[[-92, 41, 288, -37, -149, -153, -486, -116, -171],\n [146, 63, -396, 349, 145, -99, 102, -46, 183],\n [-11, 127, -16, 13, -248, -175, -396, 65, -122],\n [-95, -20, 210, -108, 44, 30, 0, -55, -24],\n [-134, -58, 480, -218, -172, -33, -429, -105, -249],\n [251, -57, -358, 413, 51, -103, -132, -127, 55],\n [-36, -68, 304, -100, -184, -50, -426, -90, -226],\n [-251, 396, -64, -136, -73, -187, 45, 234, 130],\n [171, -46, -444, 146, 165, 141, 519, 122, 210]]\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[[-240, -346, -84, -214, -462, 328, -488, 64, -120],\n [288, 210, 108, 102, 342, -192, 384, -48, 72],\n [-318, -125, -123, -32, -267, 107, -319, 38, -42],\n [-114, 266, -55, 223, 226, -267, 191, -30, 94],\n [186, 157, 69, 82, 243, -145, 269, -34, 54],\n [12, -148, 10, -114, -148, 146, -138, 20, -52],\n [366, -68, 149, -123, 88, 85, 159, -14, -26],\n [234, -264, 103, -245, -172, 271, -115, 22, -94],\n [42, 52, 15, 31, 72, -49, 77, -10, 18]]\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[[-99, -63, -230, -9, 238, 214, 62, -73, -14],\n [73, -13, 74, 215, -220, -86, -194, 171, -148],\n [86, 169, 140, 152, -525, -58, -388, 370, -123],\n [52, 0, 105, -40, 82, -143, 89, -152, 110],\n [-53, -100, 87, -273, 145, -71, 379, -131, 55],\n [-26, 70, -114, -59, 214, 91, 3, -185, 174],\n [-9, -109, 59, -188, 350, -124, 372, -338, 166],\n [-48, -280, 119, -186, 190, -147, 509, -118, -102],\n [-38, -110, 44, -86, -12, -24, 184, 50, -100]]\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[[-80, -40, -20, 45, -45, -60, -20, -5, -5],\n [160, 80, 40, -90, 90, 120, 40, 10, 10],\n [-192, -96, -48, 108, -108, -144, -48, -12, -12],\n [144, 72, 36, -81, 81, 108, 36, 9, 9],\n [272, 136, 68, -153, 153, 204, 68, 17, 17],\n [64, 32, 16, -36, 36, 48, 16, 4, 4],\n [256, 128, 64, -144, 144, 192, 64, 16, 16],\n [-192, -96, -48, 108, -108, -144, -48, -12, -12],\n [208, 104, 52, -117, 117, 156, 52, 13, 13]]\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 9x9 matrix:\n[[-60, 10, -324, 253, 141, -90, -294, 157, 121],\n [80, -90, 248, -207, -119, 74, 162, -79, -31],\n [-25, -45, -253, 189, 103, -67, -270, 149, 134],\n [-15, -95, -315, 229, 123, -81, -366, 205, 196],\n [-130, 210, -250, 228, 136, -82, -72, 20, -58],\n [-15, -135, -411, 297, 159, -105, -486, 273, 264],\n [-85, 85, -289, 238, 136, -85, -204, 102, 51],\n [15, -35, 3, -8, -6, 3, -24, 16, 25],\n [30, -70, 6, -16, -12, 6, -48, 32, 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[[227, -147, 105, -2, -24, -46, -87, -185, 2],\n [-419, 330, 266, -174, 425, -181, 200, 193, 128],\n [268, -186, -534, 300, -490, 254, -130, -44, -192],\n [-124, -78, -216, -92, 137, -113, -52, 88, 79],\n [141, -66, 261, -35, -134, 108, -17, -85, -20],\n [24, 57, -713, 368, -258, 112, -15, 76, -179],\n [-248, 474, -139, 289, -62, 132, 253, 186, -155],\n [352, -306, 297, -129, 31, -113, -167, -302, 68],\n [-179, 303, 309, -10, 181, -43, 181, 53, 11]]\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, 16, -3, -905, -498, -326, 425, -402, 207],\n [264, 334, 167, 169, -82, 300, -146, 335, 367],\n [114, -303, 156, 157, 418, -92, 321, -389, -532],\n [-258, -220, -460, 425, -404, 475, 54, 267, -619],\n [-97, -167, -176, 9, -291, -340, 425, 37, -316],\n [285, 44, 56, 162, -345, -245, 517, 111, -10],\n [188, -117, -17, 540, 610, -298, -323, -2, -55],\n [162, 429, 433, -205, -66, 339, 526, -251, 475],\n [16, -83, -87, 228, -69, 118, -81, 270, -272]]\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 9x9 matrix:\n[[-162, 23, -100, -98, -106, 111, 275, -148, -70],\n [84, 302, -51, 19, -155, 285, -36, 317, 45],\n [-87, -99, 9, -15, 42, -72, 69, -147, 0],\n [-467, -90, 104, 76, 117, 18, 208, -316, 323],\n [-86, 40, 76, 84, 54, 36, -60, 36, 178],\n [388, 395, -133, -37, -257, 312, -155, 547, -169],\n [125, 38, -169, -159, -168, 63, 162, 3, -298],\n [-314, -104, 226, 198, 240, -90, -96, -150, 436],\n [-379, 12, -54, -58, -65, 150, 370, -266, 93]]\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[[382, -129, -196, -282, 229, 125, -50, 490, -101],\n [-45, 236, -160, 345, -148, 145, 6, -135, -345],\n [288, -121, -440, -403, 250, 194, -211, 806, 66],\n [357, -265, -467, -114, 237, 137, -399, 209, -125],\n [-233, -89, 266, 343, 60, -127, 154, -131, -163],\n [-85, 269, 56, 362, -67, -146, 31, -41, -504],\n [-407, -151, 452, 53, 122, -389, -76, -197, 51],\n [-91, 324, 370, -58, -26, -527, 27, -91, -267],\n [-25, 74, 216, -280, 206, -101, 295, 573, 15]]\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[[-297, -25, -224, -807, -110, 118, 857, 54, -189],\n [3, 211, -218, 457, -237, -70, -147, -113, 250],\n [218, 71, 259, 464, 237, -165, -623, -142, -63],\n [-395, 467, 81, 126, -82, 70, -186, 178, -730],\n [-336, 351, -399, -25, 473, -216, 241, -281, 2],\n [323, -37, 197, 63, 486, -94, -59, -349, 242],\n [-104, 0, 94, 181, 51, -418, -331, 14, 141],\n [629, -236, -40, 448, 348, -109, -377, -453, 600],\n [-499, 228, -310, -252, -621, -37, 737, 192, 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[[164, -223, 170, -280, 288, 341, 209, 67, -339],\n [-160, 63, 136, 182, 86, 55, -59, 301, 245],\n [-34, -213, 260, -125, 216, 229, 134, 126, -167],\n [174, -69, 53, -119, 350, 240, 74, 193, -164],\n [174, 207, -262, 71, 44, -77, -110, 36, 87],\n [-290, -588, 457, -391, -381, 26, 337, -594, -499],\n [230, 104, -127, -9, 312, 129, -35, 216, -25],\n [-122, 229, -3, 279, 29, -1, -136, 353, 396],\n [-20, 221, -109, 192, -23, -47, -119, 188, 278]]\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[[-165, -11, -33, 154, 110, -99, -110, 132, 99],\n [-124, 72, 76, 70, 78, -234, -190, 4, 248],\n [48, 72, 96, -84, -36, -108, -60, -120, 120],\n [-123, -77, -111, 154, 86, 63, 10, 180, -75],\n [-120, -94, -132, 161, 85, 99, 35, 198, -114],\n [-203, 61, 53, 147, 131, -270, -235, 74, 283],\n [88, -40, -40, -56, -56, 144, 120, -16, -152],\n [86, 86, 118, -126, -62, -108, -50, -164, 122],\n [-72, 64, 72, 28, 44, -180, -140, -24, 192]]?\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[[-163, -98, 232, -330, -596, 92, -190, 221, 398],\n [-151, -33, 5, 8, 60, -144, 470, 406, -251],\n [18, -132, -87, -239, -37, 418, -56, -488, 13],\n [115, 419, 31, 178, -295, 700, -126, 171, -287],\n [-19, 123, 89, -118, -70, 412, 41, -413, -105],\n [321, 283, 10, 381, -307, 274, -651, 391, 274],\n [-276, -13, 46, -392, -51, 240, 389, -383, -359],\n [-256, 98, 324, -358, -203, 260, 285, -476, -62],\n [154, 149, 180, 97, -242, 514, -157, -69, 236]]?\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[[-593, -131, -201, 58, -77, 8, -211, 790, -227],\n [43, -130, -311, 705, 191, 363, 287, -503, 472],\n [100, -84, 184, -58, -67, -252, -443, -91, -357],\n [50, -97, 142, -441, 54, -659, -646, 283, -419],\n [58, -243, 365, -371, -142, -397, -204, 162, -310],\n [29, -101, 116, -303, 255, -263, -591, 321, -449],\n [112, 272, -164, 199, -12, 343, -24, -302, 127],\n [-25, -51, 250, 66, -299, 261, 246, -100, -83],\n [52, 156, -198, 117, -50, 365, -266, -122, 107]]?\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[[20, 40, -150, 20, 180, 120, 20, 70, 160],\n [14, 28, -105, 14, 126, 84, 14, 49, 112],\n [-30, -60, 225, -30, -270, -180, -30, -105, -240],\n [-10, -20, 75, -10, -90, -60, -10, -35, -80],\n [16, 32, -120, 16, 144, 96, 16, 56, 128],\n [28, 56, -210, 28, 252, 168, 28, 98, 224],\n [6, 12, -45, 6, 54, 36, 6, 21, 48],\n [-32, -64, 240, -32, -288, -192, -32, -112, -256],\n [8, 16, -60, 8, 72, 48, 8, 28, 64]]\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[[-15, 70, -30, -35, 70, 70, 50, -70, -65],\n [24, -112, 48, 56, -112, -112, -80, 112, 104],\n [-30, 140, -60, -70, 140, 140, 100, -140, -130],\n [48, -224, 96, 112, -224, -224, -160, 224, 208],\n [54, -252, 108, 126, -252, -252, -180, 252, 234],\n [0, 0, 0, 0, 0, 0, 0, 0, 0],\n [-9, 42, -18, -21, 42, 42, 30, -42, -39],\n [15, -70, 30, 35, -70, -70, -50, 70, 65],\n [15, -70, 30, 35, -70, -70, -50, 70, 65]]?\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[[-175, 263, -152, -379, 60, -465, 448, -142, -269],\n [84, -327, 165, -197, 345, 435, -329, -555, -204],\n [23, 227, -388, -303, 144, -354, 142, -367, -490],\n [-185, 127, -466, 25, 64, -81, -372, -42, -181],\n [24, -91, 219, 92, -79, -42, 360, 30, 140],\n [232, -447, 137, 206, 306, 601, -463, -382, -110],\n [318, -592, 404, 554, 153, 691, -229, -104, 196],\n [160, 193, 281, -346, -395, -278, 439, -10, 227],\n [77, -99, 34, 229, 125, 104, 24, 110, -46]]\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[[197, 71, 15, 48, 283, 179, -9, 126, -244],\n [-280, 67, 70, 202, 67, 346, -391, -345, -367],\n [16, 82, 11, 177, 363, 288, -180, -25, -433],\n [41, -28, -63, 56, 254, -213, 232, 239, 5],\n [-148, -35, -161, 138, 143, 167, -312, -184, -331],\n [-73, -41, -137, 143, 312, -90, 22, 94, -193],\n [29, 105, 157, 147, 358, 40, 168, 174, -165],\n [-230, -24, 45, 1, -255, -22, -106, -217, 119],\n [354, -36, -143, -149, 67, -48, 116, 239, 41]]\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 9x9 matrix:\n[[-216, -522, 276, 30, -40, -254, -358, -244, -298],\n [291, 53, -156, 189, 106, -136, 556, 353, -104],\n [-307, -566, 377, -42, 20, -245, -368, -269, -337],\n [-103, 183, -65, -177, -56, 258, -293, -291, 204],\n [-339, -148, 418, -198, 156, -37, -52, 80, -110],\n [301, 339, -353, 135, -100, 106, 201, 155, 218],\n [-277, 82, 241, -174, -28, 101, -268, 27, 139],\n [216, 294, -381, 0, -84, 240, -18, -219, 219],\n [-7, 227, -105, -45, -128, 166, -205, -63, 236]]\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[[367, -157, 143, -297, 414, -356, 502, -338, -816],\n [-156, -727, -306, -372, 310, 809, 31, -286, 140],\n [-104, 32, -223, 393, -87, -138, -95, 288, 161],\n [25, 35, 108, -49, 169, 142, -690, 382, 189],\n [-669, -7, -228, -541, -196, -657, 174, 677, -273],\n [-709, -105, -9, -368, 30, -434, 120, 405, -185],\n [-808, 96, 74, -174, -90, -407, -458, 670, 188],\n [143, 15, 485, 65, 429, -234, 43, 378, -315],\n [-250, -188, -401, 90, -1, -386, 428, 18, -289]]\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[[-286, -101, -20, -330, 557, 557, 215, 284, 1051],\n [100, 252, -62, -295, -487, -380, -242, -191, 199],\n [-48, 244, -368, 59, 391, 219, -265, -343, -78],\n [-20, 135, -299, 515, -71, 129, -1, -291, -703],\n [-530, -143, -159, 390, 230, 431, 297, -244, 82],\n [26, 78, -304, -241, -33, -46, -316, 71, 153],\n [-56, 279, -131, -503, -615, -355, -219, -145, 695],\n [37, -24, -59, 592, -308, 176, 334, 21, -672],\n [233, 24, 120, -171, 526, 44, -256, -136, -106]]\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[[-52, 2, 110, 141, -25, 5, -207, 296, -374],\n [26, 74, 323, -278, 349, 246, 23, 30, 176],\n [568, 310, -465, -115, -260, -403, -316, -430, 242],\n [-703, -126, 265, 591, 7, 42, 332, 651, -212],\n [465, -77, 285, -229, 484, 59, -80, -360, 364],\n [-65, -119, 488, -184, 408, 356, -40, 204, -150],\n [-401, -3, 220, 372, 46, 14, 128, 476, -150],\n [-193, -135, 263, 89, 189, 150, 116, 186, -64],\n [-56, 82, -527, 252, -518, -343, 35, -90, -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[[-557, -267, -203, 38, -273, -362, -231, 127, 94],\n [-45, -256, -123, 266, -28, 206, -177, 37, -300],\n [-47, 375, 169, -616, -315, -626, 432, 112, 457],\n [296, 421, 222, -420, 1, -188, 409, -32, 273],\n [-67, -107, -71, 194, 149, 150, -186, -69, -47],\n [181, 218, -33, -100, 196, 34, 163, -168, 96],\n [145, 109, -79, -172, -133, -98, 272, 2, -91],\n [238, -100, -176, 114, -80, 224, 137, -3, -443],\n [-278, 241, 120, -262, 115, -392, -31, -75, 621]]\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 9x9 matrix:\n[[-102, 53, -353, 289, -276, -200, -101, -37, 676],\n [-37, -41, 573, 349, -561, 114, 123, -626, 95],\n [-80, 125, 693, 271, -36, 15, -821, -368, -34],\n [406, 23, -311, 253, 181, -276, 622, 51, -14],\n [35, 593, 355, 483, -167, -425, -1011, 360, 22],\n [210, 121, 350, 359, 273, -416, -334, -41, -211],\n [43, 131, 496, 207, 71, 6, -694, -345, 57],\n [44, 151, 115, -275, 95, 678, -92, -55, -60],\n [-348, -262, 31, -94, -340, -28, 288, -10, -37]]\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[[-91, -14, 126, -7, 49, -21, -77, 35, -42],\n [-11, -208, -324, 67, 53, -195, 377, -353, -174],\n [283, 204, -128, -31, -189, 215, -61, 169, 262],\n [24, 61, 61, -17, -26, 59, -87, 90, 58],\n [-78, -12, 108, -6, 42, -18, -66, 30, -36],\n [-220, -137, 135, 17, 142, -147, 7, -94, -186],\n [231, 196, -56, -35, -161, 203, -105, 189, 238],\n [136, -2, -226, 18, -68, 10, 158, -92, 44],\n [237, 174, -102, -27, -159, 183, -57, 147, 222]]\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[[-15, 9, -1, 12, 3, -18, -10, 7, 2],\n [270, -162, 18, -216, -54, 324, 180, -126, -36],\n [-90, 54, -6, 72, 18, -108, -60, 42, 12],\n [-135, 81, -9, 108, 27, -162, -90, 63, 18],\n [270, -162, 18, -216, -54, 324, 180, -126, -36],\n [105, -63, 7, -84, -21, 126, 70, -49, -14],\n [-30, 18, -2, 24, 6, -36, -20, 14, 4],\n [-270, 162, -18, 216, 54, -324, -180, 126, 36],\n [90, -54, 6, -72, -18, 108, 60, -42, -12]]\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[[179, -3, 40, -187, -10, 93, -122, 97, 87],\n [210, 385, -234, -92, -157, 258, 205, 290, -246],\n [-531, -87, -53, 550, -46, -287, 218, -328, -158],\n [142, -71, 45, -23, 149, -9, -86, -64, 262],\n [88, -171, 176, -292, 13, 14, -239, 64, 72],\n [371, 40, -33, 0, -133, 181, -253, 18, 440],\n [-363, -82, 73, -22, -225, -94, 14, 31, -425],\n [241, 58, 65, -500, 195, 127, 7, 278, -144],\n [-286, 122, -104, 122, 168, -124, 398, -8, -408]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-413, 593, -22, -366, -297, 82, 158, -426, -441],\n [-65, -120, -36, -251, -226, -227, -183, 206, 289],\n [88, 519, -342, -87, -2, -203, -126, -474, -515],\n [71, 197, -96, -431, -169, 423, 109, -148, -158],\n [230, 278, -256, -31, -7, 149, 24, -364, -300],\n [-406, -69, 317, -209, -198, 180, 197, 158, 206],\n [-101, 398, -121, 97, -68, 329, 235, -427, -393],\n [321, -24, 65, -23, 284, -53, -5, -151, -113],\n [-279, -357, 237, -202, -313, -278, -106, 457, 549]]?\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[[36, -50, -283, -87, -95, 73, -312, -412, -88],\n [538, -443, -372, -350, -128, 211, 408, 116, 472],\n [-218, -27, -754, -339, 537, 324, -382, -1, 269],\n [-80, 351, -16, 14, 66, 400, -385, 245, -32],\n [-90, -47, -146, 274, 126, -298, 674, -39, -109],\n [-384, 74, -279, -453, -72, 195, -279, -424, -82],\n [-36, 370, 190, 520, 30, -223, -130, -247, -537],\n [-464, 45, 253, 21, 245, -156, -27, 403, 152],\n [-727, 377, 33, -62, 332, -330, 22, -289, -405]]\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[[505, -160, -286, -415, -496, -370, 407, 255, 9],\n [-240, -4, -29, 280, 188, 120, -306, -81, 254],\n [-146, 504, 767, -232, 110, -390, -133, 480, -184],\n [-294, 79, 501, -98, 122, 52, -4, 85, -483],\n [142, 100, 132, -182, -132, -44, 134, -64, -264],\n [32, -33, 70, -249, -94, -102, 239, 35, -207],\n [-134, -114, -6, -315, -170, 273, 571, -409, -123],\n [-125, -449, -387, 272, -44, 596, 157, -348, 48],\n [354, -346, -710, -79, -156, 353, 646, -420, 137]]\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[[44, -304, 144, -44, -458, -270, -168, -200, -266],\n [-87, 240, -193, -15, 225, 407, -103, 144, 316],\n [56, -76, 4, -44, 64, -56, 280, 112, -24],\n [48, -160, -30, -108, -89, 21, 194, 116, 1],\n [93, -393, -134, -306, -270, 184, 391, 312, 83],\n [-51, 200, 143, 213, 79, -223, -311, -280, -142],\n [126, -138, 24, -72, 192, -156, 642, 240, -66],\n [-34, 83, -131, -53, 103, 259, 16, 136, 195],\n [-45, -90, 25, -15, -330, 10, -395, -180, -55]]?\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[[-12, -3, 18, 18, 24, 12, 6, -27, 0],\n [48, 12, -72, -72, -96, -48, -24, 108, 0],\n [-36, -9, 54, 54, 72, 36, 18, -81, 0],\n [0, 0, 0, 0, 0, 0, 0, 0, 0],\n [36, 9, -54, -54, -72, -36, -18, 81, 0],\n [-8, -2, 12, 12, 16, 8, 4, -18, 0],\n [36, 9, -54, -54, -72, -36, -18, 81, 0],\n [0, 0, 0, 0, 0, 0, 0, 0, 0],\n [72, 18, -108, -108, -144, -72, -36, 162, 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[[-273, 420, -465, -495, 216, -114, -273, -609, 198],\n [-221, -57, 488, 235, -103, 134, 59, -19, -29],\n [282, -171, -189, -94, -129, -198, 108, 48, -379],\n [-248, 581, -136, -95, -19, 439, 29, -74, 338],\n [-194, 265, -112, -65, 173, 33, -163, -462, -6],\n [34, -233, -2, -90, 37, -343, -91, -301, -329],\n [-493, 3, 1, -565, 126, -370, -319, -424, 448],\n [67, -111, -163, 268, 616, -198, -411, -387, 57],\n [-309, -329, 441, -114, -32, -222, -103, 129, 387]]?\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[[65, 387, -5, 247, -248, -31, -17, 61, 149],\n [-213, 357, 62, 3, -266, -173, 27, 46, -79],\n [-56, -160, -160, -390, 244, -42, 24, -82, -206],\n [150, 41, 50, 136, -144, 187, -287, 189, -84],\n [282, -35, -114, 19, 230, 372, -199, -50, 147],\n [64, 83, -26, 27, -142, -16, -129, 140, -125],\n [482, 242, -158, 400, -185, 149, -199, 189, 199],\n [-21, 86, 68, 213, -86, -86, 160, -51, 211],\n [-488, -120, 122, -305, 24, -373, 326, -143, -183]]?\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[[-40, -25, 455, -48, -25, -470, -200, -12, 25],\n [58, -26, 485, 39, -195, 72, -120, 407, -28],\n [108, -249, 277, 315, -367, 420, -347, 287, 6],\n [-623, -228, 405, 64, -121, -157, 239, -122, 115],\n [-52, 408, -192, -403, 108, -377, 502, -259, 397],\n [100, -265, 256, 99, -384, 462, -168, 83, 89],\n [-491, -51, -48, -40, -31, -269, 350, -511, 330],\n [81, 205, -220, -402, -347, -206, 402, -805, 752],\n [-592, -102, -28, 86, 374, -683, -65, -139, 7]]\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[[302, 230, 305, -389, -310, -210, 202, 36, -22],\n [-75, -319, -303, 384, 138, -66, -35, 223, -111],\n [221, -45, -179, 180, 6, -116, 169, 145, -179],\n [13, 253, -151, 132, 222, 254, 67, -251, -55],\n [333, 36, -72, 15, -66, -67, 151, 24, -117],\n [386, -168, -469, 475, 128, -98, 233, 203, -322],\n [9, -156, 1, -26, -10, 73, -162, -65, 103],\n [-32, -18, 139, -103, -164, -254, 101, 235, -44],\n [201, -378, -180, 213, -108, -299, 68, 381, -153]]\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, -42, -28, 62, 111, 138, -4, 187, -125],\n [53, 133, -284, -93, -130, -163, -76, 87, 140],\n [-6, 52, 195, 200, 262, 525, 106, 276, -570],\n [102, 284, -211, 20, -106, -15, -98, 196, -62],\n [-2, -274, -6, -296, 120, 179, 368, -284, -126],\n [63, 5, 386, 41, -13, 72, 112, -344, -101],\n [91, 153, -346, -199, -289, -422, -112, -108, 403],\n [-98, -230, 147, 8, 107, 32, 58, -89, 33],\n [100, 60, 200, -44, 4, 164, 176, -232, -212]]\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[[32, 8, -26, -6, -34, 10, -4, -36, -26],\n [96, 24, -78, -18, -102, 30, -12, -108, -78],\n [64, 16, -52, -12, -68, 20, -8, -72, -52],\n [48, 12, -39, -9, -51, 15, -6, -54, -39],\n [-240, -60, 195, 45, 255, -75, 30, 270, 195],\n [240, 60, -195, -45, -255, 75, -30, -270, -195],\n [-208, -52, 169, 39, 221, -65, 26, 234, 169],\n [144, 36, -117, -27, -153, 45, -18, -162, -117],\n [192, 48, -156, -36, -204, 60, -24, -216, -156]]\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[[238, -154, -154, -182, 252, 84, 112, 126, -98],\n [-170, 110, 110, 130, -180, -60, -80, -90, 70],\n [119, -77, -77, -91, 126, 42, 56, 63, -49],\n [272, -176, -176, -208, 288, 96, 128, 144, -112],\n [306, -198, -198, -234, 324, 108, 144, 162, -126],\n [-136, 88, 88, 104, -144, -48, -64, -72, 56],\n [-85, 55, 55, 65, -90, -30, -40, -45, 35],\n [0, 0, 0, 0, 0, 0, 0, 0, 0],\n [187, -121, -121, -143, 198, 66, 88, 99, -77]]\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 9x9 matrix:\n[[-315, -68, 85, 181, 277, -237, 134, -321, 331],\n [212, -183, -164, -165, 43, -181, -521, 179, -71],\n [340, -207, 219, 203, -109, -464, 238, -142, -289],\n [134, -15, 276, 493, 242, 91, -46, -418, 278],\n [-248, 272, 232, -53, 53, 80, 636, 23, 296],\n [584, -412, -262, -100, 327, -875, 498, -272, -275],\n [-344, 246, 211, -253, -132, 505, -608, 429, 219],\n [-384, -179, -47, 347, 289, -175, 407, -559, 35],\n [526, -411, -305, -371, 865, -405, 250, 18, -87]]\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[[-235, 336, 62, 17, -386, 45, -15, 278, 432],\n [1, -7, -34, -95, -117, -131, -46, 153, 130],\n [-106, 140, -12, -58, -268, -110, -34, 268, 304],\n [186, -313, -116, 138, 409, -116, 119, -205, -422],\n [83, -113, -14, -25, 123, -7, -8, -99, -142],\n [44, -94, -24, 236, 302, 88, 146, -230, -308],\n [269, -344, -50, -311, 166, -155, -159, -114, -224],\n [267, -389, -70, 51, 509, -13, 58, -377, -562],\n [126, -190, -116, -278, -120, -364, -126, 260, 128]]\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[[-94, -348, -136, -111, -48, -411, 248, -45, 94],\n [-90, -222, 38, 32, -26, -164, 112, -16, 90],\n [-40, -168, -88, -72, -24, -216, 128, -24, 40],\n [142, 144, -372, -307, 4, -167, 56, -25, -142],\n [-83, -255, -41, -33, -33, -255, 160, -27, 83],\n [115, 327, 17, 13, 41, 299, -192, 31, -115],\n [-30, -48, 52, 43, -4, -1, 8, 1, 30],\n [51, 261, 183, 150, 39, 372, -216, 42, -51],\n [-105, -363, -113, -92, -49, -406, 248, -44, 105]]\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 9x9 matrix:\n[[424, -175, -212, -101, -205, 366, -57, 104, -163],\n [152, -63, -76, -45, -77, 134, -17, 40, -59],\n [-368, 154, 184, 158, 206, -340, 22, -112, 146],\n [-484, 196, 242, -10, 184, -378, 114, -80, 178],\n [44, -28, -22, -338, -152, 142, 122, 112, -38],\n [26, 0, -13, 351, 130, -91, -143, -104, 13],\n [506, -210, -253, -159, -260, 449, -53, 136, -197],\n [60, -35, -30, -355, -165, 160, 125, 120, -45],\n [84, -28, -42, 202, 48, 2, -98, -48, -18]]\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, -65, -96, -14, 104, 36, -4, 18, 9],\n [40, -50, -90, -60, 35, -60, -60, -55, -15],\n [-56, 215, 366, 194, -209, 144, 184, 147, 36],\n [-104, -247, -390, -130, 325, 0, -104, -39, 0],\n [168, -36, -90, -120, -45, -180, -132, -147, -45],\n [120, 169, 258, 62, -247, -48, 40, -11, -12],\n [-144, -23, -12, 62, 98, 132, 76, 100, 33],\n [-184, -2, 30, 100, 95, 180, 116, 141, 45],\n [-280, -143, -186, 46, 299, 216, 80, 147, 54]]\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[[-126, -257, -425, 546, 506, 88, 93, 450, 160],\n [45, 97, 77, -516, -362, -442, -109, -527, -415],\n [55, 13, 295, -208, -270, -76, 312, -188, 75],\n [126, 383, 440, 230, 141, -67, -98, 512, -297],\n [-58, 355, -93, -112, 375, 355, -438, -27, -203],\n [514, -240, -56, -90, 291, -31, -158, -190, -185],\n [150, 262, 70, -430, -121, 69, -391, -408, -271],\n [75, 138, 104, -442, 20, -486, -37, -391, -605],\n [265, -195, -242, 320, 191, 343, 256, 90, 368]]\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 9x9 matrix:\n[[2, -132, -366, -56, 188, 2, -384, -538, 334],\n [15, 30, -87, -51, -44, -130, -27, -13, -173],\n [48, 190, 428, -93, 120, 75, 271, 128, 278],\n [37, 154, 243, -102, 99, -8, 153, 31, 169],\n [-44, 11, 199, 113, -71, 124, 185, 287, -54],\n [-39, -97, -232, -17, 278, 126, -314, -508, 547],\n [-80, -388, -100, 342, -74, 444, -152, 32, 232],\n [-104, 251, -77, -82, 42, -262, 71, 69, -274],\n [-327, 46, -117, 232, 333, 284, -99, -133, 501]]\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 9x9 matrix:\n[[18, 36, -198, 162, -288, -36, 54, 234, 288],\n [4, 8, -44, 36, -64, -8, 12, 52, 64],\n [18, 36, -198, 162, -288, -36, 54, 234, 288],\n [8, 16, -88, 72, -128, -16, 24, 104, 128],\n [17, 34, -187, 153, -272, -34, 51, 221, 272],\n [18, 36, -198, 162, -288, -36, 54, 234, 288],\n [-12, -24, 132, -108, 192, 24, -36, -156, -192],\n [3, 6, -33, 27, -48, -6, 9, 39, 48],\n [-3, -6, 33, -27, 48, 6, -9, -39, -48]]\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[[-44, -74, -78, 118, -60, -16, -116, -72, -52],\n [32, 55, 55, -95, 60, 4, 94, 50, 36],\n [-131, -215, -240, 310, -105, -82, -302, -225, -163],\n [4, 15, -5, -75, 120, -52, 78, -10, -8],\n [-22, -63, -1, 261, -390, 160, -270, 16, 14],\n [86, 121, 187, -47, -210, 184, 34, 188, 138],\n [34, 56, 62, -82, 30, 20, 80, 58, 42],\n [-67, -92, -149, 19, 195, -158, -8, -151, -111],\n [33, 36, 87, 63, -225, 138, -72, 93, 69]]?\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[[-119, 94, 216, -350, -645, 112, 9, 484, 393],\n [397, -324, -26, 316, 82, -198, 505, -103, 401],\n [474, 89, -124, 237, -26, -514, 187, 302, 486],\n [660, 74, 241, 272, 252, -679, 55, 276, -95],\n [-105, 44, -190, 40, -46, 22, 275, -97, 447],\n [97, 214, -182, -35, 90, -79, -695, 244, -501],\n [-360, -176, 330, -394, -446, 544, -2, 60, -82],\n [-34, 31, -81, 22, 72, -74, -390, 29, -377],\n [14, 245, 156, 170, 222, -702, -101, 28, -229]]\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[[-160, 13, 180, -38, -6, -139, 46, 20, 26],\n [-108, 174, 57, -227, 103, 66, 100, 112, 78],\n [-176, 133, 213, -119, 167, 137, 76, -12, 114],\n [-462, 65, 437, -102, 110, -23, 29, -128, 23],\n [157, -183, -468, 89, -228, 51, -259, -152, -358],\n [521, -97, -195, 244, -87, -179, 103, 224, 186],\n [5, 277, 105, -298, 151, -37, 269, 336, 272],\n [-256, 102, -163, -317, -55, 66, -90, -24, -248],\n [-401, 260, 129, -463, 72, -26, 104, 136, -29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-126, -43, -213, 308, -226, 85, -242, 133, 502],\n [526, -348, -76, -13, 429, 87, 177, -150, -122],\n [-498, 372, 75, -54, -411, -42, -99, 183, 39],\n [342, -143, 73, -213, 301, 32, 363, 67, -134],\n [-248, 277, 311, -332, -122, -179, 300, 271, -42],\n [114, 12, -70, -81, 111, 139, -5, -208, -476],\n [-56, 50, 653, -390, 221, -604, 363, 35, -1],\n [-459, 257, -369, 338, -538, 283, -503, 28, 124],\n [228, -207, -48, 109, 234, -22, -152, -346, -207]]\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[[-213, -79, -61, 50, 52, 84, -40, -82, 28],\n [13, 255, -641, -432, -48, 42, 15, -203, -133],\n [145, -236, 686, 47, -255, -78, -315, 518, 105],\n [-97, -343, -22, -226, -391, 54, -449, 1, 332],\n [159, -362, 186, -125, -4, -98, -186, 160, -37],\n [-717, 22, -146, 15, 198, 224, 2, 198, -269],\n [138, -70, -512, -383, -16, 366, -129, -13, -76],\n [1, 22, -357, -186, -402, 169, -184, -203, 375],\n [-318, -343, 54, 105, 92, -157, 40, 23, -18]]\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[[288, 149, 43, 205, 127, 68, -162, 83, 53],\n [-234, -21, -35, 137, 27, 432, 312, 139, 275],\n [127, 38, 15, 104, -138, -436, -146, -539, -411],\n [-296, -250, -67, 10, 55, 280, 479, -101, 165],\n [314, 17, 35, 12, 159, -142, -180, 10, -45],\n [222, 531, 82, 460, -208, 70, -439, 57, -90],\n [-380, -174, -55, -396, -187, -272, 121, -133, -143],\n [-300, -28, -1, -309, -455, -214, -207, 78, -263],\n [294, -289, -18, 147, 373, -50, 282, -395, -18]]?\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[[-567, 87, -112, -3, -12, -167, -499, 38, 3],\n [438, -319, 130, -99, 41, 247, 438, -68, -314],\n [-407, 459, -606, -438, 232, 47, -265, 174, 337],\n [376, -193, 259, 132, -109, 147, 243, 188, -64],\n [-322, 437, 151, 6, 97, -111, -631, 192, 290],\n [-117, -442, 307, 346, -344, -180, -300, 38, -297],\n [202, 6, 319, 400, -124, -130, 261, -104, 124],\n [-47, -131, -498, -358, 73, 217, 254, 118, -101],\n [351, -135, 196, 90, 30, 83, 436, -182, -123]]\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[[272, 16, 208, -208, -32, -144, -128, 272, -224],\n [-255, -15, -195, 195, 30, 135, 120, -255, 210],\n [-238, -14, -182, 182, 28, 126, 112, -238, 196],\n [34, 2, 26, -26, -4, -18, -16, 34, -28],\n [0, 0, 0, 0, 0, 0, 0, 0, 0],\n [-187, -11, -143, 143, 22, 99, 88, -187, 154],\n [-68, -4, -52, 52, 8, 36, 32, -68, 56],\n [68, 4, 52, -52, -8, -36, -32, 68, -56],\n [85, 5, 65, -65, -10, -45, -40, 85, -70]]?\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[[36, -12, 48, 15, -42, 12, -18, -12, -18],\n [-66, 321, 50, 53, 8, -91, 217, -231, -82],\n [84, -80, 88, 21, -86, 40, -74, 16, -22],\n [66, 147, 166, 73, -116, -17, 71, -165, -98],\n [0, -442, -204, -119, 102, 102, -272, 374, 170],\n [156, 0, 232, 79, -194, 40, -46, -96, -98],\n [-24, -70, -68, -31, 46, 10, -36, 74, 42],\n [-42, -207, -158, -77, 100, 37, -115, 201, 106],\n [114, 27, 182, 65, -148, 23, -17, -93, -82]]\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 9x9 matrix:\n[[80, -213, -266, -168, 150, -7, 31, 119, 280],\n [99, -50, 106, -210, -240, -62, -46, 150, 143],\n [50, -82, -90, 91, -102, 123, -74, -24, 42],\n [67, 113, -146, 737, -228, 352, 25, -201, -409],\n [-86, -104, -240, 340, 139, 290, -157, -273, -56],\n [76, -223, -392, 119, 146, 168, -1, -7, 168],\n [-25, -194, -274, 444, -92, 460, -310, -318, -13],\n [-9, -77, -56, 454, -323, 427, -330, -298, -127],\n [-42, 4, 220, -754, 241, -480, 137, 297, 312]]\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[[128, -258, 266, -7, 175, 170, -64, -121, 53],\n [154, 88, 566, -421, -446, -398, 23, -19, 262],\n [-58, -68, 86, 280, 195, -8, -355, -392, 271],\n [56, -200, -64, -367, -168, 18, 47, -199, 132],\n [-207, 143, -260, 52, 70, 74, 56, 191, -275],\n [-13, 97, -428, 139, -9, 38, 146, 134, -98],\n [-74, 302, 110, 97, -291, -483, -277, -287, 432],\n [-289, 155, -332, 300, 206, 65, -171, -43, -126],\n [171, 33, 152, 143, -24, -84, 31, 52, 109]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[121, 386, 261, -66, -7, 270, -7, -31, 157],\n [147, -239, -303, 153, -200, -67, 340, -134, -59],\n [-165, -76, 198, 216, -36, 72, -412, 67, 102],\n [-70, 220, 222, -15, 179, -236, 18, -125, -77],\n [-226, 633, 253, 127, 22, 277, 114, -69, 443],\n [-252, 123, -347, 310, -66, 209, 271, 9, 452],\n [99, -121, -235, 173, -100, 171, 68, 12, 143],\n [-160, 602, 607, 433, -280, 274, 3, -287, 398],\n [264, -383, -510, -144, 307, 107, -230, 301, -35]]\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[[84, -226, 316, 240, 334, -148, 178, 166, -174],\n [281, 80, -88, 192, -41, -23, 129, 114, -558],\n [314, -35, -152, 278, 151, -62, 341, -339, 3],\n [-145, -51, 342, -12, 448, -25, 128, 15, 237],\n [279, -146, 156, 360, 403, -137, 389, -92, -168],\n [-24, -81, 118, 36, 77, -42, 3, 89, -27],\n [104, 478, -437, -207, -425, 219, -137, -15, -390],\n [-252, -292, 548, -6, 174, -133, -206, 615, -228],\n [-199, 56, 296, -132, 211, 31, -75, 264, -54]]\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[[-128, -33, 81, -21, 108, -87, -178, 225, -63],\n [-12, -204, 140, 71, 273, -73, -255, 114, 70],\n [-196, -150, -151, 41, 282, 218, -359, 294, 33],\n [-28, 335, -258, -246, 280, 60, -110, 269, 732],\n [-206, -157, -100, 74, 7, 200, -208, 200, -340],\n [-22, -123, 142, 62, 209, -117, -133, 30, 72],\n [40, 106, 142, 18, -228, -196, 310, -254, -158],\n [198, 82, -58, -94, 65, 17, 9, -23, 374],\n [-152, 44, 226, -19, 87, -297, -45, 128, -64]]\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 9x9 matrix:\n[[672, 118, -616, -415, -178, -408, 309, -377, 116],\n [-495, 20, -133, -189, 535, 180, -287, 341, 15],\n [-279, -226, 531, 399, -305, 299, 83, 128, -252],\n [289, 412, 273, 208, -238, -103, 557, -361, 264],\n [-296, 158, 450, 35, -344, -58, 280, -201, 0],\n [-549, 54, 624, 354, 272, 365, -254, 142, 35],\n [-431, -174, -339, -268, 240, -83, -580, 526, 137],\n [525, 112, -227, -139, -190, 22, 511, -381, 65],\n [-216, 671, 592, 345, -246, -113, 512, 96, 291]]\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 9x9 matrix:\n[[-174, -357, -36, 29, -193, -25, -103, 87, 142],\n [-251, -165, -131, -165, 223, 0, -48, -110, 55],\n [-57, -170, 90, -250, -123, -41, 325, -11, 208],\n [36, -119, -14, -187, -225, -67, 241, -85, 274],\n [-86, -141, -207, -67, 156, 96, -123, -170, 134],\n [308, 376, 38, -93, -285, -208, 296, -117, 92],\n [-414, -424, 320, 3, 203, 121, 6, 396, -231],\n [-139, -360, -97, 71, 31, 165, -203, 28, 111],\n [-6, -74, 66, -120, -452, -276, 232, 42, 198]]\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 9x9 matrix:\n[[-180, -20, 110, 70, 0, 20, -20, 20, 0],\n [0, 0, 0, 0, 0, 0, 0, 0, 0],\n [234, 26, -143, -91, 0, -26, 26, -26, 0],\n [-36, -4, 22, 14, 0, 4, -4, 4, 0],\n [-54, -6, 33, 21, 0, 6, -6, 6, 0],\n [162, 18, -99, -63, 0, -18, 18, -18, 0],\n [162, 18, -99, -63, 0, -18, 18, -18, 0],\n [-180, -20, 110, 70, 0, 20, -20, 20, 0],\n [54, 6, -33, -21, 0, -6, 6, -6, 0]]\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[[-148, -408, 151, -21, -332, 426, 179, 695, 26],\n [140, 357, -462, -349, 125, -738, -196, -440, -214],\n [314, -225, 8, 179, 100, -246, -219, -197, -313],\n [102, -135, -66, -79, 16, 57, 80, 225, -15],\n [264, -30, 228, 348, 451, 204, -27, -376, 81],\n [354, -93, -263, -150, 177, -90, 133, 246, -18],\n [-358, 66, 137, 3, -281, 48, -66, -22, 11],\n [532, -360, -358, -370, 358, 114, 306, 600, -14],\n [122, 501, -369, -256, 277, -165, 226, -86, 320]]\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[[-338, -147, 91, -253, 41, 298, -99, 6, -386],\n [25, 167, 59, 103, -3, -88, -136, -3, 423],\n [195, -51, -84, 47, -31, -89, 50, -37, 19],\n [-93, 234, 33, 186, 42, -141, 273, 147, 3],\n [-428, -109, 158, -289, 49, 355, -249, -8, -238],\n [-185, 192, 61, 112, 52, -55, 227, 143, -85],\n [-8, 90, 52, 34, -2, -22, -142, -16, 284],\n [-194, -275, 93, -369, -11, 372, -503, -162, -46],\n [-87, -34, 34, -72, 8, 84, -75, -11, -41]]\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[[-139, 40, 192, -80, -85, -56, -54, -95, 75],\n [26, -12, -246, 24, 104, -46, 79, -207, -258],\n [-71, 20, 78, -40, -35, -34, -21, -70, 15],\n [-16, 0, -192, 0, 80, -64, 64, -240, -240],\n [-181, 56, 432, -112, -187, -24, -130, 71, 309],\n [101, -24, 96, 48, -37, 104, -38, 321, 219],\n [-221, 60, 138, -120, -65, -134, -31, -330, -75],\n [-81, 20, -42, -40, 15, -74, 19, -220, -135],\n [112, -36, -330, 72, 142, -2, 101, -111, -264]]\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[[-25, -10, -114, -63, 90, -4, -94, 161, 130],\n [212, -72, -320, -160, 192, 36, -129, 123, 195],\n [377, 120, -224, 95, 78, -180, -66, -327, -324],\n [-55, 119, 279, 219, -198, -100, 143, -313, -368],\n [158, -46, 58, 14, -76, 60, 129, -231, -109],\n [-180, -60, 436, 92, -280, 136, 286, -194, -110],\n [-333, 129, 161, 121, -50, -124, -67, 161, -52],\n [-5, -193, 111, -135, -74, 244, 163, 25, 216],\n [440, 30, -458, -76, 240, -108, -183, -93, -45]]\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 9x9 matrix:\n[[-143, 153, 416, 22, -253, -394, 291, 66, -167],\n [14, 201, 145, 110, -229, 22, 364, 498, 290],\n [99, 275, 156, 54, 95, 56, -235, -326, 201],\n [-1, 87, -18, 42, 43, 32, -50, 38, 125],\n [-39, -145, -102, 6, 255, -118, -477, -518, -225],\n [-125, -83, 270, -294, -209, -247, 376, -138, -503],\n [-349, -64, 95, -48, -26, -483, 108, 88, -365],\n [-25, 347, 300, -216, -170, 28, 409, 84, 62],\n [-405, -175, -512, -128, 380, -130, -202, 220, -166]]\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[[-109, -236, -30, -37, 184, -20, 52, -84, -78],\n [-93, -208, -138, -67, 138, 20, 132, -124, -122],\n [65, 17, 48, -81, 232, -115, -15, 148, 407],\n [-120, 78, 194, 326, 251, -486, 3, 184, 269],\n [-80, -223, -298, -144, 214, 17, 273, -152, -55],\n [-137, -496, 244, -154, 327, 98, -222, -64, -50],\n [193, 3, -202, -377, -35, 327, 44, -28, 160],\n [75, -76, -232, -257, -73, 284, 103, -132, -105],\n [-72, 62, 126, 212, 165, -322, 3, 128, 193]]\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[[229, 155, 404, 227, 186, 130, 262, -132, -231],\n [223, 301, 243, 112, -57, 212, 429, -29, -321],\n [124, 348, 349, 75, -67, 110, 539, -224, -387],\n [-183, -250, -5, -178, 118, -61, -199, -111, 134],\n [169, -214, 218, 83, 337, 209, -158, 53, 41],\n [290, 50, 666, 332, 450, 148, 210, -260, -236],\n [101, -200, 124, 31, 251, 151, -166, 56, 66],\n [-547, -593, -446, -545, 2, -230, -622, -33, 476],\n [-8, 273, -23, -105, -274, 71, 371, -36, -230]]\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[[265, 74, -267, -41, 119, -48, 117, 271, 287],\n [-337, 507, 15, 214, 135, 101, 335, -118, -300],\n [-320, 385, -1, 55, 344, -390, -25, 155, -399],\n [-124, -29, -179, 270, 68, -32, 123, -187, -89],\n [-122, 348, 160, 212, 197, -109, 151, -237, -138],\n [-89, 437, -401, 50, 19, 1, 325, 45, -149],\n [145, -581, 440, 251, 388, 7, -207, -433, 136],\n [166, -211, 483, 149, -151, -91, -240, -202, 455],\n [94, -376, 22, 188, 247, -305, -239, -219, 128]]\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[[-156, -84, -12, 12, 48, -36, -36, -24, 204],\n [104, 56, 8, -8, -32, 24, 24, 16, -136],\n [208, 112, 16, -16, -64, 48, 48, 32, -272],\n [-52, -28, -4, 4, 16, -12, -12, -8, 68],\n [117, 63, 9, -9, -36, 27, 27, 18, -153],\n [208, 112, 16, -16, -64, 48, 48, 32, -272],\n [-156, -84, -12, 12, 48, -36, -36, -24, 204],\n [13, 7, 1, -1, -4, 3, 3, 2, -17],\n [169, 91, 13, -13, -52, 39, 39, 26, -221]]\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[[736, -108, -430, -99, -276, -19, -128, -11, 213],\n [-74, 92, 653, 267, 94, 50, 24, 125, 265],\n [-433, 270, 31, 97, 123, -295, 236, -140, 70],\n [-289, 333, 273, 563, -197, 265, 82, -316, 75],\n [-401, 302, -155, -181, 158, 254, -107, 377, -163],\n [371, -434, -429, -777, 72, -17, -216, 301, -25],\n [156, -248, 167, -189, -78, 289, -212, 149, 63],\n [122, -198, 283, 331, -222, 9, -24, -211, -55],\n [206, 247, 103, 65, 272, 307, 136, -117, 302]]\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[[-56, -40, -48, 4, -36, 28, -60, 20, -20],\n [-14, -10, -12, 1, -9, 7, -15, 5, -5],\n [154, 110, 132, -11, 99, -77, 165, -55, 55],\n [14, 10, 12, -1, 9, -7, 15, -5, 5],\n [182, 130, 156, -13, 117, -91, 195, -65, 65],\n [-112, -80, -96, 8, -72, 56, -120, 40, -40],\n [-238, -170, -204, 17, -153, 119, -255, 85, -85],\n [56, 40, 48, -4, 36, -28, 60, -20, 20],\n [-252, -180, -216, 18, -162, 126, -270, 90, -90]]\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[[-288, -66, -115, -108, -288, -384, -258, -245, 46],\n [152, -157, -40, -250, 210, 340, -43, 363, -13],\n [-59, 429, -309, 231, 90, -18, -113, 110, -725],\n [-122, -312, 26, 309, -375, -294, 118, -213, 158],\n [299, 476, -297, 209, 150, 163, 258, -64, -35],\n [455, 222, -156, -321, 317, 540, -12, 349, 206],\n [-310, -99, -23, -210, 12, -90, -417, 222, -509],\n [-456, -319, 196, 237, -330, -455, -159, -154, -308],\n [-232, -505, 163, -272, -96, -35, -297, 233, -54]]\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[[231, 348, -89, 672, 437, 2, -96, 4, -193],\n [417, -94, -44, -506, -78, 269, 237, -62, 337],\n [247, 362, -35, 927, 502, 90, -175, -167, -1],\n [185, -164, -1, 28, -229, 74, 42, -452, 514],\n [-161, -81, 46, -186, -87, -34, -11, 102, -66],\n [174, -283, 170, 88, -185, 233, -128, -564, 805],\n [-10, 163, -65, 319, 101, 28, 52, -95, -18],\n [-75, -227, -63, -731, -413, -61, 257, 71, 20],\n [345, -148, -13, -483, -48, -32, 3, 155, -7]]\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 9x9 matrix:\n[[-184, -124, -191, 30, -7, 300, -328, -258, -73],\n [-300, -58, 600, -379, 248, -386, 259, 62, -263],\n [-133, -290, 755, 50, -387, -356, 53, -414, -172],\n [-29, -192, 426, 514, 294, -231, 148, 354, 135],\n [165, -56, 473, 334, 227, -249, 75, 223, 298],\n [362, -40, -295, -50, 487, 314, 126, 364, 621],\n [-502, 285, -235, -55, 30, -231, -266, -168, -425],\n [-111, -228, 7, -391, -45, -153, 498, 13, -207],\n [-314, 0, 317, -499, -55, -272, 395, 70, -447]]\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 9x9 matrix:\n[[-311, -106, 150, -126, -213, 183, -91, 314, -37],\n [-158, 107, 367, -292, -685, 585, -43, 541, -33],\n [127, -251, -31, -8, 580, -149, -266, -343, -220],\n [-3, -241, -195, 296, 808, -555, 56, -290, 44],\n [-170, -318, -132, -25, -106, 320, -91, 16, -197],\n [-374, -311, -262, 157, -122, 160, 161, 102, -86],\n [96, 467, 299, -149, -293, -30, -136, 42, 206],\n [-875, -186, -413, 221, -257, 97, -333, -475, -125],\n [-223, -379, -747, 483, -168, 10, 517, -11, 189]]\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[[-144, 36, 48, 132, -12, -12, -108, 132, 84],\n [-204, 51, 68, 187, -17, -17, -153, 187, 119],\n [-96, 24, 32, 88, -8, -8, -72, 88, 56],\n [-204, 51, 68, 187, -17, -17, -153, 187, 119],\n [-48, 12, 16, 44, -4, -4, -36, 44, 28],\n [-24, 6, 8, 22, -2, -2, -18, 22, 14],\n [72, -18, -24, -66, 6, 6, 54, -66, -42],\n [-216, 54, 72, 198, -18, -18, -162, 198, 126],\n [-84, 21, 28, 77, -7, -7, -63, 77, 49]]\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[[228, 12, -228, 264, -60, 276, -216, 132, -276],\n [298, 66, -290, 380, -94, 390, -304, 178, -378],\n [59, 66, -49, 112, -35, 108, -83, 41, -93],\n [22, 215, 12, 174, -72, 151, -113, 36, -100],\n [-5, -277, -39, -198, 87, -167, 124, -33, 101],\n [54, 28, -50, 80, -22, 80, -62, 34, -74],\n [36, -61, -46, -2, 10, 7, -7, 14, -22],\n [-84, -256, 44, -272, 100, -248, 188, -76, 188],\n [55, -299, -103, -146, 79, -109, 78, -1, 37]]\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[[143, 91, 13, -39, -208, 234, 78, 52, -234],\n [55, 35, 5, -15, -80, 90, 30, 20, -90],\n [88, 56, 8, -24, -128, 144, 48, 32, -144],\n [-165, -105, -15, 45, 240, -270, -90, -60, 270],\n [55, 35, 5, -15, -80, 90, 30, 20, -90],\n [44, 28, 4, -12, -64, 72, 24, 16, -72],\n [110, 70, 10, -30, -160, 180, 60, 40, -180],\n [165, 105, 15, -45, -240, 270, 90, 60, -270],\n [22, 14, 2, -6, -32, 36, 12, 8, -36]]\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[[-316, -190, -194, 90, -138, 70, -220, 40, -106],\n [-426, -243, -105, -135, -151, -21, -426, 158, -181],\n [-294, 156, 186, -270, 189, -183, -438, -111, 111],\n [372, 154, 38, 162, 78, 54, 404, -104, 118],\n [-356, -246, -90, -144, -160, -19, -364, 186, -193],\n [638, 196, 206, -18, 103, -17, 558, 19, 89],\n [18, -68, 2, -54, -55, -3, 2, 93, -69],\n [-248, -296, -160, -36, -224, 50, -200, 216, -226],\n [8, 6, 78, -126, 16, -56, -56, 54, -20]]?\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[[255, 82, 228, -1, -234, -23, 57, 49, 286],\n [-96, -131, -122, -103, -229, 119, -56, 169, 147],\n [-195, 59, -82, -14, 265, -98, -61, -88, -279],\n [260, -248, -57, 149, -239, 277, 152, 49, 261],\n [240, -205, -37, 142, -188, 232, 140, 26, 216],\n [29, -50, -68, 149, 234, 35, 75, -149, -190],\n [350, -449, -217, 368, -76, 462, 286, -80, 136],\n [-53, 401, 341, -257, -96, -365, -159, 77, 100],\n [-2, 223, 192, -97, 11, -203, -62, -5, 11]]\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[[-349, -163, 213, -205, 387, 281, -162, 364, -512],\n [-317, -639, 189, 396, 189, -106, -386, 179, -52],\n [311, 206, 87, 838, 94, -279, 5, -159, 314],\n [-466, -274, 198, 154, 271, -114, -217, 249, -262],\n [102, -147, 5, -293, -274, 152, 6, 54, 77],\n [-497, -323, 115, 131, 263, -159, -226, 172, -230],\n [208, -102, 285, 1120, 200, -284, -204, 14, 277],\n [-209, -394, 151, 261, 467, 164, -310, 189, -296],\n [-91, -242, 329, 56, 137, 233, -184, 372, -228]]\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[[80, 256, -208, -272, 32, 256, 144, 16, 256],\n [-55, -176, 143, 187, -22, -176, -99, -11, -176],\n [-65, -208, 169, 221, -26, -208, -117, -13, -208],\n [-20, -64, 52, 68, -8, -64, -36, -4, -64],\n [85, 272, -221, -289, 34, 272, 153, 17, 272],\n [60, 192, -156, -204, 24, 192, 108, 12, 192],\n [-75, -240, 195, 255, -30, -240, -135, -15, -240],\n [-65, -208, 169, 221, -26, -208, -117, -13, -208],\n [-65, -208, 169, 221, -26, -208, -117, -13, -208]]\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[[-286, 25, 362, -430, 98, 63, 332, 49, 160],\n [349, 302, -31, 218, -24, -414, -185, -187, 236],\n [-123, 121, 202, -158, 36, -126, 202, 130, 643],\n [-404, -298, -261, -114, -154, 207, 175, 602, -7],\n [-60, -256, 18, 23, 91, 441, -49, -182, -411],\n [213, 158, 231, 65, 139, -45, -70, -389, 201],\n [-100, -143, -335, 78, -166, 0, -43, 351, -235],\n [26, -63, 94, 52, 92, 189, -26, -171, 78],\n [-62, -298, -251, 121, -47, 342, -122, 50, -580]]\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[[163, 381, -147, 27, 21, -19, -13, 238, 111],\n [96, 207, -126, 99, 63, 75, 48, 105, 36],\n [-127, -309, 87, 37, 19, 75, 49, -210, -107],\n [0, -45, -102, 215, 131, 223, 144, -91, -76],\n [77, 114, -219, 328, 202, 318, 205, -21, -59],\n [-116, -222, 216, -254, -158, -230, -148, -70, 4],\n [-45, -90, 75, -80, -50, -70, -45, -35, -5],\n [-149, -303, 237, -241, -151, -207, -133, -126, -25],\n [90, 270, 54, -270, -162, -306, -198, 252, 162]]\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 9x9 matrix:\n[[266, 208, 320, -149, -293, 76, -103, -211, 435],\n [-12, 517, -511, 77, -593, -234, -50, 293, 399],\n [395, 364, -71, 479, 33, 434, 271, 206, 332],\n [372, -36, 402, 353, -57, 443, 606, -21, 195],\n [74, 129, -7, 375, -58, 298, -155, -393, 47],\n [17, -205, 558, -46, -117, 286, 188, 4, 168],\n [-370, 214, -726, 294, 210, 162, -622, 378, 24],\n [-1, 365, -285, 174, 27, 209, -193, 502, 309],\n [-269, 147, -311, -329, 253, -584, -218, 218, -533]]\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[[-80, -166, 89, 28, -21, 107, 70, 43, -140],\n [74, -4, -43, -30, 107, -129, 156, -91, -26],\n [-236, -314, 181, -112, -105, 351, 210, 179, -336],\n [360, 306, -261, 18, 297, -567, 108, -333, 270],\n [185, 141, -180, -255, 234, -292, 409, -183, -5],\n [-71, -7, 38, -3, -88, 122, -95, 83, -1],\n [16, 90, -84, -279, 48, -8, 251, 3, -49],\n [7, 33, -90, -412, 104, -2, 482, -8, -168],\n [-42, 84, -81, -430, 17, 93, 360, 67, -122]]\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[[157, -473, 262, -161, 208, -3, -42, -431, 229],\n [133, -366, 218, -78, 192, 40, -24, -288, 128],\n [-129, 397, -196, 25, -248, -325, 124, 183, -41],\n [33, -153, 66, -153, 0, -147, -6, -255, 189],\n [-5, -61, -30, 59, 80, 413, -154, 129, -107],\n [-152, 300, -238, -96, -264, -152, -22, 88, 60],\n [-118, 148, -189, -134, -188, 10, -105, 10, 96],\n [-1, -66, 1, -84, -12, 2, -45, -102, 88],\n [120, -362, 209, -176, 124, -148, 5, -412, 246]]\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[[-33, -179, 88, 691, 476, 219, 54, 12, 185],\n [-78, 329, -149, 19, 137, 234, -136, 221, -190],\n [472, 91, 60, 337, 619, -103, 111, 90, -238],\n [229, 120, 147, -49, 292, -32, -6, 48, -208],\n [215, -118, -42, 479, 365, -103, 76, -229, 436],\n [-286, 303, -113, -69, 344, 427, -79, 24, 23],\n [181, 574, -94, -164, 432, 235, -283, -50, 118],\n [-513, -363, -557, -596, -332, -223, 661, -523, 342],\n [279, 346, 637, 98, 140, 307, -574, 582, -675]]\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[[116, -450, -506, -34, 109, 187, -24, 124, 20],\n [-100, 82, -48, -76, -382, -232, -116, 14, -94],\n [-122, -90, 194, -46, -344, -378, 34, -190, 104],\n [103, -455, -437, -29, 99, 144, 1, 81, 52],\n [88, 303, -124, 42, 276, 361, -88, 227, -189],\n [-84, 438, 528, 60, 18, -108, 60, -126, 6],\n [28, -150, -442, -74, -151, 59, -144, 176, -128],\n [59, -316, -157, 1, 103, 53, 61, -24, 103],\n [-43, -340, 41, -29, -161, -247, 91, -180, 181]]\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[[-128, -359, 655, -258, -193, 215, 124, 241, -53],\n [403, -177, 1, -263, 64, -163, -71, 582, -40],\n [-199, 424, 319, -168, 159, 413, 471, 191, -515],\n [491, 196, -320, 215, -180, -489, -341, 267, -35],\n [-317, 288, -170, 68, 298, 490, 582, -241, -208],\n [252, -204, -58, -16, -107, -180, -141, 305, 118],\n [110, 298, 207, -247, 179, -27, -13, 361, -382],\n [70, 103, 55, -394, 206, 151, 173, 276, -121],\n [-233, 290, 49, 22, 288, 218, 203, -25, -309]]\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[[338, 39, 145, 64, -161, 209, 365, 26, -22],\n [307, 118, 39, -9, -141, 110, 312, -71, 5],\n [175, 109, 575, 279, -301, 151, 233, 0, 40],\n [-112, 76, -416, -494, 182, -286, -230, -118, -78],\n [-211, -298, 204, -36, 265, 129, -569, 547, 167],\n [70, 170, -37, 365, 30, 80, -155, -25, 485],\n [-157, -116, -5, 368, -100, 28, 277, -171, -201],\n [34, 38, 78, -461, -147, -181, 241, -159, -463],\n [119, 105, 121, -39, 29, 50, -201, 135, 273]]\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[[148, 66, 96, -60, -148, 84, -36, 12, -62],\n [65, -75, 150, 177, -122, 174, 186, -81, 29],\n [-108, -81, -36, 108, 90, -18, 90, -36, 63],\n [92, -21, 124, 84, -126, 134, 98, -44, -5],\n [34, 183, -152, -342, 58, -202, -334, 142, -105],\n [115, 75, 50, -93, -102, 34, -74, 29, -61],\n [-80, -240, 160, 432, -32, 224, 416, -176, 144],\n [-159, -18, -158, -39, 188, -160, -64, 31, 38],\n [191, 87, 122, -81, -190, 106, -50, 17, -81]]?\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[[-135, 0, 153, 153, 36, -18, -144, 126, -72],\n [-255, 0, 289, 289, 68, -34, -272, 238, -136],\n [75, 0, -85, -85, -20, 10, 80, -70, 40],\n [-120, 0, 136, 136, 32, -16, -128, 112, -64],\n [75, 0, -85, -85, -20, 10, 80, -70, 40],\n [240, 0, -272, -272, -64, 32, 256, -224, 128],\n [60, 0, -68, -68, -16, 8, 64, -56, 32],\n [195, 0, -221, -221, -52, 26, 208, -182, 104],\n [60, 0, -68, -68, -16, 8, 64, -56, 32]]?\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[[-364, 93, 164, -152, -291, -46, -116, 231, -149],\n [271, 356, -78, 175, 325, 63, -223, 102, 385],\n [-119, 117, 142, -19, 340, -121, -401, 377, 450],\n [-154, -240, 36, -106, -538, 30, 398, -344, -594],\n [-64, -548, 44, -92, 147, -142, 141, -127, -21],\n [-112, -17, 334, 12, -115, -130, -20, -237, -7],\n [-72, -752, 420, -36, -101, -278, 385, -767, -237],\n [-218, -200, -130, -174, -343, 56, 209, 81, -417],\n [55, 440, -110, 59, 292, 65, -394, 483, 412]]\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[[-62, -230, -236, 395, 167, 123, -189, -22, -99],\n [-245, 153, 46, -165, -920, 159, -17, -407, -149],\n [-119, -222, 87, 211, -99, -89, -95, 93, 50],\n [88, -380, 29, 328, 793, -98, 25, 223, -7],\n [137, 289, -101, 295, -17, 85, 215, 383, -376],\n [156, 198, -120, -337, 215, -132, 234, 434, 208],\n [436, 131, 58, -359, -335, -286, -759, 7, 911],\n [-151, 123, 25, -191, -547, 99, 157, -120, -108],\n [5, 229, -165, 220, -166, 47, -116, 121, -123]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-76, -22, -328, -99, -98, 362, -301, -149, 74],\n [229, -371, 195, 44, 385, 122, 236, 42, 262],\n [-150, 27, -213, -28, 230, 214, -111, -283, 311],\n [-46, 181, -59, 308, -338, -418, 124, 385, -629],\n [88, -328, -394, 344, -128, 182, -77, 264, -292],\n [-223, 185, -450, -53, -261, 243, -384, -162, -77],\n [-23, -143, -379, 156, -379, 148, -306, 96, -228],\n [-175, 460, 181, 96, -215, -583, 167, 134, -372],\n [187, -212, 374, 50, 575, -80, 452, 35, 283]]\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[[79, 14, 39, -59, 58, 29, -71, -38, -131],\n [-169, -132, -100, 574, 86, 150, 166, 66, 68],\n [-126, -82, -137, 137, 160, -94, 81, 97, 30],\n [-6, -136, 243, 71, -282, 196, 5, -77, 102],\n [-44, -57, -294, -271, 601, -407, -70, 165, -290],\n [208, 206, 276, -410, -486, 108, -120, -176, 130],\n [-385, -261, -69, 490, -207, 22, 317, 153, 485],\n [195, 230, 89, -385, -170, -23, -129, -104, -27],\n [-262, -289, -259, -72, 471, -399, 79, 244, -40]]\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[[29, 204, -230, -48, 8, 101, -122, 71, 172],\n [-145, -254, 232, 146, -107, -317, 266, -176, -425],\n [199, 248, -412, 80, 118, -101, -6, 31, -22],\n [-133, -90, 36, 134, -117, -233, 142, -90, -259],\n [-85, -488, 646, 68, -50, 211, -142, 187, 238],\n [222, -226, 114, 166, 181, -374, 350, -191, -507],\n [-482, -64, 29, 140, -386, -428, 285, -266, -523],\n [175, -26, -36, 2, 159, -253, 292, -222, -401],\n [433, -44, 191, -268, 390, 471, -201, 159, 449]]?\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[[108, 120, 129, -237, 511, -23, -106, 75, 225],\n [-267, 55, 477, -292, 146, -550, 204, -263, -528],\n [-54, -129, 422, -442, -119, -260, 405, -285, -666],\n [23, 273, -175, 189, 293, 166, -362, 348, 738],\n [-231, 284, -51, 58, 593, -114, -384, 43, 358],\n [-86, 131, -38, -149, 137, 130, -233, -69, 88],\n [272, -113, -205, 35, -22, 299, -59, 78, 169],\n [-106, 204, -73, -108, 314, 195, -192, 100, 341],\n [307, -66, -134, -15, -130, 457, 247, 375, 421]]\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[[87, -35, -5, -44, 77, 28, -50, -75, 18],\n [-57, 245, -325, 164, -182, 392, -100, 60, -153],\n [-223, 187, -131, 172, -255, 108, 70, 197, -108],\n [-130, 10, 70, 40, -90, -120, 100, 110, 0],\n [161, -253, 269, -196, 254, -296, 20, -148, 153],\n [-149, -31, 143, 20, -78, -216, 140, 124, 27],\n [-114, 122, -106, 104, -146, 104, 20, 102, -72],\n [-35, -153, 249, -84, 68, -320, 120, 22, 99],\n [-187, 71, 17, 92, -163, -68, 110, 161, -36]]\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 9x9 matrix:\n[[52, 72, 17, -54, -297, -185, -412, -160, -178],\n [-350, -295, -86, -682, -372, 293, -534, 366, 157],\n [281, -150, -68, 193, -343, 295, 39, -90, -176],\n [-224, 46, -123, -228, 159, 115, 78, 112, 307],\n [33, -276, 185, -120, 10, -17, -281, 134, -5],\n [7, -376, -61, -375, -306, 444, -301, 212, 163],\n [-196, -158, -145, -192, -183, 269, -202, 120, 165],\n [-70, 71, -223, -417, -604, 113, -604, -119, 17],\n [-254, 22, -237, -556, 12, 225, -312, 47, 587]]\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 9x9 matrix:\n[[-88, -406, -22, -258, -107, 12, 275, -1, 252],\n [317, 473, -435, 202, -138, 477, -256, 132, 14],\n [-431, 24, -47, -40, -124, -56, 132, -370, 274],\n [-418, 73, -64, 118, -306, 385, 16, 92, 177],\n [-5, -96, -91, -136, -277, -38, 63, 52, -14],\n [-108, 111, -250, -250, -351, 539, -333, 591, -509],\n [78, 312, 90, 419, -6, 420, -184, 415, -276],\n [366, -724, -24, -574, 42, -552, 262, -122, 341],\n [-4, 61, -271, 110, -844, 348, -131, 447, 147]]\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[[-282, -41, 15, -90, -244, -189, -344, -222, 71],\n [184, -264, 185, 45, -313, -151, -759, -644, 209],\n [128, 13, 168, 9, -325, 69, -651, -738, 453],\n [93, -562, 150, 171, 622, 134, -195, 272, -657],\n [3, 104, 61, -126, -241, -31, -283, -360, 281],\n [-240, 113, 416, 30, 47, 595, -872, -773, 426],\n [155, 121, -393, -42, -242, -428, 674, 383, -34],\n [277, 14, -217, 105, -131, -149, 279, 29, 73],\n [-24, 19, -155, 60, 400, 124, 576, 562, -340]]\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[[4, 92, 26, 182, 192, -20, -144, 94, -70],\n [-47, 197, 85, -115, -126, -49, 201, -4, 148],\n [-33, 123, 55, -105, -114, -31, 159, -16, 112],\n [35, -113, -53, 139, 150, 29, -189, 32, -128],\n [-4, 88, 29, 103, 108, -20, -66, 61, -25],\n [-32, 92, 45, -145, -156, -24, 186, -39, 123],\n [-52, 352, 135, 85, 84, -84, 66, 111, 93],\n [35, -185, -75, 25, 30, 45, -105, -30, -90],\n [-11, -91, -22, -244, -258, 19, 207, -119, 107]]\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 9x9 matrix:\n[[-321, -310, 338, 400, -126, -220, 171, 68, -71],\n [230, 124, -278, -298, 125, 145, -89, -83, -19],\n [-30, 372, 222, 82, -201, 83, -75, 167, 295],\n [-168, -264, 84, 200, 30, -194, 66, -26, -130],\n [-48, -336, 84, 20, -66, 94, 270, -26, -166],\n [-300, -82, 278, 403, -69, -313, -30, 83, 40],\n [147, 178, -164, -178, 69, 79, -114, -29, 50],\n [-182, -130, 98, 237, 31, -249, -34, 3, -48],\n [-135, -266, -32, 158, 129, -257, -12, -77, -172]]\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[[-80, -256, 138, -246, 37, -237, 24, 590, 367],\n [-60, -403, -371, 73, 102, -12, 538, 8, 317],\n [-177, -339, -9, 2, 237, -321, 222, 79, 531],\n [442, 140, -30, 4, -332, 64, 186, -208, -342],\n [-378, -523, 4, 134, 462, -373, -5, 33, 636],\n [212, 641, 203, -225, -331, 143, -34, -6, -344],\n [-398, 230, 387, -55, 280, -153, -585, 99, 169],\n [161, 51, -61, 52, -98, 15, 158, -207, -97],\n [-317, -162, 6, 161, 303, -6, -318, -57, 111]]\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 9x9 matrix:\n[[78, 222, 332, -104, 268, -174, 185, -180, -138],\n [112, 264, 390, -90, 362, 24, -47, -12, -294],\n [57, 189, 285, -105, 207, -261, 288, -252, -54],\n [5, -15, -25, 25, 5, 135, -155, 120, -60],\n [104, 216, 316, -52, 324, 168, -210, 120, -324],\n [-83, -159, -231, 27, -253, -201, 244, -156, 282],\n [-52, -132, -196, 52, -172, 36, -32, 48, 120],\n [69, 177, 263, -71, 229, -57, 53, -72, -156],\n [7, -69, -111, 87, -13, 429, -491, 384, -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[[308, 177, -24, 1, -217, -99, -345, 225, -9],\n [-221, 55, 34, -188, 224, 122, 401, -662, -176],\n [-853, -51, -419, -195, 497, 112, 436, 21, -314],\n [-104, 239, -249, 453, -2, -4, 186, 174, 39],\n [484, -35, 25, 466, -695, -211, 464, -27, 212],\n [-138, -125, -188, -175, -85, -73, -262, 746, -23],\n [-19, 379, -408, -125, 317, -197, -311, -648, -581],\n [597, -4, 382, 452, -226, -192, -108, -502, 238],\n [-277, -249, -28, -17, 492, 193, 123, -566, -70]]\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[[-27, -341, -150, -105, -488, -81, -319, -24, 165],\n [-169, 211, 81, 446, 378, -163, 127, -115, -51],\n [195, -55, -58, 21, -259, 46, -392, -30, -263],\n [182, -65, 36, 200, 65, 178, -193, -269, -333],\n [-349, -31, 41, 585, 117, -309, 217, -274, 339],\n [237, -177, -144, -316, -134, 458, -326, -69, -265],\n [-344, 149, -138, -200, 256, 40, 264, 242, 364],\n [31, 529, 78, 125, 310, -17, 169, 208, -169],\n [305, 1, 114, 269, -138, -46, -299, -181, -432]]?\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[[392, -9, 240, -285, 65, -142, -297, 99, -96],\n [-351, -15, -198, 261, -45, 162, 264, -42, 162],\n [-251, -32, -126, 192, -20, 148, 187, 13, 186],\n [-98, -96, 12, 96, 40, 184, 66, 174, 348],\n [-211, 66, -174, 138, -70, -16, 165, -177, -150],\n [366, 19, 204, -273, 45, -174, -275, 37, -180],\n [267, 45, 126, -207, 15, -174, -198, -36, -234],\n [-225, 71, -186, 147, -75, -18, 176, -190, -162],\n [143, -23, 102, -99, 35, -22, -110, 76, 30]]?\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[[-30, 322, 358, -72, 100, -64, 170, -291, -277],\n [-728, -324, 228, -189, 361, 272, 639, -329, 46],\n [-184, -446, -53, -189, -123, -42, 161, 80, 316],\n [2, 474, 260, 57, 215, 60, 67, -236, -399],\n [-162, 124, -22, 366, 316, 210, 64, -323, -128],\n [206, 274, 269, 24, -90, -224, -20, -252, -150],\n [-404, 272, 108, 30, 494, 404, 266, -140, -372],\n [-162, 342, -140, 99, 397, 420, -39, 176, -369],\n [242, 154, -153, 381, 9, -16, -267, -95, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[72, -52, 68, 16, -8, -20, 8, 40, -64],\n [-36, 26, -34, -8, 4, 10, -4, -20, 32],\n [-108, 78, -102, -24, 12, 30, -12, -60, 96],\n [36, -26, 34, 8, -4, -10, 4, 20, -32],\n [216, -156, 204, 48, -24, -60, 24, 120, -192],\n [0, 0, 0, 0, 0, 0, 0, 0, 0],\n [216, -156, 204, 48, -24, -60, 24, 120, -192],\n [-90, 65, -85, -20, 10, 25, -10, -50, 80],\n [144, -104, 136, 32, -16, -40, 16, 80, -128]]?\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 9x9 matrix:\n[[11, 7, 10, -6, -15, -2, 14, -14, 9],\n [0, 0, 0, 0, 0, 0, 0, 0, 0],\n [-11, -7, -10, 6, 15, 2, -14, 14, -9],\n [11, 7, 10, -6, -15, -2, 14, -14, 9],\n [121, 77, 110, -66, -165, -22, 154, -154, 99],\n [-198, -126, -180, 108, 270, 36, -252, 252, -162],\n [55, 35, 50, -30, -75, -10, 70, -70, 45],\n [55, 35, 50, -30, -75, -10, 70, -70, 45],\n [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": "Calculate the rank of matrix A where A =\n[[135, 49, 13, -112, 114, 41, 62, 154, -97],\n [58, -42, -266, -373, -131, -50, -179, 164, -249],\n [203, 156, -209, 246, 145, 105, 93, 190, 42],\n [-146, -175, -618, -330, -266, 20, -346, 49, -167],\n [-141, -86, -315, -194, -460, -237, -360, -95, -136],\n [-119, -86, -413, -147, -349, -123, -313, -39, -103],\n [-125, -76, -109, 47, -42, 45, -54, -92, 73],\n [229, 203, 435, 249, 251, -9, 295, 76, 76],\n [109, -33, -363, -257, 138, 185, -34, 263, -162]]\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[[123, -287, -83, 22, 120, -142, -153, -211, -167],\n [107, 77, -56, 442, -116, 91, -385, -80, -158],\n [-49, -119, 201, -558, -24, -278, 365, -197, 203],\n [-20, -325, -219, 292, 444, -692, -70, 127, 877],\n [120, 495, 188, -111, -218, 157, 454, 306, 189],\n [313, 101, 300, -92, -26, -495, 300, -160, 445],\n [-335, -334, 203, -858, -218, -111, 231, -398, -167],\n [-459, -123, -254, -753, -364, 448, 121, -108, -284],\n [-474, 228, -122, -95, -608, 558, -125, 228, -226]]\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 9x9 matrix:\n[[-31, 473, -172, -380, -140, -70, -275, -225, -56],\n [-150, -48, -204, 110, -291, 269, 422, 161, -62],\n [-166, 580, -410, -502, -186, 37, 252, -93, -115],\n [181, 149, 267, 130, 70, -114, 390, -2, -306],\n [-5, 107, 18, -46, -310, -50, -635, -269, 122],\n [-416, 31, -376, 102, -822, 249, -399, -295, 162],\n [-201, -403, 28, 473, -252, 138, -101, -59, 66],\n [-293, 192, -369, -365, 267, -100, -21, -136, 76],\n [246, -43, -161, -410, -203, 186, 334, 497, 408]]\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[[228, 111, 182, 32, -552, -108, 53, 319, -170],\n [442, 226, 319, -384, -344, -83, -584, -89, -113],\n [-405, -77, 163, 174, 519, 116, -3, -68, 59],\n [-215, -162, -52, 404, 75, -40, 677, 328, -152],\n [212, 264, -478, 140, -299, -168, 143, 4, 140],\n [-194, 206, 64, 179, 230, -218, -199, -78, -44],\n [-311, -36, -193, 455, 149, -231, 506, 199, -129],\n [-252, 112, -75, 230, 66, -171, -24, 23, 13],\n [-59, -80, 327, -46, 53, -3, -87, 71, -165]]\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 9x9 matrix:\n[[-262, -6, -6, -44, 477, 100, -354, -262, -127],\n [-378, 5, 10, 212, 158, 102, 126, -280, -369],\n [836, 284, -422, -559, -123, 11, 216, 836, 546],\n [262, -128, -222, -376, 80, -293, 105, 492, 83],\n [-346, -422, -96, -374, 383, -566, -396, 92, -323],\n [-342, -590, 50, -196, 297, -632, -174, 74, -335],\n [48, 110, 112, 270, -554, 72, 294, -52, 12],\n [64, -147, -174, -414, 92, -361, -243, 310, 10],\n [226, 8, -30, -157, 403, 126, -171, 86, 267]]\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[[-657, 45, -366, 124, 435, -219, 258, -88, -137],\n [444, -458, 130, -99, -256, -505, -63, 117, 63],\n [-11, 119, 204, 313, -215, 640, -161, 148, 113],\n [-284, -162, -14, 267, 16, 41, 11, 85, -9],\n [-39, 133, -228, 155, 165, 28, 185, 22, 159],\n [446, -218, -44, -33, -290, -417, 33, 415, 91],\n [-50, -360, -79, 393, -28, -170, 98, 164, 186],\n [73, 197, -269, 145, 215, 51, 232, -49, 254],\n [204, -106, -60, -234, 68, -396, 66, -128, 0]]?\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[[-187, 437, -688, -232, -379, -338, -367, -200, -463],\n [490, 348, -454, 248, -579, 175, 27, -117, -356],\n [209, -27, 144, -49, -262, 193, -271, -23, 68],\n [118, 62, -146, 253, -259, -6, -46, -114, -45],\n [-327, -546, 312, -251, 169, -39, 144, 351, 56],\n [109, 128, 361, -255, -404, 483, -409, 114, 184],\n [113, -49, 440, 31, -451, 465, -322, 95, 294],\n [348, 77, 239, -200, -260, 365, -334, 6, 90],\n [14, -86, 229, 610, -405, 251, 53, -12, 300]]?\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 9x9 matrix:\n[[-374, 229, -51, 191, -274, -51, 143, -49, 365],\n [-210, -259, -275, 16, -23, 504, 277, 33, -112],\n [-52, -545, 185, -34, 238, 204, -44, -136, -197],\n [566, -32, 173, -212, 65, -186, -178, 177, -421],\n [486, -100, 94, -214, 215, -135, -229, 45, -313],\n [-28, 203, -239, -6, 302, 204, 68, 140, -73],\n [-304, 15, -78, 129, -387, 9, 147, -128, 320],\n [-206, 386, -217, 99, 20, -54, 32, -27, 328],\n [-190, 84, 149, 126, -139, -78, 68, 35, 99]]\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[[100, -30, 34, 38, -320, 6, -64, -36, -104],\n [150, -251, 101, 119, -124, -105, 28, -150, 56],\n [260, 14, 90, -49, -303, 84, -225, -36, -129],\n [-200, -164, -52, 184, -76, -164, 268, -56, 60],\n [445, 247, 127, -287, -125, 287, -523, 59, -183],\n [-80, -151, -3, 114, 33, -115, 159, -64, 83],\n [-90, 300, -80, -201, 301, 158, -109, 170, -21],\n [-340, 76, -152, 93, -95, -66, 239, 84, -41],\n [-20, -121, 11, 96, -91, -81, 91, -60, 23]]\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[[199, -61, -266, -388, -12, 37, -14, 456, 451],\n [-172, -41, -360, 463, -187, -232, 179, -48, -335],\n [293, 381, 226, 241, 188, 251, -8, -453, 362],\n [453, 281, -236, -263, -259, 560, 447, 202, 270],\n [69, 353, 196, -32, -187, 233, -283, 48, 71],\n [-176, -55, -234, 224, -265, -223, -162, 154, -338],\n [341, 257, 89, -321, 164, 369, 364, -204, 393],\n [303, -119, 108, -159, 380, 15, -46, -191, 422],\n [359, -51, -192, -229, -51, 331, 231, 339, 396]]?\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 9x9 matrix:\n[[-268, 80, 58, 197, 117, -4, 170, -254, -51],\n [19, -31, -41, -53, -21, 36, -82, -10, -44],\n [-79, 167, -369, -306, -58, 90, 72, -72, -291],\n [103, 145, 81, 45, 1, -171, 324, 252, 210],\n [48, -136, -260, -294, -102, 208, -412, -108, -286],\n [-113, 285, 143, 227, 107, -234, 610, 106, 224],\n [-181, 213, -311, -194, -2, 60, 188, -148, -269],\n [137, -133, -95, -175, -87, 98, -298, 46, -84],\n [13, -217, 181, 148, 24, 57, -286, -94, 55]]\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[[288, 284, -345, -37, 278, -72, -76, 139, -135],\n [-199, -320, 798, 201, -792, 247, 139, -150, 72],\n [-23, 163, 213, 443, -497, 187, -344, -342, -276],\n [-61, -76, 532, -92, -76, 741, 308, 152, 8],\n [193, 274, -866, -294, 858, -389, -56, 224, 4],\n [-379, -112, -155, 52, -166, -471, -7, -169, 107],\n [79, -57, 38, -313, 125, -55, 435, 383, 165],\n [-646, -51, 71, 221, -311, -1, -57, -353, -23],\n [-126, -380, 734, -100, -312, 493, 331, 81, 189]]?\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[[187, 255, 51, 272, 204, 289, 306, 306, 204],\n [198, 270, 54, 288, 216, 306, 324, 324, 216],\n [132, 180, 36, 192, 144, 204, 216, 216, 144],\n [-11, -15, -3, -16, -12, -17, -18, -18, -12],\n [143, 195, 39, 208, 156, 221, 234, 234, 156],\n [-187, -255, -51, -272, -204, -289, -306, -306, -204],\n [-22, -30, -6, -32, -24, -34, -36, -36, -24],\n [-176, -240, -48, -256, -192, -272, -288, -288, -192],\n [-187, -255, -51, -272, -204, -289, -306, -306, -204]]\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[[-138, 81, -155, -63, -235, 56, -128, 241, -235],\n [234, 429, -59, -294, 152, -346, 13, -47, 80],\n [-102, -279, 712, 184, 1, -92, 245, -99, 295],\n [130, 57, 209, -76, -9, -230, 227, -245, 103],\n [206, 361, 194, -285, -97, -486, 152, -77, 49],\n [22, 34, 343, -104, -404, -326, 289, -140, -82],\n [-318, -327, 574, 315, 245, 242, -158, 367, 335],\n [-250, -303, -158, 264, 128, 480, -229, 211, -30],\n [-264, 101, 97, -33, -148, 52, -245, 507, -108]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 9x9 matrix:\n[[632, -134, -34, 256, -151, 171, 161, -420, -337],\n [90, -113, -374, -77, 89, 605, 315, -231, -5],\n [168, 76, 24, 308, -143, -52, -201, -124, -213],\n [187, -226, 73, 110, -44, -130, 204, 101, 263],\n [-229, 196, 243, -241, 366, -224, -195, 83, -244],\n [147, 88, 296, 357, 454, -187, -166, -62, -392],\n [-76, 95, 83, -343, 428, -66, -137, 24, -226],\n [312, 71, 74, -32, 153, 127, 118, -347, -368],\n [-57, -96, -169, 341, -328, 245, 263, -9, 326]]\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[[331, -3, 325, -135, 299, 12, -661, -364, -162],\n [-173, 224, -342, -138, -259, 162, 547, 120, 78],\n [-257, 441, -174, -144, -2, 37, 321, -57, 423],\n [271, 140, -217, -186, -326, 356, -138, -299, -240],\n [-12, -272, 8, -147, -84, 18, 339, 161, -143],\n [-104, 18, 12, -414, -68, 85, 444, -75, 204],\n [165, 20, -100, 144, 189, 110, -479, -284, 48],\n [-34, -91, 229, -585, -140, 47, 470, -79, 84],\n [-101, 306, 543, -528, -102, -208, 300, 49, 28]]?\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[[348, -13, -131, -86, 77, -258, 150, -279, 194],\n [621, 718, -502, 821, -192, 84, -89, 66, 71],\n [-229, -37, 418, -297, 202, 317, -83, -31, -332],\n [285, 113, -332, 475, -498, -497, 283, -199, 450],\n [-280, 194, 147, 481, -412, 3, -133, -196, 158],\n [481, -17, -608, -60, 519, -345, 494, -396, 488],\n [-80, 34, 352, 137, -129, 245, -472, 84, -187],\n [-402, -49, 610, -46, -710, -167, 368, -99, -205],\n [255, 198, -165, 135, -194, 167, -248, 546, -315]]?\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 9x9 matrix:\n[[-328, -236, 140, -3, 85, -146, -344, 221, 326],\n [411, 329, -22, -128, -97, 133, 390, -58, -426],\n [-11, 81, -297, -1, -136, 295, 11, 107, 1],\n [-74, -76, 218, -366, 354, -100, -13, 208, -24],\n [136, 72, -142, -127, 153, 130, 230, -163, -188],\n [-7, -79, 96, -58, 201, -123, 43, -138, -18],\n [-151, -153, 69, -350, 445, -25, -20, 100, 35],\n [-37, 33, -270, -146, 61, 281, 46, 100, -22],\n [495, 369, 162, -198, -55, 9, 444, -36, -514]]\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[[480, -44, -147, 665, 12, -52, -283, -41, -495],\n [168, -625, 203, 132, -127, -240, 503, -202, 294],\n [73, -29, 192, -469, -75, 178, 70, -178, 224],\n [336, -408, -57, 813, -352, -709, -115, 173, -421],\n [526, 44, -427, 751, -106, -207, -695, -36, -616],\n [-469, -158, 79, 350, -471, -275, 241, 528, -88],\n [120, -418, -134, -378, -366, 62, 105, -269, 609],\n [13, -93, -637, -185, 272, 42, -347, -547, 335],\n [-20, 246, 417, -121, 50, 187, 285, 325, -178]]\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[[237, 23, 128, 157, 124, 25, 118, 119, -231],\n [119, 14, 63, 84, 70, 14, 70, 70, -126],\n [-368, -14, -210, -198, -124, -26, -88, -94, 270],\n [526, -26, 324, 186, 32, 10, -76, -58, -198],\n [475, -32, 297, 150, 2, 4, -106, -88, -144],\n [186, 17, 101, 121, 94, 19, 88, 89, -177],\n [479, -12, 289, 194, 66, 16, -18, -4, -228],\n [146, 66, 52, 206, 240, 46, 300, 290, -354],\n [130, 69, 41, 205, 246, 47, 312, 301, -357]]\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[[-35, 149, 300, 207, -35, 124, -355, 111, -472],\n [98, 244, 111, -76, 55, 239, -192, 207, -97],\n [282, -465, -161, 39, -169, -460, 367, 20, 545],\n [61, -87, 231, 285, -159, 357, -239, 19, 100],\n [174, 14, -182, 20, -94, -54, 277, -67, -194],\n [259, 120, 157, 323, -164, -137, -81, 261, -495],\n [-94, -185, 100, 433, -166, -261, -10, -92, -248],\n [-475, 72, 2, 61, 131, -128, -82, -269, -382],\n [28, 72, 173, 107, -81, 238, -181, -79, -483]]\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[[336, -21, -287, -41, 14, -72, -98, -149, 57],\n [162, -195, -110, -140, 188, 219, 337, -152, -282],\n [-322, 235, 246, 68, -155, -216, -76, 295, 140],\n [215, -247, -164, 59, 260, 235, -285, -329, -59],\n [-81, -23, 67, 96, 20, 40, -220, -34, 74],\n [-270, 84, 225, 213, -369, -24, -258, 84, 339],\n [-366, -46, 316, 182, -45, 155, -215, 35, 88],\n [74, -280, -26, 20, 93, 349, 67, -261, -122],\n [-137, 237, 82, 157, -219, -284, -418, 164, 345]]\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, 59, -90, -305, 162, -348, 16, -180, -192],\n [-160, 74, -506, -133, 62, -488, -84, -271, -48],\n [-414, 108, 92, 203, -396, 370, -290, 363, 34],\n [121, 16, 86, 328, -337, -54, 165, 158, 113],\n [-376, 74, -408, -64, -8, -96, -280, -90, 0],\n [44, 59, 216, -12, -148, -36, 60, 129, -96],\n [-93, -132, -277, 102, 229, 277, -133, -132, 223],\n [-65, -32, -297, 299, -141, -21, -13, -27, 219],\n [-404, 64, 63, 324, -408, 485, -288, 380, 136]]\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[[366, 167, 53, 136, 66, 455, -96, -367, 218],\n [298, -150, -276, 228, 124, 248, -184, -136, 326],\n [72, -131, -299, 212, 342, -205, 48, 261, 296],\n [-85, -466, -214, -113, -538, 199, -413, -193, -194],\n [346, -96, -225, 225, 106, 336, -193, -218, 327],\n [43, 164, -28, 139, 418, -231, 239, 245, 210],\n [36, -237, -258, 99, 24, -29, -123, 71, 127],\n [-134, -45, -168, 99, 352, -455, 209, 441, 133],\n [296, -50, -137, 161, 38, 336, -173, -242, 237]]\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, -108, -6, 6, 90, 54, 96, -18, 12],\n [80, -144, -8, 8, 120, 72, 128, -24, 16],\n [130, -234, -13, 13, 195, 117, 208, -39, 26],\n [-70, 126, 7, -7, -105, -63, -112, 21, -14],\n [-150, 270, 15, -15, -225, -135, -240, 45, -30],\n [70, -126, -7, 7, 105, 63, 112, -21, 14],\n [-160, 288, 16, -16, -240, -144, -256, 48, -32],\n [-20, 36, 2, -2, -30, -18, -32, 6, -4],\n [-100, 180, 10, -10, -150, -90, -160, 30, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 9x9 matrix:\n[[35, 239, 346, -470, 177, -307, -268, -173, 13],\n [-233, 400, -110, 357, -750, 214, 40, 663, -13],\n [245, -159, -169, 303, -234, 544, -41, 482, 58],\n [-631, -42, 477, 750, -332, -242, -126, -193, 276],\n [-30, 541, -374, 109, -412, 93, 84, 745, -488],\n [292, -118, 247, 130, 509, -199, -408, -62, 212],\n [-71, 102, -240, -78, -76, -62, 348, -54, -282],\n [183, 27, 201, 87, 981, -404, 63, -527, -432],\n [768, -350, 163, 189, 582, -605, -387, -112, 397]]\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[[-194, 338, 183, -330, -150, -22, 109, -130, 265],\n [63, -147, -96, 128, 23, -23, -60, 40, -108],\n [130, -178, -75, 194, 134, 54, -41, 90, -149],\n [7, -91, -84, 56, -49, -63, -56, 0, -56],\n [-230, 134, -45, -242, -362, -242, -47, -170, 157],\n [246, -174, 18, 276, 366, 234, 30, 180, -186],\n [11, 193, 198, -100, 155, 173, 134, 20, 110],\n [-133, 49, -54, -124, -229, -163, -46, -100, 74],\n [-112, -56, -141, -50, -260, -216, -103, -90, 5]]?\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 9x9 matrix:\n[[360, 145, 418, -305, 443, 63, -276, 132, -351],\n [-271, -309, -573, 440, -710, -386, 137, -132, 537],\n [-288, -110, -226, 302, -690, -711, -226, -418, 317],\n [-183, 280, 639, -96, 180, -65, -162, -131, -283],\n [-525, 153, -275, 272, -408, -94, 122, -122, 117],\n [-389, -18, -151, -170, -214, 43, 170, -133, -499],\n [108, 467, 52, -21, 133, -455, -704, -574, 237],\n [-125, -318, 2, 186, -473, -149, 333, 43, 149],\n [-71, -303, -170, -66, -279, -65, 237, -182, -56]]\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[[-149, 114, 165, -213, -1, -50, 300, 355, 42],\n [67, -151, -223, 211, -147, -32, -446, -491, -138],\n [9, 142, 120, -149, -29, 62, 128, 316, 53],\n [-73, 7, 37, -25, -35, -36, 62, -3, -26],\n [101, -120, -109, 197, 101, 30, -120, -295, -2],\n [-4, 373, 337, -292, -229, 184, 257, 577, 32],\n [91, 126, -25, 53, -490, 124, -477, -243, -207],\n [111, 349, 289, -205, -169, 252, 176, 501, 60],\n [47, -119, -17, 149, 302, 10, 191, -125, 95]]?\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[[363, 150, 527, 296, 137, 4, 434, -198, 539],\n [249, -554, 283, 499, 332, 469, 489, 78, 367],\n [-13, 10, -179, -314, 995, -9, 405, 243, -156],\n [-299, -576, -327, -64, 189, -476, 63, 222, -385],\n [-299, -286, -320, -124, 566, 317, 436, 399, -85],\n [-204, -375, -135, -186, 379, 118, 364, 220, -143],\n [259, 56, 58, -10, 95, -804, 361, -313, -12],\n [-60, -208, -75, -282, 884, 302, 343, 395, -124],\n [664, 1166, 557, 354, -364, -358, -242, -351, 685]]?\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[[-114, -239, -84, -224, 133, -44, 132, -170, 62],\n [123, 420, 90, -19, -256, 165, -57, 291, -83],\n [161, -338, -108, -129, 97, 115, 152, -264, 140],\n [-142, -31, -7, 166, 125, -194, 2, -65, -92],\n [-276, 354, -16, 96, 90, -280, 216, 36, -372],\n [-149, 81, -90, -197, 96, -93, 304, -104, -174],\n [-200, -466, -99, 6, 305, -226, 61, -318, 79],\n [-232, 93, -79, -48, 160, -220, 275, -118, -241],\n [-136, 624, 94, 196, -130, -140, 26, 296, -362]]\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[[176, 112, 64, 0, -144, 192, 192, -176, 16],\n [-198, -126, -72, 0, 162, -216, -216, 198, -18],\n [176, 112, 64, 0, -144, 192, 192, -176, 16],\n [154, 98, 56, 0, -126, 168, 168, -154, 14],\n [-99, -63, -36, 0, 81, -108, -108, 99, -9],\n [55, 35, 20, 0, -45, 60, 60, -55, 5],\n [88, 56, 32, 0, -72, 96, 96, -88, 8],\n [121, 77, 44, 0, -99, 132, 132, -121, 11],\n [-198, -126, -72, 0, 162, -216, -216, 198, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[535, 152, -591, 300, -14, 111, -231, -280, -143],\n [-84, -91, 426, 114, 275, 162, 102, -67, -318],\n [39, -204, -71, 10, 332, -171, 168, 279, 262],\n [33, 122, -340, 135, 233, -283, -41, 170, 125],\n [-227, 57, -163, 41, 349, -327, 76, 84, 70],\n [296, -211, 5, 95, 295, 177, 7, 501, 89],\n [106, -280, -126, 207, 143, -669, 351, 10, 548],\n [-137, 74, -354, 68, 113, -347, 79, -470, 13],\n [-276, 42, 378, -334, 352, 598, -124, 552, -317]]\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 9x9 matrix:\n[[502, 446, 625, -127, 80, -337, 126, 27, -121],\n [236, 234, 230, -218, -14, -244, 108, 106, 108],\n [166, 299, -11, -487, 11, 74, 138, -129, 206],\n [187, 343, -27, -584, 2, 68, 166, -128, 267],\n [-23, -85, 53, 162, -16, -108, -34, 102, -51],\n [-128, -232, -1, 345, -28, -105, -94, 147, -111],\n [29, -42, 92, 67, -59, -268, 12, 229, 63],\n [386, 475, 302, -452, 67, -53, 168, -144, 73],\n [18, 183, -151, -295, 99, 458, 34, -417, -22]]\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[[-28, -114, -375, 107, 57, -241, 100, -140, -193],\n [-26, -81, 826, 179, -88, 245, -286, 144, 52],\n [135, 183, -299, -188, -420, -43, 300, 70, 291],\n [-392, 42, 476, -282, -197, -213, -532, 301, -401],\n [-60, -42, -226, -364, -40, -63, 53, 333, 134],\n [190, -212, 104, 638, -105, 45, 438, -277, -125],\n [-69, 416, 40, -449, -387, -59, 63, 58, -355],\n [73, -493, -210, 232, 453, -30, -313, 50, 579],\n [-340, -382, -76, -82, -15, -346, -49, 361, 40]]\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[[64, 15, -337, 199, -107, 197, 30, 160, -91],\n [-78, -96, 99, -39, 246, 96, 207, -162, -279],\n [-78, 363, 284, -276, -421, -547, -75, 226, 206],\n [130, 12, -274, 241, 0, 110, 307, -8, -401],\n [-184, -282, 130, -166, 250, 322, -536, -40, 582],\n [-70, 62, 262, -161, 50, -208, 139, -100, -123],\n [-21, -6, -39, 48, 109, 66, 287, -63, -374],\n [-37, 201, 40, -88, -252, -215, -10, 179, 50],\n [7, -312, 122, 37, 495, 236, 142, -395, -209]]\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[[123, -102, -111, 383, 71, 247, -168, 331, 217],\n [306, -22, -375, -23, 72, 208, 115, -276, -154],\n [283, -156, -374, -30, -331, 605, -70, 449, 134],\n [105, -15, 422, 224, -104, -411, -160, -32, 274],\n [-147, -228, -206, 131, 125, 373, 356, 301, 472],\n [-106, 158, -160, -233, 320, 20, 421, -658, 221],\n [404, 830, -338, -378, -253, -214, -200, -264, -46],\n [-202, -134, 282, 246, 234, -308, -158, 216, 96],\n [204, -15, -247, 18, 268, -197, 177, -256, -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 9x9 matrix:\n[[108, 472, 343, 108, -590, 3, 669, -22, -234],\n [346, -205, -273, 210, 137, 184, -334, 3, 167],\n [118, -310, -620, 259, 299, -387, -607, 115, -223],\n [-156, -91, 23, -140, 16, 384, -248, -148, 350],\n [194, 237, 2, 170, -499, -595, 265, 199, -326],\n [-120, 48, 419, -526, 441, 31, 271, -97, 127],\n [248, 80, -6, -398, 674, -96, -304, -458, 137],\n [-350, -35, 15, -30, 33, -474, -80, 293, 142],\n [-46, 455, 129, 428, 144, 4, 128, -459, 162]]\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[[117, 24, -10, 104, 16, -20, -154, 93, -60],\n [-251, -368, -322, 144, 254, -108, 475, -258, 148],\n [287, -118, 99, 199, 200, 46, 91, -1, -369],\n [310, -145, 241, -183, 14, -13, 214, -76, 8],\n [-316, 82, -94, -10, -269, 150, -81, -27, -206],\n [-22, -649, -203, -247, -4, -290, 567, -424, 690],\n [324, 60, 559, -447, -90, 59, 75, -187, 93],\n [-352, -81, 5, -303, -418, 153, 205, -225, -40],\n [371, -7, 435, -287, -239, 108, -36, -64, -174]]?\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 9x9 matrix:\n[[-128, 449, 29, -548, 74, -105, -539, 315, -416],\n [241, -313, 46, 18, 246, 189, 121, -557, 459],\n [-394, 327, 140, -60, 193, -306, 78, 352, -233],\n [-167, 156, -230, -393, -213, -380, -95, 232, -245],\n [-215, 104, 56, 59, -356, 604, -132, 1045, -363],\n [-355, 405, 205, -327, 321, -96, -267, 458, -312],\n [-216, -361, -262, 511, -448, -250, 742, 357, 27],\n [346, 129, -218, -193, -573, 224, 76, -197, -6],\n [-284, -24, -78, 408, -456, -78, 241, 443, -51]]\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[[-411, -221, 81, 157, -346, -220, -476, 330, -31],\n [164, 394, -154, 11, -39, -101, -86, 193, 179],\n [750, 156, 270, -856, -271, -94, -287, 586, -98],\n [-334, 284, -33, 141, 39, 445, 198, -455, -10],\n [160, -262, 129, -147, -533, 597, -177, -404, -671],\n [-171, -354, -66, 279, -136, 175, 19, -132, -647],\n [566, -183, 35, -265, -856, -331, -795, 699, -423],\n [481, 635, 37, -467, 521, 141, 281, 51, 116],\n [-307, -801, 119, 264, 35, 113, 2, -295, -484]]\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[[-425, -243, 251, 198, 667, 178, 273, 97, 201],\n [2, -161, -401, 29, 230, 131, 135, 174, 27],\n [283, 27, 327, -122, 503, 358, 173, -429, -274],\n [-302, 124, -228, 67, -556, -67, 325, 367, 46],\n [138, 98, -271, -117, -37, -113, 14, 163, -105],\n [-302, -246, 152, 173, 364, -61, -69, 159, 275],\n [-166, 69, -417, -90, -918, -42, 477, 330, -152],\n [217, 60, -171, -40, 248, 294, 249, 25, -163],\n [-273, -30, 405, 270, 57, 382, 240, -194, 132]]?\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[[401, 133, 52, 52, -76, -236, 621, -187, -130],\n [-59, 424, -239, -81, 220, -102, -60, -116, -368],\n [106, 18, -101, -220, 109, 31, -52, 36, -313],\n [-217, -328, -112, 7, 94, 288, -373, 408, 300],\n [-183, -132, -85, 44, 18, 140, -283, 218, 217],\n [-53, -404, 236, 164, -75, 161, 95, 140, 440],\n [-179, -137, -162, 13, 158, 198, -256, 301, 161],\n [-347, 110, -163, -268, 208, 170, -681, 52, -323],\n [74, -169, -64, -217, 60, 122, -148, 155, -168]]\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 9x9 matrix:\n[[-208, 56, -48, 140, 210, -136, -52, -276, 48],\n [139, -507, 651, -328, -200, -96, -316, 634, -391],\n [-155, 91, -122, 179, 47, -24, -1, -188, 27],\n [127, 303, 159, -227, -272, -390, -287, 104, 194],\n [-79, -27, 244, -70, -29, -278, -266, 50, -44],\n [-394, 198, -68, 496, 13, 44, 28, -182, -38],\n [78, 160, 160, -27, 22, 86, 155, 182, 103],\n [27, -243, -14, -31, -61, 80, -43, 72, -171],\n [9, 111, 203, -103, 22, -198, -110, 58, 87]]\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[[-408, 258, 283, 138, 59, -144, 250, 751, 801],\n [186, 50, -255, -106, -100, -161, 318, -98, -3],\n [-151, -7, 689, 265, 238, 10, 60, 494, -262],\n [-198, 16, 602, -54, 294, 200, 29, -18, 200],\n [335, -54, 101, -45, 417, 202, -62, -277, 39],\n [270, 304, -635, 116, 57, -608, -24, -321, -97],\n [63, 381, 231, 365, 797, 128, 327, 800, 203],\n [-177, 144, 132, 322, 331, 16, 422, 806, 396],\n [632, 69, -2, 393, 529, -434, 259, 109, -507]]\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[[562, 275, -54, -211, -87, -124, 405, 34, 63],\n [654, 102, 56, 430, 402, 512, 434, 335, -98],\n [-519, -127, -135, -221, -96, -303, -310, -78, 47],\n [104, -157, -266, -417, 368, 53, -43, 312, 654],\n [-514, -83, 8, -254, -330, -338, -386, -262, 23],\n [53, -100, 153, 86, 55, 193, 163, -202, 124],\n [-37, 56, 113, 107, -172, -33, -6, -146, -196],\n [79, 293, 243, -24, -639, -329, 103, -465, -403],\n [-420, -180, 202, 378, -40, 190, -296, -149, -256]]?\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, 60, 84, 213, -34, -80, 223, 5, -71],\n [-243, 170, -212, 141, 62, -60, -39, 35, -297],\n [16, -76, 16, -144, 0, 56, -100, -12, 116],\n [41, 91, 32, 225, -18, -86, 196, 12, -128],\n [-151, 114, -132, 105, 38, -44, -11, 23, -197],\n [-151, 114, -132, 105, 38, -44, -11, 23, -197],\n [-160, -2, -136, -144, 48, 52, -206, 6, -26],\n [-177, 174, -156, 207, 42, -84, 51, 33, -291],\n [-300, 155, -260, 60, 80, -30, -135, 35, -285]]\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[[319, -74, -14, 106, -65, -149, -4, -66, -351],\n [213, 27, 89, 113, 33, -114, 78, -120, -245],\n [-162, -34, 34, -226, 218, 198, 286, -250, -66],\n [-158, -100, -176, -108, -154, 34, -92, 208, 254],\n [-245, 338, 403, 12, 476, 226, 226, -362, 59],\n [-17, -85, -164, -15, -148, 58, -341, 217, 77],\n [159, -16, -5, 120, -144, -237, 109, 63, -19],\n [-548, 338, 397, -238, 709, 598, 187, -489, 132],\n [48, 104, 99, 92, 117, 108, -257, -45, -120]]\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[[141, 177, -457, 108, 1, 448, 603, -117, 201],\n [242, 153, -375, 155, -65, 47, 346, 69, -173],\n [-130, 556, -585, 272, -35, -15, 252, -197, 357],\n [-87, 533, -529, 130, -39, 266, 317, -361, 461],\n [257, -151, 488, -279, -251, 12, -303, 259, -383],\n [153, -179, 127, 108, -61, -482, -166, 491, -514],\n [-144, 96, -275, 384, 17, -169, 180, 51, 55],\n [-14, 2, 23, 141, -128, 16, 176, 412, 22],\n [93, 59, 143, 43, -246, 155, -34, -40, -115]]\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[[243, 324, -282, 150, 18, -270, 69, -18, 138],\n [49, 76, -66, 38, 10, -54, 17, -2, 34],\n [331, 196, -174, 26, -122, -378, 23, -62, 46],\n [160, 160, -140, 60, -20, -180, 30, -20, 60],\n [-15, -420, 360, -300, -240, 0, -120, -60, -240],\n [-494, -8, 16, 168, 352, 576, 48, 136, 96],\n [152, 368, -318, 214, 110, -162, 91, 14, 182],\n [-148, 176, -148, 180, 212, 180, 66, 68, 132],\n [28, 352, -302, 246, 190, -18, 99, 46, 198]]\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[[156, -214, 33, 75, -292, -86, 309, -17, 349],\n [240, -42, 159, 179, -178, -230, 255, 157, 243],\n [-36, 224, -6, -58, 292, 38, -264, 44, -356],\n [132, -34, -207, -263, 162, 228, -117, -243, -293],\n [-288, -36, 113, 182, -181, -101, 68, 130, 304],\n [48, -148, 213, 294, -385, -281, 372, 202, 544],\n [-96, 202, -185, -267, 424, 260, -419, -157, -575],\n [102, -18, -15, -26, 1, 2, 33, -25, -21],\n [168, 4, -205, -274, 213, 225, -148, -234, -360]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-64, 83, 340, 235, -197, 325, -249, 18, 90],\n [346, 26, 177, 4, 233, -93, -1, -207, -4],\n [642, -279, 83, 59, 492, -293, -68, -266, 167],\n [141, -164, 91, 156, 199, 188, -16, -437, -491],\n [343, -220, -157, -132, 371, -249, -21, -23, 257],\n [-560, -34, -114, -320, -450, -119, 91, -162, -258],\n [-444, -511, -258, -831, -388, -455, -113, -312, -505],\n [-106, 172, 38, -496, 158, 136, -76, -214, 318],\n [196, -633, 346, -505, 157, -27, -695, -658, 392]]\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[[58, 130, 286, 159, 53, 118, -164, 89, 111],\n [41, -6, -384, -32, -169, -68, 39, -70, -120],\n [-137, -422, 18, -232, 365, -144, 237, -350, 234],\n [94, -403, 219, -425, 167, -474, 149, 5, 297],\n [182, 447, -69, 502, -214, 352, -393, 62, -30],\n [81, 486, -149, 333, -382, 276, -237, 275, -318],\n [494, -17, -116, 3, -215, -356, -313, 35, 354],\n [-20, -117, -499, 57, 15, 42, 61, -377, 3],\n [152, 482, 162, 303, -321, 206, -310, 405, -177]]\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[[-584, 272, 191, -270, 314, 199, -246, -33, 200],\n [-271, 194, 281, -156, 539, 503, -706, 508, -210],\n [-444, -212, 227, 260, 347, 195, -565, 295, -288],\n [180, -234, 191, 81, -690, -191, 216, -113, 250],\n [-193, 147, 366, -383, -427, 80, -272, 141, 619],\n [-136, 238, 112, -173, 638, 301, -449, 399, -318],\n [304, 30, -288, -125, 42, -351, 503, -134, 63],\n [-672, 44, 192, -302, -8, -20, -340, 74, 714],\n [-40, -488, 71, 591, -301, 266, -222, -7, -169]]?\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 9x9 matrix:\n[[236, -133, -137, -306, -4, -112, -40, -168, 230],\n [-308, 319, 161, 180, 24, 212, 12, -320, -12],\n [-258, 214, 193, 109, 246, 505, -80, 82, -26],\n [-151, 55, 74, 423, -311, -146, 305, -68, -318],\n [100, 355, 24, -125, -18, 292, -673, -428, 697],\n [69, 70, -32, -384, 356, 138, -392, 9, 331],\n [-107, 124, 134, 484, -181, 104, -76, 288, -185],\n [-160, 214, 74, 236, -191, 20, -60, -247, 46],\n [389, -96, -160, -462, 200, -26, -522, 105, 493]]\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[[204, 53, -482, 251, 380, 130, -92, 74, -195],\n [38, -131, -274, 98, -16, -424, 651, 167, 136],\n [-442, 155, -206, 274, -153, -476, -17, -453, 264],\n [207, 68, -101, 429, 111, -29, 371, -82, -61],\n [-10, -100, -218, 164, 130, -55, 183, 503, 602],\n [19, -445, -503, 834, -38, 42, 201, 391, 192],\n [-126, 227, -273, -531, 388, 18, -739, -190, -15],\n [10, 78, 385, -365, -76, 300, -402, -74, -194],\n [171, 169, -189, -60, 177, -232, 639, 308, 115]]?\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[[180, -120, 60, -100, 160, -100, -160, 40, -20],\n [18, -12, 6, -10, 16, -10, -16, 4, -2],\n [-306, 204, -102, 170, -272, 170, 272, -68, 34],\n [-306, 204, -102, 170, -272, 170, 272, -68, 34],\n [126, -84, 42, -70, 112, -70, -112, 28, -14],\n [288, -192, 96, -160, 256, -160, -256, 64, -32],\n [18, -12, 6, -10, 16, -10, -16, 4, -2],\n [216, -144, 72, -120, 192, -120, -192, 48, -24],\n [-216, 144, -72, 120, -192, 120, 192, -48, 24]]\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[[164, 4, 22, -180, 101, 231, -351, -340, 95],\n [186, 19, 44, 148, 8, -79, -783, -348, -278],\n [44, -214, 64, -228, -529, 276, 160, 174, 685],\n [-6, 89, 2, 266, 290, -222, -16, -233, -366],\n [-722, -93, -904, -173, -33, 533, 252, 69, 307],\n [-418, 13, -474, -65, -40, 101, 332, 61, 412],\n [-68, 13, 371, 273, -278, -497, -42, 666, -669],\n [60, -311, 66, -30, -809, 209, -312, 11, 655],\n [-44, -153, 175, -160, -453, 106, 200, 584, 102]]?\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 9x9 matrix:\n[[-40, -40, 55, -70, 35, -80, -75, 15, -85],\n [-48, -48, 66, -84, 42, -96, -90, 18, -102],\n [64, 64, -88, 112, -56, 128, 120, -24, 136],\n [40, 40, -55, 70, -35, 80, 75, -15, 85],\n [64, 64, -88, 112, -56, 128, 120, -24, 136],\n [-88, -88, 121, -154, 77, -176, -165, 33, -187],\n [16, 16, -22, 28, -14, 32, 30, -6, 34],\n [-64, -64, 88, -112, 56, -128, -120, 24, -136],\n [96, 96, -132, 168, -84, 192, 180, -36, 204]]\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[[-114, -79, 183, 174, 36, 83, -65, -86, -212],\n [-106, 236, -307, 243, -189, -53, 203, 515, -182],\n [-379, 31, -78, -166, -535, 314, 128, -139, -72],\n [-180, -32, 480, -370, 435, 25, -161, -22, 69],\n [-235, -297, 161, -484, -174, 131, -205, -516, 232],\n [-656, -51, 168, -147, -237, 584, -282, -179, -240],\n [-290, -98, 191, 76, 102, 204, -278, -61, -205],\n [213, -17, -402, 239, -313, -451, 585, 424, -58],\n [-201, -29, -337, 247, -482, -117, 261, 276, -216]]?\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[[-306, 102, 119, 272, -68, -255, -68, -306, 51],\n [-216, 72, 84, 192, -48, -180, -48, -216, 36],\n [-162, 54, 63, 144, -36, -135, -36, -162, 27],\n [-270, 90, 105, 240, -60, -225, -60, -270, 45],\n [-288, 96, 112, 256, -64, -240, -64, -288, 48],\n [-72, 24, 28, 64, -16, -60, -16, -72, 12],\n [0, 0, 0, 0, 0, 0, 0, 0, 0],\n [18, -6, -7, -16, 4, 15, 4, 18, -3],\n [72, -24, -28, -64, 16, 60, 16, 72, -12]]\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[[2, -400, 204, 196, -198, 300, -46, 195, -315],\n [32, -119, 57, 171, 64, -235, -20, 348, -200],\n [-255, 72, -38, 132, -175, -350, 283, -434, -237],\n [-169, 134, 132, 134, 31, -168, -259, 312, -49],\n [9, 127, -139, -37, 92, -214, 295, -316, 102],\n [-120, 454, -146, -146, 113, -536, -300, 172, 100],\n [304, -103, 85, -143, 198, 382, -524, 763, 210],\n [-229, 305, -137, -1, -23, -375, 337, -599, 58],\n [364, -223, 9, -109, 183, 335, -176, 477, 145]]?\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 9x9 matrix:\n[[-365, -21, 456, -67, 65, -135, -165, -595, 218],\n [-1074, 120, -90, 419, -594, -74, 20, 23, -171],\n [-101, -138, 270, 477, -127, 11, 322, -45, 44],\n [376, -70, -198, -402, -263, -287, -197, 252, 134],\n [606, -31, -108, -9, 458, 341, 174, 59, -58],\n [162, -180, 62, 489, 498, -47, 251, 463, 75],\n [-521, -185, 198, -93, 90, -463, -503, -165, 266],\n [-573, -41, 196, 321, 261, 401, -203, -571, -428],\n [751, -204, 82, -396, 382, -18, -133, -212, 344]]\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[[296, -130, -93, 81, -146, -64, -86, -174, 104],\n [313, -284, -391, 491, -144, 156, -113, 99, 201],\n [410, 11, 71, -45, -140, -45, -81, -284, -147],\n [201, -165, -131, 308, -146, 114, -122, 37, 192],\n [-129, 231, 386, -43, 16, 198, -40, 93, -172],\n [162, 54, 328, 72, -192, 122, -176, -94, 80],\n [-140, 100, -72, -643, 216, -493, 254, -310, -226],\n [-37, 209, 91, -409, 170, -173, 164, -167, -406],\n [82, 88, 46, 246, 8, 308, -42, 182, -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[[45, -192, -267, 113, -160, -231, -362, -141, 324],\n [75, 174, 348, -212, 295, -3, 539, 282, -273],\n [113, 462, 414, -403, 329, 333, 500, 556, -404],\n [126, -94, -270, 101, -262, 22, -323, -352, 93],\n [165, 186, -101, -118, -128, 273, -183, -17, -81],\n [-167, 116, 302, -100, 279, 25, 349, 378, -127],\n [225, 133, -47, -193, 16, -16, -84, 194, 72],\n [-64, -8, 68, -13, 90, -70, 69, 136, 37],\n [-39, 243, 60, -69, -57, 468, -6, 9, -276]]\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[[-131, -235, 117, 395, -251, -125, -867, -83, 423],\n [527, 486, -387, -10, -354, 202, -96, 225, -54],\n [125, -392, 262, -134, 86, -194, 143, -523, 220],\n [128, -287, 237, 8, 328, -172, 255, -499, -250],\n [-114, 154, -128, -67, -45, 80, -321, -27, 351],\n [-122, 487, -356, -212, -176, 272, 50, -156, 474],\n [198, -130, 118, 357, 71, -68, -187, -849, 41],\n [18, -550, 389, 393, -19, -207, -608, -318, 234],\n [558, -43, 16, 419, 11, -179, -161, -397, -554]]?\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[[36, 6, 4, -22, -24, -32, 22, -22, -4],\n [198, 33, 22, -121, -132, -176, 121, -121, -22],\n [180, 30, 20, -110, -120, -160, 110, -110, -20],\n [180, 30, 20, -110, -120, -160, 110, -110, -20],\n [-198, -33, -22, 121, 132, 176, -121, 121, 22],\n [216, 36, 24, -132, -144, -192, 132, -132, -24],\n [36, 6, 4, -22, -24, -32, 22, -22, -4],\n [252, 42, 28, -154, -168, -224, 154, -154, -28],\n [36, 6, 4, -22, -24, -32, 22, -22, -4]]?\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[[240, 568, 304, -268, -319, 68, -376, 53, 635],\n [2, -305, -380, 66, 301, 182, 155, -111, -235],\n [221, -241, -264, 62, 269, -328, 103, 357, -359],\n [57, 399, 6, -402, -145, -40, -439, 207, 309],\n [-608, 137, 632, 113, -298, -567, 101, 230, -40],\n [-459, -10, -72, -153, 159, -327, -46, 311, -127],\n [269, -76, -212, 77, 69, 689, 108, -557, 241],\n [-125, 449, 166, -278, -173, 102, -413, 29, 471],\n [-95, -329, -337, -4, 177, 343, 356, -356, -161]]?\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[[-396, 339, 73, 216, -235, 218, -249, -178, 303],\n [-43, 105, 119, -138, 76, 404, 15, 148, 513],\n [-292, 87, 235, 342, -331, 24, 108, -331, -123],\n [312, -235, -331, -98, 171, -556, -70, 73, -597],\n [-123, 200, -428, 118, -47, -450, -550, -94, -324],\n [-407, 292, 312, 206, -263, 478, -2, -174, 504],\n [330, -294, -178, -108, 160, -416, 114, 76, -510],\n [448, -326, -144, -310, 322, -194, 181, 273, -216],\n [-1, 13, 191, -106, 50, 364, 157, 106, 393]]?\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 9x9 matrix:\n[[212, 105, 283, -69, -196, -100, -195, 51, 294],\n [11, 120, 205, 22, -66, -161, -288, -76, 123],\n [-251, 66, -1, 198, 178, -167, -318, -153, -168],\n [263, 66, 223, -188, -258, -5, 18, 62, 303],\n [215, -142, -17, 324, 158, 75, -126, 454, 71],\n [241, -14, 137, 44, -78, 13, -78, 228, 211],\n [216, 160, 270, -498, -456, -16, 192, -211, 343],\n [-26, 85, 161, 167, 48, -170, -375, -3, 58],\n [-254, 105, 47, 145, 128, -198, -339, -214, -135]]\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[[0, 8, 11, -7, -4, 9, 1, 7, -7],\n [0, 24, 33, -21, -12, 27, 3, 21, -21],\n [0, -128, -176, 112, 64, -144, -16, -112, 112],\n [0, 80, 110, -70, -40, 90, 10, 70, -70],\n [0, -144, -198, 126, 72, -162, -18, -126, 126],\n [0, 72, 99, -63, -36, 81, 9, 63, -63],\n [0, 56, 77, -49, -28, 63, 7, 49, -49],\n [0, 88, 121, -77, -44, 99, 11, 77, -77],\n [0, 128, 176, -112, -64, 144, 16, 112, -112]]?\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[[-136, 136, 32, -120, -56, 112, -48, -120, 120],\n [-153, 153, 36, -135, -63, 126, -54, -135, 135],\n [-272, 272, 64, -240, -112, 224, -96, -240, 240],\n [-204, 204, 48, -180, -84, 168, -72, -180, 180],\n [-255, 255, 60, -225, -105, 210, -90, -225, 225],\n [-187, 187, 44, -165, -77, 154, -66, -165, 165],\n [-102, 102, 24, -90, -42, 84, -36, -90, 90],\n [-119, 119, 28, -105, -49, 98, -42, -105, 105],\n [272, -272, -64, 240, 112, -224, 96, 240, -240]]\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[[-740, -678, 56, -297, -774, 435, 474, -139, -41],\n [304, 353, -79, 268, 372, -351, -228, -94, -228],\n [94, 234, 229, 251, 361, -251, 17, -36, -85],\n [-42, 108, 219, -9, 98, 109, 231, 310, 372],\n [-328, -66, 428, 221, 9, 3, 446, 103, -13],\n [-184, -355, 91, -294, -450, 544, 183, 506, 587],\n [-174, 37, 616, 664, 122, -202, 144, 341, 56],\n [450, 378, 21, -254, 672, -84, -87, -45, 478],\n [-140, -179, 835, 258, 533, -127, 269, -125, 501]]\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[[835, -189, -423, 441, 23, 551, -48, -461, 185],\n [627, -174, 128, -358, -194, 30, -35, -208, -238],\n [92, -533, -231, -69, 38, 199, -81, -399, 154],\n [-39, -543, 211, -230, 252, 178, 195, 318, -513],\n [60, -19, -301, -85, 110, 58, 100, -323, -52],\n [12, 269, 213, 127, -182, 110, -406, 354, 220],\n [-28, -260, -175, -567, 43, 25, 355, -62, -502],\n [191, 98, -463, 274, -256, 198, 523, 11, 82],\n [-204, 351, -311, -46, -503, -223, 439, 64, 312]]\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[[-168, 192, 96, 216, 24, -36, 108, 72, 168],\n [98, -112, -56, -126, -14, 21, -63, -42, -98],\n [-196, 224, 112, 252, 28, -42, 126, 84, 196],\n [98, -112, -56, -126, -14, 21, -63, -42, -98],\n [-84, 96, 48, 108, 12, -18, 54, 36, 84],\n [14, -16, -8, -18, -2, 3, -9, -6, -14],\n [0, 0, 0, 0, 0, 0, 0, 0, 0],\n [224, -256, -128, -288, -32, 48, -144, -96, -224],\n [-224, 256, 128, 288, 32, -48, 144, 96, 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[[-395, -382, 257, 281, -453, -167, 253, -130, -491],\n [-360, -590, -199, -293, -344, -269, -230, 72, -461],\n [-342, -60, -48, -756, 300, -663, -494, 489, 9],\n [70, -186, 8, 91, 275, 466, 265, 220, -470],\n [196, 488, -40, -205, 502, 61, 209, 143, -8],\n [235, 176, 500, 736, 199, 539, 83, -17, 565],\n [-381, -38, 865, 529, 170, -71, 277, 215, -34],\n [47, -224, -638, -485, -438, -300, -82, -386, -192],\n [-320, -210, -63, -230, -78, -216, 127, 95, -625]]\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[[46, 188, -11, -230, 119, -77, -369, 130, 77],\n [55, 134, 189, -212, -136, -341, 152, -404, 125],\n [-180, 246, -206, -228, -67, -26, -551, 360, -210],\n [372, 96, 159, -186, 579, -129, -33, -96, 213],\n [-112, 142, 80, -176, -321, -340, 163, -344, -96],\n [72, -6, 117, -40, -58, 54, -164, -19, 368],\n [-164, 296, -6, -344, -330, -252, -406, -14, 32],\n [10, 278, -85, -300, 218, -306, -124, 3, -356],\n [120, -246, 34, 276, 183, 222, 283, 0, 78]]?\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[[-55, -115, 333, 216, -138, 141, 179, -281, 643],\n [515, -7, 107, -79, 196, -2, 9, -409, 60],\n [-59, 286, 208, -35, -133, -76, -282, 73, -36],\n [-386, 213, 121, 42, -288, -65, -255, 301, -50],\n [-330, -35, 39, -1, -71, 93, 33, 292, 109],\n [-116, -175, 125, -155, 221, 363, 145, 20, 107],\n [281, 80, -294, -72, -3, -295, -182, 23, -485],\n [-396, 200, 172, 66, -22, 230, -45, -69, -18],\n [-160, -1, -275, 106, -246, -285, -73, 309, -194]]\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[[-248, 129, 11, 131, -146, -270, -206, 39, 257],\n [355, 69, 6, -282, 106, -106, 486, -198, 66],\n [89, 135, 337, -25, -85, -492, 149, -84, 446],\n [202, 223, -193, -111, 0, 164, 268, 309, -197],\n [264, 239, 665, -47, 343, -241, -105, -146, 392],\n [-10, 162, 233, -291, -255, -144, 9, 37, 252],\n [-377, -649, -305, -355, -338, 443, 172, 3, -473],\n [-100, -643, -206, -544, -386, 519, 200, -262, -440],\n [-657, -195, -418, 17, -88, 239, -435, -52, -176]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[63, -37, 316, -335, 259, 280, 105, 23, -121],\n [31, 87, -513, 530, -469, -466, -382, 267, -59],\n [87, -254, 234, -359, 260, 494, 142, 185, 328],\n [21, 153, 46, -26, 75, -76, -381, 258, -682],\n [101, 291, 242, -217, 308, 672, -203, 123, -659],\n [-356, 230, 129, -141, 203, 210, -97, -432, -400],\n [297, 40, -3, 147, -191, -124, 121, 34, 509],\n [-364, -40, -316, 256, -244, -280, 454, -614, 143],\n [-359, -200, 175, -410, 22, -33, 93, -235, -71]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[32, 115, -140, 92, -7, 194, -24, 66, -88],\n [56, -20, -68, 220, 32, 192, -160, -268, -36],\n [88, 35, -160, 328, 37, 346, -216, -306, -92],\n [64, 50, -136, 232, 22, 268, -144, -180, -80],\n [-92, -25, 158, -346, -41, -354, 232, 340, 90],\n [6, 75, -69, 3, -12, 72, 24, 105, -45],\n [-74, -70, 167, -265, -23, -318, 160, 187, 99],\n [16, 20, -40, 56, 4, 72, -32, -32, -24],\n [24, -90, 36, 116, 30, 28, -112, -256, 28]]?\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 9x9 matrix:\n[[55, 5, -55, 55, 80, 10, 45, -10, -35],\n [66, 6, -66, 66, 96, 12, 54, -12, -42],\n [198, 18, -198, 198, 288, 36, 162, -36, -126],\n [33, 3, -33, 33, 48, 6, 27, -6, -21],\n [55, 5, -55, 55, 80, 10, 45, -10, -35],\n [-44, -4, 44, -44, -64, -8, -36, 8, 28],\n [-77, -7, 77, -77, -112, -14, -63, 14, 49],\n [132, 12, -132, 132, 192, 24, 108, -24, -84],\n [132, 12, -132, 132, 192, 24, 108, -24, -84]]\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[[8, 13, -4, 10, 3, 0, 6, -13, -17],\n [-72, -117, 36, -90, -27, 0, -54, 117, 153],\n [128, 208, -64, 160, 48, 0, 96, -208, -272],\n [32, 52, -16, 40, 12, 0, 24, -52, -68],\n [24, 39, -12, 30, 9, 0, 18, -39, -51],\n [-24, -39, 12, -30, -9, 0, -18, 39, 51],\n [-96, -156, 48, -120, -36, 0, -72, 156, 204],\n [-96, -156, 48, -120, -36, 0, -72, 156, 204],\n [144, 234, -72, 180, 54, 0, 108, -234, -306]]\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[[384, 478, 384, -328, -296, -352, -76, 2, 164],\n [63, 18, 39, -83, 141, 173, -67, -192, -251],\n [-128, -38, -516, 416, 124, 60, -340, 330, -460],\n [106, 289, -96, 53, -161, -234, -322, 279, -217],\n [180, 319, 183, -195, -188, -215, -188, 56, -81],\n [-73, -302, -140, 219, 160, 154, 345, -61, 335],\n [-149, -94, -251, 204, 50, 37, -125, 168, -172],\n [101, -50, -4, 11, 178, 186, 87, -195, -57],\n [-342, -392, -213, 184, 169, 231, 114, -13, -20]]\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[[33, 0, 154, 77, -110, 154, 22, 121, -121],\n [15, 0, 70, 35, -50, 70, 10, 55, -55],\n [-3, 0, -14, -7, 10, -14, -2, -11, 11],\n [-15, 0, -70, -35, 50, -70, -10, -55, 55],\n [15, 0, 70, 35, -50, 70, 10, 55, -55],\n [-27, 0, -126, -63, 90, -126, -18, -99, 99],\n [9, 0, 42, 21, -30, 42, 6, 33, -33],\n [-39, 0, -182, -91, 130, -182, -26, -143, 143],\n [21, 0, 98, 49, -70, 98, 14, 77, -77]]\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, -20, -187, -42, 207, 187, -163, 64, -24],\n [-93, 143, -171, 100, 78, 427, -264, -27, 193],\n [-56, -32, 244, -210, -106, -631, 344, 169, -192],\n [152, -17, -218, -47, 269, 177, -140, 76, -81],\n [87, -291, -95, -456, 278, -412, -36, 376, -257],\n [50, -132, 88, 151, -180, 87, 11, -217, 62],\n [91, -192, 181, 216, -291, 20, 105, -319, 44],\n [382, -157, -476, -161, 603, 321, -312, 182, -225],\n [58, -223, 232, -53, -201, -396, 240, -61, -123]]\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 9x9 matrix:\n[[-99, -126, 36, 135, 117, -27, -135, 81, -45],\n [-55, -70, 20, 75, 65, -15, -75, 45, -25],\n [165, 210, -60, -225, -195, 45, 225, -135, 75],\n [187, 238, -68, -255, -221, 51, 255, -153, 85],\n [66, 84, -24, -90, -78, 18, 90, -54, 30],\n [88, 112, -32, -120, -104, 24, 120, -72, 40],\n [-176, -224, 64, 240, 208, -48, -240, 144, -80],\n [99, 126, -36, -135, -117, 27, 135, -81, 45],\n [99, 126, -36, -135, -117, 27, 135, -81, 45]]\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[[4, 19, 92, -119, 6, 58, 15, 4, 95],\n [186, 175, 507, -34, 44, 12, 269, -74, 114],\n [208, -22, 196, -30, -52, 132, 58, -304, 110],\n [-78, -208, -307, -269, -86, 230, -282, -130, 165],\n [-70, -182, -295, -183, -74, 171, -244, -107, 103],\n [116, 279, 508, 181, 110, -202, 371, 144, -77],\n [50, 67, -17, 390, 28, -232, 121, 34, -278],\n [72, 109, 218, 89, 38, -76, 157, 22, -33],\n [42, -76, -239, 331, -38, -122, -46, -106, -243]]\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[[-288, -249, -248, -206, 72, 361, 207, -445, 196],\n [318, 84, 298, 106, -212, -196, -332, 290, -36],\n [-174, -63, -92, -89, -6, 85, 64, -106, 15],\n [-345, -27, -151, -127, -14, 39, 111, -62, -76],\n [381, -66, 197, 74, -80, 48, -203, -14, 169],\n [252, 285, 222, 219, -38, -395, -166, 474, -239],\n [264, 150, 152, 164, 16, -198, -98, 238, -80],\n [-117, -3, 9, -57, -98, -29, -55, 48, -50],\n [-147, 189, -119, 82, 180, -179, 202, 155, -213]]?\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 9x9 matrix:\n[[40, -82, 264, 234, -140, -74, -60, -38, -142],\n [130, -74, 308, 348, -290, 62, 190, 14, -434],\n [-10, 80, -236, -186, 86, 112, 134, 52, 44],\n [135, -51, 246, 306, -279, 105, 249, 33, -447],\n [5, -5, 18, 18, -13, -1, 3, -1, -17],\n [-100, 58, -240, -270, 224, -46, -144, -10, 334],\n [-10, -60, 164, 114, -34, -108, -146, -48, 24],\n [60, -102, 336, 306, -192, -78, -48, -42, -210],\n [-55, 83, -278, -258, 167, 55, 23, 31, 191]]\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[[86, -471, 128, 412, 25, -22, 118, 83, -138],\n [-47, 494, -4, -428, 223, 248, 159, -209, 293],\n [-223, 30, 57, 98, 100, 142, 423, -58, 142],\n [0, 244, 35, -174, 291, 300, 252, -152, 156],\n [245, -212, 31, 62, -52, -116, -297, 59, -137],\n [-105, -270, -17, 350, -32, -8, 157, 119, -187],\n [296, -256, 310, 36, 206, 84, 104, -150, 230],\n [-162, 408, -264, -280, -154, -68, -230, 52, -88],\n [185, -42, -124, -28, -97, -116, -417, 109, -257]]?\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[[399, 11, -166, -122, 34, 234, -15, -176, 61],\n [109, 115, -324, -362, -60, -172, 157, 140, -349],\n [94, -228, 88, 14, -214, 242, 174, -166, 18],\n [-62, -312, 291, 311, -168, 104, 113, -203, 132],\n [-236, 124, 360, 264, -75, 175, -326, -92, 213],\n [-321, -172, 391, 404, -104, -74, -37, -71, 132],\n [299, 187, 142, -106, -619, 459, -209, -456, -228],\n [-502, -277, 188, -223, -244, 382, 358, 279, 49],\n [-194, -238, 165, 337, 155, -255, 96, 40, 147]]\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 9x9 matrix:\n[[-356, -114, 206, 18, 20, -146, -70, 230, 216],\n [250, -58, -85, -101, -117, 204, 37, -286, -78],\n [192, -10, 251, -437, -381, 158, 77, 156, 208],\n [-73, 213, 184, -126, -53, -184, 40, 514, 129],\n [43, -374, 395, -541, -533, 323, 9, -115, 399],\n [-50, -223, -63, 79, 22, 117, -53, -343, -16],\n [6, -199, 218, -284, -279, 161, 2, -45, 220],\n [10, 378, -473, 591, 571, -296, -7, 14, -470],\n [-473, -209, 270, 20, 11, -154, -102, 224, 293]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 220, -206, -25, -256, -101, 196, 8, -183],\n [-118, 332, -298, -86, -234, 16, 122, 70, -200],\n [-207, 258, -219, -114, -33, 177, -75, 111, -81],\n [-273, 522, -459, -171, -255, 150, 63, 153, -258],\n [47, 2, -7, 19, -63, -68, 71, -23, -32],\n [81, -254, 229, 62, 191, 1, -107, -49, 159],\n [103, -122, 103, 56, 9, -91, 43, -55, 35],\n [97, -38, 25, 44, -81, -121, 109, -49, -31],\n [-271, 54, -21, -117, 287, 362, -351, 135, 130]]\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[[121, -396, -424, 599, -61, -374, 305, -524, 465],\n [144, -70, -119, 45, 56, 14, -66, -216, -38],\n [-201, -167, -143, 392, -22, -168, 370, -154, 334],\n [403, -98, -383, 290, -117, -361, 203, -302, 110],\n [569, -91, -357, 194, -238, -565, 102, -204, 83],\n [227, -99, -118, 173, -228, -738, 258, -54, 106],\n [-93, -158, 333, -380, 41, 334, -723, 152, -7],\n [686, 31, -469, 129, -89, -181, 17, -328, -108],\n [242, 194, -297, 65, 130, 378, 104, -192, -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[[-54, 36, 9, -39, 33, 18, 24, -3, 3],\n [-90, 60, 15, -65, 55, 30, 40, -5, 5],\n [108, -72, -18, 78, -66, -36, -48, 6, -6],\n [198, -132, -33, 143, -121, -66, -88, 11, -11],\n [-216, 144, 36, -156, 132, 72, 96, -12, 12],\n [-126, 84, 21, -91, 77, 42, 56, -7, 7],\n [-288, 192, 48, -208, 176, 96, 128, -16, 16],\n [144, -96, -24, 104, -88, -48, -64, 8, -8],\n [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": "What is the rank of the matrix:\n[[147, 201, 383, -361, 355, -155, -82, 62, 105],\n [-19, -754, 566, 699, 512, 69, 318, 326, 205],\n [19, -83, 16, -353, -3, 103, 69, -169, 515],\n [453, -165, 136, -422, 421, -345, -253, -295, 506],\n [-97, -95, -296, -636, -92, -280, -36, 64, 339],\n [-412, -64, -513, 201, -398, -9, 60, 349, -383],\n [-419, -378, -422, 355, 80, -218, 505, 604, -581],\n [136, -45, 313, -38, 227, 57, 374, -173, 79],\n [-49, 338, -317, -246, 11, -212, 253, 49, -552]]?\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[[-158, 70, 105, 132, -106, 217, 6, 86, -304],\n [-22, 378, 213, 28, -158, -41, 20, 6, -440],\n [-38, 166, -273, 144, 506, -115, -290, -388, 336],\n [-124, 18, 266, 52, -362, 215, 135, 276, -532],\n [-182, 30, -180, 278, 476, -77, -396, -261, -56],\n [192, -204, 10, -300, -384, 214, 442, 222, 472],\n [146, 104, -85, -132, 40, -83, 80, -116, 348],\n [-74, 194, 216, 10, -340, 260, 199, 169, -320],\n [-34, 23, -71, 78, 193, -94, -156, -116, -2]]\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[[170, 140, -20, -217, -81, -110, 30, -239, 41],\n [-142, 436, 374, -377, 246, -442, 344, -37, 53],\n [43, 70, -19, -65, -114, -37, -26, 58, -77],\n [75, 342, 165, -378, 300, -325, 282, -193, 164],\n [-184, -336, -36, 381, 84, 261, -102, 109, 29],\n [-28, 288, 234, -297, 99, -298, 214, -205, 73],\n [177, -262, -227, 155, -573, 262, -334, -296, -111],\n [25, -190, -245, 248, -66, 245, -190, 451, -154],\n [-169, -210, 33, 246, 288, 136, 36, 53, 126]]\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 9x9 matrix:\n[[-196, 366, -209, -147, -120, -187, 403, 77, -193],\n [179, 309, -138, -330, 33, 135, 133, 84, -478],\n [283, 379, -32, -273, 217, 107, 235, -88, -233],\n [-73, -121, 70, 478, -9, -137, 34, -100, -94],\n [337, 354, 115, -134, 373, 13, 319, -279, 51],\n [-306, -439, 103, 293, -212, -228, -172, 25, 256],\n [-329, 604, -381, -197, -151, -127, 498, 159, 64],\n [87, -440, 93, 203, -105, 157, -453, 97, -334],\n [550, -299, 395, 164, 378, 170, -265, -309, -169]]\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 9x9 matrix:\n[[-100, -190, -32, 68, -108, 45, 7, 85, -69],\n [-220, 366, 64, -164, 76, -69, -175, 243, 285],\n [-5, 239, 41, -96, 94, -51, -60, 22, 135],\n [-110, 8, 2, -12, -32, 3, -45, 109, 45],\n [135, -433, -75, 184, -130, 87, 158, -164, -291],\n [55, -39, -7, 20, 2, 6, 31, -57, -42],\n [20, -256, -44, 104, -96, 54, 70, -38, -150],\n [245, 119, 19, -28, 126, -36, 67, -233, -24],\n [-75, 435, 75, -180, 150, -90, -135, 105, 270]]\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[[80, 70, 0, 60, 150, 50, 170, 110, -30],\n [48, 42, 0, 36, 90, 30, 102, 66, -18],\n [104, 91, 0, 78, 195, 65, 221, 143, -39],\n [120, 105, 0, 90, 225, 75, 255, 165, -45],\n [-72, -63, 0, -54, -135, -45, -153, -99, 27],\n [64, 56, 0, 48, 120, 40, 136, 88, -24],\n [-120, -105, 0, -90, -225, -75, -255, -165, 45],\n [-128, -112, 0, -96, -240, -80, -272, -176, 48],\n [112, 98, 0, 84, 210, 70, 238, 154, -42]]\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[[-309, -217, -87, -352, 289, 165, 237, -124, 99],\n [-301, 14, -357, -622, -113, -27, 64, -25, -164],\n [-272, -295, 160, -46, 257, 339, -37, 32, 180],\n [431, 64, 216, 413, -128, -237, -96, -113, -63],\n [-95, 353, -224, -613, -125, -252, 187, -253, -378],\n [-50, 105, 100, -333, 26, -179, 63, -79, -157],\n [-105, 409, -26, -402, 56, -241, -78, -244, -582],\n [140, 312, -145, -404, -421, -515, -436, -190, -776],\n [256, -1, -390, -65, -42, -615, -51, -205, -438]]\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 9x9 matrix:\n[[160, 114, -137, -34, 114, -158, -136, 164, 141],\n [64, 276, -170, 12, 20, -268, -208, 296, 274],\n [-176, 24, 76, 54, -142, 41, 50, -31, -14],\n [208, 384, -296, -18, 122, -415, -334, 449, 406],\n [-48, -90, 69, 4, -28, 97, 78, -105, -95],\n [-160, -348, 254, 8, -88, 366, 292, -398, -362],\n [-192, 108, 42, 68, -164, -28, 0, 48, 62],\n [-256, -402, 329, 30, -158, 448, 364, -482, -433],\n [-48, -198, 123, -8, -16, 193, 150, -213, -197]]\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[[344, -187, 166, -228, -441, 381, -482, -392, -411],\n [436, -91, -161, -677, 35, 408, -259, 5, -48],\n [-536, 155, 52, 288, 688, -616, 357, 567, 616],\n [130, -74, -228, -310, -370, 232, -102, 76, -290],\n [-90, -57, 368, 198, 67, -104, -238, -163, 57],\n [-283, 56, 489, 558, 365, -351, -27, -176, 314],\n [206, -49, -256, -82, -221, 44, 224, -61, -247],\n [-89, 90, 501, 560, 645, -365, 242, -419, 502],\n [352, -216, 243, -213, -175, 188, -417, -327, -258]]\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[[51, 262, -180, 291, 304, -15, 262, 134, -249],\n [986, 706, -24, 228, 843, 239, -54, -269, 583],\n [428, 228, 182, 142, 120, 306, -17, 425, 72],\n [-50, 361, -201, 267, 451, -11, 417, 242, -433],\n [356, -199, -208, -155, -92, -331, -604, -21, 391],\n [275, 61, -225, 204, -72, -333, -403, -291, 42],\n [-589, 49, -88, 194, -63, -247, 349, -110, -546],\n [-25, -41, -533, -64, 448, -391, 67, 713, -179],\n [-293, -540, -60, -171, -591, -320, -367, 348, -55]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 64, 44, -14, -72, -76, -38, 70, 22],\n [42, 32, -68, 56, 18, 106, 134, -10, -106],\n [78, 288, -12, 84, -198, -6, 186, 210, -174],\n [21, -64, -74, 35, 90, 124, 89, -85, -61],\n [-76, -256, 24, -84, 168, -16, -188, -180, 172],\n [-170, -240, 220, -217, 39, -331, -512, -70, 418],\n [-36, -176, -16, -35, 135, 41, -74, -140, 76],\n [-112, -112, 168, -147, -21, -259, -350, 0, 280],\n [114, 224, -116, 140, -90, 166, 326, 110, -274]]?\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[[513, 612, -223, -394, -173, -144, -396, -518, -129],\n [-14, 206, 52, -32, -327, 179, 459, -102, 231],\n [-342, 38, -94, 328, -122, -499, -184, 107, 288],\n [-146, -102, 197, 516, -65, -84, 315, -246, 453],\n [144, -184, 131, -194, 134, 691, 390, 62, -442],\n [191, 72, 239, -137, 16, 292, 381, -309, -35],\n [-44, 12, 97, -439, 23, 309, 273, 217, -378],\n [-31, -422, 147, -235, 332, 197, 27, 386, -179],\n [49, 452, -87, -216, -354, 34, 185, -175, -22]]?\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[[-240, 204, -91, -160, 268, -260, -136, -371, 14],\n [-86, -150, 279, -74, 398, -354, 348, 228, 446],\n [22, 42, -12, 154, 182, -234, 12, -33, 116],\n [-101, -142, 250, -147, 287, -223, 298, 198, 346],\n [65, -10, -4, 119, 21, -53, 14, 44, 34],\n [-273, -64, 213, -407, 271, -147, 210, 10, 244],\n [271, 100, -246, 441, -245, 105, -246, -61, -254],\n [195, -358, 389, 213, 251, -251, 530, 635, 540],\n [201, -132, 109, 319, 113, -181, 190, 290, 232]]?\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 9x9 matrix:\n[[16, -167, 100, -66, -90, -27, 161, 97, -8],\n [14, 144, 198, 220, 202, 29, 59, -2, -4],\n [92, -83, 310, 176, 98, 31, 303, 33, 14],\n [266, 160, 103, 443, 302, 205, 171, -438, 125],\n [208, -285, 342, 152, 2, 67, 511, -37, 58],\n [86, 202, -251, 125, 110, 109, -201, -336, 71],\n [124, -423, 307, -57, -166, -15, 501, 141, 15],\n [230, 89, 77, 339, 216, 168, 166, -361, 107],\n [-282, -93, -465, -579, -396, -186, -444, 273, -99]]\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 9x9 matrix:\n[[-406, 158, 397, 2, 83, 171, -362, -201, -13],\n [194, -155, 404, 35, -233, 274, 126, 312, 32],\n [-17, 38, -572, -41, 251, -325, 12, -390, 43],\n [221, 22, -84, -103, 61, 216, 233, -88, -195],\n [-327, 85, 19, 220, 349, 166, -252, -299, -60],\n [75, -353, 70, 328, -26, -53, -24, 124, 363],\n [465, -21, -279, -296, -147, -32, 430, 45, -140],\n [-26, -29, -152, 78, 181, 10, -15, -213, 19],\n [-253, 247, 81, -218, 79, 14, -194, -307, -118]]\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[[132, 30, -205, 378, -214, 195, -27, 80, -146],\n [250, -12, 32, 270, -45, 31, -25, 173, 233],\n [15, 48, 258, -76, 41, 54, -545, 135, 292],\n [-238, -48, 110, 457, -562, 113, 75, 436, 235],\n [-444, -379, 394, -484, -65, -185, -312, -6, 548],\n [66, -188, -71, 496, -214, 118, 716, -155, -194],\n [-142, -98, -316, -588, 476, 86, -54, -14, -404],\n [-175, 56, 225, 241, -99, 343, 210, -201, -106],\n [355, 558, -48, 240, 101, -63, 255, -329, -248]]?\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 9x9 matrix:\n[[-31, 27, 144, -291, 356, -37, -103, -222, 107],\n [-409, -5, 56, 305, 174, -603, -121, -662, -553],\n [324, -30, 211, -7, 583, 220, -143, -303, 970],\n [284, 13, 3, 24, -189, 514, 255, 1037, 5],\n [130, -321, 82, 619, 575, -128, 325, 60, -276],\n [216, -98, -42, -278, -51, 477, 184, 518, 367],\n [326, -118, -119, 219, 12, 54, 172, -335, 25],\n [-352, 77, 229, -135, 308, -169, -148, 143, -162],\n [364, 231, 251, 294, 257, 152, -91, 461, 107]]\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[[-16, -31, -222, -22, 41, 163, 33, -43, 10],\n [-25, 76, 172, -187, 126, -133, 32, 74, 29],\n [350, 12, -190, -249, 202, -322, 336, 93, -233],\n [-122, -302, 168, -16, -38, 352, -580, 98, 66],\n [-94, 72, 449, 228, -72, -101, -142, -214, -143],\n [78, -131, 146, -115, 27, -53, -189, 156, -23],\n [275, -265, -204, -647, 429, 18, -91, 329, -123],\n [-184, 151, 1, -268, 195, 52, 103, 43, 181],\n [67, -169, -34, -442, 471, 206, -163, -62, -266]]\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[[147, 191, 123, 90, 98, 71, 18, 57, -103],\n [68, -7, 20, 111, -55, 57, -305, -175, -72],\n [-135, -49, -157, 124, -122, -250, -105, -252, 418],\n [-66, -349, -40, -267, -69, 150, 210, 134, -93],\n [-129, 207, -27, -75, 120, -132, 111, 204, -111],\n [-160, 311, -84, 82, 95, -323, 91, 55, 207],\n [-210, -460, -110, -453, -74, 142, 288, 268, -215],\n [-26, 385, 2, 172, 127, -257, 107, 33, 219],\n [-101, 85, 3, -202, 136, -43, 404, 347, -93]]\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[[180, 112, 306, 198, -290, 252, -181, 113, 354],\n [-194, 220, 146, -432, 87, -375, -293, 159, -98],\n [-2, -24, 78, 281, 80, 193, 172, -74, 232],\n [-175, 193, 75, -69, 354, -98, 147, 39, 97],\n [-107, 318, 490, -227, -10, -197, -330, 213, 253],\n [-22, -271, -211, 171, 77, 45, 239, -208, -138],\n [-82, -430, -208, 40, -296, -106, -219, -221, -248],\n [-115, -201, -383, 166, 342, 47, 440, -224, -171],\n [-102, 246, 398, -374, -141, -311, -482, 218, 72]]?\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[[59, -90, -148, 177, -2, 154, -510, 357, -64],\n [-11, -201, -94, 47, 421, -60, -428, 206, -463],\n [41, 47, 458, 34, -195, 31, 98, 18, 163],\n [3, 50, 266, -45, -81, -28, 194, -101, 104],\n [-18, 94, -42, 34, -287, -24, 300, -114, 138],\n [18, 38, 84, 25, -130, 39, 38, 12, 116],\n [-66, -96, 206, -131, 373, -229, 158, -176, -370],\n [-12, -40, -256, 62, 24, 2, -116, 76, -116],\n [24, -11, 12, 171, -224, 45, -88, 165, -13]]?\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[[476, 392, -453, 729, 31, -428, 182, -580, -627],\n [-232, -171, -267, -371, -293, 397, 495, 240, 422],\n [466, 431, -301, 642, 115, -515, -150, -544, -587],\n [-170, -92, 533, -408, 169, 60, -558, 385, 254],\n [143, -89, 521, 138, 74, -100, -294, 78, -112],\n [77, 202, -28, 301, 215, -21, 89, -56, -394],\n [-38, -290, 19, -459, -111, 28, 193, 289, 427],\n [248, -356, 148, -201, -158, -88, 169, 268, 352],\n [-465, 43, -72, -417, 43, 502, 103, 361, 243]]\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[[77, -77, -49, -35, -56, 28, -63, 56, 119],\n [11, -11, -7, -5, -8, 4, -9, 8, 17],\n [-88, 88, 56, 40, 64, -32, 72, -64, -136],\n [-77, 77, 49, 35, 56, -28, 63, -56, -119],\n [-77, 77, 49, 35, 56, -28, 63, -56, -119],\n [99, -99, -63, -45, -72, 36, -81, 72, 153],\n [22, -22, -14, -10, -16, 8, -18, 16, 34],\n [-143, 143, 91, 65, 104, -52, 117, -104, -221],\n [-55, 55, 35, 25, 40, -20, 45, -40, -85]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-184, 359, 109, -59, -74, -251, 41, -54, -195],\n [250, 90, 192, -398, 252, -94, 182, 360, 510],\n [-357, 397, 36, 15, -129, 302, -246, 18, 154],\n [178, 246, 69, -457, 111, -411, 341, 230, 59],\n [37, -45, -241, -77, -81, 206, 15, 96, 93],\n [159, -40, 214, -218, 174, -133, -4, 203, 487],\n [406, -602, 138, -161, 217, -395, -2, 32, 382],\n [-169, 319, -39, 407, -91, 572, -27, 144, 43],\n [371, -14, 98, -237, 209, -84, 268, 425, 525]]\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[[259, -257, -285, 3, -168, 88, 364, -146, 124],\n [174, -30, 124, 358, -150, 78, 337, -297, 186],\n [-77, 413, -413, 19, 65, 387, 677, 624, -671],\n [-251, 369, -93, 219, -13, 47, -160, 81, -595],\n [190, 382, 48, 624, 280, 198, 0, -244, -532],\n [-239, -339, 440, -336, -610, -193, 285, 287, 442],\n [358, -340, 151, -20, -174, 10, 194, -89, 179],\n [104, 558, -933, -48, 228, 480, -54, -43, -155],\n [-513, -427, -58, -187, -687, -957, -609, -289, 711]]\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[[681, -50, -22, 35, -258, 143, -244, 502, -7],\n [-134, 189, 247, 76, 309, 368, 151, 66, 148],\n [-532, 548, 257, 148, 324, 403, 505, -33, 193],\n [-220, 193, -425, 125, -136, 110, -48, 142, 124],\n [756, -88, 82, -63, -379, -102, -157, 395, -71],\n [-371, -184, -53, -66, 279, 16, 12, -348, 139],\n [125, -357, -71, -244, -98, -263, 4, -266, 207],\n [-105, 439, 121, 211, 27, 231, 143, 260, -143],\n [449, -9, -267, -128, -538, -215, 10, 233, 226]]\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[[-254, 73, -120, 52, -335, 244, -356, 91, 63],\n [-53, 94, -63, -99, 29, 279, -134, -88, -117],\n [252, -477, -55, -109, 63, -118, -230, -400, -21],\n [-59, 283, -86, 21, 37, 483, -81, 136, -206],\n [-330, 358, 137, -377, -24, 277, 11, -361, 53],\n [-99, 360, -162, 269, 396, -32, 297, 212, -305],\n [475, -401, 23, 181, 160, -348, 179, 207, -21],\n [124, -321, -230, 211, -32, -192, -226, 206, -68],\n [-480, 552, 382, 134, -340, -227, 470, 103, 464]]\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 9x9 matrix:\n[[16, 254, -163, -38, -92, 230, 71, -126, 201],\n [-208, 392, -344, -99, -305, 508, 233, -147, 354],\n [28, -624, -171, -99, 101, -662, -580, 117, -275],\n [23, -195, 70, 187, 36, -68, -116, 219, -205],\n [-10, -405, -552, -287, 47, -548, -674, -31, -9],\n [168, 155, 115, -326, 10, -182, 128, -514, 238],\n [87, 216, 122, 445, -90, 488, 183, 247, -76],\n [30, -147, 137, -196, 241, -380, -88, -57, -68],\n [-102, -492, 115, 93, -50, -300, -160, 208, -315]]\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 9x9 matrix:\n[[40, 130, 50, -80, 0, -180, 150, -70, 100],\n [-48, -156, -60, 96, 0, 216, -180, 84, -120],\n [-56, -182, -70, 112, 0, 252, -210, 98, -140],\n [-32, -104, -40, 64, 0, 144, -120, 56, -80],\n [68, 221, 85, -136, 0, -306, 255, -119, 170],\n [16, 52, 20, -32, 0, -72, 60, -28, 40],\n [0, 0, 0, 0, 0, 0, 0, 0, 0],\n [-48, -156, -60, 96, 0, 216, -180, 84, -120],\n [12, 39, 15, -24, 0, -54, 45, -21, 30]]\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[[-225, -163, -56, 19, -42, 355, 235, -70, 516],\n [226, -321, 192, -290, -201, -19, -178, 72, 30],\n [-219, 68, -269, -7, 6, 40, 176, 67, 419],\n [-68, -80, -104, 290, 412, -512, -234, 120, -356],\n [-327, -107, -253, 47, 45, 179, 242, 31, 621],\n [100, 126, -24, -23, 18, -214, -109, 60, -234],\n [66, 101, -18, 5, 31, -161, -79, 38, -190],\n [-144, -147, 54, 333, 309, -33, -27, -78, -150],\n [-38, 69, 76, -138, -283, 527, 274, -156, 358]]\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[[385, -341, 202, 447, 214, 482, 190, -348, 72],\n [28, -20, 256, 20, 232, 160, 8, -184, -224],\n [303, -255, 68, 55, 96, 291, 303, -257, -150],\n [-25, 5, 234, 165, 196, 128, 24, -214, -182],\n [-156, 153, 51, -166, 38, -127, -258, 175, 30],\n [-76, 38, -24, 74, -43, -59, 149, -109, -135],\n [-393, 360, -229, -325, -234, -491, -496, 557, 308],\n [511, -416, 49, -23, 111, 438, 455, -324, -191],\n [-206, 193, -149, -366, -145, -298, -97, 238, -65]]?\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 9x9 matrix:\n[[-719, -164, -129, 382, 452, -371, 15, 1, -51],\n [208, 168, -501, 120, 57, 200, -85, -52, 145],\n [798, 246, 34, -357, -164, 326, 521, -141, 181],\n [-251, 88, -59, -261, -392, 6, -25, 359, -56],\n [-867, -235, -91, 705, 381, -112, 86, -286, -99],\n [-126, -71, -54, 331, 159, 98, 322, -251, 61],\n [96, -21, -117, 81, 32, -83, -419, 27, -13],\n [-357, -95, -199, 125, -414, 238, 291, 138, -162],\n [-137, -102, -63, -215, 272, -387, -295, 372, -74]]\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[[385, 115, 163, 303, -337, 302, 251, -123, -98],\n [-346, -303, -166, -277, 157, -205, -60, -188, -122],\n [277, -329, 192, 321, -389, 235, 300, -455, -333],\n [326, 499, -136, 41, -404, 439, 378, -50, -15],\n [-54, -80, -155, 82, -143, 85, -63, 52, 96],\n [-400, 186, -323, -488, 327, -225, -159, 186, 150],\n [124, -187, 344, 91, 117, -123, 62, -194, -218],\n [149, 138, -74, -50, -261, 240, 336, -267, -192],\n [-554, 173, -306, -589, 586, -433, -364, 362, 263]]?\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[[-580, -725, -13, -253, -343, 362, -771, 127, -215],\n [57, -68, 398, -363, -101, 679, -309, 148, -434],\n [-99, -165, -454, -229, 148, -229, -30, -110, 150],\n [47, -160, 691, -146, -168, 543, -161, 250, -118],\n [-158, 25, 535, 121, -30, 235, 239, 469, 47],\n [-62, 154, 21, -295, -3, 278, 217, -51, 344],\n [-395, -62, 290, 525, -76, -406, -361, -188, -140],\n [-504, 54, -71, 176, 108, -499, 247, -88, 358],\n [471, 508, -887, 133, 223, -685, 900, -183, 141]]?\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, -54, -18, 18, 84, -90, 48, 102, -36],\n [-11, 9, 3, -3, -14, 15, -8, -17, 6],\n [11, -9, -3, 3, 14, -15, 8, 17, -6],\n [-198, 162, 54, -54, -252, 270, -144, -306, 108],\n [77, -63, -21, 21, 98, -105, 56, 119, -42],\n [-66, 54, 18, -18, -84, 90, -48, -102, 36],\n [-121, 99, 33, -33, -154, 165, -88, -187, 66],\n [44, -36, -12, 12, 56, -60, 32, 68, -24],\n [-187, 153, 51, -51, -238, 255, -136, -289, 102]]\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[[-198, -200, -785, 432, 449, 185, -751, 3, -394],\n [219, -381, -159, -7, 127, -83, -398, -331, -232],\n [194, -93, 540, -540, 18, -126, 754, -1, 231],\n [132, -311, 550, -198, -415, -170, 515, 101, 422],\n [97, 317, 83, -57, 1, -181, -18, -400, 7],\n [-9, 317, -114, 135, 25, -126, -218, -340, -35],\n [134, -270, -11, -184, 175, 35, -1, -22, -151],\n [78, 235, 862, -564, -319, -102, 1145, 271, 512],\n [-57, 202, 586, -331, -240, -26, 891, 348, 442]]\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[[92, 372, 170, -15, -123, 352, 558, 119, -818],\n [-190, 196, -61, 266, 170, -305, 341, -589, 157],\n [171, -117, -52, 8, 53, 213, 389, 6, -22],\n [239, -139, 376, -76, -805, -103, -306, -376, 324],\n [53, -107, 442, 116, -569, 21, -211, 194, 103],\n [-368, -72, 134, 240, -18, -572, -268, -43, -242],\n [-76, 82, 213, 261, 517, 77, -174, 510, 68],\n [-69, -210, -357, 220, 153, -124, 581, -566, 731],\n [535, -126, 257, -398, -493, 338, 17, 78, -698]]\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 9x9 matrix:\n[[-385, 233, -318, 323, -104, 131, 558, 524, -44],\n [202, 116, 242, -36, 40, -248, 64, -426, 22],\n [147, -73, 268, 109, 133, 27, -259, -284, -38],\n [-249, 150, 62, 307, 160, -32, 255, 134, -158],\n [-94, -295, -380, 217, -447, -198, 13, 420, -256],\n [-169, -339, -44, 675, -84, 217, -302, 354, -346],\n [-212, 113, 348, 195, 467, -82, 9, -104, -208],\n [177, -26, -26, -699, 51, -82, -174, -176, 238],\n [99, -220, -128, 575, -462, -164, 11, 76, -256]]\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[[69, 47, 302, -566, 142, 155, 14, -161, -131],\n [-77, -151, 174, 418, -178, 477, -194, 459, 310],\n [-35, -594, 132, 132, -128, 267, -384, 552, 59],\n [78, -411, -92, -242, 156, -364, -172, -171, -170],\n [-96, -103, 46, -58, 87, 50, -178, 1, 140],\n [-29, -293, -163, -406, -168, -529, -63, -284, -133],\n [-158, 484, 292, 36, 84, 429, 18, -260, 534],\n [-433, -248, -111, 36, -110, 63, -447, 339, 348],\n [21, 571, -343, 350, -105, -231, 453, -116, -138]]?\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[[64, -573, -26, -448, -30, 511, 413, -418, 252],\n [-446, -173, -155, -489, -119, 418, 255, -207, 309],\n [-226, -62, 430, -61, -491, 247, -337, -99, -66],\n [53, -101, 476, 83, -422, 219, -538, -67, -241],\n [-456, 51, 392, -42, -462, 29, -217, 111, -13],\n [-99, -150, -52, -596, -531, 227, 638, -114, 127],\n [217, 482, 18, 32, -451, 91, -220, -204, -181],\n [15, 203, -406, -30, 329, 170, 105, -335, 240],\n [-370, 65, 336, -44, -442, -117, -25, 199, -29]]?\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[[-208, 60, 123, -275, -19, -38, 242, 79, 236],\n [197, 402, -511, 326, -56, 203, 714, 162, 34],\n [-447, -94, 161, -332, -74, 99, -194, 86, -376],\n [-724, 56, 290, -536, -176, 100, -56, 158, -430],\n [55, 299, -135, 257, -190, 132, 317, 186, 157],\n [-40, -16, -157, -68, 569, 665, 156, -23, 767],\n [451, -120, -316, 553, -338, -76, 18, 261, 6],\n [-113, 78, -175, 21, -452, -89, 402, 396, -178],\n [-200, 399, -376, -60, 221, 434, 581, 20, -157]]\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[[-33, 553, -92, -590, 362, -508, 90, -158, -620],\n [15, -464, 503, 618, -513, 235, -212, 50, 55],\n [-438, -195, -239, -126, -123, -64, 171, 9, -111],\n [696, 63, 156, 260, -160, -123, 22, 197, -184],\n [275, -432, 112, 224, -394, -311, 270, 383, -442],\n [-79, -138, -251, -220, 164, 0, -454, -117, 224],\n [6, -252, -188, -936, 12, 61, 125, -311, 321],\n [327, -151, -82, 69, -224, 331, 136, 21, 460],\n [-91, 101, 356, -173, -420, 55, 520, -15, -85]]\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[[89, -245, -320, -323, -294, -314, 167, -250, 20],\n [-113, -411, 354, 220, -136, 484, 69, 104, -171],\n [197, -358, 27, 87, -149, 129, 12, -34, 301],\n [136, -214, 191, 132, 254, 28, -128, -335, 218],\n [361, -239, -16, 297, 280, 324, -47, -244, 358],\n [151, -424, 264, 306, 155, 427, -30, -195, 142],\n [70, 533, -287, -117, 91, -347, -97, 182, 184],\n [90, 215, -388, -106, -31, -63, 121, 53, -51],\n [-314, -110, 131, -84, -312, 150, 160, 227, -454]]\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[[-193, 75, 131, -180, -156, -418, -389, 410, 36],\n [77, -213, 30, 89, 39, -263, -330, 100, -233],\n [-227, 197, 127, -24, -80, -345, -246, 375, 33],\n [-6, 158, -73, -46, 11, 451, 526, -260, 243],\n [109, -39, -93, -334, -164, -117, -424, -45, 21],\n [-162, 62, 103, -52, -53, -47, 126, 190, 121],\n [44, -150, 16, 115, 84, 156, 269, -90, -28],\n [53, -215, 11, -250, -116, -61, -140, 35, 29],\n [201, -17, -134, 217, 139, 47, -148, -250, -219]]\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[[-428, -267, -302, -70, 60, 78, -103, 214, -136],\n [416, 216, 211, 198, 64, 50, 227, -53, 110],\n [66, -74, 88, -112, 72, -94, 358, 124, 277],\n [64, -21, -77, 172, 246, 126, 366, 231, 50],\n [0, -123, 130, -192, -217, -83, -132, -30, 179],\n [96, 136, 24, 48, 136, -56, 216, -40, 8],\n [232, -100, 207, 78, -348, 190, -401, -9, 94],\n [60, 171, -81, 224, 120, 108, -44, -61, -234],\n [240, 90, 248, -80, -158, -106, -16, -152, 178]]\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 9x9 matrix:\n[[-216, -174, 120, 0, -12, -54, -162, -48, -36],\n [-60, 100, -160, 90, 220, -30, 210, -80, -210],\n [318, 93, 36, -99, -228, 96, -42, 144, 273],\n [46, 131, -148, 57, 144, 2, 196, -32, -119],\n [202, 138, -80, -15, -26, 53, 109, 56, 67],\n [-2, -56, 72, -33, -82, 5, -95, 24, 73],\n [256, 137, -52, -42, -90, 71, 73, 88, 136],\n [8, 135, -172, 78, 194, -11, 227, -56, -172],\n [104, 64, -32, -12, -24, 28, 44, 32, 44]]\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[[-124, -352, 93, 89, -108, 385, 6, -77, 271],\n [-211, -129, -83, 87, -181, 170, 49, -178, 93],\n [-141, -307, -85, 113, -275, 182, 11, 14, -41],\n [224, 433, 41, -151, 306, -369, -25, 78, -128],\n [358, 499, 363, -249, 700, -169, -51, -10, 330],\n [157, 375, -64, -106, 155, -395, -13, 91, -254],\n [-149, 57, 116, -2, 141, 247, 53, -335, 434],\n [311, 117, 211, -127, 321, -118, -77, 230, 19],\n [-193, -248, -94, 112, -257, 195, 32, -84, 23]]\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[[-239, 131, 55, -169, 317, -198, 54, -244, 286],\n [238, -279, 101, -187, -245, -177, -170, 85, 109],\n [139, -106, -83, -317, 43, -332, -236, -325, 209],\n [252, -187, -28, -132, -176, -112, -168, -103, -31],\n [-40, 73, -28, 134, 8, 142, 78, 47, -129],\n [65, -77, 143, 91, -107, 142, 122, 0, -174],\n [75, 84, -429, 56, -103, -39, -319, 370, 48],\n [-454, 456, -191, 228, 415, 162, 187, 57, 41],\n [89, -218, 254, -102, -162, -75, 20, 113, 95]]?\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 9x9 matrix:\n[[-168, -65, -312, 381, -181, 376, -36, 299, 191],\n [-105, 173, -73, 92, -111, 63, 56, 17, -6],\n [273, 261, -224, 18, -29, -334, -25, 292, 318],\n [169, -45, 26, -196, 37, -242, -131, 80, 98],\n [-110, -73, 1, 234, 251, 283, 300, 103, -92],\n [150, 53, -80, -225, -319, -311, -394, -13, 196],\n [-59, 67, -203, 500, 119, 336, 326, 117, 55],\n [93, -149, 170, -44, 205, -19, 87, -214, -129],\n [-44, 8, 240, -335, 282, -154, 139, 123, -175]]\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[[-244, -356, 66, 154, 196, 40, 14, -138, -56],\n [54, -180, -131, 153, -472, -17, 247, -367, 350],\n [157, -95, 320, -105, 242, 100, -366, -54, -149],\n [99, 85, -163, 34, -406, -69, 237, -163, 269],\n [-100, -309, -207, 246, 50, 76, 77, 195, 19],\n [-100, 51, 133, -74, -84, -115, 141, -381, 95],\n [-222, 406, 140, -236, 52, -404, 460, -402, 126],\n [154, 449, -135, -148, -454, -310, 481, -261, 389],\n [132, -329, 41, 134, -86, 192, -219, -57, 31]]\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[[-391, -155, -6, -40, -28, -75, -88, 99, 47],\n [-160, -102, 41, -6, -53, 144, 59, 172, 165],\n [-388, -175, -42, -52, 257, -208, -243, -52, -164],\n [3, -124, 71, 16, 194, 315, 78, 193, 154],\n [-302, -181, 86, -22, -57, 230, 103, 242, 276],\n [-135, 37, -240, 3, -39, -535, -405, -59, -422],\n [-23, -22, -170, 75, -370, 13, -108, 501, 46],\n [231, 92, 58, -7, 208, 11, 58, -269, -86],\n [-52, 35, -128, 43, -444, -84, -50, 310, 51]]\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[[303, 611, -244, 241, 226, -134, -18, -385, -242],\n [4, -534, 53, -367, -120, 459, 305, 431, 4],\n [-91, 206, 136, 365, -104, -189, -168, -18, 62],\n [-387, -360, 6, -175, 258, -139, -76, 210, -224],\n [-33, -131, -202, -317, 314, -6, 64, -53, -238],\n [171, 49, 206, -43, -556, -56, -154, -341, 808],\n [139, 165, 145, 206, -330, 25, -45, -82, 326],\n [41, -148, 23, -131, -89, 145, 88, 81, 83],\n [-109, 158, 146, 196, -179, -326, -287, -246, 341]]\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[[-41, -168, 55, -172, -240, 5, 125, -19, 297],\n [-86, 13, 73, 155, 72, 33, -287, 6, -97],\n [6, 415, -315, -48, 419, 229, -4, -198, -492],\n [60, -186, 102, -42, -212, -138, 162, 100, 254],\n [55, -286, 157, -82, -332, -173, 207, 125, 399],\n [110, 233, -145, 100, 281, -9, 44, 2, -340],\n [303, -4, -39, 45, 9, -289, 436, 197, -14],\n [116, 322, -262, -26, 328, 74, 162, -84, -386],\n [120, 412, -342, -63, 409, 130, 191, -136, -479]]\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 9x9 matrix:\n[[-180, -150, 0, -40, 30, 130, -70, -30, -50],\n [288, 240, 0, 64, -48, -208, 112, 48, 80],\n [-72, -60, 0, -16, 12, 52, -28, -12, -20],\n [90, 75, 0, 20, -15, -65, 35, 15, 25],\n [216, 180, 0, 48, -36, -156, 84, 36, 60],\n [0, 0, 0, 0, 0, 0, 0, 0, 0],\n [-306, -255, 0, -68, 51, 221, -119, -51, -85],\n [-306, -255, 0, -68, 51, 221, -119, -51, -85],\n [306, 255, 0, 68, -51, -221, 119, 51, 85]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-75, -248, 48, 12, 165, -173, 37, -173, 238],\n [-24, 298, 48, 96, -123, 10, 13, 268, -185],\n [-250, 12, 228, 244, 142, -418, 146, 126, 204],\n [-149, 20, 156, 152, 151, -303, 3, 153, 150],\n [85, -348, -102, -166, 132, 67, -74, -319, 179],\n [83, 1, -93, -83, -117, 192, 30, -100, -106],\n [-98, -346, 48, 8, 177, -192, 105, -290, 301],\n [-223, 178, 204, 256, -4, -303, 192, 207, 39],\n [57, 18, -36, -48, 12, 57, -96, 39, -33]]\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[[-225, -30, -90, -90, -45, -60, -90, 75, 75],\n [105, 14, 42, 42, 21, 28, 42, -35, -35],\n [-60, -8, -24, -24, -12, -16, -24, 20, 20],\n [-90, -12, -36, -36, -18, -24, -36, 30, 30],\n [45, 6, 18, 18, 9, 12, 18, -15, -15],\n [-90, -12, -36, -36, -18, -24, -36, 30, 30],\n [-30, -4, -12, -12, -6, -8, -12, 10, 10],\n [255, 34, 102, 102, 51, 68, 102, -85, -85],\n [90, 12, 36, 36, 18, 24, 36, -30, -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[[17, 83, 320, -63, -264, 109, 174, 84, -130],\n [-168, -123, 85, 317, 197, -370, -425, 98, -216],\n [-207, -149, 278, 401, 398, -153, -506, 195, -195],\n [-265, -73, 33, -561, -263, 132, 490, -95, 159],\n [-180, -180, 306, 627, 622, -121, -731, 293, -207],\n [-185, -57, 382, 76, 18, -12, -95, 140, -174],\n [-253, -41, 488, -190, -252, 88, 215, 150, -148],\n [138, -67, -111, 228, -195, 107, 42, 535, 97],\n [-162, -61, 117, 53, 157, -154, -183, -73, -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[[374, -13, 105, 212, -80, 146, -115, 279, -59],\n [431, 322, 339, 674, -67, -564, 431, 88, 11],\n [-205, -185, -312, -322, 583, -375, -74, -330, -346],\n [61, -154, -107, -245, -82, 232, -233, -91, -197],\n [216, -172, -361, 48, 37, -624, 199, -673, -263],\n [210, 678, 286, 175, 175, -398, -204, 200, 35],\n [-176, 131, -47, -197, -137, 92, 47, -19, 574],\n [782, 10, 337, 931, -281, -472, 596, 178, 42],\n [782, 383, 540, 739, -473, -98, 145, 572, 426]]\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 9x9 matrix:\n[[60, 66, -84, -90, 60, 12, 108, 84, -66],\n [-180, -198, 252, 270, -180, -36, -324, -252, 198],\n [-110, -121, 154, 165, -110, -22, -198, -154, 121],\n [80, 88, -112, -120, 80, 16, 144, 112, -88],\n [-40, -44, 56, 60, -40, -8, -72, -56, 44],\n [-90, -99, 126, 135, -90, -18, -162, -126, 99],\n [-100, -110, 140, 150, -100, -20, -180, -140, 110],\n [40, 44, -56, -60, 40, 8, 72, 56, -44],\n [160, 176, -224, -240, 160, 32, 288, 224, -176]]\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[[-169, 126, 111, -87, 202, 176, -65, 141, 19],\n [-46, -228, 202, -248, -120, -300, 256, -382, 330],\n [-142, 56, -22, 344, -145, -256, 172, 164, -35],\n [321, -472, -98, 38, -611, 4, 104, -113, -426],\n [438, -38, -141, 204, -76, 270, -398, 58, -406],\n [28, 180, 72, 33, 270, 42, -197, -14, 124],\n [267, -542, 121, -119, -564, 56, 95, -199, -355],\n [177, 4, -422, -19, -99, 354, -123, 229, -396],\n [134, 150, -571, 124, -32, 118, -38, 214, -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[[184, -261, -206, 346, 7, -108, -51, -195, 336],\n [693, -293, 92, -198, 407, 501, -111, -273, 585],\n [10, -535, 65, 302, 51, -325, 48, -55, -279],\n [237, -497, 67, 453, -279, -548, 541, -495, 285],\n [96, -345, 97, -37, 15, -568, 495, -50, 439],\n [-246, 495, 76, -193, -111, 81, -253, 67, 168],\n [-563, -144, -108, -115, -211, 170, 402, -464, -68],\n [356, 79, -295, 107, 151, 568, -303, -69, 142],\n [103, 31, -233, 371, -474, 247, 480, -596, -110]]?\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[[-85, -309, -42, -492, -284, 473, -22, 142, 62],\n [235, -135, 213, -219, 273, 13, 249, -148, -178],\n [-117, 235, 371, 13, -90, -468, -6, -2, 48],\n [670, -85, -32, 249, 327, -445, 308, 251, -568],\n [-336, 167, -113, 170, -438, -94, -346, 312, 75],\n [-163, -55, -14, -176, 41, 401, -72, -245, 201],\n [-305, 238, 344, -51, -301, -246, -264, 143, -18],\n [175, -207, 15, 75, 149, -391, 309, 400, -750],\n [-24, -61, -359, 16, -153, 400, -146, -49, 380]]\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[[-187, 11, 132, -165, 110, 121, -66, -44, 11],\n [306, -18, -216, 270, -180, -198, 108, 72, -18],\n [-238, 14, 168, -210, 140, 154, -84, -56, 14],\n [68, -4, -48, 60, -40, -44, 24, 16, -4],\n [-170, 10, 120, -150, 100, 110, -60, -40, 10],\n [289, -17, -204, 255, -170, -187, 102, 68, -17],\n [136, -8, -96, 120, -80, -88, 48, 32, -8],\n [-255, 15, 180, -225, 150, 165, -90, -60, 15],\n [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": "Find the rank of the matrix:\n[[-103, 18, 270, -29, 423, -478, 121, -334, 567],\n [5, -390, 166, -28, -122, 435, 113, -350, 315],\n [121, -13, 182, 47, -328, 378, -50, 156, -127],\n [-223, 166, -125, 182, -309, 92, -261, -338, -205],\n [-132, 5, -412, 90, 12, 71, 117, -237, -138],\n [12, 416, 634, -51, 337, -160, 99, -340, 451],\n [261, -103, 612, -539, -71, 186, 349, -6, -434],\n [110, -267, -193, -229, -75, 91, 290, 12, -323],\n [371, -282, 128, -302, -187, 236, -1, 191, 108]]\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[[41, 94, 41, -28, -9, 36, 34, -32, -69],\n [63, 122, 63, -32, -19, 60, 34, -56, -103],\n [285, 70, 285, 92, -197, 372, -238, -400, -401],\n [122, 218, 122, -53, -41, 120, 51, -114, -197],\n [9, -344, 9, 173, -86, 84, -289, -118, 34],\n [13, 372, 13, -177, 76, -60, 289, 94, -68],\n [-133, -232, -133, 55, 46, -132, -51, 126, 214],\n [-43, 238, -43, -136, 87, -108, 238, 136, 27],\n [192, 98, 192, 37, -121, 240, -119, -254, -277]]?\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[[165, -69, -181, -157, -379, -453, 113, -365, -366],\n [219, -67, -125, -719, 392, -28, -74, 752, -453],\n [-9, -503, 707, -109, -610, -158, 230, -374, 300],\n [-99, -241, 386, 842, -83, -10, 445, -549, 187],\n [-301, 101, 381, 788, -14, -29, -280, -367, 290],\n [-338, 135, 380, 686, -49, 169, -390, -590, 774],\n [-35, 384, 101, 79, -198, 226, -201, -259, 371],\n [-33, 366, -79, 122, -213, -241, -258, -233, -117],\n [-332, 18, 480, 476, -94, 11, -244, -176, 468]]\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[[90, -165, 180, 30, -120, -240, 210, 210, -75],\n [-36, 66, -72, -12, 48, 96, -84, -84, 30],\n [-66, 121, -132, -22, 88, 176, -154, -154, 55],\n [-84, 154, -168, -28, 112, 224, -196, -196, 70],\n [-42, 77, -84, -14, 56, 112, -98, -98, 35],\n [-36, 66, -72, -12, 48, 96, -84, -84, 30],\n [18, -33, 36, 6, -24, -48, 42, 42, -15],\n [-30, 55, -60, -10, 40, 80, -70, -70, 25],\n [84, -154, 168, 28, -112, -224, 196, 196, -70]]\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 9x9 matrix:\n[[-397, 322, -123, -170, -183, 45, -110, 61, 61],\n [102, 238, -248, -176, -268, -72, -76, 108, 78],\n [-113, -54, -141, -19, -216, -243, -152, 257, 335],\n [199, 85, -52, -53, -17, 54, 48, -64, -115],\n [175, -216, 57, 107, 72, -81, 28, 23, 47],\n [-231, 153, 198, -3, 243, 324, 120, -282, -345],\n [542, -381, 21, 163, 66, -189, 62, 61, 82],\n [-37, 248, -297, -194, -357, -153, -150, 211, 217],\n [350, -53, 57, 37, 132, 99, 130, -155, -218]]\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[[16, -379, -353, 219, -93, 498, -599, -277, -91],\n [204, -420, -428, 117, -196, 426, -448, -168, -153],\n [420, 192, -232, 342, -284, 408, -14, 48, -126],\n [-459, -255, 69, -221, 153, -436, 46, 73, -1],\n [-410, 245, 251, -240, 407, -96, -129, -157, 200],\n [-475, -191, 329, -250, 177, -706, 332, 165, 76],\n [-582, -28, -1, -103, 171, -366, 24, 126, -42],\n [231, -43, 455, 188, -87, -164, 319, -15, 164],\n [15, -461, -233, -121, 51, 320, -542, -317, -1]]\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[[180, -440, -223, -434, -551, -256, -162, 172, -326],\n [-141, 268, 190, 387, 103, 37, 34, 15, 218],\n [66, -303, -456, -400, -296, 140, 62, 161, -312],\n [130, -203, -63, -153, -95, 178, 26, -36, 195],\n [216, -361, 33, -177, -417, -28, -114, 42, 237],\n [48, -53, 25, 22, -21, 146, 32, -29, 224],\n [10, 19, 30, -53, 102, -82, -24, -56, -93],\n [60, -90, -149, -212, 135, 160, 74, -80, -52],\n [9, -81, -87, 9, -186, 117, 30, 90, 96]]\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 9x9 matrix:\n[[257, 414, -140, -299, -15, -592, 441, -445, -437],\n [124, 34, -69, 260, 42, 85, 149, 42, 88],\n [123, 2, -241, -298, 129, -126, 86, 89, 58],\n [-46, 521, 514, 709, -143, 641, -843, 534, -55],\n [-174, -548, -187, 727, -249, 652, -79, 248, 520],\n [-24, -416, 46, 340, 306, 406, 66, 270, 488],\n [152, -102, -31, -6, 963, 359, 141, 458, 369],\n [-176, -335, -29, 402, -468, 267, -149, -7, 216],\n [344, 51, -35, 139, 384, 66, 187, 234, 300]]\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 9x9 matrix:\n[[-290, 190, 418, 504, -62, 236, 128, -60, -416],\n [117, -84, -359, 28, -67, -93, -125, -264, 1],\n [83, 2, -251, -6, 35, -116, -69, -258, 0],\n [32, 112, -262, 6, -16, 125, -189, 92, 98],\n [139, 83, -331, -292, 101, -2, -188, 178, 316],\n [-62, 256, -226, 180, -26, 272, -231, 126, 3],\n [-209, 371, 29, 440, 29, 268, -89, -104, -275],\n [268, -272, -354, -402, -8, -259, -74, -42, 305],\n [-204, 404, 242, 170, 184, 211, 16, 134, -103]]\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[[162, -36, 524, -558, -620, -85, -583, -10, 163],\n [145, -103, 153, 164, -9, 298, -24, 318, 251],\n [147, -266, 345, -236, -89, -14, 44, 315, -130],\n [-216, -150, -90, -374, 442, -487, 837, 290, -795],\n [139, 284, -11, 151, 58, 3, -139, 381, -113],\n [-41, 40, -259, -332, 427, -12, 544, -203, 116],\n [324, -412, 178, -176, 67, -201, -296, -279, 222],\n [-204, -21, -206, -179, 370, -610, 343, 74, -232],\n [-2, 69, -59, 293, 111, -213, -39, 295, -384]]?\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[[108, -16, 822, 7, -392, 19, 222, 40, 195],\n [-241, -1, 427, 457, -44, -321, 416, -459, 448],\n [562, 58, 138, -223, -316, 328, 43, 77, -59],\n [-377, -454, -592, -80, 822, -228, -379, -523, 259],\n [-493, 95, 69, 61, 96, -225, 196, -451, 504],\n [-146, 356, -47, 196, -471, -52, 413, 104, -241],\n [11, 4, 416, 185, -279, 205, 490, 193, 7],\n [225, 365, 326, -100, 4, -74, -175, -272, 688],\n [18, -294, -404, -192, 519, -207, -341, -544, 320]]\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[[158, -14, 279, 411, -150, 305, -170, -115, 88],\n [251, -68, 315, 211, -168, 129, 54, -135, 639],\n [-169, -98, 264, 410, 23, 15, -209, -246, 385],\n [601, 243, -71, -407, 259, -104, 61, -205, 295],\n [-10, -230, -385, -374, 304, -69, 178, 151, -225],\n [58, -230, -123, 72, -77, 454, 171, -105, 137],\n [-126, 28, 280, 167, 21, 541, 0, -370, -23],\n [476, -146, 149, -471, 27, 138, 465, 221, 204],\n [-402, 379, 10, -129, -140, -40, 35, -236, -71]]\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 9x9 matrix:\n[[-10, -4, 30, 6, 26, -14, -6, 6, -34],\n [-30, -12, 90, 18, 78, -42, -18, 18, -102],\n [10, 4, -30, -6, -26, 14, 6, -6, 34],\n [65, 26, -195, -39, -169, 91, 39, -39, 221],\n [25, 10, -75, -15, -65, 35, 15, -15, 85],\n [-90, -36, 270, 54, 234, -126, -54, 54, -306],\n [5, 2, -15, -3, -13, 7, 3, -3, 17],\n [-55, -22, 165, 33, 143, -77, -33, 33, -187],\n [50, 20, -150, -30, -130, 70, 30, -30, 170]]\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[[-50, 165, 359, 338, 17, 184, -176, -270, -392],\n [96, -229, -22, 71, 301, -125, -224, -184, -20],\n [48, -127, -106, -67, 103, -95, -32, 8, 100],\n [12, -23, 40, 55, 59, -1, -64, -68, -52],\n [-102, 238, -17, -119, -340, 119, 272, 238, 68],\n [50, -100, 135, 195, 230, -15, -240, -250, -180],\n [-34, 136, 425, 425, 102, 187, -272, -374, -476],\n [12, 12, 306, 342, 192, 90, -288, -348, -360],\n [38, -72, 133, 181, 190, -1, -208, -222, -172]]\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[[238, -204, -40, -521, 273, 248, -144, 306, 272],\n [-4, -364, 250, -438, 242, 438, -174, 42, 196],\n [-191, 119, 138, 227, -158, -26, -264, -77, -49],\n [-350, 12, 502, 130, -232, 208, -498, -266, -20],\n [66, 9, -95, 24, 2, -90, 243, -50, -63],\n [3, -296, 5, -229, 288, 270, -27, 139, 128],\n [131, 119, -199, 117, -80, -261, 447, -110, -149],\n [-242, 10, -64, 348, 46, -12, -204, 90, -46],\n [-135, -481, 417, -488, 301, 639, -441, 64, 271]]\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[[-295, -66, 12, -41, -195, 488, 207, 101, -253],\n [150, -79, -173, 114, 6, -89, 50, -63, 117],\n [-295, 50, 184, -137, -99, 324, 47, 113, -241],\n [100, -43, -101, 68, 12, -73, 20, -41, 79],\n [-20, -3, 3, -4, -12, 31, 12, 7, -17],\n [-90, 175, 293, -174, 102, -127, -206, 51, -57],\n [-105, -81, -81, 33, -117, 255, 153, 30, -96],\n [-250, 122, 274, -182, -18, 162, -70, 104, -196],\n [75, -112, -194, 117, -57, 58, 125, -39, 51]]\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[[-283, 99, 522, 202, -574, 23, 178, -233, 38],\n [-208, -318, 66, -190, 46, 374, 201, 139, 172],\n [166, -104, -18, -49, -18, 182, 283, 192, 174],\n [114, 136, 270, 166, -315, -113, 205, -76, -91],\n [139, -53, -324, -118, 336, -1, -131, 132, 18],\n [28, 314, 234, 269, -364, -282, -45, -230, -100],\n [-258, -70, 120, -27, -64, 80, -56, -89, 6],\n [-458, -306, -276, -285, 363, 343, -302, 62, 267],\n [-339, -81, 90, -67, 74, -27, -236, -172, -204]]\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[[-245, 5, 62, 40, 186, 222, 196, -150, -199],\n [34, 50, 68, -152, 66, -126, 28, 18, 80],\n [193, 35, 10, -144, -76, -248, -112, 116, 197],\n [16, -40, -64, 112, -84, 60, -56, 12, -28],\n [151, -85, -162, 212, -263, 17, -210, 97, 38],\n [159, 75, 78, -252, 21, -291, -42, 93, 210],\n [80, -110, -184, 300, -257, 131, -182, 55, -47],\n [73, 65, 82, -204, 65, -191, 14, 41, 128],\n [-108, 90, 160, -236, 241, -67, 182, -71, 3]]\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[[12, 0, -40, 40, -36, 12, 20, -44, -52],\n [-18, 0, 60, -60, 54, -18, -30, 66, 78],\n [12, 0, -40, 40, -36, 12, 20, -44, -52],\n [36, 0, -120, 120, -108, 36, 60, -132, -156],\n [33, 0, -110, 110, -99, 33, 55, -121, -143],\n [-51, 0, 170, -170, 153, -51, -85, 187, 221],\n [-24, 0, 80, -80, 72, -24, -40, 88, 104],\n [18, 0, -60, 60, -54, 18, 30, -66, -78],\n [30, 0, -100, 100, -90, 30, 50, -110, -130]]?\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 9x9 matrix:\n[[2, 280, -24, -89, 368, 114, 191, 117, 122],\n [-158, -115, 99, -78, -205, -172, -193, 55, 1],\n [423, 174, 447, -165, 151, 348, -203, 37, 315],\n [-360, -311, -532, 92, 93, -219, 519, -365, 78],\n [469, 166, -141, -216, 445, 794, -39, -353, -196],\n [-473, 275, -163, -164, -265, -305, -362, 4, -215],\n [134, 124, -144, 154, -25, 113, 64, -263, -483],\n [-240, -494, -324, -465, 452, -200, 394, -680, 55],\n [-402, 233, -98, 281, -486, -259, -80, 40, -171]]\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[[-9, 631, 100, -158, 242, -262, 364, -52, 154],\n [717, 797, 748, -79, 48, -63, -340, -426, 163],\n [-491, 396, 203, -438, 264, -113, 285, -528, 326],\n [63, 71, 158, -12, 94, -111, -4, -342, -189],\n [-432, -465, -85, -21, -880, 49, 153, 107, 78],\n [-418, 188, -494, -40, 368, 235, 569, 245, -146],\n [680, 460, 410, 121, 392, -180, -221, -253, -104],\n [147, -667, -496, 799, 236, 314, 497, 116, -1177],\n [-343, 167, -267, -112, 152, 381, 274, 293, 234]]\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[[-120, 40, 96, 0, -64, 80, -112, -8, -128],\n [60, -20, -48, 0, 32, -40, 56, 4, 64],\n [75, -25, -60, 0, 40, -50, 70, 5, 80],\n [-30, 10, 24, 0, -16, 20, -28, -2, -32],\n [-225, 75, 180, 0, -120, 150, -210, -15, -240],\n [-105, 35, 84, 0, -56, 70, -98, -7, -112],\n [-90, 30, 72, 0, -48, 60, -84, -6, -96],\n [-180, 60, 144, 0, -96, 120, -168, -12, -192],\n [195, -65, -156, 0, 104, -130, 182, 13, 208]]\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[[25, -140, 143, 191, 138, 15, 36, 273, 109],\n [-202, 170, -100, 182, 111, -151, 40, -253, 413],\n [-229, 112, 33, -123, 14, -91, 44, -161, -197],\n [172, 345, -337, 21, -181, 146, 80, 108, -287],\n [-396, 190, 156, 585, 374, -116, 302, 311, 277],\n [-7, -171, 158, -434, -233, 75, -88, -283, -322],\n [406, -73, -469, -53, 171, -286, -412, -74, 481],\n [188, -97, -33, 182, 135, 0, -42, 337, 112],\n [296, 540, -646, 39, -424, 220, 38, -353, 163]]\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[[149, 202, -154, -63, 308, 133, 507, 104, 54],\n [334, 6, -54, 247, 219, 180, 28, 267, 9],\n [-25, -11, 95, 230, -143, -53, 87, 22, -73],\n [96, 332, -10, -5, -359, -420, 292, 222, -197],\n [126, -484, 222, 47, 445, 394, 302, -499, -62],\n [-232, 87, -347, -16, -91, -106, -193, -187, -76],\n [543, -44, 158, -466, -3, -41, 343, 279, 268],\n [369, 90, 233, 603, -245, -281, 231, 461, -234],\n [177, 22, -104, -745, 263, 195, 188, -77, 284]]\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[[225, 290, 342, 454, 164, -335, 68, -409, 151],\n [16, 126, -56, -39, -213, 101, 325, 196, -113],\n [-9, -42, 170, 324, 494, -259, -146, -143, 363],\n [93, -362, -251, -254, -258, 404, -295, -217, -301],\n [40, -2, -78, -32, -146, 140, 158, 68, -102],\n [-214, -12, -27, 73, 339, -102, 200, 434, 311],\n [143, 21, 113, 168, 45, -71, -109, -313, 8],\n [25, 115, -132, -182, -413, 218, 338, 221, -270],\n [-106, -248, -247, -426, -252, 277, -251, 94, -248]]\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[[53, 24, 223, 233, 52, 110, -74, -207, -89],\n [-15, -219, 48, -276, -238, 65, -61, 133, 156],\n [147, 39, 435, 219, -109, 161, -100, -290, -300],\n [-26, 142, -42, 38, 62, -82, 16, -28, -52],\n [-14, 2, 502, -42, -280, 129, -282, -242, 17],\n [65, -188, -441, 49, 234, -5, 272, 255, 26],\n [202, 184, 237, 149, -93, 9, 77, -173, -541],\n [113, -197, -42, 430, 320, 210, 91, -101, -1],\n [258, -46, 241, 229, -53, 160, 95, -153, -460]]?\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 9x9 matrix:\n[[61, 226, -72, 300, 147, -277, -217, 65, 138],\n [-114, 348, -255, 306, 198, -117, 51, 93, 66],\n [27, -50, 44, -36, -27, 1, -27, -13, -2],\n [205, 18, 133, 174, 39, -320, -388, 12, 152],\n [-38, -236, 93, -294, -150, 251, 179, -67, -126],\n [134, -196, 192, -120, -102, -38, -158, -50, 12],\n [-86, -108, -5, -186, -78, 217, 209, -33, -106],\n [-3, -190, 94, -216, -117, 161, 93, -53, -82],\n [49, -358, 215, -366, -213, 222, 74, -98, -116]]\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[[44, 12, -67, -226, 75, -117, 596, 419, 46],\n [-234, -142, 121, -514, -356, -99, 213, 311, 90],\n [10, -19, -321, 140, 28, -20, -217, 30, -227],\n [-46, -122, 233, 10, -111, -25, -626, -221, -146],\n [-108, 24, -279, -146, -121, 11, 380, 227, 74],\n [226, -33, 50, -34, 304, -211, 198, 341, -211],\n [-196, 39, 140, -118, -270, 165, 98, -211, 331],\n [-44, -33, 230, 14, -86, 47, -300, -229, 47],\n [302, 89, 197, 148, 425, -84, 302, 92, -3]]\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[[74, -57, -13, -526, 55, -314, -123, 31, -374],\n [-225, 675, -28, -124, 270, 331, 312, 832, 272],\n [-52, 58, 250, 144, 116, 66, 68, 42, 556],\n [173, -163, -101, -466, -33, -313, -86, -30, -244],\n [-133, -233, 44, 328, -223, -152, -373, -588, 194],\n [-19, -199, -524, 145, -494, -197, -369, -438, 35],\n [-209, 529, 45, -149, 241, 199, 187, 618, 215],\n [-388, 591, -131, -118, 45, 48, -113, 449, 450],\n [-203, 266, -432, 145, -236, 109, -122, 111, 33]]\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[[-96, -108, -66, 12, -84, 18, 24, 36, 96],\n [230, 201, 109, -31, 199, -9, -41, -30, -182],\n [476, 266, 98, -70, 406, 70, -42, 84, -252],\n [0, 0, 0, 0, 0, 0, 0, 0, 0],\n [116, 92, 47, -16, 100, 1, -18, -6, -84],\n [126, 315, 234, -9, 117, -126, -81, -216, -270],\n [-102, -57, -21, 15, -87, -15, 9, -18, 54],\n [-160, 128, 152, 32, -128, -152, -48, -240, -96],\n [270, 169, 71, -39, 231, 29, -29, 30, -158]]\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[[160, -220, 263, -120, 174, -241, -130, -12, 82],\n [-321, 508, -46, 24, 120, 233, 536, 348, -47],\n [159, -17, -166, 69, -240, 293, -34, -147, 73],\n [144, -418, 97, -42, 18, -383, -458, -222, -34],\n [-11, -8, -240, 108, -228, 141, -108, -144, -57],\n [79, -144, -28, 12, -68, -53, -172, -120, -3],\n [269, -129, -10, -3, -144, 191, -82, -147, 139],\n [102, -288, 2, 0, -52, -216, -340, -192, -34],\n [-44, 49, 263, -117, 278, -177, 152, 195, 38]]\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[[-332, -215, -132, 293, 359, -117, -98, -126, -123],\n [-155, 4, 113, -224, 89, 244, -117, -93, -2],\n [-42, 299, -351, -488, -362, -283, -191, 407, 175],\n [-64, 177, -141, -182, -70, -77, -295, -3, -17],\n [-291, -386, 25, 214, 439, 62, 131, 15, 148],\n [-197, 161, -169, 89, 38, -137, -370, -271, -382],\n [261, 29, -22, 412, -159, -229, 215, -80, -250],\n [-54, -110, 62, -394, 52, 186, 85, 324, 493],\n [-206, 10, -277, -228, -117, -237, 72, 373, 123]]?\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[[-38, 98, -53, -290, 76, -220, -161, 18, -42],\n [66, -54, 339, 402, 144, 324, 207, -162, -174],\n [-28, 84, -14, -224, 84, -168, -126, 0, -56],\n [-30, 26, -151, -184, -62, -148, -95, 72, 76],\n [-60, 36, -336, -354, -162, -288, -180, 162, 186],\n [-14, 122, 163, -182, 232, -124, -113, -90, -198],\n [-14, 34, -24, -105, 23, -80, -58, 9, -11],\n [30, -98, -2, 247, -109, 184, 140, 9, 77],\n [42, -54, 174, 273, 45, 216, 144, -81, -69]]?\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[[52, -194, -100, -36, 175, -73, -378, 363, -113],\n [-221, 426, -65, 23, 86, 54, 641, -233, 228],\n [-38, 240, 13, -437, 5, 8, 184, -135, 18],\n [27, -60, 112, 659, -155, 82, 223, -127, 92],\n [32, 222, -255, -222, 380, -15, -25, 416, -82],\n [-123, 120, 113, 73, 125, -27, 299, 150, 133],\n [-18, -650, 439, 128, -457, -108, -442, -240, 10],\n [-283, 276, -24, -63, 2, 5, 500, -333, 242],\n [85, -418, 430, 241, -386, -25, -195, -150, -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 9x9 matrix:\n[[-51, -11, -123, 232, -223, -319, 6, 44, 198],\n [-81, 167, -423, 384, -93, -264, -194, 98, 319],\n [223, -127, 225, -336, -287, -354, 369, -185, 259],\n [-268, 30, 46, 276, 146, 169, -119, 261, -177],\n [-168, -173, -556, 574, -128, -291, -429, -215, 4],\n [-86, -118, -76, 364, -330, -251, -80, 42, -85],\n [221, 171, 248, -167, -300, 3, 236, 202, -19],\n [224, -184, 47, -311, -145, -220, 168, -356, 127],\n [-9, 379, -81, 134, 63, 228, -89, 385, 17]]\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[[-209, 617, -580, 130, -191, 38, -494, -721, -166],\n [160, 368, 5, -405, 400, -569, -85, 488, -124],\n [152, -4, 652, -227, -143, -580, 631, 110, -84],\n [182, -146, 193, 437, -130, -466, -263, -177, 488],\n [304, 372, 12, -81, 411, -450, -325, 422, 222],\n [-856, -34, -179, 561, 278, -262, 752, -317, -75],\n [-121, 58, -258, 527, -27, 565, -86, -199, 105],\n [-239, 84, 248, 445, 250, -825, 466, -20, 237],\n [83, -265, 197, -50, 84, 328, 516, 502, -278]]?\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 9x9 matrix:\n[[-185, -85, -170, -170, -145, -180, -205, 90, -135],\n [56, -29, 62, 62, 112, 78, 118, 81, 51],\n [13, 68, 0, 0, -67, -14, -49, -129, -2],\n [282, 42, 276, 276, 330, 312, 402, 36, 222],\n [-318, -168, -288, -288, -222, -300, -330, 198, -228],\n [-194, -49, -186, -186, -202, -206, -256, 15, -149],\n [226, 71, 214, 214, 218, 234, 284, -45, 171],\n [-101, 74, -116, -116, -229, -150, -235, -189, -96],\n [253, 98, 236, 236, 221, 254, 299, -87, 188]]\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[[36, -12, -16, 32, 12, 12, 20, 52, 8],\n [-90, 30, 40, -80, -30, -30, -50, -130, -20],\n [-81, 27, 36, -72, -27, -27, -45, -117, -18],\n [-117, 39, 52, -104, -39, -39, -65, -169, -26],\n [-153, 51, 68, -136, -51, -51, -85, -221, -34],\n [-99, 33, 44, -88, -33, -33, -55, -143, -22],\n [63, -21, -28, 56, 21, 21, 35, 91, 14],\n [144, -48, -64, 128, 48, 48, 80, 208, 32],\n [36, -12, -16, 32, 12, 12, 20, 52, 8]]?\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 9x9 matrix:\n[[-40, 345, -328, -80, 223, -87, -86, -185, 47],\n [430, -106, 152, 261, -129, 8, 378, -445, -334],\n [161, -703, -49, -331, -318, 273, 20, 324, -381],\n [-348, -163, 491, -405, 42, 252, -43, 552, 267],\n [4, 434, 125, -1, 114, 112, -275, 111, 293],\n [240, 362, -223, 387, 49, -363, 63, -635, -193],\n [-47, -400, 431, -197, -122, 195, 216, 241, -70],\n [-159, 44, -299, -81, -13, -248, -300, 27, -64],\n [-540, -314, 191, -155, 85, -81, 191, 325, 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[[213, 180, 68, 90, -224, 355, -112, -101, 62],\n [-136, -473, 86, -163, 66, -216, 442, 74, 116],\n [149, -312, 126, 111, -54, 650, 150, 150, 143],\n [-226, -208, 445, -276, -338, -47, 180, -144, -291],\n [215, -11, -429, 103, 280, -368, 217, 42, 507],\n [-288, -437, 317, -105, -144, 117, 337, 69, -77],\n [215, -42, -236, 137, 250, 180, -39, 151, 195],\n [72, 12, -53, 27, -116, -138, 207, -100, 278],\n [61, 96, 136, -231, 2, -54, -266, -76, -409]]\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[[-393, 60, -192, 174, 381, 54, -324, -72, 333],\n [-199, 166, -110, 98, 101, 90, -216, 6, 87],\n [97, -276, 72, -62, 83, -134, 180, -64, 75],\n [-81, 261, -63, 54, -90, 126, -162, 63, -81],\n [-26, -99, -3, 4, 95, -44, 18, -37, 84],\n [127, -263, 85, -74, 42, -130, 198, -53, 39],\n [252, -154, 134, -120, -166, -88, 252, 10, -144],\n [-20, -228, 12, -8, 176, -104, 72, -76, 156],\n [-96, -239, -23, 24, 265, -104, 18, -97, 234]]\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[[81, 72, -117, -126, -9, -153, -99, 81, 36],\n [162, 144, -234, -252, -18, -306, -198, 162, 72],\n [27, 24, -39, -42, -3, -51, -33, 27, 12],\n [72, 64, -104, -112, -8, -136, -88, 72, 32],\n [135, 120, -195, -210, -15, -255, -165, 135, 60],\n [-144, -128, 208, 224, 16, 272, 176, -144, -64],\n [54, 48, -78, -84, -6, -102, -66, 54, 24],\n [-18, -16, 26, 28, 2, 34, 22, -18, -8],\n [36, 32, -52, -56, -4, -68, -44, 36, 16]]\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[[60, 150, -20, -130, -70, -40, -20, -180, -50],\n [-108, -270, 36, 234, 126, 72, 36, 324, 90],\n [12, 30, -4, -26, -14, -8, -4, -36, -10],\n [-24, -60, 8, 52, 28, 16, 8, 72, 20],\n [-96, -240, 32, 208, 112, 64, 32, 288, 80],\n [84, 210, -28, -182, -98, -56, -28, -252, -70],\n [0, 0, 0, 0, 0, 0, 0, 0, 0],\n [-90, -225, 30, 195, 105, 60, 30, 270, 75],\n [-42, -105, 14, 91, 49, 28, 14, 126, 35]]\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 9x9 matrix:\n[[35, 675, 145, -45, -54, -252, 258, 604, -396],\n [-238, -80, 253, -196, -67, -281, -265, 528, -270],\n [-152, 130, 166, 435, 31, 314, 191, -39, -257],\n [-525, -599, 366, -136, 209, 308, 48, -386, 492],\n [91, 379, -157, 88, -211, 41, 192, 85, 148],\n [276, 450, -609, -643, 143, -343, 645, 208, 391],\n [-690, -297, 594, 254, -279, 325, -269, -90, 121],\n [-662, -230, 87, -330, -27, -31, 586, 451, 117],\n [-279, 103, 242, 201, -213, 152, 141, 141, -11]]\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[[173, 309, 183, -237, -226, -182, -159, -137, 129],\n [425, 8, 672, 184, 102, -362, 129, 321, 240],\n [44, -492, 67, -286, 726, -79, 331, 88, -298],\n [-106, 387, 385, -149, -333, -748, 20, -250, 144],\n [-37, -503, -2, 123, 456, -74, 3, -330, 95],\n [358, -399, -457, 229, -10, 568, 386, -85, 52],\n [-474, 176, -418, -202, -143, 409, 29, 410, -498],\n [397, -79, 149, 563, -358, 418, -217, 129, 329],\n [465, 261, -36, 527, -277, 266, -186, 221, 179]]\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 9x9 matrix:\n[[1, 302, -294, -357, -356, -322, 87, 194, 408],\n [-116, 205, -342, -182, -298, -66, -30, 6, 190],\n [9, -154, 162, 79, 88, -178, 203, 54, 16],\n [-155, 83, -270, -90, -245, -128, 82, -9, 156],\n [-151, 162, -342, -257, -408, -458, 283, 150, 424],\n [79, 178, -78, -161, -82, 10, -109, 68, 100],\n [-239, -193, -102, 126, -113, -240, 314, -53, 60],\n [-44, 148, -198, -233, -277, -372, 207, 165, 346],\n [-85, 250, -348, -282, -367, -258, 82, 113, 342]]\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[[-202, -151, 289, 394, 318, -130, -113, -635, -627],\n [116, -152, 402, 195, 120, -119, 80, -207, -390],\n [-371, -206, 782, 141, -723, -134, 801, -556, 324],\n [-186, 411, -234, -126, 148, 328, -68, 497, -66],\n [-125, -692, -50, -343, -85, -98, 103, -684, 550],\n [140, -156, 43, 258, -540, -721, -111, -689, 434],\n [198, -281, -217, -26, 19, -194, -207, -102, 266],\n [531, -29, -143, -28, 135, -227, -308, 274, -39],\n [-540, -39, -265, 6, -294, 81, 103, -341, 504]]?\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[[34, 51, 33, 109, 141, -74, 109, 137, 18],\n [-140, -210, -198, 118, -6, -200, 250, 26, 120],\n [-144, -216, -192, 15, -114, -111, 126, -84, 87],\n [-74, -111, -85, -117, -185, 54, -89, -173, 2],\n [-2, -3, -1, -15, -17, 12, -17, -17, -4],\n [-186, -279, -229, -154, -323, 11, -51, -289, 53],\n [78, 117, 87, 147, 219, -78, 123, 207, 6],\n [-40, -60, -52, -8, -44, -20, 20, -36, 20],\n [-40, -60, -44, -81, -118, 45, -70, -112, -5]]?\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[[-28, 355, -114, -137, 190, 261, -127, -358, -144],\n [-27, -63, 261, -563, 176, -225, -84, -470, -248],\n [-421, -188, 206, -180, 185, 246, -1, -191, 18],\n [127, 171, -118, -56, 416, 382, -435, -278, 153],\n [-488, -28, 259, -189, 121, 207, 161, -304, -68],\n [-225, -548, 59, 299, -49, 148, -18, 498, 358],\n [263, -285, 82, -202, -163, -397, -271, -73, -61],\n [-14, -561, 94, 231, 42, 46, -197, 399, 427],\n [98, -268, 49, 114, -387, -380, 96, 269, -6]]?\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[[-162, 217, 140, 169, 507, -96, 294, 194, 152],\n [89, -60, -41, 100, -1, 81, -252, -373, 276],\n [274, -239, -18, -305, -421, -44, -318, 70, -456],\n [235, 414, 39, 3, -31, 493, 122, -186, -63],\n [-96, -344, 290, 647, -83, -104, -41, -52, 526],\n [-367, -218, 24, 86, -34, -381, 300, 460, -46],\n [-56, 197, -163, -557, 34, -12, 248, 499, -646],\n [263, 22, -78, -102, 63, 25, -416, -510, 113],\n [-56, 384, -54, -142, 313, 192, 280, 120, -95]]\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[[192, -78, -255, 87, -150, -174, -144, 159, -42],\n [100, -138, -115, -39, -14, -36, -56, 27, -48],\n [158, -36, -215, 96, -142, -159, -124, 147, -27],\n [72, 104, -120, 148, -144, -140, -80, 136, 20],\n [156, 34, -225, 155, -186, -196, -136, 185, -8],\n [204, -6, -285, 159, -210, -228, -168, 213, -24],\n [-130, 122, 160, 1, 56, 79, 84, -68, 47],\n [-108, 254, 105, 133, -54, -20, 40, 31, 80],\n [-84, -176, 150, -220, 204, 194, 104, -190, -38]]\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[[-157, -242, -463, 254, 7, 427, 514, 63, -196],\n [423, 74, -149, -59, 70, -51, 30, 293, -132],\n [339, 420, 460, -333, 100, 76, 127, 257, 146],\n [-130, -339, -41, 97, -326, 47, -117, 174, -248],\n [247, 359, 534, -193, -133, -11, 80, 273, 59],\n [-474, -382, -224, -59, 133, 456, 132, -196, 27],\n [-388, -302, -167, -166, 122, 659, 301, -80, -73],\n [-312, 68, 8, 156, -336, 480, 496, -172, -413],\n [459, 187, -268, -48, 276, -12, 175, 189, -27]]?\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[[492, -184, -333, -55, 281, 202, 220, -25, 687],\n [180, 80, 293, -48, -325, 384, 136, 171, -152],\n [-408, 158, -389, 62, 256, -334, -247, 24, -217],\n [-232, 284, -463, -192, -74, -494, 27, -653, -172],\n [-247, -479, -198, 393, 502, -335, 44, -27, 252],\n [-108, 244, 125, 126, 249, 188, -126, 128, -305],\n [443, 510, 54, -397, 193, 499, 10, -270, -160],\n [374, -40, 70, -110, -59, 132, 347, -479, 79],\n [-519, -79, -245, -93, 381, -571, -271, -371, -289]]\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 9x9 matrix:\n[[-385, -94, -111, 31, -10, 139, 316, 627, 174],\n [353, -62, -571, 301, -15, -469, -136, -5, -22],\n [-299, -414, 65, -55, 10, -70, -103, 100, 295],\n [-324, -167, 115, -306, 158, 209, 33, -365, 85],\n [-160, -203, 1, -116, 108, 71, -29, -213, 105],\n [-9, 46, 34, 93, -275, -10, 95, 175, -38],\n [66, 18, -335, -36, 173, -239, 29, -238, -204],\n [592, -131, -46, 461, -476, -236, -326, -235, 9],\n [-110, 260, 314, -187, -207, 323, 267, -253, -335]]\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[[0, 0, 0, 0, 0, 0, 0, 0, 0],\n [-255, -153, 34, -85, 102, -34, 153, -85, -102],\n [240, 144, -32, 80, -96, 32, -144, 80, 96],\n [150, 90, -20, 50, -60, 20, -90, 50, 60],\n [135, 81, -18, 45, -54, 18, -81, 45, 54],\n [150, 90, -20, 50, -60, 20, -90, 50, 60],\n [30, 18, -4, 10, -12, 4, -18, 10, 12],\n [-15, -9, 2, -5, 6, -2, 9, -5, -6],\n [180, 108, -24, 60, -72, 24, -108, 60, 72]]?\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[[164, -54, -272, -259, -404, 250, -70, -478, 173],\n [-184, 174, 232, 179, 124, -50, -130, 218, -13],\n [1, 56, -38, -57, -166, 116, -104, -161, 91],\n [-185, 242, 190, 114, -70, 86, -254, 31, 94],\n [111, -108, -138, -105, -66, 24, 84, -123, 3],\n [-111, 46, 178, 166, 246, -150, 30, 297, -102],\n [-199, 78, 322, 302, 454, -278, 62, 545, -190],\n [-197, 128, 286, 249, 302, -172, -32, 397, -107],\n [144, -120, -192, -156, -144, 72, 72, -216, 36]]\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[[-303, 349, -86, -586, -332, 168, 167, -39, 192],\n [416, 33, -31, 270, -2, -39, -187, 14, -58],\n [178, 322, 192, -296, -199, -155, -248, -100, 346],\n [266, 233, -405, 26, -296, 333, 125, 220, -302],\n [282, 74, -75, 96, -62, -79, -205, 157, 5],\n [-139, 55, 292, -131, -50, 316, 485, -198, -337],\n [6, -386, 449, 421, 424, -97, 107, -360, -142],\n [39, 58, 84, 27, -69, 313, 357, -131, -338],\n [-232, 160, 90, -274, -186, 436, 558, -140, -332]]\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[[-52, 34, 113, 150, -18, -15, -81, 142, -144],\n [-74, -34, -53, -18, 96, 63, 177, -100, 156],\n [-59, -64, -138, -118, 131, 88, 272, -215, 286],\n [213, 78, 101, -4, -247, -161, -439, 215, -362],\n [-177, -66, -87, 0, 207, 135, 369, -183, 306],\n [-44, 32, 104, 136, -20, -16, -80, 132, -136],\n [-36, 30, 95, 122, -22, -17, -79, 122, -128],\n [132, 30, 15, -54, -126, -81, -207, 66, -144],\n [-298, -104, -128, 20, 338, 220, 596, -282, 484]]?\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 9x9 matrix:\n[[-112, -224, 28, 224, 126, 42, -14, 56, 98],\n [-48, -96, 12, 96, 54, 18, -6, 24, 42],\n [-32, -64, 8, 64, 36, 12, -4, 16, 28],\n [88, 176, -22, -176, -99, -33, 11, -44, -77],\n [16, 32, -4, -32, -18, -6, 2, -8, -14],\n [-96, -192, 24, 192, 108, 36, -12, 48, 84],\n [-56, -112, 14, 112, 63, 21, -7, 28, 49],\n [64, 128, -16, -128, -72, -24, 8, -32, -56],\n [-88, -176, 22, 176, 99, 33, -11, 44, 77]]\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, -169, -260, 372, 108, -156, -271, -248, -102],\n [-66, 76, 569, -128, 355, 251, -527, -520, 13],\n [390, 159, -235, 101, -384, 288, 59, 346, 69],\n [-352, -285, 523, -158, 284, -16, -306, -351, 273],\n [54, -219, -292, 153, -41, -230, 167, -37, 357],\n [-168, -163, -384, 152, 242, -560, 285, 668, -414],\n [51, 61, 158, -367, 95, 30, 57, 167, -12],\n [-118, -468, -408, 257, -475, -3, -189, 156, 8],\n [150, -250, 208, -253, -59, 314, -341, -134, 424]]?\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[[28, -119, 77, 0, -28, 98, -98, 21, 56],\n [-32, 136, -88, 0, 32, -112, 112, -24, -64],\n [20, -85, 55, 0, -20, 70, -70, 15, 40],\n [56, -238, 154, 0, -56, 196, -196, 42, 112],\n [-52, 221, -143, 0, 52, -182, 182, -39, -104],\n [64, -272, 176, 0, -64, 224, -224, 48, 128],\n [-12, 51, -33, 0, 12, -42, 42, -9, -24],\n [-24, 102, -66, 0, 24, -84, 84, -18, -48],\n [-32, 136, -88, 0, 32, -112, 112, -24, -64]]\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 9x9 matrix:\n[[156, -112, 293, -338, -593, -402, 449, -467, 52],\n [121, -2, -26, -18, 240, -225, 304, 162, -322],\n [166, 78, -166, -636, 79, -235, 95, -3, -17],\n [-107, 192, -309, -46, 100, 152, -100, 256, 201],\n [-50, -7, -33, -343, -476, -534, 222, -312, -54],\n [70, -113, 302, -242, -82, -611, -130, -105, -576],\n [56, 90, -317, -275, 147, -108, 264, 76, 24],\n [-50, -20, 83, -213, -365, -260, -56, -236, 22],\n [80, -116, 7, -265, 245, -432, -85, -66, -515]]\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[[443, -105, -7, -106, -320, 56, 332, -356, -57],\n [121, -469, -848, -52, -701, -160, 687, -364, -409],\n [74, 87, -168, 334, -107, -323, 339, -171, 117],\n [614, -41, 465, -22, -62, 106, 121, -76, -232],\n [422, 70, 393, -242, -398, -13, 385, 150, -358],\n [253, 382, 114, 88, -33, -109, 165, -54, -467],\n [123, -438, 259, 399, 418, -122, 229, 172, 327],\n [493, -143, -43, 223, -102, 71, 259, -542, -137],\n [281, 326, -45, 502, 53, -242, 247, -214, -597]]?\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[[50, -80, 90, 50, -65, -5, 30, 40, -35],\n [40, -64, 72, 40, -52, -4, 24, 32, -28],\n [-50, 80, -90, -50, 65, 5, -30, -40, 35],\n [10, -16, 18, 10, -13, -1, 6, 8, -7],\n [20, -32, 36, 20, -26, -2, 12, 16, -14],\n [100, -160, 180, 100, -130, -10, 60, 80, -70],\n [10, -16, 18, 10, -13, -1, 6, 8, -7],\n [10, -16, 18, 10, -13, -1, 6, 8, -7],\n [140, -224, 252, 140, -182, -14, 84, 112, -98]]\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 9x9 matrix:\n[[-48, 17, -60, 50, 30, 131, 106, -168, -141],\n [-372, 262, 541, -155, -304, -5, -297, 191, 396],\n [-178, 129, 64, -261, -192, 84, 28, 247, 120],\n [-30, -120, -237, -54, -174, 87, 214, 146, -144],\n [310, -416, -492, 508, 236, -14, 304, -340, -438],\n [-112, 134, 351, -112, -146, -108, -289, 116, 251],\n [107, -162, 218, 42, -262, -331, -358, 206, 157],\n [370, 62, -255, -154, 530, -100, 57, -10, 9],\n [42, -129, -216, 177, 96, 43, 209, -31, -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[[-387, -256, 126, 352, 294, -181, 0, 407, -67],\n [78, 124, -60, -64, -24, 211, 111, -278, 169],\n [-43, -139, 94, 88, 146, 96, 60, 68, 177],\n [-354, 58, -60, 272, 192, 37, 147, -56, 13],\n [155, 257, -158, -200, -250, -30, -48, -238, -165],\n [176, -53, 64, -88, 32, 242, 81, -137, 293],\n [375, 214, -102, -336, -278, 147, -20, -341, 51],\n [-117, 101, -78, 56, -14, -59, 13, -46, -116],\n [-128, -20, -16, 64, -36, -281, -127, 232, -299]]\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[[204, 90, 324, 478, 252, -20, 40, -275, 301],\n [393, -113, 99, 256, 94, 81, 273, -548, 156],\n [37, 140, 311, 38, 156, -15, 442, -101, 254],\n [-451, 478, -116, -228, -39, -183, -365, 0, -186],\n [157, 236, 178, 522, 588, -194, 466, -74, 491],\n [-239, 504, -276, -226, -35, -380, 95, -704, -339],\n [214, -410, 37, -374, -556, 371, 66, -15, -135],\n [-77, 222, 356, -232, 360, -703, 326, -180, -252],\n [631, 93, 124, -365, -5, 141, 164, -5, 493]]?\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[[169, 4, -179, 221, 93, 180, 6, -176, -39],\n [-194, 46, 214, -226, -168, -90, 24, 226, 114],\n [171, -209, -217, 107, 352, -309, -124, -279, -331],\n [-143, 172, 181, -91, -291, 252, 102, 232, 273],\n [32, 12, -32, 48, 4, 60, 8, -28, 8],\n [208, -207, -256, 156, 371, -267, -122, -317, -338],\n [-211, 194, 257, -167, -357, 234, 114, 314, 321],\n [169, 4, -179, 221, 93, 180, 6, -176, -39],\n [-249, 251, 307, -185, -448, 327, 148, 381, 409]]\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[[93, 232, -422, -401, 62, -2, 71, 265, 309],\n [-7, -274, 170, 45, 129, -459, 303, 111, 216],\n [-113, 302, -254, -166, -71, 55, 71, 130, 16],\n [-167, 220, -150, -95, -24, 92, 55, 143, -49],\n [-181, 264, -258, -218, 29, 37, 137, 280, 66],\n [-367, -121, 388, 361, 11, 72, 42, -24, -389],\n [-223, -97, 16, -101, 202, -371, 404, 388, 216],\n [-352, -60, 32, -91, 263, -117, 300, 477, 71],\n [454, -69, -354, -430, 149, -158, -7, 139, 556]]\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 9x9 matrix:\n[[-339, 96, 58, 74, -78, -378, 638, -162, -206],\n [-210, -179, -144, 263, -317, -180, -113, 136, -77],\n [250, -229, 180, -423, 11, 7, -336, 178, -119],\n [544, 173, -92, -43, 213, -145, 22, -6, -261],\n [354, -313, 98, -309, -103, -195, -216, 188, 29],\n [-33, 246, -119, 302, 25, -410, 805, -271, 68],\n [218, 21, 279, -611, 344, 544, -708, 155, -369],\n [187, -60, 1, -37, 21, 10, 21, -19, 310],\n [111, 36, -120, 139, 114, 588, -540, 36, 466]]\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 9x9 matrix:\n[[-60, 255, -30, -75, -15, -120, 180, -210, -150],\n [16, -68, 8, 20, 4, 32, -48, 56, 40],\n [-56, 238, -28, -70, -14, -112, 168, -196, -140],\n [-56, 238, -28, -70, -14, -112, 168, -196, -140],\n [-4, 17, -2, -5, -1, -8, 12, -14, -10],\n [-8, 34, -4, -10, -2, -16, 24, -28, -20],\n [-64, 272, -32, -80, -16, -128, 192, -224, -160],\n [-44, 187, -22, -55, -11, -88, 132, -154, -110],\n [16, -68, 8, 20, 4, 32, -48, 56, 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[[67, 308, -142, -223, -639, -74, 79, -192, -369],\n [604, 560, 74, -504, 122, -343, 178, 541, 462],\n [131, 75, -197, 179, -227, -74, 48, 232, -93],\n [212, -327, -96, 84, 338, 142, -95, 322, -11],\n [-104, -139, -431, -35, -278, 0, 219, -568, 89],\n [-197, 42, -228, 50, 253, 391, -501, -141, 372],\n [57, -287, 567, 223, -171, -300, 382, 67, -573],\n [-161, -82, 343, 31, 227, 519, -727, 126, -368],\n [-28, -551, -73, 91, 330, -180, 488, -90, 69]]\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[[-58, 0, 15, -119, -49, -173, 211, 495, -368],\n [-204, -469, 10, -251, -558, -259, 14, 149, -126],\n [2, -48, 44, 117, -94, -189, 10, -78, 58],\n [-90, -92, 0, -53, -72, 233, -262, -580, 424],\n [-84, -135, 1, -95, -150, 19, -69, -117, 81],\n [224, 375, 14, 303, 407, -63, 154, 198, -131],\n [140, 119, -35, 207, 218, 321, -281, -663, 497],\n [-72, 207, 15, -119, 207, 153, 61, 118, -86],\n [-14, -214, -103, -187, -119, 347, -235, -285, 204]]\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[[-79, -440, -421, 9, 452, -535, 592, -362, -94],\n [199, 228, -725, -126, -89, -202, 125, -750, -864],\n [-14, -339, 454, -101, 459, -415, 64, -121, -16],\n [445, -521, -249, 226, -84, -297, 447, -303, 166],\n [288, -137, -330, 181, -604, 12, -281, -245, -228],\n [250, -625, -138, -50, -85, -68, 67, 700, 513],\n [535, 39, -25, 222, -535, 293, -19, -167, 97],\n [-99, 265, -569, 210, -139, -192, 418, -398, -372],\n [181, 39, -798, 76, -167, 18, 399, -323, -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[[-170, -330, -306, 285, -150, 188, -238, -186, 78],\n [192, -40, -243, 137, -243, -446, -163, 384, 192],\n [148, 144, 72, -105, -6, -100, 134, 84, -84],\n [220, 144, 7, -78, -79, -190, 125, 156, -76],\n [48, -156, -268, 195, -206, -180, -186, 144, 136],\n [-225, -15, 177, -60, 210, 204, -24, -153, 39],\n [-190, -82, 49, 29, 107, 110, -105, -78, 98],\n [-280, -304, -190, 248, -26, 44, -354, -24, 280],\n [119, 241, 233, -218, 118, -60, 212, 63, -113]]?\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 9x9 matrix:\n[[261, 159, -55, 222, 45, -271, -67, -14, 408],\n [55, -129, 137, -37, 100, 45, 241, -18, -279],\n [630, -207, 180, 128, 51, -237, 360, -129, -140],\n [3, -261, -397, 53, -153, 33, -111, 397, 31],\n [236, 48, 513, 52, 335, -219, 320, -296, -27],\n [-1, 202, -384, 235, -53, -131, -241, 236, 464],\n [112, -10, 100, 89, 149, -128, 114, 6, 67],\n [18, 45, 559, -151, 210, 2, 254, -406, -260],\n [393, -114, 109, 200, 186, -292, 215, 41, 136]]\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[[133, -343, -92, 409, -345, -83, -119, -141, 99],\n [-230, 73, 84, -102, -251, 345, 318, 304, -294],\n [-123, 91, -59, 39, -381, -222, 357, 140, -118],\n [-31, 180, 73, -358, 604, -43, -193, -4, 50],\n [-100, -253, 308, -57, -60, -81, 105, 208, -78],\n [-299, 217, 49, -168, -352, 168, 516, 370, -340],\n [166, -16, 19, 210, -337, -33, 129, -131, 105],\n [-143, 8, 223, -192, 23, 141, 168, 226, -150],\n [-417, 58, -1, -422, 454, 25, -35, 384, -306]]?\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[[545, 46, 60, 222, 148, 175, 333, -636, 460],\n [-386, -144, 95, 545, 42, -365, -237, 192, -567],\n [-112, -198, -311, 42, 26, 329, 251, 383, -32],\n [-118, 176, 164, -26, 34, 35, 703, -222, 193],\n [-533, -363, 549, -511, 314, 520, 105, -145, -15],\n [-17, 95, 204, -845, -92, 757, -740, 142, 51],\n [-167, 184, 451, 12, -346, 316, -394, 94, -82],\n [-103, 155, 88, -344, 441, 986, 310, -283, 52],\n [-413, 87, -421, -92, 791, 529, 657, -8, -408]]?\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[[37, -397, 141, 421, 93, -242, -7, 175, -124],\n [-447, 84, 342, 92, -161, 68, 279, -110, -35],\n [326, -341, -106, 197, 264, -294, -3, 257, -99],\n [-85, -362, 312, 374, 89, -410, 499, 240, -197],\n [135, 396, -331, -468, -35, 332, -310, -190, 179],\n [290, -32, -25, -40, -334, -352, 375, 96, -30],\n [173, -596, 51, 512, 471, -322, -92, 338, -185],\n [-327, -387, 287, 607, 77, 92, -421, -7, -80],\n [514, 86, -352, -310, -22, -180, 76, 102, 48]]?\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[[-313, 200, -32, 113, 461, 259, 341, -15, -108],\n [-65, 59, 147, -209, -141, -207, -15, 198, -253],\n [58, -16, 165, -125, -197, -168, -98, 134, -134],\n [283, -111, 463, 181, -167, 61, -179, 52, 29],\n [5, 18, 173, -190, -202, -217, -73, 185, -212],\n [222, -117, 207, -180, -436, -300, -274, 151, -89],\n [120, -35, 286, 27, -125, -32, -92, 91, -69],\n [-182, 43, -445, -428, -188, -376, -14, 75, -129],\n [-94, 104, 313, -121, -33, -104, 54, 230, -310]]?\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 9x9 matrix:\n[[-132, 64, -40, 134, -132, 82, -95, -292, -15],\n [-53, -122, 77, -82, -149, 125, -69, -319, -106],\n [149, -74, -60, -65, 105, -92, 140, 270, 94],\n [-36, 105, -260, 344, -146, -47, 47, -118, 122],\n [-179, 23, 303, -310, 135, 188, -226, -175, -102],\n [-156, 128, 110, -186, 268, 114, -140, 18, 146],\n [8, 70, -31, 107, -16, -63, 12, 79, -25],\n [-18, -26, 17, -121, 102, 55, -11, -1, 96],\n [-123, 95, -99, 374, -361, 16, -85, -393, -171]]\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[[-90, -111, 250, -191, 297, 187, -273, 161, 149],\n [316, -26, -88, 142, -62, -94, 134, 250, 190],\n [-78, 15, 28, -95, 41, 77, -157, 48, 40],\n [166, 121, -268, 139, -281, -133, 125, 58, 22],\n [-20, 115, -211, 139, -266, -151, 224, -245, -212],\n [290, 116, -319, 222, -331, -196, 229, 109, 58],\n [94, -125, 196, -105, 257, 129, -189, 301, 255],\n [130, 58, -133, 40, -119, -34, -19, 157, 112],\n [-236, -68, 262, -312, 314, 276, -462, 154, 144]]\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[[120, 167, -260, -309, -88, 171, -303, 10, -264],\n [-184, 41, 183, 293, -1, -25, 143, 29, 135],\n [250, -237, -101, 232, -483, -144, 30, 326, -203],\n [6, 125, -362, -334, 12, 275, -262, -142, -223],\n [-434, -63, 115, 461, 41, 37, 391, -209, 317],\n [283, 288, 271, -154, -174, -275, -142, 242, -46],\n [-300, 247, 344, 361, -136, -201, 371, -126, 374],\n [326, -418, -120, -39, 38, -1, -171, 299, -262],\n [136, -27, 448, 188, -64, -423, 240, 166, 243]]?\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 9x9 matrix:\n[[-268, 112, -569, -159, -58, -234, 7, 265, -203],\n [-274, 367, 35, -122, 280, -248, -718, -15, 137],\n [339, -352, 132, 237, -106, 283, 431, 1, -173],\n [-7, -180, -400, -33, 193, 74, -73, -81, -156],\n [-148, -226, -421, -105, -305, 213, 687, 251, -210],\n [44, -413, -593, -138, -46, 222, 526, -194, -101],\n [51, 258, 88, -54, 50, -325, -343, -111, 119],\n [388, -158, 653, 297, 147, 171, -109, -306, 210],\n [340, -265, -304, 250, 232, -92, -133, -53, -314]]\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, -314, 203, -106, 421, -371, 14, 231, 252],\n [296, 27, 239, -306, -17, 23, 161, 335, 111],\n [-12, -457, 118, 36, 715, -442, -267, 128, 545],\n [93, -334, -218, 138, 41, -120, 134, -106, 42],\n [319, -189, -545, -147, -392, 9, 215, -474, -139],\n [454, -113, -292, 233, 17, 134, -167, -233, 169],\n [69, 392, 194, 136, -165, 350, -78, 166, -130],\n [263, 176, 78, -381, -71, 48, -66, 33, 106],\n [-366, 125, 145, 312, -1, 93, 11, 119, -195]]\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[[-196, -165, 248, 64, -83, 90, -91, 175, -308],\n [-370, -64, 80, -101, -435, -209, -88, 236, 40],\n [-313, -59, -71, 13, -280, -113, -76, 262, 119],\n [48, 74, -572, -104, 298, 56, -15, -33, 95],\n [235, -156, 197, 287, 582, 408, 87, -66, -448],\n [142, -116, 528, 317, 174, 118, 223, -40, -162],\n [-633, -467, 323, 296, -71, 278, -200, 634, -657],\n [277, 253, -279, -226, -48, -113, -47, -286, 321],\n [-362, 42, -176, -333, -501, -317, -154, 150, 136]]\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[[334, 38, 119, 154, -376, 518, 428, -721, 372],\n [21, -467, -327, 226, 57, 348, -55, 265, 468],\n [251, 264, -128, 332, -588, 545, 468, -875, 350],\n [217, -313, 361, 48, -74, -232, -367, 317, -392],\n [328, 8, 395, -272, -115, -168, -36, 461, 44],\n [123, 107, 235, -380, 219, -359, 307, 183, 167],\n [261, -208, 466, -140, 96, -179, 182, 33, -52],\n [168, -77, 43, 98, -113, 59, 136, 160, 444],\n [281, 23, 394, -211, 35, -277, 231, 42, 253]]\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 9x9 matrix:\n[[37, -226, -403, -213, 49, 111, 449, -664, 108],\n [436, -509, -33, -753, 284, -1001, 723, -12, 179],\n [-143, 92, 122, 406, 142, 322, -546, 356, -6],\n [-392, 399, -200, -74, -176, 358, -212, -383, 302],\n [-144, 243, 175, 757, -4, 173, -214, 210, -182],\n [-531, 307, -6, -115, 70, 134, 438, -69, 166],\n [-231, 278, 63, -373, -439, 587, -63, 66, 82],\n [-283, 267, 343, -115, 54, -264, -518, 809, 43],\n [25, -149, -226, 284, 392, 326, -142, -451, 124]]\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[[289, 7, 229, 217, -51, -124, 314, -390, -219],\n [-222, -317, 195, -184, -765, -119, 108, 201, -220],\n [331, 503, -65, 103, 36, 772, -222, -397, 309],\n [-644, 98, -174, -288, 115, 274, -189, -141, -228],\n [-280, -470, 116, -137, -426, -482, 253, 167, -482],\n [266, 38, -276, 72, 76, 440, -206, 446, 95],\n [-288, -308, -114, -93, 23, -447, 175, 200, -297],\n [6, 218, 669, 291, -29, 312, 192, -452, 246],\n [50, -472, 576, 260, 70, -473, 255, -94, -47]]\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 9x9 matrix:\n[[-529, -558, -329, 453, 96, 99, 211, 17, 158],\n [-265, -254, 34, -44, 220, -7, 36, -88, -385],\n [847, 533, 99, -229, -100, -320, -167, -165, -137],\n [479, 391, 222, -332, 92, -302, -43, -197, -333],\n [675, 283, 62, -216, -350, -354, -90, 266, 10],\n [-817, -757, -146, 79, 203, 395, 160, 201, 87],\n [-186, 134, -187, 442, -207, 103, 167, 45, 731],\n [-471, 80, 20, 49, -191, 560, 97, 291, 994],\n [399, -145, 172, -595, 417, -531, 194, -186, -734]]\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[[-70, 155, 263, 303, 73, 428, -848, -698, 220],\n [-435, -647, 55, 558, 402, -18, -483, 431, -141],\n [135, 122, -534, -234, -131, -503, 1026, 626, -266],\n [-15, 101, -108, 743, 154, -249, -488, 281, 144],\n [-293, -380, 131, -263, 140, 485, -173, -398, -114],\n [-346, -324, -515, 27, 307, -10, 362, 212, -154],\n [-167, 272, -398, 369, 197, 172, -25, -319, 371],\n [246, -63, 219, -144, -269, 190, -340, 91, -106],\n [-39, 58, 163, -324, 12, -246, 402, -183, -215]]?\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[[-100, 3, 242, -68, 538, 200, 288, 94, -232],\n [457, -31, 440, 180, 93, -50, 78, -432, 309],\n [423, -144, 316, 24, 83, 145, 199, -242, 269],\n [87, -347, -142, 6, 97, 92, 222, 262, -209],\n [136, -531, -599, 93, 552, 26, 115, 267, -246],\n [-6, 220, 407, -33, -214, 73, 58, -141, 122],\n [-100, 8, 348, 4, -80, 192, 300, 156, -196],\n [-210, -254, -573, -245, 116, 123, 33, 470, -264],\n [275, 11, 466, -108, 303, 387, 330, -225, 255]]\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 9x9 matrix:\n[[94, -378, 155, 317, -37, -87, 419, 176, 105],\n [92, -376, 227, 131, -25, -83, 371, 202, 235],\n [-306, -116, -46, 158, -177, 320, -66, -112, -462],\n [-138, 226, 60, -290, 84, 152, -220, -66, -54],\n [41, 239, -122, 111, 108, -44, -62, -73, -127],\n [-205, 197, 315, -368, 211, 247, -81, 33, 6],\n [246, -158, -118, -202, -154, -286, -70, 48, 434],\n [-80, 574, -221, 10, 196, 83, -317, -217, -358],\n [149, 649, -230, -244, 259, -166, -378, -158, 54]]\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[[35, -40, 301, 109, -235, 386, 116, -396, -48],\n [30, -391, 125, -260, -101, -462, 299, -149, 50],\n [239, -490, 286, -590, -141, -237, 550, -45, -346],\n [103, -773, 400, 174, 8, -192, -134, -80, -83],\n [-112, -160, -222, -336, -156, -866, 317, 64, 456],\n [257, 408, -318, -3, 211, 78, -62, 34, -262],\n [-207, 493, -64, 32, 97, 94, 1, 43, 98],\n [590, -554, -561, 62, -232, -745, -16, -390, 197],\n [8, 117, 411, 174, 297, 726, -190, 27, -568]]\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[[397, -57, 250, 174, 428, -51, -141, 65, 79],\n [-230, -79, 86, -247, -229, -112, 375, -40, -158],\n [717, -395, -137, -95, -338, 263, 370, 121, 226],\n [-118, -177, 93, 270, -97, 107, 45, 33, 106],\n [-24, -233, 515, -101, 84, -64, 150, 141, -3],\n [-97, -18, -334, 407, -309, -156, 392, -408, -203],\n [-418, 44, -36, 463, -589, 12, 327, -117, 61],\n [-228, -22, 122, 404, -160, -49, 173, -77, 25],\n [481, -538, -187, 152, 320, 181, -66, -95, 6]]\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[[-390, 375, 134, -227, 268, -110, 65, -119, 399],\n [171, 168, 259, 266, -674, 401, 321, 92, 0],\n [414, 335, 674, 617, -161, -146, 247, -108, 157],\n [-622, 407, 219, -238, -496, 303, -405, 498, 198],\n [200, -247, -217, 42, -18, 71, 167, -80, -146],\n [-564, 282, 115, -145, 22, 75, -87, 299, 520],\n [272, -30, 113, 113, 653, -519, 5, -376, -2],\n [-613, 434, -12, -145, -397, 314, 12, 300, 380],\n [-323, -15, -2, -68, -143, 272, 115, 319, 397]]?\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[[-544, -49, 315, -463, 454, -712, 681, 251, -359],\n [-623, -298, 265, -922, 252, -557, 499, 104, 12],\n [-454, -171, 36, -202, 46, 149, 255, -80, -78],\n [-135, -128, 309, -578, -276, -18, -67, 327, 224],\n [-21, 193, -270, 429, -53, 90, -202, -121, -284],\n [212, 447, -43, 669, -61, 235, -228, -183, -321],\n [306, 70, 185, 323, 78, -205, 438, 731, -381],\n [-578, -143, 244, -408, 565, -569, 584, -27, -90],\n [-207, 115, -11, 34, 200, -417, 522, 237, -684]]?\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[[-135, -163, 48, 101, 204, -307, 248, -42, 124],\n [99, 20, 106, -105, -29, -7, -8, 104, -30],\n [-63, -99, 110, 35, 257, -324, 271, -44, 262],\n [-189, -10, -196, 205, 134, -28, 63, -254, 200],\n [45, -66, 110, -67, -31, -75, 34, 136, -122],\n [-85, -8, -16, 85, 228, -176, 175, -162, 324],\n [0, 5, -12, 2, -18, 23, -19, 0, -20],\n [26, -88, 176, -58, 144, -256, 194, 84, 104],\n [-46, -209, 88, 0, -100, -125, 47, 208, -368]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -63, -126, 126, -105, -112, -49, -77, 49],\n [0, 27, 54, -54, 45, 48, 21, 33, -21],\n [0, 72, 144, -144, 120, 128, 56, 88, -56],\n [0, 18, 36, -36, 30, 32, 14, 22, -14],\n [0, -36, -72, 72, -60, -64, -28, -44, 28],\n [0, -9, -18, 18, -15, -16, -7, -11, 7],\n [0, -81, -162, 162, -135, -144, -63, -99, 63],\n [0, 27, 54, -54, 45, 48, 21, 33, -21],\n [0, 9, 18, -18, 15, 16, 7, 11, -7]]\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[[282, -236, 85, 210, -193, -154, 517, 199, 0],\n [476, -465, -430, -144, 268, -607, 840, 94, 255],\n [-39, 81, 106, -342, 65, -136, -6, 169, 360],\n [-182, -155, -476, -80, 392, -71, 76, 232, 143],\n [-261, -61, -209, 508, 36, 256, 84, 263, -260],\n [-307, -28, -229, 302, 93, 190, 142, 319, -96],\n [-342, 304, -127, -6, 307, 82, -407, -85, 36],\n [-156, -108, -328, 402, 247, -51, 342, 370, -1],\n [268, -263, 22, 58, -133, -72, 169, 45, -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[[475, 422, 37, -4, -665, -32, 574, -495, 598],\n [-265, 310, -104, 284, -393, -241, -602, 668, 88],\n [134, 634, -66, 167, -113, -55, 86, 319, 3],\n [139, 242, -140, 122, -118, 118, -19, 32, 31],\n [292, -258, -167, 117, -147, -564, -273, 320, 91],\n [-60, -180, -579, 314, -744, -299, -308, 591, 140],\n [465, 91, 770, -621, 127, -633, 135, -250, 294],\n [-17, 187, 256, -437, 350, 74, 9, 274, -285],\n [101, -374, 344, -102, 273, -327, -107, -97, 214]]\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[[-423, -663, 287, 25, -21, -202, -103, -416, 15],\n [-204, 58, -39, -321, -92, -896, 882, 516, -360],\n [277, -553, 612, -448, 528, -211, 290, -583, -153],\n [-315, 427, -461, 118, -558, -122, 463, -60, 171],\n [-202, 416, -247, 358, 243, -57, 150, 414, 239],\n [777, -316, 423, -176, 767, 327, -646, -294, 336],\n [-247, 432, -464, -78, -252, -419, 524, 135, 240],\n [557, 211, 52, -548, 238, 47, 148, -299, -89],\n [184, 199, -45, -222, 594, 227, -507, 93, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[57, -35, 38, -121, -95, -53, 4, -100, -12],\n [-156, 128, -188, 436, 212, 80, 44, 196, 180],\n [66, 113, -138, -51, -343, -148, -37, -266, 56],\n [-162, 109, -143, 394, 256, 121, 19, 251, 107],\n [63, -264, 203, -65, 239, -40, 213, 3, 191],\n [-18, 22, -5, 7, 13, 31, -32, 41, -49],\n [-99, 258, -108, -36, -138, 177, -327, 174, -444],\n [-24, -116, 5, 227, 241, -41, 220, 35, 333],\n [-12, -235, 167, 96, 390, 33, 221, 145, 217]]?\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[[-360, 168, -54, -129, -27, -318, 186, 174, -192],\n [287, 90, 130, -153, -172, 190, 32, -237, 103],\n [57, -10, -66, 25, 4, 34, -48, -11, -15],\n [127, -27, 254, -56, -57, 135, 48, -141, 175],\n [-152, -53, -418, 188, 156, -149, -158, 230, -232],\n [105, -91, 294, 0, -7, 147, 28, -119, 217],\n [382, 7, -190, 18, -76, 239, -174, -172, -2],\n [260, -284, 172, 222, 126, 304, -188, -112, 276],\n [145, -397, -40, 409, 284, 231, -314, 55, 185]]\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[[109, 322, -350, -437, -456, -123, 170, -14, 68],\n [-302, 369, -730, -346, -120, -514, 358, 255, -56],\n [-350, 121, -690, -474, -433, -169, -103, 115, 602],\n [86, 45, -163, -666, -658, -488, 28, 692, -134],\n [481, 560, -85, -591, -627, -318, 209, 539, -579],\n [-274, 153, -646, 26, 211, 249, -195, -341, 15],\n [23, -62, -20, -93, 83, 57, 155, 289, -742],\n [-77, -327, 243, 483, 507, 165, 213, -613, 123],\n [-173, -9, -316, -406, -337, 260, -483, 284, -369]]\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 9x9 matrix:\n[[247, -328, 90, -359, -104, 457, -254, 25, -128],\n [-312, -25, 188, -435, 242, 39, -209, 174, -291],\n [-216, -274, 605, -33, 255, -174, -316, -507, -111],\n [-195, 314, -234, 351, 98, -249, 360, 17, 116],\n [385, -245, 239, 235, 165, 196, -202, -386, 73],\n [-363, -37, 663, -441, -200, 321, -103, -235, -424],\n [66, -209, -145, 114, -229, -243, 11, -121, 248],\n [68, -305, 309, 351, -89, -343, -116, -609, 252],\n [-94, -125, 455, 66, 70, 74, -82, -446, -101]]\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[[-433, 577, 300, 425, -343, 775, 768, -253, -63],\n [385, -149, -22, 77, 440, 223, 358, -168, 72],\n [-80, 78, -80, 49, 288, -451, -173, 74, -21],\n [63, 111, 103, 23, -223, 332, 445, -489, -263],\n [497, 166, 138, 70, 76, -135, 141, -652, 109],\n [291, -350, -17, -459, 422, -439, -215, 64, -230],\n [318, 49, 139, -252, 75, 168, 195, -151, -92],\n [-303, 209, 270, 61, -439, 353, 112, 21, 52],\n [-264, -98, -22, 45, -251, 496, 97, 349, 49]]\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 9x9 matrix:\n[[334, 218, 373, 43, 52, 66, 282, -636, -123],\n [-17, -509, 140, 101, -187, 14, 189, 169, 126],\n [1, 195, 85, 121, -492, 23, 218, 146, -18],\n [18, 158, 157, 129, 518, 273, -69, -543, -60],\n [-52, 149, 167, 125, -360, 299, 389, -92, -72],\n [274, 175, 110, -121, -422, -355, 97, 65, -240],\n [-2, 159, -223, -472, -257, -105, 109, 180, -462],\n [294, -48, 144, -330, 812, 48, -38, -830, -294],\n [304, -3, 369, 174, 474, 85, 69, -739, 159]]\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[[-5, 207, -11, -14, -18, 73, -151, -302, -428],\n [353, -75, -51, -283, 243, -159, 70, 9, 373],\n [-86, -520, 77, -411, 495, -374, -124, -340, -77],\n [-604, -400, 74, 36, -35, 92, -285, -503, 175],\n [215, 291, -148, 124, -95, -13, 287, 420, -243],\n [-9, 60, -181, 66, 140, -83, 110, -339, -19],\n [-294, -504, 56, -383, 86, -9, -300, -244, 309],\n [155, -97, 369, -26, 1, -4, -35, 496, 301],\n [-62, -434, 460, -97, 98, -125, -307, 73, 78]]\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 9x9 matrix:\n[[98, 429, -100, -534, -342, -235, -124, -754, -516],\n [225, -93, -605, -132, 31, 150, -318, -472, -222],\n [571, 167, 257, -81, 67, 533, -267, 222, -225],\n [39, -258, -155, -550, 402, -854, 357, -108, -608],\n [-33, -121, 119, -105, -208, -413, 191, -346, -126],\n [29, 24, -251, -209, 46, 12, -240, -155, -107],\n [-306, 686, 15, -497, -757, -230, 290, -381, -215],\n [-260, -243, 70, 128, -61, -353, 708, 176, 116],\n [-779, 581, -113, -16, -411, 289, 132, -437, 479]]\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 9x9 matrix:\n[[110, -176, 187, -88, 77, -187, 110, 110, 187],\n [-110, 176, -187, 88, -77, 187, -110, -110, -187],\n [140, -224, 238, -112, 98, -238, 140, 140, 238],\n [-180, 288, -306, 144, -126, 306, -180, -180, -306],\n [140, -224, 238, -112, 98, -238, 140, 140, 238],\n [-60, 96, -102, 48, -42, 102, -60, -60, -102],\n [30, -48, 51, -24, 21, -51, 30, 30, 51],\n [-140, 224, -238, 112, -98, 238, -140, -140, -238],\n [-70, 112, -119, 56, -49, 119, -70, -70, -119]]\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[[-90, -72, -99, 117, -153, 153, 45, 99, 144],\n [0, -8, -188, 76, -180, 204, 204, -12, 72],\n [-80, -70, -229, 161, -271, 289, 193, 79, 182],\n [-135, -97, 110, 71, 18, -51, -213, 165, 117],\n [350, 262, -38, -284, 190, -136, 284, -412, -398],\n [0, -12, -282, 114, -270, 306, 306, -18, 108],\n [-240, -186, -123, 255, -273, 255, -33, 273, 330],\n [-275, -209, -44, 253, -220, 187, -143, 319, 341],\n [-180, -142, -151, 215, -261, 255, 39, 201, 270]]\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[[52, -51, 407, -174, 204, -80, 327, -564, 315],\n [147, 239, -150, 98, 7, -237, -10, 190, 9],\n [-452, -126, -336, 88, 26, 16, -269, 219, -35],\n [-37, -76, 556, 152, 163, 425, 284, -497, -573],\n [285, -201, 180, -285, -151, 81, 55, -79, 183],\n [-400, -54, -194, 187, 204, -108, -147, 111, -290],\n [141, -276, 51, -121, -111, 125, -108, 159, -310],\n [-225, -510, -314, -324, -273, 173, -390, 319, 261],\n [-350, 217, -317, 317, 188, -210, -131, 202, -194]]\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[[178, 103, 57, 41, 116, -1, -93, -38, -118],\n [-390, -237, -115, -3, -252, 75, 255, 66, 274],\n [-54, -27, -21, -45, -36, -27, 9, 18, 30],\n [159, 69, 71, 213, 108, 147, 21, -69, -74],\n [377, 227, 113, 19, 244, -59, -237, -67, -262],\n [-491, -305, -139, 47, -316, 137, 351, 73, 354],\n [112, 91, 13, -175, 68, -169, -177, 16, -110],\n [-496, -304, -144, 16, -320, 112, 336, 80, 352],\n [-17, -47, 27, 281, -4, 239, 177, -53, 62]]?\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[[-16, 44, -40, 0, 12, 0, -72, -12, 0],\n [236, 235, 214, -96, -77, 288, -162, -35, 0],\n [-97, 101, -172, 18, 54, -54, -207, -33, 0],\n [18, -160, 92, 12, -26, -36, 234, 40, 0],\n [226, 373, 142, -108, -57, 324, -360, -69, 0],\n [-214, 36, -300, 60, 98, -180, -198, -28, 0],\n [-262, -53, -326, 84, 109, -252, -108, -11, 0],\n [266, 263, 242, -108, -87, 324, -180, -39, 0],\n [-168, -201, -138, 72, 51, -216, 162, 33, 0]]\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[[-828, -18, 2, 90, -743, 473, 227, 10, -218],\n [-273, 210, 493, 44, -317, 234, -397, -222, -250],\n [141, -225, -377, -130, 274, -504, 221, 246, 651],\n [286, -288, 50, -462, 51, 458, 317, 361, -166],\n [-60, 136, 298, 175, 25, 383, 297, -388, -617],\n [-200, -159, 262, 70, -439, 521, 57, -59, -522],\n [-351, 228, -385, 281, -357, -233, -531, 269, 472],\n [-186, 382, -134, 132, -303, -149, -558, 200, 325],\n [145, -14, 449, -121, -97, 604, 120, 114, -313]]\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, -9, 357, -225, -39, -243, -312, 381, -156],\n [195, -146, 115, 139, 795, 395, -37, 230, 50],\n [47, 101, -296, 262, 357, 367, 31, -453, 244],\n [-14, 130, -54, 340, 29, 154, 118, -250, 281],\n [103, 43, -642, 186, 391, 503, 271, -629, 196],\n [-30, -15, 29, 176, 374, 195, -308, -226, 70],\n [109, 485, 118, 284, 453, 266, -297, -183, 529],\n [49, -357, -272, -311, -83, -22, 339, 150, -390],\n [-184, -410, 60, -70, -499, -297, 170, 120, -392]]\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[[-14, -12, -1, 15, -13, 1, 9, -3, 2],\n [168, 144, 12, -180, 156, -12, -108, 36, -24],\n [-182, -156, -13, 195, -169, 13, 117, -39, 26],\n [-182, -156, -13, 195, -169, 13, 117, -39, 26],\n [0, 0, 0, 0, 0, 0, 0, 0, 0],\n [182, 156, 13, -195, 169, -13, -117, 39, -26],\n [154, 132, 11, -165, 143, -11, -99, 33, -22],\n [98, 84, 7, -105, 91, -7, -63, 21, -14],\n [-224, -192, -16, 240, -208, 16, 144, -48, 32]]\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[[45, -270, -120, 255, -255, 105, -240, -180, 0],\n [-54, 324, 144, -306, 306, -126, 288, 216, 0],\n [36, -216, -96, 204, -204, 84, -192, -144, 0],\n [33, -198, -88, 187, -187, 77, -176, -132, 0],\n [54, -324, -144, 306, -306, 126, -288, -216, 0],\n [33, -198, -88, 187, -187, 77, -176, -132, 0],\n [0, 0, 0, 0, 0, 0, 0, 0, 0],\n [6, -36, -16, 34, -34, 14, -32, -24, 0],\n [30, -180, -80, 170, -170, 70, -160, -120, 0]]\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[[308, -324, 424, -183, -218, 532, -334, 3, 265],\n [275, -398, 215, -44, -482, 236, 353, 83, -303],\n [53, -87, -269, 162, 64, -530, -60, -113, -114],\n [26, -184, -371, 126, -68, -701, -246, -77, -130],\n [352, -12, 44, -18, -61, -157, 378, -115, 19],\n [460, -278, 463, -112, -161, 506, 6, -74, 205],\n [-7, 265, -372, -457, -79, -586, 197, 54, 116],\n [-165, 231, -67, 317, -14, -110, 16, 22, -11],\n [-447, -71, -67, 419, -116, 178, 214, 178, -591]]\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[[56, 47, -86, -39, 59, -90, -52, 401, 67],\n [374, -241, -222, -183, 357, -691, 330, 424, -442],\n [96, -13, 218, 111, -137, 249, -166, -251, 19],\n [511, 108, -483, -366, 42, 372, -281, -223, 325],\n [144, 466, -24, -163, -255, 44, 186, 281, 89],\n [-783, 159, 468, 218, -217, 23, -34, 90, 33],\n [-225, 161, 69, 20, -92, 24, 361, 89, 172],\n [-36, -147, 127, 55, -66, 455, -609, -574, 108],\n [44, -469, -49, 161, 394, -508, 29, 410, -298]]\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 9x9 matrix:\n[[91, -147, -323, -164, -146, 194, 166, -157, -178],\n [-501, 152, 117, -148, -336, 97, 133, 51, 63],\n [-672, 241, 185, -197, -467, 152, 211, 117, 66],\n [-178, 193, 137, -107, 43, 302, 75, -239, -312],\n [104, -31, -83, -9, -59, 18, 81, 97, -16],\n [205, -15, 76, 119, 321, -59, -180, -142, -59],\n [-434, 93, -10, -200, -384, 164, 200, 14, -4],\n [128, -34, -49, -27, 261, 159, -92, -389, -265],\n [-283, 98, 107, -32, -262, -58, 90, 241, 178]]\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 9x9 matrix:\n[[-524, 58, 262, -231, -158, 222, 20, 311, 633],\n [67, -505, -49, -87, -149, -534, -239, -158, 266],\n [-152, 13, 202, -153, -252, -88, -173, 12, 469],\n [-263, -157, -295, -189, 327, 174, 351, 194, 326],\n [-528, -48, 245, -409, 70, 562, 322, 300, 726],\n [-579, -124, 408, -397, -144, 389, 97, 240, 758],\n [-444, 229, 365, -118, -108, 539, 47, 493, 3],\n [-582, 248, 47, -113, 96, 455, 214, 339, 223],\n [-53, 38, -262, 60, 156, -110, 129, -34, 154]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[291, 132, -212, 156, 131, 74, -9, -132, 22],\n [-105, -355, 172, 138, 6, -302, -47, 372, 38],\n [268, -39, -169, -69, 314, 100, 6, -94, -101],\n [-65, -135, 87, 123, -59, -162, -27, 182, 53],\n [-485, -131, 347, -33, -383, -202, -7, 254, 81],\n [-52, -464, 129, -357, 373, -68, 8, 214, -219],\n [47, -231, 0, -402, 374, 114, 33, -20, -230],\n [-251, -90, 205, 243, -324, -262, -39, 266, 159],\n [210, -2, -123, 171, 113, -32, -22, 6, 29]]\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[[-97, 42, 26, -74, -172, 180, 47, 213, 94],\n [50, 112, 16, 155, 468, -90, -39, 106, 130],\n [160, -27, 43, -28, 46, 36, -230, -171, -1],\n [141, -51, 87, -183, -294, 270, -306, -114, 33],\n [-12, 159, 81, 18, 210, 216, -96, 339, 273],\n [-118, -39, -113, 136, 118, -324, 308, -69, -165],\n [20, -59, -45, 41, 26, -162, 51, -167, -123],\n [21, -13, -39, 92, 178, -180, 53, -100, -67],\n [-5, -197, -135, 48, -142, -396, 203, -446, -379]]\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 9x9 matrix:\n[[-104, 96, 174, 107, -65, 196, -180, -278, 20],\n [24, -53, 97, 522, -308, -454, -425, -59, 312],\n [211, 109, -165, -599, -283, -62, 891, 159, 277],\n [232, 200, -298, -219, -67, 128, 300, -275, -213],\n [110, -535, -89, 32, 141, -685, -304, 167, -232],\n [176, -477, -242, -352, 155, -465, 155, 9, -46],\n [-135, 7, 195, 238, -201, 137, -420, -480, -222],\n [101, 83, 246, -94, 80, -98, -113, -295, 39],\n [0, -388, 51, 124, -368, -570, -177, 13, 37]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-188, -175, -159, -3, 155, 199, 372, 7, 203],\n [53, -143, -32, -168, -71, 250, 92, 98, 3],\n [-350, -91, 141, 411, 326, -359, 18, -494, 158],\n [-121, -6, 193, 191, 151, -217, -170, -292, -87],\n [25, -396, 56, -90, -169, 192, 70, -127, 229],\n [-313, -98, 228, 316, 352, -246, -68, -476, -42],\n [-174, 79, -69, 365, 78, -441, 62, -226, 350],\n [-375, 210, -138, 308, 477, -214, 278, -113, 43],\n [-332, 13, 82, 344, 368, -284, 58, -359, 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[[16, 35, 150, -74, 142, -122, 41, 96, 49],\n [200, 37, -14, -358, 230, -146, -113, 300, 235],\n [-102, 185, 460, -202, 411, -281, 143, -17, 332],\n [76, 44, 276, -152, 274, -254, 68, 270, 46],\n [-168, -25, -98, 266, -240, 196, 41, -326, -121],\n [236, -133, -286, -66, -124, 52, -151, 314, -177],\n [166, 10, 70, -234, 202, -172, -44, 316, 84],\n [52, 116, 348, -272, 394, -302, 68, 222, 238],\n [4, 13, -226, -78, -92, 148, -113, -146, 161]]\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[[-82, -32, -55, 665, 18, -243, -18, -25, -368],\n [-145, 47, 324, 264, -280, 151, 252, -250, -76],\n [-772, -199, 28, -72, 367, -177, -564, -120, 232],\n [178, 516, -321, 591, -285, -10, -160, 348, -531],\n [266, 78, -446, -27, -7, 90, -231, 205, 101],\n [194, -218, -502, -369, 169, -107, 306, 268, 138],\n [-358, -492, 13, -581, 211, -34, 274, -202, 207],\n [91, 83, 236, 115, -233, 82, 391, -74, -61],\n [137, -115, -106, -112, 121, -333, 166, 246, -25]]\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[[309, 393, -9, 7, 310, 158, -649, 531, 552],\n [903, -14, -426, 68, 79, 264, -783, 511, 714],\n [3, -40, -124, 219, 97, -447, -225, -458, -115],\n [-450, 287, 755, 12, 491, -209, -22, 383, 75],\n [-121, -298, -189, -72, -134, -152, 457, -246, -264],\n [-735, 477, -59, -241, -34, 280, 356, 147, -473],\n [-82, -357, 49, -81, -718, 8, 16, -512, 32],\n [201, -447, -69, 50, -393, -509, -528, -569, 429],\n [-340, 208, 530, 51, 216, 119, 122, 309, -214]]\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, -63, 119, -91, -91, -28, 70, 42, 0],\n [-28, -63, 119, -91, -91, -28, 70, 42, 0],\n [-44, -99, 187, -143, -143, -44, 110, 66, 0],\n [-32, -72, 136, -104, -104, -32, 80, 48, 0],\n [12, 27, -51, 39, 39, 12, -30, -18, 0],\n [60, 135, -255, 195, 195, 60, -150, -90, 0],\n [0, 0, 0, 0, 0, 0, 0, 0, 0],\n [-60, -135, 255, -195, -195, -60, 150, 90, 0],\n [52, 117, -221, 169, 169, 52, -130, -78, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 9x9 matrix:\n[[289, 192, -12, -1, 11, 189, -65, 11, 148],\n [-183, 184, -62, 255, 83, 131, 209, 319, 2],\n [-34, 12, 215, -104, 39, -337, -121, -342, -366],\n [346, 166, 220, -325, 172, -79, -192, 60, -15],\n [510, 322, 229, -415, 279, 73, -196, 289, 117],\n [158, 392, 246, -80, 201, -118, -84, -116, -313],\n [-321, 276, -207, 217, 125, 349, 321, 300, -25],\n [26, -208, -2, 90, -190, -148, -96, -310, -10],\n [73, -32, 259, -429, 258, -249, -105, 342, -64]]\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[[-153, -87, 212, 378, 52, -354, 203, -118, 186],\n [324, -6, 228, 154, -414, -344, 0, 100, 330],\n [-227, 210, -138, -103, 335, 350, 13, -70, -367],\n [-266, 294, 48, 162, 326, 144, 148, -126, -286],\n [-138, 48, 12, 79, 147, 22, 69, -65, -81],\n [228, 402, 308, 262, -242, -176, 92, 48, 54],\n [115, 519, 32, -76, 6, 302, -33, 58, -316],\n [-178, -393, -186, -120, 148, 6, -37, -51, 64],\n [22, 579, 30, -40, 116, 350, 7, 17, -400]]\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[[196, 72, 63, -142, -153, -494, 218, -272, -355],\n [-229, -390, -132, 251, 185, 235, -160, -2, -217],\n [-54, -140, -81, -630, -240, -409, 352, 281, 112],\n [-413, 247, 377, -150, 143, -289, -80, 78, -325],\n [-377, -274, -497, 146, 139, 180, 168, 8, -397],\n [317, 245, 152, 324, -67, 57, -9, -285, -133],\n [-32, 373, 228, 508, 304, 146, -541, -336, -95],\n [-47, 360, 392, 591, 313, 340, -544, -381, -25],\n [300, 713, 144, -150, 290, -140, 4, 243, 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[[-393, -45, 207, -89, 295, 50, -21, 203, -162],\n [52, 166, 114, -334, -6, -317, -129, -130, 409],\n [413, -64, -302, 125, -193, 66, 178, -330, -30],\n [127, 352, -46, 51, -19, 270, 86, -266, -390],\n [104, -298, -180, 459, -99, 344, 163, 146, -388],\n [41, 131, -137, -51, -11, 12, 61, -205, -48],\n [362, -331, -237, 260, -186, 82, 163, -81, -10],\n [-307, 191, 201, -270, 80, -265, -229, 167, 305],\n [62, -19, -35, -281, 431, 162, 368, -569, -390]]?\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[[-146, 95, -183, -244, 105, 208, 398, -220, 416],\n [28, 206, -389, -55, -25, 218, 12, 92, 237],\n [682, 765, 231, 38, -273, -416, 158, 68, -4],\n [-174, -471, -245, 292, -186, 202, -116, 287, 163],\n [-90, -31, 230, 67, 393, -144, -204, 59, -226],\n [-408, -309, -314, 37, 353, 324, -132, 125, 172],\n [-57, -41, -21, 105, 167, 8, -82, 135, 36],\n [-177, -127, 306, -238, 187, -88, -16, -344, -330],\n [-524, -648, -114, -68, 121, 294, -146, -129, -115]]?\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[[-19, -105, 233, -567, -276, -124, -122, 148, 544],\n [201, -153, -265, 505, 480, -60, -396, -122, -410],\n [35, 219, 153, 1, -21, 18, -65, -320, -56],\n [127, 2, -25, 198, 171, 10, -162, -117, -171],\n [421, -146, 64, 16, 261, -229, -335, 358, 130],\n [-237, -325, -500, 299, 227, -27, -34, 117, -253],\n [-23, 169, 505, -853, -480, -194, -44, 18, 762],\n [85, -501, -352, 461, 265, 260, -74, 273, -341],\n [-85, -54, -76, 54, 15, 50, -47, -122, -74]]\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[[193, -313, 358, 350, 347, -425, -257, -164, -208],\n [-16, -33, -149, 622, 295, 385, -170, 92, -68],\n [-44, 423, -258, 399, -110, 226, 67, -339, 120],\n [-669, 252, -559, -328, -308, 423, 490, 217, -207],\n [-488, 59, 227, -597, 94, 255, 81, 111, -120],\n [963, 132, 565, 323, 373, -777, -379, -614, 339],\n [525, 163, 350, 97, 287, -544, -465, -268, -70],\n [-1134, 224, -105, -1074, -608, 282, 105, 246, -577],\n [-125, -543, -146, -8, -133, 103, -203, 632, -306]]?\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[[-235, -190, -225, -215, -215, 20, 65, 195, 180],\n [95, 71, 146, 93, 184, -67, -52, -182, -70],\n [274, 247, 21, 224, -175, 235, 37, 225, -222],\n [174, 159, -7, 140, -147, 171, 33, 181, -142],\n [-211, -163, -274, -201, -320, 95, 92, 310, 158],\n [130, 106, 116, 118, 104, -2, -32, -92, -100],\n [-241, -202, -163, -213, -101, -52, 35, 73, 188],\n [344, 296, 160, 296, 16, 152, -16, 32, -272],\n [-92, -86, 22, -72, 110, -110, -26, -130, 76]]\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 9x9 matrix:\n[[293, 193, -400, -213, -43, 87, 99, 108, -489],\n [365, 422, -136, -338, 133, 248, -133, -375, -13],\n [-269, -65, 340, 215, -72, -368, -440, 115, 529],\n [-233, -1, 121, -241, 300, 98, 44, 301, 73],\n [-5, 275, 330, 274, -295, 72, -161, -889, 180],\n [62, -234, -133, 217, 274, 507, 726, 657, -685],\n [-88, -280, 189, 811, -486, -127, 155, -139, -216],\n [-83, 300, -259, -445, 275, 479, 552, 264, -737],\n [628, -10, -335, 216, -27, 103, 51, -9, -28]]\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 9x9 matrix:\n[[-63, -109, 367, 283, 116, -354, -312, -613, 265],\n [424, 308, 20, -397, 294, 354, 138, 363, -20],\n [-242, 185, -70, -13, -588, 75, 209, -191, 11],\n [-407, -38, -709, -252, 188, -447, 306, 594, 46],\n [25, 420, 221, -188, -350, 112, 217, -351, 310],\n [139, 599, -15, -223, -90, -5, 439, -236, 347],\n [190, 572, -188, 92, -138, 43, 222, -369, -194],\n [659, 401, 195, 138, -68, 653, 106, -195, -379],\n [-156, 36, -177, 60, -474, 189, 143, 34, -242]]\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[[10, 256, -350, 133, -92, 241, 126, -62, 66],\n [-235, 450, 92, -162, 73, 57, -207, 70, -399],\n [-86, 327, -117, 54, 158, 381, -135, 119, -460],\n [5, -253, 135, -2, 12, -292, 176, -175, 377],\n [-189, 215, -72, 87, 145, 145, -212, 209, -380],\n [59, 345, -38, -125, 4, 407, -176, 113, -504],\n [234, -308, -185, 300, 202, 366, 266, -108, 115],\n [62, -271, -267, 336, 58, 101, 79, 101, 144],\n [178, 43, -180, -34, -257, 153, -101, 149, -81]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[180, 270, 105, -15, 210, 195, -225, 0, -180],\n [84, 126, 49, -7, 98, 91, -105, 0, -84],\n [-156, -234, -91, 13, -182, -169, 195, 0, 156],\n [216, 324, 126, -18, 252, 234, -270, 0, -216],\n [-48, -72, -28, 4, -56, -52, 60, 0, 48],\n [0, 0, 0, 0, 0, 0, 0, 0, 0],\n [48, 72, 28, -4, 56, 52, -60, 0, -48],\n [204, 306, 119, -17, 238, 221, -255, 0, -204],\n [-72, -108, -42, 6, -84, -78, 90, 0, 72]]?\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[[437, -135, 718, -321, -307, 580, 223, -251, 12],\n [-130, 117, -239, 230, 235, -140, 113, 252, -373],\n [-5, -99, 34, 87, 44, -114, -37, -36, -83],\n [30, -286, 146, 71, -246, 160, 85, -76, 265],\n [171, 304, 115, -305, 41, 154, 2, -26, -108],\n [10, 179, 108, -184, 93, 179, 9, -34, -104],\n [-290, 289, -310, -154, 161, -17, -183, 32, 194],\n [-134, 181, -358, 103, 90, -123, 34, 229, -34],\n [-323, 163, -498, 218, 272, -332, -96, 226, -114]]\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 9x9 matrix:\n[[187, 204, 204, -51, -204, -34, 85, 17, 136],\n [-121, -132, -132, 33, 132, 22, -55, -11, -88],\n [0, 0, 0, 0, 0, 0, 0, 0, 0],\n [-165, -180, -180, 45, 180, 30, -75, -15, -120],\n [88, 96, 96, -24, -96, -16, 40, 8, 64],\n [-66, -72, -72, 18, 72, 12, -30, -6, -48],\n [22, 24, 24, -6, -24, -4, 10, 2, 16],\n [77, 84, 84, -21, -84, -14, 35, 7, 56],\n [44, 48, 48, -12, -48, -8, 20, 4, 32]]\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[[31, -166, 310, -461, -36, 113, 596, 564, 506],\n [26, -493, 1021, -616, 78, -669, 111, 37, 25],\n [215, 182, 270, -114, -206, -225, -91, 86, 670],\n [-426, -168, -97, 9, -183, -361, -588, -365, -360],\n [-142, 347, 598, -679, 235, -44, -241, 678, 38],\n [319, 723, -119, -209, 672, -253, -277, -215, -210],\n [-132, -151, 360, -302, -368, -276, -643, 211, -72],\n [382, 613, -624, -176, 191, -660, 114, -198, 460],\n [472, 284, 261, -13, 231, -150, 219, 138, 152]]\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 9x9 matrix:\n[[-342, 21, -189, 265, -412, 434, 228, -198, -397],\n [78, 128, 132, 282, -30, 178, -122, -36, 442],\n [-21, 40, -90, 172, -401, 280, 59, -243, -197],\n [320, -119, 171, -42, 296, -261, -182, 133, 615],\n [57, -278, -66, 435, -341, 341, 95, -210, 431],\n [-35, -206, -96, -216, 105, -194, 105, 77, -197],\n [-381, -79, -153, 490, -357, 543, 247, -156, -12],\n [-403, 10, -75, 26, 167, 70, 172, 166, -206],\n [-298, 351, 69, 140, 90, 191, -16, 91, -97]]\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[[321, -140, -13, -64, -506, -90, 581, 88, -211],\n [-275, -560, 101, -371, 211, -9, -85, 373, 193],\n [94, -174, 242, -230, -174, -66, 337, 255, -151],\n [-542, 128, 438, -114, 54, 74, 184, -80, 632],\n [-66, 131, 566, 398, -40, -42, -15, -172, 145],\n [180, -154, 199, -24, -90, -10, -5, 90, -229],\n [-130, 98, 554, -85, -251, 31, 387, -36, 199],\n [-344, 612, 460, -142, 281, 130, -106, -119, 181],\n [3, -306, -460, 487, -110, -145, 19, -149, 292]]\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 9x9 matrix:\n[[-2, -57, 303, 11, 66, -257, -385, 12, -345],\n [-140, -103, -290, 78, 258, 49, 192, -347, 271],\n [208, 188, 260, -132, -528, 256, 200, -260, 412],\n [-4, 125, -8, 44, -180, 263, 236, -143, 181],\n [-210, 40, -372, 198, 201, 267, 321, 21, 7],\n [106, 191, 265, -19, -372, 187, 37, 78, -43],\n [-174, -46, -175, 153, 297, -42, -59, 249, -355],\n [-142, -90, -40, 106, 216, -25, 5, -465, 120],\n [-162, 146, 28, 218, -42, 309, 183, -211, -66]]\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[[-158, 222, 23, -31, -47, -65, -325, 249, -336],\n [-254, -382, -378, -150, 246, 402, -2, 70, -106],\n [-155, 222, 203, 139, -86, -262, -239, 153, -43],\n [179, -195, -352, -380, -17, 3, 62, 467, -176],\n [-163, 59, 70, 26, 32, -126, -262, 50, -209],\n [-135, 149, 212, 198, -106, -297, -86, 178, 219],\n [227, -478, -589, -337, 148, 676, 549, 13, 179],\n [-107, -359, -159, 1, 154, 129, 169, -56, 244],\n [-82, -121, -304, -250, 36, 98, -104, 441, -233]]\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[[138, -24, -330, -342, -210, -90, 48, 390, -354],\n [-104, 180, -90, -190, 74, 124, -208, 172, -138],\n [159, -164, -95, -17, -171, -151, 200, 57, -67],\n [89, -220, 215, 345, -29, -129, 248, -337, 283],\n [276, -342, -45, 129, -267, -282, 408, -66, 27],\n [296, -354, -75, 103, -293, -298, 424, -34, -3],\n [262, -314, -65, 93, -259, -264, 376, -32, -1],\n [129, -146, -50, 22, -132, -127, 176, 9, -22],\n [-66, 216, -270, -402, -6, 114, -240, 402, -342]]\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[[-57, 224, -122, 56, 224, -422, -367, -219, -52],\n [428, 48, -326, 416, 188, -533, -124, -374, 183],\n [-123, 61, -217, 126, 5, -162, -361, -98, -26],\n [-58, 71, -11, 131, -399, 126, -87, 90, 173],\n [-233, -27, -19, -44, 547, -37, -381, -98, -585],\n [-131, 57, 327, -310, 63, 176, 199, 152, -126],\n [71, -220, -100, 226, -143, 287, 25, 70, -64],\n [-227, 37, -77, -33, 259, -81, -350, -65, -296],\n [299, -17, 147, 267, -222, 174, 230, 30, 88]]?\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 9x9 matrix:\n[[112, 56, 64, -40, 8, 88, -80, -24, 136],\n [-196, -98, -112, 70, -14, -154, 140, 42, -238],\n [0, 0, 0, 0, 0, 0, 0, 0, 0],\n [224, 112, 128, -80, 16, 176, -160, -48, 272],\n [-42, -21, -24, 15, -3, -33, 30, 9, -51],\n [14, 7, 8, -5, 1, 11, -10, -3, 17],\n [-154, -77, -88, 55, -11, -121, 110, 33, -187],\n [252, 126, 144, -90, 18, 198, -180, -54, 306],\n [-14, -7, -8, 5, -1, -11, 10, 3, -17]]\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, 113, 75, 444, 219, -504, 373, 8, 185],\n [91, 248, -365, -317, -531, 222, -561, -73, -46],\n [237, -448, -97, -95, 157, 36, -236, 641, -176],\n [11, 58, 665, 32, 74, -70, 23, -256, -359],\n [256, 10, -113, 85, -45, -222, -76, 113, 44],\n [-330, 173, 415, 263, 141, -203, 159, -25, -173],\n [-42, 58, 12, 246, 355, -461, 791, -214, 561],\n [213, 125, -212, -380, -343, 52, -294, -80, 84],\n [-152, 206, 624, -405, -89, -4, 63, -397, -147]]\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[[144, -50, -34, -100, 70, -48, -180, -20, -74],\n [-51, 57, -33, 91, 72, 40, 81, -14, 54],\n [63, -150, 132, -225, -285, -96, -135, 60, -123],\n [-54, 29, 1, 52, -1, 24, 72, 2, 35],\n [-120, 28, 44, 64, -92, 32, 144, 24, 52],\n [39, -5, -19, -15, 40, -8, -45, -10, -14],\n [-69, 135, -111, 205, 240, 88, 135, -50, 114],\n [126, -177, 123, -276, -267, -120, -216, 54, -159],\n [180, -83, -19, -154, 37, -72, -234, -14, -107]]\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[[-40, 135, 96, -261, 486, -694, 16, 553, -511],\n [133, -39, -74, -297, 550, -438, 319, 374, -216],\n [75, 93, 330, 183, -241, -256, -42, 17, -531],\n [-439, 378, 141, 499, -106, 486, -796, -797, 204],\n [83, -834, 166, 49, -59, 145, 136, -111, 13],\n [-154, -459, 274, 221, -187, 84, -291, -364, -269],\n [-112, -54, -148, -165, 366, -39, -46, 103, 178],\n [111, 96, -186, -292, 296, -328, 287, 213, -216],\n [389, -243, -103, -311, -144, -253, 640, 549, -99]]?\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[[-207, -124, -215, 100, 33, -441, 438, 26, 372],\n [11, 24, 232, -61, -49, 358, -166, -104, -287],\n [204, 84, -191, 13, 244, -241, -52, 36, 253],\n [231, 104, 13, -29, 501, -18, -36, -247, 198],\n [-34, -48, -425, 110, -4, -632, 266, 247, 469],\n [92, 20, -419, 77, -68, -529, 36, 336, 345],\n [-365, -176, 31, 57, -335, -52, 316, 57, -52],\n [132, 56, -338, 34, -348, -294, -240, 488, 42],\n [-462, -216, 83, 56, -532, 34, 310, 117, -187]]\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 9x9 matrix:\n[[-21, -19, 174, 46, 158, 76, 68, -91, 73],\n [227, 101, -60, 23, -360, -86, -109, 130, 28],\n [-73, -421, 87, -103, 322, -83, 520, 80, 178],\n [421, 29, 231, 99, -358, -71, 82, 136, 262],\n [169, 339, 180, 164, -214, 126, -336, -119, 9],\n [-293, -143, -522, -215, 40, -148, -9, 132, -286],\n [-106, -62, -120, -60, 68, -28, 28, 18, -70],\n [71, 223, -63, 51, -222, 23, -276, -14, -88],\n [-10, 318, 18, 100, -104, 126, -378, -142, -126]]\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 9x9 matrix:\n[[-263, -199, 177, 82, 334, 132, 308, -84, 188],\n [159, 28, -173, -37, 72, -455, -292, -218, -543],\n [132, 188, -439, 73, -169, -90, -508, 54, 84],\n [-166, -384, -229, 222, 288, -332, -499, 173, -147],\n [-204, -148, 62, -152, -22, 90, 302, 186, 54],\n [99, 6, -9, 240, -57, 22, -199, 194, 279],\n [141, -24, -101, -205, -254, -531, 136, 284, -443],\n [144, -253, 75, 165, -50, -362, -351, 326, -275],\n [105, 169, -33, -177, -221, 8, 97, -7, -99]]\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[[529, -113, 111, 105, -144, -242, 47, 259, -26],\n [-477, -136, -22, -114, 315, 8, -158, 270, -371],\n [-513, 434, 218, -454, 120, 242, 102, -168, 502],\n [-265, 416, -510, -28, -220, -185, 416, -266, 292],\n [-229, -351, 49, -247, 242, -24, -309, 443, -546],\n [474, 347, -427, 387, -403, -588, 613, 13, 321],\n [-36, 42, 306, -79, 229, -213, 49, 507, -20],\n [-16, -30, 166, 5, 210, -308, 61, 561, -167],\n [501, -27, -339, 486, -253, -453, 292, 102, -88]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[15, -188, -53, 5, -56, -106, -208, 96, 235],\n [114, 504, 314, 341, 83, -360, 266, -421, -294],\n [-282, -103, 327, 389, 183, -110, -79, 256, -100],\n [226, 58, 180, 87, 339, -89, 189, 177, 412],\n [203, -428, -265, -278, -13, 164, -192, 269, 431],\n [-336, 169, 241, 34, 394, 202, 259, 467, 318],\n [-86, 190, 376, 473, 115, -454, -34, -79, 2],\n [-116, -96, -100, 70, -337, -159, -295, -230, -292],\n [-33, 212, 347, 321, 275, -247, 143, 76, 155]]?\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[[33, -68, 622, -344, -229, -249, 127, -74, -469],\n [-73, -8, 138, 76, 5, -379, 57, 154, -271],\n [70, -133, -668, 415, 160, 279, -122, 62, 385],\n [-28, 283, -166, 163, 340, 73, 455, 201, -211],\n [110, -20, -186, 32, 94, 166, 80, -24, 40],\n [19, -24, 305, -50, -47, -107, 291, 67, -440],\n [-231, 308, 240, -248, -95, 230, -165, -148, 358],\n [-267, -41, -193, 337, -153, 229, -331, 35, 482],\n [-354, -180, 410, 400, -382, 28, 84, 200, -266]]\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[[-26, 174, -52, 236, -75, -91, 170, -234, -183],\n [45, -26, -57, -24, -4, -63, 45, -36, -47],\n [78, 62, -156, 108, -59, -195, 210, -234, -223],\n [-100, 220, 40, 280, -70, 10, 100, -180, -110],\n [-46, 218, -44, 292, -89, -89, 190, -270, -205],\n [44, -126, -2, -164, 45, 19, -80, 126, 87],\n [-113, -58, 209, -112, 70, 257, -265, 288, 281],\n [-45, 172, -21, 228, -67, -54, 135, -198, -146],\n [97, 64, -187, 116, -67, -232, 245, -270, -260]]?\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[[4, 228, -104, 96, -24, 164, 180, -32, 16],\n [0, -125, 40, -70, 40, -75, -105, 10, -35],\n [-10, 55, 60, 110, -140, -35, 75, 30, 135],\n [3, 221, -94, 100, -34, 153, 177, -28, 26],\n [13, 191, -162, 4, 98, 203, 123, -60, -102],\n [14, -27, -100, -126, 180, 79, -63, -46, -175],\n [15, -220, -46, -242, 254, -30, -228, -34, -241],\n [-12, 141, 48, 174, -192, 3, 153, 30, 183],\n [-21, 178, 106, 266, -314, -36, 210, 58, 301]]\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[[149, 30, -3, -156, -15, 155, 91, 184, -87],\n [81, -180, -173, -302, -327, 337, -111, -46, -321],\n [46, -351, 50, -275, -300, 51, 134, -87, 7],\n [-195, 39, -69, 325, 35, -28, -355, -247, -66],\n [108, -591, -222, -547, -756, 597, -228, -231, -533],\n [-163, 21, -72, 223, 7, -36, -262, -211, -50],\n [242, 0, 274, 88, 152, 146, 108, 332, 64],\n [-178, 183, 92, 387, 292, -331, -52, -93, 253],\n [-172, -222, -1, -12, -161, -196, 2, -288, 121]]?\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[[-77, 330, 172, 48, -26, -415, -13, -287, -126],\n [-102, -157, -546, 487, 12, -197, 271, 224, 534],\n [-588, -272, -279, 212, -229, -148, -64, -65, 866],\n [-409, 58, 455, -120, -136, -173, -394, -576, 30],\n [-95, -68, 424, -232, 25, 151, -320, -289, -240],\n [111, -251, 31, 24, 330, 297, -67, 161, -90],\n [0, -288, 90, -188, 279, 1084, -409, 84, 234],\n [-98, 53, 495, -432, 139, 960, -629, -322, 2],\n [277, 153, 206, -24, -26, -614, 218, -64, -710]]\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[[-329, 105, -78, 62, -87, 226, -113, 171, 265],\n [366, -23, 666, 176, -112, -21, 44, 148, 116],\n [-325, 219, 703, -231, -59, 311, -559, 609, -32],\n [295, -132, 427, -13, -225, 46, -230, -21, 170],\n [-146, -83, 177, -210, -43, -83, -362, 75, -231],\n [226, 106, -191, -24, 217, -365, 164, -64, -75],\n [54, 47, -252, 77, 279, -371, 332, -188, -40],\n [-178, 571, -451, -163, 657, -153, 376, 274, -210],\n [-92, -24, 49, -95, 39, -216, -187, 2, -42]]\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 9x9 matrix:\n[[-429, -92, -64, 131, -176, 88, -77, 28, -24],\n [-70, 170, -304, -42, -154, 284, 258, -233, 457],\n [264, -55, 358, -4, 231, -147, -326, 213, -442],\n [59, 13, 98, 108, -73, 262, -197, -76, -31],\n [-51, -153, -78, -28, -27, -314, 229, -10, 25],\n [408, 55, 4, 421, -39, -426, -168, 36, 37],\n [-64, 81, 79, 335, -41, -49, -398, 176, -152],\n [-95, 120, -315, -98, -68, -4, 349, -119, 380],\n [-8, 4, 93, -271, 44, 442, 32, -122, -15]]\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[[-323, -35, -202, -317, 248, 220, 477, 284, -438],\n [-92, 29, -47, -104, 78, 93, 153, 88, -149],\n [196, 45, 129, 184, -146, -115, -279, -168, 251],\n [-255, -577, -308, -57, 92, -254, 135, 124, -4],\n [-138, -110, -112, -102, 88, 20, 162, 104, -128],\n [-225, -166, -179, -171, 146, 43, 270, 172, -217],\n [197, 335, 208, 83, -92, 110, -153, -116, 72],\n [20, 274, 86, -76, 36, 198, 90, 32, -142],\n [45, -151, -14, 99, -64, -152, -135, -68, 158]]?\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[[155, -155, 288, 58, -27, 65, -156, -124, -209],\n [104, -336, 13, 80, 80, -7, -113, -120, 164],\n [346, -362, -96, -164, 2, -218, -589, 385, -122],\n [238, -686, -343, 321, -75, 45, -274, 526, 137],\n [367, -696, -255, 382, -178, 58, -234, 66, 409],\n [104, -180, -229, 75, -39, 145, -251, 523, -167],\n [92, -481, -72, 179, 60, -90, -26, -102, 323],\n [150, 63, -118, 140, -235, 28, 168, -595, 604],\n [-350, 373, 53, 471, -175, 609, 692, -191, -47]]\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[[95, -150, 270, -140, -90, 332, 494, -200, -241],\n [-446, 84, -160, -330, -458, 262, -696, -172, 218],\n [-148, 31, 74, -405, -268, 97, -211, -384, -143],\n [-132, -490, 318, -424, -607, 514, 38, -290, -352],\n [-10, -22, -166, -300, -283, 306, 1, -94, 152],\n [145, -192, 369, -310, -422, 287, 262, -178, -252],\n [415, -378, 346, 132, -36, -196, 275, 184, -351],\n [114, 442, -517, -331, -79, -96, -611, -81, 495],\n [88, 11, -57, -79, -154, 38, -142, 70, 118]]\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[[-370, -306, 118, 16, -154, 334, -250, -116, 290],\n [305, 241, -63, 24, 149, -279, 205, 106, -225],\n [497, 361, -6, 144, 305, -465, 331, 202, -327],\n [-13, -117, 328, 352, 203, -23, -19, 94, 143],\n [133, -3, 302, 368, 277, -157, 79, 146, 37],\n [17, -95, 327, 360, 221, -51, 1, 106, 123],\n [-78, -78, 66, 48, -6, 66, -54, -12, 78],\n [306, 162, 180, 288, 306, -306, 198, 180, -126],\n [225, 217, -166, -112, 33, -193, 155, 42, -215]]\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[[-548, 314, -135, -218, 594, -22, -568, 376, 58],\n [-594, 291, 266, -368, 340, 100, -211, -196, 210],\n [347, 96, -300, -23, 141, 382, -548, -7, 329],\n [-249, -144, -207, -7, 235, 32, -432, 472, -91],\n [526, 142, -213, 163, -591, -471, -539, -6, -821],\n [0, 537, -216, -1, 528, 413, -380, -22, 304],\n [-99, -373, -87, 93, 233, 388, 427, 249, 391],\n [597, 87, -728, 70, -415, 174, -95, -9, -170],\n [-914, 365, 610, -270, 466, -415, -192, 6, -187]]\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 9x9 matrix:\n[[-88, 58, 5, 272, 16, -232, -394, 132, -550],\n [-6, 68, -261, -22, 78, -58, 288, -184, 88],\n [352, -317, 67, -155, -215, 195, 62, 332, 288],\n [118, -197, 209, -419, -417, 250, 7, 372, 721],\n [216, -154, 164, 195, 278, 185, 5, -89, -338],\n [35, 148, 27, -123, 214, -85, 20, 21, -27],\n [-270, 42, 133, 301, -154, -146, -240, -225, -179],\n [-149, 234, -129, 325, 479, -152, -41, -325, -696],\n [-76, 73, -291, -251, -426, -282, -21, 326, 393]]\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[[60, -52, -182, 428, 54, 18, -87, 299, -225],\n [-61, 147, 50, -435, -24, -4, 24, -400, 265],\n [53, -12, 107, -207, -145, -123, 133, -85, 18],\n [-52, -114, 387, -183, 54, 35, -95, -30, 386],\n [-286, -121, 310, -79, 283, 334, -63, 14, 168],\n [45, -113, 130, 1, -106, -80, 138, 132, -125],\n [-132, -80, -95, 403, 246, 249, -118, 279, -193],\n [-165, 27, 147, -288, 90, 141, 42, -213, 144],\n [343, 43, -378, 343, -302, -360, 83, 227, -384]]\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[[159, -325, -606, -286, -679, -86, 327, 4, -512],\n [69, 181, 93, -368, -184, 64, 4, -241, 167],\n [-124, -488, 353, 373, 34, 459, -796, 623, -475],\n [-68, 249, 242, 135, 110, -199, -103, -160, 66],\n [-498, -439, 145, -11, 152, 110, -191, 289, 29],\n [423, 399, -327, -184, 69, -395, 267, -435, 95],\n [275, 145, -106, 189, 306, -363, 561, 61, 288],\n [-493, -18, 185, -50, -534, 344, -441, 323, -151],\n [-283, -110, 199, 248, 149, 87, -352, 101, -127]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-705, 12, -85, 170, 237, 213, -645, -50, 16],\n [-948, 159, -275, 284, 461, 272, -625, -158, -382],\n [-148, 36, 11, 382, -9, -228, 57, -28, 286],\n [-37, 399, -114, -97, 270, 157, -135, 138, -46],\n [-252, 461, 130, -183, -99, 593, -38, 107, -538],\n [-122, -19, -236, -672, 94, 603, -259, -94, -844],\n [340, -144, 225, -258, -522, 122, 377, 19, -130],\n [515, 235, 249, -537, -335, 284, 357, 308, -248],\n [51, -223, 60, 136, -65, -304, -225, 79, 776]]\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[[-97, -69, -241, -203, -80, 212, -17, -199, -68],\n [15, 112, 35, -28, 70, -79, -27, -96, -59],\n [-24, 186, 240, 126, 156, -174, -12, 30, -6],\n [-41, 475, 427, 143, 360, -378, -63, -123, -108],\n [206, -3, -44, -24, -26, -136, -15, -3, -29],\n [32, 150, 204, 116, 124, -184, -10, 46, -2],\n [-324, 143, 18, -90, 110, 172, -25, -221, -73],\n [-258, 139, -26, -125, 94, 143, -34, -251, -95],\n [27, 289, 345, 174, 232, -307, -26, 29, -26]]\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[[-36, 60, -40, -36, -72, -40, -40, 56, 32],\n [135, -225, 150, 135, 270, 150, 150, -210, -120],\n [-144, 240, -160, -144, -288, -160, -160, 224, 128],\n [-162, 270, -180, -162, -324, -180, -180, 252, 144],\n [45, -75, 50, 45, 90, 50, 50, -70, -40],\n [72, -120, 80, 72, 144, 80, 80, -112, -64],\n [-90, 150, -100, -90, -180, -100, -100, 140, 80],\n [45, -75, 50, 45, 90, 50, 50, -70, -40],\n [-18, 30, -20, -18, -36, -20, -20, 28, 16]]\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[[576, -268, 184, 136, 126, 151, -34, -590, 157],\n [185, -403, 66, 69, 270, 60, 587, -208, -128],\n [-321, -24, -26, 350, -83, -59, -25, 263, -101],\n [587, -387, 428, 611, 677, 302, -381, 173, -208],\n [282, 393, -151, -429, -155, -47, -443, -460, 428],\n [349, 83, 7, 36, 414, -34, -274, 36, 39],\n [207, -7, -290, -166, 212, 146, -191, 69, 168],\n [242, 706, 335, 205, -40, -179, -220, -233, 83],\n [536, -264, -206, 50, 604, 358, -44, -34, 144]]\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[[106, 258, -156, 154, -274, -436, -320, -212, 166],\n [157, -226, 292, 247, -138, -66, 68, 354, 19],\n [12, -182, 164, 24, 62, 152, 152, 208, -60],\n [-55, 30, -60, -85, 70, 70, 20, -70, -25],\n [-145, -149, 38, -217, 285, 402, 256, 66, -151],\n [-140, 129, -198, -218, 155, 128, 4, -236, -44],\n [-191, -159, 18, -287, 359, 494, 304, 46, -185],\n [15, -324, 288, 33, 120, 282, 276, 366, -111],\n [64, -70, 100, 100, -66, -48, 8, 120, 16]]\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[[-134, -98, -124, 55, -15, -45, 156, -80, -141],\n [174, 50, 26, 354, -282, 264, -148, -34, -32],\n [103, 49, 31, 172, -152, 141, -130, 33, 1],\n [83, -107, -35, 203, -43, 114, 306, -433, -42],\n [-158, -92, -44, -296, 277, -237, 263, -114, 13],\n [-344, -130, -126, -452, 369, -399, 283, 32, -61],\n [18, -40, 72, -276, 287, -147, 249, -234, 147],\n [-375, -121, -221, -153, 85, -252, 106, 193, -232],\n [-88, 18, -34, -52, -9, -57, -107, 192, -43]]?\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[[-134, 11, 255, -560, -326, -198, -140, 340, -148],\n [129, -354, 93, -343, -26, -328, 172, -167, 114],\n [269, 324, -579, 173, 688, 64, 200, -790, -926],\n [464, -668, -519, -398, -217, -231, 217, 167, 130],\n [-261, 389, 315, -188, -244, 260, -407, 483, 275],\n [-458, 608, 508, -12, -50, 286, -385, 227, 101],\n [-490, 195, 607, 57, -483, 206, -410, 848, 737],\n [-152, -92, 420, -312, -310, -272, -36, 99, -84],\n [35, -222, -374, 615, 123, 258, 157, -19, 284]]\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 9x9 matrix:\n[[533, 44, -132, 216, 167, -38, 39, 322, -28],\n [-64, 119, -371, -270, 98, -174, -142, 314, -221],\n [-156, -110, 619, -175, -106, 202, 23, -441, 93],\n [581, -107, 40, 164, 26, -87, -320, 173, 167],\n [-474, 2, 87, -98, -91, 93, 165, -193, -176],\n [91, 211, -290, 195, -218, -531, 117, 28, -52],\n [561, 143, 65, 154, -66, -359, 22, 73, -103],\n [360, -420, 614, 782, -102, 149, 732, 768, 116],\n [496, -207, 172, -49, 91, 136, -581, -18, 310]]\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[[-128, -217, 61, 6, -22, 205, -189, 168, -109],\n [16, -241, 103, -102, -106, 175, -57, 144, -67],\n [214, -385, 210, -290, -269, 219, 96, 176, -38],\n [58, 254, -192, -14, 145, -273, -9, -76, -38],\n [-280, -256, 278, 260, -128, 434, -16, 8, 142],\n [60, -141, 258, 36, -222, 204, 279, -108, 228],\n [458, -239, 142, -446, -291, -11, 288, 80, 6],\n [144, 126, -158, -148, 76, -230, -18, 16, -98],\n [202, 192, -231, -204, 115, -336, -25, 16, -137]]?\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[[-16, 83, -73, -52, 14, 93, -53, -92, 90],\n [-72, 3, 23, -120, 82, -47, -77, -72, -146],\n [-20, -140, 140, 10, 30, -190, 40, 110, -250],\n [44, -43, 25, 86, -48, -23, 65, 82, 28],\n [66, -123, 93, 147, -69, -108, 123, 177, -45],\n [-22, -115, 117, -1, 31, -160, 27, 85, -217],\n [110, -10, -30, 185, -125, 65, 120, 115, 215],\n [-4, 50, -46, -22, 2, 60, -26, -50, 66],\n [-12, -6, 10, -18, 14, -16, -10, -6, -34]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[153, 257, 30, -275, -419, -232, 222, 287, -66],\n [348, 171, 435, -43, 20, -321, 22, -446, -7],\n [267, -704, 32, 234, 91, -168, -517, 109, 111],\n [98, 250, 399, -62, 29, -461, 112, -455, -95],\n [-14, -67, -224, -37, -585, -366, 266, 331, 432],\n [473, -52, 233, -70, 301, -209, -300, -445, -139],\n [20, -137, 124, 114, -185, -306, 38, 27, 181],\n [-441, -241, -237, 231, -282, 31, 136, 704, 145],\n [610, -508, 200, -61, -128, -46, -486, -164, 123]]\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[[28, 24, -24, 30, 12, 8, 12, -14, 0],\n [-28, -24, 24, -30, -12, -8, -12, 14, 0],\n [-98, -84, 84, -105, -42, -28, -42, 49, 0],\n [224, 192, -192, 240, 96, 64, 96, -112, 0],\n [28, 24, -24, 30, 12, 8, 12, -14, 0],\n [182, 156, -156, 195, 78, 52, 78, -91, 0],\n [-28, -24, 24, -30, -12, -8, -12, 14, 0],\n [84, 72, -72, 90, 36, 24, 36, -42, 0],\n [140, 120, -120, 150, 60, 40, 60, -70, 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[[-184, -133, -171, -102, 384, 273, 346, -118, 426],\n [-50, -427, 27, 164, -263, 79, -76, 62, 144],\n [-357, 140, -94, 420, -9, 185, 416, 100, 462],\n [56, 139, -45, -288, 395, 59, 93, -94, 3],\n [-221, 100, -24, 424, -279, 9, 159, 108, 183],\n [159, 320, 114, -120, 89, -139, -130, 60, -288],\n [50, 206, -164, -440, 536, 48, 167, -252, -3],\n [-12, 180, -224, -308, 326, -12, 166, -296, -6],\n [-226, -72, -40, 242, 35, 196, 262, 88, 378]]?\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[[56, 106, -5, 494, -215, -10, 63, -281, -618],\n [57, -197, 58, -54, 269, -203, 43, -420, 193],\n [-213, 83, 92, 424, -135, -332, -226, -184, -867],\n [228, -281, -60, 89, 410, -32, -2, 237, 588],\n [-282, -396, 369, -121, -227, -232, -168, -525, -122],\n [-148, 59, -17, -294, -173, -49, -574, -358, -177],\n [28, 527, -266, -143, 192, 55, 108, 93, 21],\n [446, -97, -852, -148, -684, 593, -304, -211, -216],\n [719, 23, -409, 165, -246, 847, -61, 355, 413]]\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[[-308, -230, 62, -266, 636, 131, -96, 33, 16],\n [14, 22, 28, 214, -152, -206, 18, -70, -132],\n [-54, -60, 515, -276, 412, 403, 261, 502, -319],\n [827, 150, -100, 269, -177, -157, -184, 191, 464],\n [-608, -246, 83, -508, 154, 138, -113, -51, -321],\n [-368, -702, -146, -136, -78, -273, -525, -708, 33],\n [37, 375, 166, -17, -419, 24, 252, 360, -382],\n [-98, 251, 34, 226, -103, 40, 346, 21, -167],\n [-65, -189, 332, 157, -268, -265, -12, -16, -491]]\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 9x9 matrix:\n[[-48, 115, -168, -73, -119, 663, 243, -473, -144],\n [119, -10, 235, -282, -71, -287, -227, -81, -185],\n [18, 290, -164, 109, -144, 517, 555, -168, 167],\n [-321, -305, -245, 162, 9, 349, -442, -478, 143],\n [62, -158, -162, 46, 255, -82, -124, -232, -173],\n [-4, -15, -143, 435, 230, -320, -142, 294, 393],\n [94, 58, 275, -163, -9, -290, -589, 119, -190],\n [84, 161, -54, 247, 12, -185, 91, 39, 405],\n [-286, -264, -75, 173, -155, -106, 52, -9, 540]]\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[[-62, 104, -232, 61, 370, 58, 97, 242, -99],\n [-404, -175, 107, -402, -676, -462, 271, -392, 491],\n [92, 335, 837, -155, 265, 45, -493, -315, -79],\n [-108, 13, 448, -93, 283, -67, -210, -271, -74],\n [-120, -192, -415, -218, -60, -390, 15, 202, 93],\n [-110, 338, -9, 90, 354, 278, 130, 120, -109],\n [115, -341, 215, 185, 66, 10, -63, -223, -86],\n [-84, 57, -380, 107, -97, 217, 210, 157, -82],\n [169, -193, 167, 182, -645, 119, 250, -270, 250]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[401, -200, -298, 179, -108, -212, 149, 144, -97],\n [-83, 479, 425, -207, -489, 145, -419, 265, -109],\n [-197, 461, 430, -382, -410, 246, 182, 283, 187],\n [-430, 258, 495, 237, -132, 170, -233, -223, -183],\n [322, 79, -292, -170, -75, -69, -147, 414, 322],\n [-224, -6, 169, 23, -28, 110, 340, -169, 17],\n [64, 189, 133, -162, 11, 329, 30, 213, 298],\n [-395, 315, 599, 262, -47, 537, -349, -212, 11],\n [281, 58, -152, -61, 132, 320, -19, 306, 507]]\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[[-229, 80, 254, -308, -50, -84, 159, 139, -34],\n [-92, 300, -384, 78, 428, -273, 101, 107, -149],\n [50, -186, 18, -388, -422, 225, -111, -153, 315],\n [-231, 44, 326, -19, 225, 54, 306, -14, -100],\n [-301, -19, 521, -395, -131, 63, 258, 70, 14],\n [-413, 108, 346, -356, 242, 86, 469, -51, 4],\n [-56, 79, -163, -216, -10, -52, 11, 9, 79],\n [91, -222, 44, -167, -283, 298, -70, -234, 266],\n [284, -92, -296, -107, -479, -93, -446, 96, 147]]\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[[34, -226, 182, -395, -507, -234, 244, -297, 282],\n [-194, -98, 208, 34, 150, 57, 316, -499, 9],\n [-44, 352, -90, -54, 2, -597, -398, 189, -275],\n [120, -221, -366, -116, 23, 77, 212, -159, -487],\n [412, 571, -213, 116, 560, 91, -53, 186, -290],\n [194, 225, -670, -334, -64, -262, -367, 12, -419],\n [94, -114, -100, 66, -408, 355, -636, 280, 279],\n [46, -482, -60, -563, -814, -398, 35, -455, -207],\n [-190, 87, -520, -411, 51, -21, -387, -165, -2]]\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 9x9 matrix:\n[[-146, -420, -10, 217, 256, 100, 95, 155, 102],\n [218, -28, -40, -475, -5, -205, -46, -389, -285],\n [118, -113, -71, -230, 164, -140, 127, -223, -87],\n [-335, 69, 69, 377, -170, 200, -44, 393, 230],\n [-214, 278, 78, -63, -425, 39, -200, 101, -31],\n [-129, -56, -4, -210, -108, -66, -22, -79, -87],\n [455, 50, 42, -375, -77, -111, -308, -382, -400],\n [247, 183, 21, -160, -96, -58, -143, -172, -160],\n [167, -462, 110, 255, 167, 213, -318, 104, -148]]\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[[-150, 70, -40, -100, -160, -170, 110, 180, -20],\n [-240, 112, -64, -160, -256, -272, 176, 288, -32],\n [105, -49, 28, 70, 112, 119, -77, -126, 14],\n [135, -63, 36, 90, 144, 153, -99, -162, 18],\n [-270, 126, -72, -180, -288, -306, 198, 324, -36],\n [255, -119, 68, 170, 272, 289, -187, -306, 34],\n [240, -112, 64, 160, 256, 272, -176, -288, 32],\n [75, -35, 20, 50, 80, 85, -55, -90, 10],\n [-15, 7, -4, -10, -16, -17, 11, 18, -2]]\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[[-174, -31, -188, -183, 188, 273, 129, -7, -187],\n [-45, -56, -240, -144, 75, 202, 142, 40, -251],\n [-223, -327, -396, -175, -289, 220, 164, -184, -1],\n [-73, 355, -87, 310, 179, -190, 82, 560, 163],\n [-306, -319, 463, -242, -128, 64, -291, -667, 420],\n [25, -34, 236, -142, -17, 18, 37, 543, 31],\n [-303, -298, 247, -238, -191, -66, -164, -24, 260],\n [-191, -317, 412, -311, -147, 64, -183, -199, 233],\n [-63, 67, -303, 101, -21, -99, 109, 309, -79]]\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 9x9 matrix:\n[[-190, -196, -26, -396, -92, -80, -464, -378, -228],\n [23, -232, -128, 22, -137, 55, -88, 44, 31],\n [0, -62, -4, -139, -8, -18, -131, -113, -21],\n [-278, 358, 230, -215, 176, -166, -99, -295, -293],\n [-68, -12, -36, 134, -56, 20, 62, 94, -38],\n [211, -516, -243, -133, -218, 110, -259, -8, 181],\n [-163, 222, 108, 33, 77, -65, 63, -39, -146],\n [-18, 162, 150, -305, 156, -102, -149, -277, -71],\n [-340, -128, -94, 86, -198, -14, -146, -20, -284]]\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[[-10, -206, -174, -582, -286, 18, 150, -223, 270],\n [-145, -38, -381, -107, 169, -69, -24, 241, 21],\n [192, 231, 354, 273, -99, -99, 58, -192, 31],\n [20, 160, -216, -150, -250, -234, 98, -115, 158],\n [109, -262, 579, -27, -197, 387, -50, -311, -149],\n [-2, 119, -291, -288, -371, -234, 113, -173, 185],\n [71, -185, 449, -8, -288, 306, -74, -295, -190],\n [-23, -244, 183, -127, -109, 267, -64, -112, -121],\n [-114, 144, -582, -202, 10, -318, 80, 172, 194]]\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 9x9 matrix:\n[[-158, -80, 54, -326, 104, 0, -58, 210, 168],\n [2, 170, -242, 42, 83, 76, -341, -41, -280],\n [401, -119, -33, 306, -27, 286, -189, -258, 0],\n [217, -83, 165, 74, 136, 158, -92, 17, 84],\n [241, -309, 234, 15, -30, 174, 117, -46, 366],\n [23, -75, -86, 107, -225, -30, 164, -179, 50],\n [-19, -163, 239, -186, 73, 6, 131, 162, 280],\n [-93, 56, -233, -61, -57, 8, -154, -50, -112],\n [-343, 244, 248, -162, 169, -364, 293, 343, -98]]\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[[484, -213, -485, -122, -259, 26, -278, 185, 146],\n [168, -84, -216, -216, -336, -276, -324, 126, 144],\n [-132, -361, -131, -188, -5, 30, -68, 404, -370],\n [-344, 373, 793, 258, 377, -118, 559, -451, -177],\n [-162, 310, 544, 95, 88, -297, 259, -352, 1],\n [-38, 125, 205, 31, 15, -135, 89, -144, 17],\n [344, 390, 180, 192, -50, -150, 113, -493, 399],\n [-102, -400, -458, -117, 32, 367, -190, 480, -216],\n [-316, -150, 276, 6, 262, 72, 275, 143, -459]]\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[[-353, -42, -3, -94, -63, -110, 75, 88, 220],\n [43, -49, 79, 119, -325, -160, -545, 371, 37],\n [-688, 527, -160, -28, -445, -90, -55, -293, 96],\n [258, 58, 35, 182, -6, -366, -168, -199, -447],\n [-256, 27, 260, 194, -78, 439, -44, 153, -101],\n [-276, 292, -67, 90, -318, -359, -304, -278, -238],\n [86, 14, 202, 148, 473, 327, 853, -162, -241],\n [269, -177, -146, -99, -173, -323, -743, 1, -49],\n [-121, 169, -264, -232, -121, 50, 13, -107, 333]]\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[[-221, 195, 234, -182, -65, 182, -208, -91, -91],\n [102, -90, -108, 84, 30, -84, 96, 42, 42],\n [-170, 150, 180, -140, -50, 140, -160, -70, -70],\n [17, -15, -18, 14, 5, -14, 16, 7, 7],\n [102, -90, -108, 84, 30, -84, 96, 42, 42],\n [-187, 165, 198, -154, -55, 154, -176, -77, -77],\n [306, -270, -324, 252, 90, -252, 288, 126, 126],\n [-289, 255, 306, -238, -85, 238, -272, -119, -119],\n [51, -45, -54, 42, 15, -42, 48, 21, 21]]\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[[-28, -104, 170, -114, -14, -315, -177, 320, 112],\n [-183, -25, -230, -93, -19, -39, 109, -25, 142],\n [-119, -224, 270, -370, -277, -443, -139, 550, 296],\n [-196, -170, 46, -260, -78, -445, -127, 418, 284],\n [266, 98, 216, 334, 358, -52, -296, -22, -284],\n [-69, -57, 0, -267, -447, 240, 294, -45, 126],\n [-83, -191, 258, -319, -259, -359, -115, 469, 242],\n [-328, -27, -450, -171, -84, 33, 271, -125, 242],\n [-94, 63, -274, 19, -22, 233, 219, -267, 6]]\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[[-35, 240, 5, 254, 60, -231, -364, 201, -73],\n [398, 18, -89, 183, 226, 200, 136, 380, -186],\n [-211, -52, 175, -147, -160, -75, -25, -110, -22],\n [-317, 251, -226, -107, 106, -345, -12, -280, -101],\n [-231, -213, -298, -15, -280, -173, 237, -91, 222],\n [-263, 141, -122, -25, -18, -323, 20, 4, -191],\n [-114, 150, 492, -335, 116, 46, -51, -101, -437],\n [-176, 120, -42, 24, -20, -204, -142, -74, 2],\n [-145, -21, 18, 103, -176, -215, -29, 261, -130]]\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[[49, 41, 161, 41, -84, 139, -39, 133, -163],\n [-3, 15, -21, -24, -45, -30, -39, 42, 45],\n [26, -86, 154, 154, 264, 206, 234, -238, -302],\n [24, 34, 70, 3, -81, 51, -52, 105, -52],\n [-5, -63, 21, 68, 177, 58, 143, -182, -101],\n [26, 46, 70, -8, -114, 44, -78, 140, -38],\n [64, 10, 238, 107, 15, 235, 52, 49, -300],\n [31, -67, 161, 140, 213, 202, 195, -182, -289],\n [-39, -25, -133, -42, 45, -120, 13, -84, 145]]\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[[-139, 86, 390, -147, 303, 260, -149, -421, 36],\n [-91, 41, 171, -279, 285, 44, -206, -328, 39],\n [273, -103, 51, 53, -71, 132, -170, 340, -81],\n [-70, 45, 275, -210, 280, 160, -205, -315, 25],\n [111, -72, -270, -57, -105, -222, -27, 231, -18],\n [-124, 61, 205, -192, 248, 90, -129, -341, 41],\n [-269, 95, -97, -105, 85, -186, 144, -340, 85],\n [84, 3, 295, 232, -44, 346, 13, 85, -49],\n [-29, -14, -254, -53, -71, -244, 69, 53, 20]]\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[[-232, -247, -248, 535, -695, -422, -301, -391, 705],\n [285, 53, 312, -137, 243, 62, 305, -147, -356],\n [-288, 288, -197, -27, 7, 259, -292, 205, 341],\n [27, -412, 135, -108, -559, -525, -476, -301, 574],\n [-127, -27, -237, 9, 91, 81, -17, 427, -174],\n [-259, 902, 388, -346, 502, 715, 342, -282, -144],\n [122, 413, 364, 57, 138, 248, 259, -284, -42],\n [-126, -530, -640, 262, -331, -351, -452, 153, 406],\n [336, 534, 426, 200, 448, 437, 668, -122, -539]]\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[[-426, -39, -346, 191, 180, -447, -216, -256, 666],\n [-395, -426, 73, -22, 50, -201, 136, -309, 641],\n [-497, -53, -217, 64, -40, -451, 213, -335, 910],\n [121, 388, -162, -22, 135, -363, 112, 204, 162],\n [192, -307, 405, -321, 132, -39, 369, -159, 30],\n [413, -185, 548, -262, -56, -22, 493, -315, -42],\n [-347, 58, -284, 268, -182, -102, -164, -283, 375],\n [44, 56, 103, 242, -452, 199, 36, -298, -22],\n [-266, 164, -377, 227, 39, -20, -358, 286, 54]]\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[[-364, 225, 106, 253, 27, 237, 442, -321, 278],\n [-457, 368, 292, 244, -112, 23, 429, -474, 457],\n [-133, -34, -135, 261, 258, 493, 300, -19, -33],\n [-206, 152, -7, -61, -160, -34, 301, -207, 156],\n [-135, 11, -167, 40, 49, 264, 326, -62, -9],\n [201, -104, -101, -287, -144, -259, -212, 157, -151],\n [-300, 227, 166, 175, -47, 63, 302, -299, 282],\n [269, -242, -337, -313, -30, -25, -124, 295, -335],\n [-30, -41, 38, 299, 269, 321, 16, 29, -12]]\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[[-80, -170, 80, -110, -30, 50, 40, -50, 80],\n [112, 238, -112, 154, 42, -70, -56, 70, -112],\n [104, 221, -104, 143, 39, -65, -52, 65, -104],\n [96, 204, -96, 132, 36, -60, -48, 60, -96],\n [-104, -221, 104, -143, -39, 65, 52, -65, 104],\n [32, 68, -32, 44, 12, -20, -16, 20, -32],\n [48, 102, -48, 66, 18, -30, -24, 30, -48],\n [8, 17, -8, 11, 3, -5, -4, 5, -8],\n [72, 153, -72, 99, 27, -45, -36, 45, -72]]\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 9x9 matrix:\n[[-441, -473, 164, 206, -118, -193, 86, 389, -366],\n [323, -332, 209, 3, -41, 74, -310, 494, 580],\n [108, -158, -8, -7, -8, 129, 334, 34, 215],\n [125, 229, -186, -401, -319, -164, 48, -250, 177],\n [-299, 36, -127, 81, 92, -439, -563, 270, -541],\n [136, -493, 651, 208, 230, -148, 302, 90, 140],\n [338, 353, -281, -306, -93, 146, -262, -81, 476],\n [182, -740, 542, 173, -354, -71, 303, 260, 139],\n [-49, -189, -56, -3, 137, -96, 156, 232, 82]]\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[[-389, 321, -43, -168, 188, -386, 147, -44, 261],\n [-157, 179, 105, -310, 246, -134, 149, 206, 45],\n [-28, 9, -38, 57, -35, -34, -15, -67, 36],\n [42, -102, -162, 348, -252, 12, -138, -300, 54],\n [103, -90, -1, 69, -67, 100, -48, -11, -63],\n [128, -117, -14, 111, -101, 122, -69, -37, -72],\n [23, 20, 99, -181, 123, 40, 62, 179, -63],\n [340, -261, 86, 51, -97, 346, -93, 127, -252],\n [35, -26, 11, 1, -7, 36, -8, 17, -27]]\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[[-705, 54, -280, 198, -631, -388, -180, -260, -761],\n [410, 21, 213, 311, 363, 188, -24, -282, 14],\n [-266, 186, -58, 352, -306, -36, -339, 187, -480],\n [-142, -104, 14, -402, -32, -692, -200, 614, 90],\n [3, -124, 303, -125, -256, 108, 0, 221, 197],\n [-327, -246, 88, -432, -210, -577, -390, 563, 283],\n [-12, -244, 352, 229, -94, 74, -298, -369, 38],\n [-132, 159, -15, 409, -80, 311, -548, -123, -32],\n [391, -121, -49, -215, 541, -421, 534, 15, -33]]?\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 9x9 matrix:\n[[-181, -193, 162, 83, 233, -128, -115, 162, 129],\n [-168, -147, -157, 84, 295, -120, 267, -124, 224],\n [-49, 30, -95, -87, 304, -230, 266, 62, 341],\n [-379, -557, 6, -226, -97, -213, -341, 203, 57],\n [149, -111, 62, -90, -25, -504, 134, -236, 565],\n [332, 126, 202, -96, -240, -69, 203, -317, -12],\n [257, 385, -330, 355, -214, 229, -109, -226, -13],\n [-156, -200, 123, -283, 126, -349, -133, 341, 296],\n [-188, -72, -593, 278, -91, 335, 47, -304, -198]]\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[[23, 27, 59, -17, -73, -66, -50, 19, 54],\n [-21, 33, -79, 17, 247, 78, 158, -41, -36],\n [-134, -354, -258, 94, -190, 324, -92, -30, -360],\n [-75, -66, -202, 56, 307, 222, 206, -71, -171],\n [106, 294, 198, -74, 194, -252, 100, 18, 288],\n [100, 270, 190, -70, 160, -240, 80, 20, 270],\n [155, 399, 303, -109, 187, -378, 86, 39, 414],\n [90, 243, 171, -63, 144, -216, 72, 18, 243],\n [6, 63, -9, -3, 156, 0, 96, -18, 27]]?\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 9x9 matrix:\n[[342, -332, 130, -71, 312, 457, -63, 140, -9],\n [-222, -79, -333, -189, -77, 61, -227, -253, 335],\n [-552, 620, -4, 35, 15, -165, -113, -505, -83],\n [240, -17, 293, 80, 175, 182, 126, 149, -242],\n [-176, -29, -246, 65, 145, -261, -257, 18, 177],\n [152, -323, -95, -121, 262, 337, -211, 22, 179],\n [234, -380, -142, -31, -98, -47, 17, 286, 159],\n [-162, 206, 33, 33, 79, -31, -55, -150, -57],\n [50, -83, 43, 14, 442, 240, -236, -18, 4]]\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 9x9 matrix:\n[[-112, 16, 16, -136, -40, -112, -96, -64, 128],\n [56, -8, -8, 68, 20, 56, 48, 32, -64],\n [56, -8, -8, 68, 20, 56, 48, 32, -64],\n [-252, 36, 36, -306, -90, -252, -216, -144, 288],\n [-224, 32, 32, -272, -80, -224, -192, -128, 256],\n [224, -32, -32, 272, 80, 224, 192, 128, -256],\n [-140, 20, 20, -170, -50, -140, -120, -80, 160],\n [210, -30, -30, 255, 75, 210, 180, 120, -240],\n [42, -6, -6, 51, 15, 42, 36, 24, -48]]\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[[538, -19, 394, 396, -70, -294, 397, -103, -103],\n [-18, -126, -24, -66, 138, 96, -38, 84, -52],\n [5, -137, -10, -225, 19, -60, 43, 64, 173],\n [-151, 106, 30, 265, 373, 608, -438, 363, -356],\n [177, -174, 1, 54, -40, -250, 287, -228, -115],\n [-61, 212, 177, 77, 150, 389, -352, 422, 88],\n [-87, 186, 36, -156, -129, -249, 139, -441, 107],\n [22, 229, 243, 304, 231, 511, -393, 514, -93],\n [84, 66, 58, 167, -38, -97, 115, -194, -141]]?\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[[154, -99, 143, -44, -121, 66, -11, -44, 77],\n [-42, 27, -39, 12, 33, -18, 3, 12, -21],\n [112, -72, 104, -32, -88, 48, -8, -32, 56],\n [196, -126, 182, -56, -154, 84, -14, -56, 98],\n [56, -36, 52, -16, -44, 24, -4, -16, 28],\n [0, 0, 0, 0, 0, 0, 0, 0, 0],\n [238, -153, 221, -68, -187, 102, -17, -68, 119],\n [0, 0, 0, 0, 0, 0, 0, 0, 0],\n [42, -27, 39, -12, -33, 18, -3, -12, 21]]\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[[-255, -199, -288, 285, 14, -452, 345, -827, -205],\n [795, -409, 136, -248, 323, 233, 402, 470, 253],\n [619, 207, -78, -512, -291, 747, -61, 479, 532],\n [64, -456, 41, 105, 124, -788, 217, -664, -30],\n [-243, 387, -95, 368, 3, -206, -31, -501, -157],\n [-147, 254, -29, 454, 464, 67, 494, -165, -305],\n [-292, 126, -133, 112, 6, -20, -455, 180, 148],\n [-198, -148, -247, 9, 342, -276, 261, -365, 208],\n [-153, -311, 283, 41, 12, -634, -202, -154, -185]]?\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[[-192, -284, 55, 144, -171, -51, -73, -94, 51],\n [165, -252, 202, 243, 102, -69, -266, 240, 159],\n [-639, -83, -189, 69, -619, -58, -15, -367, 350],\n [19, 409, -313, -299, -164, 26, 97, -20, 290],\n [-120, 225, -195, -27, 473, -544, -168, -61, -155],\n [93, -329, -138, 170, 325, 274, 468, 215, -797],\n [620, -100, 182, 199, 131, 268, -121, 613, 306],\n [-360, 581, -183, -502, -404, 323, 279, -420, -99],\n [-172, -130, -201, 209, -381, 375, 17, 327, 231]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-32, -295, -206, 289, 669, 207, -121, -400, 597],\n [395, 168, 21, -317, 6, 126, -470, 153, 166],\n [-51, 186, 182, 466, 203, -297, -138, 344, -7],\n [-161, -237, -107, 613, -34, -317, -46, -201, -83],\n [-41, 155, 95, -325, -36, 386, 241, 8, 53],\n [617, -796, 42, -340, -138, -52, -446, 220, 68],\n [-609, 523, 72, 334, -488, -202, 494, 70, -575],\n [65, 81, -28, -639, -559, 22, 284, -25, -373],\n [-384, 226, -55, 293, -547, -252, -186, 191, -669]]?\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[[-167, -290, -242, -28, 151, 6, -408, -302, 91],\n [221, -208, -226, 282, 147, -138, -28, -294, 79],\n [-318, 51, 96, -303, -66, 144, -198, 132, -30],\n [-193, 152, 170, -234, -111, 114, -4, 222, -59],\n [-141, -186, -150, -48, 93, 18, -288, -186, 57],\n [278, 146, 92, 186, -54, -84, 356, 108, -38],\n [124, 181, 148, 35, -92, -12, 270, 184, -56],\n [-133, -7, 14, -115, -11, 54, -110, 22, -3],\n [61, 307, 274, -73, -173, 42, 342, 346, -101]]\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 9x9 matrix:\n[[-140, -100, 276, 0, -16, 71, 198, -112, 206],\n [-75, 19, -115, -10, 179, -119, -24, -61, -13],\n [-428, -303, 18, -359, -47, 5, -358, 79, 132],\n [-378, -281, 239, -159, 76, -152, -189, -128, 131],\n [-523, -151, -181, -143, 113, -63, 237, -26, 416],\n [-261, -256, -150, -83, -197, 270, -8, -202, 205],\n [-753, -340, -72, 7, 389, -526, 67, -421, 346],\n [222, 23, 910, -77, 53, -57, -123, 118, -141],\n [156, 175, 419, -96, 240, -179, -54, 229, -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[[76, 55, 23, 35, -26, -173, -118, -1, 131],\n [-225, -68, 138, -350, -172, -249, -41, 192, -91],\n [121, 90, 40, 77, -18, -257, -184, -10, 192],\n [22, 27, 43, -196, -228, -383, -169, 107, 228],\n [-86, -12, 68, 49, 134, 94, 37, -4, -183],\n [307, 118, -120, 217, -42, -131, -146, -118, 374],\n [33, 127, 205, 168, 172, -324, -264, 3, 11],\n [-56, 10, 82, 0, 56, -62, -42, 26, -76],\n [-84, 20, 132, 14, 100, -96, -70, 36, -122]]\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[[100, 362, 112, 289, 17, -515, -139, 375, -104],\n [253, -245, -284, -70, 227, 151, -36, -301, 246],\n [65, -227, -150, -172, 103, 305, 20, -239, 130],\n [60, -147, -99, -231, 138, 375, -42, -111, 78],\n [-100, 515, 337, 52, -35, -190, -199, 666, -314],\n [-449, 164, 373, -80, -352, 97, 131, 249, -320],\n [-334, -23, 199, -61, -284, 107, 174, -7, -162],\n [-7, -218, -129, 197, -131, -244, 194, -362, 136],\n [66, -357, -223, -147, 72, 297, 98, -421, 202]]\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[[-45, -107, 232, -97, 227, -133, -184, -115, 132],\n [127, -197, 286, -236, 265, -192, 52, 80, 6],\n [196, 504, -475, 129, -220, 113, 562, 258, -171],\n [-69, 377, -169, 108, 24, 31, 62, -77, 66],\n [421, -180, -146, 125, 199, -320, -259, 15, 417],\n [196, 1103, 112, -260, 447, -210, 329, 109, -708],\n [-336, -384, -83, -37, -115, 450, 274, 200, 72],\n [214, -632, -348, 434, -380, -72, -540, -149, 612],\n [10, -62, 81, -26, 334, -86, -248, -53, 201]]?\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[[-182, 63, -115, 184, -58, -66, 118, 133, 215],\n [-325, 211, -363, 270, 174, 118, -305, -200, -112],\n [-472, 444, -273, 144, -97, -434, 273, -104, 204],\n [478, -456, 497, -279, -138, -260, 444, 90, 405],\n [431, -382, 404, -288, -111, -165, 308, 95, 235],\n [-113, 154, -86, 169, 260, 209, -379, -445, -266],\n [250, -318, 194, -140, -117, -147, 273, 204, 304],\n [653, -586, 537, -292, 77, 98, 28, -123, 77],\n [-179, 105, -137, 431, 304, 499, -527, -292, -237]]?\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[[-17, 423, -357, 89, -476, -350, -86, -201, -208],\n [122, -313, 107, 25, 392, 283, 124, 170, -12],\n [-208, 556, 312, 179, 143, -257, 199, -330, 114],\n [-117, -313, -213, 413, -173, -221, 304, -166, 236],\n [177, -100, -61, 28, -171, -240, -363, 24, 193],\n [489, -249, -328, 165, -133, -23, -59, 246, -141],\n [420, -85, -42, 764, -32, -608, 241, -187, 437],\n [117, -263, 96, 29, -75, -174, -351, 76, 361],\n [-205, 191, 58, 457, -142, -557, 265, -471, 413]]\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 9x9 matrix:\n[[-12, -78, -36, -66, 144, 138, 30, -42, 90],\n [38, -122, -183, -169, 246, 301, -59, -119, 138],\n [-124, -27, 255, 116, 6, -132, 234, 98, 37],\n [-110, -182, 99, -59, 306, 199, 223, -21, 214],\n [200, 111, -357, -118, -138, 78, -384, -112, -137],\n [102, 89, -156, -27, -132, -25, -199, -35, -107],\n [124, 150, -156, 10, -240, -114, -246, -14, -178],\n [190, 169, -288, -47, -252, -53, -371, -63, -203],\n [90, 216, -27, 117, -378, -297, -189, 63, -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[[-195, -123, 19, 180, 334, 175, 256, 312, 587],\n [33, -86, 269, -66, -43, 61, 136, 104, 272],\n [291, 90, 131, -270, -493, -256, -304, -405, -695],\n [19, -234, 120, 78, -117, -369, -155, -232, -245],\n [85, -231, 74, 120, 142, -86, -121, -47, 55],\n [0, -211, 201, 78, 127, 11, 83, 107, 327],\n [-181, 215, -133, -36, 6, 160, 210, 165, 138],\n [-21, 272, -281, -66, -43, 102, -48, -31, -247],\n [232, -374, 612, -108, -274, -284, -64, -168, 34]]?\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, 346, 372, -523, 26, 326, 74, 158, -176],\n [-5, 99, 31, 358, 140, 161, 171, -243, 236],\n [-250, 65, -317, 448, 445, -70, 375, 81, 483],\n [-223, -364, -251, -62, 506, 216, 588, -474, -297],\n [336, 105, 160, -41, 73, 47, -544, -161, -385],\n [267, 269, -87, 389, 52, -126, -336, 218, 279],\n [148, 212, -21, -50, 12, 49, -355, 44, 26],\n [-177, -456, -171, 2, -160, -391, -2, 91, 296],\n [205, -350, -141, 8, -428, -320, 65, 254, 37]]\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[[745, 50, 383, 130, -374, 53, 202, -32, 19],\n [-225, -276, -171, 115, 608, -104, -476, -124, 221],\n [336, -83, 120, -186, 85, 2, -410, 279, 245],\n [-186, -72, 31, 122, 151, 237, -83, 21, 179],\n [-231, -168, -130, 449, 286, 24, 144, -726, 33],\n [949, 319, 383, 4, -672, 206, 217, -8, 117],\n [42, 503, 263, -105, -417, 109, 430, 185, -75],\n [568, -1, 483, 123, -397, 432, 203, -81, 267],\n [-44, 212, -267, 307, 473, -402, -202, -362, -6]]\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[[-146, 674, 85, -93, 124, -341, 414, 483, -63],\n [524, 303, 245, -474, 189, 324, 48, 146, -309],\n [475, -163, 157, -351, 7, -117, 245, 118, -524],\n [18, -35, 233, 167, 575, 37, -122, -370, 19],\n [327, -134, 255, -248, 177, 232, 465, 206, -300],\n [-360, 224, 558, -278, 265, -249, -168, -70, -66],\n [-257, -647, -252, 422, -233, 181, 139, -102, 127],\n [56, -132, -87, -381, -685, 557, -46, 324, 75],\n [200, -161, 384, -393, 281, -115, 357, 40, -368]]?\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[[240, 32, -94, -231, -134, -275, -141, 24, -107],\n [624, -35, 322, -138, 443, -332, -72, -288, 91],\n [-198, 370, -150, 5, -408, 6, 52, 244, 21],\n [391, -185, -395, -193, 674, 134, -335, 211, -361],\n [184, 78, -503, -122, 283, -164, 166, 276, -389],\n [-321, 209, -173, 0, -498, -128, 177, 239, 40],\n [279, 102, -20, -133, 26, -5, -211, -74, -149],\n [0, 333, -37, -497, -536, -44, -883, 532, 302],\n [-222, 56, 261, 23, -725, 153, -292, -187, 184]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[163, -571, 184, -36, -6, 43, -61, -29, -87],\n [37, 279, 118, -273, 343, -383, 152, 91, -407],\n [-421, 112, 714, -123, 226, 408, -358, 56, 51],\n [98, 403, -356, -68, 225, -206, -366, -93, 356],\n [37, -321, -187, -303, 68, -12, -159, -355, 227],\n [509, 86, -307, 187, 77, -572, 207, 284, -295],\n [-363, -194, 140, -432, -54, 113, 324, -366, 241],\n [-308, -138, -97, -373, -74, 175, 98, -442, 328],\n [-103, -249, -21, 103, -260, 305, 25, -103, 93]]?\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[[-210, -58, 139, -130, -44, -13, 305, -51, -135],\n [-611, -315, -54, -171, 193, -298, 357, -67, -166],\n [196, -76, 127, -45, -219, 232, 115, -236, -169],\n [-516, -104, 71, -73, 283, -240, 269, -66, 3],\n [71, 27, 339, -110, -220, 262, 354, -250, -220],\n [-618, -286, -338, -8, 429, -475, 32, 86, -144],\n [-252, -66, 45, 194, 175, -43, -12, -403, 308],\n [-65, 169, -292, 221, 372, -256, -380, 282, 52],\n [290, -214, -257, -12, -162, 41, -287, 21, 87]]\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[[-125, 139, -429, 182, -125, 208, 88, -163, -110],\n [54, -12, 156, -467, 193, -186, -585, -380, 87],\n [-28, 15, -525, 212, 177, -43, -3, -324, 442],\n [-287, 52, -363, 139, -45, -100, 99, -90, -107],\n [-197, -96, -614, 147, 121, -201, 146, -97, -65],\n [-86, 141, 205, -148, -270, 236, -91, -153, 24],\n [88, -479, -174, -377, -111, 30, 308, -169, 607],\n [-153, 106, 76, 320, -62, -58, 228, 240, -50],\n [92, -273, 151, -426, 261, -382, -258, 31, -160]]\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[[-256, -138, 85, -379, -527, -276, 413, 93, -126],\n [430, -64, 141, 519, 179, 76, -297, -193, -399],\n [343, 280, -80, 60, -194, 238, 9, -383, 548],\n [-354, -640, 134, -436, -587, -85, 20, 108, -299],\n [-270, -411, 466, -200, 921, 224, -11, -449, -150],\n [-15, -510, -1, 408, -182, -151, -48, 210, -836],\n [-90, -91, -84, -348, 7, 320, -53, -157, 421],\n [-97, -385, 225, -424, 381, 357, -38, -549, 242],\n [-198, 23, 418, -310, 67, -320, 81, -193, 127]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-120, 117, 172, -62, -101, -126, -87, 84, -28],\n [-168, 216, 322, -110, -66, -246, -116, 106, -16],\n [-144, -45, -82, 8, -389, 96, -125, 142, -116],\n [120, -207, -312, 102, -29, 246, 77, -64, -12],\n [-192, -18, -44, -8, -458, 72, -162, 180, -136],\n [144, -207, -310, 104, 25, 240, 97, -86, 4],\n [-156, 45, 57, -33, -286, -21, -125, 133, -84],\n [-120, 0, -10, -10, -270, 30, -100, 110, -80],\n [-96, 63, 90, -36, -125, -60, -73, 74, -36]]\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[[-344, -144, 234, -370, 234, -252, -202, -316, -58],\n [10, -70, 45, 5, -10, 70, 105, -10, 120],\n [-440, -284, 369, -481, 295, -238, -125, -430, 85],\n [50, -2, -18, 52, -35, 56, 60, 40, 45],\n [148, 240, -225, 173, -93, -42, -151, 182, -259],\n [-140, -64, 99, -151, 95, -98, -75, -130, -15],\n [-40, -68, 63, -47, 25, 14, 45, -50, 75],\n [102, -134, 54, 96, -77, 224, 296, 48, 299],\n [-310, -150, 225, -335, 210, -210, -155, -290, -20]]?\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[[-50, 30, 175, 350, -105, 310, 205, 75, 20],\n [-97, -39, -79, 4, 96, 2, 44, -30, -80],\n [-40, -48, -170, -220, 138, -196, -98, -70, -72],\n [-238, -66, -66, 216, 144, 188, 216, -20, -160],\n [73, -33, -209, -436, 120, -386, -260, -90, -16],\n [-44, -60, -218, -292, 174, -260, -134, -90, -88],\n [-176, -24, 58, 332, 30, 292, 250, 30, -88],\n [104, 60, 163, 122, -159, 110, 19, 65, 108],\n [-245, -87, -150, 90, 207, 76, 153, -55, -188]]\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 9x9 matrix:\n[[12, -204, -600, -192, 148, 224, 290, -298, -264],\n [-186, 43, 678, 169, -156, -101, -98, 394, 293],\n [-62, -100, 164, -70, -78, -4, 70, 172, -28],\n [-144, 55, 318, 175, -26, -3, -45, 129, 239],\n [178, 60, -160, -90, -6, -90, -97, -79, -146],\n [-106, -26, -416, 112, 218, 242, 168, -354, 70],\n [462, 239, -138, -163, -92, -341, -380, -56, -275],\n [-210, -381, 90, -243, -92, 161, 377, 257, -165],\n [-38, 117, 14, 171, 68, 19, -75, -99, 169]]\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 9x9 matrix:\n[[-153, 144, -108, -27, 27, 81, 117, -108, 27],\n [-289, 272, -204, -51, 51, 153, 221, -204, 51],\n [187, -176, 132, 33, -33, -99, -143, 132, -33],\n [-85, 80, -60, -15, 15, 45, 65, -60, 15],\n [-255, 240, -180, -45, 45, 135, 195, -180, 45],\n [68, -64, 48, 12, -12, -36, -52, 48, -12],\n [-68, 64, -48, -12, 12, 36, 52, -48, 12],\n [-136, 128, -96, -24, 24, 72, 104, -96, 24],\n [85, -80, 60, 15, -15, -45, -65, 60, -15]]\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[[-375, 213, 466, -225, 20, 84, 307, -340, -205],\n [216, 17, 315, 132, 27, 301, 304, -229, 65],\n [-113, 209, 456, -115, -31, 105, 31, -177, -447],\n [243, 106, -576, -110, 90, -344, -51, -41, 22],\n [21, -202, 731, 307, -72, 594, 229, -26, 132],\n [-322, -97, -436, 238, 718, -634, 300, -570, 236],\n [71, 410, -242, -271, -114, -217, -251, -66, -373],\n [114, -148, -289, 242, 143, -170, -218, 107, 85],\n [40, -52, 205, -377, -284, 215, 248, 197, -14]]\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[[-298, 353, -395, 84, -291, -443, -52, -16, 376],\n [199, -313, 156, -526, -609, 67, -75, 158, 19],\n [-450, 30, -325, 98, -467, -327, -517, 108, 8],\n [-146, 125, -655, 2, -69, -555, -156, 462, 504],\n [161, -15, -178, -4, 146, 279, 53, -208, -369],\n [-317, 293, -340, -28, -537, -554, -40, 106, 538],\n [121, 199, 302, 118, 392, 55, 216, -154, -102],\n [-115, 314, -114, 451, 345, 49, 152, -323, -419],\n [127, -21, -387, -148, 68, -205, -139, 324, 60]]\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[[-77, 180, -56, 404, -238, -287, -264, 117, -161],\n [232, -21, -179, 39, -23, -28, -2, 530, -371],\n [-383, 392, 454, -57, 379, 105, -339, -54, 298],\n [571, -176, -124, -303, -398, -116, 438, 126, 3],\n [284, -216, -116, -55, -223, 497, -219, -410, 29],\n [-429, -137, 16, 10, 205, 151, 275, -378, -345],\n [-169, 318, 281, 83, -136, -46, -191, -141, -164],\n [-381, 497, 399, -50, 287, -50, -346, 260, -408],\n [44, 149, 325, -576, 333, 555, -24, 155, -529]]\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 9x9 matrix:\n[[-30, -151, 273, 206, -99, 55, 18, 153, 254],\n [-456, -121, -101, 340, -75, 102, -310, -29, 317],\n [-482, -178, 104, 320, -84, 3, -26, 220, 561],\n [112, 61, 20, 320, 20, 126, -118, -178, 43],\n [-344, -261, 65, -163, 48, 102, -167, -11, 176],\n [198, 366, -398, 203, -47, -88, -77, -168, -333],\n [-386, 278, -447, 170, 25, -257, 164, 115, 215],\n [10, 156, -233, -250, 231, -49, 104, -195, -135],\n [-100, -12, 131, -57, 184, -64, 333, 89, 337]]\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[[118, 404, -161, -137, 346, -353, 11, -282, -159],\n [230, -216, 337, 36, 206, 105, -31, -94, -288],\n [-125, -475, 268, -223, -317, 466, -69, 199, -262],\n [-43, -175, 192, -407, -53, 206, -98, -38, -527],\n [116, 92, 287, 177, -223, 82, -37, -162, 112],\n [-211, 35, -24, 53, -374, 47, -76, 128, 114],\n [-304, -16, -227, -147, -392, 143, 12, 201, 212],\n [-123, 179, -255, -187, 108, -200, -22, 3, -133],\n [240, 156, 244, -367, 204, 24, -22, -406, -455]]\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 9x9 matrix:\n[[46, 84, 160, 214, 298, -204, -278, -204, 254],\n [-88, -152, 320, 8, -44, -88, 84, 12, -12],\n [126, 218, -432, 6, 85, 106, -139, -33, 37],\n [144, 252, -288, 144, 270, -36, -306, -162, 198],\n [63, 106, -432, -141, -139, 218, 85, 114, -145],\n [-162, -288, 0, -378, -576, 288, 576, 378, -468],\n [63, 112, 0, 147, 224, -112, -224, -147, 182],\n [54, 90, -432, -162, -171, 234, 117, 135, -171],\n [156, 276, -96, 300, 474, -204, -486, -306, 378]]\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, 248, 147, -151, -312, -140, -131, -20, -192],\n [298, -187, 21, -145, -302, 44, -100, -77, -25],\n [-340, -170, 61, 300, 523, 268, 407, 282, 209],\n [79, 365, -285, -154, -141, -416, -434, -359, -144],\n [-79, 355, 88, 52, 64, 36, -131, 95, -221],\n [192, -588, 114, 114, 94, 484, 292, 222, 194],\n [-101, -310, 217, -151, -316, -144, 379, 40, 222],\n [-175, 67, -252, 29, 188, -270, -24, -188, 135],\n [-505, 229, 224, -39, -56, -350, 342, 90, 85]]\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[[443, -4, 167, -48, -376, 133, 331, -233, 161],\n [-520, 23, -46, 417, 124, 123, -304, 487, 221],\n [-102, 66, 191, -68, -548, -131, 483, -84, -1],\n [71, -306, 227, 832, 337, 349, -549, 517, 230],\n [-60, 494, 482, -138, -47, -498, -75, -43, -80],\n [-50, -187, 502, 576, 335, 204, -27, 514, 520],\n [28, 137, -136, -22, -27, -531, -69, 304, 155],\n [554, 103, 81, 454, -389, 342, 162, 257, 454],\n [-388, 452, 299, -332, -173, -588, 27, -128, -195]]\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[[-276, 230, -214, -154, -174, -98, 86, 286, 38],\n [-50, -45, -35, -205, 25, 191, 51, -65, -125],\n [-328, 105, -247, -527, -97, 289, 171, 113, -211],\n [277, -75, 208, 473, 73, -277, -150, -77, 199],\n [258, -145, 197, 287, 117, -77, -109, -173, 71],\n [-229, 155, -176, -201, -121, 5, 86, 189, -23],\n [-134, 160, -106, 24, -116, -164, 22, 204, 92],\n [111, -160, 89, -76, 114, 202, -7, -206, -118],\n [-330, 140, -250, -460, -120, 208, 158, 160, -160]]\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[[-60, 149, -646, 486, -477, 193, 267, 36, 445],\n [145, 327, 279, 59, -167, -5, -113, -142, 68],\n [216, -161, 107, -111, 148, 465, -193, -83, 192],\n [-95, 25, -668, -356, -592, 401, 66, 355, 28],\n [0, -314, -35, 133, -109, 324, 209, -333, 206],\n [192, 67, 155, 207, -172, 342, -12, -322, 325],\n [98, -292, -10, -54, -96, 494, 150, -350, 176],\n [-367, -233, 145, 405, 283, -807, 503, -302, -302],\n [-19, -221, 18, 326, -36, 127, 218, -339, 230]]\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 9x9 matrix:\n[[-200, 739, -11, 406, 573, -724, 519, -301, -308],\n [66, 357, 361, -56, 157, -566, 191, 115, -139],\n [426, 144, 8, 273, -150, 42, 43, 250, -127],\n [-34, -348, 264, -312, -190, 170, -217, 183, 180],\n [30, 316, -38, 221, 214, -236, 244, -75, -159],\n [349, 181, 60, 25, -146, -170, -3, 197, -113],\n [-76, 331, -115, 368, 281, -188, 273, -165, -156],\n [575, -58, 257, -4, -429, 70, -192, 505, -22],\n [4, -79, 175, -441, -105, -182, -129, 70, 62]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[235, -142, 140, -95, 219, -93, 139, -196, 252],\n [-409, 322, -135, 107, -168, 231, -122, 96, -380],\n [-209, -365, -152, -454, 256, -373, 169, -134, -45],\n [-16, 327, 46, 63, 109, 170, 144, -278, -151],\n [-205, -33, -128, 138, -340, 61, -295, 434, -113],\n [252, -288, -37, -186, 105, -321, 155, -76, 136],\n [50, -101, -43, -73, 14, -122, 43, -2, 9],\n [302, -88, 32, 190, -222, -30, -122, 240, 164],\n [-30, 416, 8, 298, -194, 302, -78, 32, -204]]?\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 9x9 matrix:\n[[-204, -192, -120, 60, -84, 180, 180, 48, 0],\n [153, 144, 90, -45, 63, -135, -135, -36, 0],\n [-272, -256, -160, 80, -112, 240, 240, 64, 0],\n [-170, -160, -100, 50, -70, 150, 150, 40, 0],\n [-306, -288, -180, 90, -126, 270, 270, 72, 0],\n [289, 272, 170, -85, 119, -255, -255, -68, 0],\n [306, 288, 180, -90, 126, -270, -270, -72, 0],\n [-221, -208, -130, 65, -91, 195, 195, 52, 0],\n [-85, -80, -50, 25, -35, 75, 75, 20, 0]]\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[[-270, 39, -40, -434, 413, 60, -264, 45, -37],\n [44, -173, 253, 218, -360, -240, 169, -149, 335],\n [-181, 281, -99, -263, 142, 163, -113, 108, -69],\n [-156, -732, -275, -136, 283, 137, -189, 54, -41],\n [90, -284, -82, -154, 28, -131, 96, 170, 61],\n [654, 291, 142, 138, -415, -471, 576, 277, 42],\n [-109, -141, -195, -11, -154, 182, 37, 118, 54],\n [159, 236, 38, 334, -647, -3, 360, 62, 185],\n [-445, 230, -213, -61, -493, 434, 43, 139, 269]]\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[[-126, -46, 314, 6, -152, -144, 2, 162, 154],\n [233, 17, -151, -110, 62, -40, -126, -156, 80],\n [226, -67, 10, -79, 9, -112, -204, -183, 177],\n [-237, -50, 259, 105, -109, -24, 88, 171, -1],\n [-10, 36, -158, 31, 76, 112, 59, -33, -137],\n [-190, 15, 42, 91, -17, 80, 136, 123, -125],\n [351, -62, -45, -144, 29, -152, -279, -258, 242],\n [69, -152, 37, 105, 47, 24, -152, -225, 11],\n [-63, 143, -15, -108, -56, -40, 138, 222, 10]]\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[[158, -173, -96, -240, -77, 248, -120, 82, 22],\n [214, 228, 85, 313, -126, -86, 203, -205, 58],\n [-733, 253, 115, -368, -81, -193, 180, -204, 261],\n [-229, 208, 462, -321, -68, -19, 33, -485, -143],\n [-331, -214, 115, -806, 102, 305, -209, -52, 2],\n [234, 301, -164, 982, -215, -480, 251, 90, -1],\n [61, -242, 9, -150, 211, 128, -220, 141, -194],\n [-404, 139, 378, -768, -85, 198, 48, -478, 108],\n [-204, 50, 225, -51, 62, -138, -72, -129, -217]]\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[[235, 58, 32, 337, -142, -38, -209, -129, -54],\n [-388, 7, 114, -154, 40, -21, -29, -63, 253],\n [39, -302, 19, -287, -220, -34, -209, -49, -129],\n [110, -8, -64, 75, 403, -58, 411, -123, 301],\n [94, -512, -297, -585, -121, 192, 454, 39, 78],\n [-231, 54, -48, -452, 2, -72, -119, 456, -564],\n [-511, 386, 43, 373, -136, -22, -107, -105, 363],\n [52, -302, 310, -116, 30, -44, -253, -344, 272],\n [399, -108, -50, 79, -110, -16, -119, 11, -290]]\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[[245, 198, -63, -174, -67, -102, -210, 177, 196],\n [-137, -159, 69, 141, 129, -113, -6, 57, 317],\n [335, 282, -147, -369, -134, -125, -84, 78, -173],\n [210, 258, -18, -6, -186, 270, -276, 102, 18],\n [-14, -55, 30, 40, 85, -150, -86, 121, 348],\n [-175, -161, 21, 56, 70, -14, 224, -154, -210],\n [-51, 1, 9, 56, -56, 182, 68, -112, -250],\n [217, 254, -9, 7, -168, 235, -320, 148, 135],\n [-146, -221, 36, 29, 206, -337, 104, 50, 319]]\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[[173, -501, -49, -52, -195, -80, -122, 45, 197],\n [82, -875, -149, 364, 168, -169, -647, -196, 607],\n [-17, -496, -169, 440, 37, 104, -285, -25, 505],\n [54, 519, 62, -125, 27, -26, 110, -36, -291],\n [49, -29, 123, 611, -271, 215, 43, -41, 461],\n [-522, 207, -421, 91, 334, -40, 170, 116, -337],\n [461, -28, 441, 84, -843, -58, 364, -103, 102],\n [-311, 23, -314, -220, 55, -75, 351, 81, -463],\n [-107, -263, -197, 279, 211, 201, -241, 74, 361]]\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[[-260, -231, -107, 57, -170, 98, 112, -22, 213],\n [36, -126, 138, 26, 48, 320, -44, -380, -38],\n [-88, 36, -340, -206, -7, -109, 31, 252, -16],\n [-32, -107, 137, 107, -37, 137, 11, -186, 61],\n [-203, -50, 26, 214, -220, -296, 138, 316, 266],\n [29, 77, 13, 21, -2, -138, 2, 130, -3],\n [-214, -15, -379, -135, -118, -218, 104, 394, 117],\n [-6, -45, 111, 87, -24, 48, 6, -90, 39],\n [435, 227, 203, -155, 341, 219, -229, -358, -409]]\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 9x9 matrix:\n[[100, -200, 300, -100, -170, -210, 75, -360, -345],\n [389, 223, -65, -235, -207, 7, 388, 78, -137],\n [47, 309, -355, 15, 103, 233, 74, 426, 323],\n [-1, -167, 205, -25, -75, -137, -17, -246, -200],\n [-124, 92, -180, 100, 140, 132, -108, 216, 240],\n [-380, -280, 140, 220, 174, -58, -385, -168, 59],\n [191, -83, 205, -145, -189, -155, 172, -246, -299],\n [-118, 54, -130, 90, 118, 98, -106, 156, 188],\n [147, 109, -55, -85, -67, 23, 149, 66, -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[[-157, 72, -103, 37, 506, 181, -489, 338, -59],\n [-428, -428, 92, -196, 20, 336, -50, -138, 98],\n [82, 52, -162, 278, 200, -286, 52, 50, 156],\n [395, 448, -93, 157, 68, -239, -91, 226, -205],\n [-45, -378, -211, 339, 90, -293, 270, -161, -232],\n [133, 380, -96, 92, 366, -23, -382, 362, 11],\n [-189, -496, 181, -210, -551, 113, 489, -490, -42],\n [207, 384, -39, 48, 155, -67, -215, 246, 16],\n [-172, 8, 12, -53, 205, 136, -202, 100, 279]]?\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[[224, 26, 189, 472, 122, 131, 521, -185, -129],\n [68, -548, 58, -65, 9, -30, -541, 242, -299],\n [-111, 549, -241, 59, -441, -49, 572, 210, 233],\n [310, -39, -19, -143, -126, -47, 191, -106, 158],\n [-182, -163, 33, 68, -88, -51, -174, 207, -364],\n [-113, 484, -130, -253, -57, -198, -14, 519, 401],\n [-283, -29, 204, -300, 279, -154, -210, -257, -452],\n [-179, -39, 250, -218, 213, -264, -276, 30, -304],\n [73, -395, -88, -1, 3, 122, -461, 77, 64]]?\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[[-147, -380, 0, -108, -171, -38, -44, 211, 214],\n [38, -132, -230, 281, 508, -260, -178, -233, 545],\n [103, -146, -211, 146, 144, -289, -142, -257, 505],\n [-149, 700, 584, -18, 54, 209, 453, 455, -160],\n [-91, 173, 416, 7, 467, 338, 366, 812, -53],\n [-233, 358, 232, 51, 237, 339, 114, 166, -460],\n [-197, -125, -71, -39, -13, 333, -123, 14, -389],\n [416, -375, -250, -209, -390, 16, -40, 13, -21],\n [328, -229, -345, -97, -374, -177, -191, -425, -57]]\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[[386, 92, -190, -184, 446, 193, 248, -53, 393],\n [273, 3, -66, 219, -281, -342, 147, -180, -421],\n [32, 50, 164, -227, 32, 157, -118, 165, 51],\n [227, 214, 150, -618, 467, 252, 424, 143, 372],\n [153, 440, -412, 543, -297, 27, 42, -82, 303],\n [18, 156, 13, -303, 245, 271, 118, 80, 334],\n [-4, -5, -202, -109, -114, -29, 213, -408, -276],\n [193, 303, 191, -297, 206, 48, 381, 257, 294],\n [-282, -344, -99, 284, -415, -276, -238, -363, -651]]\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 9x9 matrix:\n[[-696, 583, -429, -39, 87, 52, -594, 478, -170],\n [-2, 210, 337, -249, -212, 12, 25, 328, 5],\n [325, 4, 97, 140, -323, 56, 59, 59, 91],\n [383, -936, 215, -41, 311, 282, 774, -585, 697],\n [114, 68, -357, 431, -128, 69, -214, -9, 46],\n [-227, 98, -104, -52, 13, 35, 63, 115, -223],\n [223, -404, 7, -193, -231, 405, 204, -145, 790],\n [-169, 104, -34, -536, -267, -35, -124, -56, -143],\n [-147, -35, 18, -398, -62, -112, 151, -166, -379]]\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[[-196, -238, -14, 210, -56, -140, -182, -252, -252],\n [-268, -19, -167, 180, -173, 100, 79, -171, 129],\n [94, 298, -82, -165, -31, 242, 284, 225, 405],\n [-190, -6, -122, 125, -125, 78, 64, -117, 103],\n [306, 106, 150, -235, 171, -34, 0, 243, -17],\n [-188, -310, 26, 230, -28, -212, -262, -288, -368],\n [200, 202, 34, -200, 70, 104, 142, 234, 194],\n [510, 272, 204, -425, 255, 34, 102, 459, 119],\n [-144, 152, -168, 40, -144, 208, 216, 0, 320]]\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[[-289, 154, 231, -104, -137, -155, 114, 188, 237],\n [95, -108, -75, 6, -341, -129, 284, 164, 51],\n [103, 18, 17, -193, 459, 482, -374, -577, -5],\n [-17, -42, -59, 163, -293, -314, 238, 375, -49],\n [132, -10, -176, 261, 524, 123, -442, -169, -412],\n [-123, 16, -27, 265, -291, -470, 232, 555, -93],\n [-158, 136, 120, -17, 278, 67, -232, -89, 0],\n [184, -38, -144, 85, 488, 295, -406, -365, -276],\n [-62, 1, 89, -141, -276, -57, 233, 80, 217]]\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[[-84, 112, -112, 182, -224, -238, 154, -238, 140],\n [72, -96, 96, -156, 192, 204, -132, 204, -120],\n [-12, 16, -16, 26, -32, -34, 22, -34, 20],\n [42, -56, 56, -91, 112, 119, -77, 119, -70],\n [-12, 16, -16, 26, -32, -34, 22, -34, 20],\n [-24, 32, -32, 52, -64, -68, 44, -68, 40],\n [78, -104, 104, -169, 208, 221, -143, 221, -130],\n [30, -40, 40, -65, 80, 85, -55, 85, -50],\n [-78, 104, -104, 169, -208, -221, 143, -221, 130]]\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[[27, 60, 95, -11, 42, -15, 37, -63, -113],\n [-97, 256, 184, -148, 545, -135, -104, -396, -48],\n [-27, 6, 43, -226, -351, -25, 129, 81, -164],\n [223, 229, 321, 364, 175, 60, 72, -155, -162],\n [291, 245, 291, 606, 49, 144, 62, -57, 38],\n [-151, 140, 130, -367, 40, -131, 160, -174, -271],\n [-368, 86, -314, 352, 230, 42, 360, 32, 539],\n [4, 302, 110, 383, -63, 80, 150, -44, 316],\n [-245, 382, 290, -667, 424, -283, -82, -536, -240]]?\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[[-80, 34, 154, 224, 107, -72, -278, -214, -32],\n [164, -56, 410, 414, 363, 902, -14, 729, -395],\n [-87, -306, -239, -221, -150, -78, -325, -103, 88],\n [198, -287, -364, -24, 50, 323, 37, 641, 38],\n [35, 13, -298, -246, -400, -532, -203, -118, 51],\n [-70, -193, 16, 324, -5, 186, 57, 68, 110],\n [122, -152, -71, -136, 515, 514, -309, 421, -396],\n [-6, -310, -104, -199, 102, 346, -236, 200, -69],\n [64, 160, -382, -173, 88, -484, -28, -130, -127]]?\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[[-325, 356, 34, -260, -455, 646, 216, -248, 122],\n [314, -202, -132, -39, 89, -390, 53, -15, -640],\n [176, -302, 69, -51, -36, 56, -198, 136, -476],\n [505, -240, 63, -2, 366, -494, 185, -91, -122],\n [37, 121, -36, 113, -2, -71, 385, -122, -532],\n [-736, 523, 88, 479, 389, 190, -315, 32, 105],\n [274, -413, 183, -18, -355, 451, 117, 274, -32],\n [-171, -222, -192, 52, -217, 70, 74, 439, 16],\n [92, -236, -159, -242, -61, -243, 32, 179, 577]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-159, -232, -203, 264, 199, -373, -141, -257, 130],\n [-15, -145, 382, -143, 5, 168, -4, 217, -304],\n [-293, 47, -596, 622, 121, -170, 374, -50, 98],\n [-159, 9, 96, 137, 209, -18, 98, -129, -20],\n [199, 543, -57, -184, -31, 168, 278, -333, 600],\n [39, 301, -307, 94, -14, -18, 166, -205, 351],\n [-174, 9, -3, 237, 164, 17, 325, -54, 66],\n [-87, -62, -178, 105, 171, -329, -419, -313, 12],\n [-375, -253, -128, 530, 379, -288, 292, -230, 122]]\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[[-131, 240, 210, -149, -125, -14, 3, 235, 165],\n [-60, -24, 30, -48, 72, -36, 66, 36, -42],\n [-118, 56, 110, -110, 42, -48, 80, 126, 8],\n [-160, -64, 80, -128, 192, -96, 176, 96, -112],\n [118, -56, -110, 110, -42, 48, -80, -126, -8],\n [88, -240, -180, 112, 160, -8, 36, -200, -180],\n [69, -24, -60, 63, -33, 30, -51, -69, 3],\n [13, -184, -100, 39, 167, -34, 77, -109, -157],\n [-42, -120, -30, -18, 150, -48, 96, -30, -120]]\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[[-24, -177, 92, 17, -135, 251, 337, 536, 100],\n [46, -4, 118, 618, -313, 385, 94, -590, -747],\n [238, 156, 430, 155, -293, -557, 155, 95, -25],\n [190, -213, 31, 227, -94, 36, 47, -106, -166],\n [304, 210, -28, 15, -20, -506, -90, -190, 158],\n [-228, -306, 430, 350, -173, 412, 627, 398, -149],\n [536, 469, 90, 237, -742, -296, 58, 169, -323],\n [-232, -104, 63, -238, 181, -256, -157, 228, 134],\n [165, -430, -476, -148, 468, 584, -108, -365, 311]]\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 9x9 matrix:\n[[30, -202, -529, -318, 107, 322, -537, 82, -193],\n [-54, 115, 418, 383, -177, -361, 350, 450, 439],\n [-137, 168, 257, -118, 119, -80, 327, 406, -294],\n [-148, 146, 387, 87, 43, -133, 441, 317, -187],\n [40, 64, 285, 277, -173, -211, 231, 95, 331],\n [-195, -113, -166, -2, 115, 56, -166, 493, -100],\n [-43, 137, 239, -429, 112, 223, 339, 681, -716],\n [163, -130, -216, -51, -170, 93, -322, 360, 280],\n [97, 214, 403, 219, -173, -353, 361, -26, 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 9x9 matrix:\n[[-15, -485, -127, 156, 93, 364, -138, -441, 396],\n [9, 667, -190, -743, 132, -894, 185, -279, -276],\n [303, 812, 86, -339, 74, -775, 60, -231, -290],\n [-148, 368, -227, -239, -120, -573, 31, -74, -240],\n [-189, -541, -127, 618, -289, 595, -273, -166, 207],\n [-276, 86, 273, 169, 181, -157, -184, 85, -27],\n [108, -79, 247, -166, 561, -69, -83, -185, 256],\n [-215, 5, -779, 611, -978, -72, -189, -317, -158],\n [597, -371, 252, 240, -283, 572, 35, 67, -21]]\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[[123, 187, -472, -303, 312, 35, 182, -263, -249],\n [-120, -133, 209, 257, -204, 154, 114, 106, 15],\n [61, -39, -404, -262, 225, 78, 83, -162, -225],\n [212, 193, -410, -299, 237, -117, 67, -219, -104],\n [-56, 171, 78, 434, -66, 212, 250, -196, 332],\n [-108, 215, -74, 159, 189, 215, 161, -239, 118],\n [271, 99, -129, -307, -51, -324, -7, 76, -204],\n [145, -295, -335, -361, 132, -155, -315, -9, -3],\n [-168, 465, 198, -50, 294, -24, -62, -72, -24]]\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[[-236, -214, -30, -46, -60, 12, 34, -96, 222],\n [-132, -233, 37, -158, 2, -91, 192, 14, 118],\n [-128, 159, -243, -59, -25, -53, -34, -70, -47],\n [95, -76, -102, -74, 485, -431, 191, 317, -357],\n [137, 383, 5, 414, -244, 435, -526, -223, 53],\n [-220, -97, -281, -220, 239, -358, 215, 98, -116],\n [-694, 158, -746, -164, -118, -124, -114, -334, 170],\n [118, 78, 12, 403, 188, 97, -367, 26, -83],\n [-149, -38, -256, -158, 247, -323, 157, 109, -157]]?\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[[34, 17, -17, -51, 153, -119, -221, 85, -221],\n [-16, -8, 8, 24, -72, 56, 104, -40, 104],\n [0, 0, 0, 0, 0, 0, 0, 0, 0],\n [-28, -14, 14, 42, -126, 98, 182, -70, 182],\n [-34, -17, 17, 51, -153, 119, 221, -85, 221],\n [12, 6, -6, -18, 54, -42, -78, 30, -78],\n [14, 7, -7, -21, 63, -49, -91, 35, -91],\n [22, 11, -11, -33, 99, -77, -143, 55, -143],\n [-4, -2, 2, 6, -18, 14, 26, -10, 26]]\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[[80, -69, 241, 130, -220, 99, 14, 20, -127],\n [161, 171, -216, 23, 88, -192, 132, 214, 213],\n [534, -9, -65, 236, 382, -258, 290, 388, -244],\n [-520, -68, -152, -342, -73, 311, -155, -556, 124],\n [-69, 148, -271, -121, 68, -86, 36, 2, 271],\n [188, -64, 404, 256, -438, 133, 56, 108, -145],\n [120, -70, -66, 16, 306, -80, 58, 48, -182],\n [-445, -101, -262, -361, 57, 347, -21, -618, 57],\n [-272, 284, 80, -38, -653, -7, -211, 76, 586]]\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[[667, -198, 286, -384, -318, 435, -566, 52, -271],\n [207, 79, 177, -375, 325, -54, 343, 534, 585],\n [7, -471, 250, -129, 29, 171, -329, 116, -82],\n [112, -156, -82, -50, 109, 177, -189, -21, -32],\n [139, 461, -177, 5, -30, -111, 298, -21, 135],\n [-418, 60, -265, 372, 34, -171, 110, -290, -137],\n [-34, 230, -292, 252, -169, -3, -47, -373, -278],\n [-70, 126, -47, 176, -263, -54, -57, -251, -271],\n [-51, -272, 308, -34, -222, 33, -238, 10, -209]]\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[[-85, 142, 661, -105, 294, 299, -23, -112, 500],\n [-92, 132, -160, 283, -304, 150, 412, -66, -640],\n [357, -323, 454, 17, 187, 67, -158, 39, 382],\n [-184, 239, 327, -376, 157, 174, 54, -3, 57],\n [-156, 207, -164, -220, -128, 476, 435, 310, -617],\n [-17, 56, 622, 322, 137, -45, -82, -441, 490],\n [-495, 519, 517, 417, 60, -99, 37, -734, 420],\n [-119, 132, 365, 128, 112, -121, -112, -342, 371],\n [134, -136, 461, -247, 409, 190, -301, 137, 772]]\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[[53, 305, -27, -36, -275, -62, -97, 255, -280],\n [219, 47, 311, -262, -140, 82, 407, 8, -139],\n [99, 41, 524, 144, 306, 293, 299, 151, -650],\n [290, -183, 527, -206, 280, 207, -167, 81, -421],\n [-190, 130, 84, -246, -201, 158, 197, -79, -63],\n [188, -161, 337, 124, -2, 161, -160, -47, -200],\n [133, 115, 296, 38, 228, 93, 636, 145, -359],\n [-197, 134, 221, -14, 145, 242, 297, 43, -369],\n [-96, 72, -9, 84, 440, 7, 210, 163, -226]]\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[[0, 160, 256, -192, 96, 128, 128, 288, -256],\n [0, -140, -224, 168, -84, -112, -112, -252, 224],\n [0, -50, -80, 60, -30, -40, -40, -90, 80],\n [0, -40, -64, 48, -24, -32, -32, -72, 64],\n [0, 130, 208, -156, 78, 104, 104, 234, -208],\n [0, -20, -32, 24, -12, -16, -16, -36, 32],\n [0, 140, 224, -168, 84, 112, 112, 252, -224],\n [0, 60, 96, -72, 36, 48, 48, 108, -96],\n [0, 60, 96, -72, 36, 48, 48, 108, -96]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-329, 353, 12, -620, -357, 580, -354, 344, 109],\n [-196, 224, 360, -49, -166, 404, 182, 156, 641],\n [160, -205, -90, 290, -303, -400, -9, -18, -563],\n [591, -298, 292, -320, 11, -120, 720, 272, 277],\n [118, 295, 174, -102, 152, 149, -204, -150, 80],\n [159, -18, 123, 322, 7, -246, -348, -320, -375],\n [-336, -268, -152, 164, -270, -24, 67, 161, 6],\n [62, -48, -216, -245, -107, 18, 141, 212, -78],\n [613, 68, 254, 262, 524, -302, 464, -317, 218]]\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[[61, -93, 37, 244, -27, 143, -93, 214, -217],\n [139, 73, 103, 200, -5, 61, -63, 114, -55],\n [-165, -235, -135, -13, -1, 112, -48, 109, -201],\n [-12, 211, -19, 28, 226, 170, -248, 109, 36],\n [-258, -56, -216, -80, 250, 278, -294, 182, -150],\n [-513, -100, -406, -469, 329, 190, -236, -30, 3],\n [0, -5, -5, 67, 34, 77, -73, 84, -66],\n [-97, -119, -69, -150, -65, -93, 119, -112, 25],\n [19, 41, 33, -231, -121, -282, 262, -305, 251]]?\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 9x9 matrix:\n[[45, 367, 39, -277, -279, -64, -72, 186, -305],\n [-37, 461, -293, -194, -262, 268, 329, -18, 28],\n [17, -119, 223, 153, 207, 199, -102, 82, 194],\n [60, 172, -210, -96, -200, -98, 172, -86, -108],\n [-29, -165, -320, 206, 106, 108, 345, -309, 317],\n [-99, -521, -100, 345, 359, 21, 94, -277, 369],\n [0, -368, 83, 115, 141, -313, -181, -75, -73],\n [120, -434, 382, 223, 265, -251, -361, 64, -28],\n [-20, -14, -401, -81, -195, -318, 227, -259, -152]]\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[[-84, 137, -282, -163, 80, -242, -15, 252, -121],\n [-448, 131, 176, -319, 108, -15, -310, -519, -207],\n [298, -449, -822, 668, -88, -168, -500, 216, -76],\n [-222, -72, -448, 64, -184, -210, -12, 804, -226],\n [116, -453, -97, 220, 449, 126, -570, -46, -391],\n [-711, 211, 152, -308, 80, 409, -58, -158, -361],\n [-432, 85, -56, 31, -163, 377, 64, 53, -141],\n [-176, -86, -99, -41, -80, -240, -223, 118, -134],\n [248, 177, 425, 7, -135, 116, 155, -940, 494]]\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[[-83, -279, -292, -284, 235, -219, -114, 181, 53],\n [-526, -153, 177, 511, 40, 38, 129, 137, -474],\n [-130, 308, 147, 380, -159, 514, 33, 359, 357],\n [-490, -129, -33, 350, 23, 451, -254, 400, 172],\n [-309, 0, 66, 162, -15, 115, 194, 125, -335],\n [259, 226, -76, -256, -107, -292, 187, 20, 72],\n [-420, -249, 48, 95, 205, 59, -41, 375, -288],\n [275, 439, 149, -479, -471, 296, 34, -323, -200],\n [26, -34, 92, -256, -112, 487, -229, -331, -169]]\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[[-283, -123, 33, -190, -142, 446, -176, 354, 54],\n [-126, 298, 116, 66, 220, -337, 181, 144, 491],\n [-305, -275, -264, 7, -177, -62, -92, -412, -339],\n [-54, 390, 98, -146, 0, -294, -64, -30, 482],\n [146, -195, -83, 72, -156, 107, 90, -35, -227],\n [-81, -145, 165, -157, 324, -61, 112, 293, 555],\n [389, -170, 11, -430, -133, -55, -493, -225, -108],\n [-406, 224, 47, -194, 40, -243, -294, 224, 326],\n [-431, -32, 92, 164, 392, 257, 146, 318, 71]]\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[[116, 600, 20, 508, -182, -367, 311, 321, -160],\n [-366, 253, -31, 578, -269, -605, 13, 1, 142],\n [48, 450, -211, -27, 21, 124, -398, 166, -460],\n [370, 3, 355, 148, -441, 586, 687, -293, -169],\n [255, 477, -45, -62, -144, 79, -216, 257, -516],\n [-532, -194, 133, -77, -191, -67, -394, 167, -220],\n [-11, 175, 153, -167, 93, -398, -285, 282, -121],\n [159, -265, 110, -289, 246, 127, -262, -449, 159],\n [227, -457, -208, -262, 434, -55, 163, 662, 202]]\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 9x9 matrix:\n[[-378, 413, 418, 553, -354, 387, 277, 247, 537],\n [259, 168, -128, -190, 108, -155, -306, -341, -325],\n [-37, 239, 73, -38, -268, 359, -50, -224, 182],\n [-40, -164, 348, -140, -197, -160, 350, 549, 381],\n [-46, 46, 88, -34, 259, -398, -88, 319, -25],\n [78, 533, -13, 30, -28, 93, -290, -346, -134],\n [269, -91, -44, 239, 326, -499, -259, -223, -493],\n [4, -251, 77, 78, 43, -50, -158, -138, 10],\n [144, 183, 428, 351, 17, -514, 75, 269, -33]]\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 9x9 matrix:\n[[-15, 158, 52, -312, 674, -440, -690, -153, -98],\n [-646, 258, 182, 202, -270, 200, -414, -43, 231],\n [-224, 4, 200, -37, -200, -136, -108, -277, 34],\n [-57, 235, 292, 252, -268, 367, 127, 133, 449],\n [104, 321, 276, 127, 276, 416, -573, 204, 148],\n [-442, -340, -68, -384, -389, -218, 465, -238, 168],\n [109, -295, -86, -263, 30, -120, 437, 208, 79],\n [23, -185, 114, -82, -116, -2, 143, 94, 1],\n [-162, 267, 180, 72, 29, -140, -22, -38, 392]]\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[[264, -14, -340, -140, -71, -85, -395, 332, 157],\n [-74, 527, -221, -443, -77, 83, -307, 306, 26],\n [47, 434, 102, -144, -287, -281, -137, -314, 239],\n [80, -487, -102, -215, 440, 532, -219, -170, -432],\n [-18, -100, 252, -93, 81, 409, -126, -150, -193],\n [-6, 138, -162, -387, -186, 47, -512, 19, 91],\n [463, 133, -72, 0, 537, 391, 130, 421, -260],\n [127, 542, -283, -309, 74, -106, -162, -366, -147],\n [382, -254, -454, -29, 149, -25, -349, -61, -118]]?\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[[306, -2, 118, 12, -68, 188, -368, 34, 174],\n [4, -307, 39, -283, 36, -236, 184, -500, 504],\n [3, -40, -183, 132, -111, -131, -224, -272, 444],\n [228, 20, 8, 280, -47, 209, -258, 178, -33],\n [486, -261, 175, -17, -333, 331, -258, -146, 507],\n [111, -182, 205, -330, -281, 200, 268, -65, 111],\n [207, -108, -81, 610, -43, 271, 4, 284, -210],\n [-165, 125, -185, 230, 178, -181, -80, 30, -106],\n [84, 11, -145, 427, 69, 22, -202, 81, -4]]\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[[82, -236, -513, -229, 265, -45, -263, -55, -127],\n [-144, 50, -344, -775, 274, 251, -39, -512, -246],\n [197, 328, -172, 97, -144, -185, 232, 159, 136],\n [-102, -374, -298, 151, 153, 26, -312, 426, 186],\n [-654, -288, 131, -532, 447, 490, -510, -461, -433],\n [-577, -87, -14, -155, 58, 78, 17, 228, -74],\n [776, 363, 198, 480, -397, -335, 464, -306, -73],\n [-182, 319, 272, 28, -44, 316, 133, -530, -395],\n [-6, 104, 5, -426, -30, 9, 235, -233, -25]]\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[[-243, -107, 41, 303, -296, 32, 273, 350, -211],\n [-393, -624, -318, 550, 72, 350, -17, 38, -251],\n [-422, -212, 153, 472, -96, -5, -216, 229, -357],\n [-378, -531, 5, 461, -176, 375, 208, 108, -25],\n [226, 191, -136, -240, 93, -227, -79, -69, -154],\n [77, -202, 116, -137, -156, -185, -21, -228, -308],\n [295, 46, 151, -396, -226, -54, 345, -201, 203],\n [187, 367, 174, -260, -4, -245, -99, 45, 10],\n [-269, -293, 91, 316, -286, 75, 191, 216, -268]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[401, 390, -90, 307, 274, 305, 579, 349, 264],\n [-67, -212, -379, -116, -19, -168, 289, -190, -210],\n [66, 359, 7, 128, 256, 338, 378, -121, 234],\n [385, 356, 597, 52, 36, -180, -880, 263, 61],\n [78, 118, 49, -193, 522, -529, 125, -239, 67],\n [292, -126, 131, -23, -268, -198, -944, 694, 91],\n [395, 183, -318, -142, 103, 5, -376, 468, 352],\n [241, 412, -101, 186, 361, 653, 406, 81, 172],\n [-151, -260, 141, 358, -209, -268, 7, 109, -1]]\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[[164, -462, -225, 93, -251, -144, 50, -186, -27],\n [267, -231, -117, -81, -72, 36, -51, -300, 180],\n [265, -275, -138, -60, -101, 12, -39, -298, 159],\n [-74, -148, -69, 117, -117, -120, 68, 82, -141],\n [133, -219, -108, 6, -103, -36, 1, -150, 45],\n [208, -234, -117, -39, -91, 0, -26, -234, 117],\n [172, -286, -141, 9, -135, -48, 2, -194, 57],\n [-286, -2, 6, 198, -84, -168, 118, 320, -300],\n [-40, 230, 111, -75, 137, 96, -42, 46, 57]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[87, -4, -43, -76, 70, -80, 100, -43, -50],\n [-21, -26, -152, -137, 149, -10, 89, -152, 32],\n [117, 66, 372, 309, -345, -30, -165, 372, -120],\n [-297, -26, -92, 31, 5, 230, -175, -92, 200],\n [2, -26, -157, -151, 161, -30, 111, -157, 18],\n [-67, -26, -142, -109, 125, 30, 45, -142, 60],\n [198, 48, 246, 156, -192, -120, -12, 246, -156],\n [139, -36, -247, -292, 294, -160, 284, -247, -58],\n [-28, 42, 259, 259, -273, 70, -203, 259, -14]]\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 9x9 matrix:\n[[-485, 66, 20, 302, -161, -277, -81, 88, -471],\n [-128, 336, -492, 209, -186, -4, -71, 165, 14],\n [427, -424, -359, -539, 203, -173, -626, 177, -3],\n [-15, -18, -14, -354, -644, -244, -66, -82, -13],\n [196, 143, -468, 190, 402, -204, -238, 527, 131],\n [-264, 334, 442, 492, 2, 144, 690, -368, -104],\n [-374, 167, -259, 197, -77, -81, -148, -2, -447],\n [889, 212, -164, -90, -67, -59, 477, -106, 825],\n [-15, 115, -350, 227, 591, -133, -154, -34, -544]]\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 9x9 matrix:\n[[-140, -419, 151, -551, 164, -400, -363, -2, -90],\n [525, -126, -216, 103, 3, 146, 55, 435, 279],\n [-165, -266, -147, -176, 254, -391, 276, -5, -57],\n [-7, -153, 926, 9, 499, -237, -376, 94, 730],\n [-48, 154, -426, -229, 192, 170, 92, 112, 53],\n [-19, 44, 491, 96, 15, 95, -323, -37, 158],\n [227, -478, -148, 27, -441, -202, 75, 119, -431],\n [-543, 519, -504, -24, -8, 166, 312, -486, -527],\n [484, -461, -419, 155, 253, 147, 147, 589, -212]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -22, -44, -32, 27, -42, -4, 13, 7],\n [94, -92, 68, 52, -8, 42, 94, -8, 14],\n [195, -276, 6, 10, 71, -45, 195, 25, 54],\n [160, -164, 104, 80, -6, 60, 160, -10, 26],\n [241, -284, 98, 78, 29, 33, 241, 3, 50],\n [292, -308, 176, 136, -2, 96, 292, -14, 50],\n [149, 80, 466, 342, -245, 417, 149, -123, -44],\n [167, -82, 250, 186, -98, 201, 167, -54, 1],\n [-125, -122, -478, -350, 262, -435, -125, 130, 53]]?\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[[-145, 34, 481, -43, -428, -705, 277, -372, -251],\n [-282, -85, 231, 259, 8, 225, -363, 33, 367],\n [68, 278, -222, 78, 72, -260, 636, -36, -480],\n [-110, -70, 463, -116, -82, -273, -217, -549, 106],\n [-3, 172, -197, 71, -227, 36, 417, 609, -237],\n [130, -50, -35, -226, 443, 453, -472, -309, 299],\n [-199, -3, 265, 258, -599, -882, 553, -33, -400],\n [-121, 188, -65, 145, 437, 543, -152, -18, 198],\n [-167, -47, 42, 198, 365, 497, -474, -108, 426]]\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[[-355, -329, -508, -24, 420, 140, -51, -76, -319],\n [-99, -282, -131, 291, 111, 186, 155, 334, 226],\n [88, 492, 289, -465, -250, -344, -138, -515, -173],\n [3, -11, -14, -391, 231, -350, -145, -104, -378],\n [339, 357, 505, 60, -465, -90, 65, 43, 361],\n [125, 47, 32, 174, -130, 176, -27, 20, 59],\n [-139, 14, 29, -91, 9, -114, 99, -22, 112],\n [-439, -87, -427, -8, 165, 226, 15, -331, -129],\n [16, -110, -41, -258, 253, -266, -102, 43, -296]]\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[[-43, 250, -44, -67, -84, -206, 48, -8, 54],\n [-238, -426, -234, -294, -106, 184, -238, 360, -48],\n [112, 576, 96, 112, -32, -352, 224, -256, 96],\n [103, 236, -46, -1, -54, -4, 208, -200, 48],\n [17, -217, 281, 257, 217, -35, -214, 88, -75],\n [-7, -336, 144, 133, 152, 127, -189, 116, -81],\n [-91, -309, 27, -7, 59, 88, -203, 196, -60],\n [50, -267, 15, 46, 71, 250, -27, -4, -54],\n [-42, -8, -386, -350, -242, 249, 189, -28, 45]]\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 9x9 matrix:\n[[40, -66, -26, 34, 0, -32, 20, 14, -38],\n [75, 130, 234, -16, 377, 27, 52, 164, 168],\n [135, -319, -195, 145, -143, -141, 62, -5, -219],\n [240, -431, -195, 215, -52, -204, 118, 65, -261],\n [25, -190, -182, 68, -221, -71, 4, -72, -164],\n [-185, 69, -143, -83, -351, 67, -106, -193, -47],\n [20, 177, 221, -49, 312, 56, 22, 121, 179],\n [-260, 289, 13, -177, -208, 160, -138, -167, 115],\n [-110, 304, 208, -132, 182, 130, -48, 28, 220]]\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[[222, 125, 199, 312, 35, 16, 146, 241, 107],\n [-165, 118, 74, 112, -228, 396, 12, 63, -287],\n [-107, -367, -8, 46, 175, 97, 213, 135, 450],\n [-307, 107, -206, -228, -127, 245, -135, -327, -590],\n [-170, 311, 4, -48, -361, 303, -197, -118, -609],\n [26, -104, 23, -351, -332, -357, -409, 25, 369],\n [89, 259, 143, 359, 17, 278, 198, 126, -309],\n [30, 312, -24, -12, -108, 24, -120, -150, -486],\n [55, 41, -167, -96, 257, -198, 28, -238, -180]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-571, -9, -334, -37, 393, 48, -369, -229, 417],\n [-64, 39, -141, -91, -123, -91, 41, -121, -136],\n [-248, 98, 86, 99, 115, -99, -425, 181, 115],\n [-401, -138, -19, 276, 365, 91, 334, -761, 643],\n [-79, -473, -290, 190, 198, 81, -52, -142, 76],\n [-66, -31, 487, 526, 85, -76, 60, -175, 373],\n [-352, -101, -350, -44, 88, -149, -663, 247, -143],\n [10, 291, 5, -204, -108, 38, 275, -234, 82],\n [-338, 323, 285, 101, 69, -225, -599, 331, 90]]\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[[171, 89, -12, 78, 1, -203, -153, 9, -310],\n [163, 103, 63, 44, 253, -213, 215, 320, -208],\n [73, -15, -21, 86, 281, -137, 35, -40, 94],\n [-132, -225, -158, -141, 38, 140, 117, -67, 372],\n [133, 236, 167, 239, 13, -163, -270, -147, -300],\n [37, 96, 110, 158, 210, -80, -21, -81, 43],\n [149, 68, 63, 73, 443, -229, 308, 307, -38],\n [130, 76, 69, 134, 406, -212, 154, 119, 2],\n [-105, -135, -73, -174, -11, 135, 253, 178, 192]]\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[[-84, -18, -26, -96, 58, -88, -16, -10, 20],\n [-96, -331, 129, 86, 111, -310, -90, 47, -52],\n [80, 348, -60, 28, 4, 202, 82, 14, -30],\n [114, 234, -158, -150, -218, 368, 80, -94, 116],\n [-127, 250, -34, -67, 234, -129, 23, 49, -61],\n [-50, 342, -74, -70, 138, 34, 58, 24, -34],\n [203, 29, 169, 411, -13, 80, 24, 105, -158],\n [-195, 32, -256, -541, -76, 42, -2, -162, 234],\n [34, 409, 17, 150, 187, 43, 75, 96, -139]]\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[[197, -166, 89, -381, 67, -185, 180, -198, 30],\n [-5, -82, 77, -37, 111, 111, -104, 174, -80],\n [289, -252, 153, 34, 181, -440, 287, 0, 161],\n [-221, 106, -31, 59, 84, 243, -169, 298, -93],\n [-318, 72, 31, 107, 233, 431, -334, 616, -195],\n [-21, 36, -23, 272, -69, 42, -85, 40, 3],\n [150, -10, -35, 356, -338, 70, -168, -334, -19],\n [-123, -56, 95, 16, 368, -22, 30, 532, -2],\n [-69, -152, 161, 4, 230, 362, -336, 460, -224]]\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[[235, -390, 36, 468, -174, -622, -105, 138, -88],\n [-147, 74, -198, -237, -92, 418, 144, -140, 134],\n [-141, 171, 19, -19, 68, -401, -259, 193, 22],\n [-139, -94, -260, 50, -246, -294, -109, 86, 148],\n [195, -306, -42, 177, -156, 150, 204, -132, -30],\n [105, -173, 7, 185, -80, -201, -13, 33, -34],\n [59, 60, 64, -181, 104, 620, 260, -218, -34],\n [-75, -201, -289, 91, -308, -181, -11, 17, 146],\n [-13, -187, -165, 162, -218, -319, -72, 73, 72]]\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[[298, -126, 392, 400, 222, -216, 444, 86, -6],\n [308, -74, 407, 381, 183, -205, 442, 82, -4],\n [-15, 119, -31, -91, -126, 43, -58, -21, 1],\n [80, -136, -198, 48, -292, -180, 114, -22, -80],\n [325, -59, 174, 290, -195, -286, 430, 35, -67],\n [39, -211, 107, 189, 280, -73, 124, 47, 7],\n [-18, -32, 133, 61, 249, 47, 4, 30, 38],\n [156, -218, 124, 267, 131, -185, 269, 49, -28],\n [-101, 171, -145, -216, -205, 110, -191, -48, 3]]?\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 9x9 matrix:\n[[-42, -22, 301, -199, -93, 154, -498, 69, 633],\n [-21, 760, 23, 662, -63, -491, -619, -437, 46],\n [-404, 250, -260, 43, 238, -453, 120, -313, -235],\n [271, -445, -65, -501, 112, 180, 318, 514, 119],\n [-371, 20, -453, 76, 91, -48, -47, 0, -399],\n [-76, 589, -159, 138, 42, -231, -362, -30, 114],\n [128, 642, -453, 435, -239, -4, -159, -273, -407],\n [-110, 527, 54, -52, -131, -341, -221, 77, 269],\n [-75, -283, -50, -336, -3, 383, 492, 132, -171]]\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 9x9 matrix:\n[[-542, 6, 153, -407, 84, 326, 129, 411, -39],\n [-159, -596, -183, 102, -104, 33, 138, 84, 43],\n [-189, -52, 257, -316, -120, -59, 205, 396, -68],\n [-387, 237, 172, -310, 404, 316, -106, 518, -143],\n [56, 257, -120, 16, 162, 375, -5, 222, -246],\n [-19, 501, 598, -171, -217, -193, 179, -40, 61],\n [-353, 244, 244, -397, 194, 321, -51, 112, 109],\n [303, 235, -381, 299, 447, 116, -501, 49, -117],\n [-191, -382, -277, -415, -23, 401, 45, 219, 68]]\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[[247, 137, 269, 394, -359, -279, 212, -364, 530],\n [324, -30, 47, -418, 75, 332, -302, 103, 31],\n [42, 237, 470, -211, -48, -203, -25, -266, 216],\n [207, -501, -249, 516, 207, -268, 146, -46, -409],\n [-575, 375, 50, -228, -410, 353, 226, 357, 569],\n [-190, 304, -74, -450, -216, 252, 171, -268, 583],\n [10, -2, -215, 170, 17, -124, 86, -259, -25],\n [374, -162, -348, 289, 46, -28, -70, -237, -101],\n [30, 255, -312, -523, -94, 410, -63, -278, 401]]\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[[-93, -178, 123, 1, 95, -72, 121, -85, 28],\n [-99, 524, -66, -77, -49, 189, -44, 377, -236],\n [-129, -8, 34, 61, 69, 39, 66, 37, -14],\n [376, -40, -501, 338, -262, 159, -438, -159, 279],\n [205, 214, -70, -167, -145, -15, -129, 74, -73],\n [127, 332, 53, -309, -105, -42, -34, 180, -197],\n [103, -38, -248, 239, -87, 117, -187, -64, 147],\n [364, 82, -309, 60, -242, 51, -323, -70, 118],\n [-8, 384, -157, 26, -86, 183, -122, 253, -117]]?\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, -248, 183, 101, 12, -242, -256, 275, 125],\n [188, 84, -155, 7, 76, -170, 228, -59, -133],\n [171, -219, 153, 93, 18, -237, -213, 246, 102],\n [-40, -40, 55, 5, -20, 30, -80, 35, 45],\n [-127, -49, 97, -7, -50, 117, -143, 32, 84],\n [-12, -116, 120, 32, -24, -20, -172, 116, 92],\n [90, -378, 342, 126, -36, -198, -486, 396, 252],\n [186, -74, 3, 53, 48, -212, 2, 101, -13],\n [13, -13, 8, 6, 2, -17, -11, 15, 5]]?\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[[257, 64, -194, -368, -130, -328, -314, -388, 139],\n [-10, 304, 565, -507, -83, 150, 342, -139, -454],\n [-44, -107, 71, 169, 307, -170, -84, -248, 70],\n [-80, -245, 563, -343, -201, -481, -308, -518, 588],\n [-202, -616, 139, 391, 400, -393, 89, 264, -74],\n [-567, -305, 147, -512, 91, 68, 438, -268, -306],\n [-79, -315, -25, -19, 118, -188, 118, 61, -146],\n [522, 143, -1111, 556, 236, -108, -354, 338, -103],\n [-210, -16, 768, -291, -119, -706, 1, 449, 55]]\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 9x9 matrix:\n[[-40, 393, -30, -76, -134, -245, -46, -74, -119],\n [190, 320, -125, -99, 42, 50, -60, 322, -66],\n [-4, -203, -19, -197, -30, -50, 75, -91, 320],\n [-133, -138, 53, 252, -90, -53, -122, 7, 62],\n [63, -110, -172, -253, 110, 15, -8, -323, 82],\n [-41, 291, 77, 242, -186, -126, -122, 419, -23],\n [25, 496, -184, 17, -151, -251, -275, 126, -57],\n [70, -25, -220, -236, 191, 49, -39, -503, -160],\n [157, -115, -271, -344, 279, 153, 2, -479, -95]]\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[[-126, -42, -91, -49, -70, 7, 56, -112, 35],\n [-54, -18, -39, -21, -30, 3, 24, -48, 15],\n [126, 42, 91, 49, 70, -7, -56, 112, -35],\n [-90, -30, -65, -35, -50, 5, 40, -80, 25],\n [-180, -60, -130, -70, -100, 10, 80, -160, 50],\n [-234, -78, -169, -91, -130, 13, 104, -208, 65],\n [54, 18, 39, 21, 30, -3, -24, 48, -15],\n [-126, -42, -91, -49, -70, 7, 56, -112, 35],\n [234, 78, 169, 91, 130, -13, -104, 208, -65]]\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[[-86, -174, -112, 203, -258, 92, -69, -113, -209],\n [-228, -145, -245, 203, -75, 107, -131, 215, 121],\n [148, -34, 138, 4, -198, -14, 64, -348, -352],\n [288, 296, 328, -376, 312, -184, 184, -88, 88],\n [42, 99, 57, -114, 153, -51, 36, 78, 132],\n [40, 123, 59, -139, 201, -61, 39, 121, 187],\n [-92, 99, -73, -85, 273, -25, -27, 343, 385],\n [218, 64, 222, -115, -72, -70, 113, -327, -275],\n [112, 130, 130, -162, 150, -78, 74, -10, 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[[-212, 302, 45, 138, 129, -405, -179, 641, 396],\n [-408, -746, -73, -135, -520, 210, 184, -823, -573],\n [-356, 276, -95, 446, -327, -340, -292, 146, -127],\n [322, 495, 87, 58, -197, -56, -473, 54, 29],\n [-265, -24, -464, 110, -110, 298, 370, -27, 312],\n [-383, 157, -27, -359, -343, 305, 290, 414, 481],\n [-149, -556, 68, -500, -260, 345, 760, -365, -85],\n [-246, 144, -51, 593, -375, -455, -363, -153, -303],\n [-88, -483, 105, -323, -847, 170, 471, -832, -410]]?\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[[0, -39, 27, -39, -12, -42, -33, -33, 36],\n [0, -221, 153, -221, -68, -238, -187, -187, 204],\n [0, 130, -90, 130, 40, 140, 110, 110, -120],\n [0, -39, 27, -39, -12, -42, -33, -33, 36],\n [0, 130, -90, 130, 40, 140, 110, 110, -120],\n [0, 156, -108, 156, 48, 168, 132, 132, -144],\n [0, -104, 72, -104, -32, -112, -88, -88, 96],\n [0, 169, -117, 169, 52, 182, 143, 143, -156],\n [0, 65, -45, 65, 20, 70, 55, 55, -60]]\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, 99, -820, 282, 195, 565, 11, 241, 4],\n [-194, 175, -321, -155, -104, 95, -5, 383, -32],\n [-134, 20, 12, 251, 307, 13, -271, 121, -226],\n [244, 395, 143, 459, -75, -70, -175, -408, 122],\n [31, -152, 180, 274, 273, 35, -153, -224, -126],\n [214, 147, -436, 346, 30, 344, 49, -168, 152],\n [-79, 235, 393, -161, 92, -375, -214, 270, -192],\n [-27, -454, -11, 358, 419, 86, -100, -139, -140],\n [-119, -135, -793, -54, -569, 653, 408, -229, 375]]\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[[9, 219, -54, 153, 147, -15, 129, -162, 66],\n [66, 370, -108, 294, 274, -50, 250, -300, 184],\n [27, 348, -90, 252, 240, -30, 213, -264, 123],\n [-219, 27, 66, -135, -93, 105, -123, 94, -306],\n [234, 132, -108, 252, 204, -120, 222, -216, 366],\n [147, -337, 30, -123, -145, -55, -97, 166, 128],\n [-120, 273, -24, 99, 117, 45, 78, -134, -105],\n [-102, -10, 36, -78, -58, 50, -70, 60, -148],\n [84, 190, -72, 186, 166, -50, 160, -180, 166]]\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[[-159, -343, 217, -693, -79, -280, -532, 430, 180],\n [-204, 233, -152, -261, -348, -23, -883, 619, 85],\n [-297, 206, 181, -347, -85, -292, -3, 173, 208],\n [-147, -321, 351, -575, 365, 230, -89, 207, -333],\n [-393, 4, -25, -335, 83, -221, -20, 139, 165],\n [867, 91, 77, -176, -198, 314, -297, 63, 24],\n [363, 353, -167, 593, 46, 285, 369, -441, -47],\n [496, 872, -135, 90, 49, 735, -244, -3, -136],\n [413, -630, -230, 264, 165, 77, 305, -360, -73]]?\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, 56, -210, 14, 168, -168, -252, -196, -70],\n [117, 36, -135, 9, 108, -108, -162, -126, -45],\n [208, 64, -240, 16, 192, -192, -288, -224, -80],\n [65, 20, -75, 5, 60, -60, -90, -70, -25],\n [-221, -68, 255, -17, -204, 204, 306, 238, 85],\n [52, 16, -60, 4, 48, -48, -72, -56, -20],\n [182, 56, -210, 14, 168, -168, -252, -196, -70],\n [-65, -20, 75, -5, -60, 60, 90, 70, 25],\n [-52, -16, 60, -4, -48, 48, 72, 56, 20]]?\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[[-76, -7, -321, -92, 51, 93, 174, -208, 393],\n [250, -371, 140, 484, -105, 380, -284, -161, -323],\n [67, 160, 505, 140, 123, -135, -66, 382, -786],\n [-187, 82, -15, -388, -93, -255, 14, 170, 272],\n [-216, -528, -178, -64, 36, 560, 88, -84, 142],\n [-27, 8, -255, 68, 177, 205, 238, -204, 130],\n [84, 605, 265, -148, -9, -692, -32, 279, -182],\n [237, -209, 211, 288, -252, 40, -396, -42, -174],\n [-36, -256, 57, 200, 186, 433, 106, 3, -362]]\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 9x9 matrix:\n[[-378, -119, 71, -299, -9, -35, 469, -21, 88],\n [92, -165, 77, -663, 535, 666, -379, -301, -155],\n [-1, 86, 504, -60, -269, 79, 418, 383, -283],\n [-316, -344, 326, -674, 368, 886, 294, -368, 68],\n [-39, 178, -318, -210, -104, 97, -99, 4, -98],\n [-358, -124, -74, -366, 507, 270, 41, -283, 67],\n [-329, 14, -324, -389, 79, 47, 244, -272, 173],\n [-686, -558, 368, -137, 258, 160, 336, 53, 56],\n [-295, -284, -358, -105, -22, 159, 79, 299, 442]]\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[[193, 325, 296, 20, 227, 277, 160, -126, 400],\n [8, -112, -260, 286, -320, -28, -328, 174, -250],\n [-92, -46, 93, -327, 206, -123, 271, -116, 60],\n [251, 131, -254, 502, -395, 201, -418, 198, -48],\n [-349, -319, 67, -53, 55, -202, -55, 18, -316],\n [11, 79, 156, 108, 73, 123, -28, -22, 84],\n [327, 259, -152, 58, -123, 147, 12, 16, 234],\n [33, -65, -209, 340, -303, 32, -345, 169, -205],\n [-21, -207, -417, 6, -321, -222, -165, 147, -303]]\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[[108, 266, -34, -130, -358, 322, 73, 338, 52],\n [386, -125, -348, 43, -442, -181, -244, 248, -302],\n [196, 457, -4, -280, -366, -318, -328, -189, 290],\n [630, 407, 179, 10, -729, -116, -462, 309, -184],\n [-315, -81, 167, -1, 257, 272, 206, -19, -88],\n [533, -504, -92, 249, -374, -124, -495, 79, -317],\n [223, 436, 495, -14, -161, 120, -97, 206, 8],\n [444, -118, -338, 135, -546, 110, -153, 459, -397],\n [607, -683, -101, 365, -224, -171, -431, 144, -283]]\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[[524, 126, -274, 533, -351, -292, -183, -166, -289],\n [-150, 301, -284, 594, -86, -402, -189, -324, -78],\n [406, -445, 528, -468, 58, -82, 542, 746, 75],\n [-420, 332, -430, 147, 115, -2, -350, -424, 248],\n [307, -31, -59, 9, -127, -21, -21, 49, -61],\n [-639, 217, -109, 36, 235, 128, 95, -101, 364],\n [129, -74, -130, 166, 65, -181, -264, -56, 62],\n [-153, -219, 86, -176, 263, -73, -446, -166, -41],\n [254, -110, -218, 140, -39, 211, -522, -296, -139]]\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[[145, -97, 16, 59, -355, -15, 121, -82, -151],\n [-183, 173, -191, 95, -359, 166, 21, 22, -220],\n [103, 33, 18, 48, -136, 49, 131, -26, -22],\n [135, -91, -2, 71, -415, -3, 127, -86, -185],\n [-245, -151, -92, -76, 20, -129, -305, 14, -124],\n [418, 104, 205, 65, 79, 91, 402, -40, 234],\n [35, -13, 109, -85, 445, -68, -57, 42, 244],\n [-149, -77, -25, -74, 178, -90, -205, 30, 15],\n [61, 87, -42, 87, -287, 107, 157, -26, -105]]\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[[-122, 69, 62, 85, -62, -170, 275, -39, 241],\n [-300, -51, -56, 231, -50, 42, 43, 315, -193],\n [205, 240, -101, -89, 354, -62, -188, -189, 161],\n [-183, -234, 122, 60, -358, 96, 131, 60, -239],\n [297, 92, 108, -234, 10, -162, 135, -380, 407],\n [20, 187, 11, 17, 116, -235, 224, -94, 419],\n [-427, 188, 59, 290, 4, -43, 74, -347, -267],\n [-95, -169, -192, 106, 78, 295, -378, 523, -508],\n [37, 166, 161, -64, -44, -201, 238, -539, 287]]?\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 9x9 matrix:\n[[10, -270, -225, 40, -416, 133, -267, 135, 341],\n [-136, 36, -381, 229, 60, -141, 614, 83, -26],\n [40, 12, 273, 238, 66, -26, 102, 79, -186],\n [106, 308, -6, 309, -23, -120, 608, -1, 39],\n [84, 69, 495, -294, -122, -382, -196, -78, 201],\n [90, 247, 84, 438, -314, 334, -157, 448, -33],\n [227, 45, 35, -141, -68, -99, 268, -128, -408],\n [-181, 220, 380, -330, 144, -384, -133, -1, 141],\n [-232, -186, 245, -780, 520, -325, -181, -581, -87]]\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[[178, -77, -97, 104, 19, -14, -181, 130, -281],\n [62, 11, 33, 98, 197, -246, -153, 176, -169],\n [26, -121, 51, 451, 33, -144, 8, -69, -126],\n [16, 154, 104, -135, 426, -470, -249, 375, -135],\n [8, 77, -32, -267, 24, 38, -51, 93, 27],\n [136, -176, -52, 432, -60, -8, -60, -48, -252],\n [-16, 11, 44, 64, 82, -116, -18, 34, -14],\n [-142, 176, 147, -211, 263, -288, -12, 143, 158],\n [88, 55, 0, -73, 216, -222, -209, 255, -183]]\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[[-392, 254, -47, -181, 568, -23, 141, 81, 74],\n [181, -174, 187, 297, 9, 0, 53, -29, -239],\n [-101, 21, 26, 82, 588, -324, -46, 439, 409],\n [-506, 516, 68, -411, 295, -380, -51, 29, 270],\n [-378, 54, -297, 146, 193, -335, 210, 200, 220],\n [-145, 118, 54, -90, 271, 115, 88, -66, -137],\n [-406, 95, -314, 74, 474, -543, 84, 508, 633],\n [57, 29, 539, -11, 496, 216, 122, -103, -66],\n [65, -94, 669, 125, 422, 684, 475, -510, -532]]\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[[-432, 2, -470, 171, 258, 390, 603, -284, 311],\n [36, 260, -3, 497, -45, 401, -57, 16, -229],\n [-64, 252, -523, -139, -208, 103, -204, 482, -33],\n [2, -165, -385, -200, 116, -425, 551, -28, -105],\n [-235, -96, 356, -264, 12, 186, 155, -627, 39],\n [279, 130, -669, 12, 84, -56, 97, -122, 116],\n [-272, 142, -478, 112, -249, 206, 238, 627, -6],\n [-175, 105, -116, -99, -369, 164, -269, 703, 143],\n [264, 81, -65, -346, -35, -116, -558, -76, 158]]?\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 9x9 matrix:\n[[-203, -12, 366, -55, 706, 290, -479, 494, 204],\n [402, -360, -475, 199, -93, -188, 560, -85, -112],\n [-256, -130, 177, -200, -18, 37, -28, -105, -188],\n [6, 325, 104, 125, -266, -112, -243, -151, 284],\n [23, -114, -276, -182, -681, 134, 280, -227, -311],\n [-410, 126, 206, -515, 181, 539, -147, 321, -500],\n [21, 30, 334, 340, -5, -119, -36, -127, 126],\n [76, -67, -448, -191, -740, -266, 511, -535, -356],\n [113, -43, -433, -216, -244, -15, 570, -128, -540]]\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[[64, -60, 64, 52, 36, -28, 44, -40, 0],\n [-32, 30, -32, -26, -18, 14, -22, 20, 0],\n [-288, 270, -288, -234, -162, 126, -198, 180, 0],\n [-240, 225, -240, -195, -135, 105, -165, 150, 0],\n [-64, 60, -64, -52, -36, 28, -44, 40, 0],\n [32, -30, 32, 26, 18, -14, 22, -20, 0],\n [32, -30, 32, 26, 18, -14, 22, -20, 0],\n [48, -45, 48, 39, 27, -21, 33, -30, 0],\n [-80, 75, -80, -65, -45, 35, -55, 50, 0]]\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[[145, -66, 175, 19, 110, -160, 6, -225, 96],\n [-184, -24, 182, 176, 40, -278, -150, -234, -168],\n [-336, 84, -147, 84, -140, 63, -105, 189, -252],\n [-258, 96, -231, 6, -160, 189, -39, 297, -180],\n [-221, -6, 133, 169, 10, -232, -150, -171, -192],\n [34, -96, 343, 154, 160, -397, -105, -441, -12],\n [79, -102, 343, 133, 170, -382, -84, -441, 24],\n [-267, 30, 21, 135, -50, -114, -132, -27, -216],\n [250, -108, 280, 22, 180, -250, 18, -360, 168]]\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 9x9 matrix:\n[[33, -48, 128, -267, 132, 269, -118, -45, 200],\n [-78, -52, -48, 52, 38, -44, -52, -40, 30],\n [132, 146, -8, 115, -187, -133, 204, 119, -227],\n [-12, 60, -112, 246, -138, -250, 128, 54, -202],\n [-306, -160, -256, 358, 56, -330, -116, -118, -16],\n [-69, 20, -144, 277, -106, -275, 86, 23, -174],\n [24, 62, -56, 145, -109, -151, 108, 53, -149],\n [36, 106, -104, 263, -191, -273, 188, 91, -263],\n [-291, -222, -136, 96, 201, -64, -250, -174, 197]]\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[[-371, -104, -28, 259, -130, -120, -5, -144, -198],\n [434, 48, 120, -402, -384, 274, -1, -107, -224],\n [351, 313, 181, -396, -330, 378, 16, -6, 328],\n [-251, -11, -349, -134, 56, 108, -6, 168, 453],\n [189, 78, 526, 278, -158, 163, 239, 144, 83],\n [161, -61, -13, -128, -383, 51, -184, -40, -353],\n [424, -71, 449, 35, -662, 359, -82, -20, -10],\n [-161, 505, 455, -225, -333, 375, 585, -458, 73],\n [-187, -108, -360, -110, 405, 4, 155, 198, 352]]\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 9x9 matrix:\n[[-24, 112, -98, -191, -151, -335, 174, -78, 59],\n [209, -628, -117, 339, 78, 271, 290, 43, 253],\n [352, 68, -132, 49, -557, 297, -49, 196, 326],\n [297, -95, -278, 225, 24, 611, 174, 560, -161],\n [148, 343, 129, 108, -392, 126, -594, -253, 382],\n [-185, -140, 72, -127, 235, -123, 208, 64, -254],\n [428, -132, -368, 392, 20, 800, 130, 608, -78],\n [-140, 442, 132, -172, -50, -144, -326, -104, -116],\n [-247, 130, 239, -40, 155, -344, -311, -461, 61]]\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[[288, 107, 279, 132, 250, -47, 244, -74, 347],\n [162, 209, 263, 96, -69, -1, -146, 231, -69],\n [36, -326, 342, -249, 284, 176, 272, 41, 208],\n [-260, -536, -60, -382, 186, 188, 244, -120, 64],\n [-152, -249, 11, -214, 18, 121, 20, 48, -77],\n [92, -150, 78, -32, 290, 6, 340, -214, 342],\n [10, 1, 143, -49, -43, 57, -86, 158, -91],\n [-178, 162, -280, 58, -365, -50, -386, 133, -404],\n [198, -36, 258, 18, 267, 12, 270, -75, 318]]\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 9x9 matrix:\n[[-37, 16, -29, 50, 81, 89, -71, -33, -96],\n [-208, 34, 124, -40, -36, -244, 226, -42, -24],\n [-57, 6, 51, -30, -39, -111, 99, -3, 24],\n [-80, 29, -34, 76, 126, 118, -91, -57, -156],\n [-325, 79, 61, 86, 171, -37, 64, -132, -276],\n [164, -33, -66, -4, -26, 110, -109, 49, 76],\n [-129, 39, -15, 78, 135, 87, -60, -72, -180],\n [77, -19, -13, -22, -43, 5, -12, 32, 68],\n [-374, 89, 80, 88, 180, -68, 95, -147, -300]]\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[[-96, 84, -17, -48, 84, -144, 155, 132, 59],\n [-332, 387, -74, -273, 281, -413, 465, 343, 212],\n [-198, 393, -108, -309, 177, -381, 351, 261, 318],\n [348, -202, -52, 146, -250, -94, -146, 30, 248],\n [-26, 241, -105, -197, 45, -325, 214, 205, 341],\n [246, -141, -55, 117, -165, -195, -14, 135, 259],\n [-24, -123, 67, 105, 3, 189, -100, -111, -223],\n [23, -178, 99, 125, -51, 403, -274, -298, -353],\n [-296, 110, 43, -46, 226, -54, 225, 118, -165]]\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[[132, -475, -74, -204, 160, -381, -182, 169, -433],\n [149, -21, 153, -80, 92, -15, -202, -312, 44],\n [-245, -170, 347, 269, -159, -8, -245, -443, 333],\n [173, -39, -78, -103, 45, -32, -76, -19, 91],\n [-102, 522, -231, -226, -46, 45, -263, 135, -37],\n [-110, 582, 25, -243, -11, 49, -564, -287, 23],\n [73, 32, 141, -222, 148, -144, -406, -271, -253],\n [-411, -112, 59, 469, -353, 126, 215, 57, 509],\n [-6, -447, 174, 126, 69, -138, 159, -6, -234]]?\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 9x9 matrix:\n[[-16, -15, 262, -162, -188, 124, 159, 341, 78],\n [-58, 151, -400, 248, 100, -58, -337, -399, 198],\n [-128, 93, -322, 191, 203, -268, -515, -243, 251],\n [20, 155, -474, 300, 94, 48, -187, -573, 56],\n [139, 24, -157, 109, -22, 209, 263, -337, -236],\n [-108, 25, -134, 74, 156, -248, -373, -47, 174],\n [90, -26, 238, -139, -231, 286, 410, 196, -117],\n [-63, -90, 189, -126, 63, -189, -99, 279, 27],\n [121, -156, -151, 93, 344, -229, 45, -359, -462]]\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[[62, -186, 338, 96, 256, -318, 142, 154, 268],\n [292, -366, 18, 156, 246, -198, 252, 314, -202],\n [174, -120, -292, 36, -38, 132, 70, 108, -402],\n [-125, 21, 411, 12, 150, -261, 3, -25, 476],\n [-113, 48, 282, -6, 81, -162, -21, -46, 347],\n [97, -177, 177, 84, 186, -207, 129, 149, 92],\n [232, -315, 89, 138, 241, -219, 220, 269, -91],\n [101, -75, -153, 24, -12, 63, 45, 67, -218],\n [-213, 195, 209, -72, -44, -39, -125, -171, 354]]\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[[-670, -389, -473, -277, -375, 214, 261, 171, -76],\n [-219, -20, -211, -413, 341, -53, 511, 32, -386],\n [-227, -416, 291, -469, -461, 487, -245, 212, -40],\n [-254, -174, -520, -20, 148, 12, 278, 105, -533],\n [81, 30, 266, -9, -268, 35, 25, -103, 412],\n [344, 392, 153, 263, 292, -279, 33, 127, -116],\n [-81, -254, 134, -76, -428, 186, -81, 531, -733],\n [331, 184, -83, 42, 479, 48, 375, 248, -519],\n [-226, -542, -16, -126, -484, 492, -500, 50, -49]]\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 9x9 matrix:\n[[-15, -87, 6, 498, 215, -183, -159, 457, 271],\n [238, -334, -168, -44, -110, 112, 147, -9, -19],\n [-94, -6, 53, 504, 200, -213, -162, 465, 256],\n [180, -196, -97, 244, 210, -29, -132, 201, 198],\n [-169, -49, 70, 622, 89, -269, -69, 615, 253],\n [-119, 45, 43, -114, -231, 12, 174, -59, -144],\n [151, -329, -142, -82, -287, 107, 285, -3, -109],\n [-155, 221, 102, -134, -45, -11, -3, -131, -93],\n [200, 96, -64, -576, 72, 252, -66, -610, -174]]\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[[54, -41, 50, -103, 41, 89, 218, -41, -6],\n [30, -50, 20, -70, 20, 80, 260, -80, -60],\n [-191, -41, -230, 277, -164, -106, 178, -246, -366],\n [264, 1, 302, -409, 221, 209, 38, 223, 390],\n [79, 48, 104, -100, 71, 9, -232, 167, 216],\n [15, 24, 24, -12, 15, -15, -120, 63, 72],\n [-177, 1, -202, 275, -148, -142, -34, -146, -258],\n [-74, 58, -68, 142, -56, -124, -308, 60, 12],\n [-91, 70, -84, 174, -69, -151, -372, 71, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[31, 10, -620, 276, 234, 155, 260, 362, 163],\n [-56, 311, 300, -228, -9, 234, -184, -150, 39],\n [136, 248, 186, -264, 268, -106, -400, -141, 73],\n [215, -68, -558, 41, -63, 77, -112, -89, 276],\n [469, -95, 31, 113, -459, 66, -177, 11, 171],\n [238, -116, 240, 342, -206, 118, 192, 352, 26],\n [228, -250, 7, 292, -287, -17, 155, 201, 19],\n [-282, 425, 514, -311, 421, 57, -148, -55, -138],\n [247, 192, 246, 107, -340, 248, 14, 268, 5]]\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[[152, 219, -147, 296, -207, 148, -460, -429, 395],\n [73, 62, 36, 48, -156, 75, -195, -121, 5],\n [-116, 77, -270, 59, 354, 84, 170, 25, 332],\n [139, 230, 33, -18, -288, 96, -72, 308, -265],\n [-119, 93, -246, 291, -404, -251, -1, 51, -145],\n [208, 52, 14, 36, -904, 210, -616, -85, -296],\n [-145, 152, -224, 112, -382, 247, -239, -65, -151],\n [160, 213, -36, 141, 348, -352, 390, 359, 202],\n [566, 50, 133, -15, -97, -32, -288, 30, 395]]\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[[-262, -29, -259, -315, 17, -166, -143, 23, -116],\n [262, -5, 200, 247, -6, 135, 59, -49, 129],\n [36, -192, -152, -113, -270, -523, 95, 15, 21],\n [-360, 42, -283, -376, 147, 13, -248, 18, -159],\n [350, -255, -30, 40, -218, -368, -44, -108, 206],\n [-202, -25, -155, -172, -93, -249, 64, 70, -111],\n [-256, 230, 40, -31, 270, 447, -71, 49, -141],\n [-202, 85, -45, -77, 47, 46, 39, 65, -116],\n [-144, 136, 126, 138, -50, 36, 314, 134, -124]]\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[[338, -6, -53, -16, -68, -245, 64, 119, 380],\n [-46, -162, -48, 42, -333, -359, 596, 188, 402],\n [-211, -131, 22, 310, -131, -368, 711, -120, 172],\n [200, 149, 448, 734, 20, 230, 548, -126, -332],\n [306, 216, -37, 518, 139, -232, 576, -299, 152],\n [-127, -337, 12, -727, -184, -130, -711, 448, 270],\n [-128, -136, 219, 73, 30, -120, -6, -23, -40],\n [-483, -400, 265, -574, -259, 161, -571, 449, -156],\n [-112, -74, -161, -67, 30, -258, 72, -101, 174]]?\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[[-19, -143, 139, -103, 297, -27, 31, -433, -331],\n [-273, 484, 173, 472, -356, 289, -285, 35, -32],\n [-468, 17, 280, 209, -391, 334, -154, 28, -127],\n [-22, 140, 96, 108, 118, 34, -72, -261, -190],\n [179, -279, -154, -320, 320, -239, 361, -47, -16],\n [-890, 240, 436, 470, -626, 558, 22, 54, -274],\n [58, -103, 14, -149, 393, -136, 262, -359, -275],\n [-278, 90, 169, 179, -233, 208, -106, 0, -85],\n [60, 3, 144, 63, 3, 82, -434, -222, -93]]\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[[-190, -136, -48, -80, 20, -294, -138, -158, -38],\n [128, 10, -94, 148, -28, 580, 190, 62, -162],\n [199, -62, 327, 179, 286, -228, -141, 140, 173],\n [210, -131, 347, 240, 350, -194, -163, 127, 137],\n [10, 230, 184, -214, -56, -616, -112, 106, 348],\n [-301, -25, -247, -236, -204, -185, -30, -214, -96],\n [-197, 18, -265, -157, -218, 112, 79, -144, -143],\n [-256, -273, -150, -17, 42, -111, -127, -254, -203],\n [86, -382, 199, 343, 412, 35, -180, -45, -124]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-60, -32, 14, -52, 24, 98, -12, 66, 40],\n [44, 26, -18, 24, -22, -66, 2, -52, -30],\n [-32, 45, -182, -374, -95, 196, -173, -53, 5],\n [194, 125, -111, 48, -115, -267, -19, -244, -135],\n [-220, -149, 148, -14, 143, 286, 41, 287, 155],\n [156, 68, 10, 220, -36, -290, 72, -150, -100],\n [-86, -113, 225, 300, 151, -15, 163, 190, 75],\n [-156, -144, 222, 204, 168, 114, 132, 258, 120],\n [12, -24, 90, 180, 48, -90, 84, 30, 0]]\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 9x9 matrix:\n[[-182, -61, -191, -8, 194, 139, -33, 179, 165],\n [-14, -40, -23, -38, 44, 46, -15, 47, 21],\n [-126, -156, -159, -126, 228, 210, -63, 231, 141],\n [-336, 77, -308, 186, 202, 67, 6, 152, 260],\n [-280, 118, -244, 212, 124, 2, 24, 76, 204],\n [-98, -93, -117, -68, 154, 135, -39, 153, 103],\n [378, -25, 361, -144, -278, -137, 15, -229, -307],\n [-98, -8, -97, 22, 84, 50, -9, 73, 83],\n [84, -83, 62, -114, 2, 47, -24, 22, -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[[25, -15, 65, -75, -25, 50, 15, 20, 35],\n [-60, 36, -156, 180, 60, -120, -36, -48, -84],\n [5, -3, 13, -15, -5, 10, 3, 4, 7],\n [-30, 18, -78, 90, 30, -60, -18, -24, -42],\n [50, -30, 130, -150, -50, 100, 30, 40, 70],\n [-45, 27, -117, 135, 45, -90, -27, -36, -63],\n [-50, 30, -130, 150, 50, -100, -30, -40, -70],\n [-60, 36, -156, 180, 60, -120, -36, -48, -84],\n [70, -42, 182, -210, -70, 140, 42, 56, 98]]\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 9x9 matrix:\n[[70, 156, 213, -29, -168, 36, 134, 16, 135],\n [-105, -15, -185, 86, 106, -77, -73, 8, -112],\n [-5, -301, -23, -84, 10, 95, -275, -170, -144],\n [-355, 33, -26, 211, -326, -53, -507, -368, -391],\n [35, -233, -38, -83, 70, 69, -141, -72, -65],\n [185, -193, 339, -220, -210, 217, -83, -156, 94],\n [-120, 348, 105, 153, -228, -90, 78, -6, 15],\n [-275, -18, -104, 165, -158, -59, -386, -249, -316],\n [185, -113, 237, -178, -90, 149, 49, -32, 140]]\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[[166, 129, 252, -193, 614, 44, 941, -403, 552],\n [-211, -117, -198, 146, -45, 301, 193, -116, -192],\n [396, 193, 214, -234, -64, -186, -43, 441, 184],\n [-61, -528, 31, 243, -304, 64, -221, -257, -116],\n [116, -209, 180, 377, -202, -21, 130, 346, -352],\n [48, -301, -330, -114, -270, 344, -138, -58, -237],\n [417, -284, -369, -72, 2, 281, -99, -483, -25],\n [-946, 39, -102, -154, 75, -61, -171, -167, -125],\n [-552, 433, -155, -98, -35, -78, -190, 591, -425]]\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[[151, 138, 186, -98, -164, -178, -34, 13, -182],\n [-17, -206, 113, -43, 238, 243, -27, 178, -95],\n [-23, -64, 7, 15, 92, 91, 7, 30, -13],\n [-121, -178, -71, 133, 314, 303, 69, 2, 17],\n [13, 94, -142, -226, -452, -378, -162, 91, 322],\n [-142, -438, -3, -103, 356, 409, -95, 353, 113],\n [-170, 214, -418, 338, -66, -96, 186, -448, 282],\n [140, 188, 19, -341, -602, -531, -213, 141, 187],\n [-100, -320, 110, 174, 620, 578, 110, 86, -226]]\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[[174, -16, -222, -180, -182, -64, 156, 24, -92],\n [-215, -16, -33, 154, 67, -48, -166, -20, -2],\n [-388, -47, 320, 453, 221, -255, -400, -58, 100],\n [238, 31, -38, -219, -79, 137, 214, 28, -12],\n [209, -40, -37, -96, -173, -230, 116, 14, -54],\n [-221, -70, 203, 329, 67, -375, -279, -41, 36],\n [87, 42, 49, -100, 39, 198, 98, 12, 34],\n [-307, -40, -233, 172, 7, -122, -216, -22, -70],\n [-250, 2, 362, 306, 244, -26, -256, -40, 132]]?\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[[-156, -117, -65, -221, -65, -182, -143, -234, 78],\n [-12, -9, -5, -17, -5, -14, -11, -18, 6],\n [36, 27, 15, 51, 15, 42, 33, 54, -18],\n [24, 18, 10, 34, 10, 28, 22, 36, -12],\n [60, 45, 25, 85, 25, 70, 55, 90, -30],\n [-24, -18, -10, -34, -10, -28, -22, -36, 12],\n [-96, -72, -40, -136, -40, -112, -88, -144, 48],\n [-12, -9, -5, -17, -5, -14, -11, -18, 6],\n [192, 144, 80, 272, 80, 224, 176, 288, -96]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-359, -23, -252, -49, -52, 573, -241, -15, -242],\n [420, 222, 108, 179, 176, 167, 575, -534, 307],\n [98, 195, 481, -224, 28, 106, 147, 36, -197],\n [-173, -203, 83, -99, -20, 344, 21, -71, -95],\n [-283, 160, 303, -166, -658, 255, 170, 70, 85],\n [91, 444, 123, -26, -180, 507, 170, -106, -175],\n [421, 392, -448, 325, 708, 197, 165, -554, 85],\n [-421, 78, -174, -164, -34, -217, -561, 411, -231],\n [-352, -241, 257, -223, -592, -323, -222, 518, -28]]\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 9x9 matrix:\n[[-556, 224, -164, 32, -435, -239, 192, 661, 185],\n [329, 34, -442, -96, 205, -235, 58, -638, -508],\n [374, -594, 324, -228, 603, -84, -169, -456, -338],\n [-130, 106, 41, -205, 181, 83, 520, 79, 58],\n [67, -296, 341, -104, 346, 62, -69, -139, -183],\n [-696, -22, -250, -7, -280, -389, -317, 282, 442],\n [233, -248, -32, -121, 102, -145, 199, -467, -556],\n [46, -27, -44, 5, -255, -250, 172, 332, -215],\n [-906, -461, 340, -219, -366, -481, 2, 403, 506]]\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[[-230, -118, 272, -130, -338, -40, -66, 269, -398],\n [-150, 420, 182, -84, 70, 8, 254, 274, 408],\n [543, -290, -481, 390, 53, 76, 3, -360, 24],\n [172, 20, 66, 15, 150, 386, -174, 166, -14],\n [21, 252, 129, -76, 283, 300, -33, 174, 274],\n [-46, -223, 76, -80, -130, 46, -283, 30, -437],\n [315, 629, -113, 1, 269, 249, -332, 321, 229],\n [497, 351, -201, 84, 453, 505, -446, 129, 177],\n [-214, 413, 260, -159, -180, -74, 41, 455, 33]]?\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 9x9 matrix:\n[[-148, -29, -50, -16, -19, 36, 86, 55, -45],\n [44, -119, 85, -200, 241, 701, -4, -121, 291],\n [-383, -69, -335, 134, -44, 16, -104, -105, -130],\n [-99, 280, -184, -58, -461, -301, -60, -174, -127],\n [167, -224, -23, 390, 390, -224, -304, 6, -39],\n [390, 25, 263, -112, 134, 181, -50, -47, 217],\n [-270, 42, -141, 48, -195, -273, 132, 114, -210],\n [-8, 83, -100, 0, -117, -22, -122, -153, 3],\n [106, 93, 79, -296, -54, 513, -2, -203, 257]]\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[[64, 304, 107, 141, -193, -106, 236, -120, 55],\n [-165, -118, -1, 103, 43, -227, 271, -42, 32],\n [-141, -174, 80, -14, 88, -111, 4, -43, 69],\n [76, 390, 295, 97, -228, -116, 108, -180, 116],\n [169, 62, 149, -147, -79, 351, -451, -166, 216],\n [-126, -56, -272, 164, 74, -298, 494, 216, -272],\n [-57, 44, 137, -35, 40, -149, -29, 78, -91],\n [94, 12, 130, -170, 18, 208, -411, -3, 44],\n [216, 404, 183, -15, -207, 122, -144, -68, 25]]\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, 314, 649, 424, -157, 341, 325, 454, -48],\n [-232, -121, 72, -339, 74, 351, 193, 192, -224],\n [235, -50, -331, 109, 433, 345, 638, 384, 77],\n [-166, -37, -126, 209, 108, -91, -281, -344, -310],\n [-2, -79, -214, 73, -57, 420, 40, 198, -245],\n [134, -420, 414, -52, -388, -394, -222, -188, 296],\n [-315, -439, -245, -304, -219, -347, -288, -386, 161],\n [-100, -195, 432, 220, -265, -336, -271, -435, -50],\n [436, 150, 95, 204, -191, -113, 7, -126, 282]]\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 9x9 matrix:\n[[1019, -195, -438, -724, -288, 570, 192, 402, -321],\n [-198, 319, 132, -123, 174, 157, -272, 141, -474],\n [-393, 113, 183, 42, 254, 168, -160, 155, -141],\n [68, -35, 236, 152, 110, -108, -427, -203, -282],\n [-159, 158, 63, 248, -64, -391, 72, -407, 277],\n [7, 132, -218, 242, -292, -512, 155, 23, 133],\n [61, -601, -198, -120, -78, 268, 400, 282, 381],\n [-346, 15, 130, 610, 8, -559, -116, -144, 306],\n [221, 317, -437, -657, -163, 507, 460, 566, -173]]\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[[134, 112, 68, -101, -181, -680, 408, -107, -180],\n [-407, -127, 283, 198, 238, -194, 339, 182, 254],\n [-70, 868, -159, -361, -565, -119, -412, -407, 188],\n [104, -343, 101, 39, -559, 174, 127, 581, 455],\n [-62, 44, 276, 229, -71, 501, -520, 77, 147],\n [14, 412, 128, -236, -256, -62, 56, -442, 564],\n [110, -322, -107, 110, -41, 462, -320, 354, -154],\n [-106, 533, -359, -146, -24, -90, -115, -298, -16],\n [529, -388, -44, -34, -57, -420, 696, -302, 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[[245, -19, -245, -166, 68, -134, 173, -60, 506],\n [518, -34, -93, -97, 413, 308, -63, 38, -150],\n [-168, 63, 138, 145, -78, -12, 96, -368, -98],\n [309, 44, 155, -181, 170, 536, -405, -48, -106],\n [343, 95, -62, -109, 187, 128, -34, -246, 274],\n [-225, -68, 280, 188, -17, 268, -78, -74, -694],\n [-262, 57, 183, 409, 20, -119, 333, -530, -495],\n [74, 520, 183, 476, 284, -267, -129, -334, -253],\n [-183, 264, 59, 289, -32, -380, 47, -140, 8]]?\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[[-158, 334, -129, -781, -6, -80, 38, -257, -63],\n [-330, 257, 18, -299, -83, -334, 250, -28, -10],\n [131, -853, -115, -47, 188, 225, -112, 77, 797],\n [398, -394, -155, 375, 116, 236, 376, 280, -113],\n [-29, -122, -795, 364, 51, -391, 354, -325, -206],\n [261, 22, -441, 306, 55, -201, -340, -208, 148],\n [-22, -44, -320, 189, 14, -125, -558, -376, 463],\n [313, 114, -385, 457, 27, -190, -208, -101, -22],\n [417, 23, -308, 685, 28, 100, -324, -80, 94]]\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 9x9 matrix:\n[[26, -433, -95, 23, -165, -247, 138, -66, 64],\n [-120, 5, 9, -106, 147, -175, 99, 24, -7],\n [666, -70, 216, 527, 30, 146, -561, -174, 131],\n [-277, 159, -91, -208, -188, 281, 127, 106, -89],\n [573, 52, 106, 468, -37, 188, -402, -142, 76],\n [-25, -84, -62, -30, 341, -620, 292, -46, 22],\n [403, 130, 106, 317, 293, -190, -193, -112, 57],\n [-241, -140, -38, -206, 133, -324, 236, 34, -2],\n [-71, 87, -83, -38, -246, 297, 25, 42, -51]]\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, 16, -288, -64, 122, -110, -458, 174, 84],\n [407, 121, 64, -267, 52, -389, 43, 265, 338],\n [262, 86, 261, -131, -1, -266, 378, 96, 186],\n [-139, -45, 124, 91, -104, 193, 209, -173, -130],\n [-56, -5, 274, 93, -43, 24, 446, -128, -88],\n [-426, -114, -209, 307, 93, 278, -254, -164, -346],\n [119, 30, 143, -85, -74, -45, 201, -1, 88],\n [-202, -62, 254, 148, -158, 270, 422, -274, -200],\n [-75, -5, -271, 82, 219, -119, -395, 137, -44]]\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[[140, 14, -28, 70, 182, 224, 14, -252, -14],\n [-180, -18, 36, -90, -234, -288, -18, 324, 18],\n [30, 3, -6, 15, 39, 48, 3, -54, -3],\n [100, 10, -20, 50, 130, 160, 10, -180, -10],\n [-140, -14, 28, -70, -182, -224, -14, 252, 14],\n [-180, -18, 36, -90, -234, -288, -18, 324, 18],\n [-140, -14, 28, -70, -182, -224, -14, 252, 14],\n [180, 18, -36, 90, 234, 288, 18, -324, -18],\n [-180, -18, 36, -90, -234, -288, -18, 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 9x9 matrix:\n[[439, 80, 250, -122, -465, -76, 336, -1, 65],\n [595, 145, 199, 119, -866, 95, 544, 186, -222],\n [42, 192, 27, -509, -554, 387, -171, 206, -28],\n [-53, -163, 290, -256, -131, -313, 132, 498, 288],\n [42, -217, 412, -213, -51, -465, 181, 144, 441],\n [156, 227, -119, 190, 35, 299, 17, -257, -81],\n [-211, -99, -10, 77, 31, 60, -208, -325, 40],\n [221, 107, -102, 97, -155, 122, 88, -205, -234],\n [148, 350, -160, -251, -374, 565, -134, 37, -192]]\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 9x9 matrix:\n[[164, 6, -110, 53, -171, 79, 51, 36, -122],\n [178, -36, -170, 14, -385, 107, 109, 116, -264],\n [-174, -54, 60, -105, -42, -60, 6, 48, -18],\n [172, -6, -130, 43, -237, 89, 69, 60, -166],\n [-138, -108, -30, -150, -339, -15, 87, 156, -216],\n [-398, -96, 170, -212, 33, -151, -21, 60, 44],\n [250, 108, -50, 182, 203, 71, -47, -124, 120],\n [-20, 30, 50, 25, 165, -25, -45, -60, 110],\n [14, 0, -10, 4, -17, 7, 5, 4, -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[[-126, -362, 146, -244, -450, 28, -84, 86, -12],\n [236, 30, -193, -4, 60, -22, 203, 226, -108],\n [-131, 73, 96, 66, 75, 8, -119, -179, 78],\n [96, -8, -76, -16, 0, -8, 84, 104, -48],\n [-213, 55, 164, 62, 45, 16, -189, -253, 114],\n [-119, -77, 105, -42, -105, 14, -98, -77, 42],\n [347, -91, -267, -102, -75, -26, 308, 413, -186],\n [5, -137, 13, -98, -165, 6, 14, 87, -30],\n [106, 314, -124, 212, 390, -24, 70, -78, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-52, -50, -73, -78, -118, 6, 10, -95, -27],\n [-264, -294, 167, -106, 30, -206, -34, -431, -59],\n [-258, -282, 92, -142, -54, -170, -22, -428, -68],\n [-42, -30, -198, -138, -258, 66, 30, -90, -42],\n [109, 137, -278, -69, -257, 177, 47, 158, -6],\n [-3, -33, 399, 213, 465, -177, -63, 33, 57],\n [211, 233, -107, 99, 7, 153, 23, 347, 51],\n [-263, -283, 34, -177, -125, -147, -13, -442, -78],\n [10, 38, -366, -190, -422, 166, 58, -18, -50]]\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[[52, 103, 69, -28, -77, -44, -138, 59, 129],\n [-395, 144, 81, -13, 118, 98, 498, 245, 77],\n [-289, -117, -164, -65, 198, 183, 530, -5, -351],\n [-3, -88, -111, 35, 114, 80, 138, -57, -159],\n [-397, 93, -38, 91, 177, 371, 646, -7, -350],\n [188, -248, -424, -77, 229, 238, 151, -251, -630],\n [-267, 83, 410, 92, -406, -72, -167, -177, 118],\n [313, -99, -268, 61, 138, 185, -94, -215, -357],\n [-561, 12, 275, -65, -169, -58, 348, 61, 64]]?\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[[69, 83, 15, 14, 16, 22, -22, 86, 42],\n [183, -177, 84, 225, 234, 30, -243, 81, -63],\n [-438, -482, -51, -165, -76, 80, 73, -661, -245],\n [280, 139, 94, 138, 171, 124, -201, 246, 84],\n [70, 118, -26, 40, -36, -140, 60, 200, 56],\n [-115, -288, 62, -31, 113, 262, -158, -387, -133],\n [-202, -201, -61, -47, -79, -116, 106, -203, -105],\n [-146, -207, -89, 53, -77, -316, 140, -31, -105],\n [183, 44, 84, 93, 151, 154, -184, 97, 35]]?\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[[-6, 327, -471, -351, 414, 54, 132, -390, -354],\n [-8, 306, -443, -331, 390, 52, 126, -367, -334],\n [-8, 176, -258, -194, 228, 32, 76, -214, -196],\n [106, 203, -189, -101, 138, -34, -32, -148, -94],\n [272, 126, 77, 157, -138, -148, -234, 85, 178],\n [-68, -194, 212, 132, -168, 12, -4, 170, 128],\n [138, -111, 288, 264, -288, -102, -186, 249, 276],\n [90, -95, 220, 196, -216, -70, -130, 189, 204],\n [-42, 209, -337, -265, 306, 58, 124, -282, -270]]\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[[83, 60, -29, 583, -155, -194, -303, 829, -120],\n [449, 108, -170, 31, 193, 69, -287, 249, -704],\n [171, 54, -102, 62, -236, -75, 542, 92, 222],\n [651, 447, -52, -14, 57, -17, 296, -67, -278],\n [552, -134, 22, -141, 474, -42, 102, -500, -352],\n [-42, -109, -14, -164, 319, -76, -157, -34, -2],\n [199, 511, -392, 514, 155, -109, 7, 420, -296],\n [219, 248, -390, -85, 411, 49, 172, -110, -438],\n [294, -226, -119, -108, 651, 121, -237, -408, -824]]\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[[11, -6, 1, 4, -1, 3, 12, -10, -12],\n [55, -30, 5, 20, -5, 15, 60, -50, -60],\n [-66, 36, -6, -24, 6, -18, -72, 60, 72],\n [-77, 42, -7, -28, 7, -21, -84, 70, 84],\n [143, -78, 13, 52, -13, 39, 156, -130, -156],\n [-77, 42, -7, -28, 7, -21, -84, 70, 84],\n [198, -108, 18, 72, -18, 54, 216, -180, -216],\n [-22, 12, -2, -8, 2, -6, -24, 20, 24],\n [55, -30, 5, 20, -5, 15, 60, -50, -60]]?\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[[70, -140, -30, -110, -60, 130, 80, 70, -100],\n [-14, 28, 6, 22, 12, -26, -16, -14, 20],\n [-98, 196, 42, 154, 84, -182, -112, -98, 140],\n [-7, 14, 3, 11, 6, -13, -8, -7, 10],\n [-35, 70, 15, 55, 30, -65, -40, -35, 50],\n [84, -168, -36, -132, -72, 156, 96, 84, -120],\n [-7, 14, 3, 11, 6, -13, -8, -7, 10],\n [42, -84, -18, -66, -36, 78, 48, 42, -60],\n [-56, 112, 24, 88, 48, -104, -64, -56, 80]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[422, 305, -114, -96, 266, -366, -302, 29, 13],\n [-26, -161, -363, -73, -340, -83, 431, -54, -27],\n [186, -319, 712, -102, -335, 389, 29, 106, -267],\n [-71, -262, 525, 201, -258, 491, -157, 405, -279],\n [40, -425, 33, 385, -364, 23, 64, -280, 435],\n [126, -87, -70, -240, -118, 82, 420, -211, 333],\n [-410, -22, 107, 128, 60, 61, -130, 13, -308],\n [-247, 399, -799, 203, 431, -318, -121, 61, 336],\n [191, -216, 188, 173, -345, 205, -81, 377, -199]]\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[[5, 186, -242, -160, 265, -414, 164, -82, 53],\n [-129, -405, 24, -189, -303, 455, 463, 350, -226],\n [-155, 536, -241, 47, 182, -308, 90, -233, 375],\n [51, 36, -228, -42, 151, -104, -150, 238, -1],\n [9, -332, -233, -423, -676, 102, 555, -125, -430],\n [285, -478, -477, -224, -511, -301, 79, -115, -139],\n [-149, -70, -116, -116, -275, 67, 306, -170, -164],\n [44, -454, 68, 166, -384, 471, -95, 317, 87],\n [69, -57, 19, 394, 186, 3, -596, 91, 247]]\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[[-3, 173, -284, 145, 244, -23, 269, -172, -59],\n [167, 532, 220, -252, -87, 233, 204, 384, -389],\n [-131, 9, 368, -427, 250, -453, -645, -160, 83],\n [-87, 156, 150, -370, -2, -223, -247, -142, 267],\n [2, 126, -351, 210, 338, 146, 276, -134, -275],\n [67, -244, 2, 96, -108, 204, -79, -98, 86],\n [125, 341, 111, -99, 176, 195, 84, 216, -503],\n [-40, -165, -37, 151, -270, -401, 108, -160, 628],\n [238, 359, -191, 363, 256, -99, 540, -132, -140]]\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[[5, -65, -20, 65, -50, 65, -70, -65, 10],\n [3, -39, -12, 39, -30, 39, -42, -39, 6],\n [-17, 221, 68, -221, 170, -221, 238, 221, -34],\n [-12, 156, 48, -156, 120, -156, 168, 156, -24],\n [-16, 208, 64, -208, 160, -208, 224, 208, -32],\n [-3, 39, 12, -39, 30, -39, 42, 39, -6],\n [-2, 26, 8, -26, 20, -26, 28, 26, -4],\n [-9, 117, 36, -117, 90, -117, 126, 117, -18],\n [2, -26, -8, 26, -20, 26, -28, -26, 4]]\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[[111, 84, 309, 39, 60, 381, 45, -57, 462],\n [113, 4, 11, 13, 92, 59, -165, -51, 74],\n [19, -6, -23, 0, 18, -17, -45, -8, -20],\n [97, -52, -197, -7, 100, -173, -285, -39, -206],\n [-178, -14, -46, -23, -142, -124, 240, 81, -154],\n [-165, -12, -39, -21, -132, -111, 225, 75, -138],\n [-223, -12, -37, -27, -180, -133, 315, 101, -166],\n [263, -22, -91, 20, 226, 11, -465, -116, 20],\n [-165, -70, -255, -40, -110, -345, 75, 80, -420]]\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, 117, -283, 200, -199, -16, 76, -209, -210],\n [409, -467, 359, -107, -145, 270, -77, -88, 197],\n [146, 39, 219, -50, 159, 56, 38, 103, 132],\n [-238, -35, -335, 30, -179, -136, -82, -87, -184],\n [309, -105, 369, -33, 81, 204, 57, 18, 195],\n [-215, 318, -180, 176, 24, -59, 136, -61, -138],\n [175, -160, 174, -63, -6, 96, -29, 7, 103],\n [-51, -116, -94, -124, -10, -115, -132, 81, -10],\n [-144, 411, -109, 510, -193, 238, 390, -415, -216]]\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[[-6, -51, -51, 15, 24, -45, 51, 3, -21],\n [-26, -221, -221, 65, 104, -195, 221, 13, -91],\n [-16, -136, -136, 40, 64, -120, 136, 8, -56],\n [6, 51, 51, -15, -24, 45, -51, -3, 21],\n [-14, -119, -119, 35, 56, -105, 119, 7, -49],\n [30, 255, 255, -75, -120, 225, -255, -15, 105],\n [6, 51, 51, -15, -24, 45, -51, -3, 21],\n [0, 0, 0, 0, 0, 0, 0, 0, 0],\n [-18, -153, -153, 45, 72, -135, 153, 9, -63]]\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[[-71, -244, 603, -69, -433, 68, 139, 216, 316],\n [-186, -474, -140, 275, 217, 159, 386, -6, -105],\n [-21, 18, 228, -352, 255, 75, 84, 27, -161],\n [656, 106, 603, -180, -410, -63, -146, -420, 25],\n [-225, 242, -170, -71, 417, 220, 149, 360, -166],\n [-570, -339, 501, -39, -15, 184, -53, -326, -189],\n [794, -73, 17, -423, -757, -652, -257, -581, 261],\n [185, 380, 741, -145, -288, 222, -236, -268, -126],\n [592, 316, -407, -392, 321, -442, -464, 25, -56]]\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[[267, 2, 341, -110, -92, -424, -190, -341, -284],\n [48, 187, -352, -103, 252, -420, 350, -353, 408],\n [-216, 269, -317, 69, -272, -54, 415, 37, 1],\n [115, 413, -279, -477, 66, -186, 70, -182, 38],\n [239, -8, 478, -187, -227, 221, 62, 275, -338],\n [84, -235, 16, 48, 127, 302, -83, -73, 62],\n [25, -350, 162, 331, -108, -667, 252, 14, -210],\n [-161, 546, -454, -420, -122, 299, 158, 239, -8],\n [22, -150, 327, -37, -324, 352, 179, 733, -501]]?\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[[-88, 88, -8, -48, 136, 0, -48, 56, -80],\n [66, -66, 6, 36, -102, 0, 36, -42, 60],\n [55, -55, 5, 30, -85, 0, 30, -35, 50],\n [-77, 77, -7, -42, 119, 0, -42, 49, -70],\n [88, -88, 8, 48, -136, 0, 48, -56, 80],\n [198, -198, 18, 108, -306, 0, 108, -126, 180],\n [-55, 55, -5, -30, 85, 0, -30, 35, -50],\n [-11, 11, -1, -6, 17, 0, -6, 7, -10],\n [121, -121, 11, 66, -187, 0, 66, -77, 110]]\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[[-225, 225, -195, 210, -210, 0, -15, -240, 225],\n [-180, 180, -156, 168, -168, 0, -12, -192, 180],\n [180, -180, 156, -168, 168, 0, 12, 192, -180],\n [150, -150, 130, -140, 140, 0, 10, 160, -150],\n [-105, 105, -91, 98, -98, 0, -7, -112, 105],\n [-210, 210, -182, 196, -196, 0, -14, -224, 210],\n [-210, 210, -182, 196, -196, 0, -14, -224, 210],\n [225, -225, 195, -210, 210, 0, 15, 240, -225],\n [-135, 135, -117, 126, -126, 0, -9, -144, 135]]\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[[286, 279, -421, 219, -404, 193, -200, 270, 4],\n [-194, 147, 347, 156, 539, 304, -279, 6, 263],\n [54, -164, -84, -133, -189, -253, 231, -88, -143],\n [215, 195, 151, 345, 405, -44, -22, -100, 296],\n [111, 298, -141, -148, -256, 137, 43, -43, -111],\n [5, 36, 85, -510, -182, -259, 495, -411, -287],\n [20, -202, -455, -287, -760, -107, 118, 173, -388],\n [113, 141, -176, 339, -26, 230, -327, 285, 163],\n [218, -62, -122, 83, -107, -269, 189, -64, -13]]\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[[2, 94, -255, 56, -85, -241, 47, -120, -168],\n [-239, 355, 247, -550, -393, 178, 123, 238, 30],\n [44, 310, 384, -322, -428, 416, 144, 2, -178],\n [412, -194, 176, -318, -338, 319, -361, -92, -113],\n [23, -17, -68, 176, -346, 48, -197, 268, -217],\n [-194, -103, 133, -324, 404, 132, -323, 358, 227],\n [108, -76, 138, 172, -492, 72, 100, -98, 38],\n [-130, -255, -86, -190, 495, -25, -548, 370, 147],\n [295, -348, 76, -191, -246, 82, -268, -89, 187]]\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[[-24, 118, -93, 615, 43, 34, 472, -66, 96],\n [-51, -497, 0, -213, 297, 11, -10, -118, 377],\n [-536, -287, 362, 162, 79, -356, -297, -182, 8],\n [115, -79, -26, -314, -138, 58, -315, 194, -132],\n [-144, -265, 49, 269, 66, 16, 163, 10, 166],\n [-127, 34, 101, 177, -44, -7, 128, 3, -17],\n [-105, 238, 45, 410, -205, -91, 3, 72, -251],\n [-151, -514, -25, 290, -51, -149, -415, 168, -13],\n [-247, -339, 260, -417, 113, -106, -286, -79, 114]]\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[[459, -171, -17, 266, -331, -11, 13, 523, 53],\n [-82, 123, -260, 189, 369, 411, 82, -174, -164],\n [73, 395, -198, 130, 310, -280, -457, -165, 150],\n [-80, -303, 178, 228, -177, 405, 376, -514, -282],\n [135, -160, 200, 254, 275, 103, 205, 547, 84],\n [-477, 86, 75, -50, 714, 309, 230, -260, -92],\n [-161, -50, -5, -374, 22, 8, 137, 417, 49],\n [-206, 273, -38, -467, 133, -454, -311, 131, 231],\n [8, -223, -98, -81, -345, 342, 285, 11, -207]]\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[[34, -28, 8, 4, -32, -24, -22, 6, 4],\n [170, -140, 40, 20, -160, -120, -110, 30, 20],\n [102, -84, 24, 12, -96, -72, -66, 18, 12],\n [51, -42, 12, 6, -48, -36, -33, 9, 6],\n [-306, 252, -72, -36, 288, 216, 198, -54, -36],\n [-187, 154, -44, -22, 176, 132, 121, -33, -22],\n [-238, 196, -56, -28, 224, 168, 154, -42, -28],\n [221, -182, 52, 26, -208, -156, -143, 39, 26],\n [119, -98, 28, 14, -112, -84, -77, 21, 14]]\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 9x9 matrix:\n[[101, 934, 381, -178, -637, -13, 156, 547, -507],\n [126, 182, 137, -477, -437, -324, -279, 265, 673],\n [-165, -345, 94, 681, 263, -73, 204, -253, -296],\n [-62, -120, 105, -447, -353, -477, -310, 438, 487],\n [-453, -763, -26, 129, 148, -371, -392, -802, 537],\n [-53, 372, 314, 13, 26, 182, -268, -249, 302],\n [65, 52, -207, -565, 125, 253, -334, 44, 369],\n [183, -226, -368, 274, 538, 439, 333, -155, -335],\n [-84, 42, -211, -22, 337, 451, 64, -141, -508]]\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[[-186, -75, 8, 41, -68, 51, -188, 26, 335],\n [-394, -317, -203, 389, -186, 112, 158, -61, -157],\n [-109, -120, -361, 105, 286, -375, -275, 21, -200],\n [-146, -502, -807, -15, -179, -339, 191, -73, -708],\n [173, -141, -466, -87, -244, -50, 653, -131, -776],\n [110, 158, 130, 114, 419, -193, 415, -36, -132],\n [503, 525, 598, -425, 287, -281, 58, -82, 313],\n [-45, -107, 555, 213, 459, 156, 172, 163, -3],\n [112, -288, 202, -222, -458, -400, 594, -138, -262]]\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[[-130, -120, 190, -180, -30, 80, 200, 120, 130],\n [208, 192, -274, 204, 66, -110, -266, -204, -136],\n [-208, -192, 159, 118, -135, 41, 59, 250, -140],\n [130, 120, -195, 194, 27, -83, -209, -118, -142],\n [-104, -96, 187, -242, -3, 85, 223, 82, 188],\n [-65, -60, 0, 176, -72, -17, -71, 98, -163],\n [117, 108, -121, 22, 57, -42, -90, -128, 3],\n [-39, -36, 7, 86, -39, -6, -30, 56, -81],\n [-130, -120, 200, -208, -24, 86, 218, 116, 154]]?\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 9x9 matrix:\n[[-36, 96, 96, 168, 84, -72, 72, -84, 96],\n [-6, 16, 16, 28, 14, -12, 12, -14, 16],\n [-21, 56, 56, 98, 49, -42, 42, -49, 56],\n [-36, 96, 96, 168, 84, -72, 72, -84, 96],\n [30, -80, -80, -140, -70, 60, -60, 70, -80],\n [-33, 88, 88, 154, 77, -66, 66, -77, 88],\n [-45, 120, 120, 210, 105, -90, 90, -105, 120],\n [-9, 24, 24, 42, 21, -18, 18, -21, 24],\n [-9, 24, 24, 42, 21, -18, 18, -21, 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[[117, -123, 137, 409, 172, -35, 368, 276, -117],\n [36, 378, 33, 57, -267, -195, -255, 279, 333],\n [-314, -1, -201, -148, -411, 245, -217, -53, 75],\n [-190, -254, -63, 165, -113, 237, 207, 45, -181],\n [286, -34, 98, -75, 484, -132, 112, -156, -67],\n [399, 276, 330, 366, 231, -498, 153, 393, 123],\n [89, 346, -3, -333, -80, -231, -414, -124, 262],\n [357, 81, 202, 257, 413, -244, 229, 207, 33],\n [-100, -17, -275, -332, 61, 343, -213, -245, 145]]\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, -63, -154, -123, -384, 297, -66, -309, -165],\n [-48, -177, -1, 124, -217, 154, -449, -428, 119],\n [246, -367, 277, -556, 902, -99, 68, 318, 788],\n [-144, 24, -44, -344, 204, 68, 336, 188, 56],\n [-182, 243, 74, 417, -633, 172, -65, -131, -532],\n [-312, 314, 293, 134, -59, 371, 78, -85, -4],\n [28, 184, 140, 459, -166, 60, -302, -249, -17],\n [-108, 470, 276, 135, 274, 94, 366, 271, 19],\n [102, -169, 74, -298, 599, -24, -46, 9, 596]]?\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 9x9 matrix:\n[[0, 39, -12, 36, 30, 51, 24, 48, -33],\n [0, 91, -28, 84, 70, 119, 56, 112, -77],\n [0, 26, -8, 24, 20, 34, 16, 32, -22],\n [0, -78, 24, -72, -60, -102, -48, -96, 66],\n [0, -65, 20, -60, -50, -85, -40, -80, 55],\n [0, 104, -32, 96, 80, 136, 64, 128, -88],\n [0, 13, -4, 12, 10, 17, 8, 16, -11],\n [0, -221, 68, -204, -170, -289, -136, -272, 187],\n [0, 208, -64, 192, 160, 272, 128, 256, -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[[-45, -106, 212, -56, 301, -102, -656, -512, 41],\n [-136, -110, 206, -25, -616, 214, 206, 114, -241],\n [-532, 81, -101, 161, -250, 95, -64, -118, -318],\n [-68, 388, -450, -74, 213, 69, 472, 376, 217],\n [151, -51, 209, 94, 74, -136, -310, -134, -1],\n [-62, 106, -75, 271, -163, -120, 92, 269, -203],\n [-278, 417, -400, 3, 62, 148, 410, 233, 99],\n [-326, -67, 46, 35, -287, -161, -386, 233, -456],\n [-259, 442, -76, 240, -6, 291, 280, -350, 190]]\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[[343, -12, -462, -268, -95, 146, 180, -420, -480],\n [-591, 162, 307, 615, -400, 428, 77, 279, 208],\n [495, 46, 518, 89, 71, -178, -80, 372, 279],\n [73, -477, 519, 93, 171, -379, -527, -391, -306],\n [186, 346, -21, 333, -249, 67, 406, 112, 323],\n [-299, 357, -142, 295, -376, 21, 235, 95, 434],\n [-361, 323, -342, 55, 240, 870, 647, 293, -44],\n [490, 265, -392, -367, -63, -244, 200, 88, 233],\n [260, 229, -741, -93, 211, 50, 711, -348, -59]]\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 9x9 matrix:\n[[-64, 124, -60, -85, -62, 13, -28, -18, -58],\n [30, 240, 0, -195, 60, 105, -150, -90, -60],\n [108, -196, 100, 133, 106, -17, 40, 26, 94],\n [111, -66, 90, 30, 123, 33, -33, -18, 57],\n [74, 168, 40, -147, 104, 101, -138, -82, -24],\n [33, 158, 10, -131, 55, 76, -107, -64, -35],\n [87, -46, 70, 19, 97, 28, -29, -16, 43],\n [-37, 234, -50, -177, -19, 68, -105, -64, -81],\n [-15, 198, -30, -153, 3, 66, -99, -60, -63]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[192, 203, 9, 118, 125, -228, 100, -24, -137],\n [-246, -33, -193, 72, 119, -10, -4, 174, 334],\n [-143, -290, -178, 137, -308, 789, -156, 141, 590],\n [-438, 310, -181, 517, 248, -417, 434, -72, 177],\n [-301, -139, -231, 144, 156, 275, 268, 494, 432],\n [32, 217, -161, 461, 94, 193, 338, 200, 267],\n [206, 85, 253, -388, 49, -376, -152, -180, -523],\n [256, -6, 303, -624, -161, 19, -478, -195, -400],\n [-301, 89, -158, 296, -27, 336, 170, 129, 418]]\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[[99, -77, 154, 99, -11, 99, 99, -55, -121],\n [72, -56, 112, 72, -8, 72, 72, -40, -88],\n [0, 0, 0, 0, 0, 0, 0, 0, 0],\n [81, -63, 126, 81, -9, 81, 81, -45, -99],\n [-81, 63, -126, -81, 9, -81, -81, 45, 99],\n [-27, 21, -42, -27, 3, -27, -27, 15, 33],\n [108, -84, 168, 108, -12, 108, 108, -60, -132],\n [-81, 63, -126, -81, 9, -81, -81, 45, 99],\n [-81, 63, -126, -81, 9, -81, -81, 45, 99]]?\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[[-251, 208, 277, -144, -321, -229, -714, 358, -598],\n [-5, -255, 11, -23, -201, 409, 288, -47, -299],\n [53, 394, 16, 9, -237, -281, -461, 242, -202],\n [-118, 231, -267, 355, 25, 79, 58, -271, 354],\n [-120, 220, -179, 434, 131, 260, 175, -216, 73],\n [520, 256, 99, -16, 664, -86, 406, -124, -227],\n [-807, 273, 38, 719, 367, 229, 48, -199, 320],\n [-80, 439, -121, 250, 174, 357, 399, -590, -585],\n [-128, -6, 51, 62, 4, -339, -369, 287, 558]]\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[[-111, 116, 187, 301, -332, 407, 691, 66, 142],\n [-367, 410, 166, 143, -218, 316, 748, 259, -72],\n [-275, 14, 56, -140, -67, -278, 56, -50, 23],\n [113, -544, 333, -457, -359, -682, -59, -447, -321],\n [-590, 138, 135, -349, -270, -146, 433, -95, -22],\n [-577, 135, 16, -459, -491, -400, 413, -331, -29],\n [9, 327, -131, 648, -147, 236, 277, 120, 427],\n [69, 20, -120, 8, 397, 122, -134, 314, -163],\n [101, -405, -96, 32, -361, -542, -152, -514, 354]]\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[[-81, 356, -330, 457, 400, -324, -161, 570, -177],\n [21, 5, 14, 127, -28, 188, 80, -60, -122],\n [210, 9, 272, -267, -159, 515, 152, -189, 51],\n [-53, -309, 428, -260, -186, 172, 263, -226, 470],\n [74, 227, -356, 48, 51, -292, -294, 40, -327],\n [-71, 190, -54, 120, 232, -379, -81, 371, 223],\n [214, -100, 220, -114, -295, 768, 229, -446, -250],\n [89, 471, -240, 406, 278, -80, -107, 398, -248],\n [-273, -178, 168, 167, 156, -285, 158, 251, 457]]\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[[-200, -12, 130, 290, 124, -240, 2, 202, -36],\n [-309, 632, -250, -79, 68, 42, 304, 502, -291],\n [-262, 151, 265, 542, 103, -463, 492, 453, -470],\n [199, -57, 246, 98, -166, -74, 543, -53, -422],\n [-191, 180, 141, 318, -71, -312, -2, 156, -79],\n [-314, 394, -273, -11, 214, 117, 94, 273, -139],\n [74, -137, -397, 7, 107, -166, -639, -16, 474],\n [68, 182, -78, -4, -202, 78, -4, -294, -80],\n [-398, 196, 271, 641, 64, -468, 123, 241, -244]]\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[[169, -136, 55, -101, 262, 29, 201, -310, 91],\n [165, -13, 107, 178, -96, -277, 252, -23, -231],\n [-314, -165, 0, 135, 73, -126, 301, 147, -17],\n [-104, 35, 303, 239, 37, -442, 316, 108, -184],\n [-171, -384, -394, 475, -224, 399, 455, 194, -172],\n [360, 404, -43, -218, -445, 204, -594, -156, 142],\n [-140, -396, -348, 844, -162, 456, 464, 500, -530],\n [672, 470, 516, -150, 30, -328, -307, -387, -76],\n [10, 13, 90, -760, 337, -448, -140, -369, 351]]\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 9x9 matrix:\n[[244, -288, 246, 74, 332, -14, 296, -530, -12],\n [-331, 91, -172, -271, -213, -27, -179, 219, 313],\n [33, 19, 2, 43, -1, 7, -3, 25, -59],\n [-244, 288, -246, -74, -332, 14, -296, 530, 12],\n [73, 91, -22, 123, -41, 23, -43, 137, -179],\n [-374, 54, -168, -334, -202, -38, -166, 166, 402],\n [-220, 8, -86, -210, -100, -26, -80, 58, 260],\n [201, 79, 32, 241, 23, 37, 9, 91, -323],\n [120, 14, 37, 125, 40, 17, 30, -1, -160]]\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[[70, 233, -712, -259, -20, 9, -559, 330, -55],\n [-126, 125, -52, 356, -261, 359, -34, 58, 38],\n [134, -305, 434, 157, -218, 168, 204, -48, -296],\n [247, 150, 109, -170, 395, -304, 48, -173, -120],\n [379, 55, -160, -193, 120, -219, -186, 39, -331],\n [-139, -85, 67, -235, 19, -551, -74, -577, -78],\n [-85, 228, -110, 4, 232, 165, 1, 195, 256],\n [-173, 66, -205, 260, -277, 570, -106, 411, 152],\n [173, 96, 207, -276, 505, -496, 140, -323, -28]]\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[[-22, 44, -99, 187, -55, 143, 165, 132, 143],\n [0, 0, 0, 0, 0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0, 0, 0, 0, 0],\n [12, -24, 54, -102, 30, -78, -90, -72, -78],\n [18, -36, 81, -153, 45, -117, -135, -108, -117],\n [-20, 40, -90, 170, -50, 130, 150, 120, 130],\n [-18, 36, -81, 153, -45, 117, 135, 108, 117],\n [12, -24, 54, -102, 30, -78, -90, -72, -78],\n [8, -16, 36, -68, 20, -52, -60, -48, -52]]\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[[-135, -524, -560, -295, 69, 28, 250, 337, 294],\n [-471, -326, 92, 300, 5, 185, -43, -180, 19],\n [467, 317, 12, 92, 413, 35, 236, 82, 506],\n [-497, -705, -392, -299, -111, 99, 138, 229, -40],\n [-107, 138, 306, 298, -327, 17, -112, -201, -401],\n [-344, -308, 24, 313, -200, 162, 108, -58, -121],\n [-232, -114, 136, 469, 428, 170, -142, -298, 381],\n [-217, -501, -438, -43, -99, 82, 274, 243, 194],\n [-336, -641, -580, 7, -258, -55, -34, 146, -71]]\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[[-88, 241, -77, 149, -239, -186, 259, -73, -267],\n [202, 61, 130, -296, -61, -47, -351, -43, -115],\n [4, -603, -32, -457, -246, 430, -538, 864, 112],\n [244, -196, -287, 153, 343, -292, 206, -239, 642],\n [235, -66, -121, 259, 53, 235, -260, 123, 275],\n [-119, 238, 25, 111, -35, 131, 82, -152, -152],\n [-156, 336, -240, -334, -215, -471, 488, -477, -254],\n [60, -146, -562, -348, 86, 124, 464, -209, -427],\n [162, 55, -72, 43, 216, 186, -174, -245, 149]]?\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[[342, 39, -358, 209, 141, -7, -415, -278, 139],\n [96, 17, -12, 51, 141, -41, -103, 262, -13],\n [222, 6, -166, 220, 252, 94, -276, 2, 48],\n [-180, -26, 202, -87, -36, 32, 216, 179, -82],\n [-228, 50, 124, -446, -522, -394, 318, 0, -14],\n [63, -79, -19, 372, 396, 457, -132, -143, -14],\n [-168, -50, 212, 20, 90, 166, 186, 174, -94],\n [-159, -3, 75, -170, -246, -71, 194, -157, -8],\n [-162, 4, 128, -191, -204, -114, 208, 49, -38]]\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[[-2, -78, 437, 99, -202, 64, -10, 64, -213],\n [3, -108, 357, 114, -222, 54, -60, -21, -168],\n [-3, -72, 453, 96, -198, 66, 0, 81, -222],\n [-36, 324, 90, -234, 396, 0, 396, 576, -90],\n [16, -168, 68, 132, -232, 16, -184, -248, -12],\n [20, -210, 85, 165, -290, 20, -230, -310, -15],\n [34, -300, -112, 214, -360, -4, -372, -546, 98],\n [6, -24, -150, 4, 4, -20, -56, -106, 80],\n [12, -60, -246, 22, -20, -32, -116, -208, 134]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 225, -45, 45, 195, -255, -30, 60, -105],\n [0, -255, 51, -51, -221, 289, 34, -68, 119],\n [0, 270, -54, 54, 234, -306, -36, 72, -126],\n [0, -240, 48, -48, -208, 272, 32, -64, 112],\n [0, -225, 45, -45, -195, 255, 30, -60, 105],\n [0, 255, -51, 51, 221, -289, -34, 68, -119],\n [0, 120, -24, 24, 104, -136, -16, 32, -56],\n [0, -225, 45, -45, -195, 255, 30, -60, 105],\n [0, 255, -51, 51, 221, -289, -34, 68, -119]]\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[[84, 30, 21, 27, 147, 315, 9, 468, -162],\n [-399, -300, -286, 212, -184, -281, 24, 13, 229],\n [304, 0, -68, -55, 215, 348, -135, 265, -313],\n [-188, 262, 73, -37, 179, -9, 181, 380, -6],\n [-191, 162, -213, -68, 238, -206, 54, 146, -78],\n [342, 42, 209, -59, 27, 349, -68, 57, -152],\n [161, 98, -193, -90, 344, 198, -90, 342, -336],\n [-42, 76, 120, -68, -142, -270, 39, -463, 172],\n [152, -172, 402, 128, -376, 278, 26, -96, 206]]\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[[308, 152, -100, -228, -103, 547, -215, 115, -48],\n [-208, -28, 158, 160, 193, -306, 209, -28, -2],\n [-331, -107, 126, 309, 233, -388, 278, -95, 78],\n [295, 116, -152, -196, -125, 590, -216, 178, 17],\n [-195, 69, 164, 273, 310, -138, 147, -723, -168],\n [-355, 137, 442, 349, 650, -249, 491, -64, -74],\n [35, -241, -330, -41, -459, -204, -280, -361, 58],\n [260, -117, -332, -269, -458, 275, -296, 488, 187],\n [-62, -243, -188, -31, -381, -500, -169, -341, -1]]\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[[-10, 133, 82, -393, -223, 319, -21, 263, -115],\n [-45, 4, 199, -260, -198, 222, -14, 24, -126],\n [56, -188, -49, -5, 140, -379, 121, 202, 17],\n [105, 204, 188, 4, 218, -220, 231, -211, 205],\n [88, 383, -229, -236, 180, -55, 215, 4, -80],\n [8, 36, -120, -332, -129, 117, -9, 443, -124],\n [210, 149, 553, -47, -212, 612, -89, -19, 268],\n [629, -784, 347, 723, 171, 80, -103, 68, 194],\n [199, 132, 59, -156, 278, -390, 318, 180, 170]]\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 9x9 matrix:\n[[-63, -152, -166, 294, -81, 58, -128, 149, -554],\n [-222, 34, 380, 316, -42, -166, -28, -320, 51],\n [-153, 239, 266, 363, 232, -223, 19, -235, -156],\n [691, 839, -74, 105, 561, 602, -241, 487, -32],\n [335, 254, -338, -40, 28, 33, 104, 367, 135],\n [151, -81, -252, -22, 327, 150, -216, 184, -263],\n [353, -200, -95, -116, 457, 962, -218, 562, -33],\n [18, 284, 22, -213, 521, 162, 55, 17, -399],\n [408, 20, 45, -126, 245, 201, -488, -33, 716]]\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[[-291, 190, 137, -27, -118, -466, -225, 196, -59],\n [-20, 60, 397, -343, 25, -16, 272, -380, 148],\n [417, 62, 220, 204, -268, 265, 629, 402, -135],\n [580, -234, -241, -353, 431, 454, -233, -423, 65],\n [-134, -210, 320, -187, 373, -303, 80, 71, 595],\n [189, -1, -210, 390, -201, 426, 6, 78, -277],\n [8, 352, 223, -71, 2, -103, -391, -423, -465],\n [195, -260, 169, 322, -792, 500, 295, 381, -28],\n [394, 167, -219, -130, -305, 280, 8, 72, -370]]\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[[5, -75, 15, -60, -5, -45, 60, 35, 35],\n [10, -150, 30, -120, -10, -90, 120, 70, 70],\n [-11, 165, -33, 132, 11, 99, -132, -77, -77],\n [-6, 90, -18, 72, 6, 54, -72, -42, -42],\n [6, -90, 18, -72, -6, -54, 72, 42, 42],\n [10, -150, 30, -120, -10, -90, 120, 70, 70],\n [5, -75, 15, -60, -5, -45, 60, 35, 35],\n [8, -120, 24, -96, -8, -72, 96, 56, 56],\n [7, -105, 21, -84, -7, -63, 84, 49, 49]]\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[[-178, -197, -106, 194, -88, 27, 29, 175, -162],\n [-356, -683, -173, -45, -128, -136, 57, -42, -79],\n [-263, 227, -148, 350, -270, -13, 4, 401, -123],\n [418, -277, 301, 527, 320, 596, 341, 472, -380],\n [79, -583, 193, 91, 58, 196, 372, 208, -18],\n [321, -143, 123, -55, 298, 218, 54, -130, -64],\n [-373, 131, -213, -317, -260, -454, -266, -308, 208],\n [372, 151, 533, 120, 181, 157, 137, 108, 7],\n [-84, -219, 221, 30, -175, -49, 287, 228, 166]]\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[[24, -156, 48, 156, 120, 144, 72, -204, 36],\n [8, -52, 16, 52, 40, 48, 24, -68, 12],\n [-4, 26, -8, -26, -20, -24, -12, 34, -6],\n [20, -130, 40, 130, 100, 120, 60, -170, 30],\n [-34, 221, -68, -221, -170, -204, -102, 289, -51],\n [-16, 104, -32, -104, -80, -96, -48, 136, -24],\n [-6, 39, -12, -39, -30, -36, -18, 51, -9],\n [-4, 26, -8, -26, -20, -24, -12, 34, -6],\n [4, -26, 8, 26, 20, 24, 12, -34, 6]]\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[[182, 75, 190, -82, -67, -58, 106, -446, -396],\n [-142, -305, 334, 13, -72, 126, -118, -314, 5],\n [52, 46, 32, 140, 199, -103, 81, 368, 307],\n [-184, -337, 204, -116, -100, 201, -168, -410, -22],\n [114, -318, 629, 148, 421, 53, 198, -33, -23],\n [-210, -11, -358, -24, -98, 99, -163, 290, 203],\n [-212, -182, -18, 23, -147, 204, -134, -26, -219],\n [-272, -493, 264, -138, -69, 298, -223, -446, 31],\n [390, 108, 285, 132, 554, -132, 433, 287, -202]]\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[[-198, 760, 204, 423, 68, 15, 207, -328, -131],\n [140, 65, -34, 168, -244, -176, 99, 86, 288],\n [89, -145, 358, -130, -438, -109, 192, -108, -53],\n [-183, 14, 116, -364, -46, -182, 217, -60, -19],\n [-43, 695, -316, 390, 134, -152, -30, -364, -103],\n [-225, -223, 171, -373, -502, -259, 490, 10, -150],\n [-320, 764, 6, 271, -136, -307, 495, -192, 71],\n [-208, -170, 55, -93, -312, -72, 361, 141, -98],\n [-165, 370, -215, 329, 126, 81, 19, -180, -288]]?\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[[-22, 363, -109, 57, -499, -107, -811, 59, -8],\n [11, 269, 212, 161, 263, 435, 268, 21, -17],\n [113, -431, -93, 192, 156, 239, 726, -113, -329],\n [85, 330, 65, 160, -313, 471, -43, 152, -85],\n [-392, 458, 449, -422, -164, 538, 232, 44, -24],\n [617, -252, -234, 529, 399, -227, 59, 183, 621],\n [-428, 462, 419, -807, 106, 99, -355, -222, -629],\n [174, 501, 474, -219, 398, 551, 144, 6, 219],\n [-30, 233, 276, -505, 180, -65, -307, -212, 108]]?\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[[-279, -140, -150, 329, 365, 86, -283, 371, 15],\n [-83, 255, -506, -304, 193, -43, 591, -422, 283],\n [129, -33, 223, -175, -250, 387, -406, 281, 212],\n [128, -145, 94, 281, -429, 189, -515, 205, -76],\n [-265, -47, -208, -79, 85, 319, -111, 383, 682],\n [326, 139, -259, 57, -493, 399, -692, 152, 77],\n [813, 52, -363, -212, -394, -328, -304, -264, -358],\n [-201, -171, 513, 146, 245, -450, 409, -74, -338],\n [-372, 88, 131, 615, -227, 346, -158, -86, -284]]\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[[72, 29, -47, -53, 7, 53, 232, -67, -178],\n [0, 345, -207, -193, 225, -272, -91, -36, -106],\n [-78, -155, 113, 129, -79, 92, -117, 46, 164],\n [-144, -179, 101, 187, -43, 272, 121, -68, 30],\n [102, 82, -22, -112, -16, -255, -265, 127, 118],\n [171, 283, -199, -254, 125, -220, 148, -47, -261],\n [54, 335, -233, -213, 217, -165, 174, -115, -284],\n [-207, -70, 28, 165, 64, 264, 165, -133, -41],\n [-372, 98, -38, 162, 226, 100, -150, -112, 112]]?\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[[-83, -44, 136, 228, -454, 49, -38, 41, -407],\n [14, 356, -106, -184, 191, 226, -4, -309, 133],\n [-156, -429, -172, 595, 764, 321, -324, 139, 711],\n [48, 51, 209, 498, -218, 218, -487, 494, 79],\n [-77, -795, 38, -164, 23, -429, 60, -448, 172],\n [-342, -101, 370, -303, -674, -327, -97, 52, -362],\n [-229, 210, 390, -56, -430, 163, -485, 32, 5],\n [442, 13, -159, 510, 308, 309, 16, -88, 233],\n [-86, -239, -68, 239, -85, -190, 195, 408, -273]]\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[[20, -209, -165, -315, -35, 241, -68, 394, -222],\n [2, -96, 263, -185, 2, -248, -148, 86, 320],\n [330, 258, 209, -139, 51, 38, -403, 222, 389],\n [-262, -152, 300, 227, 246, -393, 444, -483, 145],\n [77, 486, 35, 608, -297, 5, -176, -301, -102],\n [-240, -309, -223, -80, -247, 94, 96, 177, -461],\n [-26, 94, -601, 137, -182, 384, 98, -24, -504],\n [258, 67, -437, -346, 134, 438, -111, 313, -54],\n [29, -231, -179, -423, 203, 111, 77, 214, 60]]\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[[163, 106, 791, -46, -214, -112, 162, 321, 398],\n [423, 21, 543, 197, -403, -160, 30, 294, 74],\n [230, -79, -258, 162, -327, 168, 302, -44, 97],\n [473, 99, -113, -562, -146, 129, 168, -305, 229],\n [82, 241, 149, -2, -431, -174, -79, -265, 88],\n [-11, 97, -476, 90, 79, 52, -259, -182, -592],\n [461, 349, -250, -805, -157, 233, 140, -547, 96],\n [198, 48, -391, -255, 230, 210, -24, -88, -339],\n [15, 365, -408, -80, -362, 300, 61, -456, -338]]\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 9x9 matrix:\n[[322, 43, -76, 543, -97, -151, 256, -230, 319],\n [394, -27, -104, 342, -473, -323, 141, -781, -209],\n [-89, 47, 101, 7, 10, 249, 194, -509, -334],\n [-104, -46, 348, -548, 257, 279, 65, -315, -556],\n [-385, -81, -90, 158, -219, 294, -137, 486, 232],\n [116, 406, 284, 349, 168, -83, 10, -160, -176],\n [-399, 129, 276, -140, -281, -321, -582, 390, -61],\n [328, 38, 424, -49, 93, 167, 338, -842, -610],\n [46, -3, -255, 136, -406, -513, -132, -373, 74]]\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 9x9 matrix:\n[[-19, 261, 260, -139, -162, -338, -243, -361, 215],\n [-67, 81, 169, -213, 318, 275, 418, 430, -286],\n [15, -227, -316, 239, -106, 14, -133, -87, 39],\n [-194, 52, -71, -28, 8, -135, -53, -175, -41],\n [-15, 4, 105, -149, 308, 337, 424, 484, -285],\n [-415, 274, 95, -249, 128, -253, 34, -246, -145],\n [118, -328, -309, 232, 64, 323, 141, 311, -119],\n [-263, 216, 141, -229, 156, -99, 124, -48, -149],\n [-328, -139, -315, 18, 274, 191, 283, 197, -370]]\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[[218, 408, -524, 260, 442, -34, -198, 48, -154],\n [-131, -337, 328, -137, -308, -74, -37, -92, 15],\n [112, 372, 98, -86, -286, 416, 110, 14, 154],\n [150, 96, 4, -28, -126, 146, -102, -12, -58],\n [243, 433, 6, -53, -232, 468, -153, -4, 51],\n [-79, -344, 180, -44, -146, -182, -315, -129, -107],\n [16, 292, 31, -57, -59, 299, 252, 83, 194],\n [572, -74, 163, -285, -213, 610, -569, 93, -247],\n [-267, -312, 456, -180, -440, -46, 191, -99, 163]]\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[[33, -145, -103, 11, 170, -185, -129, -25, 152],\n [-341, 8, 203, 11, 68, -151, 109, 111, -443],\n [307, -18, -189, -9, -48, 121, -107, -101, 407],\n [301, 104, -115, -19, -196, 287, -5, -87, 307],\n [102, 30, -42, -6, -60, 90, -6, -30, 108],\n [-117, -251, -77, 25, 334, -403, -171, 13, 40],\n [-121, -82, 23, 11, 128, -171, -31, 31, -93],\n [157, 139, -11, -17, -206, 267, 67, -37, 96],\n [-85, 238, 187, -17, -272, 289, 221, 51, -289]]\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[[-215, 85, 63, 120, 225, 19, 74, 412, -436],\n [53, -68, 287, 27, 184, -408, -124, 472, 97],\n [-230, -235, 286, -533, -162, -232, 179, 207, 380],\n [-109, 444, 100, 41, -240, -132, -268, 413, 138],\n [229, -174, -18, 37, 150, 190, 0, -219, -26],\n [-154, 179, 356, 82, 27, 26, -296, 149, 356],\n [237, 31, -439, 294, 84, 274, 87, -361, -475],\n [164, -358, 396, -346, 66, -114, -50, 35, 527],\n [-177, 3, -189, -389, -407, -170, 258, -15, 81]]\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[[-254, -330, -11, 58, -133, -164, 176, 271, 179],\n [416, 3, 398, 103, -347, -106, -1, -104, -203],\n [-206, -108, -114, 93, 128, -242, 38, 267, 2],\n [165, 254, -56, -80, -54, 134, -260, -305, 319],\n [237, -32, 166, 326, -54, -62, 202, -187, -37],\n [38, 406, -256, -204, 394, 469, -154, -384, -85],\n [-415, -297, -123, -324, -122, 199, 97, 231, 188],\n [-186, 277, -323, -490, 132, 426, -359, -184, 306],\n [-171, -325, 169, -478, -510, 298, 33, 137, 137]]?\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[[14, -629, 104, -151, 209, 2, 531, -571, 253],\n [-159, -438, 531, -26, 311, -191, 189, -375, -10],\n [-192, -14, 27, -296, 98, 230, 393, -482, -63],\n [25, 267, -146, 299, -115, -178, -469, 694, -66],\n [-377, -233, -247, -6, 413, -19, 491, -152, -311],\n [725, -6, 7, 172, -754, 2, -321, 333, 494],\n [-168, -163, 249, 300, 383, -455, 372, 134, -480],\n [-198, 129, -254, 36, 425, -139, -87, 160, -41],\n [621, -8, 78, 110, -742, 70, -208, 199, 363]]\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[[165, 498, 66, -615, 828, -494, -11, 165, 359],\n [519, 226, 466, -431, 438, -567, -244, 524, 388],\n [-391, -143, -79, -125, -243, 147, 250, 43, 89],\n [-496, 512, 117, 5, 14, -89, -62, -601, -105],\n [153, -334, -191, -158, 76, -351, 178, -3, -118],\n [-246, -156, -224, 343, -352, 1195, 41, -7, 79],\n [-17, 331, -295, 173, -75, 185, -16, -626, 49],\n [-742, 226, 35, -3, -166, 271, 133, -179, -157],\n [49, -866, 19, 354, -461, 60, 53, 0, -414]]\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[[297, -397, -314, 426, -596, -215, 265, 300, -70],\n [-749, -350, -191, 543, -475, -94, 34, 457, 249],\n [440, 344, -81, -361, 330, 166, 198, -151, -237],\n [275, 86, 176, 152, -486, 231, -279, -177, -187],\n [223, 107, -239, -165, 272, -211, 87, -15, 553],\n [-245, 188, -608, 131, 300, 38, 215, 603, 5],\n [-275, 270, 165, -255, 1, 61, -62, -163, -391],\n [198, -74, 386, -244, -111, 186, 61, -359, -181],\n [-593, 78, 370, -200, -269, 136, 3, -209, -458]]\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 9x9 matrix:\n[[-349, 304, -329, -285, 90, 8, -35, -226, -197],\n [125, -89, -68, -318, 158, 70, 65, -103, 117],\n [177, 192, -76, 203, -207, -349, 229, 32, -217],\n [-443, -255, -258, 469, -312, -52, -559, -248, -38],\n [306, 19, 400, -430, 374, 306, 280, 253, 266],\n [-226, 388, -184, -156, 120, -94, 63, -28, -207],\n [307, -44, 635, 36, -184, 254, 65, 35, 476],\n [-212, 242, -361, 310, -348, -396, -73, -229, -316],\n [121, 172, -72, -94, -504, -28, 303, -386, -153]]\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[[120, -352, 414, -431, 55, -184, -10, -89, 0],\n [191, 285, -72, -252, -54, 401, 73, 72, -401],\n [-197, 175, -15, 397, 347, 107, 331, 24, -190],\n [-114, 18, -195, 190, -496, -144, -444, -35, 567],\n [-258, -56, 431, 160, -148, -238, -433, 344, 691],\n [-2, -60, -94, -537, -53, 17, -162, -244, -223],\n [-359, -105, 179, -43, 15, -277, -61, -136, 128],\n [-172, -48, -191, 54, 23, -308, -266, 233, 254],\n [385, 68, -343, -223, -84, 367, 339, -411, -589]]\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[[70, -49, -77, -28, 105, 63, 14, -14, -7],\n [160, -112, -176, -64, 240, 144, 32, -32, -16],\n [150, -105, -165, -60, 225, 135, 30, -30, -15],\n [-170, 119, 187, 68, -255, -153, -34, 34, 17],\n [120, -84, -132, -48, 180, 108, 24, -24, -12],\n [-140, 98, 154, 56, -210, -126, -28, 28, 14],\n [0, 0, 0, 0, 0, 0, 0, 0, 0],\n [110, -77, -121, -44, 165, 99, 22, -22, -11],\n [-20, 14, 22, 8, -30, -18, -4, 4, 2]]\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[[835, 274, 449, -277, -639, 54, -399, -183, 14],\n [-122, -41, 40, 230, -125, -105, 442, 350, -630],\n [-295, 222, 0, -220, 66, 240, -72, -208, 270],\n [-497, -596, -457, 286, 556, -225, 2, -55, 97],\n [294, 417, -155, 113, 85, -33, -193, -173, -25],\n [546, 183, 7, -104, 24, -34, -475, -442, 289],\n [292, 227, 228, -60, -315, -141, 432, 295, -367],\n [153, 55, -488, 195, 384, -206, -494, -369, 328],\n [-37, 531, 566, -411, -454, 572, 133, 154, 77]]\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[[20, -59, 40, -304, 56, 23, 168, 101, 73],\n [135, -266, 2, -497, -186, 219, 69, 246, 24],\n [-54, 98, 19, -10, 138, -105, 93, -33, 57],\n [125, -179, -117, -363, -284, 151, -144, 244, 16],\n [69, -199, 111, -291, -4, 167, 204, 92, 0],\n [15, -32, 5, -77, -12, 24, 24, 33, 9],\n [114, -162, -110, -286, -272, 142, -156, 208, 0],\n [-17, 140, -187, 163, -140, -116, -312, 13, 5],\n [6, -85, 131, -194, 130, 58, 261, 16, 30]]\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 9x9 matrix:\n[[499, -157, -336, -141, 281, -171, 106, -50, -328],\n [358, 23, -217, 126, 53, -240, -64, -187, -296],\n [180, 208, -209, 283, -8, 264, 80, -138, -467],\n [-567, 309, 389, 366, -441, 147, -218, -68, 287],\n [-64, -287, 127, -384, 115, -282, -20, 169, 416],\n [102, -67, -146, -145, 191, 288, 224, 121, -173],\n [-388, 237, 300, 317, -369, -42, -244, -113, 235],\n [-48, 135, 63, 222, -171, -126, -156, -141, -6],\n [-286, -60, 249, -103, -108, -114, -100, 88, 397]]\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, -371, -142, -754, 517, 6, -33, -451, 480],\n [39, 434, -237, 328, -101, 108, 106, 200, -363],\n [-142, -467, 108, 412, 91, -134, 558, 276, 90],\n [140, 239, -55, 83, 28, 237, 301, 224, 416],\n [528, -2, -124, -632, 367, 326, -265, -28, -160],\n [259, -22, 105, 95, -153, 202, 377, 256, -412],\n [-277, 17, -181, 52, 131, -10, 365, 98, 293],\n [-10, 62, -32, 72, -23, -84, 22, -248, 33],\n [-124, 345, -54, 547, -316, -137, -66, 73, -353]]\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[[-21, -30, -186, 114, 320, 86, 175, 156, 142],\n [-75, 191, 256, -384, -184, -263, 47, -322, -89],\n [108, -169, 184, 219, -619, 109, -553, -85, -230],\n [-25, 27, -198, 9, 413, 33, 298, 179, 154],\n [184, -88, -14, 63, -217, 84, -157, 255, -179],\n [28, 64, -178, -99, 381, -12, 341, 245, 87],\n [221, -129, -168, 156, -12, 169, -45, 458, -117],\n [54, -88, 166, 99, -449, 36, -375, -121, -163],\n [153, -183, -240, 318, 106, 247, -55, 420, -1]]\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[[-489, -49, 352, 251, -530, -176, -387, 228, 210],\n [503, -53, -363, -335, 441, 91, 309, -259, -306],\n [91, 61, -184, -133, -218, -212, -227, -206, -180],\n [662, -68, -494, -466, 386, 34, 342, -92, -278],\n [324, 102, -323, -194, 383, 36, 87, -721, -467],\n [-436, 72, 303, 302, -319, -61, -270, 75, 194],\n [-301, -30, 309, 239, -235, 53, 3, 642, 473],\n [90, 1, 3, 14, 221, 165, 250, 204, 141],\n [-256, -209, 215, 36, -255, -138, -253, -76, -108]]\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[[157, -39, -72, 17, -532, -23, -195, -183, -338],\n [-156, -69, 367, -226, 160, -5, -486, -61, -160],\n [148, -100, 256, -222, -56, -146, -520, -62, -312],\n [150, 149, 101, -263, -227, -36, -469, -136, -190],\n [20, -100, -6, -115, -39, -365, -59, -63, 18],\n [24, 478, 176, -471, 222, 329, -203, 234, 142],\n [-104, -157, -183, 424, -386, 197, 193, -204, -170],\n [-281, 86, -159, 395, 97, 276, 150, -250, 280],\n [84, 204, -139, -22, 377, 155, 508, 386, 356]]?\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 9x9 matrix:\n[[-7, 3, -5, -13, 13, -11, -4, 0, -6],\n [-126, 54, -90, -234, 234, -198, -72, 0, -108],\n [-49, 21, -35, -91, 91, -77, -28, 0, -42],\n [-126, 54, -90, -234, 234, -198, -72, 0, -108],\n [63, -27, 45, 117, -117, 99, 36, 0, 54],\n [35, -15, 25, 65, -65, 55, 20, 0, 30],\n [0, 0, 0, 0, 0, 0, 0, 0, 0],\n [-35, 15, -25, -65, 65, -55, -20, 0, -30],\n [-35, 15, -25, -65, 65, -55, -20, 0, -30]]\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[[-387, 53, 188, 243, 149, 99, -371, -321, -353],\n [-29, -140, -142, 192, -290, 131, -178, -20, 45],\n [345, -113, -218, -153, -299, -39, 251, 261, 353],\n [287, 20, -47, -273, -25, -134, 322, 200, 240],\n [-280, 149, 316, -3, 257, -44, -185, -313, -294],\n [199, -93, -117, -84, -284, -12, 95, 101, 228],\n [-33, -168, -309, 333, -159, 204, -138, 156, 18],\n [16, -4, -52, 24, 48, 12, 36, 68, 4],\n [71, -72, 50, -84, -366, -17, -78, -136, 137]]?\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[[22, -92, 190, -178, 56, 70, -22, -544, -276],\n [-148, -117, -246, 232, -164, -253, -285, 587, -175],\n [655, 355, 191, 498, -238, 230, 86, 694, 297],\n [10, -118, 49, -247, -536, 52, -381, -428, -32],\n [459, -635, -482, -78, -18, -150, 317, -185, 155],\n [-265, -278, 73, 36, 436, -597, 395, -115, -230],\n [261, -7, -143, 286, 215, 32, 192, 460, 12],\n [-486, -279, -143, -172, 82, -422, -59, -163, -194],\n [21, -730, -654, -218, -46, -363, 156, -170, 126]]\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[[70, -50, 94, -125, 199, -141, 305, 132, 421],\n [500, -46, -633, 101, -202, 25, 274, 58, 350],\n [-302, 433, 18, -181, -65, -66, -892, -492, -815],\n [193, 162, -221, -212, -10, -23, -287, -190, -336],\n [197, -27, 173, -481, 406, 50, -73, 199, -187],\n [322, 133, -108, 210, 255, -346, 131, 42, -47],\n [-385, 386, -307, 495, -818, 252, -266, -513, 95],\n [-213, -788, 644, -75, 450, 49, 272, 598, -116],\n [112, -550, 51, 399, 37, -283, 785, 324, 901]]\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 9x9 matrix:\n[[69, -93, 152, -84, 78, -170, -256, 365, 35],\n [79, 134, -77, 28, 96, -5, -118, -103, 138],\n [-194, -299, -95, 264, 324, -81, -144, 218, -249],\n [239, 248, 1, -84, 132, -107, -346, 21, 332],\n [38, 122, 52, -144, -282, 112, 254, -192, 44],\n [-379, -489, -144, 388, 324, -18, 42, 203, -491],\n [-336, -356, -250, 436, 381, 26, 19, 17, -391],\n [-273, -345, -182, 372, 390, -40, -92, 139, -329],\n [16, -28, 164, -176, -252, 12, 156, 84, -32]]\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[[-59, -60, 192, -160, 2, -185, -66, 260, 266],\n [-186, -27, -195, -155, 461, -109, -67, -384, -317],\n [110, 107, -18, 154, -406, 183, -53, 81, 46],\n [-81, 217, -37, 115, -127, -322, 217, -376, 427],\n [-264, -319, -172, 270, 154, -319, 242, -343, -588],\n [70, 480, -334, -297, -67, 88, -328, -314, 19],\n [-79, -194, 272, 275, 31, -173, 366, -4, 357],\n [-350, -564, 298, 380, -198, -66, -2, 209, -236],\n [77, 247, -77, 161, -605, -418, 223, -32, 341]]?\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[[492, 255, -216, 139, 18, -175, 338, -388, 104],\n [-175, -341, -95, 13, 217, 2, 154, -315, 330],\n [135, 61, 24, -343, 43, -439, 16, -24, 258],\n [129, -214, -251, -10, 137, -74, 21, 32, -4],\n [275, 299, -176, 21, 175, -208, 299, -729, 364],\n [-499, 146, 253, 22, -136, 405, -308, 332, -472],\n [364, 625, -195, 78, 66, -113, 269, -623, -10],\n [-282, -370, 219, 512, -214, 600, 85, 224, -166],\n [-1, 191, -274, -75, 209, 41, -216, -134, -194]]\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[[193, 434, -182, 76, 89, 169, 156, 208, 283],\n [-136, -95, 326, -22, 232, -46, 576, 89, 308],\n [-71, 148, 16, 128, -59, 151, 188, -52, 39],\n [344, 201, -355, 32, 256, 70, -35, 286, 267],\n [-95, -220, 57, 114, 125, 47, 259, -57, 44],\n [-136, -257, 259, -118, 54, -167, 110, -36, -8],\n [325, 149, 55, -318, 459, -258, 200, 518, 561],\n [65, 76, 112, -282, -73, -232, -279, 98, -28],\n [56, 235, -304, 218, -200, 254, -198, -115, -166]]\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, 126, 49, -98, 7, -77, 63, 70, -119],\n [-176, 198, 77, -154, 11, -121, 99, 110, -187],\n [32, -36, -14, 28, -2, 22, -18, -20, 34],\n [-160, 180, 70, -140, 10, -110, 90, 100, -170],\n [272, -306, -119, 238, -17, 187, -153, -170, 289],\n [-240, 270, 105, -210, 15, -165, 135, 150, -255],\n [112, -126, -49, 98, -7, 77, -63, -70, 119],\n [-32, 36, 14, -28, 2, -22, 18, 20, -34],\n [-128, 144, 56, -112, 8, -88, 72, 80, -136]]\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 9x9 matrix:\n[[334, 148, 75, -1009, -247, -633, 297, 283, 18],\n [-34, -380, -354, 162, 476, -177, 483, -222, -65],\n [64, 40, -492, -605, -344, -793, 556, 164, 291],\n [-96, 11, -226, -8, 443, -419, 475, -12, 305],\n [-338, 170, 219, -12, 351, 45, -200, -71, -73],\n [16, 3, -519, 225, -54, 44, 508, -283, 304],\n [700, -238, 541, 108, 451, 166, -47, 24, -722],\n [314, 39, 594, 43, -301, 416, -621, 271, -221],\n [-397, -161, -629, 157, 232, -78, 107, -310, 24]]\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 9x9 matrix:\n[[603, 203, 118, 352, -211, -442, -573, -69, -499],\n [-223, -46, 161, -109, 273, -415, -88, -196, -69],\n [-25, -322, -254, -71, -96, 169, 383, -214, 63],\n [-68, 40, -272, -105, 4, 93, -137, -279, -245],\n [257, 36, -131, 9, -77, 200, -171, -166, -570],\n [-425, 196, 258, -348, 212, 203, 188, 697, 670],\n [-238, -190, -48, -201, 160, -116, 115, -127, 23],\n [-411, 116, 261, -27, 223, -38, 93, 254, 514],\n [-177, -612, -524, 200, -176, -207, -9, -425, 121]]\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[[-95, 240, 180, 67, 278, -191, -89, 46, 76],\n [-15, 303, 141, -33, 309, -219, -54, -69, 150],\n [-160, -199, 47, 212, -135, 108, -59, 251, -186],\n [-230, 120, 240, 238, 212, -134, -146, 244, -56],\n [220, -64, -208, -236, -152, 92, 132, -248, 80],\n [30, 270, 90, -78, 258, -186, -24, -114, 156],\n [225, 200, -100, -285, 110, -95, 95, -330, 220],\n [-160, -272, 16, 224, -208, 160, -48, 272, -224],\n [-20, -399, -153, 88, -391, 280, 49, 139, -218]]\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[[-857, -25, 248, -229, -157, -490, -167, 323, -370],\n [-96, 270, -520, -147, -190, -306, 138, 8, 476],\n [-161, 50, -20, 65, 176, -321, 12, 336, 386],\n [115, 113, 114, 759, 437, 129, -265, -42, 516],\n [-541, 36, 91, -82, 3, -426, -91, 329, -24],\n [-659, -153, 415, -127, -66, -330, -138, 301, -182],\n [-239, 73, -76, -8, -315, 20, -61, -291, 130],\n [-226, 159, -65, 169, 214, -244, -146, 224, -114],\n [-498, -201, 318, -410, -395, -66, -37, -44, -550]]?\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 9x9 matrix:\n[[-238, -152, 154, -329, 70, 152, -429, 182, -355],\n [124, 55, 3, 195, -31, -63, 149, 46, 174],\n [86, 120, -13, 140, -69, -98, 202, -151, 66],\n [66, 206, 490, 103, -150, -130, -157, 240, -181],\n [78, -51, -436, 39, 70, 9, 307, -293, 314],\n [-168, -168, -333, -195, 107, 126, 41, -273, -79],\n [90, 38, -49, 298, -41, -64, 282, -55, 122],\n [38, 31, -204, 67, -6, -37, 239, -255, 104],\n [62, -100, -119, 354, 29, 18, 266, 85, 180]]\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[[304, 95, -15, 3, 166, 28, -138, 123, -1],\n [228, -114, 190, 369, 159, 199, -93, -97, 40],\n [69, 95, 138, -39, -352, -203, 429, 366, 667],\n [243, 97, -315, -325, -19, 5, 17, 270, 50],\n [326, 98, -12, -25, 28, 8, -3, 233, 195],\n [-147, -94, 234, 154, -467, -87, 519, 163, 667],\n [-21, 125, -144, -306, -226, -131, 132, 237, 166],\n [-217, 56, -384, -495, -198, -150, 182, 142, -33],\n [57, -96, -171, -43, 25, 116, 34, -8, -42]]?\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[[81, 237, 40, 140, -116, -420, 138, 59, 283],\n [117, 442, 214, -214, -55, 93, 6, -197, 87],\n [237, 256, -19, -38, -264, 144, 105, -420, -326],\n [206, 476, 55, 123, -311, -270, 205, -203, 101],\n [-57, -88, -185, 299, -218, 73, 93, 2, -178],\n [217, -94, 76, -281, 221, -348, -34, -97, 65],\n [41, -276, -218, 207, -95, -124, 76, -23, -209],\n [39, -363, -194, 134, 24, -214, 36, 39, -137],\n [-69, 172, -170, 494, -411, -59, 210, 45, -15]]\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[[157, 339, 114, 278, -303, -38, -92, 247, -76],\n [138, 63, -216, -19, -37, 80, -123, -260, 115],\n [-170, -147, 72, -97, 153, -80, 199, 76, -103],\n [-324, -123, -148, -219, 334, -302, 703, -46, -392],\n [-211, -120, -154, -189, 258, -178, 453, -115, -225],\n [-72, 216, 96, 140, -85, -214, 318, 280, -305],\n [118, 171, 176, 201, -226, 42, -205, 224, 38],\n [43, -114, -14, -57, 27, 124, -201, -113, 174],\n [51, 84, -310, -71, 50, -46, 151, -293, -51]]\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[[260, 34, -329, 97, 157, -69, 93, 239, 113],\n [-82, 133, 7, 168, 105, 364, 138, 178, -211],\n [368, -62, -13, -197, -453, -88, 397, 166, 323],\n [-269, 646, -93, -748, -513, 253, 38, -613, -196],\n [-186, 472, -314, -862, -182, 163, 102, -518, -120],\n [-155, -307, 536, 206, -138, 73, -198, -165, 115],\n [25, -535, 425, -96, 195, 245, -276, -151, 20],\n [-306, 528, 64, -397, -679, 648, 429, -268, -268],\n [222, 87, -190, -258, -130, -305, 202, 53, 234]]\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[[-313, 161, -185, -606, 49, -465, -714, -127, -308],\n [289, -180, 168, -68, -153, 17, 13, 407, 235],\n [427, 93, 1028, 195, -696, 540, 170, -351, -726],\n [275, 685, 89, -619, 88, 78, -513, -448, -796],\n [390, 31, 291, 142, 12, -129, 629, 350, 556],\n [123, -508, 128, 367, -296, -385, 264, 537, 546],\n [-288, -299, -486, -196, -198, 6, -353, -104, -523],\n [-457, -941, -87, 232, 74, 222, 128, -20, 181],\n [248, -551, 437, 132, -197, 499, 246, 62, -70]]\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[[-26, 97, 110, 61, -198, -146, 41, 199, -59],\n [224, -40, 60, 126, 90, -157, -249, -102, 157],\n [207, -317, 134, -109, 18, -255, 405, 298, -426],\n [195, -2, 200, 106, -86, -542, 69, 161, -214],\n [179, -221, -19, 107, 167, 339, 63, -198, 227],\n [396, -135, 60, 32, -38, -140, -225, -126, 493],\n [-200, 137, -218, -367, -221, 110, 125, -159, 360],\n [-170, 76, 144, 250, -165, 180, 416, 168, -227],\n [407, -101, -78, 78, 268, -29, -651, -449, 648]]\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 9x9 matrix:\n[[-78, -125, 260, -36, -106, 60, -52, 42, 9],\n [30, 35, -80, 60, 40, -30, 70, 30, -15],\n [72, 186, -348, -216, 102, -18, -222, -288, 54],\n [62, 112, -226, -16, 85, -41, -7, -78, 4],\n [-70, -8, 74, -400, -89, 109, -445, -330, 100],\n [-128, -206, 428, -56, -174, 98, -82, 72, 14],\n [-98, -120, 270, -176, -131, 95, -207, -78, 44],\n [68, 51, -138, 236, 89, -83, 267, 168, -59],\n [78, 6, -78, 456, 99, -123, 507, 378, -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[[1, 80, 55, 316, -30, 113, -104, 198, -8],\n [577, 176, -30, 597, 183, 360, -49, 165, 155],\n [-31, -288, -116, 183, -362, 228, -159, 282, -396],\n [-112, -186, 81, 147, -603, 344, -207, 477, -251],\n [542, -106, -172, 542, 141, 425, 14, 269, -223],\n [280, 210, 71, 11, 204, 44, 99, -106, 318],\n [-757, 208, 292, -103, 302, -384, 131, 162, -24],\n [767, -204, -394, 448, 505, 305, 179, -33, -301],\n [510, 232, -60, 112, -148, 62, -226, -388, 540]]\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[[-306, 132, -342, -270, -27, 9, -324, -144, -51],\n [190, 144, -107, 51, -31, 95, 33, 191, 76],\n [-313, -93, 31, -141, -30, -113, -100, -243, -179],\n [406, 90, 51, 213, 4, 116, 203, 307, 159],\n [75, -17, -103, 9, 146, 63, -106, 23, 247],\n [269, 117, -49, 111, -8, 103, 90, 229, 119],\n [-56, 286, -367, -165, -117, 95, -185, 99, -50],\n [-104, 4, -73, -75, 12, -10, -95, -69, -5],\n [27, 249, -148, -54, -217, 48, 35, 152, -211]]\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 9x9 matrix:\n[[501, 600, 595, 46, -49, -280, 93, 32, 123],\n [68, 334, -410, -272, 112, -59, -758, -235, -219],\n [-153, 50, -131, 89, 139, -29, -332, 249, -381],\n [32, -13, -155, -152, -275, -128, 350, -297, 263],\n [165, 126, 307, -410, 163, -82, -293, -91, 480],\n [-169, -547, 74, -269, 348, 353, -120, 37, 293],\n [131, -431, 71, -363, 249, 349, 189, -259, 339],\n [-256, -256, 274, 300, -186, 98, 182, 130, 486],\n [-228, -431, -202, -364, 230, 196, -201, -61, 191]]\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[[50, 368, -169, 190, 25, 235, 35, 304, 55],\n [84, 506, -142, 216, -44, 196, 136, 248, 30],\n [-264, 107, -98, 174, 27, 329, -171, 456, 60],\n [166, -6, 135, -301, 0, -351, 339, -718, -60],\n [-94, 291, 29, -158, 26, -20, 324, -396, 1],\n [188, -576, -134, 40, 190, 38, -473, 378, 66],\n [-226, 535, 263, -170, -252, -206, 606, -692, -117],\n [-292, 287, 300, -50, -319, -177, 342, -378, -134],\n [598, -87, -81, 158, -54, -216, -93, 146, -33]]\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[[117, -88, 327, -22, 37, -268, 34, 135, 76],\n [178, 28, 2, -136, 426, 252, -12, -274, 172],\n [594, 398, 130, -355, 545, -25, -278, 215, 475],\n [-17, -306, 277, 85, 156, 77, 304, -192, 65],\n [-422, -139, -255, 246, -483, 55, 125, -26, -333],\n [-137, 203, -320, -185, -29, -170, -581, -314, -378],\n [-475, -226, -223, 274, -473, 72, 174, -123, -376],\n [-421, -133, -226, 218, -488, -36, 50, -38, -376],\n [-462, -118, -400, 216, -390, 215, 75, -223, -377]]\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[[26, -76, 54, -320, -42, -112, -56, 70, 48],\n [38, -220, 20, -118, -256, 82, -310, 300, 98],\n [-121, 315, -44, 266, 373, -59, 450, -464, -148],\n [153, -21, -38, -2, -33, 61, -66, 158, -16],\n [-321, 103, 161, -54, 56, -339, 190, -452, 75],\n [-462, -141, -99, -216, 228, 345, 108, -123, -78],\n [-283, -212, 144, -36, -320, -98, -276, 1, 193],\n [24, -133, 176, -14, -395, -269, -310, 109, 209],\n [-57, -113, 15, -430, 42, -11, -18, 68, 13]]?\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[[117, 108, -99, -126, 108, -108, -45, 54, 18],\n [-234, -216, 198, 252, -216, 216, 90, -108, -36],\n [26, 24, -22, -28, 24, -24, -10, 12, 4],\n [104, 96, -88, -112, 96, -96, -40, 48, 16],\n [39, 36, -33, -42, 36, -36, -15, 18, 6],\n [-104, -96, 88, 112, -96, 96, 40, -48, -16],\n [-130, -120, 110, 140, -120, 120, 50, -60, -20],\n [-117, -108, 99, 126, -108, 108, 45, -54, -18],\n [156, 144, -132, -168, 144, -144, -60, 72, 24]]\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[[447, 293, 297, 231, -134, 427, -590, -513, 199],\n [-341, -287, -350, -368, 59, -203, 137, -576, -290],\n [65, 230, -53, 139, 384, 89, 403, -92, 121],\n [339, 306, 267, 252, -80, 369, -326, -303, 77],\n [-223, -88, -9, -135, -64, -216, -38, 31, -225],\n [-182, 77, 146, 134, -272, 9, -600, 86, -598],\n [-225, -141, -83, -215, 33, -270, 238, 30, -78],\n [-59, -443, -237, -180, -301, -21, 178, 364, 46],\n [256, -270, 4, 28, -473, 253, -404, 235, 187]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 9x9 matrix:\n[[262, -91, 309, -296, -21, -79, 11, 152, -206],\n [66, 99, 76, 46, 93, -68, -100, -81, -121],\n [-337, -288, -269, -192, -324, 195, 252, 348, 476],\n [-276, 60, -59, -98, -60, -47, -145, 195, 197],\n [182, -168, -39, 50, -48, 125, 253, -99, -45],\n [-12, -63, -234, 258, -9, 150, 192, -207, 81],\n [334, 257, 243, 196, 303, -169, -211, -346, -452],\n [287, -50, 273, -184, 30, -71, 10, 40, -244],\n [-33, -207, 42, -288, -189, 54, 135, 288, 138]]\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[[390, 408, -346, 48, -70, 168, 170, 52, -394],\n [60, -18, 41, 317, 245, -28, -270, 183, -101],\n [60, 138, -141, -281, -249, 76, 302, -155, -23],\n [60, 54, -43, 41, 17, 20, -6, 27, -65],\n [60, 102, -99, -143, -135, 52, 170, -77, -41],\n [60, -24, 48, 340, 264, -32, -292, 196, -104],\n [0, 102, -119, -391, -323, 68, 374, -221, 51],\n [-15, -108, 121, 352, 295, -68, -345, 198, -31],\n [-345, -336, 277, -138, -17, -132, -59, -100, 361]]\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[[-237, 234, 107, -83, -338, -486, 612, -453, -11],\n [39, -67, 5, 190, -177, 239, -200, 392, -149],\n [-76, 78, -90, 150, -110, 111, -3, 78, -73],\n [183, 75, 37, 34, -78, -212, 245, -327, 128],\n [563, -24, 327, 361, -256, 114, -90, 375, 98],\n [334, 102, 70, 246, 257, 267, -225, 189, 237],\n [-364, 286, -100, -16, -159, -253, 439, -389, -27],\n [453, -24, 355, 281, -440, -77, 107, 243, 20],\n [-705, 0, 155, -517, -5, -347, 239, -24, -197]]?\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 9x9 matrix:\n[[304, 21, 340, -534, 534, -137, -172, 86, 22],\n [456, 488, -183, 11, 299, 308, 148, 333, -474],\n [-192, 377, 596, 373, -163, 192, -90, 124, -221],\n [-463, 86, -233, -587, -448, -367, -643, -406, 393],\n [-44, 463, 193, -88, -9, 281, -454, 370, -375],\n [-571, 218, 347, -111, -326, -111, 72, 108, -315],\n [-86, 347, 10, 119, 48, 233, 224, 413, -571],\n [220, 588, 227, -2, 369, 489, -20, 652, -804],\n [19, 58, -151, 715, -390, 308, 392, -22, -173]]\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[[-125, 214, -180, -63, 250, -268, 15, 169, 171],\n [369, 294, -163, 607, 481, -201, -162, 25, 200],\n [-69, -203, 90, -190, -409, 426, 357, -42, -141],\n [-306, -301, 104, -278, -2, 201, 18, -302, -110],\n [-430, 210, 72, -131, -124, 102, 88, 621, -305],\n [-69, 315, -335, 169, -174, -128, 782, 552, -45],\n [-452, -149, 110, 58, 121, -376, -286, -164, -3],\n [573, -32, -228, 276, 244, -338, 15, -410, 206],\n [5, -156, 53, 365, -78, -296, -79, -283, 116]]?\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[[124, -94, 114, -179, -124, 107, 109, -102, -249],\n [-100, 70, -87, 140, 100, -86, -85, 84, 204],\n [24, -284, 248, -234, -24, 34, 154, 60, 98],\n [124, -74, 97, -164, -124, 106, 99, -108, -260],\n [-16, -264, 220, -184, 16, 0, 124, 96, 184],\n [-52, -98, 69, -28, 52, -38, 23, 84, 180],\n [80, 40, -12, -40, -80, 64, 20, -96, -216],\n [16, 164, -135, 109, -16, 5, -74, -66, -129],\n [-60, 70, -76, 105, 60, -53, -65, 42, 107]]\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[[-424, 164, 419, -31, -437, -300, 322, 157, 190],\n [-192, -66, 99, -49, -82, -194, 21, 94, 149],\n [147, 198, 206, 236, -247, 93, 270, -95, -106],\n [395, -71, -210, 336, 5, 210, -232, 42, 89],\n [-1, -161, 30, 188, -21, -442, 119, -98, -272],\n [-342, -141, 345, -23, -292, -389, 114, 167, 505],\n [-294, 36, 122, -206, -114, -268, 72, 14, 94],\n [-564, 160, -3, -713, 197, 136, -46, 143, 70],\n [229, 306, 86, 100, -171, 213, 201, -223, -181]]\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[[381, -53, -83, -416, 147, -152, 521, -508, -28],\n [-96, -161, 80, 68, -292, -369, 79, -77, -428],\n [142, -387, 16, -8, 197, 411, 424, -369, 93],\n [-152, 764, -498, 553, -262, 162, -306, -138, -521],\n [451, -176, 2, -389, 263, 209, 387, -422, 590],\n [187, -335, 43, -311, -68, -90, -42, -94, 203],\n [117, 24, -321, 371, -346, -283, -488, 366, 66],\n [-105, -285, 119, -325, -311, -27, -281, 61, -18],\n [138, 552, -343, 435, -617, -274, -485, -220, 60]]?\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[[-135, 56, 46, -139, 308, -135, -7, -156, -16],\n [-111, 389, 245, -534, 346, -73, -172, -183, 198],\n [335, -684, -176, 520, -221, 141, 149, 57, 210],\n [572, -55, 526, 267, 312, 372, -170, -91, -6],\n [-54, -392, -251, 174, -52, 504, -567, 512, 436],\n [325, -368, 77, 313, 430, 413, -93, 318, 376],\n [-425, 341, -211, -391, -167, -413, 220, -108, -140],\n [54, 280, 160, -56, 220, -378, 586, -271, -322],\n [556, -354, 186, 384, -60, 432, -90, 163, 266]]\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[[17, -237, -19, 50, -248, 17, -34, -177, -374],\n [-42, 250, 6, -106, 258, -42, 230, 94, 456],\n [127, -259, 185, -255, -295, 127, 277, -113, 24],\n [-110, 294, -98, 10, 314, -110, 178, 42, 344],\n [-18, 62, -46, 123, 75, -18, -241, 96, -82],\n [38, 190, 104, -152, 190, 38, 100, 202, 460],\n [-162, 16, -193, 28, 21, -162, 462, -370, -64],\n [80, -288, 24, 144, -296, 80, -416, -16, -544],\n [99, -275, 99, -55, -297, 99, -55, -77, -264]]\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 9x9 matrix:\n[[101, -803, -267, -110, 132, -112, 26, 127, -98],\n [154, -102, 499, -164, 402, 90, -92, -91, 433],\n [310, -447, 95, 60, 58, 10, -361, -175, -108],\n [294, -80, 481, 74, 90, 286, -651, -277, -116],\n [-114, -260, -358, 55, -23, 261, 448, 365, 12],\n [-201, 31, -663, 339, -284, 25, 622, 103, 190],\n [-183, 678, 134, 154, -100, 480, 56, -222, 379],\n [-268, 984, 427, 456, -145, 632, -74, -44, 147],\n [-495, 379, 120, 102, 19, -74, -221, -299, 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[[-140, -224, -182, -238, 168, 126, -210, -196, -98],\n [100, 160, 130, 170, -120, -90, 150, 140, 70],\n [-130, -208, -169, -221, 156, 117, -195, -182, -91],\n [140, 224, 182, 238, -168, -126, 210, 196, 98],\n [100, 160, 130, 170, -120, -90, 150, 140, 70],\n [-90, -144, -117, -153, 108, 81, -135, -126, -63],\n [130, 208, 169, 221, -156, -117, 195, 182, 91],\n [60, 96, 78, 102, -72, -54, 90, 84, 42],\n [90, 144, 117, 153, -108, -81, 135, 126, 63]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[75, -93, -244, -35, -30, -260, -239, -140, -92],\n [-93, 223, 36, 605, -330, -236, -39, -200, -312],\n [204, -13, -364, 14, -483, -168, -134, -363, -227],\n [-48, 35, -55, 242, -24, -249, -155, -84, -140],\n [121, -34, -74, -227, -161, 190, 111, -51, 53],\n [49, -117, 18, -365, 190, 198, 73, 140, 204],\n [42, 3, -98, 44, -123, -82, -58, -103, -79],\n [94, -158, -89, -406, 157, 117, -9, 77, 173],\n [131, 15, -262, 93, -376, -170, -117, -286, -206]]\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[[264, -27, -120, 117, -114, 87, 201, 63, -162],\n [-152, -56, 2, 139, 63, -55, -244, 369, 131],\n [-114, 172, 42, -188, 146, -90, -104, 18, 41],\n [372, 38, -168, 88, -118, 100, 286, 76, -244],\n [-284, -73, 146, -60, 55, -56, -185, -160, 189],\n [-88, -304, -20, 390, -106, 42, -184, 362, 138],\n [234, 234, -114, -134, 50, -4, 166, 80, -193],\n [100, 370, -40, -340, 170, -80, 90, -40, -140],\n [-210, -97, 66, 83, 40, -45, -217, 135, 163]]\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[[-679, -31, -199, 206, -358, 90, -68, 311, 358],\n [-296, -115, -555, 304, 175, 14, -269, 36, -154],\n [294, 129, 664, -61, -332, -14, 131, -171, 84],\n [-81, 28, 79, -364, 116, -550, 374, -231, 573],\n [-459, 96, 331, -130, -514, -171, 219, 101, 651],\n [106, -123, -172, -184, 189, -17, -116, -107, -398],\n [-293, 128, 410, 41, -523, -247, 37, -164, 431],\n [-369, 338, -163, -101, -152, -171, -218, 84, 274],\n [-21, 9, 155, 608, -372, 521, -299, 201, -276]]\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 9x9 matrix:\n[[82, 273, 353, 229, 138, 451, 241, -22, -126],\n [716, -293, 430, -371, -359, 430, 162, -334, -17],\n [-499, 10, -782, -358, -140, -47, -325, 462, -18],\n [-228, -327, 58, 4, -643, -62, 201, 101, 135],\n [585, -421, 565, -143, -405, 493, 338, -351, 72],\n [-504, -6, -287, 28, -82, -56, -21, 311, 111],\n [-230, 69, -390, -199, 345, -208, -282, 178, 133],\n [-465, 120, -483, -299, 91, 533, -97, 487, 55],\n [285, -364, 450, 298, -374, -60, 301, -352, 8]]\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[[43, -514, 157, -200, 457, 270, -90, -56, 228],\n [-191, -198, -177, -60, 217, -228, 220, 10, 254],\n [37, -272, 101, 386, -314, -221, 201, -249, -147],\n [215, 210, 1, -289, 197, 436, -428, 100, 14],\n [191, -218, -17, 444, -416, -140, 36, -357, -149],\n [-96, 260, -48, -160, 32, 86, -54, 168, 52],\n [642, 76, 230, 296, -257, 1, -307, -237, -681],\n [-262, -441, 187, 221, -97, -180, 381, -112, 99],\n [227, 24, 217, 59, -82, 152, -166, -45, -269]]\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[[-7, -64, 306, 282, -569, -338, 23, -303, 52],\n [-66, 19, 305, -34, -393, -157, 427, -327, 456],\n [-165, 40, -339, -524, 661, 276, 252, 180, 241],\n [74, 22, -46, -16, -172, 120, 346, 164, 256],\n [18, -69, 159, -198, -330, -243, 153, -402, 315],\n [-73, -150, -297, -96, 163, -156, -264, 62, -223],\n [-176, 153, 162, 580, 201, 172, -97, 326, -377],\n [245, -89, 151, 76, -781, -207, 250, -177, 309],\n [-165, 111, 332, 50, -77, -11, 339, -218, 298]]\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[[-265, -5, -346, -213, -18, 97, 46, -260, -30],\n [104, -44, 308, 153, -18, -221, 76, 397, 201],\n [119, 230, 53, 288, 124, -192, -40, -157, -193],\n [360, 394, 166, 267, -126, 153, -396, -273, -317],\n [-540, -105, -326, -419, -103, 143, 88, 92, -7],\n [-494, -39, -208, -326, -245, -34, 118, 233, 272],\n [132, 87, 91, -274, -605, 466, -381, 56, 292],\n [87, 152, 34, 290, 272, -210, 29, -146, -305],\n [147, -237, -322, -406, -128, 646, -178, -521, 13]]\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 9x9 matrix:\n[[34, -22, 44, -436, 77, 296, -236, -190, -280],\n [264, -479, -400, 118, -156, -39, -188, 17, 232],\n [-22, -52, -100, 340, -635, 328, -432, 78, 496],\n [150, -89, -84, -324, 185, 14, -42, -78, -236],\n [148, -71, -239, 55, -79, -433, -51, 501, -102],\n [-97, -329, -123, 258, -503, 343, -475, -23, 336],\n [-175, 186, 292, -175, 148, 328, 64, -364, -94],\n [328, -94, -434, 352, -368, -443, -96, 579, 328],\n [225, -240, -301, 156, -133, -154, -61, 136, 208]]\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 9x9 matrix:\n[[-51, 155, -152, -62, -2, -16, 104, 95, 58],\n [-9, -83, 44, 134, 26, -44, -50, -101, 2],\n [35, 159, -66, -306, -62, 110, 93, 218, -20],\n [-18, 102, -84, -84, -12, 12, 66, 84, 24],\n [-34, -120, 42, 252, 52, -94, -69, -175, 22],\n [-155, 253, -322, 98, 46, -130, 181, 56, 160],\n [-66, -162, 36, 396, 84, -156, -90, -264, 48],\n [29, 59, -8, -158, -34, 64, 32, 103, -22],\n [-144, 146, -242, 208, 64, -154, 113, -43, 142]]\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 9x9 matrix:\n[[-203, -238, 263, -96, -189, 215, 190, 80, -150],\n [-670, -275, 191, -345, 49, 575, -127, 150, -142],\n [92, 147, -187, -51, -98, -19, 20, 181, 388],\n [-452, -227, 191, -189, 84, 359, -98, 9, -256],\n [-186, 129, -221, -117, 259, 115, -321, 20, 134],\n [-65, 80, -111, 30, 322, -39, -293, -179, -160],\n [-469, -299, 284, -183, 28, 380, -25, 0, -340],\n [-12, -42, 44, -54, -175, 68, 141, 133, 130],\n [314, 344, -382, 108, 154, -286, -184, -16, 348]]\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[[-218, -23, -33, -3, 43, 88, 121, 44, -37],\n [-356, -146, -16, 68, 90, 356, 140, 74, -92],\n [-18, -33, 22, 38, 39, 28, -12, -17, -34],\n [288, 84, -47, -122, -221, -13, -103, 51, 178],\n [300, 48, 30, -19, -83, -125, -154, -46, 71],\n [-402, -189, 143, 284, 434, 7, 85, -150, -352],\n [414, 195, 29, -72, -68, -519, -157, -116, 84],\n [302, 185, 32, -49, -2, -537, -102, -125, 33],\n [-190, -193, -20, 49, -42, 565, 34, 121, -1]]\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 9x9 matrix:\n[[224, 655, 49, 147, 347, 2, 39, -277, 530],\n [28, -173, 315, -101, 123, -310, 179, -178, -110],\n [-83, -93, -366, -88, -72, 174, -470, 81, -296],\n [52, 81, -329, -141, -419, 61, -432, 278, -178],\n [124, -97, 102, 31, 303, -64, -18, -119, 190],\n [-129, -56, -163, 51, 102, 149, 14, -71, 0],\n [-261, -387, -347, 48, -64, 340, -119, 162, -212],\n [90, -362, 110, -66, 213, -168, -12, -80, 58],\n [-281, -318, -264, -93, -531, 243, -267, 411, -654]]\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[[-234, -126, -198, -108, -180, 18, -162, 144, -270],\n [169, 91, 143, 78, 130, -13, 117, -104, 195],\n [-117, -63, -99, -54, -90, 9, -81, 72, -135],\n [117, 63, 99, 54, 90, -9, 81, -72, 135],\n [208, 112, 176, 96, 160, -16, 144, -128, 240],\n [91, 49, 77, 42, 70, -7, 63, -56, 105],\n [-221, -119, -187, -102, -170, 17, -153, 136, -255],\n [104, 56, 88, 48, 80, -8, 72, -64, 120],\n [130, 70, 110, 60, 100, -10, 90, -80, 150]]\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[[27, 99, -63, 126, 126, -45, 45, 126, -153],\n [51, 91, -115, 78, 110, -97, 97, 158, -209],\n [-111, -167, 249, -118, -198, 215, -215, -318, 429],\n [51, 187, -119, 238, 238, -85, 85, 238, -289],\n [75, 107, -168, 70, 126, -146, 146, 210, -285],\n [-99, -171, 223, -142, -206, 189, -189, -302, 401],\n [114, 154, -255, 92, 180, -223, 223, 312, -426],\n [-9, 15, 19, 38, 22, 21, -21, -2, 11],\n [96, 88, -213, 8, 96, -193, 193, 228, -324]]\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[[184, 167, -63, 135, -267, 153, -294, 447, -57],\n [-384, 124, 309, 685, -75, 553, -510, 386, 153],\n [154, -41, -114, -458, -14, -456, 410, -437, -186],\n [304, -219, -32, -358, -116, -300, 278, -123, -217],\n [102, -323, -230, -452, 107, -146, 442, -261, 209],\n [448, -217, -179, -427, 66, -317, 246, -23, -166],\n [14, 465, -235, -265, -354, -307, 130, -241, -129],\n [193, 239, 133, 134, -362, -86, -251, 248, -387],\n [10, 49, 4, -150, -143, -188, 152, -199, -124]]\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 9x9 matrix:\n[[-168, 241, 383, 172, 80, 150, 241, -258, 183],\n [54, -74, -486, -151, 263, -262, 10, -77, -119],\n [-410, -435, -484, -293, 40, 450, 401, -24, 442],\n [338, -292, 386, 601, 208, -63, 190, -200, 28],\n [-181, 183, 31, -231, -68, 74, -268, 172, -251],\n [-69, -177, -615, -294, 24, -143, 131, 33, 193],\n [-334, 289, -36, -260, 1, -122, -55, -151, -289],\n [-34, 139, 326, 161, -69, 66, 163, -496, -267],\n [306, 48, -440, -147, 0, -607, -275, 135, -266]]\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[[128, 0, 224, -80, -256, -144, -176, 0, 208],\n [-32, 0, -56, 20, 64, 36, 44, 0, -52],\n [80, 0, 140, -50, -160, -90, -110, 0, 130],\n [-112, 0, -196, 70, 224, 126, 154, 0, -182],\n [-136, 0, -238, 85, 272, 153, 187, 0, -221],\n [56, 0, 98, -35, -112, -63, -77, 0, 91],\n [-56, 0, -98, 35, 112, 63, 77, 0, -91],\n [-144, 0, -252, 90, 288, 162, 198, 0, -234],\n [72, 0, 126, -45, -144, -81, -99, 0, 117]]?\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[[10, 72, 70, -222, -240, -36, 154, -110, 106],\n [-273, -63, -41, 6, 555, 218, 19, 325, -24],\n [96, -67, 262, -33, -305, -204, -76, -244, -13],\n [138, 239, 244, -413, 291, -260, -470, -233, 110],\n [-483, -31, -32, -121, 865, 360, 105, 499, -2],\n [-184, 401, -52, -709, 469, 142, 88, 119, 282],\n [-120, -58, 99, 564, -124, -27, -20, -75, -456],\n [-49, 406, 84, -679, 176, -35, 3, -110, 239],\n [-318, -236, 0, 361, 228, 229, 190, 293, -216]]\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[[-446, -236, -112, 583, -373, -443, -11, 186, 581],\n [-52, 168, -684, 42, 32, 230, -329, 699, 43],\n [-321, -102, -18, 293, -138, -181, -129, -43, -43],\n [446, 244, -261, -457, 135, 598, 114, 273, 93],\n [370, 272, 200, -411, 141, -41, 57, -322, -269],\n [-185, 4, 325, 161, -152, -170, 162, 60, 165],\n [80, 106, -52, -209, -198, 107, 386, 36, -449],\n [111, 254, 438, -277, 82, 509, 34, -262, -46],\n [80, -10, 197, -136, -352, -410, 544, -435, -496]]\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[[-314, 26, 988, -368, -226, 504, -518, -364, -66],\n [-65, 255, 597, -21, -119, 59, -387, -549, 323],\n [-59, -271, -195, -165, 355, 93, 330, 76, -636],\n [-391, 428, -70, 364, 191, -305, -281, -59, 451],\n [-259, 27, 538, -263, -419, 340, -183, -71, -4],\n [96, 70, -204, 134, -20, 10, -136, 143, 336],\n [92, 365, -313, 358, 149, -569, -189, -92, 145],\n [104, 285, 84, -57, -518, -107, -141, -202, 26],\n [128, -405, 318, -195, 0, 523, -435, 505, 96]]\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[[18, -110, -752, 163, 119, -539, -491, 28, -695],\n [88, -81, 167, -401, -190, 104, 42, 421, -6],\n [740, -35, 500, 203, 546, 187, -423, 473, 19],\n [-80, 82, 104, -345, -50, 172, 364, 88, 763],\n [-17, -257, -34, 211, 228, 161, -394, 171, -49],\n [-224, 81, 347, 732, 215, 289, 243, 106, 782],\n [30, 192, -243, -224, -1, -178, 137, 260, 472],\n [-168, 196, 110, 767, 298, 26, 274, 124, 171],\n [759, -337, 263, 188, 290, -232, -287, 862, 34]]\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[[0, 0, 0, 0, 0, 0, 0, 0, 0],\n [22, 24, 24, -20, 32, 6, 12, 2, 12],\n [-198, -216, -216, 180, -288, -54, -108, -18, -108],\n [143, 156, 156, -130, 208, 39, 78, 13, 78],\n [-33, -36, -36, 30, -48, -9, -18, -3, -18],\n [22, 24, 24, -20, 32, 6, 12, 2, 12],\n [-11, -12, -12, 10, -16, -3, -6, -1, -6],\n [-77, -84, -84, 70, -112, -21, -42, -7, -42],\n [-99, -108, -108, 90, -144, -27, -54, -9, -54]]\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, 339, 57, -6, -426, 160, -151, -470, 152],\n [-882, 507, 171, 709, 211, 250, 487, 519, 70],\n [404, -203, 63, -78, 48, -188, 377, 133, 191],\n [-383, 127, 251, 99, -69, -176, -259, -346, -613],\n [-431, -123, -3, 194, -622, 26, -16, -616, -13],\n [97, 241, 273, 209, 99, -164, 449, 298, 267],\n [438, -510, -144, -180, 315, -286, 151, 206, -50],\n [-408, 506, -264, 642, -94, 480, 441, 334, 417],\n [-139, 19, -398, -391, 160, 512, -718, -207, -553]]?\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[[-284, 9, -106, -108, -113, -575, -132, 156, 26],\n [-386, -193, -205, -105, -176, 236, 450, -201, -143],\n [168, -529, -101, -162, 139, -783, -258, 296, 430],\n [611, -86, 115, -41, -23, -220, -716, 305, 601],\n [-132, 122, -201, -124, -114, -270, 473, -40, -394],\n [353, 160, -53, 448, 213, 61, -510, 307, -522],\n [-78, -236, 250, -276, 109, 398, -319, -196, 592],\n [413, 603, -173, 79, 64, -169, -14, -23, 7],\n [-245, 3, -27, -318, -37, -696, 291, 8, 52]]?\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[[91, -142, 229, -65, -175, 187, 412, -214, 108],\n [-22, -43, -215, 222, -130, -243, -606, 194, 32],\n [-303, 423, 101, -207, 314, -279, -198, 293, -132],\n [215, -289, -147, 244, -304, -23, -140, -32, 186],\n [207, -290, 64, 21, -160, 384, 468, -363, 40],\n [35, -53, -24, 28, -29, 46, 16, -43, 2],\n [-100, 211, 332, -221, 21, -194, 280, 142, 146],\n [102, -284, -34, 190, -314, 130, -152, -176, 56],\n [-44, 95, 4, -132, 235, 174, 234, -97, -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[[-123, -154, -50, 257, 191, 0, -234, 253, 162],\n [308, 134, 90, -21, 391, -90, -101, 32, -7],\n [5, 244, 228, 76, 2, -302, 61, -231, -129],\n [-182, 82, 156, 267, 17, -264, -79, -50, -5],\n [298, 256, 179, -73, 262, -191, 17, -146, -109],\n [175, -44, -138, -318, -106, 252, 149, -29, -41],\n [140, 252, 154, -180, -110, -146, 208, -308, -192],\n [266, -46, -108, -189, 193, 192, -23, 110, 35],\n [-331, -118, -110, -101, -583, 140, 232, -139, -56]]\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[[73, 196, -321, -465, -91, -41, -45, -6, -280],\n [343, -581, 177, 232, -137, -304, -47, 112, 307],\n [-617, -276, 462, -135, 69, 328, 201, 403, -113],\n [-397, -212, -166, -283, 291, 148, 173, -82, -464],\n [-646, 216, 81, 189, -35, 352, -75, -152, 49],\n [-99, 170, -12, 178, -227, -30, -71, -135, 283],\n [171, -227, 139, 372, 82, -293, 306, -111, 357],\n [332, 47, 481, 217, -219, 51, -221, 435, 353],\n [-284, 84, 204, 228, 60, 274, -102, 19, 43]]\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[[-220, -307, 28, -95, 409, 101, 12, 491, -46],\n [34, -216, 332, -375, -231, -189, 383, -316, -329],\n [341, -105, 140, 158, -28, -285, -91, -393, 271],\n [76, 70, -404, -102, 300, 122, -160, 216, 8],\n [-194, -77, -147, 99, 89, 48, -32, 254, 14],\n [-160, 44, -96, -29, 88, 164, -203, 378, -79],\n [-9, 393, -511, 170, 231, 327, -427, 384, 159],\n [-357, -46, 179, 232, -228, -41, 205, -79, -121],\n [-259, 477, -215, 90, -54, 299, 46, -86, -290]]\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 9x9 matrix:\n[[146, -313, -230, 67, -24, -131, 336, 107, -244],\n [341, 316, -547, -240, -21, -162, 143, -102, -111],\n [395, 370, 10, -297, 373, 161, -487, -201, 293],\n [30, -292, -686, 7, -226, -27, 489, 30, -408],\n [502, 442, 88, -202, 306, -186, -216, -266, 362],\n [-74, 268, 210, -30, 0, -155, -68, 2, 96],\n [-2, 240, -145, -152, -6, 322, -353, -121, 138],\n [51, 651, -84, -250, -3, 164, -431, -271, 327],\n [240, -232, 114, -33, 196, 348, -397, 239, -12]]\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[[74, 23, -19, 150, 14, 54, -44, -20, 58],\n [116, -82, -54, 52, 84, 68, -72, 8, 44],\n [216, -150, -100, 101, 155, 127, -134, 14, 83],\n [-236, 148, 106, -135, -161, -141, 146, -10, -97],\n [-88, -40, 20, -198, -10, -66, 52, 28, -74],\n [232, -320, -140, -138, 250, 114, -148, 68, 26],\n [148, 46, -38, 300, 28, 108, -88, -40, 116],\n [-90, 225, 75, 210, -150, -30, 60, -60, 30],\n [194, -199, -103, -9, 173, 105, -122, 34, 49]]\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[[-169, -134, 88, -3, -86, 0, 172, 24, 131],\n [-264, 13, -15, -3, -55, 8, 184, 66, 152],\n [-264, 85, -292, -212, 96, -253, -207, -54, -138],\n [267, -45, 182, -179, 29, -22, -197, 124, -359],\n [-106, -27, 241, 189, -154, 253, 432, 156, 318],\n [-114, -50, 334, -124, -128, 122, 260, 336, -50],\n [47, -143, 23, 386, -92, 167, 268, -236, 475],\n [-56, -151, 156, 218, -131, 156, 321, -36, 342],\n [-81, 201, -76, -149, 61, -36, -85, 156, -179]]?\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[[-144, -369, 9, 270, 198, 234, 180, -261, 63],\n [37, 159, -21, -110, -137, -13, -69, 141, 61],\n [130, 343, -11, -250, -192, -204, -166, 247, -45],\n [17, -149, 55, 90, 235, -169, 47, -191, -239],\n [-91, -327, 33, 230, 251, 79, 147, -273, -73],\n [53, -37, 47, 10, 159, -213, -5, -103, -231],\n [117, 285, -3, -210, -141, -201, -141, 195, -69],\n [74, 160, 4, -120, -62, -142, -82, 100, -68],\n [115, 191, 23, -150, -19, -263, -107, 89, -175]]\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[[244, 405, 333, -588, -38, 257, 174, -68, 46],\n [-82, 256, 12, -150, 67, -320, 217, 6, -116],\n [-258, -293, -91, -146, 69, 278, -141, -149, 322],\n [-259, 134, 152, 183, 231, -187, -194, 259, 243],\n [-41, 137, 52, -355, 195, 331, 249, -60, -22],\n [-86, 121, -492, -54, 48, 449, 327, -76, -643],\n [-102, -220, -61, -33, -601, 49, -240, 226, 155],\n [-262, -255, -153, 223, -219, 333, -79, 103, -94],\n [413, 54, -102, 65, -274, 277, 167, -273, -556]]\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, -248, 151, -159, -85, -119, 19, -247, -79],\n [-105, 348, 11, -25, 227, 125, -63, 120, 120],\n [6, 0, 159, -43, 235, 73, -33, -257, 63],\n [100, 62, -296, 315, -118, 69, 38, 333, 4],\n [137, 208, -131, 399, 377, 301, -29, 26, 176],\n [-204, 456, -94, -118, 2, 26, -54, 414, 66],\n [55, -250, -95, 10, -329, -154, 65, 77, -134],\n [-147, -120, 87, -359, -349, -265, 21, 56, -150],\n [-51, 228, 17, 13, 201, 111, -45, 40, 96]]\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[[112, -288, 16, 144, 208, -160, -160, -160, 160],\n [-35, 90, -5, -45, -65, 50, 50, 50, -50],\n [-49, 126, -7, -63, -91, 70, 70, 70, -70],\n [28, -72, 4, 36, 52, -40, -40, -40, 40],\n [-84, 216, -12, -108, -156, 120, 120, 120, -120],\n [-14, 36, -2, -18, -26, 20, 20, 20, -20],\n [-14, 36, -2, -18, -26, 20, 20, 20, -20],\n [-14, 36, -2, -18, -26, 20, 20, 20, -20],\n [-42, 108, -6, -54, -78, 60, 60, 60, -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 9x9 matrix:\n[[195, 187, 35, 41, -294, 419, 100, 136, -324],\n [-61, -160, -270, 157, -602, -302, -181, -6, 31],\n [-105, 196, 64, -77, 319, 357, -194, -230, 12],\n [-507, 84, -187, -502, 8, -199, -134, 112, 121],\n [360, 39, -88, 323, -422, -68, 81, -99, -585],\n [392, 515, 348, 123, 117, 145, 236, -479, -24],\n [-69, 500, -116, -309, -92, -129, 169, -422, -347],\n [393, -18, 467, 334, 482, 157, 79, -45, 173],\n [-24, -338, 120, 262, 255, -576, -208, -131, 555]]\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[[163, 9, 913, 684, 321, -24, 144, 34, 806],\n [-106, -320, 300, 478, -217, -311, -223, -134, 439],\n [78, 69, -499, -54, 23, 66, 96, 194, -400],\n [344, 98, -440, -65, -740, 36, -774, 71, -127],\n [-280, 81, 324, 105, 54, 19, -260, 39, 139],\n [150, 104, -173, -12, -59, 143, 522, -446, 164],\n [-218, -126, 143, 364, 44, -186, -41, 70, 121],\n [-274, -283, -434, -342, -214, -257, -249, 66, -486],\n [140, -246, 14, 287, -251, -140, -645, 255, 104]]\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[[40, 348, 201, 290, -322, -197, -178, 159, -443],\n [-242, -466, -333, -274, 98, 201, -20, -109, 437],\n [252, 566, 231, 228, -198, -247, -4, 95, -497],\n [117, -151, 48, -134, 380, 124, 245, -109, 265],\n [-175, -219, -234, -138, -64, 78, -83, -39, 179],\n [-36, -98, -162, -146, 44, 54, 34, -68, 146],\n [194, 36, 270, 66, 308, 30, 208, -18, 32],\n [134, 130, 174, 84, 92, -38, 86, 16, -92],\n [36, 285, 33, 127, -262, -151, -117, 78, -303]]\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[[325, 244, -328, 133, -374, 310, -334, -68, -190],\n [-282, 228, -119, -311, -285, 18, -103, 120, 283],\n [60, -664, 63, -65, 752, -91, 490, -25, 328],\n [228, -51, -45, -399, 542, 383, -63, 549, -166],\n [-283, 352, 135, 476, -721, -380, -135, -550, -328],\n [-595, -190, -332, 191, -50, -459, 460, -636, 54],\n [-275, -498, -543, -18, 441, -146, 557, -382, 232],\n [-379, -110, -181, 10, -127, -206, 181, -502, 7],\n [-56, 53, -160, -426, 362, 247, -13, 416, -129]]\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[[-148, 383, 302, 382, 8, -215, -127, -154, -162],\n [215, 38, 205, 79, -197, 177, -126, 53, 55],\n [-200, 160, 32, 128, 116, -216, 24, -140, -88],\n [-244, 58, -204, 68, 238, -174, 26, 162, -256],\n [51, -214, -297, -155, 82, 157, 4, 400, -129],\n [-237, 210, 25, 195, 151, -239, -10, -63, -181],\n [-69, -215, -267, -253, 116, -22, 161, -16, 81],\n [68, -202, -182, -194, 13, 114, 60, 125, 52],\n [-142, 9, 22, -90, 51, -199, 161, -419, 196]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-107, -64, 26, 10, -64, -108, -37, 493, -297],\n [89, -196, 589, 35, -183, 45, 67, 368, 343],\n [-323, -436, -29, -139, 226, -68, -82, -54, -160],\n [-284, -343, -230, -221, 629, -123, 177, -121, -118],\n [127, 62, 40, -210, 214, -176, 327, 332, 172],\n [-465, -142, 687, 423, 428, 632, 144, -728, 498],\n [127, 482, -355, 133, 166, -62, 252, 14, -104],\n [102, 17, -203, -518, -482, -348, -133, 407, -174],\n [143, -257, 436, -57, -264, 46, -427, -260, 340]]?\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[[262, 224, -318, 470, 23, -204, 89, 299, -305],\n [56, 146, -29, 377, 201, -132, 407, 712, -64],\n [155, 202, -140, 371, -31, -136, 155, 172, -105],\n [165, -93, -173, -15, 175, -42, -177, 228, -430],\n [235, 194, -56, -243, -260, -172, -316, -381, -84],\n [26, 132, 142, -382, -188, -104, -130, -206, 208],\n [280, 232, -40, -230, -162, -240, -224, -76, -152],\n [-355, -293, -175, -302, 224, 126, -97, 240, 236],\n [49, 159, -20, -134, -66, -154, -4, 118, 110]]?\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[[104, 104, -24, -32, -8, -120, 144, -120, -16],\n [13, 13, -3, -4, -1, -15, 18, -15, -2],\n [208, 208, -48, -64, -16, -240, 288, -240, -32],\n [-26, -26, 6, 8, 2, 30, -36, 30, 4],\n [-130, -130, 30, 40, 10, 150, -180, 150, 20],\n [-195, -195, 45, 60, 15, 225, -270, 225, 30],\n [-39, -39, 9, 12, 3, 45, -54, 45, 6],\n [-39, -39, 9, 12, 3, 45, -54, 45, 6],\n [130, 130, -30, -40, -10, -150, 180, -150, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 9x9 matrix:\n[[387, -268, 348, 136, 368, -245, 219, 242, 523],\n [72, -176, 239, 131, -276, -250, -243, 64, 84],\n [135, -123, -171, -343, -304, 212, -216, -275, -211],\n [-143, -95, -58, -263, 91, 146, -21, 373, 278],\n [417, -389, -448, -24, -320, -173, 83, 33, 172],\n [-30, 28, 354, 435, 167, -482, 212, 12, -207],\n [527, -317, 293, -59, 120, -47, -47, -24, 541],\n [-138, -68, 269, 4, 410, -139, 166, 398, 466],\n [-138, -99, 132, 93, 31, -451, 161, -158, -256]]\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[[215, 70, 280, -44, 177, 619, 118, 156, -4],\n [-1039, -110, 102, 422, -665, -716, -859, -30, 329],\n [-314, 160, 120, 312, 168, 147, -13, 562, -141],\n [245, 74, 231, -122, 526, 538, 381, 306, -174],\n [104, -419, 168, -272, 245, -191, -68, -458, 353],\n [321, 121, -268, 388, 262, 152, 148, 462, -27],\n [810, 245, -334, 248, 244, 577, 604, 265, -160],\n [529, 67, -62, -389, -139, -44, -17, -75, 519],\n [-94, -28, 31, -38, 8, 19, -61, -86, -154]]\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 9x9 matrix:\n[[265, -293, 28, -74, 223, -148, 36, 207, 339],\n [-110, 172, 112, 121, -54, -151, 68, -262, 128],\n [-371, 380, 44, 285, -226, -172, 149, -365, -136],\n [-360, 191, -108, 433, -235, -345, 297, -117, -315],\n [356, -191, 96, -366, 105, 355, -317, 42, 61],\n [136, -148, 28, 51, 2, -124, 24, 3, -6],\n [424, -188, 164, -377, 26, 398, -396, -103, -42],\n [-76, 176, 148, 155, -162, -134, 20, -387, -46],\n [296, -145, 216, 92, -189, -131, -111, -388, -201]]\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[[373, 64, 46, 63, -145, 86, -191, -22, -372],\n [107, -397, -307, 197, 47, -110, 188, 271, 108],\n [-93, 270, 186, -510, -202, 238, -113, -328, -123],\n [-282, -296, -247, 108, 104, -113, 292, 179, 323],\n [-22, 745, 349, 493, -23, 72, -439, -149, -81],\n [243, 113, 31, 111, -515, 8, 338, -113, -44],\n [392, 175, -93, 322, -345, 61, -22, 52, 31],\n [379, -73, 56, -193, -583, 9, 454, -178, -225],\n [-210, 670, 330, 239, 101, 81, -416, -177, 74]]\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[[168, -196, 84, -168, 84, 252, -196, -224, 140],\n [192, -224, 96, -192, 96, 288, -224, -256, 160],\n [-60, 70, -30, 60, -30, -90, 70, 80, -50],\n [-84, 98, -42, 84, -42, -126, 98, 112, -70],\n [-144, 168, -72, 144, -72, -216, 168, 192, -120],\n [192, -224, 96, -192, 96, 288, -224, -256, 160],\n [216, -252, 108, -216, 108, 324, -252, -288, 180],\n [96, -112, 48, -96, 48, 144, -112, -128, 80],\n [168, -196, 84, -168, 84, 252, -196, -224, 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 9x9 matrix:\n[[98, 22, 840, -18, -5, 170, 374, -564, -59],\n [248, 535, 210, 323, -440, -34, 481, -181, 55],\n [481, 554, -442, -145, -116, -467, 480, -385, 155],\n [-90, -67, -580, -35, -71, -116, -48, 103, 282],\n [-192, 393, 42, 16, -568, 95, 313, -334, -190],\n [-218, 330, -504, -284, -153, -368, 128, -58, -313],\n [-206, -460, 384, -20, 500, 300, -375, 28, -412],\n [454, 151, 202, 362, -8, 307, -22, -244, 41],\n [-53, -426, -522, 271, 260, 141, -301, 281, 365]]\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[[818, 270, 416, 61, -58, 675, -349, -461, -72],\n [-313, -348, -139, 130, -36, -139, -159, -220, 458],\n [-578, -175, 282, 45, 400, -184, -103, -43, 245],\n [587, 184, -231, -392, 328, 486, -48, 99, -497],\n [52, -79, -18, -80, 202, 594, -12, 195, 52],\n [-637, -482, -99, 516, -285, -245, 91, -155, 650],\n [-155, 101, 348, -104, 356, -549, -280, -613, 82],\n [141, 107, 401, -121, -273, 242, -122, 27, 458],\n [129, 224, 123, 253, -227, -340, -54, -478, -150]]\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[[-36, 0, 60, 144, -168, -24, -216, 216, 132],\n [-6, 0, 10, 24, -28, -4, -36, 36, 22],\n [-12, 0, 20, 48, -56, -8, -72, 72, 44],\n [-36, 0, 60, 144, -168, -24, -216, 216, 132],\n [-33, 0, 55, 132, -154, -22, -198, 198, 121],\n [-9, 0, 15, 36, -42, -6, -54, 54, 33],\n [-6, 0, 10, 24, -28, -4, -36, 36, 22],\n [-3, 0, 5, 12, -14, -2, -18, 18, 11],\n [-27, 0, 45, 108, -126, -18, -162, 162, 99]]\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[[-412, 32, -99, -831, 85, -454, -328, -369, -50],\n [369, 87, 244, 690, -249, 228, 167, 286, -287],\n [-109, 60, -75, -508, 57, -325, 75, -197, -92],\n [-238, 98, -56, -490, -19, -285, 113, -163, -2],\n [-13, -493, 41, 103, 188, -183, 490, -141, 586],\n [193, 205, -275, -26, 448, 300, 658, 188, 124],\n [113, 39, 285, 286, 488, 65, 137, 60, -271],\n [391, 93, 378, 228, 420, 221, 84, 455, -153],\n [-375, 72, 260, 25, 281, -262, -166, -369, -456]]\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[[419, -121, -85, -279, -211, 131, 244, 75, 13],\n [-142, 4, -222, 146, -71, -501, 268, -121, 330],\n [12, -426, 206, 32, -346, -124, 128, 12, -192],\n [-482, 189, 77, 318, 331, -110, -298, -98, 18],\n [29, -365, -45, 131, -177, -153, 316, -33, 23],\n [45, 146, -274, 203, 196, 477, -32, 157, -139],\n [381, -383, 217, -289, -273, 215, 146, 67, -207],\n [53, -560, 102, 142, -480, -83, 268, 75, -263],\n [-217, 9, -7, 185, 149, -115, -28, -75, 69]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[168, 61, 276, -324, -419, 394, 33, 11, -100],\n [115, -348, -750, 225, 255, 46, -299, 433, -584],\n [-163, -401, 107, 272, -325, -21, -263, 174, -58],\n [233, 96, -915, 402, 619, -215, 3, 440, -270],\n [496, 373, 204, -439, -92, 532, -216, -255, 190],\n [-82, -228, -198, 207, -253, 316, 35, 118, -394],\n [278, 487, 217, -309, 253, -311, 411, -478, 515],\n [-25, 47, 518, -516, -483, 616, 51, -380, -105],\n [-579, -309, -130, 523, 186, -308, -76, 90, -44]]\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[[-16, -56, 16, 0, 128, 48, 136, -104, -112],\n [-8, -28, 8, 0, 64, 24, 68, -52, -56],\n [10, 35, -10, 0, -80, -30, -85, 65, 70],\n [4, 14, -4, 0, -32, -12, -34, 26, 28],\n [-18, -63, 18, 0, 144, 54, 153, -117, -126],\n [12, 42, -12, 0, -96, -36, -102, 78, 84],\n [26, 91, -26, 0, -208, -78, -221, 169, 182],\n [28, 98, -28, 0, -224, -84, -238, 182, 196],\n [10, 35, -10, 0, -80, -30, -85, 65, 70]]?\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 9x9 matrix:\n[[208, 78, 143, 169, 221, 169, 78, 91, -143],\n [96, 36, 66, 78, 102, 78, 36, 42, -66],\n [-256, -96, -176, -208, -272, -208, -96, -112, 176],\n [-192, -72, -132, -156, -204, -156, -72, -84, 132],\n [96, 36, 66, 78, 102, 78, 36, 42, -66],\n [64, 24, 44, 52, 68, 52, 24, 28, -44],\n [144, 54, 99, 117, 153, 117, 54, 63, -99],\n [-112, -42, -77, -91, -119, -91, -42, -49, 77],\n [-176, -66, -121, -143, -187, -143, -66, -77, 121]]\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[[142, -291, -235, -107, 67, 352, 396, -17, -10],\n [-90, -222, 118, -579, -298, -5, 111, 148, -184],\n [334, -30, -22, 100, 92, 160, 190, 0, 162],\n [377, -174, -570, 308, -221, 169, 40, 39, 513],\n [-276, 122, 316, -205, 4, -200, -149, 12, -266],\n [216, -269, -559, 43, -409, 107, 2, 105, 404],\n [537, 85, -237, 454, -48, 45, -47, 20, 543],\n [21, -172, -500, 77, -401, -26, -161, 81, 319],\n [281, -59, 363, -402, -64, 49, 225, 124, -65]]\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[[13, -333, 293, -573, 96, -108, 236, 196, -158],\n [-98, -206, 4, 302, -204, 425, 62, 586, -82],\n [-158, -323, 286, -32, -266, -233, 23, -510, 170],\n [14, -303, -54, -327, 169, -125, 445, 464, 115],\n [-27, 193, 225, 57, -161, -172, -408, -872, -46],\n [287, 223, -269, -7, 206, 88, 34, -124, 94],\n [-400, 434, -4, 366, -104, -432, -458, -332, -26],\n [-71, 59, 327, -160, -97, -115, -292, -436, -219],\n [-137, -465, 217, -141, -152, 13, 260, 274, 30]]\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 9x9 matrix:\n[[145, -259, -245, 59, -143, 69, 132, -489, 185],\n [-214, -390, -115, -128, -134, -136, 338, 129, -148],\n [518, 35, 894, -308, 27, -202, -384, -183, 544],\n [94, -403, 194, -15, -23, 63, -218, 264, 249],\n [36, -310, 415, -415, -203, -312, 284, 211, -89],\n [108, 238, -58, -1, -213, -68, 336, -316, -323],\n [275, 324, 50, 240, -115, 91, -36, -241, -78],\n [-56, 517, -256, -96, 540, 363, -698, 246, 280],\n [-50, -162, 60, 405, -188, 43, 90, 209, -255]]\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 9x9 matrix:\n[[-614, 296, -183, -222, -256, -247, 322, -257, -359],\n [-388, 597, 223, -49, 692, 127, 128, -128, -13],\n [-109, -131, 214, 152, 624, 522, -307, -515, -230],\n [-271, 624, -218, -182, 399, 188, -58, 10, -28],\n [-240, 625, -258, -299, 546, 290, -344, -110, -213],\n [255, -391, 11, -42, -481, -585, 15, -213, -610],\n [8, -390, 344, 153, -361, -113, 323, 286, 559],\n [-151, -154, -623, 24, -32, 901, -298, -178, 122],\n [-189, 264, 319, -159, 46, -391, 313, 253, 141]]\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 9x9 matrix:\n[[-60, 61, -408, 87, 235, 102, 230, 272, -34],\n [-79, -232, 500, -48, -118, 250, 67, 145, 5],\n [-261, 483, -130, -373, 264, -297, -90, -216, 20],\n [175, -274, 334, 150, -499, 5, -137, -272, -183],\n [-38, 236, -760, 34, 696, 24, 219, 498, 315],\n [-356, -10, 145, -492, -25, -86, 53, 43, 12],\n [-101, 98, 103, -192, -270, -225, -126, -369, -205],\n [285, 230, -156, 444, 234, 72, -50, -45, 24],\n [121, 32, 208, 312, 196, 304, 83, 179, 37]]\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[[88, 228, 28, -124, 380, 120, 220, -344, 140],\n [-79, -189, -24, 97, -330, -120, -190, 287, -120],\n [36, 225, 21, -171, 249, -54, 153, -324, 105],\n [-6, -210, -16, 186, -164, 144, -108, 294, -80],\n [-108, -192, -28, 72, -404, -216, -228, 300, -140],\n [-62, -192, -22, 116, -290, -60, -170, 286, -110],\n [-85, 84, -5, -158, -151, -354, -67, -91, -25],\n [75, 3, 10, 69, 188, 252, 96, -27, 50],\n [63, -3, 8, 63, 154, 216, 78, -15, 40]]\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[[14, 36, 17, -32, 37, 49, -23, 26, 34],\n [4, 104, 110, -112, 118, 174, -2, 172, 188],\n [-100, -222, -82, 190, -224, -290, 166, -124, -176],\n [100, 263, 128, -235, 271, 360, -164, 196, 254],\n [-156, -243, -12, 183, -231, -276, 264, -12, -78],\n [-104, -203, -54, 167, -201, -254, 174, -80, -130],\n [-120, -168, 12, 120, -156, -180, 204, 24, -24],\n [-30, -1, 49, -15, 8, 25, 53, 78, 72],\n [-36, -34, 22, 18, -28, -26, 62, 36, 24]]?\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[[-258, -231, -145, 161, 68, -135, -148, -22, 251],\n [-397, -204, 65, 181, 68, -76, -259, -382, 397],\n [701, -285, 137, -437, 141, 719, 296, -417, -306],\n [261, 111, 592, -319, -28, 22, -6, 591, -108],\n [-164, 107, 263, -41, 586, -288, 201, 238, 178],\n [-225, -91, -257, 239, -463, 28, -217, -340, 86],\n [59, -84, -452, 109, 19, 203, 339, -586, -121],\n [-205, -14, -116, 140, 193, 77, -81, -701, 176],\n [-253, -146, -195, 202, -202, -152, 107, 23, 124]]\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[[386, 67, 371, 512, 108, -110, 87, -168, -299],\n [-390, 209, -586, -61, 302, 89, -226, -205, 219],\n [196, -242, -19, -191, -387, 403, 61, -14, 331],\n [-491, 208, -211, -196, 126, 18, 100, 45, 227],\n [419, 195, -275, 325, 477, -199, -372, -487, -87],\n [20, 50, -213, -222, 210, -270, -318, 37, -82],\n [115, -490, 408, -151, -598, 105, 235, 412, -181],\n [272, 14, 141, 73, 309, -641, -239, 62, -517],\n [-511, -231, 48, -312, -446, 278, 223, 445, 82]]\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 9x9 matrix:\n[[-180, 306, 223, -271, 152, -55, 303, -238, -236],\n [-19, -76, -57, -210, 338, -230, 295, -98, 153],\n [-474, 245, 348, -183, -60, -316, 229, -478, -379],\n [-137, -324, -71, -130, 258, -534, 261, -102, 207],\n [104, 66, -103, 151, -105, 295, -230, -36, 55],\n [19, -36, -24, -399, 550, -305, 534, -32, 161],\n [-231, 282, 181, -166, 62, -28, 171, -370, -209],\n [-278, -147, 124, -19, -72, -424, 89, -150, -91],\n [420, -73, -267, 162, 12, 429, -238, 368, 255]]\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 9x9 matrix:\n[[10, 257, -428, -323, 193, 274, -359, -142, 571],\n [-259, 650, -193, -160, -125, 319, -104, -453, 327],\n [-286, 73, 483, 81, -95, 342, 87, 9, 137],\n [509, -7, 5, -466, 247, -57, -479, 241, -4],\n [171, 183, -279, -55, 138, -64, 231, -51, -150],\n [-39, -501, 191, 242, -233, -215, -100, -340, -313],\n [272, -842, 324, 166, 296, 67, 254, 124, -284],\n [52, -331, -409, 31, 237, 188, 53, -225, 245],\n [136, 612, -19, -486, 82, -62, -490, 249, 256]]\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[[-3, -9, -42, 24, -51, 24, -54, -15, 48],\n [-12, -36, -168, 96, -204, 96, -216, -60, 192],\n [8, 24, 112, -64, 136, -64, 144, 40, -128],\n [0, 0, 0, 0, 0, 0, 0, 0, 0],\n [7, 21, 98, -56, 119, -56, 126, 35, -112],\n [3, 9, 42, -24, 51, -24, 54, 15, -48],\n [6, 18, 84, -48, 102, -48, 108, 30, -96],\n [6, 18, 84, -48, 102, -48, 108, 30, -96],\n [4, 12, 56, -32, 68, -32, 72, 20, -64]]\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[[24, -60, -16, -64, -32, 36, -64, -4, -40],\n [18, -45, -12, -48, -24, 27, -48, -3, -30],\n [48, -120, -32, -128, -64, 72, -128, -8, -80],\n [36, -90, -24, -96, -48, 54, -96, -6, -60],\n [90, -225, -60, -240, -120, 135, -240, -15, -150],\n [48, -120, -32, -128, -64, 72, -128, -8, -80],\n [96, -240, -64, -256, -128, 144, -256, -16, -160],\n [12, -30, -8, -32, -16, 18, -32, -2, -20],\n [-96, 240, 64, 256, 128, -144, 256, 16, 160]]\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[[-287, -373, -65, 95, 27, -370, -172, -215, -386],\n [-865, 33, 56, -93, 664, -452, -253, 352, -429],\n [122, -497, 151, -35, -11, -388, -273, -107, 15],\n [163, -258, -87, 503, 66, 20, -31, -231, -116],\n [549, -98, 16, 143, -412, 143, -25, -92, 97],\n [-50, 625, -386, 570, 425, 178, 199, 294, -18],\n [63, 119, -30, -230, -45, -352, -158, 282, 75],\n [352, -302, 180, -114, -407, -114, -225, -27, -36],\n [310, 505, -495, 421, -256, -9, 104, 161, -153]]?\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[[90, -72, 40, -225, 285, -150, -196, -90, -155],\n [-291, 512, -133, -264, -158, -386, 28, -148, -200],\n [-891, -64, -194, -19, -51, -324, 237, 474, -289],\n [307, -577, -409, -126, 120, 213, 487, 367, 173],\n [-342, 57, 91, -475, 278, 332, 74, -242, 49],\n [-112, 65, -73, -68, 137, -416, 113, -130, -320],\n [-125, -512, -338, 141, -30, 378, 551, 631, 110],\n [149, 452, -68, -108, 29, -169, 136, -296, -237],\n [-224, 38, -294, -200, 13, -568, 202, 71, -343]]\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[[43, 249, 216, -193, -1, -283, -379, -261, -69],\n [45, -90, -63, 19, 27, 52, 98, 80, 30],\n [-200, -87, -228, 155, -97, 197, 290, 117, 15],\n [-270, 306, -180, -198, -198, -270, -126, -306, -90],\n [-143, 140, 134, 66, -66, 8, -125, -98, -56],\n [245, -129, 174, 15, 151, 39, -55, 109, 45],\n [-21, -54, -117, 9, -15, 36, 114, 48, 18],\n [207, 76, 301, -103, 113, -150, -308, -94, -16],\n [142, 10, -41, -179, 49, -172, -75, -58, 14]]\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[[21, 337, -50, 21, 26, -626, -193, 243, 339],\n [-224, -79, 523, -54, 340, -561, 453, -132, 39],\n [395, -137, -187, -156, -117, 69, 36, -258, 463],\n [-76, -120, 41, 15, 103, 255, 63, 26, -160],\n [-178, -43, 199, -84, -235, -499, 221, -323, 220],\n [-533, -12, 235, 167, -308, 97, 58, -116, -726],\n [-439, 151, 2, 455, -152, -614, -521, 663, 293],\n [-223, 290, -280, -216, 234, -303, -159, 430, 544],\n [-466, -352, 389, -15, 31, -450, 369, -161, 377]]\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 9x9 matrix:\n[[-176, 41, 166, 279, -337, 302, -82, 123, 334],\n [-193, -94, -54, 20, 240, -356, 191, 54, -159],\n [251, 484, 144, -1, -127, 393, -195, -28, -25],\n [-107, 64, -21, 199, -765, 501, -429, -120, -244],\n [88, 29, 147, -372, -44, -57, -40, -185, -189],\n [262, -386, -461, -156, 184, -130, 131, 125, -28],\n [-191, 73, 123, 44, 110, 213, 0, 20, 411],\n [-252, 269, 605, 180, -454, 187, -29, 82, 276],\n [374, -392, -256, -362, 506, -650, 372, 66, -162]]\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 9x9 matrix:\n[[-47, 212, -347, -46, 328, -90, 132, 445, 13],\n [-149, -318, 11, 401, -600, -149, 206, 184, -429],\n [-142, 638, 56, 200, 242, -128, 274, 380, -146],\n [63, 185, 71, -166, 2, -5, 450, 93, -600],\n [313, 47, -259, -645, 466, 2, 144, -2, 42],\n [123, -430, -352, -198, -79, -83, 40, 122, -23],\n [169, 152, -132, -538, 379, 169, 334, 30, -465],\n [-250, -38, -411, -17, 455, 392, -328, 216, 120],\n [155, 240, -157, -214, 60, -290, 640, 407, -529]]\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 9x9 matrix:\n[[602, -355, 190, -180, -332, -696, 32, -486, -348],\n [223, -3, 20, 349, -100, -518, -272, -145, -369],\n [-446, 226, 202, 349, -294, 94, 336, -151, -289],\n [-86, -755, 332, 496, -183, 301, 221, -124, 266],\n [-14, 21, 288, 539, -149, -305, -139, -389, -417],\n [133, -88, -14, 157, 373, 127, -491, -45, 189],\n [212, 373, -25, -107, 326, -54, -640, -554, -184],\n [389, 196, 260, 248, 202, -660, -560, -398, -470],\n [-205, 78, 229, 56, -214, 208, 180, -540, -172]]\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 9x9 matrix:\n[[10, 338, -418, -387, -397, 161, 130, 166, -548],\n [140, 10, 188, 184, 218, -115, -144, -9, 193],\n [-61, 491, -309, -385, 183, 262, 469, -16, 11],\n [-369, 491, 45, 201, -124, -166, -504, -438, -156],\n [92, -217, -349, -99, -258, 366, 74, 561, 82],\n [-27, 857, -359, -639, -382, -333, 536, -68, -680],\n [-242, 3, -215, -121, -439, 211, 205, 420, -435],\n [21, -165, 193, -57, 33, 43, 95, -86, -242],\n [-181, 271, -439, 54, -416, -156, -359, -11, 11]]\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[[-167, 114, 386, -136, -281, 94, 354, 111, -332],\n [517, 68, -134, -599, 537, -142, 357, -84, 440],\n [219, 100, 9, -183, -186, -203, 80, -139, 204],\n [317, 173, 216, 133, 416, 197, 20, -126, 138],\n [12, 89, 182, 280, -73, 111, -115, -74, -54],\n [161, -41, 89, -131, -263, -62, 216, -97, 182],\n [111, -2, 91, -316, -354, -157, 321, -50, 112],\n [-348, -29, -275, -226, -422, -354, -119, 131, -210],\n [-204, 230, 362, 78, -124, 116, 82, 92, -412]]?\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[[-255, 51, -221, 306, 204, -238, -204, -238, -255],\n [60, -12, 52, -72, -48, 56, 48, 56, 60],\n [-75, 15, -65, 90, 60, -70, -60, -70, -75],\n [255, -51, 221, -306, -204, 238, 204, 238, 255],\n [225, -45, 195, -270, -180, 210, 180, 210, 225],\n [-180, 36, -156, 216, 144, -168, -144, -168, -180],\n [-15, 3, -13, 18, 12, -14, -12, -14, -15],\n [-105, 21, -91, 126, 84, -98, -84, -98, -105],\n [210, -42, 182, -252, -168, 196, 168, 196, 210]]\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[[61, -199, 241, -201, 28, 570, 567, -371, 238],\n [27, 232, -23, 24, 11, -293, -338, 255, -185],\n [107, 88, -246, -127, -217, -53, -249, 57, -5],\n [-201, 308, 244, 96, 254, -98, 246, 343, 21],\n [252, 21, 275, -59, -119, 43, -361, -16, 17],\n [-184, -29, 149, 260, 16, 10, 60, 98, 261],\n [-394, 59, 308, 519, 547, -519, -324, -26, -669],\n [247, 251, 211, -175, 17, -109, -98, 343, -2],\n [-264, -91, 185, 268, 216, 2, 79, -170, -103]]\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 9x9 matrix:\n[[-353, 37, 96, -12, -129, -100, -548, 506, -41],\n [-48, 491, -318, 544, 226, 347, -155, -174, 8],\n [427, -619, -246, -323, -439, -703, -215, 425, 155],\n [513, -194, -343, -350, -180, -568, 335, 208, 605],\n [-181, 119, 422, 197, -353, 336, -449, -13, -343],\n [-316, 227, 39, 565, 431, 12, -176, -467, -156],\n [-377, -76, -19, 240, 346, 417, -819, -12, -263],\n [-154, 319, 23, 362, 150, -469, -54, -160, 359],\n [392, -453, -231, -353, -157, -482, 434, 127, 48]]\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[[88, 151, 125, -286, -113, 159, -107, 329, -272],\n [55, -79, -198, 54, -143, 72, 105, 146, -36],\n [-485, 71, 340, 34, -309, -34, -683, -578, 2],\n [636, 201, -304, -74, 327, 77, 742, 633, -158],\n [233, 306, -292, 278, -134, -3, 281, 7, -28],\n [-89, -363, -287, 352, 107, -144, 223, -283, 331],\n [158, -71, -154, -15, 92, 144, 218, 45, -228],\n [430, 345, -169, -55, 70, 188, 371, 265, -396],\n [-493, -162, 68, 95, -549, 72, -606, -386, -15]]\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[[-452, -76, -236, -371, -90, -101, 595, -546, 585],\n [-164, -69, 293, 380, 244, -26, -383, 424, 119],\n [-253, 244, 155, 264, 130, -61, 182, 290, 466],\n [5, -22, 167, -116, 305, -420, -267, 37, -124],\n [567, 84, -135, 61, 573, 438, 278, 447, -513],\n [-199, 83, 181, 229, 300, -29, 16, 405, 291],\n [-311, -23, -206, -8, -216, -259, -63, -24, -148],\n [-277, -351, 129, -180, -180, -55, -220, -541, 407],\n [310, -75, 332, -350, 249, -407, 260, -84, 1]]\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[[-170, 417, -466, 250, 356, 4, 128, 295, 70],\n [-354, 40, -397, 362, -51, -127, -120, 144, -138],\n [56, -457, 212, -105, -278, 74, 156, -275, -199],\n [304, 119, 137, -229, 193, 95, 462, 23, 69],\n [-27, -209, 173, -25, -261, -94, -225, -108, -63],\n [206, 460, 112, -122, 164, -202, -38, 278, 234],\n [23, -119, 206, -44, -270, -189, -191, -28, -44],\n [-244, -19, -366, 324, -124, -210, 306, 181, -276],\n [-78, -74, -36, 26, 28, 118, -158, -92, 22]]\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[[-359, 141, 97, -84, -570, -299, 170, 498, -357],\n [-128, -163, 206, 9, 355, 274, -232, -379, 933],\n [-409, -130, 126, 71, -229, 61, 268, 233, 178],\n [-85, -462, 321, 590, 501, 223, 614, 16, 306],\n [842, 673, 182, -1137, -533, -156, -339, -233, 501],\n [-245, -314, 338, 549, -77, -357, 154, 219, -828],\n [287, 310, -153, -294, -94, -19, -157, -489, 377],\n [37, 26, 306, -201, -31, -87, -299, 147, 246],\n [344, -30, 593, 182, -236, -327, 441, -659, 120]]\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[[248, -112, 112, -126, -344, -152, 150, 75, -300],\n [-405, -259, 16, -488, 156, -134, 180, 200, -169],\n [498, 231, -668, 12, -334, -42, 8, 277, 176],\n [-315, 379, -381, 86, -15, 63, -276, 927, 169],\n [156, 220, 275, 380, -167, 153, -24, 69, -195],\n [182, 196, -84, -277, 152, 147, 134, 257, -228],\n [-347, 86, 190, 13, 132, 105, -9, 286, -128],\n [-609, -123, -51, 199, 47, -242, -340, 534, 135],\n [395, -501, 216, 154, -248, -344, 11, -852, 27]]\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[[-265, 287, -281, -171, 278, 229, -285, -641, -161],\n [271, -340, 296, 56, -159, -155, 153, 533, 114],\n [108, 5, 91, -248, 4, -32, -259, -216, 73],\n [-158, -85, -112, -103, 342, 256, -141, -211, -240],\n [64, 168, 0, 196, -220, -144, 164, 152, 192],\n [131, -91, 123, -268, 109, 37, -294, -175, 35],\n [-444, 758, -532, 353, -163, -8, 233, -454, 12],\n [129, 53, 127, 100, -509, -377, 248, 279, 211],\n [209, -289, 268, -326, -90, -131, -191, 42, 22]]\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[[-120, 165, 225, 210, 45, 15, 15, 165, -150],\n [247, -239, -282, -280, -160, 12, -128, -274, 132],\n [-196, 212, 264, 256, 112, 0, 80, 232, -144],\n [248, -111, -51, -86, -247, 67, -253, -191, -94],\n [102, -54, -36, -48, -96, 24, -96, -84, -24],\n [-233, 191, 204, 212, 174, -26, 154, 236, -64],\n [-62, 114, 168, 152, 4, 20, -20, 104, -128],\n [331, -297, -336, -340, -230, 26, -194, -352, 136],\n [191, -162, -177, -182, -139, 19, -121, -197, 62]]\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[[-36, 4, 34, -34, 8, -34, -18, -20, 20],\n [-144, 16, 136, -136, 32, -136, -72, -80, 80],\n [306, -34, -289, 289, -68, 289, 153, 170, -170],\n [270, -30, -255, 255, -60, 255, 135, 150, -150],\n [126, -14, -119, 119, -28, 119, 63, 70, -70],\n [54, -6, -51, 51, -12, 51, 27, 30, -30],\n [-108, 12, 102, -102, 24, -102, -54, -60, 60],\n [-72, 8, 68, -68, 16, -68, -36, -40, 40],\n [36, -4, -34, 34, -8, 34, 18, 20, -20]]?\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[[-114, 81, -95, 170, 70, -618, 355, -98, -386],\n [526, 257, -45, 40, 91, 508, -250, 448, 144],\n [149, -189, 120, 28, -49, 384, -416, 252, 298],\n [305, -444, -416, 355, -290, 262, -23, -379, 660],\n [641, -26, -254, 374, -325, 487, -199, -34, 326],\n [10, 247, 28, -257, -122, -120, -66, -23, -220],\n [-307, -167, 270, 150, 120, -144, 45, 66, -188],\n [-109, -55, 314, -229, 200, 359, -364, 409, 140],\n [-190, -121, -71, 65, 423, 29, 327, 51, 188]]?\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[[-102, 44, 22, -94, -120, 0, -120, 79, 53],\n [174, -114, -66, -186, 60, 48, 42, -168, 192],\n [214, -152, -90, -334, 32, 76, 4, -217, 325],\n [183, -97, -65, -13, 270, 168, 237, -176, 236],\n [33, -33, -27, -147, 30, 96, 9, -51, 219],\n [-198, 84, 54, -174, -360, -144, -336, 171, -87],\n [-235, 139, 84, 128, -194, -115, -165, 223, -245],\n [-4, 34, 9, 257, 268, 143, 252, 7, 19],\n [38, 22, 2, 346, 364, 164, 346, -24, -8]]?\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[[-184, -238, -234, 43, 163, 52, -46, 159, -1],\n [-95, 344, -75, 170, -252, -346, -98, -14, -10],\n [358, -403, 241, -172, 73, 408, 88, 66, -80],\n [-256, 386, 26, -120, 178, -112, 136, -304, 188],\n [-131, -229, 107, -401, 498, 444, 324, -90, 164],\n [-570, 388, -384, 143, -115, -460, -10, 197, 81],\n [119, -77, -140, 286, -413, -226, -226, 340, -198],\n [-130, -401, -229, 15, 204, 164, -38, 229, -29],\n [-140, -419, -304, 104, 97, 82, -104, 343, -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[[-420, 437, 148, -595, -161, -232, 57, -205, -351],\n [-1, -191, -46, 167, -119, -129, -256, 148, 415],\n [-439, -488, 102, -183, -418, -1183, -410, 65, 938],\n [431, 8, 279, 414, 442, 411, 304, -131, -217],\n [-706, 253, 133, 43, -402, 97, 145, 225, 254],\n [251, 283, -395, 549, 67, 798, 139, -66, -250],\n [-316, 66, 23, -142, -541, -578, -110, -209, 83],\n [-472, 45, -407, -18, -955, -106, -238, 256, 235],\n [-583, 162, 115, -241, -430, -327, -115, 13, -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 9x9 matrix:\n[[-139, -135, -72, 8, -38, 9, -64, -103, -106],\n [464, 302, 468, -30, 72, 244, 100, 462, 94],\n [-26, -240, -48, 22, 308, 6, -176, -152, 346],\n [199, -30, 281, -5, 150, 222, -79, 188, 96],\n [283, 107, 346, -16, 78, 229, 2, 295, 40],\n [-124, 178, -381, 4, -76, -391, 171, -212, 141],\n [-347, -179, -343, 18, -122, -184, -39, -317, -149],\n [-317, 31, -399, 6, -270, -298, 113, -267, -229],\n [137, -206, 268, 7, 262, 269, -196, 102, 169]]\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 9x9 matrix:\n[[-36, 25, -112, -174, 22, 250, 17, 39, 157],\n [-52, -169, -122, -23, 94, -122, 168, -285, 269],\n [-28, -224, -52, 172, 28, -348, 116, -292, 148],\n [-106, 220, 422, -20, -22, 174, 0, 154, -314],\n [-241, 298, 512, -290, 121, 463, 196, 37, -160],\n [-51, -212, -169, 84, -33, -123, 44, -163, 249],\n [246, 19, -31, 291, -100, -396, -230, 165, -348],\n [253, -119, -502, 110, -135, -129, -279, 196, 89],\n [310, -70, -536, -40, 38, -150, -146, 52, 134]]\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[[-137, -456, 386, 346, -414, 703, 224, 315, 361],\n [91, -281, 52, 197, 173, 80, -214, -388, 284],\n [240, -151, -243, 55, -59, -487, -224, -190, -140],\n [-494, 413, -578, -732, -314, -172, -584, 43, -143],\n [159, -256, 423, 256, -21, 85, 239, 74, 75],\n [288, -242, 143, 568, 406, -11, 171, -528, -254],\n [111, 103, -2, 192, 267, -35, 211, -148, -273],\n [-143, 332, 55, -201, 423, -49, -71, -349, -221],\n [-331, -220, 246, -72, -484, 582, -13, 386, 402]]?\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[[304, 1077, 1131, -806, 844, 958, 49, -90, 26],\n [-465, 239, 14, -50, 292, 383, -381, 34, 62],\n [26, -325, -176, 25, -282, -295, 212, -225, 240],\n [349, -7, 312, -232, -110, -14, 301, -201, 235],\n [36, -239, 22, -46, -739, -51, -385, -860, 719],\n [410, 238, 189, -370, 537, -39, 360, 304, -573],\n [-493, -280, -495, 259, -122, -130, -65, 213, 51],\n [-81, -450, -61, 701, -221, -269, 205, 255, 189],\n [-396, 111, 0, -309, 206, 267, -147, -196, 274]]\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[[194, -9, -10, -246, -92, -28, 40, 59, 82],\n [64, -302, 190, -288, -354, -36, -182, 138, -44],\n [-108, -24, 48, 128, 44, 28, -24, -48, -80],\n [-291, -258, -123, 34, -476, -181, -465, 372, 176],\n [-339, -291, -69, 84, -462, -159, -477, 339, 114],\n [-430, -212, 230, 412, 12, 78, -198, -104, -304],\n [58, -159, -56, -254, -354, -120, -202, 253, 166],\n [-309, -8, -111, 310, -22, -47, -181, 74, 28],\n [-460, -222, 98, 376, -130, -8, -314, 50, -156]]?\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 9x9 matrix:\n[[205, -82, -108, -264, 508, 350, -383, -232, 217],\n [96, 405, 153, 64, -526, -241, -55, 133, -264],\n [2, 67, 194, -396, -192, -100, 76, 276, -16],\n [-444, 376, 32, -231, -657, -149, 346, 181, 37],\n [-407, 281, -361, -446, -235, 215, 315, -77, -167],\n [-62, -238, 209, -349, 313, 106, -97, 74, 631],\n [-433, 276, -143, -203, -453, -113, 511, 79, -105],\n [57, -536, 107, 112, 463, 100, -102, 46, 290],\n [91, -312, -135, -125, 346, 276, -147, -10, -152]]\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[[-47, 538, 312, 470, 364, 140, -559, 183, -322],\n [163, -134, -151, -606, -387, 33, 699, -277, 455],\n [-157, -206, 250, 176, 453, 477, 97, 117, 192],\n [343, 592, -172, -416, -322, -342, -133, -23, -249],\n [-222, 98, 175, 473, 159, -92, -300, -39, -99],\n [403, 208, -132, -127, 116, -8, -253, 330, 1],\n [-401, -182, -107, 80, -490, -554, 137, -493, -163],\n [110, 310, -13, -141, -199, -204, 72, -173, 113],\n [135, 348, -172, -82, -624, -546, 35, -333, 35]]\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[[16, -256, -1, -42, 347, 131, -155, 186, -123],\n [859, -276, 121, -206, 872, 595, -207, 268, 213],\n [-265, -97, 41, -237, -30, 110, 197, 325, 669],\n [-73, -414, 473, -9, 517, 117, -300, 55, 120],\n [322, 311, -720, -319, -314, -410, 272, -82, -55],\n [44, 588, 162, -95, -795, 68, 412, 108, 346],\n [-24, 22, -416, -481, 113, -38, 118, 417, 569],\n [-435, 344, -220, 214, -420, -660, -2, -176, 508],\n [-213, 518, -19, 86, -471, -114, 27, 32, 173]]\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[[174, 2, 161, 20, -244, 52, -92, 479, -183],\n [24, -263, -89, 160, -404, -268, -367, 259, -168],\n [-204, -127, -254, 207, -440, -391, -417, 113, -191],\n [175, -457, -9, 81, -194, -259, -295, 320, 45],\n [130, 170, 167, 46, -276, 298, 32, 7, -369],\n [495, -217, 375, -56, -54, 390, 113, 149, -133],\n [-44, 160, 31, -159, 500, 243, 382, -496, 257],\n [264, -529, 54, -11, 96, -117, -103, 59, 227],\n [80, -213, -12, 88, -244, -144, -223, 214, -93]]\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[[146, -7, -341, 45, -300, -420, -268, 329, 379],\n [-234, 192, 124, -38, 215, -52, -21, 86, 22],\n [-223, -221, 201, -32, 234, 258, 414, -391, -492],\n [-192, 524, 87, -395, 227, 264, -59, -104, -149],\n [-208, 77, 452, 116, 453, 395, -49, -151, 37],\n [236, 27, -195, -91, -273, -50, -5, 33, -35],\n [337, -132, -313, 198, -455, -489, -157, 406, 325],\n [77, -501, -92, 73, -193, -40, 517, -279, -515],\n [367, -283, -11, 198, -234, 132, 6, -69, 40]]\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[[266, 170, -65, 120, 338, -330, -57, -283, 167],\n [-268, 130, 75, -28, -56, -217, 130, -44, -284],\n [222, 192, -202, 598, 108, -421, -9, -263, 137],\n [258, -6, 16, -109, 33, 332, -68, 51, 170],\n [-74, -55, 142, -532, 59, 296, -7, 68, -104],\n [-88, -326, -445, 244, -80, 104, -148, -175, -18],\n [316, 210, 56, 99, 291, -273, -29, -156, 227],\n [210, -94, -148, 150, 86, 33, -115, -67, 221],\n [12, -101, -29, -355, 76, 301, -67, -39, -42]]\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[[110, 114, -49, 245, -91, 56, -269, 59, -287],\n [-212, -260, 126, -466, 322, -52, 502, 22, 466],\n [-301, -15, -277, -211, 21, -187, 342, 78, 108],\n [133, 33, 203, 156, -280, 334, 220, -188, -163],\n [173, -109, 330, -8, 106, 211, -3, -59, 69],\n [-68, 96, -182, 118, -103, -2, 10, 86, -233],\n [-76, 26, -98, 3, -39, -11, 94, 38, -67],\n [289, 103, 140, 258, -152, 47, -473, -145, -93],\n [288, -128, 459, 75, 178, 322, -131, -15, -22]]?\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[[-185, -12, -11, -240, 566, 410, 39, 202, -64],\n [-303, -176, 114, 79, -290, 28, -518, 14, 113],\n [118, -487, 162, 95, -269, -522, 410, 506, 10],\n [192, 123, -49, -73, 293, -12, 422, 26, -80],\n [-33, -360, 258, -193, 326, -44, 266, 576, -39],\n [-239, -51, -115, 33, -514, 222, -812, -286, 129],\n [-309, -555, 162, -295, -37, -62, 163, 232, 346],\n [124, 15, -281, 200, -266, 30, -190, 68, -220],\n [199, 194, 86, -131, 195, 54, 89, -102, -32]]?\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 9x9 matrix:\n[[460, 151, -116, -230, 105, 71, -47, 191, -359],\n [215, 140, -310, 135, 285, 125, 176, -276, 124],\n [-167, -191, -85, 310, -238, -134, 170, 298, -21],\n [780, 319, -39, -192, -79, -38, 84, -103, -84],\n [113, 188, -257, 247, -214, 83, 142, -324, -123],\n [-360, -371, -456, 130, -410, 258, 120, 153, 265],\n [379, 123, -239, 302, 20, -108, 292, 62, -103],\n [-3, -101, -4, 356, 150, -265, 206, 425, -176],\n [581, 426, 228, -371, 672, 22, -54, -679, 454]]\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[[-355, -218, -27, 28, -189, 6, 7, -264, 261],\n [418, -63, -447, 467, -384, -93, 723, -133, 277],\n [-34, -300, 242, -372, -311, -269, -173, -104, 176],\n [330, 299, -449, 465, -230, 115, 407, -233, 331],\n [248, -100, 44, -145, 169, -261, 95, 270, -232],\n [363, 402, -97, 204, 244, 209, 74, 248, -283],\n [5, 69, 326, -563, 46, -232, -583, -15, 52],\n [-193, -69, 118, -38, 359, 67, -74, 251, -360],\n [315, -32, 97, -269, 9, -304, -53, 147, -63]]\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 9x9 matrix:\n[[88, -16, 150, 114, 178, -4, -12, 38, 80],\n [74, 70, 11, -61, 67, -76, -92, 59, -78],\n [129, 33, 142, 61, 205, -55, -73, 74, 19],\n [111, 159, -58, -193, 47, -161, -191, 106, -211],\n [137, -47, 264, 219, 299, 13, 3, 52, 163],\n [-23, -175, 208, 307, 131, 157, 179, -68, 291],\n [-28, -260, 318, 462, 206, 232, 264, -98, 436],\n [-7, 205, -293, -392, -216, -177, -199, 63, -361],\n [86, -50, 194, 176, 208, 26, 22, 26, 138]]\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[[-126, 874, 96, -34, 439, -359, 108, -292, 359],\n [114, 455, 184, -350, 484, -506, 135, 886, -604],\n [-191, -98, 336, -408, 363, -409, -90, -2, -6],\n [-336, 148, 70, -128, 190, -311, 68, -463, -175],\n [-113, 125, 102, -316, 423, -645, 355, -427, -217],\n [98, 51, 74, 60, 37, 74, 104, -284, 469],\n [320, 642, 29, -258, 238, -280, 226, 88, -1],\n [-242, 464, 186, -380, 836, -974, -46, 306, -38],\n [273, 63, -83, -238, 268, -468, 166, 37, 75]]?\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[[-512, 132, -597, -439, -300, 264, -87, 134, 118],\n [-37, 289, -170, -92, -395, 227, -215, -198, -400],\n [-619, -118, 62, 410, 140, 51, -41, 103, -25],\n [386, -77, -66, -386, 185, -198, 442, 93, 507],\n [-234, 135, 19, -92, -100, -137, -112, 368, 524],\n [-119, 231, 87, -23, -198, 118, -233, 102, -47],\n [-187, -182, 327, 449, 250, -136, -93, 121, 46],\n [-337, 180, 362, -14, 195, 161, 193, 363, 341],\n [-57, -99, 107, -200, 454, 336, 635, -25, -35]]\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[[-388, 382, 29, 215, 235, -75, -166, 52, 77],\n [212, 40, 226, 491, -26, -157, -38, -61, -354],\n [-281, 361, 36, -87, 82, 16, -351, -262, 235],\n [-252, -53, 116, 132, -63, -163, -522, -114, 60],\n [-195, -47, -148, 164, 149, -53, 145, 259, -101],\n [302, 54, -92, 257, 18, 19, 232, -239, -402],\n [165, 192, 410, 594, 1, -210, -137, -9, -289],\n [-21, 38, -122, 279, 81, -59, 15, -120, -279],\n [134, -79, -57, 342, 68, -67, 264, 127, -355]]\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[[-228, 38, -188, -228, 173, 148, -515, 34, -300],\n [121, -95, 115, 106, -48, -138, 396, 54, 188],\n [-18, 262, 467, -86, -410, -200, 69, 172, 13],\n [71, 513, 336, 375, -375, 156, -66, -323, 32],\n [348, -244, -668, 0, 258, 80, -222, -300, 176],\n [-230, 202, 369, -56, -129, -48, -4, 188, -167],\n [-469, -274, -182, 26, 875, 98, 174, 288, -359],\n [211, -53, 153, -139, 126, -556, 462, 391, 185],\n [-180, 208, 360, 341, -83, 162, 245, -83, -57]]\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[[-45, 178, 173, -29, 100, -177, 437, -397, -34],\n [-847, 469, 22, 748, -199, -101, -116, -89, 4],\n [-601, 349, 184, 13, 256, 341, 36, -91, -300],\n [257, -97, -41, -265, -305, 158, -241, -19, 608],\n [-370, 20, -42, 216, -52, 70, 314, -342, -74],\n [-17, 143, 48, -62, -34, 156, -192, 175, -46],\n [365, -522, -105, -566, 81, 285, 329, -331, 202],\n [90, -233, -110, 82, -194, -184, 524, -528, 214],\n [-873, 482, 42, 718, -192, -74, -32, -179, 8]]?\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[[96, 189, 214, 270, -49, -194, 99, 50, 237],\n [-445, -293, 366, -149, -193, -205, -509, -315, 248],\n [407, -229, 197, 214, 153, -50, 335, 138, -171],\n [-65, -139, 265, 202, 47, -198, -207, -76, -139],\n [-486, 149, -214, -84, 7, -124, -481, -190, -67],\n [-119, 105, -128, 223, 193, -97, -259, -5, -468],\n [99, -69, -44, -40, 30, 172, 38, 59, -221],\n [-98, -597, 541, -254, -226, -30, -158, -218, 300],\n [335, 172, -270, 124, 187, 28, 437, 210, -85]]?\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[[-225, 127, 350, -100, -41, -111, 242, -302, -20],\n [-155, 8, 33, -43, -47, -145, -72, -32, -64],\n [-349, -33, -140, -52, -103, -423, -504, 138, -194],\n [175, 174, 2, 133, 166, 129, -471, 150, 119],\n [-413, -288, -163, -197, -287, -407, 278, -60, -278],\n [139, -95, -215, 42, 2, 177, -169, 160, 39],\n [184, -315, -397, -11, -106, 266, 146, 176, 0],\n [63, -408, -249, -177, -273, 621, 444, -120, 60],\n [157, 75, 20, 94, 121, -85, 94, 66, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}