{"messages": [{"content": "Find the rank of the matrix:\n[[-25, -8, 28, -25, 105, -140, 182],\n [-3, -93, -9, -25, 134, -227, 153],\n [-143, -177, 178, -89, -261, 33, -98],\n [-96, 4, 45, -134, -162, 124, -65],\n [-107, -240, 71, 3, -208, 24, -197],\n [2, -123, 12, 7, -38, -31, -84],\n [110, -32, 177, -245, -74, -267, 104]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[20, 80, 110, 120, 0, -40, 20],\n [24, 96, 132, 144, 0, -48, 24],\n [-10, -40, -55, -60, 0, 20, -10],\n [16, 64, 88, 96, 0, -32, 16],\n [6, 24, 33, 36, 0, -12, 6],\n [0, 0, 0, 0, 0, 0, 0],\n [10, 40, 55, 60, 0, -20, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[72, 48, 60, 12, 132, 144, -36],\n [-84, -96, -114, -90, 30, 0, -66],\n [-26, -4, -7, 21, -109, -108, 49],\n [126, 124, 149, 97, 47, 84, 45],\n [-16, 6, 5, 29, -106, -102, 53],\n [-16, -4, -6, 10, -60, -60, 26],\n [-10, -20, -23, -27, 43, 36, -31]]\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[[-80, -100, -110, 100, 70, -120, 0],\n [-126, -148, -64, 110, -37, -18, -76],\n [98, 118, 83, -100, -16, 66, 36],\n [68, 78, 13, -50, 49, -24, 56],\n [76, 96, 116, -100, -82, 132, -8],\n [84, 104, 104, -100, -58, 108, 8],\n [-18, -22, -19, 20, 8, -18, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 7x7 matrix:\n[[-119, 147, 25, -54, -81, -27, 227],\n [8, 104, -16, -79, 4, -16, 115],\n [-213, 263, -51, -81, 361, -99, 382],\n [-76, 84, 87, -185, -69, -111, 64],\n [-108, 324, -150, -90, 516, -90, 408],\n [167, -106, -124, 190, 44, 186, -76],\n [29, -100, -208, -54, 108, 146, 60]]\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 7x7 matrix:\n[[44, 77, -33, 110, -77, 99, -66],\n [28, 49, -21, 70, -49, 63, -42],\n [-36, -63, 27, -90, 63, -81, 54],\n [8, 14, -6, 20, -14, 18, -12],\n [-12, -21, 9, -30, 21, -27, 18],\n [-12, -21, 9, -30, 21, -27, 18],\n [48, 84, -36, 120, -84, 108, -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[[177, 56, 205, -153, 128, 116, 47],\n [-118, 111, -175, -9, 18, -135, -106],\n [89, 207, 68, -229, 189, 23, -14],\n [161, -127, 159, -21, 18, 203, 128],\n [-84, 73, -169, 18, 19, -131, -149],\n [84, -208, 82, 133, -85, 90, 21],\n [-229, 58, -212, 87, -99, -176, -43]]\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[[100, -30, 40, 90, 120, 90, 120],\n [-120, 36, -48, -108, -144, -108, -144],\n [-50, 15, -20, -45, -60, -45, -60],\n [-10, 3, -4, -9, -12, -9, -12],\n [-50, 15, -20, -45, -60, -45, -60],\n [110, -33, 44, 99, 132, 99, 132],\n [-90, 27, -36, -81, -108, -81, -108]]\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[[82, -31, -87, 57, -103, 16, -90],\n [93, -8, -74, 35, -105, 14, -66],\n [65, 124, 66, -117, -17, -10, 126],\n [-150, -4, 104, -38, 162, -20, 84],\n [-68, 96, 136, -124, 116, -24, 168],\n [21, 32, 14, -29, -9, -2, 30],\n [141, 9, -93, 30, -150, 18, -72]]\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 7x7 matrix:\n[[-186, -81, 122, 0, 171, -25, 96],\n [14, 33, -65, 67, 25, 3, -113],\n [-46, 93, 66, -107, 209, 94, -40],\n [-52, 34, 6, -49, 47, 36, 51],\n [-107, 36, -33, 27, 101, 20, -21],\n [-51, -59, -84, 60, -260, -117, 76],\n [119, -207, 106, 203, 139, -47, -61]]\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 7x7 matrix:\n[[-44, -77, 33, 77, -22, -99, 22],\n [40, 70, -30, -70, 20, 90, -20],\n [36, 63, -27, -63, 18, 81, -18],\n [24, 42, -18, -42, 12, 54, -12],\n [48, 84, -36, -84, 24, 108, -24],\n [36, 63, -27, -63, 18, 81, -18],\n [36, 63, -27, -63, 18, 81, -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 7x7 matrix:\n[[-152, -8, -188, -96, -120, 56, -72],\n [-2, 57, 53, 33, 80, -89, 79],\n [-16, 1, -18, -9, -10, 3, -5],\n [-116, 16, -122, -60, -60, 8, -24],\n [-132, 17, -140, -69, -70, 11, -29],\n [42, 28, 77, 42, 70, -56, 56],\n [-40, -50, -96, -54, -100, 90, -86]]\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[[-126, 59, -97, 130, 51, -21, -57],\n [113, -132, 6, -77, 94, 218, 221],\n [72, -39, 228, -160, -32, -240, 96],\n [-105, 78, -80, 81, 12, 36, -175],\n [84, -3, -127, 80, -131, 45, 43],\n [89, 4, -93, 38, -136, 59, -15],\n [208, -19, 136, -147, -253, -176, 11]]\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 7x7 matrix:\n[[-193, 45, -121, -103, 59, -3, 122],\n [-209, -78, 83, -241, 125, 33, 181],\n [47, 81, -24, 98, -301, 85, -140],\n [-66, 4, 138, -106, -214, 172, 10],\n [212, -5, 14, 206, -190, -51, -239],\n [12, -36, 48, -10, -28, -5, -28],\n [110, 25, 103, 41, -100, 110, -37]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-186, -90, -30, -144, 14, 183, 40],\n [8, 57, -22, -34, 44, 19, 29],\n [44, 143, -34, -38, 48, -9, 67],\n [32, 35, 26, 58, -108, -87, 19],\n [32, 84, 26, 56, -156, -110, 58],\n [-80, -106, 16, -12, -48, 46, -22],\n [38, 84, 2, 20, -50, -59, 42]]\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[[-103, -148, 99, -31, 4, 11, -18],\n [-55, -44, 107, -7, -52, 103, 70],\n [-74, -120, 50, -26, 24, -30, -44],\n [-36, -78, -6, -18, 42, -69, -66],\n [48, 60, -60, 12, 12, -30, -12],\n [-61, -68, 89, -13, -28, 61, 34],\n [47, 56, -63, 11, 16, -37, -18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-44, 16, 13, 36, 59, 59, -6],\n [74, -22, 25, -8, -57, -77, -2],\n [67, 91, 157, 62, 107, -19, 26],\n [10, 124, 33, -72, 67, -13, 72],\n [-111, 33, 27, 90, 141, 147, -18],\n [-74, -59, -121, -40, -57, 41, -19],\n [18, 126, -30, -156, 6, -54, 96]]\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[[136, 144, -4, -88, -124, -104, 76],\n [185, 228, 31, -74, -152, -76, 83],\n [-157, -180, -11, 82, 136, 92, -79],\n [23, -20, -51, -78, -44, -108, 41],\n [-9, -8, 2, 8, 9, 10, -6],\n [14, 24, 10, 4, -8, 8, 2],\n [93, 100, -1, -58, -84, -68, 51]]\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[[74, -168, -52, 30, -82, 24, 76],\n [37, 70, -23, -141, 188, 16, -147],\n [-225, -28, 118, 45, -39, 36, 142],\n [32, 29, -14, 0, 3, -14, -29],\n [145, -15, -82, -69, 68, -2, -101],\n [-217, 40, 121, 57, -40, 12, 111],\n [133, 3, -68, 15, -32, -30, -49]]\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[[-121, 132, -99, 132, -55, -22, -44],\n [-33, 36, -27, 36, -15, -6, -12],\n [121, -132, 99, -132, 55, 22, 44],\n [55, -60, 45, -60, 25, 10, 20],\n [0, 0, 0, 0, 0, 0, 0],\n [-88, 96, -72, 96, -40, -16, -32],\n [110, -120, 90, -120, 50, 20, 40]]?\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[[22, 8, 20, 24, -16, -6, -20],\n [-88, -32, -80, -96, 64, 24, 80],\n [-132, -48, -120, -144, 96, 36, 120],\n [-99, -36, -90, -108, 72, 27, 90],\n [-44, -16, -40, -48, 32, 12, 40],\n [0, 0, 0, 0, 0, 0, 0],\n [132, 48, 120, 144, -96, -36, -120]]\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 7x7 matrix:\n[[-12, 72, -53, 128, 72, -101, 65],\n [45, 162, 59, 43, -15, -10, 13],\n [-42, 36, -254, 2, 186, -236, -70],\n [43, 84, -11, -165, -16, 4, -140],\n [-34, -84, -3, 86, 10, 3, 79],\n [-1, 42, -119, -83, 73, -98, -99],\n [54, 0, 177, -126, -152, 187, -47]]\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[[18, 27, 18, 125, -80, -58, -71],\n [-48, -14, 96, 182, -36, -156, -94],\n [-48, -59, 62, 88, 51, -89, -33],\n [57, -94, -73, 43, 86, 71, 7],\n [-189, 69, 223, -3, -41, -242, -30],\n [-108, 105, 106, -144, -53, -77, 39],\n [-15, -58, 65, 242, -11, -138, -111]]\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[[-151, -36, 73, -15, 192, 154, 85],\n [176, 176, -40, 106, -256, -68, 66],\n [-20, -116, 126, 54, 92, 190, 41],\n [-133, -32, 62, 158, -39, 184, 76],\n [0, -50, 176, 239, -121, -91, 64],\n [8, -244, 112, 49, 8, -87, -46],\n [24, -76, -79, -166, 85, 17, 5]]?\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[[-183, 171, 13, -85, 156, 297, 68],\n [47, 103, -213, 153, 46, 107, 70],\n [-39, 142, -216, 120, 75, 77, -23],\n [-7, -294, 327, -265, 115, 11, 31],\n [4, -24, 14, -18, 82, 116, 70],\n [-33, -190, 306, -270, 31, 19, 69],\n [-98, 18, 132, -152, 46, 118, 58]]\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[[-99, -29, 206, -91, -124, 210, 130],\n [90, -44, 85, -34, -144, 192, -199],\n [-45, 17, -16, 7, 55, -63, 108],\n [71, 111, -39, 71, 110, -80, 22],\n [-71, -157, -152, -31, -26, -124, -76],\n [51, 19, 181, -37, -74, 216, 64],\n [123, -47, -178, 59, 95, -147, -77]]\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[[43, -129, 51, 220, -179, -11, -8],\n [-158, 61, -38, 20, -33, 33, -49],\n [215, -30, -84, 149, -16, -151, 17],\n [79, 208, -149, 160, 91, -267, -183],\n [169, -12, -66, 128, -27, -141, -18],\n [156, 82, -241, 57, 13, -192, -2],\n [-186, -45, 123, 24, 6, 180, 48]]\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 7x7 matrix:\n[[168, 119, 236, -189, 108, -95, 265],\n [-83, 222, 147, -230, 186, -137, -66],\n [150, 102, 126, -120, 99, -114, 143],\n [69, 98, 221, -186, 116, -115, 83],\n [-63, 20, -82, -180, -58, 172, 191],\n [71, 110, 266, -94, 150, -118, 27],\n [28, 107, 189, 45, 161, -112, -128]]\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 7x7 matrix:\n[[44, 214, -78, 79, -61, 7, 12],\n [-172, -206, 240, -128, 2, -134, -84],\n [26, 25, 112, 4, -115, 9, 102],\n [148, 39, -100, 62, -23, 131, 136],\n [48, 154, -40, 60, -66, 18, 40],\n [102, 89, -102, 63, -18, 82, 74],\n [-124, -52, 200, -68, -64, -116, -44]]\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, 104, -24, 88, 144, 12, -140],\n [36, 109, 46, 48, 24, 27, -65],\n [93, 63, 68, 2, -60, 24, 10],\n [0, -86, -20, -48, -48, -18, 70],\n [78, 57, 58, 4, -48, 21, 5],\n [-12, 64, 8, 40, 48, 12, -60],\n [117, 64, 82, -6, -84, 27, 25]]\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[[-66, 54, 24, 30, -42, 36, -54],\n [-55, 45, 20, 25, -35, 30, -45],\n [132, -108, -48, -60, 84, -72, 108],\n [-11, 9, 4, 5, -7, 6, -9],\n [-66, 54, 24, 30, -42, 36, -54],\n [-22, 18, 8, 10, -14, 12, -18],\n [-55, 45, 20, 25, -35, 30, -45]]\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[[-140, 230, -108, -139, 61, 56, 135],\n [-123, 117, -77, -16, 89, 175, -71],\n [7, -46, -14, -68, -69, -45, 103],\n [-172, 309, -113, -92, 140, 118, 48],\n [124, -176, 94, 107, -53, -76, -87],\n [-110, 301, -57, -24, 158, 52, 2],\n [51, 191, 81, 148, 163, -79, -133]]\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[[-96, 15, 54, -67, -11, 6, 74],\n [16, 55, -74, 37, -99, -106, 26],\n [6, 81, -96, 41, -143, -150, 50],\n [63, -12, -33, 43, 11, 0, -50],\n [39, -60, 39, 3, 99, 96, -66],\n [-116, -2, 88, -90, 22, 44, 76],\n [-24, 90, -84, 22, -154, -156, 76]]\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[[38, 132, 60, -146, 73, 78, -147],\n [142, -97, 104, -11, -29, 11, -52],\n [-8, 83, -184, 93, 103, 113, 126],\n [-122, 188, 2, -10, -56, 41, -53],\n [-106, -90, -54, 8, 4, -129, 77],\n [-81, 49, -8, -41, 4, -32, -20],\n [152, -21, 42, -77, 91, 72, -69]]\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[[-219, 172, -226, -23, -63, -20, -141],\n [27, -79, -96, 35, -159, -136, -92],\n [-171, 190, -151, -80, 30, 73, -6],\n [-37, 73, 16, -14, 3, -5, -11],\n [-33, -85, 52, 169, -59, -126, -236],\n [-226, 258, -190, -54, -108, -72, -140],\n [55, 26, 49, -104, 136, 159, 214]]\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, 161, -9, -34, 92, 15, -68],\n [-52, -36, 44, -88, 24, -4, 32],\n [75, 95, -15, 2, 44, 9, -44],\n [44, 92, 32, -104, 92, 8, -24],\n [-106, -98, 62, -108, 4, -10, 64],\n [71, 83, -22, 22, 29, 8, -42],\n [-78, -54, 66, -132, 36, -6, 48]]\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[[51, 38, 92, -118, -72, 53, 42],\n [134, -30, 52, -12, 24, 68, -48],\n [8, 5, 98, -32, -20, 91, 18],\n [65, 40, 56, -122, -72, 15, 36],\n [70, -80, -16, 132, 112, 50, -96],\n [110, -41, -26, 36, 52, 3, -66],\n [-19, -57, 78, 110, 76, 128, -42]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[354, -78, -89, 203, -142, 302, -13],\n [72, 14, 51, 2, -22, 174, 103],\n [-143, -94, 47, -167, 196, -394, -163],\n [223, -127, -229, 12, -199, 114, 108],\n [10, -62, 72, 137, -69, 126, -11],\n [-128, 226, 127, 27, 141, -24, -105],\n [-93, -180, -59, -156, 11, -240, 49]]\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, 125, 75, -111, -234, 238, 212],\n [-141, -230, 83, 137, 43, -154, 68],\n [-16, -202, 109, 86, -37, -61, 148],\n [-70, -90, -5, -42, 124, -273, -3],\n [27, -30, -119, 213, 0, 15, -172],\n [155, -125, 214, -108, -72, 41, 222],\n [88, 31, 12, -244, -21, -148, 225]]\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[[112, 280, -47, -23, 112, 14, 47],\n [19, -111, 95, 70, -72, 6, -20],\n [-61, -31, -195, -9, 99, -54, 54],\n [3, -129, -28, 65, -104, 8, -49],\n [-198, -294, 9, 124, 13, -2, -87],\n [5, -106, -7, 132, 31, -20, 12],\n [-136, -232, 68, 18, -26, -20, -24]]\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[[-44, -22, -7, 155, 0, 33, -71],\n [103, 99, 1, 173, -66, -12, 2],\n [-71, -119, -27, -127, 18, 64, -10],\n [-65, 9, 22, -73, 75, -46, 9],\n [-50, 16, 81, -151, 62, -145, 9],\n [-17, -153, 67, -13, 128, -75, -69],\n [-80, -90, -23, 224, -85, 92, -141]]\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[[28, 20, -68, -28, 88, 96, 176],\n [70, -54, 38, -70, -204, 32, 40],\n [-3, -17, 37, 3, -70, -40, -76],\n [61, -53, 45, -61, -202, 16, 12],\n [-64, 36, -8, 64, 132, -56, -88],\n [-6, 31, -56, 6, 125, 50, 98],\n [-15, 19, -23, 15, 74, 8, 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[[-153, 81, 137, -10, -191, -80, -114],\n [103, 86, 83, 81, 100, 126, 28],\n [-13, 43, -45, 118, 18, 33, 12],\n [-93, 13, -111, 78, 23, -29, -49],\n [51, 114, 231, -3, -36, 75, -27],\n [98, -24, 92, -144, 95, 39, -8],\n [77, -36, -41, 11, 45, 34, 73]]\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 7x7 matrix:\n[[-25, -183, -49, -193, 38, 238, -142],\n [100, -88, -116, -36, 24, 108, -300],\n [-284, -344, 23, 70, -164, 160, -19],\n [-88, -52, -119, 220, -50, -6, -89],\n [-163, -247, -20, -48, -81, 177, -52],\n [60, -59, -73, 94, -38, 1, -218],\n [159, 110, 44, -38, -14, -112, -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[[-38, 176, 120, 134, 16, 86, 36],\n [79, 77, 27, 14, 58, -58, -99],\n [-132, -66, -6, 18, -84, 114, 162],\n [25, -55, -41, -48, 2, -40, -27],\n [144, -33, -59, -89, 70, -153, -171],\n [-15, 165, 107, 116, 26, 60, 9],\n [-71, -88, -36, -25, -56, 47, 90]]\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, 0, -35, 35, -56, -14, 84],\n [60, 0, -30, 30, -48, -12, 72],\n [30, 0, -15, 15, -24, -6, 36],\n [-60, 0, 30, -30, 48, 12, -72],\n [-60, 0, 30, -30, 48, 12, -72],\n [-90, 0, 45, -45, 72, 18, -108],\n [10, 0, -5, 5, -8, -2, 12]]\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, -10, 110, -100, 80, 80, 70],\n [-5, -5, 55, -50, 40, 40, 35],\n [-9, -9, 99, -90, 72, 72, 63],\n [3, 3, -33, 30, -24, -24, -21],\n [10, 10, -110, 100, -80, -80, -70],\n [-3, -3, 33, -30, 24, 24, 21],\n [-1, -1, 11, -10, 8, 8, 7]]\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[[-21, -88, 140, 111, 19, 136, -2],\n [-104, 42, -291, -153, -58, -82, 35],\n [52, 32, 179, 48, -42, -66, -15],\n [52, -254, 124, 27, 268, 28, -104],\n [142, 204, 6, -6, -46, -74, 14],\n [77, -96, 171, 111, 127, 116, -41],\n [4, -68, -80, -60, 100, -34, -32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[77, 55, 11, -121, -44, -88, 77],\n [-7, -5, -1, 11, 4, 8, -7],\n [77, 55, 11, -121, -44, -88, 77],\n [14, 10, 2, -22, -8, -16, 14],\n [14, 10, 2, -22, -8, -16, 14],\n [-49, -35, -7, 77, 28, 56, -49],\n [-7, -5, -1, 11, 4, 8, -7]]\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[[155, -18, -263, -62, 111, 92, 73],\n [82, 248, 2, -142, -44, -28, -140],\n [23, 162, -40, -85, -122, -60, 12],\n [42, 54, 20, -263, -38, -43, 35],\n [256, 65, -147, -177, -18, 186, -65],\n [-40, -227, 43, 131, 69, 79, 43],\n [155, -7, -32, -128, -16, 138, -53]]\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[[-11, -19, 25, -9, -19, 0, -34],\n [-33, -53, 67, -27, -53, 2, -93],\n [44, 60, -68, 36, 60, -8, 100],\n [-55, 9, -83, -45, 9, 52, 64],\n [44, 56, -60, 36, 56, -10, 91],\n [44, 76, -100, 36, 76, 0, 136],\n [-33, -69, 99, -27, -69, -6, -129]]?\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[[59, 82, 9, 65, -44, 56, 54],\n [2, -128, -108, 76, -24, -8, -182],\n [20, 136, 64, 121, -151, -18, 20],\n [66, -160, -104, 182, -68, -10, -250],\n [-82, 66, 81, -123, 29, -53, 107],\n [52, -196, -298, 78, 50, 142, -222],\n [45, -22, 75, -12, 48, -17, 42]]?\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[[-36, 120, -153, -62, 137, 13, -27],\n [42, 12, 36, 28, -49, 7, -54],\n [-18, -12, -9, -10, 16, -4, 27],\n [64, 0, 72, 48, -88, 8, -72],\n [4, 120, -108, -32, 82, 18, -72],\n [44, 120, -63, -2, 27, 23, -117],\n [68, 24, 54, 44, -76, 12, -90]]\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[[-27, -12, 82, 14, -27, -33, 70],\n [-63, 78, -3, -38, -10, -24, -31],\n [-18, 84, -114, -52, 28, 24, -122],\n [45, -78, 43, 42, -4, 6, 63],\n [27, 18, -93, -18, 30, 36, -81],\n [-45, 126, -131, -74, 28, 18, -151],\n [-36, 48, -8, -24, -4, -12, -24]]\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 7x7 matrix:\n[[38, -98, -195, 346, 317, -134, 180],\n [188, -213, -45, -6, -67, -99, 108],\n [-103, -73, -80, -16, 209, 4, -21],\n [-44, 121, 63, -246, 11, 108, 34],\n [70, -60, 103, -92, -176, -59, -150],\n [190, -323, -116, 210, -11, -191, 60],\n [81, -280, -188, 274, 126, -124, 99]]\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[[128, -220, -64, 104, -54, -56, 168],\n [92, -244, 22, -54, -170, -146, 22],\n [241, -324, 36, 70, -87, -173, 125],\n [61, -200, -60, 34, -83, -69, 133],\n [89, -24, -180, -60, -211, 80, 132],\n [282, -140, 61, -5, -58, -113, 63],\n [135, 121, 61, -244, -136, -36, -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 7x7 matrix:\n[[-114, 25, 149, 6, 176, -14, -1],\n [-47, -90, -35, -221, 5, -71, -42],\n [111, -33, 37, 270, 123, 79, 121],\n [17, -214, 109, 174, 97, 129, -48],\n [-110, -98, 86, -166, 7, 30, -187],\n [-131, -207, 32, 74, -113, 241, -283],\n [-72, -158, 195, -54, 290, -20, -6]]\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 7x7 matrix:\n[[42, 5, 86, -226, 92, -26, -138],\n [15, -120, -143, 195, -17, 126, -24],\n [93, 109, -1, -155, -59, -2, -66],\n [-178, -94, 96, 118, 109, 17, -4],\n [45, -32, 23, -113, 63, -27, -54],\n [-185, -163, 57, 171, 137, 102, -86],\n [2, -61, -50, 52, 16, 103, -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[[219, -63, 72, -6, -9, -168, -42],\n [24, -191, -25, 67, 70, -64, -80],\n [-217, -28, -34, 16, 60, 136, -27],\n [-148, -67, 121, -57, 99, 64, -135],\n [-10, -88, 249, 45, 161, -96, -149],\n [215, 27, -40, -46, -103, -104, 48],\n [48, 75, -290, -40, -184, 80, 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[[-62, -96, -48, -16, -56, 86, 0],\n [71, 132, 85, 3, 96, -66, -19],\n [-33, -36, -5, -19, -8, 68, -13],\n [5, 60, 75, -35, 80, 70, -45],\n [46, 48, 4, 28, 8, -98, 20],\n [7, 84, 105, -49, 112, 98, -63],\n [-23, -96, -100, 36, -108, -57, 52]]\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[[50, -107, 268, 166, -131, -41, 12],\n [-71, -16, 94, 100, -60, -122, -90],\n [131, -111, -23, -107, 0, -43, -52],\n [-148, 24, 214, 182, -124, -32, 26],\n [-245, 30, 64, -58, -122, -66, -10],\n [-228, 96, -101, -177, -27, 50, 78],\n [-8, 32, -115, 97, 101, -190, -160]]?\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[[-60, -132, 108, 0, 96, 36, -132],\n [-50, -110, 90, 0, 80, 30, -110],\n [-25, -55, 45, 0, 40, 15, -55],\n [15, 33, -27, 0, -24, -9, 33],\n [-40, -88, 72, 0, 64, 24, -88],\n [45, 99, -81, 0, -72, -27, 99],\n [5, 11, -9, 0, -8, -3, 11]]\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[[8, -24, 10, -2, -24, -10, -18],\n [12, -36, 15, -3, -36, -15, -27],\n [-8, 24, -10, 2, 24, 10, 18],\n [-16, 48, -20, 4, 48, 20, 36],\n [20, -60, 25, -5, -60, -25, -45],\n [-20, 60, -25, 5, 60, 25, 45],\n [-40, 120, -50, 10, 120, 50, 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[[-82, 153, -28, -24, 52, 10, -35],\n [-202, 133, -4, 51, 154, 166, 100],\n [-7, 54, -108, -42, -137, -60, 46],\n [-46, 106, -101, 120, 74, 101, -102],\n [-293, 79, -163, 19, -178, 83, 150],\n [-185, 15, -71, 87, 138, 113, -56],\n [28, 137, -18, -85, -30, -109, -115]]\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[[49, -196, 168, -132, -36, -64, -19],\n [-147, 188, 111, 213, -129, 181, 44],\n [128, -160, 55, 233, -225, 60, 239],\n [-61, 67, -150, 7, 252, 154, -34],\n [-54, 134, -92, 39, -40, -6, 97],\n [-178, 176, 105, -159, 81, 12, -139],\n [135, -91, 93, 42, -141, -77, 25]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-109, 153, 308, -37, 3, 48, 55],\n [135, 0, -312, -72, -170, -24, 74],\n [-31, 47, -15, -88, -149, -84, 79],\n [90, -40, -83, 36, -2, -35, 6],\n [-113, 84, -98, -197, -248, 23, 52],\n [138, 94, -16, -9, -72, 91, 56],\n [69, 165, 165, -21, -76, -42, 160]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[149, 17, 6, 6, 92, -65, 61],\n [22, -147, 137, -220, -330, 15, -200],\n [57, 112, 7, 44, 52, 42, -25],\n [-9, 144, 66, -66, -72, 114, -99],\n [3, -117, -3, -16, -48, -55, -1],\n [-95, -27, -25, -58, 42, -27, 121],\n [-3, 72, 91, -143, -129, 79, -91]]?\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[[190, 66, -109, 261, -3, 132, -115],\n [-53, -45, -67, -155, -34, 6, -245],\n [91, -131, -7, 222, 45, 162, 128],\n [-129, 47, 193, -129, -138, -16, 43],\n [57, -59, -146, -22, -17, 192, -216],\n [-59, -179, -27, -92, -19, 115, -128],\n [-53, -127, 12, -86, -31, 171, 18]]?\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[[116, -81, 166, 21, 160, -46, 40],\n [-53, -122, -36, -155, -111, 145, 18],\n [41, 138, -84, 123, -44, 38, -52],\n [-115, 116, -222, -43, -243, 89, -78],\n [175, -127, 113, -51, 59, 125, -17],\n [-49, -90, 96, -92, 37, -73, 77],\n [97, 15, 72, 199, 247, -81, -9]]\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[[122, -20, -127, 51, -25, -51, 12],\n [164, 69, -181, 56, -107, -134, -127],\n [215, 57, -338, 244, -159, 60, -126],\n [-16, 111, 88, -137, -17, -34, -151],\n [-315, -76, 402, -196, 189, 89, 237],\n [-239, -137, 349, -250, 192, -113, 104],\n [-127, 19, 114, 13, 16, 27, 178]]\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[[286, 310, -279, 83, -38, -94, 16],\n [265, 223, -108, 44, -11, -41, -13],\n [-169, -198, 17, 89, -146, 41, 99],\n [287, 230, -44, 171, 87, -46, 45],\n [-21, 126, 226, -22, 430, -30, -143],\n [-202, -91, -69, -137, -46, -9, -57],\n [14, 97, -24, 170, 139, -50, 42]]\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 7x7 matrix:\n[[-9, -296, 21, -22, 76, -246, -34],\n [-128, 78, -52, -145, 223, 73, 157],\n [11, 48, -43, 29, -101, -27, -116],\n [199, -98, -102, 325, -265, -120, -41],\n [-155, -8, 91, -232, 274, 46, 114],\n [-68, -106, -32, -31, 1, -156, -132],\n [-198, 28, 3, -240, 156, -71, -122]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[39, 37, -97, -1, 19, 204, 88],\n [44, 99, -143, -11, -11, 286, 121],\n [-34, 4, 60, -12, -36, -84, -42],\n [25, 9, -58, -7, 22, 195, 79],\n [30, -90, -9, 12, 83, 109, 47],\n [-11, -93, 68, -1, 44, -1, -7],\n [16, 92, -75, 6, -39, -15, 3]]\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[[-14, 63, -28, -28, 77, -56, 28],\n [24, -108, 48, 48, -132, 96, -48],\n [12, -54, 24, 24, -66, 48, -24],\n [-16, 72, -32, -32, 88, -64, 32],\n [-16, 72, -32, -32, 88, -64, 32],\n [-8, 36, -16, -16, 44, -32, 16],\n [6, -27, 12, 12, -33, 24, -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[[79, 103, -73, -67, -40, -107, -17],\n [-50, 26, -166, -178, -202, -46, 62],\n [54, -4, 60, 61, 61, -50, -28],\n [-100, 6, -38, -73, -31, 72, -20],\n [-137, -31, 29, -70, 5, 17, -97],\n [-67, -55, 7, 12, -9, 95, 34],\n [-125, 13, -31, -70, -7, 117, -33]]\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[[-35, 71, 54, 80, -61, 34, 60],\n [120, -99, -41, -16, 122, -90, -56],\n [-41, 161, -66, 32, -23, 142, 28],\n [51, 123, -11, 14, -40, 138, 31],\n [159, -49, 222, 160, -61, -86, 98],\n [-134, 150, -189, -110, 3, 180, -47],\n [13, -34, -181, -120, 137, 4, -108]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[188, -38, 71, 179, 125, -350, -138],\n [61, 103, 66, -3, 51, 19, 33],\n [-207, 136, -32, 215, 12, 22, 266],\n [208, -129, -28, -152, 149, -122, -68],\n [66, -9, -150, 171, -136, 7, 312],\n [-61, -38, -10, 100, 23, -126, -57],\n [76, -1, -5, 55, 40, -52, 102]]\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[[53, 43, -32, -231, -63, 91, -13],\n [4, 120, -4, -36, -160, -12, 180],\n [16, 231, 131, 19, 44, -64, -31],\n [-119, -106, -175, -29, -64, -111, 47],\n [-9, -15, -17, -89, 101, -5, -158],\n [-49, -126, -144, -74, -40, 6, 0],\n [-204, 22, -255, -176, -32, -226, -63]]\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[[-44, 200, 4, -47, 39, 43, -4],\n [-14, 36, 37, 68, 126, 53, -20],\n [-69, 14, -53, -4, 7, 42, -67],\n [-6, -9, 90, 101, 103, -50, -94],\n [-107, 247, 14, -40, 86, 20, -66],\n [-87, 58, -113, -24, -52, 114, -124],\n [-28, 43, -71, -22, -46, 88, -48]]\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[[-333, 254, 182, 222, -67, 218, -134],\n [-134, 3, -131, 25, -36, -161, 4],\n [41, -78, -15, -12, 268, -21, -142],\n [38, -112, -150, 88, 200, -106, -12],\n [135, -67, -84, -45, 225, -25, -72],\n [277, 124, -164, -28, 34, -49, -52],\n [141, -66, 74, -4, 176, 31, -108]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 7x7 matrix:\n[[48, 98, -227, -83, 227, 133, 122],\n [85, -65, 126, -116, -223, 38, 159],\n [18, 73, -33, -158, 103, 139, 162],\n [-48, 11, -138, -119, 148, 134, 109],\n [-13, 136, -201, 45, 57, -176, -189],\n [216, -132, -14, 135, -35, 41, 199],\n [-114, 18, 80, -74, 192, 142, 73]]\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[[-96, 15, 12, 146, -60, -216, -33],\n [21, -168, -163, -21, -42, 67, -81],\n [-12, -109, 40, 82, 113, -18, -134],\n [-174, 6, 6, 90, -125, -150, 75],\n [-16, -44, -123, -93, -106, 84, 69],\n [7, -34, 14, -38, 192, -20, -165],\n [58, 48, 40, 76, 8, -71, -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[[-1, 3, -72, -55, 86, -96, 75],\n [-36, 15, -112, -58, 89, -139, 96],\n [69, -27, 168, 75, -114, 204, -135],\n [-73, 27, -136, -47, 70, -160, 99],\n [-28, 6, 64, 72, -114, 94, -84],\n [12, 0, -96, -84, 132, -132, 108],\n [45, -12, -40, -67, 107, -67, 69]]\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 7x7 matrix:\n[[-35, 30, -72, 17, -39, -53, -32],\n [-11, 6, -21, 8, -9, -20, -14],\n [56, -96, 138, 10, 108, 38, -4],\n [26, -116, 98, 60, 118, -52, -84],\n [26, -76, 79, 29, 80, -13, -38],\n [29, 6, 45, -38, 3, 74, 62],\n [19, 106, -19, -104, -95, 148, 158]]\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[[131, -53, -37, 56, 64, -179, -108],\n [-25, 111, 48, 74, 55, 165, 216],\n [-203, 15, -63, -21, -130, 64, 152],\n [-10, 25, -109, -79, -68, -25, 153],\n [34, -151, -23, -15, 42, 78, -147],\n [90, -103, 79, 61, 100, -22, -259],\n [-73, -5, -112, -190, -177, -114, 20]]\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[[81, 16, 36, -2, 49, 19, -11],\n [-64, -261, -95, 15, 29, -164, -22],\n [-357, 22, 42, -8, -19, -15, -47],\n [-198, -141, -20, 19, 16, -135, -38],\n [52, 144, -15, -20, -91, 125, 50],\n [-117, 102, 159, 12, 124, -4, -74],\n [-175, -62, 12, -18, 122, -13, -69]]\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[[43, 9, 62, -194, -66, 131, -76],\n [-67, -135, 177, -73, 208, 5, 16],\n [-104, -140, -28, 44, 24, -141, 44],\n [73, 117, -64, 4, -120, 65, -34],\n [65, 76, -78, -66, -71, 39, -17],\n [-55, -112, 96, -56, 169, -32, 31],\n [22, 34, 112, 56, 196, 40, 32]]\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[[0, 0, 0, 0, 0, 0, 0],\n [33, -18, 36, -36, 18, -12, 30],\n [99, -54, 108, -108, 54, -36, 90],\n [44, -24, 48, -48, 24, -16, 40],\n [-99, 54, -108, 108, -54, 36, -90],\n [-121, 66, -132, 132, -66, 44, -110],\n [-110, 60, -120, 120, -60, 40, -100]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-107, 34, 26, -3, 97, 36, -164],\n [14, -172, -68, 174, -46, 72, 80],\n [-90, -88, 19, 45, 59, 56, 4],\n [-28, -6, -29, 67, 22, 36, -110],\n [-92, 62, 41, -47, 90, 12, -138],\n [36, -178, -91, 205, -66, 76, 70],\n [-147, -176, 22, 101, 90, 104, 26]]\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, 5, 8, -8, -1, 9, -10],\n [-36, -30, -48, 48, 6, -54, 60],\n [-36, -30, -48, 48, 6, -54, 60],\n [0, 0, 0, 0, 0, 0, 0],\n [36, 30, 48, -48, -6, 54, -60],\n [-12, -10, -16, 16, 2, -18, 20],\n [-60, -50, -80, 80, 10, -90, 100]]\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[[-66, 8, 110, 3, -164, -21, 109],\n [38, -76, 3, -39, -12, 5, -49],\n [107, -146, -24, -76, -70, 31, 72],\n [-42, 35, -75, 20, 224, -16, -182],\n [-125, -90, -175, -122, 26, 157, -34],\n [-189, 19, -56, -47, -55, 91, 52],\n [-52, -368, -218, -303, -123, 260, -56]]\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, 10, 45, -45, -30, 15, 55],\n [-24, -16, -72, 72, 48, -24, -88],\n [36, 24, 108, -108, -72, 36, 132],\n [9, 6, 27, -27, -18, 9, 33],\n [18, 12, 54, -54, -36, 18, 66],\n [3, 2, 9, -9, -6, 3, 11],\n [36, 24, 108, -108, -72, 36, 132]]?\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 7x7 matrix:\n[[90, -27, -27, -99, -36, 36, -18],\n [80, -24, -24, -88, -32, 32, -16],\n [90, -27, -27, -99, -36, 36, -18],\n [80, -24, -24, -88, -32, 32, -16],\n [-50, 15, 15, 55, 20, -20, 10],\n [40, -12, -12, -44, -16, 16, -8],\n [30, -9, -9, -33, -12, 12, -6]]\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[[-81, 0, -27, -75, -96, -15, 123],\n [124, 80, -132, 20, -96, 140, -92],\n [-123, -48, 63, -57, 0, -93, 129],\n [74, 46, -75, 14, -52, 81, -57],\n [104, 88, -156, -8, -144, 148, -52],\n [-61, -62, 114, 17, 116, -102, 18],\n [108, 0, 36, 100, 128, 20, -164]]\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[[-53, 127, -198, 67, -197, -131, -146],\n [-45, -37, 87, 10, 153, 83, 173],\n [-103, 115, -75, 35, -68, 16, 142],\n [-328, 128, -10, 10, 82, -176, -250],\n [50, 14, 46, -20, -31, 51, 307],\n [-29, -9, 156, 96, 62, -151, -128],\n [-223, 77, -82, -204, 46, -43, 60]]?\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[[-50, -13, 81, 96, -18, 143, 130],\n [30, 17, 104, -64, -44, 100, 24],\n [-165, -177, 1, 257, -4, 44, 91],\n [94, 71, -50, -129, 130, -170, 45],\n [-17, 82, -59, 201, -16, 118, -63],\n [-39, -208, 38, -193, 46, -233, 86],\n [60, -11, -59, -205, -32, -163, -176]]\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 7x7 matrix:\n[[48, -173, -44, -7, -14, -80, -138],\n [135, 44, -85, 116, 15, 72, -24],\n [-90, -38, 55, -86, -18, -57, 6],\n [105, 66, -60, 122, 41, 89, 18],\n [96, 9, -63, 71, 2, 35, -36],\n [45, 24, -15, 120, 93, 80, 48],\n [-141, -78, 78, -182, -77, -127, -30]]\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[[104, 52, -27, 111, 16, 186, 201],\n [-156, -114, 246, -101, 16, 50, -61],\n [-20, 100, -100, 68, -37, -97, -35],\n [-132, 123, 207, -9, -126, -30, 33],\n [-90, 58, 57, 18, -14, 80, 48],\n [2, -61, -91, -29, 63, -3, -62],\n [201, -16, 14, -73, -84, -157, 4]]?\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 7x7 matrix:\n[[24, 17, 15, -8, -34, -23, 4],\n [3, -32, -69, 62, 43, -16, -31],\n [-48, -73, -111, 88, 122, 31, -44],\n [-57, -42, -39, 22, 83, 54, -11],\n [-72, -51, -45, 24, 102, 69, -12],\n [66, 11, -33, 44, -44, -77, -22],\n [-63, -17, 18, -30, 51, 71, 15]]\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[[-94, 34, -47, -102, -180, -199, -63],\n [-75, -199, -59, -134, 33, 247, 196],\n [123, 53, 183, 232, 70, 164, -159],\n [58, 203, 114, 96, 232, 13, 79],\n [-144, -71, -83, -230, -98, -228, 7],\n [-76, 64, 3, -48, -186, -200, -118],\n [-107, -23, 186, -50, 104, 267, 125]]\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[[21, 66, 30, -66, -23, -100, -31],\n [236, 90, -41, -101, -104, -82, -84],\n [-9, 148, -36, -165, -20, -72, -56],\n [-150, 150, -185, -63, 32, 39, -210],\n [-143, 54, -89, 50, 36, 139, -92],\n [44, -98, 130, -104, 54, -45, 250],\n [-125, 86, -145, 116, -94, 116, -166]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[21, -113, -102, 34, -91, -112, 128],\n [153, 40, -21, 40, 117, 29, -106],\n [27, 192, 147, -66, 109, 81, -42],\n [-42, -20, -12, 66, -112, -200, 224],\n [60, -38, -54, 136, 80, 2, -184],\n [-6, 92, 84, -154, 32, 124, 10],\n [74, -134, -136, 60, -46, -80, 42]]\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 7x7 matrix:\n[[-42, -103, 146, 37, 19, 97, -89],\n [-40, -135, 66, 10, -8, 94, 78],\n [-119, -2, -21, 1, -2, -8, 105],\n [-143, 34, -2, 19, 106, -55, 99],\n [80, -168, 115, 4, -134, 171, -104],\n [-102, 38, -72, -11, 1, -47, 135],\n [134, 13, -32, -21, -63, 5, -71]]\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[[16, 114, 56, 54, 29, -88, -133],\n [-87, -26, 99, -54, 0, 58, -39],\n [-100, -129, -43, -15, -25, 154, 104],\n [-129, -41, 98, -20, 4, 80, -64],\n [16, -79, 31, -78, -11, -26, 22],\n [9, -8, -41, 122, 23, -102, -110],\n [95, 143, -24, 94, 29, -140, -99]]\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[[-105, 78, -18, 48, 0, 147, -45],\n [21, -45, 96, 3, 84, -42, -33],\n [42, 8, -116, -36, -112, -42, 74],\n [77, -74, 66, -28, 48, -115, 9],\n [0, 70, -220, -30, -200, 30, 100],\n [-126, 95, -26, 57, -4, 177, -52],\n [105, -71, -4, -51, -20, -144, 55]]\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, -30, -25, 0, -35, 25, -55],\n [-15, -18, -15, 0, -21, 15, -33],\n [35, 42, 35, 0, 49, -35, 77],\n [-60, -72, -60, 0, -84, 60, -132],\n [-55, -66, -55, 0, -77, 55, -121],\n [-5, -6, -5, 0, -7, 5, -11],\n [-55, -66, -55, 0, -77, 55, -121]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 7x7 matrix:\n[[5, 10, 15, 50, 0, 50, -10],\n [2, 4, 6, 20, 0, 20, -4],\n [12, 24, 36, 120, 0, 120, -24],\n [-9, -18, -27, -90, 0, -90, 18],\n [7, 14, 21, 70, 0, 70, -14],\n [-3, -6, -9, -30, 0, -30, 6],\n [-7, -14, -21, -70, 0, -70, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[80, 26, 165, -44, 40, 144, 52],\n [93, 79, -103, 26, 7, -60, -74],\n [-43, -109, -72, -44, 111, -224, -78],\n [91, -46, -91, -86, -27, -135, -48],\n [-40, -210, 104, -132, -52, -54, 116],\n [-10, 113, 95, 143, -80, 220, 120],\n [-148, -82, 44, 134, -231, 92, 242]]\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[[45, 62, 12, 25, 185, 29, -79],\n [158, 68, -175, -131, 137, 105, 117],\n [231, 237, -48, -45, 147, -60, -309],\n [39, -4, -51, 110, 142, 144, 74],\n [11, -8, -33, -74, 32, 30, 60],\n [-69, -37, 72, -139, -11, -12, -25],\n [108, 91, -54, -118, 121, 16, -62]]\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[[21, -24, -9, 12, 6, 30, 36],\n [56, -64, -24, 32, 16, 80, 96],\n [70, -80, -30, 40, 20, 100, 120],\n [77, -88, -33, 44, 22, 110, 132],\n [-28, 32, 12, -16, -8, -40, -48],\n [-70, 80, 30, -40, -20, -100, -120],\n [42, -48, -18, 24, 12, 60, 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[[-37, 190, -101, -79, 162, 23, 32],\n [-48, 94, -155, -5, -23, 69, 63],\n [70, 74, 4, -128, -62, 128, -10],\n [201, -151, 63, 221, -64, -187, -158],\n [-92, 214, -79, -159, 66, 178, 90],\n [-224, 55, -8, 22, -96, 196, 180],\n [-42, 43, -127, -25, -116, 142, 20]]\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[[0, 36, -48, -12, -12, -84, 72],\n [0, 27, -32, -20, 16, -11, 45],\n [0, 21, -20, -29, 43, 55, 24],\n [0, -8, 4, 21, -39, -68, -1],\n [0, -1, 4, -7, 17, 37, -8],\n [0, 14, -16, -12, 12, 2, 22],\n [0, 22, -16, -44, 76, 122, 14]]\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[[36, 54, -72, 30, 0, 0, -24],\n [-72, -108, 144, -60, 0, 0, 48],\n [60, 90, -120, 50, 0, 0, -40],\n [-18, -27, 36, -15, 0, 0, 12],\n [-30, -45, 60, -25, 0, 0, 20],\n [-18, -27, 36, -15, 0, 0, 12],\n [-60, -90, 120, -50, 0, 0, 40]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 7x7 matrix:\n[[36, -36, -24, -20, 48, 0, -28],\n [-72, 72, 48, 40, -96, 0, 56],\n [-63, 63, 42, 35, -84, 0, 49],\n [54, -54, -36, -30, 72, 0, -42],\n [0, 0, 0, 0, 0, 0, 0],\n [108, -108, -72, -60, 144, 0, -84],\n [9, -9, -6, -5, 12, 0, -7]]\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[[-40, -39, 70, 202, -23, 158, 84],\n [56, 24, -62, -200, 16, -160, -78],\n [-120, 70, -10, 100, 30, 100, 10],\n [64, 25, -68, -222, 17, -178, -86],\n [72, -93, 66, 78, -45, 42, 60],\n [-104, 89, -42, 10, 41, 30, -28],\n [100, -30, -25, -160, -10, -140, -45]]\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, 33, -39, -42, -111, -78, 69],\n [130, 69, -51, 181, 200, -7, -112],\n [-329, -43, 83, -270, -143, 118, 217],\n [19, 114, -60, 183, 189, -91, -27],\n [12, 14, 16, -126, -145, -31, 111],\n [184, -59, -165, 61, -82, 67, -142],\n [-45, 11, 0, 50, 195, 157, -60]]?\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 7x7 matrix:\n[[-10, -83, -101, 51, 43, -41, 128],\n [-20, -52, -31, 7, 10, -6, 66],\n [-30, 3, 75, -57, -39, 45, -36],\n [-20, -58, -40, 12, 14, -10, 76],\n [-20, 2, 50, -38, -26, 30, -24],\n [-120, -84, 156, -148, -92, 116, 16],\n [80, 58, -101, 97, 60, -76, -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 7x7 matrix:\n[[-24, -84, -50, 64, -30, 36, 28],\n [-113, -85, -61, 102, -124, 66, 105],\n [-110, -34, -32, 68, -118, 48, 98],\n [122, 76, 57, -100, 133, -66, -112],\n [12, -120, -66, 72, 6, 36, 0],\n [35, -107, -56, 54, 31, 24, -21],\n [-141, 33, 2, 38, -147, 36, 119]]\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[[-53, -98, 269, 13, 125, -26, 86],\n [-135, 173, 127, -44, 50, 23, -12],\n [200, -223, -113, -37, 58, 43, 31],\n [98, -239, 71, 115, 162, -161, 199],\n [-17, -42, 183, -152, 61, 118, -91],\n [-86, 183, -99, 121, -50, -59, 77],\n [20, -126, 167, -69, 3, 180, -26]]?\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[[-120, 172, 101, -32, 166, 63, 143],\n [86, -134, -76, 22, -136, -56, -118],\n [96, 28, -25, 40, 130, 117, 125],\n [88, -28, -41, 32, 34, 53, 37],\n [105, -1, -38, 41, 92, 96, 91],\n [72, -140, -73, 16, -158, -75, -139],\n [17, -65, -28, 1, -88, -50, -79]]?\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[[96, -81, -241, 8, 84, -13, -147],\n [-136, 111, 131, -128, -134, 73, 127],\n [60, -5, -165, -80, 100, -105, -55],\n [6, 31, -10, 90, -86, 140, -25],\n [-74, -33, 69, -24, -75, 80, 20],\n [-164, 80, 158, -60, -222, 212, 102],\n [-98, -15, -102, -226, -50, 36, -7]]\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[[16, 4, 8, 18, -14, -20, 0],\n [-96, -24, -48, -108, 84, 120, 0],\n [-96, -24, -48, -108, 84, 120, 0],\n [96, 24, 48, 108, -84, -120, 0],\n [-24, -6, -12, -27, 21, 30, 0],\n [72, 18, 36, 81, -63, -90, 0],\n [-24, -6, -12, -27, 21, 30, 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[[-36, 11, -38, -125, -10, 68, -109],\n [30, 1, -50, 21, 64, -62, -25],\n [75, -96, -70, 53, 112, 43, -45],\n [-170, 41, -18, -145, -34, 4, -111],\n [140, -252, -86, 8, 51, -32, 164],\n [338, 124, -146, 132, 47, -68, 48],\n [-75, 125, 26, -46, -8, 201, -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[[77, -121, -11, 11, 99, -110, 77],\n [77, -9, -74, 57, -5, -10, 43],\n [63, -144, -57, -79, 73, 55, -90],\n [-60, 76, 78, 40, -20, -80, 80],\n [-31, 74, 82, 93, -1, -165, 170],\n [-17, -38, -16, -81, 1, 105, -122],\n [-126, 210, 63, 36, -138, 60, -12]]?\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[[-23, -65, -57, -10, -55, 7, 38],\n [-16, 22, 57, -80, 93, 1, -34],\n [45, -139, -138, -30, -136, 140, 58],\n [-41, -3, 29, -30, 58, -32, -5],\n [75, -69, -62, -180, -51, 176, -10],\n [70, 72, 67, 180, 85, 29, -40],\n [183, -83, -131, -200, -167, 306, -11]]?\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[[-119, 126, -13, -3, 100, 153, -130],\n [-67, -129, 129, -36, 20, 141, -316],\n [-51, 66, 9, 72, 240, -138, 47],\n [119, -220, 32, 117, -59, 93, -108],\n [-53, 19, 10, 54, 250, -96, -36],\n [-93, 108, -14, 52, 149, 74, -59],\n [35, -47, -48, -59, -87, 20, 9]]\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, -100, 25, 164, 108, 80, 22],\n [40, 68, -41, -70, 97, -123, -77],\n [-145, 155, -171, -140, 9, 18, 111],\n [-363, -189, 35, 163, -251, 59, 32],\n [-77, -23, -52, 9, -154, 256, 9],\n [-332, 4, 117, -150, -293, -13, -137],\n [281, 81, 4, -74, 163, -5, -19]]\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[[-36, -6, 30, 24, -27, -18, 6],\n [-36, -6, 30, 24, -27, -18, 6],\n [-12, -2, 10, 8, -9, -6, 2],\n [72, 12, -60, -48, 54, 36, -12],\n [-96, -16, 80, 64, -72, -48, 16],\n [24, 4, -20, -16, 18, 12, -4],\n [-132, -22, 110, 88, -99, -66, 22]]?\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[[148, -82, 69, -65, 77, -19, -3],\n [88, 232, 201, -12, 186, -119, -131],\n [14, -33, -152, 85, -190, 123, 137],\n [45, 147, 56, -31, 40, -50, -51],\n [65, -28, 151, -87, 69, -202, -102],\n [-82, 22, 42, -260, -78, -64, -93],\n [-112, 181, -40, -237, 168, -43, -149]]\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, 35, 77, 7, -77, -7, 63],\n [48, -30, -66, -6, 66, 6, -54],\n [-88, 55, 121, 11, -121, -11, 99],\n [-64, 40, 88, 8, -88, -8, 72],\n [24, -15, -33, -3, 33, 3, -27],\n [-8, 5, 11, 1, -11, -1, 9],\n [-8, 5, 11, 1, -11, -1, 9]]\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[[133, 118, -133, -75, 68, -7, 75],\n [-63, -45, 63, 90, -90, 0, -27],\n [-135, -126, 135, 45, -36, 9, -81],\n [-17, -22, 17, -25, 28, 3, -15],\n [-151, -144, 151, 35, -24, 11, -93],\n [180, 168, -180, -60, 48, -12, 108],\n [72, 81, -72, 45, -54, -9, 54]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-20, 70, -63, 97, -69, -44, -23],\n [25, -179, -1, -116, 102, -8, 64],\n [-84, -81, -124, 68, -22, -101, 30],\n [51, -140, 7, -190, -22, 137, -64],\n [161, -105, -91, -161, 109, -103, 189],\n [-290, 24, -16, 134, -174, 78, -182],\n [-14, 254, -29, 84, -10, -141, 150]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-126, 44, 52, 99, -66, -15, -3],\n [-14, 28, 52, 63, -42, -123, -87],\n [-21, -12, -30, -27, 18, 99, 72],\n [-14, 48, 92, 108, -72, -228, -162],\n [-14, 40, 76, 90, -60, -186, -132],\n [0, 4, 8, 9, -6, -21, -15],\n [49, -28, -42, -63, 42, 63, 42]]?\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[[-26, 12, -30, 53, 97, 44, 17],\n [-16, 0, -32, 56, 88, 48, 24],\n [-6, -12, -34, 59, 79, 52, 31],\n [18, -30, -19, 32, 16, 31, 28],\n [16, -30, -23, 39, 27, 37, 31],\n [-12, 18, 9, -15, -3, -15, -15],\n [-72, 60, -34, 62, 166, 46, -2]]\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[[-114, -27, -204, 83, -96, -49, -110],\n [-15, -29, 6, 43, 112, 24, 90],\n [-39, -1, -33, 32, -178, -40, -61],\n [-163, -31, -282, -31, -64, -122, -206],\n [127, 5, 267, -6, 158, 96, 235],\n [-97, -18, -195, 42, -54, -48, -120],\n [-106, -78, 6, 155, -84, -25, 139]]\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[[-60, -45, 5, 5, -50, 20, -50],\n [24, 18, -2, -2, 20, -8, 20],\n [-24, -18, 2, 2, -20, 8, -20],\n [-144, -108, 12, 12, -120, 48, -120],\n [-144, -108, 12, 12, -120, 48, -120],\n [-108, -81, 9, 9, -90, 36, -90],\n [-72, -54, 6, 6, -60, 24, -60]]?\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[[-45, 100, -15, -90, 54, 24, -42],\n [100, 85, 1, -186, 52, 22, -148],\n [-66, 182, 60, -9, -45, 114, -153],\n [82, -74, 50, -132, 106, 83, -47],\n [38, 123, -73, -150, 37, -66, -80],\n [-114, 75, 93, -72, 96, 120, 48],\n [-19, -12, 83, -138, 128, -28, 226]]\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 7x7 matrix:\n[[36, -20, -32, 24, 48, -40, 0],\n [81, -45, -72, 54, 108, -90, 0],\n [-81, 45, 72, -54, -108, 90, 0],\n [18, -10, -16, 12, 24, -20, 0],\n [99, -55, -88, 66, 132, -110, 0],\n [9, -5, -8, 6, 12, -10, 0],\n [9, -5, -8, 6, 12, -10, 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[[56, -35, 56, -84, 21, 84, 21],\n [56, -35, 56, -84, 21, 84, 21],\n [8, -5, 8, -12, 3, 12, 3],\n [40, -25, 40, -60, 15, 60, 15],\n [-88, 55, -88, 132, -33, -132, -33],\n [-72, 45, -72, 108, -27, -108, -27],\n [-48, 30, -48, 72, -18, -72, -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[[-50, 50, -69, 9, -65, -32, 92],\n [99, -42, 42, -3, 123, 93, -18],\n [-82, 6, 13, -5, -99, -92, -68],\n [62, -46, 59, -7, 79, 48, -68],\n [142, -36, 20, 2, 174, 146, 44],\n [-62, -4, 24, -6, -74, -74, -76],\n [80, 10, -39, 9, 95, 98, 112]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[40, -12, 55, 78, 19, -97, 138],\n [-92, 36, 75, 106, 37, -103, 118],\n [198, -58, 11, -36, -8, -19, 96],\n [-232, -22, 29, 62, -3, -6, -154],\n [-6, -52, -108, 110, -52, -19, -108],\n [-186, 30, 18, -54, 8, 72, -148],\n [-63, 63, -50, -151, -4, 150, -146]]?\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[[44, -172, -105, 78, 12, 81, 55],\n [47, -74, -88, 113, 69, 113, -12],\n [4, -33, -21, 27, -7, 34, 23],\n [62, 104, -42, 112, 106, 98, 50],\n [96, -270, -128, -51, 40, -105, 66],\n [-4, 93, -1, 102, 57, 119, -71],\n [40, -205, -83, -17, -15, -32, 57]]\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[[50, -54, -148, 106, 92, 119, 107],\n [-137, 76, -46, -239, 94, 71, -123],\n [-169, 173, -82, -278, 142, 111, -62],\n [-28, -83, 48, -67, -32, -26, -141],\n [-56, 7, -33, 1, 70, 222, 83],\n [124, -48, 68, 180, -112, -152, 64],\n [34, -29, -73, 107, 50, 124, 121]]\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[[16, 120, 112, 110, 40, 24, -86],\n [-72, 10, -9, 0, -15, 57, -163],\n [-88, -20, -40, -29, -28, 60, -167],\n [-48, -10, -21, -15, -15, 33, -92],\n [8, 110, 101, 100, 35, 27, -93],\n [96, 180, 186, 174, 78, -18, 24],\n [-56, -30, -41, -34, -23, 33, -89]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0, 0, 0, 0],\n [8, -5, 8, 12, -4, -12, -7],\n [-40, 25, -40, -60, 20, 60, 35],\n [-8, 5, -8, -12, 4, 12, 7],\n [80, -50, 80, 120, -40, -120, -70],\n [80, -50, 80, 120, -40, -120, -70],\n [72, -45, 72, 108, -36, -108, -63]]?\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[[12, -62, 36, 18, -20, 222, 148],\n [-68, 54, -4, -10, 52, 66, 48],\n [-39, 29, 8, -16, 20, 26, 19],\n [94, -100, 52, -14, -108, -46, -38],\n [130, -142, 0, 72, -72, 124, 78],\n [25, -53, 60, -30, -64, 40, 23],\n [57, -84, -14, 73, -6, 217, 145]]?\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[[-1, 211, 80, -266, -60, -97, -12],\n [4, -128, -26, 205, -60, 23, 89],\n [131, -81, -136, 126, -36, 3, 152],\n [-70, 96, 60, -189, 126, 19, -184],\n [-105, -7, 84, -7, 42, 28, -112],\n [-9, -13, 46, 89, -156, -52, 125],\n [-110, -20, 40, -65, 210, 95, -250]]?\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 7x7 matrix:\n[[-299, -92, -116, 175, -151, 296, -40],\n [77, 62, 167, -115, -62, 46, 160],\n [6, -84, -108, 52, 26, -9, -87],\n [-35, 138, -153, -22, 118, -89, 3],\n [97, 122, -18, -20, 109, -129, 16],\n [-340, -16, -41, 25, -197, 301, 80],\n [133, -10, 123, -92, -6, -66, 48]]\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[[141, -4, 8, 69, -35, -72, -8],\n [57, -67, -121, -46, -191, 44, -98],\n [273, 284, 68, 20, -89, 318, 80],\n [-130, 21, -2, 55, -93, -38, 35],\n [-45, 58, -71, -168, 185, -122, 162],\n [175, 36, -31, -215, 9, 206, -7],\n [12, 105, -15, 242, -192, -4, -9]]?\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[[-50, -5, -126, -48, 124, 108, -105],\n [-12, 10, -84, -44, 60, 36, -42],\n [106, 55, 54, -27, -143, -189, 156],\n [40, 10, 72, 21, -83, -81, 75],\n [-30, -5, -66, -23, 69, 63, -60],\n [-50, -15, -78, -19, 97, 99, -90],\n [-98, -45, -78, 8, 148, 180, -153]]\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[[3, 290, -55, 115, 21, 69, -135],\n [-52, -10, -65, -35, -69, -26, -85],\n [-91, 20, -50, 64, -90, 125, -86],\n [44, 170, 25, 97, 69, 66, -3],\n [-41, 30, -41, 15, -45, 29, -65],\n [43, 90, -35, -51, 33, -123, -51],\n [-80, 130, -103, 44, -87, 54, -171]]\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 7x7 matrix:\n[[-10, 4, -20, 4, 0, -8, -22],\n [-10, 4, -20, 4, 0, -8, -22],\n [35, -14, 70, -14, 0, 28, 77],\n [-10, 4, -20, 4, 0, -8, -22],\n [-25, 10, -50, 10, 0, -20, -55],\n [45, -18, 90, -18, 0, 36, 99],\n [-50, 20, -100, 20, 0, -40, -110]]\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 7x7 matrix:\n[[229, -222, -68, 31, 74, -143, 328],\n [-53, -64, 107, 254, -162, -64, -146],\n [-22, -233, 65, 223, -15, -240, 52],\n [93, 13, -193, -56, -81, 4, -46],\n [-309, -113, -120, 27, 263, -364, -250],\n [103, 80, -174, -53, -103, -27, 142],\n [102, -232, 329, 133, 163, 3, 272]]\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[[-30, -15, 9, -33, -33, -12, 0],\n [-40, -20, 12, -44, -44, -16, 0],\n [100, 50, -30, 110, 110, 40, 0],\n [-90, -45, 27, -99, -99, -36, 0],\n [-70, -35, 21, -77, -77, -28, 0],\n [30, 15, -9, 33, 33, 12, 0],\n [-110, -55, 33, -121, -121, -44, 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[[-66, -33, 44, 22, 55, 110, 99],\n [-30, -15, 20, 10, 25, 50, 45],\n [-54, -27, 36, 18, 45, 90, 81],\n [0, 0, 0, 0, 0, 0, 0],\n [-24, -12, 16, 8, 20, 40, 36],\n [48, 24, -32, -16, -40, -80, -72],\n [12, 6, -8, -4, -10, -20, -18]]\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[[-178, -43, 325, -145, -221, -142, -184],\n [37, 100, 148, -12, -207, 44, 33],\n [103, 170, -54, 132, -110, -51, -126],\n [160, 157, -163, 79, 33, 142, 222],\n [-89, -62, 58, -101, -34, -32, -32],\n [181, 228, -187, 46, -54, 171, 257],\n [31, 154, 144, -2, -121, 22, 103]]?\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 7x7 matrix:\n[[112, -29, 16, 7, 81, 17, 140],\n [-107, 30, 155, -94, 176, -174, 72],\n [-2, 24, -188, 183, -140, 270, -177],\n [20, 96, 50, -108, 95, -103, 265],\n [122, -90, -1, -33, -139, 15, 18],\n [-20, 49, -70, 75, -80, 162, -23],\n [53, -63, 132, -118, -30, -98, 116]]\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[[100, -60, -100, 50, -20, -60, -40],\n [-56, -72, 200, -172, -128, 0, -16],\n [78, 50, -210, 171, 112, -16, 4],\n [6, 102, -150, 147, 138, 30, 36],\n [-50, -58, 170, -145, -106, 2, -12],\n [50, -118, 70, -95, -126, -58, -52],\n [-98, 50, 110, -61, 8, 56, 36]]\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[[-162, 118, 8, -25, -33, -138, -96],\n [105, -15, -92, 74, -83, 89, -187],\n [184, -10, -43, -100, 76, 71, -86],\n [106, -78, -152, 166, 17, 126, 115],\n [-28, -9, -23, 66, 70, -1, 93],\n [-41, 113, -23, -75, 48, -90, -157],\n [-145, 10, 77, -24, 6, -90, 193]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[50, -96, 67, 77, 115, 115, 46],\n [-8, -4, -16, 0, 8, 8, -32],\n [26, -42, 37, 35, 49, 49, 34],\n [-2, -34, -13, 21, 47, 47, -50],\n [-32, 72, -40, -56, -88, -88, -16],\n [12, -49, 9, 35, 63, 63, -22],\n [-18, 35, -24, -28, -42, -42, -16]]\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[[199, -177, 94, -52, 78, -19, -72],\n [4, -116, -65, 53, -48, 124, 83],\n [-94, 134, 5, -179, 62, -200, -113],\n [107, 123, 49, -295, 124, -228, 11],\n [-131, -41, -87, 8, -37, 45, -34],\n [162, -77, 159, 17, 29, -123, -48],\n [-19, 30, -1, 37, 1, 32, -24]]\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[[-59, 76, 8, 68, 82, -27, -60],\n [31, -162, 165, 152, -101, -35, 117],\n [56, 174, -159, -144, 59, 107, -95],\n [-237, -14, -9, 117, 122, -44, -160],\n [-7, -44, 216, 220, -166, -148, 188],\n [-87, -136, 6, 102, 14, 123, -28],\n [-49, 200, -18, -10, 20, -124, 24]]\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[[-133, -9, 162, 133, 79, -85, -76],\n [-77, 42, 117, 112, 102, -23, 49],\n [-122, -8, 32, 88, -60, -46, -238],\n [14, 39, -40, 1, -19, 36, 11],\n [-129, 12, 28, 124, 118, 77, 3],\n [246, -17, -214, -243, -87, 100, 199],\n [142, 52, -25, -90, -32, -10, 155]]\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[[71, -106, 65, 120, 221, 105, -35],\n [90, -65, 66, 250, 222, 170, 136],\n [-182, 169, -67, -246, -248, -152, -105],\n [20, -55, 78, 74, 86, 51, -67],\n [137, -54, -98, 47, 28, 151, -20],\n [89, 35, -49, 134, -113, 169, 55],\n [-14, 93, 60, 182, -118, 178, -6]]\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 7x7 matrix:\n[[19, 17, 27, -30, 101, -64, -83],\n [81, -144, 217, 157, 77, 54, 89],\n [176, 2, 46, 55, 141, -159, 75],\n [-90, -27, 115, -64, 43, 212, -64],\n [79, -155, 176, 207, -4, 56, 114],\n [-190, 78, -25, -215, 63, 72, -248],\n [-99, 191, -235, -216, -33, -30, -196]]\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 7x7 matrix:\n[[-21, 77, -42, -35, -70, 14, 21],\n [0, 0, 0, 0, 0, 0, 0],\n [12, -44, 24, 20, 40, -8, -12],\n [-24, 88, -48, -40, -80, 16, 24],\n [-3, 11, -6, -5, -10, 2, 3],\n [-15, 55, -30, -25, -50, 10, 15],\n [-6, 22, -12, -10, -20, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[72, -90, -72, -27, 0, 0, -36],\n [-64, 80, 64, 24, 0, 0, 32],\n [56, -70, -56, -21, 0, 0, -28],\n [96, -120, -96, -36, 0, 0, -48],\n [72, -90, -72, -27, 0, 0, -36],\n [16, -20, -16, -6, 0, 0, -8],\n [8, -10, -8, -3, 0, 0, -4]]?\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 7x7 matrix:\n[[-196, 272, 198, 0, -47, -117, -146],\n [-101, -77, 188, -64, 91, -28, 86],\n [117, -59, -129, 22, 119, 91, -27],\n [-262, 144, 363, -147, 82, -33, -17],\n [46, 50, -35, 36, 138, 43, -79],\n [-16, 65, 57, -59, 44, 38, -83],\n [264, -151, -102, -49, 52, 81, -154]]\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 7x7 matrix:\n[[76, -19, 49, 105, 55, -80, 30],\n [-122, -211, -160, 138, 62, -308, -95],\n [4, 30, 13, 130, 110, 37, -141],\n [-126, 12, -43, -177, -162, 86, 82],\n [-26, 89, -64, -84, -150, 162, 31],\n [-73, -72, -34, 71, 161, -80, -191],\n [284, 75, 192, 233, 162, -29, 50]]\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[[-77, -97, -120, 160, -35, 29, -88],\n [-33, 5, -20, 174, 5, 127, -150],\n [-22, -54, -96, 104, -26, 30, -56],\n [88, 83, 34, -20, 19, 64, -13],\n [0, -36, -76, 57, -21, 13, -24],\n [99, 152, 138, -51, 53, 98, -27],\n [-77, -120, -146, 136, -46, -7, -55]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-40, -61, -71, 108, -62, 20, -51],\n [60, 88, 68, -120, 100, -44, 108],\n [30, 43, 23, -48, 52, -26, 63],\n [-40, -48, 72, -48, -88, 72, -168],\n [-20, -32, -52, 72, -28, 4, -12],\n [-20, -36, -96, 120, -20, -12, 24],\n [-60, -77, 53, -12, -122, 88, -207]]\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[[12, -48, -10, 25, 28, -5, 28],\n [-147, 60, 128, -221, -200, -35, -134],\n [-66, -216, 60, -60, -24, -60, 36],\n [51, 132, -46, 52, 28, 40, -14],\n [92, 144, -82, 109, 76, 55, 12],\n [41, 204, -38, 26, -4, 50, -50],\n [112, 0, -98, 161, 140, 35, 84]]\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[[18, -27, -18, 54, 95, 4, -195],\n [-98, 157, -52, -86, -167, 70, 161],\n [-55, 95, 26, -164, -200, 57, 17],\n [-68, -8, -9, 112, 172, 11, 74],\n [-64, -79, 177, -94, 45, 9, 31],\n [79, -101, 67, -8, -26, -84, 215],\n [-138, 72, 52, -72, -8, 78, 36]]\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[[-83, -227, -15, -224, 98, -216, 196],\n [13, 122, 109, 148, -87, 5, 38],\n [-133, 199, -113, 23, -192, 39, -191],\n [80, -95, 50, 14, 7, 115, -90],\n [175, 10, 83, 73, -3, -10, 93],\n [-41, 105, -6, -51, -137, 119, -207],\n [-51, -46, -201, -105, 61, 38, -129]]\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[[-141, -148, 81, 89, 19, -136, 45],\n [67, 67, -39, -33, 63, -171, 169],\n [42, -5, -8, 126, -20, -43, 66],\n [133, 122, -70, -28, 13, -15, 77],\n [105, 48, -44, 122, -21, -41, 97],\n [29, 2, -59, 5, -27, 16, 15],\n [-26, 68, 26, -226, 68, 30, -66]]\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[[-54, 72, 27, 36, 0, -54, -72],\n [-18, 24, 9, 12, 0, -18, -24],\n [-36, 48, 18, 24, 0, -36, -48],\n [66, -88, -33, -44, 0, 66, 88],\n [24, -32, -12, -16, 0, 24, 32],\n [42, -56, -21, -28, 0, 42, 56],\n [-42, 56, 21, 28, 0, -42, -56]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 7x7 matrix:\n[[85, -65, -151, 278, -49, 50, 3],\n [-20, 21, 65, 28, -43, -128, 264],\n [-97, 3, 184, -58, 31, -133, 120],\n [47, -29, 342, 6, -29, 34, 6],\n [70, 25, -32, 20, -63, 18, 109],\n [74, -13, -40, 100, -49, 45, 31],\n [-111, 82, -22, -230, 38, -127, 125]]\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[[-294, -30, -73, 189, 3, -154, -132],\n [211, -231, -205, 75, -13, 99, -112],\n [-99, -60, 16, 34, 200, -90, -161],\n [-84, -111, -110, 182, -65, -70, -106],\n [-22, -3, 39, 53, 35, -15, 9],\n [-195, 2, 85, 48, 251, -124, -132],\n [-182, 62, 136, 10, 129, -157, -87]]\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 7x7 matrix:\n[[-27, 21, 30, 33, 33, 0, 12],\n [27, -21, -30, -33, -33, 0, -12],\n [-9, 7, 10, 11, 11, 0, 4],\n [45, -35, -50, -55, -55, 0, -20],\n [90, -70, -100, -110, -110, 0, -40],\n [-108, 84, 120, 132, 132, 0, 48],\n [27, -21, -30, -33, -33, 0, -12]]\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 7x7 matrix:\n[[8, -42, -81, 72, 78, 89, -70],\n [-112, 172, -62, 32, -52, -50, 148],\n [48, -60, 66, -48, -12, -18, -36],\n [-100, 169, -11, -10, -85, -89, 163],\n [24, -54, -36, 36, 54, 60, -66],\n [16, -12, 45, -36, -24, -29, 4],\n [-36, 17, -130, 106, 79, 94, -29]]\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[[24, -103, 77, 46, -44, -151, 1],\n [52, -5, -21, 186, -128, 3, -69],\n [11, -73, 111, 7, 51, -78, 54],\n [36, -19, 104, 115, 46, 38, 46],\n [-13, 33, -35, -33, 11, 40, -4],\n [64, 64, 6, 250, -52, 162, -30],\n [-12, 138, 42, 0, 204, 294, 102]]\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[[66, -78, 35, 79, -5, -109, 54],\n [133, -75, 150, 58, 48, -107, 28],\n [-67, -31, -191, 33, -127, -28, -2],\n [82, -58, 61, 41, -1, -77, 6],\n [68, -82, -23, 57, -70, -100, -8],\n [123, -123, 81, 117, 0, -171, 72],\n [59, -125, -102, 102, -132, -153, 12]]\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[[9, -51, 105, -59, -30, -27, -2],\n [153, -21, -1, 31, -40, 105, -128],\n [162, -9, -29, 49, -35, 120, -137],\n [-36, -21, 55, -39, -5, -42, 33],\n [153, -57, 75, -13, -60, 81, -124],\n [-9, 33, -67, 37, 20, 15, 4],\n [-9, 24, -48, 26, 15, 9, 5]]\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[[17, -4, -24, -91, -29, 23, 78],\n [-40, 44, -120, -116, 76, -108, 152],\n [-117, 96, -85, 215, 186, -193, -135],\n [-46, 14, -2, 92, 94, -104, -46],\n [-57, 117, -169, -2, 39, -36, 5],\n [43, 49, -51, -34, -151, 192, -53],\n [52, 28, -55, -116, -145, 170, 37]]\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 7x7 matrix:\n[[-92, -57, -65, 57, -154, -17, 104],\n [14, 64, -43, 108, -172, 187, 27],\n [88, 48, 68, -112, 216, -52, -44],\n [-82, 125, -77, -7, 11, 7, 48],\n [106, -221, 118, 37, -48, -16, -119],\n [-54, 214, -83, 54, -28, 143, -47],\n [-64, -240, 7, 36, -138, -133, 62]]\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[[91, 181, 118, -2, 24, -57, -15],\n [222, 75, 335, 5, 70, -11, 37],\n [161, 52, 186, -82, -65, -92, 194],\n [-41, 193, -74, -107, -257, -70, 169],\n [-300, 86, -113, -144, 22, -104, -163],\n [85, 388, 147, -139, -204, -116, 242],\n [-199, 95, -158, -30, -126, 70, -22]]\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 7x7 matrix:\n[[80, -3, -138, -169, 54, -17, 209],\n [-41, -22, -21, -112, 67, 4, 174],\n [30, -99, -88, -91, 76, 59, 148],\n [-109, 6, 162, 24, 27, 28, -44],\n [-128, -17, 222, -17, 74, 69, -14],\n [-13, 61, -171, 55, -95, -129, 31],\n [75, 43, 76, -151, 65, 25, 99]]\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 7x7 matrix:\n[[33, 132, 110, -55, 11, 110, -132],\n [3, 12, 10, -5, 1, 10, -12],\n [24, 96, 80, -40, 8, 80, -96],\n [-27, -108, -90, 45, -9, -90, 108],\n [24, 96, 80, -40, 8, 80, -96],\n [0, 0, 0, 0, 0, 0, 0],\n [12, 48, 40, -20, 4, 40, -48]]\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[[-231, -78, -36, 153, 200, -50, -21],\n [14, 138, -227, 91, -51, 197, 192],\n [-24, -60, 66, -48, 42, -78, -84],\n [-25, 120, -221, 118, -17, 181, 183],\n [-93, -102, 72, -36, 112, -118, -123],\n [-8, -2, -29, -28, 15, 3, -10],\n [-82, -114, 133, -14, 97, -143, -132]]\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[[-107, -26, 91, 85, -92, 58, 92],\n [38, 2, -34, -46, 50, -10, -32],\n [22, 17, -16, 8, -9, -29, -20],\n [-81, -2, 73, 103, -112, 18, 68],\n [89, 59, -67, 11, -13, -103, -80],\n [-1, 52, 13, 115, -126, -76, -4],\n [-5, -41, -5, -83, 91, 61, 8]]\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[[12, -30, 36, 60, -30, 36, 30],\n [14, -35, 42, 70, -35, 42, 35],\n [-10, 25, -30, -50, 25, -30, -25],\n [24, -60, 72, 120, -60, 72, 60],\n [12, -30, 36, 60, -30, 36, 30],\n [-16, 40, -48, -80, 40, -48, -40],\n [-4, 10, -12, -20, 10, -12, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 7x7 matrix:\n[[-97, -97, 49, -89, 157, 63, -294],\n [90, 120, -67, -260, 195, 201, -154],\n [-82, 44, 82, -141, 183, 135, -229],\n [113, -83, 24, -257, 0, 163, -55],\n [-162, 99, 45, 175, 78, -27, -24],\n [-37, -104, -47, 114, 1, -140, -11],\n [-175, -150, 170, 53, -3, -1, -169]]\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[[134, 3, 131, 38, 120, 22, -92],\n [118, 31, 127, 6, 80, 14, -44],\n [-87, -109, -129, 79, 19, 6, -80],\n [-62, -129, -113, 106, 60, 14, -124],\n [-48, -11, -51, -4, -34, -6, 20],\n [66, 122, 114, -98, -50, -12, 112],\n [34, 83, 67, -70, -44, -10, 84]]\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 7x7 matrix:\n[[-92, -26, 201, -129, -206, 97, 173],\n [118, -107, 36, 91, 22, -101, 53],\n [-58, -15, -61, -146, 44, 200, -128],\n [60, -72, -69, -7, 96, 45, -96],\n [50, -165, 161, -62, -100, 56, 124],\n [-42, 67, -28, -1, 0, -3, -18],\n [-14, 3, -35, -34, 28, 52, -52]]\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, -144, -56, 8, 64, -88, -48],\n [92, 8, -20, 196, -148, -76, -188],\n [-67, 74, 31, -23, -19, 53, 43],\n [-20, -52, -6, -118, 112, 18, 100],\n [9, 54, 9, 99, -99, -9, -81],\n [-54, 16, 16, -84, 54, 44, 86],\n [-107, 38, 33, -157, 97, 87, 163]]\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[[-40, -132, -101, 45, -45, -87, -104],\n [-110, -217, -150, -4, 4, -148, -67],\n [60, 74, 43, 41, -41, 53, -30],\n [80, 136, 90, 22, -22, 94, 16],\n [20, 102, 82, -54, 54, 66, 106],\n [-120, -220, -149, -19, 19, -151, -48],\n [50, 23, 2, 68, -68, 20, -83]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-170, -54, -33, -174, -121, 292, -56],\n [54, -188, -98, 40, 126, -276, -158],\n [-83, 120, 34, -50, -62, 182, 73],\n [-122, 25, 16, 103, 62, 103, -4],\n [-116, -31, -31, -146, -99, 215, -38],\n [-105, 95, 11, 9, -13, 173, 40],\n [160, -166, -86, 9, -16, -96, -94]]?\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[[-14, 53, 150, -25, -52, -90, 61],\n [14, -89, -263, 28, 64, 162, -129],\n [37, -67, -139, 53, 164, 72, 48],\n [45, 46, 138, 77, -12, -102, 63],\n [-52, 70, 198, -92, -80, -108, 86],\n [68, 36, 116, 116, 16, -96, 64],\n [30, 78, 214, 54, -72, -144, 64]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[30, 30, -110, -80, 20, -30, -40],\n [-33, -33, 121, 88, -22, 33, 44],\n [24, 24, -88, -64, 16, -24, -32],\n [33, 33, -121, -88, 22, -33, -44],\n [-21, -21, 77, 56, -14, 21, 28],\n [-36, -36, 132, 96, -24, 36, 48],\n [27, 27, -99, -72, 18, -27, -36]]?\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[[66, -30, 51, 54, 66, 6, 30],\n [-6, -60, 34, 16, -96, 25, 57],\n [132, -100, 127, 138, 67, 43, 92],\n [-96, 110, -116, -144, 19, -74, -91],\n [8, -34, 27, 114, -80, 99, -3],\n [122, -80, 112, 228, 32, 127, 35],\n [-194, 154, -193, -298, -46, -148, -108]]\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[[3, 11, 0, 9, 12, 7, 5],\n [33, 121, 0, 99, 132, 77, 55],\n [-9, -33, 0, -27, -36, -21, -15],\n [12, 44, 0, 36, 48, 28, 20],\n [3, 11, 0, 9, 12, 7, 5],\n [-15, -55, 0, -45, -60, -35, -25],\n [-27, -99, 0, -81, -108, -63, -45]]\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[[-7, 14, -7, -46, -49, 20, 31],\n [20, -40, -16, 80, 104, -88, -68],\n [25, -50, -20, 100, 130, -110, -85],\n [-23, 46, 3, -114, -135, 88, 87],\n [-3, 6, -27, -54, -45, -12, 27],\n [-20, 40, 2, -100, -118, 76, 76],\n [22, -44, -26, 76, 106, -104, -70]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[21, 1, 7, 26, -6, -10, -8],\n [128, 118, 1, 18, -83, -180, -69],\n [-15, 53, -25, -86, -18, -50, -4],\n [108, 126, -9, -18, -81, -180, -63],\n [-62, -88, 11, 30, 53, 120, 39],\n [-104, 4, -38, -140, 26, 40, 38],\n [33, 109, -29, -94, -54, -130, -32]]?\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[[68, 69, 42, -225, -47, 202, 7],\n [182, 147, -212, 147, -13, -160, -99],\n [-17, 141, 12, 67, 81, -93, -138],\n [-34, -44, -47, 23, -24, -6, -51],\n [28, -91, -16, -33, -247, -90, 120],\n [12, 159, 10, -49, 165, 108, -161],\n [-175, -268, 157, -119, 22, 209, 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[[-63, 59, 72, -83, 104, 65, 55],\n [48, 44, -279, -82, -118, -33, -127],\n [80, 161, -127, -188, -59, -38, -38],\n [-108, -2, -260, -154, -6, 77, -32],\n [-100, -91, 173, 82, 97, 53, 96],\n [-60, 71, 15, -47, -109, -112, -38],\n [-64, -50, -77, 43, -188, -136, -65]]\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[[-2, 22, 6, -12, 8, -6, -12],\n [-5, 55, 15, -30, 20, -15, -30],\n [-10, 110, 30, -60, 40, -30, -60],\n [10, -110, -30, 60, -40, 30, 60],\n [-6, 66, 18, -36, 24, -18, -36],\n [10, -110, -30, 60, -40, 30, 60],\n [-6, 66, 18, -36, 24, -18, -36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 123, 52, -24, 87, 60, -58],\n [-239, -118, -169, -15, -171, 29, -33],\n [52, -40, -200, -197, -80, -295, 120],\n [-31, -168, -227, -36, -266, -185, 116],\n [-62, -78, -263, -147, -30, -89, 173],\n [151, -2, -150, -24, 66, 27, 22],\n [-55, 4, -113, -290, 61, -306, 157]]\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[[-274, -15, -145, -136, 72, 0, 51],\n [-84, -97, -125, 41, -10, 100, 114],\n [174, -100, -125, -28, -109, 66, 93],\n [-30, -62, 144, 49, -116, -87, 174],\n [-176, -29, -88, -176, 49, -93, 75],\n [-68, 62, 49, -5, -55, 15, -27],\n [96, 160, 172, -76, 4, -132, -180]]\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 7x7 matrix:\n[[-210, -88, -57, -69, 222, 35, -170],\n [-158, -241, 16, -37, 217, 115, -145],\n [-112, -154, 7, -28, 147, 70, -98],\n [-136, -229, 21, -30, 193, 110, -127],\n [-126, -29, -36, -45, 117, -5, -85],\n [86, 233, -65, 17, -114, -65, 37],\n [84, -65, 73, 32, -85, 0, 97]]\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, -92, 30, -73, -192, -136, 76],\n [-70, -77, -31, -64, -150, -109, -68],\n [43, -4, 33, 15, 158, 126, -85],\n [-221, 55, 82, 6, -173, -27, 115],\n [-102, 43, -70, -13, -13, -19, -59],\n [-150, 226, -58, 156, -30, 44, 16],\n [144, 25, -206, 21, 51, -89, -113]]\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[[96, 6, -28, 172, 80, 24, 152],\n [-22, 13, 38, -73, -51, 5, -81],\n [139, -11, -35, 103, 216, -35, -12],\n [-114, 24, -38, -115, -29, -33, -137],\n [-108, -65, 32, -291, -19, -85, -269],\n [-51, 19, -138, 153, 57, -6, 168],\n [18, 102, -106, 53, 191, -41, -177]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[90, 9, 99, -54, 81, 108, -90],\n [-10, -1, -11, 6, -9, -12, 10],\n [-110, -11, -121, 66, -99, -132, 110],\n [50, 5, 55, -30, 45, 60, -50],\n [-60, -6, -66, 36, -54, -72, 60],\n [40, 4, 44, -24, 36, 48, -40],\n [90, 9, 99, -54, 81, 108, -90]]\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[[-39, 4, 53, -1, 91, -68, 125],\n [-9, -49, -50, -29, 17, -13, -20],\n [-99, -101, -120, -37, 68, -20, 15],\n [59, -82, -23, -81, 58, -85, -10],\n [-38, -47, -13, -30, 83, -62, 70],\n [-23, -119, -126, -69, 36, -26, -55],\n [-109, 60, -17, 83, -42, 93, 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[[-63, 175, -28, 41, 49, -89, -137],\n [96, -58, -14, -61, -22, 20, 30],\n [25, 80, -32, -38, 6, -61, -76],\n [72, -105, 6, -48, -33, 48, 75],\n [58, -22, -26, -163, -78, -70, -6],\n [22, 45, -6, 104, 73, 42, -31],\n [-221, 113, 34, 106, 27, -55, -55]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[247, 78, -22, -172, -87, 216, -107],\n [90, 28, 142, -5, 68, -75, 250],\n [143, -94, 52, -271, 71, -139, 193],\n [34, 86, 92, 77, -92, 95, 225],\n [-15, -4, -61, -167, -24, -90, -43],\n [50, -66, 215, 56, 225, -225, 396],\n [4, -66, 32, 92, -6, 8, -87]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-114, -81, 83, 188, -292, 76, -233],\n [-95, -38, 126, -135, -38, 154, -112],\n [-152, -106, 153, -8, -201, 214, -108],\n [119, 91, 37, -203, 72, -52, 161],\n [-204, -129, -115, -268, 205, 214, 156],\n [-146, -27, 92, -6, -200, 98, -349],\n [35, 35, 26, -155, 104, 29, 122]]\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 7x7 matrix:\n[[68, 6, 51, -71, 40, -77, 6],\n [41, 33, 0, -68, 43, -152, 45],\n [107, -61, 114, -14, -55, -58, -101],\n [-126, 38, -139, 83, -30, -1, 60],\n [-177, 110, -187, 5, 117, 116, 183],\n [125, -85, 163, -19, -45, 55, -133],\n [-50, 30, -31, -17, 70, 135, 56]]\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 7x7 matrix:\n[[-54, 168, -125, 89, -39, -52, -118],\n [141, -108, 136, -37, 72, 167, 206],\n [137, -33, -8, -81, 92, 84, 69],\n [100, -163, 76, -148, 92, 55, 113],\n [38, 13, 40, 26, 28, 81, 101],\n [134, 252, -265, -34, 152, 53, -40],\n [43, -146, 134, -28, -15, 48, 74]]\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, 41, 79, -49, -193, 69, -214],\n [170, 30, 268, -216, -19, -14, -42],\n [-22, 6, -30, 82, 90, -126, 252],\n [-111, 39, -46, 242, -7, -115, 91],\n [-65, 116, -27, 157, -122, -84, 120],\n [47, -23, 177, -233, 238, 71, 38],\n [37, -201, -181, -44, 230, -18, 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[[-210, 44, 50, -264, 198, -3, 276],\n [66, -28, -60, 106, -64, -15, -108],\n [48, 8, 45, 31, -43, 21, -36],\n [126, 12, 90, 96, -114, 45, -108],\n [198, -44, -55, 253, -187, 0, -264],\n [-156, 32, 35, -195, 147, -3, 204],\n [-108, 0, -45, -99, 99, -27, 108]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-62, 35, -132, 60, -35, -94, -55],\n [-48, 12, -72, 28, 14, -56, 22],\n [60, -42, 144, -68, 56, 100, 88],\n [152, -44, 240, -96, -28, 184, -44],\n [-76, 40, -156, 70, -35, -112, -55],\n [-80, 44, -168, 76, -42, -120, -66],\n [-104, 50, -204, 90, -35, -148, -55]]?\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[[36, -12, -32, 36, -12, -36, 4],\n [-9, 3, 8, -9, 3, 9, -1],\n [81, -27, -72, 81, -27, -81, 9],\n [81, -27, -72, 81, -27, -81, 9],\n [-72, 24, 64, -72, 24, 72, -8],\n [-18, 6, 16, -18, 6, 18, -2],\n [45, -15, -40, 45, -15, -45, 5]]\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[[91, 142, 103, -50, 63, 30, -11],\n [209, 3, 97, 11, 199, -71, 4],\n [-245, 232, 51, -120, -161, 24, -8],\n [31, 190, 63, 119, 52, 174, -117],\n [-79, 87, 53, 177, 159, -41, -29],\n [-62, 282, 130, 81, 136, 31, -19],\n [3, -36, -65, 4, -112, 111, -69]]\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[[-112, -106, 60, 165, 61, 34, -104],\n [-189, 59, -20, 31, 20, -122, 12],\n [50, 37, 89, -83, -24, -35, 104],\n [-8, -34, 48, 23, -21, 26, 16],\n [-97, -20, 27, 79, 69, -41, -58],\n [-50, -109, 47, 149, 78, 55, -124],\n [77, 72, 8, -103, 17, -54, 55]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-201, -102, -105, -159, -93, 159, -159],\n [137, 55, 21, 67, 24, -4, 60],\n [-66, -48, 6, -118, -76, 110, -68],\n [138, 29, 146, -66, -62, 75, 50],\n [17, 4, 57, -17, -9, -13, 21],\n [82, 56, 18, 126, 82, -130, 86],\n [-2, -35, -106, -102, -94, 239, -110]]\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[[-124, 38, 38, 29, -5, 71, -127],\n [14, -51, -39, -133, -80, -39, 160],\n [-87, 90, 70, -98, 85, 87, -69],\n [-77, -47, -15, 201, -73, 28, -125],\n [-18, 111, 43, 25, 151, -41, -187],\n [-39, -67, -87, -86, -126, -26, 47],\n [37, -75, -123, -135, -119, -156, 109]]\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[[155, 104, 100, -165, 231, 97, -240],\n [73, 77, 9, -37, 49, 44, 13],\n [-126, -160, -51, 195, -97, -67, 152],\n [80, 75, 80, -169, 121, 46, -245],\n [141, 160, 45, -129, 101, 84, -76],\n [130, 134, 42, -124, 116, 76, -82],\n [31, 21, 58, -140, 90, 13, -219]]\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[[60, 93, -98, -34, 96, 247, 39],\n [170, 61, -88, -54, 198, 354, -10],\n [-158, 38, -78, -104, 24, -4, 247],\n [-152, -85, -16, -100, -6, -149, 211],\n [102, -44, 162, 28, 82, -67, -145],\n [126, 137, -62, 16, 104, 290, -68],\n [-102, -17, -24, -30, -48, -87, 104]]\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[[8, -122, 4, 88, -52, 28, -42],\n [-4, 21, 78, -44, 42, -30, 13],\n [6, -54, -72, 66, -54, 36, -24],\n [4, -71, 22, 44, -22, 10, -23],\n [-9, 116, 38, -99, 67, -40, 43],\n [5, 15, -180, 55, -69, 54, -8],\n [-4, 6, 108, -44, 48, -36, 10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[47, 114, 95, 54, 42, -143, -119],\n [44, -37, -21, -7, 60, -5, -49],\n [5, 39, 25, 17, -26, -69, -29],\n [27, -103, -68, -37, 78, 102, 10],\n [-126, -56, -73, -44, -192, 111, 203],\n [-132, -58, -74, -46, -192, 126, 214],\n [-33, 40, 4, 12, -146, -118, 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[[55, -131, 97, -15, -106, 46, 148],\n [-75, -102, -159, -33, -96, 111, 12],\n [-20, -2, -40, -4, -4, 14, -16],\n [-10, 41, -16, 6, 34, -19, -40],\n [-60, 99, -110, 8, 78, -23, -128],\n [-60, 78, -112, 4, 60, -10, -112],\n [-40, 38, -76, 0, 28, 2, -64]]\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[[-18, 0, 99, -54, -99, 0, -99],\n [-24, 0, 132, -72, -132, 0, -132],\n [8, 0, -44, 24, 44, 0, 44],\n [8, 0, -44, 24, 44, 0, 44],\n [-12, 0, 66, -36, -66, 0, -66],\n [20, 0, -110, 60, 110, 0, 110],\n [14, 0, -77, 42, 77, 0, 77]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[95, -90, 49, -15, 19, 49, 34],\n [-36, 13, -15, 17, 6, -144, -170],\n [14, -119, -14, 57, 12, -92, -109],\n [64, -177, 2, 74, 11, -40, -50],\n [-51, -11, -42, 52, -11, -69, -62],\n [-60, 47, -18, -67, 14, 54, 59],\n [46, 19, 47, -82, 21, 80, 67]]\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[[-120, 132, -180, 81, -66, -240, 156],\n [-26, 16, -96, -46, -10, -208, 140],\n [-44, 42, -84, 5, -24, -142, 94],\n [71, -71, 120, -25, 40, 187, -123],\n [0, 174, -192, 200, 118, -102, 66],\n [-75, -19, -12, -74, -108, -117, 77],\n [-72, -80, 48, -148, -144, -96, 64]]\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[[-81, 15, -127, -10, -38, -69, -1],\n [51, 65, 72, -10, 23, 74, 36],\n [-61, -83, -98, 24, -72, -72, -23],\n [-75, -155, -109, 36, -67, -119, -64],\n [-72, -208, -92, 42, -41, -148, -101],\n [62, 182, 78, -36, 32, 130, 90],\n [103, 217, 142, -44, 66, 176, 103]]\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 7x7 matrix:\n[[-165, 164, 84, 298, -133, -63, -109],\n [78, -106, 229, -134, 97, -58, -162],\n [-12, -28, 178, -32, 91, 42, -55],\n [14, -60, -216, -83, -132, -356, -170],\n [34, -51, -157, -88, 59, 118, 149],\n [12, -16, -5, -7, 55, 0, -42],\n [68, -56, -136, -134, -48, -110, 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 7x7 matrix:\n[[-35, -69, 163, -16, -1, -227, 10],\n [96, 117, -200, 29, -177, 1, -29],\n [-6, -71, -78, -79, -1, 96, 122],\n [6, -73, -146, -69, -83, 10, 200],\n [157, 45, -47, -180, -222, -45, -175],\n [101, -98, -53, -259, -194, -57, 34],\n [-88, 2, 32, 148, 100, -51, 89]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, -33, -36, -12, 30, 57, 24],\n [58, -87, 70, -69, 88, -37, -35],\n [-4, 152, -32, 16, -72, -68, 68],\n [118, 58, -48, -228, 192, -72, 222],\n [167, -112, 130, -221, 228, -137, 20],\n [-16, 48, -136, -60, 56, 88, 164],\n [-25, -10, 84, 102, -102, -45, -141]]\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[[4, -28, -20, 40, 8, -48, -20],\n [-11, 77, 55, -110, -22, 132, 55],\n [-4, 28, 20, -40, -8, 48, 20],\n [-1, 7, 5, -10, -2, 12, 5],\n [9, -63, -45, 90, 18, -108, -45],\n [-4, 28, 20, -40, -8, 48, 20],\n [-4, 28, 20, -40, -8, 48, 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 7x7 matrix:\n[[-45, -31, 115, 156, -91, -75, 72],\n [-27, 23, -87, -156, 39, 7, -92],\n [-18, 6, -23, -48, 5, -7, -31],\n [-90, 18, -70, -168, -2, -50, -116],\n [9, 11, -41, -60, 29, 21, -30],\n [153, 23, -82, -36, 124, 152, 23],\n [36, -32, 121, 216, -55, -11, 127]]\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[[-19, -35, -30, -7, 6, 27, 28],\n [-46, -80, 84, 90, -22, 10, -64],\n [73, 121, -40, -74, 11, -50, 24],\n [-54, -27, 72, 48, -3, 30, -60],\n [-120, 13, -80, -104, 69, 162, 60],\n [125, 114, 2, -23, -21, -123, -8],\n [135, 25, -134, -63, -14, -97, 116]]\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 7x7 matrix:\n[[132, -144, -12, -108, -24, -96, -132],\n [-99, 108, 9, 81, 18, 72, 99],\n [66, -72, -6, -54, -12, -48, -66],\n [44, -48, -4, -36, -8, -32, -44],\n [0, 0, 0, 0, 0, 0, 0],\n [99, -108, -9, -81, -18, -72, -99],\n [110, -120, -10, -90, -20, -80, -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[[77, 17, 121, -55, 2, -58, 62],\n [-15, 32, -26, -45, -48, 40, -28],\n [-13, -8, 152, 5, -4, -39, 157],\n [-37, 20, -24, -33, -59, 35, 5],\n [197, -20, 98, -25, 104, -144, -20],\n [-37, 72, -150, -85, -91, 120, -158],\n [-110, 56, 0, -22, -66, 122, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-182, 137, 64, -83, -90, -61, 217],\n [131, -70, 175, -59, -242, 66, 31],\n [184, -124, -274, -160, 46, -133, -50],\n [-86, 191, 228, -78, -268, 107, 280],\n [103, -42, -155, -24, -194, 123, 20],\n [150, -18, -48, 81, -100, 219, -87],\n [44, -95, -260, 10, -62, 36, -76]]\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 7x7 matrix:\n[[172, -4, -4, -100, -200, -106, 136],\n [354, 10, 21, -53, -428, -74, 179],\n [6, -88, -15, -65, -60, -77, 125],\n [-50, -128, 81, 63, -87, 27, 68],\n [-24, 128, -32, -96, 153, -60, -85],\n [136, 66, 72, -160, -139, -157, 81],\n [-108, 12, -121, 141, 193, 159, -134]]\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[[-118, 19, -167, -93, -234, -44, 22],\n [-139, -151, 123, 242, 321, 207, 95],\n [166, 106, 188, 62, -92, 120, 16],\n [137, 142, 43, -173, -146, -106, -38],\n [81, 106, 211, -112, -30, 88, -130],\n [-55, 51, 79, -70, -173, 152, -140],\n [-143, -68, -81, -52, -32, 43, -155]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 7x7 matrix:\n[[26, 229, 179, 87, 61, -30, -170],\n [-35, 71, -95, 48, 48, -38, 163],\n [-60, -76, -196, 144, -152, 160, -124],\n [-68, -241, -53, 84, 80, -78, -42],\n [44, 6, 160, -75, 61, -66, -52],\n [-16, -184, -186, -93, -96, 65, 165],\n [-84, 249, -153, 261, 32, 17, 49]]\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[[29, 132, 54, -59, -3, 11, -60],\n [31, 188, 63, -83, 5, 27, -104],\n [18, -136, 9, 56, -40, -64, 148],\n [-21, 12, -27, -3, 21, 27, -48],\n [-52, -96, -81, 46, 30, 26, -12],\n [11, 108, 27, -47, 9, 23, -72],\n [-75, -60, -108, 33, 57, 63, -84]]\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[[-60, -48, -60, 144, -72, -108, 60],\n [-5, -4, -5, 12, -6, -9, 5],\n [-35, -28, -35, 84, -42, -63, 35],\n [-20, -16, -20, 48, -24, -36, 20],\n [50, 40, 50, -120, 60, 90, -50],\n [-40, -32, -40, 96, -48, -72, 40],\n [15, 12, 15, -36, 18, 27, -15]]?\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 7x7 matrix:\n[[-50, -80, 120, -20, -50, -120, 60],\n [60, 96, -144, 24, 60, 144, -72],\n [-40, -64, 96, -16, -40, -96, 48],\n [50, 80, -120, 20, 50, 120, -60],\n [-25, -40, 60, -10, -25, -60, 30],\n [30, 48, -72, 12, 30, 72, -36],\n [25, 40, -60, 10, 25, 60, -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[[-79, -46, -33, -56, 82, -65, 48],\n [138, -17, 15, 21, -89, 75, -104],\n [64, 111, 177, 49, -58, 132, 39],\n [29, 50, 130, 132, 1, 3, 26],\n [-50, -15, 16, 73, 247, 10, 85],\n [-230, 198, 4, 280, 40, -172, 162],\n [81, -92, 62, -136, 36, 78, -23]]\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[[149, 27, -71, 117, -2, 76, 177],\n [-68, -26, -2, -49, 28, 60, 139],\n [-8, -2, 9, 1, -2, -31, -71],\n [-92, 34, 95, -171, -62, -41, -107],\n [-124, 12, 87, -172, -38, -27, -72],\n [50, 54, 20, -50, -56, 38, 78],\n [132, -36, -109, 236, 66, -7, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[45, 90, 90, 54, 81, 90, -18],\n [15, 30, 30, 18, 27, 30, -6],\n [60, 120, 120, 72, 108, 120, -24],\n [40, 80, 80, 48, 72, 80, -16],\n [0, 0, 0, 0, 0, 0, 0],\n [60, 120, 120, 72, 108, 120, -24],\n [-50, -100, -100, -60, -90, -100, 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[[82, -81, 53, -36, -169, 56, -71],\n [-19, 99, 79, -16, 95, 4, 3],\n [-75, 132, -71, 69, 144, -67, 18],\n [34, -36, 74, -132, 128, 152, -26],\n [-81, 129, 27, 72, 105, -162, -21],\n [-30, 53, 138, -98, 219, 29, -14],\n [-76, 159, 18, 55, 135, -75, 69]]\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[[22, 13, 69, 58, -70, 23, 105],\n [107, -174, 36, -62, -210, 15, -226],\n [149, 164, -54, 24, -25, 190, 146],\n [-278, -121, 34, -99, 65, -191, 36],\n [-241, -165, -1, -141, -5, -213, -8],\n [-128, -313, 71, -111, -175, -101, -343],\n [149, -118, 81, 122, -140, -89, -177]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-35, 129, 90, -407, 328, 131, 234],\n [25, 3, 115, -185, 162, 170, 96],\n [56, -175, 80, 241, -254, -127, -338],\n [-61, 185, -24, -373, 284, 107, 251],\n [-132, 75, 255, -253, 124, 138, 62],\n [-98, 139, -283, 191, -190, 96, 68],\n [-45, 82, -151, 94, -124, -73, 20]]\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[[-16, -44, -129, -11, -22, -104, -8],\n [-32, 56, -68, 164, -88, 146, -82],\n [192, 45, 164, -25, -57, -130, 156],\n [49, -60, 28, -9, 88, 59, -34],\n [4, 53, -16, 62, -171, 98, -67],\n [-31, -89, -102, -41, -25, 85, -143],\n [-23, -20, -76, -75, -52, -149, 32]]\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[[-208, 192, 247, 88, 90, -44, 109],\n [141, -117, -188, -46, 38, -127, -16],\n [29, 31, -46, 105, 42, -53, -51],\n [27, -39, -8, -40, 264, 5, 120],\n [-164, 77, 58, 12, 227, 224, 170],\n [123, -109, -232, 38, 164, 207, -34],\n [-28, -91, 56, -108, -45, -40, 83]]?\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[[-43, 43, 15, -102, -131, 154, 161],\n [26, -26, 62, 62, 231, -87, -110],\n [-73, 73, 5, -86, -152, 159, 183],\n [-46, 46, 22, 100, 146, -76, -54],\n [44, -44, -28, -2, -32, -36, -48],\n [-36, 36, 20, 150, 214, -142, -120],\n [-21, 21, -47, 70, -23, -68, -41]]?\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[[-150, -137, 56, -89, 6, -15, -7],\n [-25, -15, 243, -314, 96, 288, 200],\n [-212, 32, -56, -140, 174, 202, 188],\n [-96, 150, 20, 162, 20, -58, 102],\n [-11, -123, -239, 100, 17, -76, -178],\n [190, -37, 113, 78, -40, 24, -29],\n [-262, -26, -84, -44, 209, 169, 96]]\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[[29, -30, 203, 218, 7, 334, 157],\n [23, -159, -209, 60, -162, -62, -120],\n [-90, 37, -37, -60, 9, -191, 2],\n [44, -121, -70, 58, -165, 12, -57],\n [-1, 38, 129, 32, 7, 78, 74],\n [-184, 48, 66, 156, 86, -30, 158],\n [-79, -44, 50, 188, -43, 75, 100]]\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[[-4, 103, 102, 103, -96, 60, -61],\n [72, -104, -72, -104, 104, -128, -8],\n [22, -129, -120, -129, 122, -92, 59],\n [88, 109, 150, 109, -92, -28, -159],\n [-41, -38, -57, -38, 31, 20, 66],\n [-85, -30, -69, -30, 19, 68, 106],\n [101, -132, -87, -132, 133, -172, -20]]?\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[[-59, -158, 123, 78, 152, 161, -46],\n [-25, 109, -10, 197, -108, 44, -86],\n [6, 177, -216, -117, -189, -171, -15],\n [74, 231, -132, 143, -287, -202, -41],\n [27, -17, -48, -145, -30, -127, 14],\n [37, 12, -17, 27, -84, -100, -61],\n [-97, -173, 98, 77, 189, 230, -77]]?\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[[-267, -127, 95, 81, 184, 84, 20],\n [-64, -148, 218, -22, -120, -186, -150],\n [106, 177, 178, 293, 148, -152, 89],\n [-24, 9, 22, 137, 289, 63, 176],\n [-77, -190, 49, -26, -118, -116, -13],\n [51, 348, -225, 250, 110, 188, 175],\n [30, 149, -230, 29, 64, 209, 99]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 7x7 matrix:\n[[-190, -221, 319, 19, -88, 220, -26],\n [141, 195, -225, -162, 166, -166, -85],\n [72, 5, -6, -27, 98, 21, -78],\n [274, 213, -221, 119, 14, -102, 121],\n [-190, -175, 183, -29, -60, 92, -42],\n [75, -4, 224, 21, -56, 194, 52],\n [-19, 68, 140, -113, 10, 116, -9]]\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[[-150, -70, 72, 26, 16, 116, 50],\n [-170, -58, 60, 44, 14, 112, 82],\n [-27, 69, -106, -29, -118, -52, 19],\n [-33, 35, -23, 70, 29, -21, 100],\n [-180, 28, -50, 51, -69, 38, 138],\n [-5, -45, 64, 17, 62, 42, -5],\n [209, -39, 60, -75, 68, -38, -179]]?\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[[163, -95, 148, 44, 104, -80, 92],\n [-254, 161, -147, -56, -91, 62, 22],\n [31, -64, 98, -54, 43, -120, 133],\n [99, -70, -8, 112, 38, 102, 11],\n [-87, 67, 80, 20, 54, 4, 92],\n [-210, 198, 116, -25, 40, -12, -6],\n [-99, 3, -172, 95, -80, 268, -118]]\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[[-70, -25, -191, 3, 94, -25, 72],\n [-19, 21, -41, -85, 11, 22, -52],\n [31, 124, 66, -82, 99, -14, 3],\n [-14, 127, -47, -149, 142, -5, -12],\n [-16, -145, -27, 127, -132, 11, 6],\n [-65, -126, -166, 100, -23, -13, 64],\n [37, 69, 87, -21, 35, -10, 4]]\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[[-53, -61, -58, -11, -43, -8, 23],\n [-90, -157, -120, -9, -125, 9, 5],\n [103, 82, 98, 28, 48, 31, -68],\n [29, 39, 34, 5, 29, 2, -9],\n [98, 65, 88, 29, 33, 35, -73],\n [-8, -57, -28, 7, -53, 19, -27],\n [-40, 13, -20, -19, 25, -31, 55]]?\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 7x7 matrix:\n[[174, -220, 23, 194, -9, -235, 23],\n [-6, -10, -130, -15, -137, 43, 90],\n [-142, 215, -29, -175, 33, 207, -65],\n [81, -24, -173, -49, -141, 126, -101],\n [120, -190, 168, 186, 84, -251, 17],\n [-72, 42, 50, -42, -22, 49, 49],\n [-88, 22, 164, -5, 69, -23, 70]]\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[[-77, 11, -111, 211, 12, -191, -105],\n [264, -7, 9, -103, 39, -31, 13],\n [-109, -119, -77, 234, -111, -92, -55],\n [-26, -107, -64, 190, -66, -142, -47],\n [-124, -220, 51, 143, -132, -66, 68],\n [76, -12, -28, 157, 153, 143, 52],\n [152, -192, 35, 26, -66, -245, 27]]\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[[-44, -32, -124, -58, -69, 32, -58],\n [-47, 229, -147, 35, 46, 19, -194],\n [-34, -4, 12, -37, 62, -3, 1],\n [-1, -199, -23, -80, -120, -14, 85],\n [64, -42, 186, 54, 60, -28, 128],\n [15, -24, -38, -5, -68, -60, 1],\n [95, -169, 47, 16, -179, -126, 135]]?\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[[-6, 42, -72, 21, 162, -150, 9],\n [76, -112, 79, -210, 52, 57, 19],\n [64, 2, 73, -6, 160, -78, -113],\n [76, -7, 145, 42, -2, 84, -173],\n [-32, 42, -107, 56, -28, 17, 51],\n [12, -68, 109, -118, 52, -83, 5],\n [-58, -75, 87, -83, -200, 57, 90]]\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, -45, -257, -21, -172, -203, -39],\n [32, -24, -260, -122, -215, -213, -38],\n [34, 48, 173, 66, 178, -55, -102],\n [-56, 26, -24, -145, -104, -143, -38],\n [-58, 81, 142, 99, 77, 31, 3],\n [-80, 30, 36, 18, -44, 52, 62],\n [-8, -10, 31, 28, 26, 73, 32]]?\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[[102, -179, 44, -65, -209, 163, 163],\n [-48, -159, 175, -175, -273, 108, 31],\n [26, 124, -200, 26, 102, 22, 97],\n [-53, 214, -283, -70, 136, 24, 8],\n [3, 170, -244, 289, 276, -93, -17],\n [-160, 257, -67, -183, 131, -150, -211],\n [-9, 68, 189, -9, 150, -186, -79]]\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[[-16, -106, -2, -89, 10, -24, 132],\n [-11, 71, -161, -80, -172, 95, -151],\n [-104, 209, -56, -5, -61, 159, -48],\n [139, -10, -181, -73, 144, -22, 75],\n [25, 51, -45, -10, -64, 59, -69],\n [234, 144, -47, -13, -167, 61, -188],\n [26, 212, -153, -64, 75, -81, 0]]\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 7x7 matrix:\n[[-108, 198, -36, 0, -45, -144, -90],\n [114, -160, 8, -2, 16, 100, 96],\n [5, -142, 256, -147, 64, 140, -98],\n [-10, -165, 114, 3, 113, 181, -15],\n [64, -158, 148, -88, 39, 124, -6],\n [15, -51, -118, 122, 40, 51, 91],\n [-45, -51, 82, -8, 65, 81, -49]]\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 7x7 matrix:\n[[-15, 22, -171, 70, 158, -170, -51],\n [196, 248, 115, -204, -122, -251, 187],\n [-143, -115, -43, 81, -190, 274, -59],\n [-34, 169, -24, 55, -107, -130, 172],\n [-231, -291, 56, 245, 71, 392, -119],\n [-15, 46, -134, -34, -22, -25, 69],\n [-99, 34, -277, 74, 89, -63, 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[[40, -128, 48, 100, -88, -72, 156],\n [-10, 56, 6, -48, 83, 68, -31],\n [0, 36, -8, -24, 18, 12, -58],\n [-130, 44, -110, -66, 23, 44, 19],\n [-145, 83, -111, -102, 83, 95, 5],\n [5, 65, -7, -43, 40, 27, -101],\n [30, -24, -10, 36, -93, -84, -59]]\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[[21, 42, 7, -21, -70, 0, 70],\n [81, 26, -61, -41, -70, -88, 54],\n [129, -48, -155, -39, 20, -198, -56],\n [33, 15, -22, -18, -35, -33, 29],\n [126, -54, -156, -36, 30, -198, -66],\n [-39, -10, 31, 19, 30, 44, -22],\n [33, -36, -55, -3, 40, -66, -52]]\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[[-18, -66, 30, -60, -54, 42, 18],\n [-36, -57, 0, -78, -21, 69, -3],\n [-3, 14, -15, 4, 20, 2, -10],\n [-30, -135, 70, -114, -119, 75, 43],\n [69, -47, 125, 62, -141, -101, 87],\n [-18, 109, -110, 38, 149, 7, -73],\n [-39, -93, 25, -102, -59, 81, 13]]\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, 0, 46, 3, 0, 34, 6],\n [-49, 0, 77, 63, -84, 77, 63],\n [26, 0, 220, 53, -56, 176, 64],\n [122, 0, -2, -94, 136, -34, -86],\n [67, 0, -129, -94, 124, -125, -95],\n [-35, 0, -111, -10, 4, -83, -17],\n [-42, 0, 66, 54, -72, 66, 54]]\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[[-15, -40, 20, 45, 0, 50, 20],\n [24, 64, -32, -72, 0, -80, -32],\n [-18, -48, 24, 54, 0, 60, 24],\n [9, 24, -12, -27, 0, -30, -12],\n [-15, -40, 20, 45, 0, 50, 20],\n [-36, -96, 48, 108, 0, 120, 48],\n [-24, -64, 32, 72, 0, 80, 32]]\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 7x7 matrix:\n[[43, 45, 51, 0, -41, 142, -144],\n [-120, -87, -8, 60, 39, -61, 80],\n [6, -115, -32, 46, -101, 76, 94],\n [-69, 61, 43, -8, 97, -45, -96],\n [-75, -31, 22, 41, 26, 7, -17],\n [30, -40, 55, 105, -105, 205, -65],\n [-29, 63, 12, -47, 80, -71, -57]]\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[[11, -132, 110, 88, 110, -11, 132],\n [-1, 12, -10, -8, -10, 1, -12],\n [-6, 72, -60, -48, -60, 6, -72],\n [7, -84, 70, 56, 70, -7, 84],\n [-4, 48, -40, -32, -40, 4, -48],\n [-4, 48, -40, -32, -40, 4, -48],\n [-5, 60, -50, -40, -50, 5, -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 7x7 matrix:\n[[-64, -88, 137, -86, -14, -68, 105],\n [-10, 86, 27, 34, -50, 94, -1],\n [44, -95, -19, 10, 51, 7, 88],\n [52, -19, -185, -16, 57, -157, -190],\n [66, 128, -99, 211, 83, 236, -3],\n [-40, -61, 73, -159, -110, -139, -4],\n [7, 37, -39, -1, -19, -13, -65]]\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[[-229, 217, 66, -7, 232, 63, 1],\n [13, -14, -12, -21, -4, -21, -32],\n [51, -60, -72, -147, 12, -135, -222],\n [-79, 69, -6, -77, 112, -39, -111],\n [191, -182, -60, -7, -188, -63, -20],\n [-45, 40, 0, -35, 60, -15, -50],\n [156, -146, -36, 28, -168, -24, 34]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[55, 48, -57, -77, 63, 62, 55],\n [-25, 2, -46, -28, 159, 83, 113],\n [130, 48, -120, -92, 60, -138, 178],\n [-220, -80, 12, -68, 180, 72, -60],\n [-42, 10, -99, -217, 138, -41, 4],\n [-110, -36, 68, 90, 72, 187, -28],\n [65, 2, -57, -45, -30, -204, 67]]?\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[[24, -1, -29, -13, 2, 21, 19],\n [192, 72, -120, -120, 112, -72, -24],\n [48, 28, -16, -32, 40, -48, -28],\n [-60, -10, 55, 35, -20, -15, -20],\n [-12, -42, -45, 15, -52, 117, 84],\n [84, 24, -63, -51, 40, -9, 6],\n [36, 26, -5, -25, 36, -51, -32]]\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[[-108, 96, 156, 157, 122, 40, -279],\n [-176, -161, -303, 114, -16, -97, 85],\n [58, -119, 51, 0, 16, -128, -49],\n [-41, 272, 115, 18, 66, 198, -96],\n [141, 7, -36, -117, 225, 82, -76],\n [31, 31, 166, -28, 89, 38, -63],\n [-54, 123, 40, 1, -24, 97, 45]]\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, 0, -11, 22, -44, -121, 44],\n [27, 0, -3, 6, -12, -33, 12],\n [27, 0, -3, 6, -12, -33, 12],\n [-45, 0, 5, -10, 20, 55, -20],\n [-54, 0, 6, -12, 24, 66, -24],\n [-63, 0, 7, -14, 28, 77, -28],\n [-99, 0, 11, -22, 44, 121, -44]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-80, 72, -24, -40, 62, 112, -28],\n [90, -111, 72, 45, -36, -156, 54],\n [110, -29, -72, 55, -164, -84, -14],\n [-110, 53, 36, -55, 137, 108, -4],\n [-10, -73, 120, -5, 100, -68, 58],\n [20, 82, -144, 10, -128, 72, -68],\n [120, -84, 0, 60, -120, -144, 24]]\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 7x7 matrix:\n[[36, 13, -150, -76, 209, 60, 18],\n [54, 181, -274, -7, 111, 237, 165],\n [108, -98, 181, 100, -249, -7, -60],\n [-118, 78, -87, 25, 95, 58, 9],\n [-57, 208, -80, 121, 242, 312, 119],\n [-42, -28, -196, 7, 227, 181, 202],\n [-124, 74, 61, 146, 53, 123, -64]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[32, -262, 150, 24, 119, 89, -269],\n [26, -33, 147, -50, 80, 167, -37],\n [26, 157, -49, -80, -20, 11, 165],\n [-54, 121, -1, 22, -57, 22, 118],\n [14, 170, -25, -55, -44, 41, 166],\n [12, 28, 45, -82, 76, 61, 52],\n [-10, -232, 208, -1, 166, 144, -218]]\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[[-4, -81, -15, -4, -7, -57, 106],\n [163, -65, 223, -38, 92, -145, -175],\n [140, -161, 1, 20, 169, -185, 140],\n [20, -74, 12, 44, -6, -90, 138],\n [160, 165, -123, 190, 238, 27, -25],\n [-159, 35, 321, -284, 37, -7, -75],\n [36, 70, 77, -6, 168, -34, 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[[0, 99, -81, 81, -18, 54, -18],\n [0, 0, 0, 0, 0, 0, 0],\n [0, -11, 9, -9, 2, -6, 2],\n [0, -33, 27, -27, 6, -18, 6],\n [0, -110, 90, -90, 20, -60, 20],\n [0, -99, 81, -81, 18, -54, 18],\n [0, -132, 108, -108, 24, -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[[-9, -4, -5, 7, -25, 22, -12],\n [-76, 11, 30, 49, -58, 24, -58],\n [-56, 44, 80, 28, 80, -112, -8],\n [-23, -24, -35, 21, -111, 106, -44],\n [-117, 41, 85, 70, -7, -50, -66],\n [107, -11, -35, -70, 97, -50, 86],\n [-107, 11, 35, 70, -97, 50, -86]]?\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 7x7 matrix:\n[[-59, 1, -196, -10, -31, -30, 142],\n [-157, 189, 142, -64, -224, 78, -42],\n [-31, 226, 179, -182, -156, -49, -220],\n [-54, -228, 39, 315, 19, 16, 87],\n [-41, 31, 199, 51, -99, -108, -179],\n [94, 77, -46, -150, 28, 44, -58],\n [61, -107, 39, 158, -97, 127, 90]]\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 7x7 matrix:\n[[70, 129, -192, -86, 302, 22, -16],\n [-6, 118, -118, -28, -129, -259, -45],\n [126, 122, -65, 32, -228, -149, 144],\n [129, 20, -50, -24, 154, 98, -44],\n [-36, 7, 39, 254, -181, -54, -235],\n [-74, -41, 51, -145, -86, -59, 220],\n [-117, -47, 73, 23, -164, -89, 4]]\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[[-57, 62, 77, 28, 4, 62, 39],\n [168, -60, -160, -72, -68, -76, -168],\n [-18, 33, 84, -114, 87, 93, 90],\n [-45, 38, 57, 16, 12, 42, 39],\n [-108, -48, 56, 38, 84, -26, 146],\n [45, -83, -95, 12, -15, -97, -41],\n [45, 8, -37, 0, -42, -8, -67]]?\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 7x7 matrix:\n[[-17, 14, 47, 29, -2, 43, -47],\n [150, 125, 27, -109, 200, 206, -40],\n [56, 158, -4, 60, 166, 88, 86],\n [-223, 6, 9, 306, -95, -68, -8],\n [-123, -76, -139, 105, -93, -126, 58],\n [112, 239, 192, 39, 231, 268, -57],\n [300, 242, 71, -201, 369, 276, 19]]\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 7x7 matrix:\n[[7, -72, 110, -40, -54, -145, -124],\n [-2, -277, -40, 18, -14, -61, -52],\n [24, 148, -72, -52, 56, 180, 96],\n [-138, -83, 83, 102, 171, 11, -47],\n [55, -127, -55, -33, -77, -40, -13],\n [-21, 104, -175, 83, 89, 221, 199],\n [34, 115, -102, -6, 0, 123, 114]]\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[[36, 183, -120, 10, 76, -105, 145],\n [45, 22, -58, 36, 49, -130, 187],\n [-30, -201, -72, -38, 19, 69, 13],\n [288, -203, 206, 106, -68, 21, 73],\n [-69, -94, -62, -52, 9, 86, -63],\n [23, 60, 32, -12, -21, 76, -103],\n [17, 17, 54, 46, -10, -105, 82]]\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[[-28, 87, -127, -143, 45, -162, -5],\n [159, 116, -148, -192, 223, -164, 5],\n [11, 99, -234, -221, 100, -117, 52],\n [12, -67, -55, -46, -83, 58, 72],\n [140, 23, -39, -28, 65, -11, -100],\n [51, 51, 75, 28, 100, 41, 28],\n [46, -47, -157, -86, -15, -19, -17]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[94, -40, -86, -17, -69, 181, 202],\n [177, -45, 16, 9, 0, 81, 126],\n [95, -44, 74, -34, 69, 68, -151],\n [-66, 42, 124, -30, 52, -38, -264],\n [-96, 31, 76, -16, 56, -84, -233],\n [22, -17, -102, -13, -81, 141, 189],\n [-27, -63, -184, 18, -21, 0, 174]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-50, -28, 40, -33, -85, -28, -47],\n [30, -16, 58, 110, 10, 66, -62],\n [50, 32, -50, 22, 90, 22, 58],\n [25, 20, -35, 0, 50, 5, 40],\n [10, 44, -104, -99, 65, -52, 115],\n [-90, -36, 36, -99, -135, -72, -45],\n [10, 44, -104, -99, 65, -52, 115]]\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[[-106, -109, 58, -7, 7, 126, 59],\n [-99, -3, -48, 26, -6, -170, -59],\n [76, 40, -82, -149, -82, 60, 130],\n [59, 128, -54, 130, -72, -187, -150],\n [-281, -128, -6, 75, -33, -114, 8],\n [289, 34, 108, -166, 267, 204, -4],\n [-163, 74, -150, 169, -282, -275, -58]]?\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[[-204, 18, 167, -22, 81, -83, 119],\n [5, -92, -110, -315, 168, 32, -138],\n [36, 19, -32, 48, -89, 202, -58],\n [-193, -70, -114, 116, -217, 146, 9],\n [-36, 106, 57, 60, 136, -124, 50],\n [-27, -95, -23, 56, -290, 148, 14],\n [231, -65, -49, -56, -163, 117, -84]]\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[[17, -29, -12, 31, -101, -7, -49],\n [18, 38, 5, -20, 68, 11, 32],\n [120, 24, -2, -4, -68, 14, -12],\n [-107, -55, -35, 85, -99, -24, -95],\n [-64, 106, -62, 96, 92, 16, -64],\n [-145, 1, -36, 73, 37, -13, -55],\n [13, -62, 48, -79, -1, -10, 69]]?\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[[-96, 16, 8, -8, 0, 24, -40],\n [-84, 14, 7, -7, 0, 21, -35],\n [96, -16, -8, 8, 0, -24, 40],\n [72, -12, -6, 6, 0, -18, 30],\n [-108, 18, 9, -9, 0, 27, -45],\n [-72, 12, 6, -6, 0, 18, -30],\n [-108, 18, 9, -9, 0, 27, -45]]\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[[13, 40, 11, 98, 55, 65, 102],\n [3, 32, 31, -40, -30, -22, -59],\n [-14, -24, 12, -158, -95, -101, -179],\n [-19, -56, -13, -150, -85, -99, -158],\n [1, 32, 37, -72, -50, -42, -97],\n [11, 80, 67, -44, -40, -20, -81],\n [22, 96, 54, 88, 40, 64, 70]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-59, 10, -125, -22, -24, -62, 114],\n [40, 66, -3, -60, 26, 36, -32],\n [3, 62, -31, -98, 32, 26, -26],\n [-64, -74, 47, -10, 10, -1, -54],\n [104, -26, 103, 164, -34, 16, -8],\n [-105, -148, 84, 34, -2, -18, -66],\n [-70, -146, 143, 44, 10, 14, -120]]\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[[-69, -154, 33, -155, 141, 30, -225],\n [-12, -64, 7, -36, 55, 21, -182],\n [-41, 158, -147, 70, 169, -343, -37],\n [-23, -83, 70, -53, 9, 20, 91],\n [43, 16, 9, -55, -57, 157, -138],\n [-117, -21, -61, -2, 152, -249, 194],\n [15, -231, 132, 96, -65, 118, -64]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[147, 59, 93, -17, -92, 105, 15],\n [21, 37, 27, 33, 4, 63, 17],\n [27, -31, -3, -55, -42, -51, -19],\n [132, 54, 84, -14, -82, 96, 14],\n [48, -19, 12, -53, -53, -30, -15],\n [-168, -46, -96, 46, 118, -84, -6],\n [63, -39, 9, -87, -78, -63, -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[[150, -33, -99, 39, -84, -39, -108],\n [154, -22, -33, 11, -11, -44, -198],\n [-36, 0, -22, 10, -30, 12, 84],\n [128, -44, -176, 72, -172, -28, 24],\n [54, 0, 33, -15, 45, -18, -126],\n [-114, 15, 17, -5, 0, 33, 156],\n [-12, 3, 10, -4, 9, 3, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[262, 248, 74, -52, 70, -84, 46],\n [56, 48, 78, 156, 1, 66, 119],\n [17, -45, -59, -47, -138, 32, -79],\n [-99, -96, 73, 218, 6, 145, 74],\n [-313, -377, -120, 160, -176, 156, -161],\n [-106, 7, 83, -26, 114, -42, -9],\n [-114, -133, -23, 60, -128, 96, -21]]\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[[110, 63, 142, 89, 158, 151, 9],\n [-19, -83, 46, -160, -132, 86, 92],\n [164, 85, 109, 173, -38, 303, 176],\n [136, -84, 263, 74, 234, 100, 133],\n [16, -40, -19, -74, -130, 90, 115],\n [237, -4, 181, -19, 250, -47, -92],\n [65, 4, 131, 78, 223, -202, -189]]\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[[-15, -12, 21, 9, 33, -33, 21],\n [50, 40, -70, -30, -110, 110, -70],\n [-40, -32, 56, 24, 88, -88, 56],\n [-20, -16, 28, 12, 44, -44, 28],\n [35, 28, -49, -21, -77, 77, -49],\n [30, 24, -42, -18, -66, 66, -42],\n [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[[-104, 26, -135, 12, -59, 140, 74],\n [141, -74, 151, -33, 51, -177, -78],\n [51, -153, -117, -73, -133, 80, 5],\n [80, -98, -102, -52, -62, 102, -42],\n [66, -194, -44, -82, -72, -60, 72],\n [-94, 63, 167, 40, -1, -191, 49],\n [-49, 157, 6, 63, 34, 96, -81]]\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[[28, 253, -53, 60, 293, 150, -151],\n [-22, -62, 21, 27, -50, -31, 33],\n [33, 53, 92, -59, 123, 25, 90],\n [-27, 129, -84, 169, 163, 63, -194],\n [-26, -17, 72, -53, -91, 132, 168],\n [5, -8, -10, 98, 106, -132, -118],\n [-53, 68, -11, 133, 28, 130, -53]]?\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[[189, -21, -21, -162, 66, 78, 198],\n [25, -40, 108, 64, 176, 20, 100],\n [85, -68, -100, -119, -25, 64, 72],\n [103, 83, -82, -209, -159, 6, -11],\n [151, 32, -33, -107, 11, 44, 163],\n [-147, -245, -105, -57, -39, 50, -222],\n [-112, -33, 7, 155, 21, -26, -58]]\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[[-74, -54, -47, -54, 91, 75, -89],\n [9, -30, 24, 93, -159, -54, 69],\n [3, -32, 19, 83, -142, -45, 58],\n [13, 8, 9, 13, -22, -15, 18],\n [62, 50, 37, 34, -57, -57, 67],\n [-50, -46, -27, -14, 23, 39, -45],\n [23, 4, 21, 47, -80, -39, 48]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 7x7 matrix:\n[[-97, 25, -26, -122, -96, -51, 139],\n [40, 105, 27, -68, -48, 96, -248],\n [92, 182, -109, 27, -42, 150, -3],\n [52, 285, -58, -166, -150, 166, -74],\n [-102, 10, 35, -155, -102, -36, -91],\n [-50, -329, 62, 203, 186, -200, 159],\n [72, 224, -78, -72, -84, 132, 64]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[24, -135, 193, 46, 226, 53, -4],\n [79, -31, -171, -150, 170, 51, 210],\n [-339, 14, -236, 113, -104, -102, -77],\n [-31, -6, -55, -92, 80, -148, 38],\n [111, 31, -59, 197, -70, 289, -7],\n [172, -63, -103, -69, 41, 53, 90],\n [-79, 140, -197, 80, -240, 37, -38]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-108, -53, -193, -84, 31, -33, -18],\n [-129, -74, -123, -114, 31, 58, -58],\n [165, -95, -126, -108, 97, -86, 38],\n [-111, -154, 81, -68, -103, 138, -60],\n [78, -3, -147, -18, 108, -128, 16],\n [76, -123, 7, 118, 175, -157, -148],\n [-47, -46, -1, 94, 48, -77, -86]]?\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[[-24, 155, 35, 105, 38, -66, -103],\n [-62, 220, -70, -25, 134, -306, -78],\n [-47, 92, 100, 79, 109, -196, -108],\n [-79, -16, -78, 74, -191, 110, 138],\n [85, -44, 164, 29, 117, 34, -142],\n [40, 0, -50, -25, -40, 112, 16],\n [-71, 223, -251, -72, -31, -145, 66]]\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[[-38, 48, -108, -63, -9, 41, 56],\n [-8, 72, -8, -98, -94, 114, 0],\n [3, -96, 0, 72, 108, -135, -6],\n [27, -78, 120, -132, -48, -3, -108],\n [14, -137, 36, 78, 126, -172, -33],\n [5, -45, 52, -146, -46, 17, -67],\n [32, -87, 100, 28, 32, -76, -67]]\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[[72, 163, -146, -26, 62, -68, -14],\n [74, 135, -57, 2, 181, -101, -31],\n [-4, 10, -15, -60, -9, -15, -9],\n [94, -83, 169, -106, -9, -211, -173],\n [42, 31, -42, 106, -38, 10, 6],\n [17, 4, 3, -90, -19, -58, -43],\n [-24, -259, 262, -70, -168, -52, -104]]?\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 7x7 matrix:\n[[-60, 17, 4, -84, 35, -42, -139],\n [-67, 211, -63, 89, -105, 17, 90],\n [-85, -3, -17, -175, 214, 9, -308],\n [15, 74, -7, 81, 59, 164, 48],\n [108, -110, -9, -117, 147, -21, -110],\n [43, 52, -154, -104, 374, 138, -181],\n [-31, 194, -163, 83, 200, 202, 32]]\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[[-191, -112, -35, -12, 3, 25, 0],\n [-97, -145, -105, -69, 92, 67, -15],\n [-309, -89, 9, -128, 210, -133, -132],\n [-40, -180, -26, -131, 190, 7, 54],\n [-74, 16, 46, 76, -90, -8, 15],\n [132, -59, -50, -6, 103, 64, 7],\n [53, -93, 105, 77, -26, 27, 163]]\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[[47, 15, -66, -18, -15, -114, 15],\n [104, -4, 45, -89, 114, -96, -99],\n [-192, -152, -54, -52, 81, -126, -36],\n [181, 150, 196, -35, 16, 231, -92],\n [-5, -172, 166, 11, 262, 51, -112],\n [-56, -247, 11, 192, 176, -21, 78],\n [94, -13, 9, 10, 60, -57, -10]]\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[[-13, -30, 43, -55, -23, -34, -37],\n [-42, -125, -168, 38, -64, 5, 133],\n [25, -64, -115, -109, 75, -160, -21],\n [-12, 6, 72, -12, -30, 18, -30],\n [9, -15, 51, -105, 24, -93, -84],\n [-5, 38, -5, 97, -21, 98, 55],\n [27, 26, 83, -111, 55, -98, -117]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-43, 129, -9, -19, 140, 117, 21],\n [-48, 162, -54, -6, 153, 174, 174],\n [-15, 38, -72, -24, -2, 94, 169],\n [54, -121, -141, 60, -179, -14, 277],\n [-60, 158, 78, -58, 146, 98, 116],\n [-22, 18, -2, -66, 9, 38, -88],\n [8, -41, 35, -15, -41, -53, -62]]\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[[-40, -49, -16, 100, 127, 140, 30],\n [-116, -140, -43, 202, 230, 125, 154],\n [92, 70, -10, 4, -36, -30, 24],\n [52, 71, 9, -226, -187, 29, -48],\n [-9, 17, 30, -79, -74, -59, -95],\n [36, 61, 44, -58, -82, -92, -152],\n [128, 97, -32, -44, -31, 188, 42]]\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[[-57, -24, 125, -11, 26, 11, 93],\n [-67, -106, -263, 152, -131, -162, 3],\n [-43, 110, -18, -22, 91, 230, -218],\n [-58, 55, 131, -30, -16, 116, 51],\n [79, -23, 128, -67, -10, -99, 173],\n [7, -60, -41, 126, -55, -152, -109],\n [86, 106, 170, -237, 235, 269, -30]]?\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[[2, -17, -1, 16, -19, -41, -22],\n [-111, -195, -31, -1, -151, -272, -47],\n [-26, -59, -129, -20, -35, 75, 24],\n [54, -44, 74, 86, -150, -196, -48],\n [322, 6, 116, 8, -216, 84, -7],\n [-22, 130, 149, 10, 187, 95, -31],\n [103, -11, 114, -46, -36, 84, -18]]\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[[-25, 5, -83, -64, 119, 62, 39],\n [-54, 26, -71, -49, 111, 53, 25],\n [-13, -16, -65, -59, 67, 22, 67],\n [-35, -116, 92, 27, 21, 45, -50],\n [42, 54, -85, -43, 29, 3, 43],\n [2, 157, -194, -93, 100, 10, 92],\n [46, 54, -79, -38, 20, -1, 39]]\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 7x7 matrix:\n[[-127, 17, 342, 236, 52, 269, 49],\n [25, -74, 9, -188, -73, -53, 17],\n [-32, -43, -178, -110, 319, 56, 33],\n [-10, 133, -67, 273, 8, -18, -42],\n [-119, 75, -96, 95, 279, 83, 61],\n [-156, 154, 132, 70, 2, 51, 109],\n [54, -61, -67, 87, 32, 2, -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[[72, 48, -96, 0, 84, -144, -36],\n [72, 48, -96, 0, 84, -144, -36],\n [36, 24, -48, 0, 42, -72, -18],\n [0, 0, 0, 0, 0, 0, 0],\n [66, 44, -88, 0, 77, -132, -33],\n [-12, -8, 16, 0, -14, 24, 6],\n [42, 28, -56, 0, 49, -84, -21]]?\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 7x7 matrix:\n[[-54, 92, -103, -230, -7, -116, -90],\n [65, 32, 82, 93, 18, 135, 39],\n [69, -99, -132, 90, -90, -237, 156],\n [205, -5, -172, -8, -184, -59, 161],\n [-10, 102, -140, -88, -5, -59, 38],\n [-139, -69, -28, -8, 38, -5, -59],\n [-138, 20, 0, -114, 63, 1, -124]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-13, -115, -78, 67, -145, 17, 75],\n [-73, 81, -29, 18, -117, -55, 58],\n [-43, 212, 95, -10, 91, -37, -158],\n [61, -83, -54, -35, 93, 25, 85],\n [20, 135, 69, -97, -15, -97, -38],\n [258, -2, -17, -303, 147, -141, 218],\n [161, 75, 65, -290, 147, -127, 148]]\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[[-45, -35, -15, 30, 30, -25, -25],\n [-99, -77, -33, 66, 66, -55, -55],\n [-45, -35, -15, 30, 30, -25, -25],\n [-108, -84, -36, 72, 72, -60, -60],\n [36, 28, 12, -24, -24, 20, 20],\n [54, 42, 18, -36, -36, 30, 30],\n [-72, -56, -24, 48, 48, -40, -40]]?\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[[97, 2, -44, -91, 115, -97, -34],\n [-14, 62, 61, 29, -26, 71, 29],\n [35, 4, -13, -32, 41, -32, -11],\n [74, -40, -70, -80, 94, -112, -42],\n [53, -106, -118, -77, 79, -151, -60],\n [26, -100, -100, -50, 46, -118, -48],\n [-45, 116, 123, 72, -71, 152, 61]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-83, 53, -105, 36, 30, 19, -110],\n [-7, 1, -9, 0, 6, 5, -10],\n [-109, 91, -137, 66, 18, 4, -140],\n [-75, 45, -95, 30, 30, 20, -100],\n [-52, 28, -66, 18, 24, 17, -70],\n [55, -49, 69, -36, -6, 1, 70],\n [109, -91, 137, -66, -18, -4, 140]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-147, -49, -76, -56, 36, 39, -124],\n [-22, -32, 239, 71, 81, 89, 108],\n [126, 82, 8, -27, -83, -72, 42],\n [-324, -182, 53, 33, 199, 189, -108],\n [132, 44, -44, 33, -55, -66, 66],\n [267, 143, -59, -18, -160, -156, 90],\n [-103, -33, 86, -20, 52, 65, -32]]?\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[[59, 103, 87, 31, -60, 66, -83],\n [32, -26, 12, -140, 138, -102, 28],\n [10, 6, 22, -120, 70, -30, 36],\n [-143, -117, -137, 36, -53, 33, 138],\n [17, 59, 49, -31, -26, 48, -13],\n [35, 54, 47, 18, -28, 30, -48],\n [6, 30, 12, 85, -71, 49, -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[[-63, -145, -67, -14, -20, 161, -24],\n [-177, -113, -77, -88, -31, 70, 120],\n [12, -24, -36, 78, 33, 123, -48],\n [107, 9, 135, -73, 63, -107, -97],\n [77, 83, 129, -53, 77, -155, -29],\n [-137, -9, -141, 163, 96, 266, 73],\n [-112, -108, -96, -34, -76, 94, 62]]\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[[54, 16, -72, -48, 44, 80, 46],\n [-273, 14, 54, -87, 4, 100, -73],\n [149, -90, 18, 23, -44, -64, -31],\n [-59, -14, 102, 89, -64, -136, -55],\n [132, -6, -66, -13, 26, 28, 48],\n [239, -58, -42, 33, -12, -52, 31],\n [124, -192, 48, -64, -72, 0, -116]]?\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[[-57, 75, 20, -90, 42, 47, -84],\n [59, -3, -16, 10, 20, 0, 65],\n [250, 20, -60, 0, 140, 40, 270],\n [-55, 93, 44, -134, 170, 135, -70],\n [-77, -18, 46, -16, 82, 72, -59],\n [120, 50, -4, -68, 208, 118, 134],\n [-183, -55, 52, 34, -86, -21, -178]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-98, -55, 120, 97, 96, -180, 122],\n [48, -6, -144, 36, 48, 0, -102],\n [49, 36, -27, -85, -100, 114, -46],\n [47, 22, -39, -76, -108, 78, -53],\n [15, -34, -93, 45, 20, -82, -60],\n [71, 64, -69, -71, -28, 190, -74],\n [-129, -57, 213, 68, 44, -194, 186]]\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[[-89, 332, 211, -189, 125, -128, -90],\n [-145, 10, 81, -10, 8, 115, 0],\n [-33, 108, 50, -47, 20, -110, -18],\n [-65, -47, 107, -58, 88, 62, -176],\n [33, -126, -149, 125, -119, -82, 114],\n [-1, 28, -21, 9, -25, -142, 10],\n [-88, 253, 128, -107, 49, -60, 22]]\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 7x7 matrix:\n[[-156, 11, -168, 47, -107, -1, -85],\n [-2, -13, -17, 14, -128, -35, 17],\n [-166, 37, -119, -28, 152, 283, -71],\n [236, -120, 3, 197, -363, -228, 112],\n [171, -14, 179, -74, 87, -186, 22],\n [-117, 114, -84, 60, -135, -81, 12],\n [-24, -133, -281, 100, -183, 152, -170]]\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[[-72, 48, 32, -64, -24, -56, 16],\n [90, -60, -40, 80, 30, 70, -20],\n [36, -24, -16, 32, 12, 28, -8],\n [-99, 66, 44, -88, -33, -77, 22],\n [-36, 24, 16, -32, -12, -28, 8],\n [-9, 6, 4, -8, -3, -7, 2],\n [54, -36, -24, 48, 18, 42, -12]]\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[[-13, -24, 16, 1, 9, 26, 15],\n [-15, 8, 64, 11, 19, -2, 21],\n [-1, 16, 24, 5, 5, -14, 3],\n [-14, -66, -34, -10, 0, 64, 12],\n [-19, -15, 49, 7, 18, 20, 24],\n [45, 63, -81, -9, -36, -72, -54],\n [57, 103, -73, -5, -40, -112, -66]]\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[[-51, -66, -20, 16, 280, -45, -57],\n [-105, 126, -16, -127, -24, 99, -4],\n [-90, -53, -64, 68, 142, 70, 79],\n [55, 151, -29, -143, -52, 69, -6],\n [-85, -66, -98, 98, 330, 71, 72],\n [-29, -19, -96, 5, 98, 75, 89],\n [-140, -96, -51, 3, 122, -376, -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[[-30, 40, -120, -60, 0, -100, 60],\n [0, 0, 0, 0, 0, 0, 0],\n [15, -20, 60, 30, 0, 50, -30],\n [-18, 24, -72, -36, 0, -60, 36],\n [21, -28, 84, 42, 0, 70, -42],\n [-30, 40, -120, -60, 0, -100, 60],\n [-6, 8, -24, -12, 0, -20, 12]]\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[[0, 48, -62, -46, -102, 56, 44],\n [2, -52, 70, 50, 113, -62, -50],\n [20, 80, -75, -75, -145, 80, 50],\n [-76, -16, -87, 9, -61, 32, 74],\n [-72, -48, -40, 40, 12, -8, 40],\n [48, 48, 6, -42, -42, 24, -12],\n [-60, -48, -23, 41, 27, -16, 26]]\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[[80, 284, 158, 144, 159, 104, -93],\n [-73, -59, -118, -47, 36, -90, -71],\n [-45, -69, -91, -2, 60, -55, -83],\n [17, -24, -33, -72, 3, -101, -85],\n [26, 75, 33, -21, 31, -47, -46],\n [-21, 172, -27, -10, 178, -127, -202],\n [-110, -164, -64, 30, -100, 90, 232]]\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[[-77, -94, 50, 62, -23, 52, 29],\n [-17, -46, -10, 182, -71, -32, 5],\n [-65, -70, 50, -10, 5, 60, 25],\n [43, 56, -25, -58, 22, -23, -16],\n [-4, 22, 25, -176, 69, 49, 3],\n [-44, -46, 35, -16, 7, 43, 17],\n [-45, -54, 30, 30, -11, 32, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[155, -46, -107, 79, -106, 25, 66],\n [83, -70, -73, 94, -8, 2, -1],\n [-19, -66, -128, 12, 328, 119, -81],\n [35, 84, -58, -147, 72, 180, 50],\n [122, -75, -119, 107, -29, 0, 34],\n [81, -138, -96, 210, -36, -135, -3],\n [134, -60, -88, 105, -114, -21, 53]]\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, -172, -48, 148, -93, 94, -105],\n [2, 133, 216, 29, 66, -185, 119],\n [-245, -154, -79, -100, -46, 16, -120],\n [240, 229, -23, -15, 41, -30, 101],\n [-91, -68, 79, -87, 36, -2, -20],\n [13, 36, -8, 239, -109, 58, -61],\n [144, 105, -105, -29, -19, 105, -28]]\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[[-74, 113, -53, -83, 87, -21, -20],\n [28, 108, -86, -58, 138, 16, 12],\n [198, -54, -13, 16, 43, 51, 59],\n [281, -88, 13, 6, 23, 76, 109],\n [162, -86, 52, -95, -8, -11, 23],\n [-77, -115, 98, -123, -88, -141, -151],\n [194, 3, -40, 62, 56, 107, 128]]\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[[-164, 64, -100, 187, 27, 195, -137],\n [-26, -164, 4, 86, -118, -8, -110],\n [-58, 62, 42, 84, 62, 154, -16],\n [71, -153, -59, -84, -135, -221, -22],\n [-114, 138, -42, 114, 96, 192, -42],\n [-148, -30, -86, 195, -39, 151, -169],\n [-111, 97, -77, 108, 55, 141, -66]]\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 7x7 matrix:\n[[104, 54, -25, 133, -60, 34, -77],\n [-148, 73, -48, -64, -99, 17, 161],\n [90, 18, 109, 33, 133, -121, -134],\n [-16, 178, -52, 158, -111, -72, -31],\n [26, 98, -43, 201, -104, -109, -165],\n [-90, -127, -48, -250, 17, 238, 303],\n [48, 230, 64, 179, -19, -189, -132]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 6, 168, -107, 121, -51, -145],\n [-124, -159, 17, -74, -345, 49, -162],\n [114, -19, 164, 79, 247, -132, -133],\n [-26, -47, -177, -17, -30, 110, 314],\n [37, 41, 17, -94, -11, 48, -22],\n [64, -37, 110, 225, 230, -197, -148],\n [7, 235, 22, 173, 38, -90, -33]]\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[[1, 50, -9, -61, -20, -48, 150],\n [-46, -113, -72, 52, 110, 102, -96],\n [-62, -103, -108, 8, 130, 90, 24],\n [-53, -139, -81, 71, 130, 126, -138],\n [50, 124, 78, -58, -120, -112, 108],\n [48, 78, 84, -4, -100, -68, -24],\n [-26, -31, -48, -12, 50, 26, 48]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 7x7 matrix:\n[[-88, 40, -64, 0, -72, 40, -16],\n [-110, 50, -80, 0, -90, 50, -20],\n [55, -25, 40, 0, 45, -25, 10],\n [22, -10, 16, 0, 18, -10, 4],\n [77, -35, 56, 0, 63, -35, 14],\n [11, -5, 8, 0, 9, -5, 2],\n [-99, 45, -72, 0, -81, 45, -18]]\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[[16, 8, -28, 40, 32, 12, 8],\n [-32, -16, 56, -80, -64, -24, -16],\n [28, 14, -49, 70, 56, 21, 14],\n [-36, -18, 63, -90, -72, -27, -18],\n [-8, -4, 14, -20, -16, -6, -4],\n [20, 10, -35, 50, 40, 15, 10],\n [-12, -6, 21, -30, -24, -9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[79, -102, -37, -26, -94, 116, -21],\n [-84, 109, -110, -126, 253, 160, 79],\n [77, 181, 81, -66, -99, 10, -118],\n [-99, 295, 57, -178, 227, -26, 72],\n [139, 249, 76, 39, -103, -158, 14],\n [53, 448, 92, -31, 13, -102, -107],\n [-128, 92, -32, -44, 211, 5, 50]]?\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, -71, 30, 79, 13, 8, -62],\n [72, -86, -74, 133, 67, 100, -47],\n [-11, -111, 42, -92, 66, 48, 20],\n [-18, 22, -5, -153, 22, 12, 84],\n [1, 39, -24, -143, 45, 12, 71],\n [157, 63, -123, 230, 159, 4, -186],\n [164, -4, -137, 115, 230, 76, -124]]\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 7x7 matrix:\n[[-7, 4, -10, 6, -6, -7, -10],\n [84, -48, 120, -72, 72, 84, 120],\n [-56, 32, -80, 48, -48, -56, -80],\n [21, -12, 30, -18, 18, 21, 30],\n [-56, 32, -80, 48, -48, -56, -80],\n [-7, 4, -10, 6, -6, -7, -10],\n [77, -44, 110, -66, 66, 77, 110]]\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[[-224, -82, -49, 82, 211, 231, -14],\n [130, 282, 28, -87, -194, -130, 77],\n [-68, 174, -49, 125, -57, 101, 222],\n [-73, -40, -75, 47, -74, 15, -106],\n [118, 180, -2, -145, -40, -169, 92],\n [100, 230, 163, -64, -459, -282, -166],\n [199, -20, -179, -91, 79, 15, 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[[0, 0, 0, 0, 0, 0, 0],\n [108, -27, -45, -81, -18, 63, 99],\n [-96, 24, 40, 72, 16, -56, -88],\n [144, -36, -60, -108, -24, 84, 132],\n [144, -36, -60, -108, -24, 84, 132],\n [72, -18, -30, -54, -12, 42, 66],\n [48, -12, -20, -36, -8, 28, 44]]\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 7x7 matrix:\n[[-40, 43, -201, -75, 118, 100, 0],\n [-73, 45, -45, 62, -142, 1, -22],\n [17, -13, -98, -45, -72, 120, 19],\n [-17, -18, -50, -27, -27, 22, 26],\n [-52, 96, -133, -113, 148, -48, -107],\n [-90, 22, -264, -41, 213, -55, -23],\n [101, -30, 58, -5, -52, 118, 16]]\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 7x7 matrix:\n[[36, 24, 21, 9, -27, 9, 21],\n [84, 56, 49, 21, -63, 21, 49],\n [-60, -40, -35, -15, 45, -15, -35],\n [120, 80, 70, 30, -90, 30, 70],\n [-132, -88, -77, -33, 99, -33, -77],\n [0, 0, 0, 0, 0, 0, 0],\n [-60, -40, -35, -15, 45, -15, -35]]\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[[56, -14, 35, 42, -7, 42, -63],\n [72, -18, 45, 54, -9, 54, -81],\n [-24, 6, -15, -18, 3, -18, 27],\n [-80, 20, -50, -60, 10, -60, 90],\n [-80, 20, -50, -60, 10, -60, 90],\n [-64, 16, -40, -48, 8, -48, 72],\n [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[[-115, -54, -171, 174, 216, -206, 133],\n [51, 109, 53, -208, -180, 167, -59],\n [27, -87, 96, -126, -118, -3, -73],\n [-12, 107, 91, -23, -84, 263, -235],\n [76, -200, 41, 129, 112, -242, 93],\n [29, -19, -110, 12, 55, -200, 302],\n [81, -116, -16, 87, 118, -208, 112]]?\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[[170, 191, 87, -14, 4, 110, 98],\n [-79, -128, -195, 132, 34, -82, -146],\n [-123, 71, -115, 26, -144, 313, 83],\n [-90, 27, -128, -37, 8, 223, -124],\n [-2, -52, 71, -77, 98, -186, -26],\n [-73, -99, -104, 196, -198, -2, 101],\n [-56, -129, -53, -22, 96, -118, -188]]\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 7x7 matrix:\n[[-30, 80, 90, 30, 0, 30, -10],\n [36, -96, -108, -36, 0, -36, 12],\n [12, -32, -36, -12, 0, -12, 4],\n [33, -88, -99, -33, 0, -33, 11],\n [33, -88, -99, -33, 0, -33, 11],\n [-18, 48, 54, 18, 0, 18, -6],\n [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[[-16, 143, -82, -16, 0, 153, -362],\n [-45, -2, 41, -57, -98, -15, 58],\n [-38, -141, -24, 54, 79, -43, 10],\n [184, 179, 191, 78, 9, 170, -52],\n [95, -220, 253, -179, -250, -127, -49],\n [44, 244, 116, 118, 7, 180, 99],\n [124, -40, -78, -24, 132, 38, -302]]\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[[-45, -35, 30, 50, 40, 60, -10],\n [-63, -49, 42, 70, 56, 84, -14],\n [99, 77, -66, -110, -88, -132, 22],\n [-54, -42, 36, 60, 48, 72, -12],\n [45, 35, -30, -50, -40, -60, 10],\n [81, 63, -54, -90, -72, -108, 18],\n [108, 84, -72, -120, -96, -144, 24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[81, -115, -42, -51, 18, -15, 240],\n [-121, 164, -37, 19, 37, 6, -94],\n [-32, -88, -56, 42, -22, 98, 30],\n [-34, -164, -166, 147, -137, 85, -37],\n [-119, 199, 64, -83, 152, 55, 4],\n [-32, -98, -50, 90, -76, 92, -86],\n [-126, 45, -33, -44, 123, 161, 132]]\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[[4, -22, 26, -4, -86, -86, -64],\n [104, 13, -46, -58, -67, -54, -15],\n [108, -33, -42, -114, 7, 152, -5],\n [-100, -142, 130, 196, -152, -195, -210],\n [47, 85, -65, -179, 94, 171, 129],\n [-46, 38, -5, -20, 86, 83, 73],\n [-14, -114, 86, -34, -134, -11, -160]]\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[[75, -43, 181, 287, -228, -102, 23],\n [70, 91, 117, -95, -16, 150, -61],\n [103, 128, -89, 11, -91, 111, -103],\n [202, 144, 93, -242, 20, 307, 70],\n [-47, -149, 50, 27, 44, -85, 189],\n [111, 28, 70, 87, -219, 40, 57],\n [-86, 35, 61, -49, -154, 38, -129]]?\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[[97, -93, -84, 54, -7, -48, 141],\n [29, -99, -142, 112, 76, -184, 360],\n [71, -62, -12, -255, -107, 189, -244],\n [55, 117, -160, 33, -56, 53, 76],\n [102, 199, -176, 26, -157, 166, 10],\n [-196, 25, 64, -51, 169, 1, 6],\n [65, 66, -119, 163, -57, 20, 269]]\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, -44, 20, 107, 12, 14, -42],\n [-16, -43, -52, -177, -34, -2, 81],\n [26, 297, -8, -28, -208, 103, 57],\n [-66, -269, -12, 1, 188, -100, -63],\n [-12, -170, 96, 116, 196, -82, -14],\n [248, -60, 136, 78, 43, 16, 139],\n [-158, 14, -96, -28, -14, -16, -120]]\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 7x7 matrix:\n[[184, -7, 26, 34, 162, -267, 56],\n [-157, -25, -88, -44, 42, 11, 132],\n [-310, -305, -275, 203, -79, -390, 58],\n [182, 137, 319, -103, 43, 106, 46],\n [-289, -238, -224, 156, -41, -224, 57],\n [111, -15, 81, -35, 33, -192, -21],\n [-26, -102, -99, 151, 26, -163, 17]]\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[[109, 113, -170, 219, -183, 200, 332],\n [-133, -65, 127, 41, 147, 2, 77],\n [-35, -84, -160, 42, 3, 16, 51],\n [39, 1, -93, 179, 128, -78, -24],\n [83, 70, -45, 76, -155, 138, -127],\n [-165, -142, 147, -131, 286, -225, -204],\n [60, 5, -52, -60, 76, -181, -146]]\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 7x7 matrix:\n[[174, 29, -121, -98, 286, -94, -115],\n [49, 104, 93, -167, 92, -92, -146],\n [23, 175, 235, 43, -7, 225, -106],\n [-114, 93, 98, -276, -44, -102, 81],\n [-95, -141, -126, -67, -183, -179, 248],\n [324, -84, -221, 188, 224, -12, -78],\n [2, 47, -13, 12, 236, 66, -219]]\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[[-98, 15, 90, 70, -29, -175, 88],\n [306, 237, -312, -126, -78, 74, -68],\n [61, 40, -126, -6, 24, -56, 3],\n [-53, -76, 126, 97, 160, 159, -178],\n [-38, -84, -42, -46, -19, -47, 92],\n [-140, 71, 234, 160, -11, -171, 20],\n [-59, -12, 108, -18, -87, -13, 67]]?\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 7x7 matrix:\n[[82, 122, 3, 119, 236, -101, 153],\n [-226, -278, -66, -148, -180, -92, -274],\n [125, 185, 90, 72, 29, -1, 29],\n [-19, 14, 147, -28, -142, 4, -64],\n [-30, 10, 60, -4, -42, -122, -146],\n [4, -13, -21, -52, -125, 83, -91],\n [22, 16, -138, 35, 135, -86, -45]]\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[[130, -124, -123, 24, -110, 85, -25],\n [139, -37, -36, 54, -107, -62, -46],\n [-56, -20, 52, 42, 17, -12, 6],\n [60, -114, 23, 134, -99, -45, -37],\n [14, 98, 116, 54, -5, -192, -30],\n [178, -128, -81, 92, -160, -9, -55],\n [-47, -53, 5, 22, 11, 51, 13]]\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, -88, -124, -128, -46, 58, -70],\n [107, -155, -212, -140, -18, 131, -103],\n [-99, 153, 210, 148, 25, -126, 104],\n [-63, 117, 162, 132, 33, -90, 84],\n [88, -130, -178, -120, -17, 109, -87],\n [66, -138, -192, -168, -48, 102, -102],\n [-75, 39, 48, -36, -48, -57, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[19, -8, -18, 12, 33, 37, -22],\n [-2, 164, 119, 24, 1, -36, -64],\n [-25, -147, -92, -51, -46, -8, 71],\n [74, -21, -36, 159, 111, 43, 135],\n [138, 21, -29, 285, 212, 87, 185],\n [-2, 270, 210, 102, -6, -112, 18],\n [-58, 171, 141, -93, -84, -71, -153]]?\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[[-43, 138, 112, 79, -191, -196, 48],\n [74, 62, 94, 103, -60, -96, 99],\n [6, -28, -24, -18, 38, 40, -12],\n [-56, 42, 14, -7, -70, -56, -21],\n [33, -60, -42, -24, 87, 84, -9],\n [118, -18, 38, 71, 56, 16, 87],\n [-4, 144, 136, 112, -188, -208, 84]]?\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 7x7 matrix:\n[[127, -30, -193, -8, 42, 79, 195],\n [-61, -36, 154, 64, -54, -47, -152],\n [139, -31, -210, 128, 152, 174, 156],\n [-28, -12, 68, 0, -24, -68, -76],\n [59, -131, 75, 60, -68, -133, -92],\n [6, -80, 48, 16, -100, -70, -24],\n [-185, -99, -39, 112, -220, -68, 67]]\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[[55, -161, 87, 35, 66, 46, -18],\n [50, -23, 163, 6, 19, 41, -176],\n [99, -273, 52, -25, -146, 10, 7],\n [-44, -46, 1, 14, -232, -90, -21],\n [-230, 132, -165, 59, -37, -66, 119],\n [-244, 130, -71, -25, 177, 137, 30],\n [-206, 179, -85, -47, 112, 94, 25]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[36, -171, -165, 36, -102, 33, 69],\n [-15, 192, 242, 27, 137, -40, -97],\n [60, -152, -88, 124, -76, 40, 36],\n [45, -27, 55, 141, 1, 25, -26],\n [24, -67, -44, 47, -35, 17, 18],\n [-21, -93, -176, -108, -80, 7, 73],\n [9, -85, -99, -19, -51, 7, 44]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-61, -235, -34, 60, -176, -155, 194],\n [89, 131, 230, 132, 4, -32, 5],\n [68, -203, 43, -31, 42, 41, -65],\n [40, -25, 63, 19, -17, 15, 1],\n [-23, -131, -188, -174, 44, 137, -92],\n [74, -65, 33, -59, 51, 115, -97],\n [41, 126, 97, 47, -37, 28, 17]]\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[[144, 9, -18, -90, 0, -162, -81],\n [-24, 21, -2, 60, -50, 42, 51],\n [-20, 1, 2, 17, -5, 24, 15],\n [84, 39, -18, 15, -75, -72, 9],\n [-72, -27, 14, 0, 50, 66, 3],\n [-96, 12, 8, 96, -40, 120, 84],\n [-64, -49, 18, -50, 100, 42, -39]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-75, 60, 110, 110, 5, -20, 35],\n [42, -28, -52, -53, -3, 11, -18],\n [-150, -20, -20, 5, 15, -35, 30],\n [-75, 32, 62, 67, 6, -19, 27],\n [30, 4, 4, -1, -3, 7, -6],\n [-90, -12, -12, 3, 9, -21, 18],\n [-18, 20, 36, 35, 1, -5, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[162, 46, 8, -184, -120, 50, -138],\n [-165, -95, 44, 76, 12, -141, -3],\n [-11, -90, 173, -86, -115, -143, -81],\n [-49, 45, -122, 120, 118, 79, 99],\n [95, 145, -231, 26, 97, 219, 42],\n [-31, 29, -43, 122, 109, 61, 138],\n [133, 27, 74, -104, -70, 37, -27]]\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 7x7 matrix:\n[[-180, -38, 48, -92, -16, -64, 72],\n [112, -228, 14, -299, -66, -80, -106],\n [96, 56, 94, 126, 92, -2, -2],\n [-56, -24, -103, -71, -78, 25, -7],\n [-18, 5, 88, 21, 50, -38, 28],\n [268, -166, -13, -174, -32, -19, -157],\n [80, -180, 17, -237, -50, -67, -79]]\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[[-147, -179, 25, -81, 180, -41, 257],\n [-103, -16, 202, -84, 172, -116, 271],\n [272, 247, -38, 122, 7, 26, -171],\n [-194, -37, 155, -58, -158, -47, 10],\n [19, -151, 70, -49, 181, -5, 172],\n [-72, -291, -111, 165, -42, 183, -96],\n [-86, 71, 36, -240, -33, -38, 53]]\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[[-31, -9, -59, 94, 120, -26, 57],\n [88, -179, 174, -174, -18, -173, 12],\n [-38, 160, -125, 202, 84, 71, -13],\n [-19, 6, 102, -30, -42, 6, 76],\n [-117, -65, -76, -86, -124, 112, -82],\n [8, -190, 91, -198, -76, -71, -13],\n [80, 237, 80, 174, 64, 7, 104]]\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[[-239, -71, 88, 46, -64, 64, -32],\n [-160, 1, 124, 181, -177, 94, 44],\n [48, 49, 91, 75, -164, 44, -54],\n [-133, -60, -22, 120, -186, 144, 20],\n [214, -25, 73, 98, -1, 104, -61],\n [-31, 56, 230, 152, -68, 14, 5],\n [-13, 26, 223, 188, -19, 44, 35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-56, 77, -70, 7, -49, -7, -42],\n [16, -22, 20, -2, 14, 2, 12],\n [16, -22, 20, -2, 14, 2, 12],\n [0, 0, 0, 0, 0, 0, 0],\n [72, -99, 90, -9, 63, 9, 54],\n [-64, 88, -80, 8, -56, -8, -48],\n [8, -11, 10, -1, 7, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-150, 54, 188, 133, -11, -50, 145],\n [-260, 172, 333, 44, -228, 136, 127],\n [62, -121, -158, 11, 165, -92, 5],\n [-6, -21, 9, 236, 109, -156, 217],\n [-2, 51, 124, -31, -66, 8, -29],\n [224, -99, -199, 27, 103, -86, 42],\n [-20, 84, 16, -87, -167, 80, -39]]?\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 7x7 matrix:\n[[11, -206, 47, 79, -156, 71, 22],\n [109, -109, 69, 178, 41, 168, 90],\n [-76, -26, 77, -203, -136, -16, 136],\n [-1, -200, -116, 108, -66, -29, 20],\n [-18, 128, 139, -99, -35, 30, -71],\n [-117, 225, 1, -284, -1, -152, -34],\n [-45, 180, 107, -115, -36, -31, -176]]\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[[52, 16, 88, -56, 84, -40, 88],\n [1, 94, 48, -14, 105, -4, 48],\n [72, -18, 102, -72, 72, -54, 102],\n [-96, 111, -93, 84, 0, 69, -93],\n [95, -31, 131, -94, 87, -71, 131],\n [-58, 29, -75, 56, -42, 43, -75],\n [64, -74, 62, -56, 0, -46, 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[[81, 80, 93, 29, 120, -170, 37],\n [-254, -245, 110, -317, -155, 58, -158],\n [-127, -150, 9, -235, -121, 66, -16],\n [148, 224, 53, 120, 241, -165, 5],\n [-76, -58, 40, 14, -31, 21, -100],\n [17, 45, 50, -94, -3, -49, -23],\n [-144, -151, -107, -113, 15, 110, -31]]?\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[[90, 58, -34, -93, 30, -93, 137],\n [168, 23, -79, -29, 29, 15, 134],\n [-105, 56, 106, 85, -47, 73, -158],\n [96, 68, 123, 28, 75, 64, -83],\n [-186, 11, -173, 91, -239, 55, 46],\n [165, 113, 98, -130, 135, -118, 85],\n [-18, -4, 132, -70, 106, -94, -68]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -60, -48, 30, 66, 66, 48],\n [-7, 70, 56, -35, -77, -77, -56],\n [-5, 50, 40, -25, -55, -55, -40],\n [-2, 20, 16, -10, -22, -22, -16],\n [-5, 50, 40, -25, -55, -55, -40],\n [-11, 110, 88, -55, -121, -121, -88],\n [-10, 100, 80, -50, -110, -110, -80]]\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[[99, 0, 75, -66, 42, -225, -129],\n [33, -55, -95, -77, 169, -45, -83],\n [-60, 30, 20, 70, -110, 120, 100],\n [-42, 10, -10, 38, -46, 90, 62],\n [-15, -20, -55, -10, 50, 45, 5],\n [36, -18, -12, -42, 66, -72, -60],\n [51, -64, -101, -98, 202, -81, -113]]?\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[[63, -130, 177, -111, -124, -155, 86],\n [34, 13, 60, -112, -216, -75, -30],\n [2, -249, 120, -162, 136, -199, 37],\n [46, -46, 58, -118, 112, -88, 20],\n [21, -110, 41, -272, 16, -67, 147],\n [147, -123, 88, -285, -72, -210, 27],\n [-46, 42, -154, -238, 196, 122, 122]]\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 7x7 matrix:\n[[-60, -15, 95, -112, -63, 11, 101],\n [-177, -183, 118, -58, 5, 40, -7],\n [-91, -74, 79, -66, -18, 1, 30],\n [-24, -84, -40, 100, 64, 56, -104],\n [18, -3, -32, 45, 22, 16, -36],\n [166, 161, -110, 67, -8, 10, 10],\n [-109, -119, 60, -20, 19, 6, -29]]\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[[66, -9, -68, -1, -157, 38, -8],\n [-10, -31, -126, -145, -13, -104, 100],\n [-8, -86, 111, 13, 97, 59, -106],\n [-81, 51, 79, 32, 173, -46, 25],\n [61, -62, -10, -2, -101, 67, -65],\n [-18, 57, -67, -26, -14, -65, 86],\n [9, 12, 66, 76, 1, 59, -57]]?\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 7x7 matrix:\n[[102, 114, 172, -133, 76, -98, 133],\n [-21, -43, 124, 16, 59, 159, -75],\n [-31, 129, 248, 88, 22, 123, 78],\n [-195, 146, 28, 79, -155, 48, 120],\n [-6, 54, 18, 74, -2, -31, 46],\n [20, -232, -110, -28, 151, 29, -213],\n [-53, -193, -78, -15, 81, 104, -192]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 171, -90, 33, 36, -150, -204],\n [-150, 194, -36, -169, -218, 68, 70],\n [-52, 83, 15, -41, 0, 17, 16],\n [-90, -4, 138, -69, 66, 150, 194],\n [112, -178, -69, 72, -76, -43, -44],\n [92, 37, -102, 99, 52, -170, -220],\n [-18, -35, 123, 18, 174, 69, 94]]?\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 7x7 matrix:\n[[-54, 2, -8, -35, -38, -150, 171],\n [61, -66, 58, -15, 107, 62, -53],\n [-13, 90, -10, -93, -47, 22, 47],\n [113, 31, 41, -152, 132, -173, 57],\n [68, -21, 47, -121, 111, -151, 80],\n [-70, -162, 229, -28, 156, -69, 20],\n [-64, -180, 243, 82, 166, 71, -23]]\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[[25, -9, -22, 52, -4, -15, -32],\n [-17, 18, 18, -81, 52, 67, -6],\n [-57, -10, 50, -19, -57, -51, 52],\n [120, 12, -128, 122, -79, -98, 158],\n [86, 29, -96, 31, -47, -48, 180],\n [76, 34, -64, -48, 141, 146, -86],\n [-69, -5, 70, -68, 21, 33, -46]]\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[[-207, -23, -130, 22, 92, -82, 97],\n [-194, -302, 46, 54, 84, 31, 24],\n [-167, 13, -76, -136, 410, -67, 197],\n [-2, 162, 48, -62, -39, 74, 9],\n [-115, -95, -82, -66, 326, -65, 95],\n [-176, -100, 38, -11, 248, -125, -21],\n [-89, 183, 46, -92, 150, -74, 79]]?\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[[-134, 12, 232, 20, 118, 98, 12],\n [76, 21, -139, 101, -88, -127, 84],\n [28, 17, -11, -105, -44, 119, -198],\n [-65, -102, 66, -109, 147, -10, 111],\n [-33, -63, 19, -27, 85, -54, 126],\n [-121, 46, 246, -33, 75, 202, -153],\n [84, 66, -106, 36, -136, 12, -126]]\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[[-49, -17, -43, 42, -76, 15, 13],\n [66, -32, -128, -113, 69, 0, 18],\n [-5, -13, 105, 27, -5, -119, 33],\n [12, 38, -62, -19, 27, 142, -56],\n [26, 33, 167, 17, 59, -70, -12],\n [82, -11, -157, -133, 97, 70, -12],\n [-51, -54, 50, 57, -87, -155, 73]]\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[[-28, -63, 21, 42, -21, -49, 21],\n [-32, -72, 24, 48, -24, -56, 24],\n [-40, -90, 30, 60, -30, -70, 30],\n [-48, -108, 36, 72, -36, -84, 36],\n [44, 99, -33, -66, 33, 77, -33],\n [20, 45, -15, -30, 15, 35, -15],\n [-24, -54, 18, 36, -18, -42, 18]]\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[[-34, 8, -39, -22, 33, -60, 17],\n [-15, -123, 63, 42, 6, -144, 66],\n [54, -102, -129, 150, -189, 0, 57],\n [82, -104, 27, 126, -149, 60, 19],\n [21, -12, -222, 96, -153, 18, 36],\n [-70, 110, 114, -164, 208, -24, -52],\n [19, 63, -25, -14, -16, 96, -40]]\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 7x7 matrix:\n[[-170, -154, 422, -119, -137, -150, -277],\n [-75, -42, 223, 149, 4, -94, -195],\n [-295, -220, 153, -97, -177, -109, -97],\n [-123, -97, -111, -151, -56, 25, 220],\n [-143, -113, -27, -292, -156, 0, 147],\n [-115, -93, 50, -90, -89, 15, -34],\n [-133, -77, -147, 88, -20, 66, 69]]\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[[22, 17, -57, -367, 39, 225, 152],\n [212, -9, 27, 63, 31, 29, -116],\n [-28, 210, -148, 4, 157, -103, 96],\n [156, 33, -57, -169, 94, -16, 76],\n [-26, 73, -21, -7, 68, 48, 48],\n [-17, -210, 138, 5, -184, 105, -46],\n [20, 247, -171, -95, 183, 39, 44]]\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[[-30, -52, -124, -5, 64, 53, -28],\n [16, 32, 76, 4, -40, -32, 18],\n [-14, -52, -122, -11, 68, 49, -33],\n [54, 36, 90, -9, -36, -45, 9],\n [28, 8, 22, -8, -4, -14, -3],\n [-12, 24, 54, 12, -36, -18, 21],\n [56, 48, 118, -6, -52, -56, 17]]\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[[38, -20, 136, 20, 11, 13, 133],\n [-83, -30, -198, -131, -66, -32, -215],\n [-120, -89, 314, 242, 68, 91, 115],\n [-12, -120, 248, 0, -13, 33, 159],\n [67, 61, -144, -8, 89, -30, -106],\n [21, 139, -212, -8, 136, -71, -164],\n [111, 24, -110, -119, 61, -17, -76]]?\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 7x7 matrix:\n[[31, -61, -29, 12, -132, -25, -64],\n [66, -48, 48, -108, 21, 33, -69],\n [95, -75, 41, -36, -73, 48, -53],\n [-190, 80, -178, 198, -121, -169, 54],\n [185, -77, 173, -186, 115, 166, -48],\n [-4, -20, -52, 144, -160, -20, 32],\n [93, -51, 57, 0, -42, 75, 0]]\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 7x7 matrix:\n[[136, -76, -102, 22, 282, -56, -60],\n [406, 80, 56, -43, -14, -101, 28],\n [-90, 27, -31, 12, -59, -135, -32],\n [-20, 24, 17, 75, 65, -13, -109],\n [-41, 44, -13, 74, -272, -87, -1],\n [170, 98, 46, 124, -84, -111, -129],\n [205, -18, -45, -122, -86, -78, 168]]\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[[-22, -141, 79, 131, 203, -168, -160],\n [-15, 141, -18, -111, -153, 162, 114],\n [-21, -40, 71, -18, 43, -27, -48],\n [42, 52, -96, -38, -105, 57, 94],\n [-33, -53, 78, 43, 99, -60, -86],\n [15, -119, 38, 23, 88, -111, -76],\n [71, 39, -192, 93, -54, -3, 84]]\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, 18, 81, 186, 42, -132, -81],\n [144, -124, 14, -68, 40, 8, 38],\n [42, -34, -10, -48, 3, 24, 23],\n [120, -112, 68, 56, 68, -80, -16],\n [-96, 90, -57, -50, -56, 68, 15],\n [-36, 42, -75, -126, -54, 108, 51],\n [6, 6, -72, -148, -43, 112, 63]]\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[[9, -84, 51, -48, 33, 33, -12],\n [80, -160, -38, -126, -110, -88, 62],\n [-26, 136, -58, 84, -22, -26, 4],\n [74, -104, -72, -94, -132, -110, 70],\n [-45, -60, 147, -6, 165, 147, -78],\n [36, -176, 70, -110, 22, 28, -2],\n [-4, 144, -112, 76, -88, -84, 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[[-48, 8, 56, -80, 40, 64, 24],\n [-7, 12, 2, 2, 5, -9, 10],\n [33, -103, 17, -68, -20, 121, -75],\n [14, -24, -4, -4, -10, 18, -20],\n [-30, 135, -39, 114, 15, -180, 93],\n [-61, 86, 28, -6, 45, -47, 76],\n [48, -8, -56, 80, -40, -64, -24]]\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 7x7 matrix:\n[[63, 9, 9, 36, 108, 27, -81],\n [21, 3, 3, 12, 36, 9, -27],\n [-7, -1, -1, -4, -12, -3, 9],\n [28, 4, 4, 16, 48, 12, -36],\n [-49, -7, -7, -28, -84, -21, 63],\n [-28, -4, -4, -16, -48, -12, 36],\n [-21, -3, -3, -12, -36, -9, 27]]\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[[73, 74, 148, -132, -36, 76, 133],\n [0, 240, 42, -144, -172, -10, 92],\n [-62, -76, -128, 120, 40, -64, -118],\n [15, -90, 12, 36, 68, 20, -13],\n [-34, 28, -58, 24, -28, -38, -38],\n [35, -50, 56, -12, 44, 40, 31],\n [106, -52, 187, -96, 62, 117, 132]]\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[[-80, -80, -30, -30, -90, 20, 110],\n [-32, -32, -12, -12, -36, 8, 44],\n [-64, -64, -24, -24, -72, 16, 88],\n [-56, -56, -21, -21, -63, 14, 77],\n [-72, -72, -27, -27, -81, 18, 99],\n [32, 32, 12, 12, 36, -8, -44],\n [64, 64, 24, 24, 72, -16, -88]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-111, -4, -96, -21, 122, 33, 74],\n [5, 154, -19, -105, 0, 69, -32],\n [132, -1, 108, 118, 127, -253, 236],\n [-288, 82, -148, 7, 125, 150, 35],\n [41, 19, 62, 91, 8, -19, 73],\n [-22, 31, -40, -4, 193, -125, 190],\n [-105, 165, -14, 6, 43, 41, 26]]\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[[196, -71, -12, -217, 61, -91, 19],\n [70, 39, -59, -66, -47, -57, 141],\n [23, 22, 30, 70, 65, 38, -32],\n [-221, 4, 115, 65, -17, 80, -142],\n [-195, 119, 216, 172, -26, -188, -138],\n [76, 106, 71, -46, 30, -235, -11],\n [-92, 161, 42, 33, -15, -59, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-119, 56, 197, -35, 96, 113, 241],\n [-31, -40, -74, -62, -177, -226, -17],\n [-110, 222, -107, 29, 18, 297, 276],\n [59, -199, 136, -139, -110, -24, 45],\n [19, -414, 164, 48, 11, 164, -33],\n [-11, -140, 8, 74, -43, -240, -211],\n [89, -113, 82, -144, 150, 214, 184]]?\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[[49, -35, -84, 77, 77, 14, 42],\n [49, -35, -84, 77, 77, 14, 42],\n [-28, 20, 48, -44, -44, -8, -24],\n [-70, 50, 120, -110, -110, -20, -60],\n [49, -35, -84, 77, 77, 14, 42],\n [42, -30, -72, 66, 66, 12, 36],\n [35, -25, -60, 55, 55, 10, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[42, 90, -30, -94, 61, -72, 13],\n [-170, 16, 62, -6, -43, 90, -187],\n [-11, 121, -47, -87, -27, -113, 47],\n [83, -39, 52, 67, 87, -12, 70],\n [-16, 175, -82, -76, 35, -57, -76],\n [143, 83, 63, 135, 221, -71, 73],\n [118, 106, 72, 54, 217, -94, 59]]\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[[-1, 175, 88, 148, -80, 135, -201],\n [-11, 38, -134, -42, -146, 117, -55],\n [111, 21, 38, 79, 14, -33, -22],\n [50, 59, -6, 32, -37, 84, -7],\n [-10, 173, 160, 149, 4, 134, -123],\n [-6, 57, 40, 95, -53, -24, -182],\n [-120, 35, -104, -79, -118, 132, -47]]?\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[[42, 78, -62, -14, 71, 21, -90],\n [60, -68, -140, -113, 187, 48, 59],\n [114, -110, 34, 94, 132, 155, 109],\n [-93, 114, -65, -86, -219, -212, -224],\n [-175, 200, 45, -45, -245, -201, -165],\n [-163, 184, 217, 76, -15, 41, 135],\n [-54, 32, -22, -85, 119, 24, 109]]\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[[53, -37, 97, -13, -18, 40, -104],\n [-12, -54, 82, -8, -78, -20, -122],\n [-12, -54, 82, -8, -78, -20, -122],\n [1, -62, 104, -11, -81, -10, -145],\n [-100, -13, -45, 10, -75, -90, 3],\n [-133, -19, -57, 13, -102, -120, 0],\n [0, 0, 0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-64, 12, -33, 81, 123, -72, -124],\n [62, 20, -3, -58, -82, 32, 96],\n [-72, -20, -9, 69, 39, -40, -76],\n [-16, 15, -42, 27, -93, -30, 47],\n [68, -111, 177, -148, -22, 190, 65],\n [-216, -101, 9, 180, 6, -70, -157],\n [-104, -122, 102, 40, 28, 52, -90]]?\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[[81, -18, 9, -27, 63, 36, 90],\n [27, -6, 3, -9, 21, 12, 30],\n [45, -10, 5, -15, 35, 20, 50],\n [-81, 18, -9, 27, -63, -36, -90],\n [0, 0, 0, 0, 0, 0, 0],\n [54, -12, 6, -18, 42, 24, 60],\n [54, -12, 6, -18, 42, 24, 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[[55, 99, 52, 69, -165, -194, 1],\n [51, -60, 156, -18, -9, -132, 69],\n [72, -85, -87, -231, 2, -79, 91],\n [-46, 7, -47, 17, 60, 109, -31],\n [-39, 57, 89, 121, 17, 10, -26],\n [-20, 75, 154, -37, 114, -119, 106],\n [38, -12, -141, -170, -14, -32, 43]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 7x7 matrix:\n[[-66, 66, 12, 24, 0, -36, -24],\n [66, -66, -12, -24, 0, 36, 24],\n [132, -132, -24, -48, 0, 72, 48],\n [44, -44, -8, -16, 0, 24, 16],\n [0, 0, 0, 0, 0, 0, 0],\n [-121, 121, 22, 44, 0, -66, -44],\n [121, -121, -22, -44, 0, 66, 44]]\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[[110, -51, 114, 30, 102, -90, 317],\n [100, 16, 31, 11, 93, -195, 300],\n [222, -268, 70, -266, -153, 61, -8],\n [-27, 72, 181, 127, 103, 20, 218],\n [120, -64, -7, -58, -60, 108, -74],\n [115, -132, -36, -44, -24, -33, 198],\n [46, -138, -45, -152, -112, -6, -56]]\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[[69, -41, 51, -29, 92, -102, -64],\n [47, -96, 48, 5, 83, -96, -10],\n [111, -76, 84, -43, 151, -168, -98],\n [-105, 126, -90, 21, -159, 180, 66],\n [-5, -93, 15, 37, 22, -30, 52],\n [59, -73, 51, -11, 90, -102, -36],\n [-103, 117, -87, 23, -154, 174, 68]]\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[[-89, 4, 67, 72, -81, -30, -121],\n [29, -4, 67, -43, -44, -71, 135],\n [-261, 152, 135, 168, -35, -68, -131],\n [-70, 152, 48, -4, 56, 28, 176],\n [164, -148, -135, -75, -2, 95, -77],\n [-116, 84, 61, 79, 64, -87, -21],\n [-76, 21, 197, 48, -125, -71, 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[[32, -8, 20, -20, 48, -24, 4],\n [-96, 24, -60, 60, -144, 72, -12],\n [32, -8, 20, -20, 48, -24, 4],\n [-88, 22, -55, 55, -132, 66, -11],\n [-56, 14, -35, 35, -84, 42, -7],\n [-8, 2, -5, 5, -12, 6, -1],\n [-16, 4, -10, 10, -24, 12, -2]]\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 7x7 matrix:\n[[24, 18, 9, -12, 0, -24, 27],\n [-8, -6, -3, 4, 0, 8, -9],\n [-32, -24, -12, 16, 0, 32, -36],\n [56, 42, 21, -28, 0, -56, 63],\n [80, 60, 30, -40, 0, -80, 90],\n [64, 48, 24, -32, 0, -64, 72],\n [24, 18, 9, -12, 0, -24, 27]]\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 7x7 matrix:\n[[-84, 59, 55, -16, -14, 39, 61],\n [90, -49, 21, 84, -34, 73, -39],\n [129, -57, -64, 52, 46, -56, -115],\n [-2, 3, 95, 5, 29, -124, 33],\n [28, 21, 89, 63, 27, -36, -13],\n [-7, -12, 70, -34, 44, -190, 38],\n [27, -54, -6, -13, -25, -25, 16]]\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 7x7 matrix:\n[[-111, -94, 68, -126, 20, 76, 25],\n [-26, 68, 46, -17, -41, -93, -13],\n [68, 41, -4, -16, 159, -81, -26],\n [-67, -9, 70, 191, 90, -214, -149],\n [-39, -4, 36, -236, 58, 86, 80],\n [-180, 141, -146, 50, -68, 162, 30],\n [170, 93, -28, -156, 11, 3, 89]]\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 7x7 matrix:\n[[42, 66, 39, -75, -48, 33, 3],\n [-30, -6, -21, -3, 0, 9, 27],\n [16, 56, 20, -71, -44, 37, 23],\n [-98, -34, -71, 10, 12, 18, 78],\n [112, 32, 80, -2, -8, -26, -94],\n [-104, -40, -76, 16, 16, 16, 80],\n [78, -18, 49, 54, 28, -50, -94]]\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[[44, 98, -7, 69, 102, 207, 107],\n [72, 148, 44, 128, 65, 81, 135],\n [-43, -183, 12, -137, -65, -112, -172],\n [-163, 107, 42, -82, -90, 118, -32],\n [-131, -45, -50, -116, -85, -7, -87],\n [-43, 105, 192, -11, -74, 5, -37],\n [-93, -7, 72, -102, -57, 71, -93]]?\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[[-298, 102, 201, 107, -169, -259, -24],\n [108, 105, 47, 39, 139, -99, 26],\n [55, 27, 23, -35, 42, 34, 46],\n [10, 14, -23, -29, -11, 20, 115],\n [82, 32, -91, -5, 51, -13, 170],\n [-149, -52, 17, -11, -144, 20, -16],\n [-182, 111, 179, 19, -109, -140, 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[[-122, -13, -133, 35, 3, 9, -45],\n [129, -163, 6, 5, -225, 18, -166],\n [47, 85, -1, -76, 92, 70, 128],\n [24, 205, 10, -94, -46, 16, 78],\n [72, -259, -5, 15, 97, 67, -77],\n [13, 72, -289, -174, -146, 204, -68],\n [-47, -158, -155, 24, -36, 62, -126]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 7x7 matrix:\n[[-56, -23, 99, 62, 55, -49, 18],\n [40, 2, -12, 12, -45, 14, -15],\n [82, -99, -12, 48, 32, -106, 32],\n [-46, 16, 33, 2, 21, 7, 2],\n [192, -131, -27, 102, -52, -117, 11],\n [-18, -51, 18, 12, 78, -72, 36],\n [34, -17, 84, 100, -53, -16, -19]]\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[[201, -77, -80, 86, 86, 138, 66],\n [-49, -54, -5, -27, 69, -129, 9],\n [72, 0, 123, 60, -57, 117, 36],\n [25, 36, 167, 68, -142, 138, -21],\n [127, 124, -145, 17, -181, 153, -105],\n [39, -84, -57, 29, 95, -27, 15],\n [109, 143, -188, -28, -92, 156, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-24, 45, -4, 88, 101, -56, -78],\n [50, 72, -19, 73, -160, 5, 30],\n [-70, -39, -4, -44, 169, 8, -22],\n [-32, -30, 131, 52, -67, -90, -27],\n [212, -54, -49, -119, -64, -55, -30],\n [-181, 247, -70, 228, 7, -114, 100],\n [238, -130, 105, -61, -232, 7, -98]]\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[[-16, 144, 186, 6, 170, -80, 76],\n [-34, 42, 90, -34, 78, -16, 24],\n [15, -75, -105, 5, -95, 40, -40],\n [-58, -30, 36, -76, 24, 32, -12],\n [-61, 81, 168, -60, 146, -32, 46],\n [31, -27, -69, 33, -59, 8, -16],\n [-50, -102, -57, -79, -61, 72, -50]]\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[[78, 94, -110, 20, 160, 74, 168],\n [-29, -21, 33, -10, -40, -27, -44],\n [-96, 158, 11, -81, 128, -91, 20],\n [53, 95, -88, 7, 144, 50, 136],\n [14, -6, -33, 13, 46, 21, 116],\n [-138, -48, 132, -58, -126, -128, -160],\n [212, -28, -121, 103, 6, 185, 4]]\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[[100, 100, -96, -36, 84, -120, 68],\n [35, 77, 0, -84, -21, -42, -56],\n [90, 98, -80, -46, 66, -108, 46],\n [55, 21, -80, 38, 87, -66, 102],\n [70, 74, -64, -32, 54, -84, 40],\n [-70, -114, 32, 100, -6, 84, 36],\n [80, 146, -24, -141, -12, -96, -71]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 7x7 matrix:\n[[-9, 27, 72, 81, 36, -81, 63],\n [-14, 18, 97, 114, 62, -126, 113],\n [-16, -8, 93, 116, 78, -144, 147],\n [1, -11, -13, -13, -2, 9, -2],\n [-16, 0, 98, 120, 76, -144, 142],\n [16, 40, -73, -100, -86, 144, -167],\n [6, -18, -48, -54, -24, 54, -42]]\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, -121, -121, 88, 110, -66, -99],\n [44, -121, -121, 88, 110, -66, -99],\n [36, -99, -99, 72, 90, -54, -81],\n [44, -121, -121, 88, 110, -66, -99],\n [-16, 44, 44, -32, -40, 24, 36],\n [-32, 88, 88, -64, -80, 48, 72],\n [16, -44, -44, 32, 40, -24, -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[[0, 0, 0, 0, 0, 0, 0],\n [77, 14, 28, 21, 49, -42, 21],\n [-22, -4, -8, -6, -14, 12, -6],\n [-110, -20, -40, -30, -70, 60, -30],\n [-121, -22, -44, -33, -77, 66, -33],\n [33, 6, 12, 9, 21, -18, 9],\n [-110, -20, -40, -30, -70, 60, -30]]?\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 7x7 matrix:\n[[-78, -226, 81, -64, -141, -81, -43],\n [10, -33, -11, -87, -122, -84, 76],\n [-204, -65, 91, 97, 96, -84, 28],\n [48, 149, -49, 47, 104, 60, 16],\n [-113, -39, 51, 117, 107, 6, -16],\n [-92, -161, 58, -29, -105, -99, 31],\n [230, 40, -92, -92, -102, 120, -68]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-147, -148, 131, 318, 110, 26, 58],\n [119, 329, -241, -253, 110, -210, -276],\n [-115, -113, 116, 79, -69, 133, 50],\n [50, -48, 2, 17, -130, 30, 78],\n [-68, -100, 78, 103, -168, 116, 58],\n [-48, -191, 130, 205, 96, 36, 174],\n [75, 6, -41, 7, -42, -42, 36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-132, -108, -24, -132, 96, 72, 60],\n [88, 72, 16, 88, -64, -48, -40],\n [44, 36, 8, 44, -32, -24, -20],\n [77, 63, 14, 77, -56, -42, -35],\n [132, 108, 24, 132, -96, -72, -60],\n [0, 0, 0, 0, 0, 0, 0],\n [-11, -9, -2, -11, 8, 6, 5]]\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[[32, 135, 104, -33, 69, 116, 89],\n [40, 75, 50, -51, 57, 90, 31],\n [28, 79, 49, -60, 81, 113, 0],\n [-68, 82, 43, -51, 162, 173, -135],\n [176, -99, -91, -96, -93, -76, 53],\n [140, -70, -60, -60, -90, -75, 75],\n [212, -37, -55, -156, -27, 19, 54]]\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[[162, -87, -68, -24, 132, 85, -13],\n [210, -1, 23, 11, 125, -97, 16],\n [-154, -166, -140, 22, -189, 15, -83],\n [92, 129, 190, 86, 140, 159, 155],\n [284, 304, 270, 210, 174, 200, -6],\n [33, 105, 40, 130, -4, 226, 159],\n [-180, -63, -9, -116, -4, 32, 31]]?\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[[24, 16, -8, 24, -12, -12, 18],\n [-120, -80, 40, -120, 60, 60, -90],\n [-12, -8, 4, -12, 6, 6, -9],\n [120, 80, -40, 120, -60, -60, 90],\n [-72, -48, 24, -72, 36, 36, -54],\n [-108, -72, 36, -108, 54, 54, -81],\n [-144, -96, 48, -144, 72, 72, -108]]\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 7x7 matrix:\n[[50, 14, -68, 54, -14, 24, 67],\n [-49, 29, 208, -22, 65, -77, -204],\n [75, -75, -124, 4, -31, -147, -91],\n [44, -28, 56, 12, 28, -184, -234],\n [-36, 0, 20, -30, 0, 34, 25],\n [134, 107, 48, 195, 46, -23, -46],\n [46, -23, 4, 19, 10, -123, -137]]\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[[77, -123, 163, -129, -49, -153, 295],\n [49, 35, -37, 2, -222, 8, 54],\n [-268, -25, -137, 212, -69, -115, 84],\n [77, -161, 68, -107, 59, -184, 238],\n [-172, 145, -5, 184, -85, -53, 151],\n [-53, -47, 157, -98, 104, -130, -102],\n [-142, -248, 69, 4, 46, 77, 202]]\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[[-257, 66, 23, 193, 29, 19, 96],\n [-42, -17, -12, -20, -32, -93, -32],\n [-177, -90, 42, 23, -43, -29, -154],\n [88, 101, -143, -91, -108, 60, -193],\n [-43, 24, -2, 31, 15, -135, 128],\n [20, 86, -78, -16, -32, -118, 64],\n [120, -210, 160, -70, 80, 120, -50]]\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[[15, -111, 71, 122, -104, 185, -176],\n [-16, -19, -76, 193, 30, 63, 49],\n [-93, -72, 197, 10, 2, -99, 34],\n [-133, -104, 49, 53, 47, 29, 70],\n [19, -5, -64, -47, -17, 63, -32],\n [91, 15, -37, 172, -62, 53, -60],\n [13, 38, 32, -166, -6, -109, 24]]\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[[-9, 166, -69, -50, 146, 16, 182],\n [-235, -7, 152, 275, -116, 11, -72],\n [103, -186, 50, 105, -74, 174, -27],\n [229, 117, -58, -384, 237, -29, -65],\n [63, 3, 53, -132, -8, -1, -90],\n [-46, -191, -50, 133, -191, -107, -93],\n [18, 73, 158, 142, 114, 316, 96]]\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, 38, 3, -42, -62, 65, 66],\n [-58, 28, 30, -44, -216, -2, 148],\n [60, 36, -6, -56, -2, 108, 64],\n [-59, 48, 16, -4, -160, -22, 38],\n [-96, 6, 15, 52, -107, -114, -44],\n [12, -40, 8, -26, 5, 9, 76],\n [69, -40, -4, -48, 82, 72, 78]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[77, 77, -14, -35, 28, 70, 63],\n [-88, -88, 16, 40, -32, -80, -72],\n [-110, -110, 20, 50, -40, -100, -90],\n [0, 0, 0, 0, 0, 0, 0],\n [132, 132, -24, -60, 48, 120, 108],\n [-88, -88, 16, 40, -32, -80, -72],\n [-11, -11, 2, 5, -4, -10, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-86, 82, -82, -108, 74, -28, -44],\n [14, -98, 133, 7, 14, 42, 21],\n [29, 57, -92, 47, -51, -28, 1],\n [87, -141, 165, 102, -57, 54, 54],\n [115, -129, 137, 142, -93, 46, 62],\n [74, -102, 115, 89, -54, 38, 43],\n [68, -60, 58, 86, -60, 20, 34]]\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 7x7 matrix:\n[[0, -15, -35, 26, 161, 28, 90],\n [125, 89, -204, 48, 48, 138, -34],\n [-343, 163, 66, 0, 94, -40, 88],\n [65, -47, 24, 27, 83, 35, 227],\n [114, -24, 246, -69, 21, -69, 3],\n [121, -72, 17, 12, -62, 23, 133],\n [-104, 113, -213, 86, -18, 128, 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[[70, 57, 54, 10, 137, 38, -70],\n [179, 66, 42, 101, 100, -14, -158],\n [-165, -4, -3, -92, -53, -5, 106],\n [171, 110, 40, 147, 2, -116, -206],\n [-27, 153, 56, 55, -73, -168, -120],\n [40, -196, -112, 0, -76, 96, 120],\n [154, 188, 86, 144, 38, -150, -252]]?\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, 72, 18, 42, -54, 0, 18],\n [-12, 72, 18, 42, -54, 0, 18],\n [-10, 60, 15, 35, -45, 0, 15],\n [-6, 36, 9, 21, -27, 0, 9],\n [12, -72, -18, -42, 54, 0, -18],\n [12, -72, -18, -42, 54, 0, -18],\n [-22, 132, 33, 77, -99, 0, 33]]?\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[[-3, 70, 38, 66, -47, 13, -190],\n [255, 14, -225, -126, -62, 63, -60],\n [283, 170, -118, -66, 6, 43, -173],\n [-53, 73, 222, 103, -37, 13, 120],\n [82, 156, 236, 54, 77, -59, 101],\n [-6, -112, -80, -69, -19, -6, 39],\n [98, 120, -32, 70, -269, 252, -9]]\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[[-45, -77, 85, -134, -167, 92, 35],\n [85, -81, -13, 14, -96, -87, -83],\n [244, 175, -85, 235, 139, -108, 54],\n [75, -111, -41, -93, 81, -137, 0],\n [-14, -78, -24, -201, 67, -36, -53],\n [98, 152, -48, 227, 0, -34, 114],\n [-95, -88, -36, -128, -9, -41, -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 7x7 matrix:\n[[96, -3, -55, -66, 46, -39, -45],\n [135, 103, -91, -25, -61, -60, 83],\n [105, 100, -49, -3, -85, -64, 110],\n [66, 29, 32, -14, -48, -78, 67],\n [-57, 117, -39, 103, -129, 56, 141],\n [-150, 34, 34, 114, -78, 92, 74],\n [-36, -23, -36, 0, 46, 56, -61]]\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[[61, -49, -134, 207, 26, 99, 254],\n [33, -149, 17, 20, 190, 130, 72],\n [179, 51, -59, 9, 26, 208, 141],\n [-46, 10, -60, -94, -222, 98, -48],\n [107, 121, 72, -59, 64, -78, 31],\n [74, 74, 8, -62, -38, 14, 60],\n [190, 88, 0, 184, 245, -22, 168]]?\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[[120, 183, 50, -119, 105, 69, -98],\n [-84, -112, -18, 17, 37, 45, -69],\n [97, 75, 43, -66, 128, 127, -139],\n [-30, -131, -20, 60, -36, -72, 113],\n [66, -170, -9, 88, -64, -189, 312],\n [185, 13, 45, 30, 48, 41, 51],\n [-193, 117, -48, -10, -128, 8, -123]]\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[[56, -14, -50, 72, -24, 126, 104],\n [29, 207, 121, 68, 76, -45, -297],\n [-30, -39, -153, -116, -234, 140, 339],\n [105, 56, -84, -261, -86, -49, -10],\n [-54, -21, -196, 35, -156, 122, 387],\n [235, -213, -208, 43, 230, -39, 143],\n [-9, 126, 81, 15, -12, 3, -148]]\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, 51, -46, 53, -124, 188, 64],\n [-24, -18, -51, 6, -42, 84, 75],\n [-97, 38, 52, -141, -14, 74, -111],\n [-23, -103, -149, 61, 115, -80, 164],\n [139, 94, -23, 50, 181, -144, -140],\n [-230, -160, -11, -120, -32, 12, 129],\n [26, 69, 76, -49, 52, -60, -158]]\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[[40, 67, 29, -122, 105, -103, 215],\n [86, 68, 7, -155, -56, -6, 171],\n [27, -116, -139, -1, -190, -25, -2],\n [140, 122, -50, 32, -108, 94, -140],\n [-19, 24, 18, 142, -10, 93, -229],\n [-298, -216, 84, 208, -234, -186, -18],\n [-24, 70, 110, 10, -47, 82, -50]]\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[[-22, -6, -6, -12, 4, 14, 14],\n [-55, -15, -15, -30, 10, 35, 35],\n [132, 36, 36, 72, -24, -84, -84],\n [11, 3, 3, 6, -2, -7, -7],\n [-121, -33, -33, -66, 22, 77, 77],\n [-33, -9, -9, -18, 6, 21, 21],\n [88, 24, 24, 48, -16, -56, -56]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 7x7 matrix:\n[[39, -51, 69, 48, 45, -30, 6],\n [-110, -50, -90, -100, -110, 40, -80],\n [110, 176, 22, 77, 99, -11, 121],\n [125, 11, 127, 122, 129, -56, 76],\n [-67, -145, 7, -40, -57, -2, -86],\n [32, 152, -48, 4, 20, 20, 68],\n [-111, -165, -29, -80, -101, 14, -118]]\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[[-262, -98, -114, 214, -224, 81, -89],\n [418, 228, 248, -103, 249, -155, 66],\n [-17, -39, -149, -100, 53, 120, 25],\n [-179, -157, -175, 108, -95, 86, 19],\n [142, 185, 232, -132, 31, -99, -26],\n [-261, -78, -91, -4, -158, 81, -107],\n [120, 38, 138, 47, 52, -131, 35]]\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[[30, -134, 118, 162, 110, -110, -70],\n [51, -82, 232, 29, -47, -138, 46],\n [158, 113, -187, -130, -128, 45, -75],\n [-236, -143, 105, -41, 74, 6, 127],\n [39, -48, 226, 153, -8, -149, 79],\n [-60, -96, 282, 224, -1, -294, 232],\n [-9, -134, 8, -32, 60, 16, -87]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-111, -39, -46, 143, -171, -146, 40],\n [301, -24, 109, -54, 310, 332, -56],\n [-140, 206, -107, -58, -69, -68, 68],\n [17, -72, 15, -118, -4, 44, -16],\n [112, -17, 135, 33, 104, 61, -95],\n [-284, 153, -141, 135, -288, -276, 98],\n [-215, 193, -228, 35, -153, -137, 163]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-88, -88, -48, -32, 88, -72, -88],\n [77, -77, -38, 125, -11, -2, 77],\n [-134, -78, -44, -84, 110, -86, -134],\n [98, 126, 68, 18, -110, 92, 98],\n [-39, 129, 66, -120, -33, 39, -39],\n [-44, -44, -24, -16, 44, -36, -44],\n [-83, 85, 42, -136, 11, 3, -83]]?\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[[7, 56, -44, -28, -6, 96, -28],\n [47, 147, 35, 16, 53, -50, -203],\n [41, 203, -43, 8, -91, -27, 80],\n [8, 80, -8, 42, -136, -47, 211],\n [-28, -28, -73, -77, 40, 137, -56],\n [-17, -69, -97, -74, 17, 149, 62],\n [61, 18, -96, -80, 124, -27, -45]]?\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[[9, 69, 120, -92, 98, 96, 204],\n [-8, 72, -135, -40, 32, 52, -176],\n [-12, -174, -72, 47, -91, -156, -200],\n [7, -99, 114, 93, -79, -92, 140],\n [6, 174, -12, -40, 76, 144, 72],\n [12, 66, -36, 331, -215, -60, 56],\n [8, 162, 54, -107, 127, 164, 152]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[14, 52, -178, -222, -79, 213, 122],\n [-25, 302, 64, 140, -10, -56, -38],\n [22, -149, -72, -24, 103, 17, -191],\n [62, -259, -76, -45, 24, 82, 12],\n [-89, 194, -15, 34, -72, 11, -34],\n [69, 48, -59, -13, 0, 93, 59],\n [-9, 102, -251, -37, -60, 261, -91]]?\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[[140, 121, -78, 211, -148, -46, 67],\n [101, 59, 170, 9, 44, -304, 147],\n [138, -38, 105, 127, 57, -225, 266],\n [-84, -21, -10, 49, 34, -61, -14],\n [292, -118, -84, -46, -100, 40, 46],\n [-160, -144, -129, -140, 36, 345, -172],\n [183, -119, -297, 49, -208, 200, -142]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-27, -18, 15, -21, 15, -18, -33],\n [-99, -66, 55, -77, 55, -66, -121],\n [81, 54, -45, 63, -45, 54, 99],\n [-27, -18, 15, -21, 15, -18, -33],\n [-36, -24, 20, -28, 20, -24, -44],\n [99, 66, -55, 77, -55, 66, 121],\n [-27, -18, 15, -21, 15, -18, -33]]?\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[[-95, -32, -196, 183, 158, 183, 57],\n [15, -52, 100, -30, -72, -96, -63],\n [15, 69, 76, 2, -43, -79, 19],\n [-5, -98, 4, -17, -12, 1, -61],\n [-70, -131, -96, 113, 75, 92, -38],\n [20, -53, 104, -42, -77, -99, -66],\n [-50, 7, -160, 90, 119, 153, 60]]?\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[[16, 77, 86, -91, -74, 23, 33],\n [-10, 32, 70, -74, -20, 34, 12],\n [-33, -4, 51, -33, 70, 69, -18],\n [25, 38, -30, 104, 110, 66, -27],\n [-94, -141, -16, 1, 142, 35, -57],\n [20, 68, 74, -98, -112, -10, 42],\n [67, 37, -84, 95, -60, -69, 18]]\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[[130, -120, 67, -151, -113, -78, 72],\n [27, 27, 61, 91, 17, 239, -173],\n [60, -139, -68, -71, -64, 93, -108],\n [0, 176, 246, 205, -23, 182, -26],\n [-215, 175, -80, 235, 305, -119, -17],\n [-132, -16, -33, 148, 262, -142, -44],\n [-78, -55, -280, -86, 48, -158, 23]]\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[[11, 89, 1, -83, 48, -70, -68],\n [18, 42, -2, -14, 4, -20, -24],\n [58, 148, -6, -60, 22, -76, -88],\n [-49, -70, 7, -14, 21, 14, 28],\n [76, 133, -10, -7, -15, -44, -64],\n [53, -22, -11, 130, -93, 74, 52],\n [25, 109, -1, -79, 42, -74, -76]]\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[[45, 142, 231, -69, 178, -59, 261],\n [38, 25, 155, 38, 216, -52, 44],\n [30, 81, 6, -84, 40, -101, 60],\n [-30, -124, -105, 111, -32, 49, -201],\n [-33, -58, -21, 42, -102, 111, -18],\n [-12, -71, 103, 98, 44, 116, -4],\n [23, 164, 184, -72, 146, -74, 282]]?\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[[-18, 190, 140, 77, -45, 54, 12],\n [58, -5, 109, 121, -81, 53, 53],\n [128, 0, -92, -176, 168, -80, -212],\n [-142, 21, -79, -55, 11, -21, 45],\n [-80, 59, -16, -22, 4, -3, 18],\n [10, -209, -34, 77, -79, 13, 112],\n [-38, -93, 37, 121, -113, 45, 141]]?\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[[-30, -48, 56, 2, -49, 8, -115],\n [134, -65, 72, -126, -45, 69, 231],\n [36, 12, -16, 321, 158, 40, -205],\n [-96, -387, 344, -44, -10, -9, 84],\n [-94, 58, -10, 41, 28, -12, 7],\n [-1, 115, -105, 86, 85, -12, 28],\n [54, -30, 4, -58, 27, -2, 177]]\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[[31, -14, 62, -32, -54, -5, 34],\n [187, -25, -8, 132, -61, 146, -104],\n [143, 117, 104, -179, -142, -5, 8],\n [-153, 54, -22, -9, 141, -92, 54],\n [85, 94, -58, -101, -63, 28, -86],\n [6, -50, 284, -21, -55, -73, 212],\n [123, -2, 138, 51, -55, 46, 38]]\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[[49, -4, 44, 160, 85, 87, -137],\n [94, 60, 40, 98, 174, 30, -162],\n [7, -30, -116, -100, -93, -123, -93],\n [-114, -63, 12, -48, -162, 36, 225],\n [-60, -29, -52, -122, -124, -66, 113],\n [117, 176, 68, -63, 293, -51, -33],\n [-4, 57, 52, -48, 68, 6, 115]]\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[[-217, 132, -62, 22, -171, -73, 179],\n [-137, 79, 1, 39, -64, -64, 89],\n [-72, 38, 31, 38, -5, -49, 32],\n [40, -17, -13, 13, 103, 61, -90],\n [-62, 24, 35, -16, -159, -107, 142],\n [79, -35, -92, -75, -49, 83, -7],\n [-62, 39, 7, 49, 61, -1, -24]]\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 7x7 matrix:\n[[141, 36, 59, -190, 34, 79, -17],\n [-174, -90, 13, 123, -59, -97, 26],\n [22, -40, 94, 132, -42, -78, -162],\n [-113, -144, 171, -2, -135, -91, -153],\n [65, 85, -100, -171, 54, 123, 105],\n [213, 129, -53, -152, 131, 122, 89],\n [-7, -72, 126, 135, -8, -116, -63]]\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 7x7 matrix:\n[[0, 0, 0, 0, 0, 0, 0],\n [10, 0, 25, -10, 0, -60, 25],\n [18, 0, 45, -18, 0, -108, 45],\n [22, 0, 55, -22, 0, -132, 55],\n [8, 0, 20, -8, 0, -48, 20],\n [-14, 0, -35, 14, 0, 84, -35],\n [24, 0, 60, -24, 0, -144, 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[[-201, -164, -169, 108, 23, 99, -75],\n [-5, -93, 8, 100, 87, -6, 10],\n [115, 186, 95, -95, -54, -8, 15],\n [-130, 145, -109, 20, -110, 125, -45],\n [-120, -102, -82, 186, 86, 92, -38],\n [68, -187, 56, -13, 175, 71, -138],\n [-3, -50, -9, -36, 21, 31, -55]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-22, 14, 22, -6, 14, -20, 12],\n [99, -63, -99, 27, -63, 90, -54],\n [88, -56, -88, 24, -56, 80, -48],\n [-22, 14, 22, -6, 14, -20, 12],\n [22, -14, -22, 6, -14, 20, -12],\n [33, -21, -33, 9, -21, 30, -18],\n [-44, 28, 44, -12, 28, -40, 24]]\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[[-68, -202, -49, -121, 20, 37, 101],\n [-40, -128, -49, -118, 30, 103, -30],\n [-21, 12, -20, 13, -10, -22, 52],\n [23, -61, -42, -8, 55, -36, 32],\n [265, 171, -15, 12, -15, 29, 134],\n [9, 88, 72, 9, -130, 8, 154],\n [39, -7, 75, -84, -125, 79, 174]]\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[[77, -71, -28, 54, 78, -177, -195],\n [195, -25, -80, 162, 154, -291, -165],\n [-47, 84, -111, -33, -62, 41, -34],\n [-38, 41, -55, -54, -46, 39, -30],\n [75, 216, -245, 243, -2, -71, 120],\n [-68, -50, -60, 42, -75, -19, -107],\n [-77, 15, 88, -111, -52, 166, 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[[-12, 143, -91, -1, 131, 70, -189],\n [-192, 116, -66, -42, 132, 92, 30],\n [120, -28, -64, -44, 152, -57, -149],\n [-108, 44, -45, -74, 144, -4, 15],\n [-152, 186, -96, -39, 210, -47, -105],\n [64, -280, -42, -223, -144, 10, -34],\n [-160, 64, -20, -3, 184, -51, 139]]?\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[[-28, 42, 0, 14, 21, 42, -77],\n [36, -54, 0, -18, -27, -54, 99],\n [-40, 60, 0, 20, 30, 60, -110],\n [-40, 60, 0, 20, 30, 60, -110],\n [12, -18, 0, -6, -9, -18, 33],\n [-12, 18, 0, 6, 9, 18, -33],\n [48, -72, 0, -24, -36, -72, 132]]\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 7x7 matrix:\n[[134, -90, -130, -126, 214, -179, 163],\n [83, -108, -106, -69, 66, 29, 197],\n [-17, 87, 67, 30, 46, -147, -156],\n [62, -31, -5, 39, 28, 8, 69],\n [-116, 9, -41, -117, -70, 53, -46],\n [-62, 0, 28, 42, -132, 166, -2],\n [7, 36, 94, 147, -74, 75, -45]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[132, 72, 33, -129, 39, -9, 87],\n [-88, -129, -88, 62, -74, 12, -61],\n [-116, -78, -41, 109, -43, 9, -77],\n [20, 114, 89, 11, 67, -9, 17],\n [-32, 174, 148, 88, 104, -12, -14],\n [-40, 123, 108, 82, 74, -8, -21],\n [-108, 0, 21, 123, 3, 3, -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[[-39, -21, 165, 180, 169, -73, 149],\n [-102, -45, -189, -63, 3, 0, -15],\n [-13, 96, 86, 143, 74, -149, 120],\n [-21, -192, 24, 51, 80, 43, 70],\n [96, 27, -4, -124, -135, 98, -132],\n [29, -61, 142, 215, 105, -153, 204],\n [-64, 15, -76, -91, 2, 82, -84]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, 6, -20, -10, 18, 18, 24],\n [-3, 3, -10, -5, 9, 9, 12],\n [-12, 12, -40, -20, 36, 36, 48],\n [33, -33, 110, 55, -99, -99, -132],\n [-15, 15, -50, -25, 45, 45, 60],\n [-9, 9, -30, -15, 27, 27, 36],\n [3, -3, 10, 5, -9, -9, -12]]\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 7x7 matrix:\n[[108, 81, -149, -9, 63, 22, -259],\n [-72, -251, 126, -202, 122, -288, 2],\n [-85, 67, -99, 45, 46, 168, 109],\n [12, -119, 16, -112, 94, -76, -61],\n [5, -46, -12, -37, 31, -164, -94],\n [37, 0, -6, 14, 15, -198, 3],\n [86, -103, -142, 26, 82, 142, -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[[-88, 24, 0, 48, -32, 16, -56],\n [112, -98, -7, 14, 0, -77, 91],\n [-8, 60, 6, -60, 32, 50, -22],\n [37, -39, -3, 12, -4, -31, 32],\n [-120, 52, 2, 44, -32, 38, -82],\n [-50, 110, 10, -80, 40, 90, -60],\n [95, -103, -8, 34, -12, -82, 83]]\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 7x7 matrix:\n[[-49, -36, 23, -20, -13, 6, -2],\n [71, 32, -57, 20, 13, 8, 32],\n [-87, -72, -15, 42, -84, 27, 83],\n [19, 34, -9, 58, -19, -14, 10],\n [-94, -38, 22, 78, -90, -2, 46],\n [-101, -41, 9, 109, -115, 1, 73],\n [103, 50, -61, 0, 42, 5, 13]]\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 7x7 matrix:\n[[70, 35, -28, 63, 35, 28, -14],\n [30, 15, -12, 27, 15, 12, -6],\n [110, 55, -44, 99, 55, 44, -22],\n [-30, -15, 12, -27, -15, -12, 6],\n [-60, -30, 24, -54, -30, -24, 12],\n [-30, -15, 12, -27, -15, -12, 6],\n [-60, -30, 24, -54, -30, -24, 12]]\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[[-50, -94, 113, -12, -17, -30, 165],\n [-3, 1, -41, -34, 49, -25, 7],\n [89, -66, -150, -64, -42, -134, 110],\n [167, 94, -76, 103, -103, 76, -97],\n [-19, -63, 20, -35, 9, -51, 111],\n [-67, 2, -12, -32, 20, -18, -72],\n [-62, 4, 87, -9, 102, 42, 42]]\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[[-101, -13, -60, -148, 161, -84, -27],\n [138, 74, -8, 56, 12, 216, -32],\n [38, 14, 8, 32, -23, 48, -1],\n [7, 31, -44, -68, 113, 60, -35],\n [1, -7, 12, 20, -31, -12, 9],\n [105, 25, 44, 124, -120, 108, 14],\n [33, 9, 12, 36, -33, 36, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-18, 144, -12, -120, -180, -66, 18],\n [42, -56, 145, 13, 128, 109, -133],\n [34, -133, 247, 80, 261, 159, -192],\n [-261, -45, -109, 3, -49, -89, 231],\n [-90, -98, -62, 142, 86, -74, 122],\n [-60, 47, -10, -114, -87, 25, 19],\n [-5, 28, -12, -17, -38, -22, 13]]\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[[-49, -54, 10, 55, 10, 100, -180],\n [-371, 101, 20, -148, 168, -127, 14],\n [-105, 38, 68, -165, 88, 4, 70],\n [82, -100, 34, 5, 43, 312, -231],\n [-35, -89, 61, -70, 116, -126, 269],\n [-65, -65, 57, 126, -28, -207, 122],\n [102, 9, 36, -190, 179, 262, 90]]\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[[8, 66, -38, 4, 35, -105, 113],\n [-27, 109, -67, -153, 63, 131, -84],\n [5, 127, -45, -115, 45, -2, 45],\n [-5, -17, 27, -59, -21, 141, -120],\n [-64, -67, -48, -8, 32, 142, -181],\n [48, 75, 96, -244, -94, -50, 17],\n [-42, 24, -70, -42, 54, 24, -48]]\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[[-150, -118, -174, -90, 181, -66, 20],\n [180, 46, 151, 66, -103, 147, -44],\n [195, 163, 238, 90, -229, 45, -55],\n [-80, -92, -145, -171, 113, 14, -105],\n [57, 73, -100, 51, 103, -13, 3],\n [-34, -16, -189, -63, 199, -47, -40],\n [136, -66, -37, -117, 173, 109, -176]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[122, -11, 124, -28, -138, -78, -58],\n [252, 23, -41, 20, -67, -39, -141],\n [132, 14, -62, 32, -26, -21, -50],\n [-138, 110, 1, -31, 112, -36, 94],\n [-188, 7, 139, -97, 74, 50, -4],\n [122, 30, 9, 9, -64, -67, -30],\n [4, -74, 58, 65, -199, -118, 173]]?\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[[-80, -140, 33, 96, 35, 49, 95],\n [-152, -93, 14, 56, 91, 61, 39],\n [173, 0, 111, 15, -45, -38, 189],\n [166, 144, 16, -122, -31, -51, 36],\n [-332, -84, -58, 92, 118, 70, -186],\n [84, 33, -56, -68, -45, -7, -9],\n [74, -103, -107, 70, -164, -14, -98]]\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 7x7 matrix:\n[[89, -91, 96, 52, -221, 173, 142],\n [-70, -83, 113, -85, -97, 76, -93],\n [-56, -37, 55, -23, -41, -4, 15],\n [-149, -43, 16, -10, 108, -44, -203],\n [117, 112, -47, -139, -13, -26, 46],\n [-158, -183, 166, -2, -105, 130, -176],\n [32, 34, -43, -1, 44, -8, -33]]\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[[28, 48, -19, -43, 105, 74, 63],\n [16, 16, 32, -16, 120, 88, 56],\n [22, 30, 14, -28, 123, 89, 63],\n [-54, -122, 147, 105, -48, -25, -70],\n [-34, -82, 112, 70, -3, 5, -35],\n [18, 42, -54, -36, 9, 3, 21],\n [12, 4, 54, -6, 132, 98, 56]]?\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 7x7 matrix:\n[[-39, -105, -87, -94, 74, -84, -68],\n [-9, 5, -17, 6, 14, -4, -8],\n [33, 7, 65, 2, -54, 28, 36],\n [36, -20, 68, -24, -56, 16, 32],\n [-3, -68, -13, -64, 12, -38, -21],\n [-48, -81, -102, -70, 86, -78, -71],\n [-102, -165, -216, -142, 182, -162, -149]]\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[[-35, -153, 37, 46, -21, 48, -60],\n [-6, 89, -92, 62, -119, -234, 50],\n [55, -71, -225, 132, -201, -7, -283],\n [-142, -76, 176, -172, 184, 84, 47],\n [-28, -112, -162, 179, -217, -172, -114],\n [-16, 53, -54, 88, -113, -240, 104],\n [26, 53, -6, -109, 110, 182, -72]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[10, -80, -100, -30, -60, -20, 20],\n [-1, 8, 10, 3, 6, 2, -2],\n [4, -32, -40, -12, -24, -8, 8],\n [-7, 56, 70, 21, 42, 14, -14],\n [2, -16, -20, -6, -12, -4, 4],\n [-11, 88, 110, 33, 66, 22, -22],\n [-5, 40, 50, 15, 30, 10, -10]]\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[[105, -164, 187, 133, 183, -190, 174],\n [-52, 18, -44, -36, -14, -30, 52],\n [114, 18, -54, 36, 51, -108, 111],\n [-38, 182, -250, -116, -135, 52, -15],\n [9, -22, -27, 5, 62, -146, 171],\n [-71, 42, -118, -80, -30, -24, 49],\n [55, -92, 156, 88, 71, -16, -10]]\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[[-20, 110, -30, 12, -50, -218, -8],\n [27, -52, 94, 14, 44, 166, -1],\n [38, 72, -6, 68, -130, -94, 8],\n [-177, 70, -176, 113, -42, -80, 69],\n [-49, 17, -27, 16, -167, 43, -27],\n [-50, -8, -65, -27, -143, 26, -32],\n [210, -90, 185, -136, -65, 126, -100]]\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[[2, 2, 12, 22, 24, -20, -24],\n [7, 7, 42, 77, 84, -70, -84],\n [12, 12, 72, 132, 144, -120, -144],\n [7, 7, 42, 77, 84, -70, -84],\n [8, 8, 48, 88, 96, -80, -96],\n [6, 6, 36, 66, 72, -60, -72],\n [-9, -9, -54, -99, -108, 90, 108]]\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[[-141, 97, 130, 39, -91, 130, 135],\n [2, 69, 158, 143, -32, -45, 52],\n [-81, 25, 121, 77, 21, 263, 60],\n [95, -11, -107, -127, 135, -4, 22],\n [5, -161, -166, -19, -104, -80, -196],\n [-157, 60, 236, 281, -192, 71, 60],\n [7, 112, -7, -292, 204, -29, -17]]\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 7x7 matrix:\n[[-267, -24, 177, -225, -108, -114, 60],\n [-57, -151, 85, 19, 196, -68, 90],\n [179, 21, -90, 68, 32, 127, 31],\n [201, 72, -93, 309, 72, 172, 79],\n [-104, -141, 118, -388, -12, -40, 50],\n [-76, -133, 193, 84, 66, 138, -64],\n [54, 33, -75, 162, 66, -38, 1]]\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[[58, 61, 152, 51, 73, -13, 0],\n [144, 88, 7, 250, 41, -175, 23],\n [12, -41, -67, -98, -34, 20, 113],\n [-26, 54, 117, -40, -99, -243, 181],\n [-245, 43, 27, -192, -211, 11, 108],\n [135, -89, -29, -56, 126, 93, 9],\n [89, 125, -108, 70, -38, 162, 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[[-136, -103, -94, -18, 148, -6, 7],\n [28, 44, -8, -82, -56, 14, 56],\n [6, 13, -6, -31, -16, 5, 21],\n [158, 134, 92, -33, -188, 15, 28],\n [38, 24, 32, 23, -36, -1, -14],\n [-30, -15, -30, -33, 24, 3, 21],\n [116, 118, 44, -98, -160, 22, 70]]?\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[[-99, 9, 355, -29, -205, -141, -138],\n [84, 115, -37, -28, -219, -195, 110],\n [-19, -99, 11, -1, 45, 45, -67],\n [-51, -27, 143, 93, -107, -22, -29],\n [34, 3, 35, -124, -43, -54, -32],\n [36, -19, 31, -36, -25, 45, 11],\n [-35, -30, -154, 27, 266, 152, -13]]?\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[[-2, -58, -20, -22, -19, 20, -5],\n [-91, -78, -56, 29, -131, -20, 122],\n [132, 94, 52, -52, 153, 21, -126],\n [4, -64, -16, -28, -8, 28, -24],\n [103, -82, -72, -109, -9, 33, 23],\n [139, -86, -128, -141, -59, 10, 126],\n [-60, -44, -56, 20, -114, -30, 132]]\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 7x7 matrix:\n[[39, 39, -25, 193, 56, -12, -6],\n [28, -225, -70, -98, -70, -26, -189],\n [-63, -57, -85, -161, 26, 144, -40],\n [-126, -49, -4, 67, 24, -102, -14],\n [-213, 123, -124, -101, 176, 75, 5],\n [-239, -48, -210, 90, 201, -20, -154],\n [-126, 200, 1, 182, 146, 3, 143]]\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[[-29, -49, -1, -25, 25, 17, -45],\n [-82, -10, 78, 118, -26, 166, 82],\n [0, -87, 59, 132, -59, 200, 153],\n [-108, -107, -77, -72, -57, -46, -185],\n [13, 187, -33, 67, -139, -113, 51],\n [123, -31, 19, -98, 172, -32, 16],\n [-72, 174, -82, -150, 28, -286, -240]]?\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, -58, 51, -91, 49, 102, -68],\n [29, -73, 85, -42, 39, 129, -77],\n [16, -47, 154, 21, -39, 153, -62],\n [-31, -19, -62, 141, 36, -69, 25],\n [17, 102, -38, -184, -65, -60, 47],\n [2, 79, -44, -95, -49, -69, 48],\n [-14, -73, -41, 116, 88, -9, -22]]\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[[-113, -27, 58, -120, -286, -57, 118],\n [-16, 0, 164, -18, -33, 5, -1],\n [180, -56, 248, 216, -45, -2, -111],\n [39, -47, -11, 36, 19, -43, 72],\n [-107, 15, -107, -146, -221, -59, 215],\n [-208, 182, 85, -244, 65, 94, 193],\n [23, -126, -74, 37, 321, -48, -54]]\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[[-109, 79, 119, -98, 79, -69, -81],\n [-39, -141, 162, -96, -21, 27, -34],\n [44, -157, 54, 50, -4, 68, -11],\n [82, -208, -93, 6, -76, 42, 35],\n [-6, -283, 20, 20, -48, 67, 149],\n [77, 355, 15, 216, -23, 93, 73],\n [43, -80, 23, -73, -33, 4, -108]]?\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[[-162, -78, 38, 110, 124, -114, -102],\n [0, 12, 8, 44, -8, 12, -12],\n [-81, -27, 27, 99, 54, -45, -63],\n [9, -6, -9, -44, 0, -4, 16],\n [180, 93, -38, -99, -142, 133, 107],\n [0, 0, 0, 0, 0, 0, 0],\n [-45, -12, 17, 66, 28, -22, -38]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-110, 70, -120, 100, -50, 80, 0],\n [-33, 21, -36, 30, -15, 24, 0],\n [22, -14, 24, -20, 10, -16, 0],\n [77, -49, 84, -70, 35, -56, 0],\n [88, -56, 96, -80, 40, -64, 0],\n [44, -28, 48, -40, 20, -32, 0],\n [110, -70, 120, -100, 50, -80, 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[[-302, 54, 16, -160, -124, -114, -202],\n [57, -13, -19, 162, -21, -94, -19],\n [142, 10, 24, 31, 221, -53, 219],\n [413, -189, 47, -21, -3, 53, 75],\n [122, -50, 50, 116, 44, -177, 53],\n [-68, 24, -23, 51, 3, 133, 21],\n [-85, -31, -97, 76, -75, 232, -101]]?\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[[90, 33, 85, -142, 136, -156, 28],\n [-289, -131, -211, -310, -233, 49, 133],\n [131, -9, 4, -16, 158, -9, 145],\n [81, 46, 33, 260, -38, 257, -137],\n [177, 24, 88, 97, 144, 51, 6],\n [147, 70, 34, -132, 189, -77, 103],\n [103, -82, -24, 210, 95, 78, 139]]?\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[[98, -173, 35, 10, 152, 64, 116],\n [-129, 40, -20, -60, 10, -113, 50],\n [42, -19, 0, 172, 0, -41, -25],\n [-24, -86, -198, -60, 89, -190, -20],\n [-12, -52, -285, -10, 38, -257, -121],\n [49, -146, 40, -20, 144, 39, 132],\n [91, -14, 172, 92, -10, 189, 48]]\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[[-48, 147, 67, -2, -32, 214, 89],\n [-134, 110, 0, -4, -22, 150, -38],\n [98, -24, 134, -116, -126, -158, -128],\n [-128, 131, 5, 22, -2, 188, 11],\n [-24, 76, -28, 189, 159, 115, 171],\n [29, -34, 9, -149, -120, 24, -23],\n [19, -141, -33, -15, 3, -295, -213]]\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 7x7 matrix:\n[[-117, -111, 0, -60, 0, -81, -27],\n [-148, -60, -128, 16, -96, -132, 84],\n [44, 92, -80, 80, -60, 12, 84],\n [-20, 74, -148, 96, -111, -48, 132],\n [-182, -140, -52, -56, -39, -138, 6],\n [190, 130, 80, 40, 60, 150, -30],\n [-78, -74, 0, -40, 0, -54, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[168, 150, -8, 1, 40, 126, -131],\n [163, 189, 53, 83, 199, -14, 179],\n [-199, -287, -177, 2, -117, -14, -24],\n [-44, 207, 173, -4, -18, 124, 17],\n [-195, 18, -242, 122, -57, 307, 54],\n [-84, -139, -137, -66, -184, 95, -246],\n [-235, -67, -49, 2, -147, 140, -30]]\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[[27, -6, -3, 36, 33, -33, 18],\n [63, -14, -7, 84, 77, -77, 42],\n [36, -8, -4, 48, 44, -44, 24],\n [-72, 16, 8, -96, -88, 88, -48],\n [-54, 12, 6, -72, -66, 66, -36],\n [36, -8, -4, 48, 44, -44, 24],\n [63, -14, -7, 84, 77, -77, 42]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 7x7 matrix:\n[[56, 16, -8, 72, 40, 32, 88],\n [14, 4, -2, 18, 10, 8, 22],\n [-70, -20, 10, -90, -50, -40, -110],\n [-42, -12, 6, -54, -30, -24, -66],\n [42, 12, -6, 54, 30, 24, 66],\n [-56, -16, 8, -72, -40, -32, -88],\n [-63, -18, 9, -81, -45, -36, -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[[207, -62, 96, -171, -118, -26, -15],\n [-87, 5, 142, 25, 199, 66, 133],\n [37, -77, 303, -30, 131, -134, 74],\n [-61, 13, 69, 15, 14, -125, 41],\n [66, -7, 94, -113, -50, -57, 61],\n [185, -31, -54, -138, -104, 155, -36],\n [129, -77, 174, -81, 23, -32, 7]]\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[[52, 69, 120, 261, -185, -83, -41],\n [235, -172, 16, -74, 132, -134, -15],\n [-55, -120, -120, -39, 23, 192, -106],\n [126, -38, -80, -247, 183, -20, 65],\n [87, -17, -136, 52, -149, -3, -162],\n [-147, 198, 19, 94, -146, -41, 63],\n [184, -116, -51, -38, 42, 147, -134]]\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[[-42, -134, 66, 84, 3, -71, -33],\n [39, 99, -45, -55, -6, 51, 28],\n [42, 126, -2, -94, -104, 82, -28],\n [-108, -160, -112, 72, 266, -128, 29],\n [54, 0, -104, 50, 133, -59, 53],\n [-197, -55, -39, -105, 98, 19, -41],\n [-22, 71, -73, -79, 48, 41, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-7, -35, 63, 84, 42, -49, 0],\n [9, 45, -81, -108, -54, 63, 0],\n [8, 40, -72, -96, -48, 56, 0],\n [0, 0, 0, 0, 0, 0, 0],\n [1, 5, -9, -12, -6, 7, 0],\n [-6, -30, 54, 72, 36, -42, 0],\n [-8, -40, 72, 96, 48, -56, 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[[117, 180, 63, 117, -99, 27, 126],\n [18, 54, -149, -114, -16, -5, 111],\n [35, 52, -37, 53, -181, -150, 40],\n [10, 14, 67, 10, 112, 129, -1],\n [-17, -58, 166, 145, -23, -33, -127],\n [27, 50, 6, -21, 73, 104, 53],\n [-39, -56, -15, -63, 101, 61, -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[[93, 36, 180, -27, 160, 148, -90],\n [-27, 276, 241, 175, 200, 77, 93],\n [-146, -137, -246, 26, -63, 20, -153],\n [-142, 108, -103, 50, -105, -130, 73],\n [53, -70, 129, -143, 63, 220, -141],\n [5, -62, -87, -103, -163, -112, 62],\n [156, -49, -64, -2, -34, -223, 71]]?\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, 47, 49, -68, -170, 1, 187],\n [62, -219, 94, 62, -77, 34, -59],\n [127, -105, -27, 4, 65, -206, 117],\n [-51, -118, 186, 42, -131, 196, 46],\n [28, -32, 130, 93, -185, -114, 6],\n [-156, -91, 139, 63, -247, 16, 130],\n [-28, 283, 23, 223, -38, 171, -134]]\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 7x7 matrix:\n[[-25, -95, -156, 0, -39, -51, -28],\n [-57, -109, -124, -16, -29, -11, -2],\n [69, 8, -26, -208, 92, 13, 17],\n [-28, -8, -17, 132, -64, -33, -26],\n [-49, 65, 242, -56, 73, 155, 96],\n [56, 77, 32, 88, -23, -52, -39],\n [-64, -115, -154, 64, -71, -46, -27]]\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[[-148, -69, 94, -8, -70, 60, -117],\n [144, 97, -16, 16, 95, -194, 115],\n [-135, -95, 164, -38, -112, 281, -232],\n [1, 26, -30, 22, -10, -185, 76],\n [97, 27, 136, -30, -72, 133, -112],\n [176, 43, -158, -8, 32, 128, 97],\n [-222, -110, -46, 4, 35, 92, -46]]\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[[-278, 123, -67, -65, -41, -134, -107],\n [151, -160, 141, 145, 128, 30, -17],\n [268, 40, 207, 83, -103, 153, 132],\n [-150, 136, 31, -14, -37, -105, -64],\n [-35, 95, -83, -191, 138, 49, -214],\n [-11, -5, 0, 176, -85, -123, 93],\n [251, 58, 12, 13, -12, 60, 107]]?\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[[4, -37, -69, 113, -122, 28, 243],\n [-32, -127, 268, -112, -50, 314, -15],\n [66, -58, 155, 28, -26, 179, -121],\n [70, -29, -19, -32, 124, -58, -121],\n [-87, 177, -103, 31, -32, -161, -73],\n [120, -8, -14, 64, 80, -37, -171],\n [-47, -140, 130, -143, 68, 211, -78]]\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, 38, 11, 41, -158, -149, -31],\n [-9, -23, 54, -72, 51, -98, 96],\n [-209, -98, -4, -45, -234, -46, -225],\n [117, 17, 44, -136, 111, -26, 94],\n [95, 60, 3, 10, 28, 25, 10],\n [219, 85, 99, -132, 174, -92, 189],\n [-104, -23, -72, 40, -8, 30, 24]]\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, -45, -18, 101, -63, 34, 75],\n [56, 50, 16, -110, 70, -36, -78],\n [71, 20, 55, -71, 28, -36, -96],\n [11, 5, 7, -14, 7, -6, -15],\n [24, 60, -24, -108, 84, -24, -36],\n [-18, -45, 18, 81, -63, 18, 27],\n [52, 40, 20, -92, 56, -32, -72]]\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[[-156, 124, -32, -8, 158, 56, -90],\n [207, -108, 99, -54, -171, -117, 0],\n [221, -94, 127, -82, -168, -141, -45],\n [144, -122, 22, 16, -151, -46, 99],\n [-94, 32, -62, 44, 66, 66, 36],\n [-74, -4, -78, 68, 32, 74, 90],\n [111, 6, 117, -102, -48, -111, -135]]\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[[-73, 111, 28, 144, 30, 40, 70],\n [45, 81, -62, -176, -93, 51, -226],\n [139, -168, 252, 109, 243, 10, 42],\n [161, -120, 22, -213, -5, 12, -173],\n [77, -234, 4, -135, 23, -130, -38],\n [71, -93, 86, 40, 84, 14, 79],\n [-181, 96, 46, 321, 84, -31, 248]]\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[[142, -66, 121, -56, 32, 6, 60],\n [-85, 26, 332, 54, -55, -15, 75],\n [-194, -22, -83, 66, -44, 17, 16],\n [201, -142, -119, -8, 51, 120, -27],\n [148, 24, 205, -17, -127, -2, 208],\n [-139, -56, 166, -54, 127, -126, -29],\n [-39, 51, 75, 25, -3, 18, -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[[9, 1, 92, -55, 11, 42, -65],\n [-218, -204, 81, 0, -74, -166, 58],\n [134, 140, -127, -40, 62, 98, 50],\n [101, 106, -126, 45, 34, 51, 29],\n [23, -3, 28, -95, -9, 16, 35],\n [-104, -96, 105, -30, -22, -48, -28],\n [-28, -15, 44, 50, 3, -3, -68]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[128, -154, 222, -109, 82, 229, -106],\n [155, -47, 76, -96, 110, 202, 30],\n [-48, 140, 148, 132, -50, -35, -64],\n [48, 19, 118, -143, 302, 279, -110],\n [-69, 191, -58, 133, -42, -131, 4],\n [-132, -34, 222, -20, -12, 34, -172],\n [-122, -39, 103, -220, 258, 212, -142]]\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, -60, 0, 10, 60, -20, -110],\n [-40, -48, 0, 8, 48, -16, -88],\n [-5, -6, 0, 1, 6, -2, -11],\n [15, 18, 0, -3, -18, 6, 33],\n [-40, -48, 0, 8, 48, -16, -88],\n [30, 36, 0, -6, -36, 12, 66],\n [25, 30, 0, -5, -30, 10, 55]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-144, -66, 54, 88, 85, 57, 78],\n [-178, -90, 78, 110, 96, 78, 104],\n [-240, -117, 45, 141, 174, 81, 102],\n [33, -36, 62, -12, -79, 35, 32],\n [-116, -117, 217, 91, -65, 136, 176],\n [115, -3, 41, -61, -135, 8, -6],\n [-4, 81, -137, -13, 112, -83, -90]]\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[[145, 15, -123, 171, -141, 61, -15],\n [55, 80, 1, -12, -103, 83, -60],\n [-74, -89, -12, 33, 132, -98, 91],\n [68, -46, -56, 78, -40, -12, -6],\n [80, -51, -138, 207, -30, -16, 69],\n [120, 51, -36, 36, -153, 84, -84],\n [146, -43, -104, 141, -118, 18, -33]]\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[[62, 82, 44, 56, -38, 57, 14],\n [-56, 108, -20, -20, -64, -38, 72],\n [122, -12, 70, 80, 6, 84, -70],\n [-43, 18, -25, -25, 1, -16, 45],\n [-110, -170, -92, -98, 146, -25, 50],\n [-180, -154, -134, -141, 154, -53, 116],\n [-149, -174, -115, -125, 147, -54, 67]]?\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[[-48, -87, -29, 126, -25, -54, 69],\n [78, 87, 0, -9, 66, 153, -123],\n [-32, 7, 37, -150, -47, -114, 59],\n [-90, -90, 9, -27, -81, -189, 144],\n [92, 98, -4, 6, 80, 186, -146],\n [70, 100, 19, -87, 49, 111, -106],\n [-16, -64, -40, 168, 8, 24, 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[[-138, -35, -139, 19, 105, 253, 70],\n [-21, -85, -116, -9, 25, 23, -9],\n [71, 20, 122, -4, 149, -76, -65],\n [153, -178, 166, -50, 71, -66, -15],\n [-7, -156, -78, -20, 55, -132, -111],\n [-111, 141, 32, 39, -38, 27, 0],\n [68, -121, -98, -32, -61, 24, 47]]?\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[[62, 0, 28, -54, -38, -123, 8],\n [-99, 249, -207, 142, 300, 155, -41],\n [-182, 226, -161, 167, 254, 124, -105],\n [-230, 142, -122, -60, 85, -8, 197],\n [58, -117, 58, -109, -128, -33, 116],\n [96, -112, 16, 12, -63, -84, -261],\n [21, -36, 82, 66, -22, 120, 30]]\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[[35, -7, -42, -42, -70, 7, -70],\n [-6, 3, -99, -18, -60, -48, -78],\n [24, -3, -135, -54, -120, -42, -138],\n [6, -1, -19, -10, -20, -4, -22],\n [67, -15, 14, -58, -70, 55, -54],\n [-54, 12, -6, 48, 60, -42, 48],\n [24, -6, 42, -12, 0, 36, 12]]\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 7x7 matrix:\n[[24, -30, -33, 0, -9, -9, 3],\n [96, -120, -132, 0, -36, -36, 12],\n [48, -60, -66, 0, -18, -18, 6],\n [-40, 50, 55, 0, 15, 15, -5],\n [-80, 100, 110, 0, 30, 30, -10],\n [80, -100, -110, 0, -30, -30, 10],\n [32, -40, -44, 0, -12, -12, 4]]\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 7x7 matrix:\n[[-15, 21, -55, 3, 62, -42, 61],\n [51, -104, 136, -91, 20, -42, -68],\n [-106, 120, -196, 28, 46, 47, 126],\n [12, -29, 10, 175, -140, -34, -1],\n [23, 147, -91, 93, -24, 79, -11],\n [35, -22, 66, -149, 102, 1, -44],\n [44, -39, 35, 160, -104, -67, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-161, -244, -54, 56, -84, -123, -78],\n [78, -73, 226, -77, -74, -4, 73],\n [173, -249, 262, -23, 27, -20, 8],\n [-50, 65, 70, 74, -144, 27, -39],\n [200, 97, 128, -130, 67, 38, 141],\n [-81, 65, 56, 23, -157, 40, -9],\n [-246, -71, -102, 61, -167, -117, -56]]\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 7x7 matrix:\n[[-82, -97, -58, 111, -108, -87, 165],\n [31, 81, 63, -14, -61, -61, 30],\n [51, 25, 6, -118, 166, 93, -174],\n [-145, 56, -71, -54, 78, 95, 69],\n [-52, -118, -68, 69, -21, -31, 66],\n [-55, 147, -8, -199, 211, 134, -102],\n [94, -183, 2, 145, -120, -125, 7]]\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[[143, 85, 84, 91, 96, 69, -12],\n [77, 47, 52, 57, 48, 39, -12],\n [-121, -73, -77, -84, -78, -60, 15],\n [-198, -110, -74, -76, -156, -84, -18],\n [22, 4, -37, -45, 42, -3, 39],\n [176, 94, 45, 43, 150, 69, 33],\n [-22, -6, 26, 32, -36, 0, -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[[11, -53, 0, -3, -74, -43, -61],\n [-7, -7, 21, 16, -18, 12, -1],\n [88, -40, 72, 0, -49, 4, 25],\n [-10, -62, -119, -43, 100, 7, -8],\n [-68, 144, 100, 66, -8, 52, 60],\n [2, -78, -126, -64, -22, -104, -112],\n [118, -18, 35, -35, 24, 5, 64]]\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, 9, -30, 67, 44, 31, 27],\n [-94, -171, -90, 86, 93, 44, -213],\n [-61, 89, 56, -43, -46, -118, 33],\n [-94, -150, 12, -22, -53, -49, -125],\n [4, 16, -20, -40, 31, 59, -31],\n [-55, -28, 44, 7, -64, -110, 1],\n [44, -75, -42, 136, 38, 19, 12]]\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[[0, -120, 51, 44, -61, 2, -227],\n [-78, 75, 102, 20, -74, -6, 69],\n [-84, -76, 42, 29, -114, 30, -107],\n [87, 34, 118, 107, 103, 85, 66],\n [31, 273, 34, -46, 131, -95, 262],\n [-39, -140, 1, 71, -73, 161, -29],\n [-49, 194, -96, -81, 87, -38, 277]]\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[[217, -135, -39, 107, 23, 15, 197],\n [-172, 190, 155, -37, 133, -65, -157],\n [-79, 87, 203, 21, -79, -61, -107],\n [69, 8, -55, 37, 91, 94, 116],\n [-37, 92, 190, 42, 82, -97, -63],\n [94, 15, -4, 68, 122, 69, 131],\n [-44, -32, -78, -61, -15, -36, -57]]\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 7x7 matrix:\n[[47, 7, 221, 93, 90, 251, -87],\n [-88, -16, 35, 92, 123, -15, 2],\n [-22, 57, -16, 37, 31, -146, 7],\n [-8, -115, 160, 33, -22, -35, 141],\n [-38, -36, 34, -31, 90, 126, -359],\n [-6, -10, 168, 38, 66, -32, -226],\n [-30, 131, -3, 125, 111, -174, 153]]\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[[-22, 20, 47, 21, 54, 26, 45],\n [-23, 80, 73, 114, 86, 109, 80],\n [38, 8, -64, 30, -72, 14, -54],\n [8, -64, -40, -96, -48, -88, -48],\n [-14, -96, -14, -156, -20, -134, -32],\n [16, 28, -17, 51, -18, 40, -9],\n [84, -48, -168, -36, -192, -60, -156]]\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[[-20, 36, 34, 16, 22, -2, 0],\n [60, -16, -50, -39, 14, -72, -51],\n [31, -20, -142, -116, 71, -29, -125],\n [7, 110, 79, 64, 21, -62, 51],\n [33, -110, 13, -78, 67, -90, -209],\n [-7, -110, 59, -61, 75, -58, -212],\n [43, 48, 70, 103, -89, -35, 158]]\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[[60, -77, 116, 84, -101, 116, -214],\n [-52, -99, 10, -58, -144, -272, 121],\n [-36, 138, 58, -38, -40, 116, -12],\n [31, -28, -3, 104, 90, 140, -78],\n [-148, 164, -71, -25, 79, 74, 290],\n [-119, 113, 12, -93, -110, -27, 204],\n [-169, 194, -78, 35, 162, 147, 299]]\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[[48, -9, -87, 16, 81, 7, 12],\n [44, -88, 209, -14, 15, -123, -85],\n [-106, 154, -200, 76, -21, 114, 121],\n [-130, 123, -325, 80, -98, 183, 117],\n [92, 46, -152, 13, 147, 13, 33],\n [38, -44, -102, 36, 13, 122, 39],\n [338, -60, -43, -30, 261, -37, -72]]?\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[[-220, 107, 163, -3, -13, -127, -287],\n [43, 3, 128, -130, -129, 121, -80],\n [184, 95, 239, -108, 67, 3, -302],\n [192, 74, 94, 118, 244, -4, -202],\n [172, 19, -48, 50, 192, -141, 8],\n [157, -74, -233, -64, -40, 92, 348],\n [254, -62, -142, 18, 116, -34, 210]]\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[[-147, 82, -127, 36, -60, 148, 38],\n [-84, 21, 39, 93, -64, 3, 85],\n [13, -128, 120, -86, 15, -91, 33],\n [-193, 91, -90, 5, -85, 170, 138],\n [98, -119, 170, 77, 17, -200, -44],\n [91, 7, -66, 37, 48, -25, -153],\n [-106, -85, -10, 23, -37, 0, -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[[60, 130, 115, -65, -35, 55, 90],\n [-58, -16, -40, -48, -42, -38, 18],\n [50, 30, 45, 25, 25, 35, 0],\n [-110, -160, -160, 40, 10, -90, -90],\n [25, -32, -8, 60, 45, 11, -45],\n [16, 66, 51, -49, -31, 19, 54],\n [23, 42, 39, -17, -8, 20, 27]]?\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[[-91, -84, -56, 123, -11, -168, 43],\n [-63, -28, -105, 55, 22, 70, -72],\n [173, 71, 64, -118, 38, 298, -14],\n [-187, -69, -12, 14, -54, -301, 94],\n [190, 76, 9, 6, 53, 282, -115],\n [-204, -89, 0, -49, -55, -262, 159],\n [14, -56, -14, 154, 0, -133, 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[[48, -6, -2, -39, 57, 20, 38],\n [-212, 8, -22, -59, -187, -2, -174],\n [-40, 4, 0, 20, -44, -12, -32],\n [-52, 4, -2, 11, -53, -10, -42],\n [52, 8, 22, 139, 11, -46, 46],\n [-96, 6, -6, 3, -93, -12, -78],\n [4, 2, 4, 28, -4, -10, 4]]?\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[[-128, 59, 11, 227, 201, -73, -127],\n [178, 58, -87, 53, -2, 96, -211],\n [74, -107, -186, -174, 63, 138, 126],\n [133, -148, 54, -62, -113, -22, -95],\n [31, 24, -97, 183, 60, -70, -192],\n [242, 82, -180, -60, -141, 123, -102],\n [-73, -171, -73, -93, 162, 33, 138]]\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[[29, -151, -196, -9, 243, -199, -99],\n [6, 65, 74, -84, -9, 89, 10],\n [-73, -1, -316, -86, 18, -20, 96],\n [35, 73, 119, -118, 6, 63, -102],\n [-10, 48, -124, -173, -15, 52, -48],\n [110, -84, 186, 55, -3, -104, -298],\n [26, 81, 209, -49, -96, 156, 12]]\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[[-89, -93, 28, 138, 84, 20, 202],\n [-64, -8, 130, -110, -277, 99, 78],\n [-80, 83, 72, 132, 217, 132, 127],\n [-1, 115, -104, 34, 159, -4, -195],\n [-174, 124, 198, -59, 17, 283, 22],\n [-86, -118, -116, 173, 31, -68, 152],\n [32, -294, -110, 46, -123, -255, 63]]\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[[21, -3, -30, 24, 24, -33, 24],\n [7, -1, -10, 8, 8, -11, 8],\n [-56, 8, 80, -64, -64, 88, -64],\n [84, -12, -120, 96, 96, -132, 96],\n [7, -1, -10, 8, 8, -11, 8],\n [28, -4, -40, 32, 32, -44, 32],\n [-7, 1, 10, -8, -8, 11, -8]]?\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[[-156, 142, 46, 14, -16, -50, 80],\n [54, -11, 28, -39, -36, -12, -89],\n [-106, 148, 99, -16, -54, -29, -17],\n [-197, 93, -47, 81, 65, -27, 232],\n [134, -39, 59, -79, -72, -5, -198],\n [30, -37, 5, 67, 52, 149, 34],\n [-220, 109, -42, 97, 74, -10, 257]]\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[[37, -143, 165, -213, -157, -55, 179],\n [-86, -50, 232, 34, -128, 76, 340],\n [150, -169, 46, -274, 21, -66, 66],\n [66, -197, 238, -158, -216, -61, 285],\n [-8, -101, 135, -69, 8, 28, 239],\n [-122, 102, 222, -88, -169, 187, 263],\n [-105, -122, -4, -121, -76, -199, -49]]\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[[9, 148, 101, -107, 198, -48, 32],\n [-272, 57, 161, 61, -62, -104, -30],\n [73, -24, -53, 77, -49, -6, 117],\n [-29, -38, 59, -5, -27, -58, -19],\n [111, -120, -7, -2, -65, -58, 6],\n [-227, 105, 157, -88, 93, -27, -140],\n [4, -11, -16, 34, -123, -103, -73]]?\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[[94, 56, -84, 4, 82, 30, -40],\n [-80, 59, 39, -104, -47, -105, 26],\n [1, -151, 109, 186, -122, 180, -130],\n [-12, -66, 42, 64, -42, 54, -20],\n [40, -61, 35, 112, -47, 123, -110],\n [115, -70, 35, 200, -65, 240, -250],\n [89, 13, -37, 62, 26, 90, -102]]\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[[-107, -107, -49, -77, 130, -69, 34],\n [-209, -46, 116, 47, 208, -218, 200],\n [16, 34, -32, -132, -30, 10, 100],\n [-49, 51, 143, 85, -102, -51, -78],\n [92, 81, 12, 38, -230, 83, -33],\n [28, 23, -24, -84, 41, 15, 41],\n [19, -79, -147, -179, 118, 47, -6]]\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, 46, -9, 18, 47, -117, 53],\n [-24, 60, -18, 36, -18, -90, -6],\n [-106, -92, 36, -72, 134, 54, 110],\n [-100, -56, 24, -48, 108, 12, 92],\n [-40, -104, 36, -72, 92, 108, 68],\n [37, -16, 3, -6, -18, 42, -20],\n [132, -24, 0, 0, -84, 108, -84]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-177, -263, -101, -103, 65, -2, -22],\n [-136, -224, 122, 68, -37, 42, 2],\n [62, 11, -184, -15, -70, 108, 13],\n [-69, -125, 51, 64, -36, 24, -85],\n [7, 129, 166, 2, 121, -114, 42],\n [-184, -158, 59, 27, 187, -54, -174],\n [118, 95, 65, 19, -152, 64, 234]]\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[[-93, -202, 199, -31, -89, 43, -38],\n [-70, -186, 146, -222, 50, 22, -12],\n [-97, 7, -81, -3, -107, -114, 45],\n [4, -25, 76, -65, -5, -90, -21],\n [-90, -136, -195, -150, -165, 133, 79],\n [73, -160, -15, 48, 1, -121, -62],\n [-116, 59, -7, -104, -116, 119, 72]]\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[[-221, 9, 150, -15, -13, 46, 106],\n [71, -324, -71, -11, -103, 400, -81],\n [204, 213, -66, -30, 70, -304, -61],\n [-103, 203, 0, 181, 29, -170, -30],\n [-103, -73, 116, -26, 167, 17, 53],\n [124, -101, -130, -168, -118, 158, -121],\n [-75, 102, -91, -157, 65, -223, 92]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-156, 226, -10, -11, -268, 82, 21],\n [212, -118, 76, -120, 173, 172, 211],\n [41, 24, 15, -3, 153, 10, -63],\n [7, -9, -105, 22, -274, 105, 161],\n [-120, -2, -156, 130, -184, -34, -182],\n [1, 28, -149, 113, -7, 11, -164],\n [81, -157, -72, 43, 108, 28, -16]]\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[[87, 58, 79, -171, -11, -133, -68],\n [-116, 32, 31, 1, -38, 74, 128],\n [-141, 138, 15, -39, -95, 37, 228],\n [-145, 34, -22, 74, -45, 113, 172],\n [-101, 50, 157, -161, -43, 15, 92],\n [-156, 64, -41, 81, -62, 110, 208],\n [-191, 38, 100, -44, -55, 117, 188]]?\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 7x7 matrix:\n[[-6, 11, -10, 12, 4, 2, 6],\n [-36, 66, -60, 72, 24, 12, 36],\n [-18, 33, -30, 36, 12, 6, 18],\n [-36, 66, -60, 72, 24, 12, 36],\n [42, -77, 70, -84, -28, -14, -42],\n [6, -11, 10, -12, -4, -2, -6],\n [60, -110, 100, -120, -40, -20, -60]]\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, -10, 34, 66, -6, -42, 42],\n [-23, -72, -95, 56, -96, -14, 4],\n [-108, 42, 30, 102, 54, -6, -114],\n [54, 57, 109, -24, 81, -13, 38],\n [-21, -23, -10, 86, -27, -31, -4],\n [15, -37, -20, 52, -45, -29, 34],\n [-150, -28, -152, -17, -54, 70, -155]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[99, -27, 81, -54, 99, -99, 72],\n [121, -33, 99, -66, 121, -121, 88],\n [0, 0, 0, 0, 0, 0, 0],\n [-99, 27, -81, 54, -99, 99, -72],\n [22, -6, 18, -12, 22, -22, 16],\n [-11, 3, -9, 6, -11, 11, -8],\n [132, -36, 108, -72, 132, -132, 96]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[73, -47, -11, 52, -18, -69, 10],\n [-45, 35, -97, -20, -54, 57, 38],\n [292, -265, -25, 296, 82, -122, -137],\n [-85, 49, -2, -51, 24, 96, -20],\n [91, -116, -143, 157, 18, 66, -77],\n [-126, 131, 62, -157, -40, 5, 81],\n [-139, 113, 5, -124, -18, 87, 38]]?\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[[-24, -30, 129, -84, 66, -78, 24],\n [66, 76, 32, 88, 72, 0, 90],\n [32, 36, 66, 24, 68, -28, 64],\n [117, 136, -19, 184, 78, 42, 129],\n [-36, -44, 134, -104, 60, -84, 12],\n [22, 26, -29, 44, -2, 22, 14],\n [-12, -16, 124, -64, 72, -72, 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 7x7 matrix:\n[[-119, 83, 4, 159, -53, 13, 69],\n [17, -15, -21, -40, 138, 72, -35],\n [132, -92, -4, -176, 56, -16, -76],\n [-3, -1, -20, -13, 127, 73, -23],\n [20, -14, -1, -27, 11, -1, -12],\n [19, -13, 1, -24, -2, -8, -9],\n [80, -56, -4, -108, 44, -4, -48]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 7x7 matrix:\n[[64, -26, -42, 126, 70, 86, 202],\n [-50, -52, -112, -61, -7, 143, 45],\n [-68, 81, 145, 40, -180, -10, -70],\n [75, -62, -108, 29, 150, 34, 128],\n [-64, -22, -54, -105, -37, 49, -73],\n [33, -43, -77, -41, 98, -12, 10],\n [9, 54, 108, 36, -45, -99, -63]]\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[[-54, 175, 34, 266, 49, -75, 18],\n [-173, -155, 42, 79, 139, -126, -20],\n [-125, 18, 23, 152, 92, -165, -63],\n [-27, 84, 118, 155, -47, -36, 41],\n [-47, -171, -61, -207, 98, 46, -46],\n [79, -30, 147, 167, -173, 73, 212],\n [-32, -220, -62, -247, 99, 110, -3]]\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[[2, -17, -4, 9, -22, -44, -31],\n [-34, -10, -36, -10, 10, -6, -32],\n [-66, -14, -68, -22, 26, 2, -52],\n [-58, -36, -68, -8, -6, -58, -90],\n [81, 36, 90, 18, -9, 45, 99],\n [-13, -16, -18, 2, -11, -33, -35],\n [-81, 10, -74, -40, 65, 71, -13]]\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[[-47, -14, -34, -132, -7, 138, -72],\n [-39, -42, -62, 7, 6, 17, -59],\n [85, 38, 54, -216, 153, 106, 8],\n [59, 28, 68, 125, -42, -87, 45],\n [61, 47, 53, -166, 117, 47, 61],\n [4, 55, 73, -10, -88, 19, 59],\n [-59, -109, -155, 38, 89, -17, -123]]\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[[185, -145, 231, 214, -289, 164, 68],\n [18, -89, 6, 58, -21, 64, 24],\n [-85, 131, -67, 4, 232, 110, 6],\n [20, 52, 3, -143, -2, -176, -112],\n [275, 39, 141, 122, -267, 86, 75],\n [20, -143, 61, -22, 81, -115, 105],\n [121, -31, 140, 61, -217, 38, -67]]\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, 8, -16, -32, 72, -48, -8],\n [33, 3, -6, -12, 27, -18, -3],\n [33, 3, -6, -12, 27, -18, -3],\n [99, 9, -18, -36, 81, -54, -9],\n [-11, -1, 2, 4, -9, 6, 1],\n [-121, -11, 22, 44, -99, 66, 11],\n [110, 10, -20, -40, 90, -60, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -48, -44, 24, -48, 12, 12],\n [4, 48, 44, -24, 48, -12, -12],\n [7, 84, 77, -42, 84, -21, -21],\n [1, 12, 11, -6, 12, -3, -3],\n [-7, -84, -77, 42, -84, 21, 21],\n [3, 36, 33, -18, 36, -9, -9],\n [4, 48, 44, -24, 48, -12, -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[[65, -45, 120, 0, 0, 85, 40],\n [120, -110, 120, 60, -20, 60, -20],\n [107, -101, 96, 60, -20, 43, -28],\n [-56, 28, -144, 24, -8, -112, -72],\n [-48, 44, -48, -24, 8, -24, 8],\n [33, -39, 0, 36, -12, -15, -36],\n [37, -31, 48, 12, -4, 29, 4]]?\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[[-136, 48, -199, 85, -115, -321, 116],\n [-167, -180, -68, -189, -25, -163, -13],\n [125, 105, -97, -25, -93, -77, 14],\n [-179, -175, -76, -118, -30, -251, 59],\n [-183, -216, 108, -116, 109, 91, -69],\n [65, -141, 150, -121, 98, 156, -44],\n [-193, -71, -52, -1, -6, -113, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[70, 110, 0, 10, -100, 50, -40],\n [-28, -44, 0, -4, 40, -20, 16],\n [-63, -99, 0, -9, 90, -45, 36],\n [-77, -121, 0, -11, 110, -55, 44],\n [63, 99, 0, 9, -90, 45, -36],\n [63, 99, 0, 9, -90, 45, -36],\n [-28, -44, 0, -4, 40, -20, 16]]?\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[[-24, -4, -16, -8, -12, -12, -22],\n [-108, -18, -72, -36, -54, -54, -99],\n [-132, -22, -88, -44, -66, -66, -121],\n [36, 6, 24, 12, 18, 18, 33],\n [-144, -24, -96, -48, -72, -72, -132],\n [-48, -8, -32, -16, -24, -24, -44],\n [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[[-64, -57, 45, -41, -12, -92, -78],\n [252, -218, -139, -68, 142, 37, -43],\n [-88, 73, -47, -53, 112, 10, -73],\n [143, -41, 21, 20, -109, 30, -165],\n [100, 42, 15, 82, -42, 43, 49],\n [127, -105, 70, 18, -119, -59, -168],\n [-159, 145, -70, -28, 115, 71, 118]]\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[[94, 103, -4, 30, -98, -24, 192],\n [17, 116, -125, -36, 65, 12, -165],\n [229, 160, -103, 84, -92, -225, 57],\n [100, -42, 80, 27, -130, -30, 192],\n [23, 172, -89, 4, 6, 7, 39],\n [-71, 179, -157, -33, 132, 43, -177],\n [85, -205, 137, -28, -123, 28, 69]]\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[[18, 289, 297, -189, 67, -268, 245],\n [267, -33, 76, -116, -191, -119, 177],\n [-47, 185, 313, -71, 33, -91, 73],\n [287, 65, 195, -82, -98, -111, 68],\n [150, -142, -51, -19, -160, -34, 116],\n [-118, 107, 186, -22, 44, -70, 80],\n [139, 54, 242, -72, -99, -9, 17]]\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[[-11, 105, -7, 131, 110, 70, -41],\n [-7, 53, -28, -95, 336, 34, 14],\n [171, -29, 85, -67, -104, -144, -99],\n [-262, 109, 26, 68, 45, 96, -139],\n [-60, -13, -105, -28, -109, -11, 120],\n [49, 83, -98, -99, 360, 11, 86],\n [135, 5, 3, -147, -92, -186, -45]]?\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[[-160, 67, -72, 18, 6, 117, -8],\n [-4, 28, -97, 151, 59, 72, 1],\n [-254, -96, -203, 139, 6, 42, -143],\n [-255, -13, -220, 136, 63, 23, -146],\n [-268, -198, -364, 291, 39, -176, -163],\n [38, -113, -80, 74, -100, -204, 85],\n [74, -97, 188, -127, -85, 113, 75]]\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[[-45, -27, -72, 36, -99, -54, -36],\n [-60, -36, -96, 48, -132, -72, -48],\n [45, 27, 72, -36, 99, 54, 36],\n [10, 6, 16, -8, 22, 12, 8],\n [-15, -9, -24, 12, -33, -18, -12],\n [35, 21, 56, -28, 77, 42, 28],\n [45, 27, 72, -36, 99, 54, 36]]\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[[-22, 72, -39, 91, 15, -73, 32],\n [-4, 238, 92, -53, -96, 95, -131],\n [140, 7, 114, 57, -153, -47, 36],\n [-137, 293, -38, 48, 35, 34, -89],\n [149, 76, 93, 52, -151, -86, 11],\n [62, -44, -3, -46, -11, -38, -5],\n [-128, 21, 44, -80, 29, 212, -77]]\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 7x7 matrix:\n[[-102, 83, 21, -51, 85, 41, -4],\n [-44, -104, -168, 122, 46, 81, -62],\n [137, 163, 233, -81, -68, 6, 85],\n [133, -119, -44, 2, -65, -8, 16],\n [23, -68, -120, 119, -2, -24, -66],\n [63, -145, -213, 246, 11, 164, -78],\n [-1, -61, 28, 8, -121, -199, 6]]\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 7x7 matrix:\n[[6, 28, 16, -9, 66, 25, -73],\n [6, 22, 40, 36, 0, 28, -52],\n [11, 50, 29, -10, 105, 49, -121],\n [-6, -11, -135, -150, 109, -11, 87],\n [-17, -70, 93, 64, -43, -153, -79],\n [-8, -12, -66, -143, 204, -71, -73],\n [-36, -129, 3, -81, 93, -282, -66]]\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[[-48, -6, 2, 88, -94, 46, 34],\n [-18, 54, -8, -112, 106, 26, -16],\n [-124, 127, -17, -140, 115, 141, 15],\n [-82, 31, -3, 44, -57, 85, 37],\n [106, -73, 9, 28, -9, -115, -31],\n [165, -165, 22, 176, -143, -187, -22],\n [83, -89, 12, 104, -87, -95, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[368, -16, 254, -179, 197, -252, -107],\n [252, -44, 199, 189, -174, 68, -39],\n [164, 73, 161, 50, -19, 9, 11],\n [-104, -78, -53, 22, -157, 77, -236],\n [-72, -23, -178, -8, 66, 10, 301],\n [29, -77, 103, 164, -20, 0, 55],\n [-36, 50, 104, -59, 141, -45, 131]]?\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[[19, -150, 87, 86, -19, 174, -289],\n [124, -99, -109, 239, -7, -135, -87],\n [3, 4, 97, -94, -171, 167, -243],\n [-92, 69, 59, 64, 232, -47, 269],\n [-141, -56, 67, 151, -169, 83, -127],\n [30, -107, 61, 89, -129, 132, -305],\n [126, -86, -66, -88, -33, 35, -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[[-35, -95, 37, 41, 5, -11, 28],\n [-34, -112, 114, 177, 204, -232, 78],\n [-14, 31, -43, 8, -88, -183, 178],\n [-44, -230, 86, 110, -81, 88, 41],\n [-124, 16, -25, -129, -95, 120, -25],\n [151, 37, -45, -23, -87, 179, -95],\n [33, -80, 98, 143, 215, -14, -106]]?\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[[-36, 24, -8, -36, -16, -20, 24],\n [-81, 54, -18, -81, -36, -45, 54],\n [72, -48, 16, 72, 32, 40, -48],\n [72, -48, 16, 72, 32, 40, -48],\n [-81, 54, -18, -81, -36, -45, 54],\n [63, -42, 14, 63, 28, 35, -42],\n [72, -48, 16, 72, 32, 40, -48]]\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[[-48, -42, -60, -72, -60, -60, 54],\n [24, 21, 30, 36, 30, 30, -27],\n [0, 0, 0, 0, 0, 0, 0],\n [88, 77, 110, 132, 110, 110, -99],\n [-72, -63, -90, -108, -90, -90, 81],\n [-56, -49, -70, -84, -70, -70, 63],\n [16, 14, 20, 24, 20, 20, -18]]\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[[-82, -178, -62, 38, -38, 19, 36],\n [42, 27, -36, 28, -37, -47, 33],\n [81, 2, -123, 90, -116, -118, 102],\n [-27, -91, -21, 86, -13, -95, 123],\n [-110, -100, 74, -36, 80, 80, -36],\n [-167, -298, -43, 52, -8, 39, 60],\n [-32, -77, -46, 0, -33, 37, -15]]?\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[[-120, -96, 132, -12, 108, -60, 48],\n [-30, -24, 33, -3, 27, -15, 12],\n [100, 80, -110, 10, -90, 50, -40],\n [20, 16, -22, 2, -18, 10, -8],\n [80, 64, -88, 8, -72, 40, -32],\n [20, 16, -22, 2, -18, 10, -8],\n [120, 96, -132, 12, -108, 60, -48]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 7x7 matrix:\n[[-187, 176, 66, -55, 99, -66, -22],\n [79, -69, -33, 27, -40, 31, 20],\n [-74, 75, 21, -18, 41, -23, 2],\n [-187, 176, 66, -55, 99, -66, -22],\n [-94, 51, 69, -54, 37, -55, -86],\n [39, -26, -24, 19, -17, 20, 26],\n [11, 86, -96, 71, 27, 60, 194]]\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[[-55, 0, 22, 132, 77, -88, 121],\n [-25, 0, 10, 60, 35, -40, 55],\n [59, -8, -8, -136, -89, 86, -109],\n [-4, -32, 64, 32, -20, -40, 92],\n [41, 8, -32, -104, -51, 74, -111],\n [-34, -32, 76, 104, 22, -88, 158],\n [-7, 24, -44, 0, 29, 14, -47]]?\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[[68, 8, -10, -30, 54, 74, -14],\n [-136, -70, -42, 132, -66, -134, 154],\n [81, 65, -37, -239, 77, -39, -17],\n [-108, 63, -42, 35, -22, -126, 46],\n [35, 138, 0, 15, 62, 92, -118],\n [67, -193, -8, 101, 13, 110, 133],\n [-59, -47, 26, -136, -88, -174, 24]]\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 7x7 matrix:\n[[-17, 15, 49, -28, -53, -43, -7],\n [66, -156, -86, 50, 42, -80, -10],\n [-47, -238, -45, 108, -12, -96, 43],\n [-132, -82, -24, -3, -27, -40, -117],\n [65, -176, -19, -117, 16, -101, -97],\n [33, -82, 59, -155, -18, 30, -45],\n [107, 303, 55, 55, -90, 26, 70]]\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 7x7 matrix:\n[[-56, -65, 20, 23, 44, 41, -66],\n [33, 30, 202, 90, 158, 11, -131],\n [-70, -3, -33, -57, 74, -4, -143],\n [-27, -10, -18, 7, -30, 58, -63],\n [-155, -143, -132, -10, -86, 153, -115],\n [94, 110, 0, -17, -56, -49, 74],\n [190, 199, 78, -31, 28, -185, 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[[126, -25, 28, -125, 222, -33, 208],\n [-70, -143, 53, 169, 102, -36, 26],\n [-117, -104, 105, 76, -221, -3, -112],\n [34, 227, 73, -152, 130, 159, 27],\n [72, -11, 3, -129, 11, 33, 54],\n [-141, -164, 210, 138, -180, -4, -123],\n [2, 2, 93, -139, -79, 77, 19]]\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[[59, 48, 200, -51, 76, 172, 79],\n [-85, -20, -123, 101, 18, -152, -5],\n [-106, 92, 45, 48, 64, -16, 52],\n [80, 24, 142, -112, -12, 168, 12],\n [-3, 128, 132, 59, 92, 68, 81],\n [40, -36, -115, 196, 66, -156, 24],\n [-117, 128, 111, -148, -49, 118, -11]]\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 7x7 matrix:\n[[137, -89, -80, 93, 253, -169, -97],\n [-4, -107, -7, 90, 7, -113, -15],\n [-103, 3, -4, -91, -115, 43, 107],\n [-43, 22, -117, 75, 76, -36, 34],\n [-58, 23, -73, -32, 12, 7, 71],\n [81, -6, 33, -33, 60, -6, -54],\n [-216, 196, -4, -224, -256, 268, 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[[-21, -159, 17, 116, -66, 49, -1],\n [14, -69, 46, 158, -59, -33, -48],\n [15, -73, 82, 71, -14, 27, -29],\n [-57, 52, 130, 38, -127, -4, -73],\n [123, -28, 48, 197, 67, -108, -67],\n [41, -84, -6, 157, -11, -44, -25],\n [73, -165, 88, 46, 98, 87, 7]]\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[[88, -88, 96, 72, 32, 88, 80],\n [22, -22, 24, 18, 8, 22, 20],\n [-132, 132, -144, -108, -48, -132, -120],\n [-121, 121, -132, -99, -44, -121, -110],\n [-121, 121, -132, -99, -44, -121, -110],\n [-44, 44, -48, -36, -16, -44, -40],\n [-44, 44, -48, -36, -16, -44, -40]]\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, 7, 35, -56, -56, -56, -28],\n [2, 14, -32, 26, 6, 20, -10],\n [-120, 83, -95, 26, -74, -4, -102],\n [34, 25, -79, 76, 36, 64, -8],\n [93, 12, -93, 111, 81, 102, 21],\n [170, -88, 70, 14, 114, 44, 122],\n [219, -100, 61, 41, 151, 74, 147]]?\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[[-47, 23, 48, 74, -28, 70, 110],\n [153, 59, -38, 189, -11, 119, 66],\n [-38, 24, 26, -124, 157, -139, -58],\n [102, 54, 44, 237, -209, 256, 183],\n [138, 154, 140, 24, 14, 58, 96],\n [61, 23, 82, -85, -149, 39, -16],\n [21, 121, 110, 186, 11, 145, 228]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-44, 276, -17, 101, -167, 89, 94],\n [-8, 61, -5, 33, 3, -108, 13],\n [-12, -150, 50, -54, 108, -24, -38],\n [18, -41, -10, -8, 47, -107, -23],\n [60, 113, -96, 32, -134, 71, 15],\n [64, -124, -42, -38, 86, -170, -64],\n [30, -199, 14, -76, 109, -25, -65]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-65, 96, 137, -17, -12, 18, -74],\n [91, -293, -16, -91, 116, 123, -22],\n [-201, 125, -210, 153, 117, -233, 121],\n [12, 97, -221, 20, -44, 85, 204],\n [107, -33, 144, -104, -288, -56, -114],\n [-80, -230, -104, 25, 352, 75, 48],\n [-228, 132, 0, 158, 148, -298, -52]]\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[[123, -183, -200, 11, -78, -238, 224],\n [81, -163, 31, -13, -99, -129, 48],\n [-46, -37, 479, 78, -151, 134, -248],\n [20, -104, 42, 30, -85, -51, 0],\n [40, -98, 117, -29, -66, -30, -31],\n [-89, 14, 434, 98, -119, 188, -255],\n [-18, -79, -233, -57, 34, -9, 69]]\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[[-2, 6, 16, 4, -12, -6, -18],\n [4, -12, -32, -8, 24, 12, 36],\n [-3, 9, 24, 6, -18, -9, -27],\n [-4, 12, 32, 8, -24, -12, -36],\n [4, -12, -32, -8, 24, 12, 36],\n [7, -21, -56, -14, 42, 21, 63],\n [-7, 21, 56, 14, -42, -21, -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[[55, -28, 207, 61, 36, -73, -88],\n [-150, 66, -189, 60, 48, 51, -96],\n [70, -60, 120, -6, 20, -10, -9],\n [-90, 24, -6, 102, 84, 0, -165],\n [10, -118, -13, -8, 108, 113, -73],\n [25, -60, -35, -45, 20, 65, 30],\n [100, -94, 201, 10, 48, -19, -46]]\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[[-108, -48, 108, 108, 12, 72, 0],\n [54, 24, -54, -54, -6, -36, 0],\n [72, 32, -72, -72, -8, -48, 0],\n [36, 16, -36, -36, -4, -24, 0],\n [72, 32, -72, -72, -8, -48, 0],\n [45, 20, -45, -45, -5, -30, 0],\n [9, 4, -9, -9, -1, -6, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[90, 60, 10, 70, -110, -70, 40],\n [81, 54, 9, 63, -99, -63, 36],\n [108, 72, 12, 84, -132, -84, 48],\n [-81, -54, -9, -63, 99, 63, -36],\n [108, 72, 12, 84, -132, -84, 48],\n [18, 12, 2, 14, -22, -14, 8],\n [-27, -18, -3, -21, 33, 21, -12]]\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 7x7 matrix:\n[[130, 262, -200, -78, -41, -24, 15],\n [182, 148, -187, 71, -51, -97, 72],\n [274, -60, 58, 193, -3, -29, -45],\n [-32, -44, -40, -127, 183, 56, -36],\n [-8, -195, 83, -154, 52, -155, 88],\n [124, 134, -47, -12, -275, -231, 141],\n [-200, -78, 128, -115, -174, -103, 30]]\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[[-30, -60, -70, -80, -90, -50, 110],\n [-9, -18, -21, -24, -27, -15, 33],\n [27, 54, 63, 72, 81, 45, -99],\n [-36, -72, -84, -96, -108, -60, 132],\n [-27, -54, -63, -72, -81, -45, 99],\n [18, 36, 42, 48, 54, 30, -66],\n [-36, -72, -84, -96, -108, -60, 132]]\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, -72, -97, -145, -194, 317, -149],\n [-42, -150, -48, 92, -34, -30, 46],\n [45, 213, -3, -87, 111, 24, -93],\n [-57, -143, -31, 137, 15, -112, 85],\n [60, 110, -16, -152, -50, 182, -124],\n [-15, -23, -1, 39, 19, -46, 27],\n [24, -59, -22, -82, -135, 167, -56]]\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 7x7 matrix:\n[[58, 112, 42, -127, 93, -49, -7],\n [53, 77, 42, -72, 53, -49, 28],\n [-39, 21, -42, -82, 59, 49, -126],\n [74, 140, 54, -157, 115, -63, -5],\n [25, -35, 30, 90, -65, -35, 110],\n [48, 84, 36, -90, 66, -42, 6],\n [-75, -105, -60, 95, -70, 70, -45]]\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[[-47, 70, 6, -41, 1, -67, 1],\n [11, -52, 54, 127, -115, 79, -53],\n [-41, 76, -18, -85, 49, -85, 23],\n [-88, 119, 30, -37, -37, -104, -16],\n [-4, -13, 30, 59, -61, 28, -28],\n [33, -48, -6, 25, 3, 45, 1],\n [-57, 51, 60, 62, -108, -21, -49]]\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[[96, 34, -78, -78, -183, -129, -44],\n [5, 54, 148, 208, 31, 212, -36],\n [13, -81, 82, 124, 123, 168, -87],\n [-39, 105, 202, 155, 40, 225, 57],\n [-51, 56, 28, -81, -9, -28, 104],\n [-55, -5, -126, 55, -20, -111, -33],\n [-42, 63, 44, 40, -7, 33, 49]]\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[[198, -78, -2, -33, 57, -86, 59],\n [250, -248, 102, -24, -198, 132, 110],\n [97, -57, 131, -74, -15, -76, 0],\n [34, -7, 102, 67, -25, 86, -52],\n [10, 54, -10, 22, 88, -66, -60],\n [123, -21, 9, 60, 65, 62, 102],\n [-178, 21, 78, 8, -140, 130, -41]]\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[[32, -8, 90, -112, -163, 159, 11],\n [34, 50, -36, -2, -5, -9, -59],\n [-25, -53, 63, -31, -43, 56, 63],\n [6, -42, 108, -102, -147, 153, 51],\n [-49, -29, -45, 89, 131, -118, 33],\n [-65, -61, -9, 73, 109, -88, 71],\n [-32, -64, 72, -32, -44, 60, 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 7x7 matrix:\n[[-88, 44, -80, -112, -8, -16, -184],\n [-92, 52, -82, -122, -13, -17, -194],\n [28, 76, 50, -38, -67, 1, 34],\n [-40, 80, -20, -100, -50, -10, -100],\n [-42, 51, -30, -78, -27, -9, -96],\n [12, -24, 6, 30, 15, 3, 30],\n [6, -23, 0, 24, 16, 2, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-32, 80, 24, -48, 48, -56, 80],\n [-8, 20, 6, -12, 12, -14, 20],\n [-48, 120, 36, -72, 72, -84, 120],\n [40, -100, -30, 60, -60, 70, -100],\n [0, 0, 0, 0, 0, 0, 0],\n [44, -110, -33, 66, -66, 77, -110],\n [40, -100, -30, 60, -60, 70, -100]]\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[[56, 44, -93, 73, -64, -61, -83],\n [60, 24, -117, 93, -48, -75, -87],\n [50, 38, -84, 66, -56, -55, -74],\n [26, -58, -102, 84, 40, -61, -32],\n [52, -44, -150, 122, 16, -92, -70],\n [58, 142, -24, 14, -152, -23, -94],\n [-82, 14, 195, -157, 24, 122, 115]]\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[[-51, -63, 56, -14, -47, -4, 38],\n [216, -98, -306, -75, 167, -42, -58],\n [72, -194, -264, 13, 27, -34, 60],\n [102, 42, 0, -119, 17, -96, 52],\n [-78, -87, -71, 211, -148, 123, 96],\n [158, -49, -49, -30, -35, 53, 54],\n [170, -72, -43, -106, 23, 12, 16]]\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[[63, -4, 58, -49, -27, 26, 16],\n [126, -34, 52, -70, -9, 95, -53],\n [-78, 52, 44, 10, -48, -110, 134],\n [73, -10, 54, -51, -22, 39, 1],\n [-27, 24, 30, -3, -27, -48, 66],\n [43, -18, 2, -17, 8, 43, -39],\n [-17, -8, -38, 23, 23, 8, -34]]\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[[103, 197, -116, -27, -36, 59, 23],\n [206, 364, 106, -246, -82, 76, -154],\n [125, -70, 63, -81, -19, -64, -166],\n [-223, -47, 212, -53, 0, -159, 51],\n [109, -2, -232, 164, 6, 123, -52],\n [129, 51, -185, 6, -125, 23, -120],\n [118, 42, -76, -24, -172, -74, -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[[-53, 49, 26, 26, 2, -8, 30],\n [-114, 107, 37, 20, 29, 37, 27],\n [110, -105, -15, 20, -55, -95, 15],\n [-135, 125, 64, 62, 8, -14, 72],\n [-77, 66, 99, 154, -77, -187, 165],\n [-86, 83, 1, -36, 57, 105, -33],\n [-130, 120, 66, 68, 2, -26, 78]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-160, 31, 7, -83, -109, -77, 93],\n [64, -30, 10, -110, -16, -68, -114],\n [-184, 50, 44, -34, -83, -41, 166],\n [200, -55, -77, 67, 92, 62, -181],\n [24, 12, 126, -18, 54, 6, 48],\n [96, -47, -227, 109, 2, 60, -161],\n [-56, 11, -99, 93, -24, 46, 41]]\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[[178, -248, 172, 4, 48, 88, -431],\n [121, 93, -24, 29, -134, 96, -26],\n [178, -145, 32, -3, 47, 68, 19],\n [26, 101, 32, -31, -90, -31, 56],\n [-93, -74, 62, -64, 30, 101, -95],\n [-267, 162, -262, 68, 36, 17, 283],\n [-216, -107, -104, 57, 130, 133, -173]]\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[[22, 4, 4, -10, 12, 20, 2],\n [99, 18, 18, -45, 54, 90, 9],\n [-11, -2, -2, 5, -6, -10, -1],\n [-77, -14, -14, 35, -42, -70, -7],\n [77, 14, 14, -35, 42, 70, 7],\n [0, 0, 0, 0, 0, 0, 0],\n [55, 10, 10, -25, 30, 50, 5]]\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[[-6, -132, 54, 10, -114, -6, 112],\n [2, 70, -96, -98, 98, -64, 70],\n [11, -80, 186, 281, -115, 95, 2],\n [4, 157, -176, -172, 194, -99, 59],\n [-12, -84, -30, -120, -60, -36, 60],\n [5, 138, -50, -9, 111, 19, -156],\n [5, 12, -8, 19, 27, -23, 82]]\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[[70, 107, 53, 0, 16, -12, 113],\n [28, 52, 12, 0, -104, 32, 36],\n [-7, -13, -3, 0, 26, -8, -9],\n [-49, -77, -35, 0, 14, 0, -77],\n [-14, -26, -6, 0, 52, -16, -18],\n [-28, -56, -8, 0, 152, -48, -32],\n [21, 29, 19, 0, 42, -16, 37]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[46, 102, 23, -166, -136, -32, 252],\n [-115, 25, -179, 47, 31, 104, 22],\n [-176, 107, -84, 67, 88, -140, -153],\n [114, 33, 4, 34, 39, 118, 70],\n [103, -20, 18, -82, 91, 78, 14],\n [167, -103, 152, 52, -32, 48, -12],\n [243, 53, 180, -193, 3, -18, 149]]\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[[-251, 30, -204, -108, -144, -229, 25],\n [82, 86, 79, 127, 55, -110, -68],\n [197, 66, 118, -15, -82, -84, -164],\n [-48, -1, 145, 67, -101, -124, -223],\n [215, -8, 140, -45, -16, 166, -72],\n [84, 23, 188, -32, -190, -150, -263],\n [-6, -132, 50, 108, 206, 362, 101]]\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[[111, 77, -140, 69, -162, 199, -36],\n [-94, -104, 74, -172, 94, -90, 48],\n [88, -73, -114, -108, -198, 124, -70],\n [45, 100, -227, 78, -129, 287, -128],\n [45, -101, 156, -89, -10, -191, 112],\n [-28, 106, 64, 0, 126, 50, 222],\n [-58, -116, 73, -149, 47, -110, 20]]?\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 7x7 matrix:\n[[-90, 132, -162, 66, 30, 0, 66],\n [76, -27, -80, -3, 13, -61, 60],\n [-121, 58, 35, 22, -21, 78, -69],\n [121, -20, 85, -30, 67, -72, 97],\n [57, -69, -159, 0, -42, -45, 3],\n [114, -24, 42, -24, 54, -72, 90],\n [-179, 54, 1, 32, -63, 118, -131]]\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[[-122, 55, -184, 102, 0, 2, 148],\n [45, -9, -93, -138, 158, -60, 40],\n [27, 79, -181, -93, -105, -44, 65],\n [-119, 199, -217, -9, -185, -160, 69],\n [38, -81, -90, 108, 114, 218, 100],\n [-74, -72, -117, 17, -47, -4, 195],\n [134, 4, 203, -68, 90, 20, -233]]\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 7x7 matrix:\n[[66, 92, -179, 52, -10, 154, 70],\n [10, -156, 39, 110, -272, -173, -72],\n [-133, 43, 10, -70, 62, -42, 116],\n [-50, 234, -41, 60, 80, 116, 69],\n [-6, 10, 22, 82, -102, -45, -30],\n [6, -124, -53, -20, -94, -58, 30],\n [-22, -136, 38, -66, -28, -97, -3]]\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 7x7 matrix:\n[[-2, 42, 46, 40, 24, 2, 4],\n [35, 5, 25, 0, 50, -5, 10],\n [-62, 118, 98, 120, -8, 14, -4],\n [42, 6, 30, 0, 60, -6, 12],\n [51, -35, -11, -40, 46, -9, 10],\n [140, -54, 17, -70, 153, -23, 32],\n [-172, 60, -28, 80, -192, 28, -40]]\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 7x7 matrix:\n[[-12, -12, 21, -3, 24, 18, 30],\n [24, 24, -42, 6, -48, -36, -60],\n [24, 24, -42, 6, -48, -36, -60],\n [-36, -36, 63, -9, 72, 54, 90],\n [16, 16, -28, 4, -32, -24, -40],\n [-16, -16, 28, -4, 32, 24, 40],\n [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[[24, 43, 61, 121, 6, 94, -8],\n [-192, 23, -22, -101, -102, -58, -172],\n [136, 87, 74, -66, -31, -89, 243],\n [32, -129, -149, -246, 43, -199, 93],\n [-16, -4, -27, -115, -29, -95, 35],\n [136, 53, 49, -51, -4, -72, 218],\n [-40, 19, -16, -142, -59, -117, 31]]?\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[[40, 156, 48, 98, -28, -133, 59],\n [84, 56, -123, -226, -172, 1, -283],\n [-169, 3, 6, 23, -47, -39, -6],\n [-3, -118, -43, 62, 191, 122, 173],\n [-49, 198, -75, -153, -32, 17, -253],\n [237, -17, -64, 84, 86, 5, 182],\n [33, -74, 5, -218, 67, -57, -29]]\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, 15, -20, 50, 30, 10, 0],\n [0, -30, 40, -100, -60, -20, 0],\n [0, -21, 28, -70, -42, -14, 0],\n [0, 6, -8, 20, 12, 4, 0],\n [0, 18, -24, 60, 36, 12, 0],\n [0, -9, 12, -30, -18, -6, 0],\n [0, 18, -24, 60, 36, 12, 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[[-148, -182, 288, 50, -250, 210, -160],\n [42, 192, -184, 54, 184, -186, 74],\n [-87, 78, -90, 27, 8, 149, 229],\n [-60, -90, 91, -23, -123, 188, 35],\n [-109, -50, -120, 35, 114, -137, 163],\n [-146, -4, 214, 144, -154, 94, -179],\n [42, -48, 82, -68, -114, 182, -19]]?\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[[192, -114, -76, 0, 5, -53, -54],\n [178, 19, 187, 359, -193, -268, -129],\n [79, 1, -35, 22, -112, 86, 106],\n [-133, 3, 4, -86, 227, 58, 123],\n [-153, 19, -57, 44, 20, -68, -16],\n [-48, -8, 39, -163, 261, 182, 215],\n [-3, -61, -124, -81, -67, 26, -145]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-188, -133, -13, 73, 25, -27, 5],\n [120, 130, -15, -50, -55, 5, 45],\n [-56, -66, 2, -90, -24, -50, 25],\n [-170, -14, -87, -82, -106, -162, -10],\n [2, 161, -96, -113, -167, -117, 94],\n [168, 208, -40, -96, -100, -28, 32],\n [62, -41, 47, -135, -10, 12, 83]]?\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[[-48, 32, -64, 24, 72, -72, 72],\n [66, -44, 88, -33, -99, 99, -99],\n [-42, 28, -56, 21, 63, -63, 63],\n [54, -36, 72, -27, -81, 81, -81],\n [12, -8, 16, -6, -18, 18, -18],\n [-54, 36, -72, 27, 81, -81, 81],\n [-18, 12, -24, 9, 27, -27, 27]]\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 7x7 matrix:\n[[-19, -13, -31, -23, -29, 32, 7],\n [35, -67, -69, 33, -145, 12, 43],\n [-86, 112, 20, 18, 168, 84, -64],\n [10, 19, 73, -41, 80, -64, -16],\n [3, -15, -65, 65, -77, 52, 15],\n [-8, -32, -130, 97, -147, 110, 29],\n [45, -30, 12, 17, -42, -50, 18]]\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[[228, 52, -204, 76, -52, -60, 164],\n [24, -20, -18, 8, -24, 18, 8],\n [-36, -146, 51, -12, -92, 141, -76],\n [48, 136, -60, 16, 80, -132, 80],\n [-96, 36, 78, -32, 64, -30, -48],\n [96, 30, -87, 32, -16, -33, 72],\n [-228, 14, 195, -76, 100, -3, -140]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 2, 12, 18, 21, 7, 8],\n [-15, 15, 12, 36, 36, 15, 18],\n [5, -3, 8, 6, 9, 2, 2],\n [-50, 48, 28, 102, 99, 43, 52],\n [90, -62, 96, 36, 78, 8, 4],\n [80, -56, 80, 24, 60, 4, 0],\n [75, -63, 12, -72, -54, -33, -42]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 7x7 matrix:\n[[106, -30, -141, -142, 91, 60, 58],\n [-46, -102, -19, 0, 194, -80, -57],\n [-20, -141, -108, -143, 75, -140, -38],\n [-56, -35, -27, -21, 166, 77, -12],\n [230, -4, -242, -89, -20, 1, 43],\n [-214, 9, 213, 200, -38, -74, -105],\n [-72, -57, 46, -58, 6, -76, -14]]\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[[-183, -202, -125, 148, 90, -105, 61],\n [11, -131, 108, 54, -2, -58, -49],\n [-54, -11, -120, -64, 136, -7, 228],\n [-86, 42, -43, 146, -135, 76, -162],\n [-80, -165, 63, 246, -50, -83, -164],\n [-184, -292, 51, 69, -55, 89, 44],\n [-81, -7, -151, 38, 78, -72, 53]]\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 7x7 matrix:\n[[43, -191, 57, -177, -169, -38, -46],\n [-146, -140, -192, -25, -100, 84, 23],\n [28, 220, 24, 134, 138, -63, -1],\n [154, 220, 99, -44, 44, -187, -55],\n [32, 152, -7, 65, 152, 63, 60],\n [-116, -116, -129, 17, -14, 150, 59],\n [-111, 15, -193, 31, 13, 84, 50]]\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[[-24, 301, -209, 115, -80, -282, -63],\n [-18, 34, -90, -77, 152, 54, 84],\n [-68, 88, 48, 8, -81, -2, -23],\n [30, -162, 80, 77, -26, 2, -12],\n [-59, -91, -4, 17, -66, 75, -62],\n [-10, -39, -64, 27, 113, -10, 65],\n [11, 19, -100, 41, -54, -67, -70]]\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 7x7 matrix:\n[[4, 180, -124, -92, 61, -33, 136],\n [61, 120, -270, -200, 140, 47, -12],\n [-178, 102, -39, 92, 58, -140, -105],\n [117, -136, -30, -194, 68, 155, 108],\n [23, 98, -169, -66, 59, -2, -77],\n [74, 76, -216, -100, 63, 39, -128],\n [-16, 108, -88, -22, 33, -37, 4]]\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[[91, -103, -156, 31, 354, -158, 135],\n [17, -119, 257, 30, -165, 38, -153],\n [-15, -172, 157, -60, -24, 81, -61],\n [-46, -96, -31, -59, 45, 30, 52],\n [-54, 179, -129, -41, 34, 111, 22],\n [-3, -49, 58, 33, -42, -12, -37],\n [-1, 23, -51, 10, -52, -72, 52]]?\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[[-56, -77, 14, -14, 77, 28, 21],\n [72, 99, -18, 18, -99, -36, -27],\n [72, 99, -18, 18, -99, -36, -27],\n [16, 22, -4, 4, -22, -8, -6],\n [-64, -88, 16, -16, 88, 32, 24],\n [-88, -121, 22, -22, 121, 44, 33],\n [-40, -55, 10, -10, 55, 20, 15]]\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 7x7 matrix:\n[[96, 244, -31, 128, 164, -62, 144],\n [107, 68, 69, 104, 111, 131, 11],\n [-216, 92, -2, 14, 20, 89, 170],\n [290, 56, -130, 175, 91, -86, 46],\n [17, 170, 22, 53, -49, -162, 112],\n [259, 92, -2, 114, 106, 15, -165],\n [-161, 300, 84, 13, 141, -1, 171]]\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[[85, 18, -63, 58, 108, 118, 99],\n [-136, -64, 1, -5, -176, -6, -169],\n [224, 142, 164, -80, 296, -71, 199],\n [-9, -67, -156, 50, -28, 79, 68],\n [-159, -60, -66, 55, -228, -17, -175],\n [45, -12, -48, 52, 84, 203, 28],\n [34, 21, 39, -48, 96, 11, 59]]\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[[-104, 105, 39, -107, 58, -196, 85],\n [2, 115, 70, 101, 150, -20, -131],\n [38, -47, 47, -169, -164, -48, 85],\n [149, 77, -14, -72, 63, 138, -109],\n [57, 180, 49, -165, 112, -55, -45],\n [137, -16, 8, 15, -20, 155, -109],\n [13, -186, 9, -67, -263, 6, 120]]?\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, 81, -23, 10, -69, 136, 154],\n [-5, -11, 9, -15, 10, 0, -10],\n [-105, 12, -48, 105, -15, -120, -60],\n [-84, -120, 88, -140, 108, -32, -128],\n [89, 50, -18, 15, -43, 72, 88],\n [-50, -29, 11, -10, 25, -40, -50],\n [-62, -104, 80, -130, 94, -16, -104]]?\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[[35, -42, -44, 52, -63, 4, 46],\n [-61, 19, -16, -47, 69, 11, -40],\n [-24, 33, 48, -27, 60, 15, -54],\n [40, 22, 72, 6, -16, -14, -4],\n [-79, -96, -236, 26, -13, 38, 54],\n [18, 66, 165, -1, 82, 41, -110],\n [48, 55, 121, -32, -16, -52, 0]]?\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[[-85, -36, 106, 0, -113, -56, -4],\n [-101, -212, -87, -105, 24, 196, 58],\n [-152, -138, -10, -84, -135, 78, 86],\n [114, -64, 135, -91, -136, 24, -196],\n [7, 187, -44, 140, 116, -139, 86],\n [-2, 63, -8, -14, -113, -43, 34],\n [-151, -133, -66, -84, -95, 105, 120]]?\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[[12, 8, -169, 153, -24, -50, -27],\n [-98, 2, 4, 103, -13, 36, 6],\n [30, -3, -36, -105, -188, 22, 8],\n [400, -36, -91, -233, 120, -162, -175],\n [221, -170, -186, -73, 125, -236, -194],\n [-275, -99, -174, 394, -132, -26, 3],\n [-71, -168, 136, -44, -31, -8, -103]]\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[[40, 90, 62, 52, 98, 24, -26],\n [70, -17, -93, -84, -1, -218, -21],\n [-125, 74, 103, -25, 95, 20, 101],\n [0, 180, 108, -12, 222, -114, 36],\n [57, -205, -160, 3, -250, 60, -74],\n [180, -68, -128, 28, -88, -64, -136],\n [-47, 79, 60, -31, 103, -61, 54]]?\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[[-14, -44, 27, -6, -3, -53, -80],\n [135, 120, 189, 75, -12, -30, 45],\n [54, -116, 114, 70, 18, -46, -130],\n [197, 102, 255, 133, 1, -11, 45],\n [56, -164, -9, 104, 55, 117, -10],\n [45, 0, 84, 33, -1, -33, -35],\n [215, 30, 231, 175, 27, 55, 55]]\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[[-25, 19, 54, 36, -25, 36, -22],\n [9, -165, -28, -160, 25, -126, 20],\n [-78, -39, 101, 44, -92, 51, -16],\n [-64, -74, -46, 44, -120, 30, 82],\n [-78, -13, -5, 108, -136, 85, 60],\n [24, 24, -80, 16, 8, 0, 40],\n [-7, 88, -21, 102, -31, 75, 17]]\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, 37, -65, -145, -60, 87, -134],\n [-52, 95, 136, 162, 198, -89, -209],\n [-201, 35, 137, 36, 230, 52, 75],\n [-7, 8, -66, -27, -288, 46, 54],\n [43, -53, -109, -129, -72, 180, 302],\n [-126, 61, 70, 33, 64, 13, -114],\n [130, 16, -80, 39, -144, -55, -176]]?\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[[10, 50, -45, -25, 35, 45, 20],\n [8, 40, -36, -20, 28, 36, 16],\n [12, 60, -54, -30, 42, 54, 24],\n [-6, -30, 27, 15, -21, -27, -12],\n [-16, -80, 72, 40, -56, -72, -32],\n [-2, -10, 9, 5, -7, -9, -4],\n [24, 120, -108, -60, 84, 108, 48]]\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[[14, 77, -84, -84, 84, 56, 35],\n [-6, -33, 36, 36, -36, -24, -15],\n [16, 88, -96, -96, 96, 64, 40],\n [-2, -11, 12, 12, -12, -8, -5],\n [22, 121, -132, -132, 132, 88, 55],\n [-8, -44, 48, 48, -48, -32, -20],\n [14, 77, -84, -84, 84, 56, 35]]\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[[121, 179, -10, 84, 63, 168, -12],\n [-112, -156, -9, 77, 67, -113, 150],\n [-60, 32, -160, 9, -53, -35, -104],\n [129, 159, 26, 68, 71, 180, 16],\n [94, 116, 13, -16, 2, 132, -44],\n [-50, -84, -7, 40, 58, -4, 116],\n [17, -34, 81, 100, 111, 17, 157]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-37, 164, -136, -41, 60, -104, -127],\n [-164, 17, 37, -1, 335, -164, -182],\n [148, 113, -214, 94, -187, 56, -39],\n [-66, -159, 16, 80, 61, 90, 29],\n [125, 201, -390, 252, -146, 5, -206],\n [75, -195, 32, -26, -84, 71, 6],\n [-5, -24, -135, 150, -101, 62, -40]]\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 7x7 matrix:\n[[108, -84, 144, 144, 36, 204, 132],\n [-67, 55, -88, -84, -30, -128, -78],\n [14, 44, 44, 120, -141, -1, 91],\n [-20, -48, -56, -144, 162, -6, -110],\n [-31, -25, -64, -132, 120, -34, -104],\n [14, -34, 8, -24, 66, 38, -14],\n [25, -57, 16, -36, 108, 66, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 7x7 matrix:\n[[-110, 10, -80, -100, -10, -10, 80],\n [11, -1, 8, 10, 1, 1, -8],\n [22, -2, 16, 20, 2, 2, -16],\n [132, -12, 96, 120, 12, 12, -96],\n [110, -10, 80, 100, 10, 10, -80],\n [11, -1, 8, 10, 1, 1, -8],\n [44, -4, 32, 40, 4, 4, -32]]\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 7x7 matrix:\n[[-214, -148, -54, -210, -194, 182, 26],\n [117, 206, 124, 184, 84, -66, -78],\n [-161, -6, -176, -14, -40, 70, 130],\n [20, 44, 18, 80, -20, -34, 16],\n [28, -166, -55, -104, 6, 15, 26],\n [-43, -92, -175, 84, -80, 17, 188],\n [-254, -124, -303, -83, -95, -13, 248]]\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[[-16, 98, -59, -98, 18, 97, 113],\n [19, -95, 43, 102, -55, -105, -84],\n [-22, 110, -57, -118, 50, 119, 109],\n [-56, -38, -51, -82, 42, 41, 33],\n [17, 2, -20, 32, -88, -34, 45],\n [-48, -54, -8, -56, 86, 28, -36],\n [40, -50, 28, 112, -110, -104, -32]]\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[[84, 59, -7, -132, -28, 3, -81],\n [-35, -84, 71, -59, 40, -145, 42],\n [-142, -202, 234, -52, -122, -80, 96],\n [-60, -72, 54, 94, 28, -28, 58],\n [-136, -61, -11, 8, -100, 23, 103],\n [4, 2, 28, -26, -57, 44, -18],\n [-15, -32, 42, 152, 47, 33, 19]]\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[[82, -92, -278, -10, -90, 107, 131],\n [80, 62, -131, -97, -129, -183, -62],\n [-91, 72, -53, -125, 162, 55, 109],\n [105, -87, 107, 9, 72, 14, 62],\n [-19, -137, -31, 75, -58, 30, 64],\n [124, -51, -191, 117, 11, 197, 344],\n [100, -54, 154, 173, -1, 66, 44]]?\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[[-142, -64, 18, -154, 88, 47, -111],\n [-95, 49, 201, 156, -12, 59, 12],\n [-84, -109, -108, -124, -44, 95, -66],\n [-26, -65, -164, -86, -153, 65, -12],\n [-46, -21, 14, -30, -84, 78, -33],\n [-23, 94, -161, -6, -252, -60, 71],\n [-163, 39, -69, -108, 186, -36, -60]]\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 7x7 matrix:\n[[-60, 136, -146, 94, 13, 109, 4],\n [41, -108, 150, -53, 12, -64, -100],\n [21, -5, -8, -11, -14, -26, 31],\n [48, -45, 66, -18, -2, -50, -65],\n [121, 143, -136, 121, -30, -26, -125],\n [-34, -126, 108, -110, -2, -42, 114],\n [-104, 26, -4, 28, 44, 108, -30]]\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[[-93, -47, 64, -90, -10, -158, 162],\n [90, 72, -114, 120, -18, 108, -114],\n [42, -136, 49, -71, -90, -118, 101],\n [30, -22, -53, 21, -76, -94, 83],\n [-84, 137, -122, 79, -3, -106, 116],\n [39, -146, 61, -82, -89, -122, 105],\n [-117, 152, -36, 41, 101, 32, -8]]\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 7x7 matrix:\n[[-4, 44, 36, 32, -16, 36, 8],\n [5, -55, -45, -40, 20, -45, -10],\n [-1, 11, 9, 8, -4, 9, 2],\n [0, 0, 0, 0, 0, 0, 0],\n [-2, 22, 18, 16, -8, 18, 4],\n [2, -22, -18, -16, 8, -18, -4],\n [-2, 22, 18, 16, -8, 18, 4]]\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[[233, 81, -258, 206, -30, -86, 126],\n [-43, -47, -56, 155, -94, 72, -147],\n [83, 35, -27, 24, 88, 17, -58],\n [-6, -105, -239, 13, -44, -109, 170],\n [-45, -118, -43, 67, 20, 183, -284],\n [-100, 77, 162, -155, -24, -180, 246],\n [30, -22, -116, -17, -6, -88, 147]]\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[[36, 150, 24, -105, -195, -33, 9],\n [27, 91, 61, -25, -71, 72, -47],\n [-24, -92, -32, 50, 102, -14, 14],\n [27, 117, 9, -90, -162, -45, 18],\n [30, 134, 2, -110, -194, -68, 30],\n [24, 104, 8, -80, -144, -40, 16],\n [-27, -85, -73, 10, 50, -99, 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[[-41, -23, -122, -112, -87, 12, -71],\n [35, 17, 100, 90, 71, -10, 57],\n [-56, 70, -7, 63, 7, 7, 42],\n [62, -64, 29, -41, 9, -9, -28],\n [-140, 94, -145, -15, -83, 25, -6],\n [-35, 37, -15, 25, -4, 5, 17],\n [85, -113, 0, -110, -19, -10, -73]]\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 7x7 matrix:\n[[14, 338, -260, 76, -10, -188, -26],\n [107, -27, -12, 50, 94, -66, -36],\n [-125, 39, 8, -58, -111, 73, 42],\n [-148, 22, 84, 92, -25, 127, -10],\n [91, 133, -112, 122, 100, -130, -58],\n [-124, -116, 162, 20, -31, 172, 11],\n [-165, -45, 140, 70, -35, 175, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[10, -71, 9, 126, 96, -21, -39],\n [52, -8, -199, -4, -113, -8, 5],\n [-152, -194, -60, 132, 70, -178, -168],\n [129, 132, 23, -70, -44, 133, 122],\n [-8, -125, -12, 186, 129, -57, -78],\n [72, -132, -8, 280, 196, -12, -56],\n [98, 77, 81, 6, 44, 103, 81]]\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 7x7 matrix:\n[[67, -191, -82, -44, 25, 139, -30],\n [2, -25, -10, -7, -18, -1, 30],\n [-57, 198, 76, 75, -5, -78, -18],\n [36, -119, -28, -108, 51, -20, -29],\n [-48, 190, 70, 81, 11, -47, -47],\n [-16, 24, -12, 86, -82, 54, 82],\n [-26, 88, 26, 61, -23, -5, 9]]\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[[82, 82, 49, 126, 108, -24, -60],\n [34, 62, 49, 98, 68, -12, -72],\n [140, -10, -70, -30, 60, -30, 150],\n [78, 12, -21, 12, 48, -18, 54],\n [-122, -126, -77, -194, -164, 36, 96],\n [22, -25, -35, -43, -10, -3, 63],\n [30, 74, 63, 118, 76, -12, -96]]?\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 7x7 matrix:\n[[-144, -189, 106, 203, -115, 118, -95],\n [231, 111, 156, 99, -207, -207, -75],\n [-118, -108, -10, 34, 15, 151, -36],\n [-75, -147, 72, 232, -199, -13, -169],\n [108, 95, -51, -15, -45, -28, -88],\n [-106, -128, 99, 137, -54, 94, -25],\n [38, -27, -30, -73, -63, -66, -53]]\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 7x7 matrix:\n[[43, -225, -103, -172, -39, 130, -29],\n [-126, -90, 143, -104, -145, 109, 61],\n [-193, -101, -17, -91, -76, -65, 104],\n [132, 76, 212, 114, 60, -60, 64],\n [167, 23, 31, 119, 84, 59, -11],\n [264, 80, 113, 51, 106, -44, -63],\n [-2, -222, -178, -398, -133, 153, -189]]\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 7x7 matrix:\n[[-120, -40, 20, 90, 90, 80, 50],\n [144, 48, -24, -108, -108, -96, -60],\n [120, 40, -20, -90, -90, -80, -50],\n [132, 44, -22, -99, -99, -88, -55],\n [-48, -16, 8, 36, 36, 32, 20],\n [-60, -20, 10, 45, 45, 40, 25],\n [-72, -24, 12, 54, 54, 48, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-78, -23, 4, -37, 99, -102, 32],\n [19, -310, -72, -28, 182, -11, -97],\n [21, 350, 33, -84, -235, 187, 142],\n [21, -120, 84, 91, 49, -95, -76],\n [31, 14, -29, 52, -57, 19, 10],\n [15, -295, -50, 41, 185, -47, -21],\n [70, -224, 36, 136, 71, -45, -60]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-15, -35, 55, 5, -15, 15, 40],\n [12, 28, -44, -4, 12, -12, -32],\n [36, 84, -132, -12, 36, -36, -96],\n [33, 77, -121, -11, 33, -33, -88],\n [-30, -70, 110, 10, -30, 30, 80],\n [-27, -63, 99, 9, -27, 27, 72],\n [-9, -21, 33, 3, -9, 9, 24]]\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[[19, -61, -46, -107, 37, -69, -8],\n [-20, -176, 42, -86, -61, -185, 13],\n [44, -177, 44, 62, -27, 91, -4],\n [33, -132, 66, 121, -44, 132, 0],\n [4, -131, 156, 258, -125, 181, 16],\n [-57, 78, -18, -109, -10, -198, 12],\n [-40, -143, 166, 172, -158, 0, 29]]\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[[-5, -17, -3, 65, -20, -94, 59],\n [-20, -58, 6, 51, -59, -79, 40],\n [-112, -102, 156, 77, -7, 55, -180],\n [83, 65, -123, -22, -11, -99, 175],\n [-13, 17, 30, 45, 39, -16, -17],\n [8, 180, 66, 116, 242, -8, -48],\n [33, 107, -9, -10, 111, 39, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[11, 4, -10, -5, -3, -10, -1],\n [-55, -20, 50, 25, 15, 50, 5],\n [44, 16, -40, -20, -12, -40, -4],\n [22, 8, -20, -10, -6, -20, -2],\n [99, 36, -90, -45, -27, -90, -9],\n [33, 12, -30, -15, -9, -30, -3],\n [132, 48, -120, -60, -36, -120, -12]]\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 7x7 matrix:\n[[-8, -162, 17, 27, 162, 160, -94],\n [-42, 56, 43, -71, -56, -48, 6],\n [-11, -137, 19, 17, 137, 136, -82],\n [64, -76, -66, 106, 76, 64, -4],\n [43, 99, -52, 36, -99, -104, 80],\n [-30, -44, 35, -31, 44, 48, -42],\n [81, 11, -89, 109, -11, -24, 54]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[39, -42, 8, -81, 61, -65, 44],\n [83, -56, 64, -225, 226, 180, 70],\n [28, -177, 1, -138, 27, 67, 26],\n [-40, -66, -55, 50, -56, -200, -1],\n [10, -93, 10, -137, 169, 94, 38],\n [22, -143, 76, -79, -146, -15, 72],\n [-192, 273, 66, 281, 26, 87, -68]]?\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[[5, 2, 4, 6, -2, -2, -3],\n [15, 6, 12, 18, -6, -6, -9],\n [-15, -6, -12, -18, 6, 6, 9],\n [-10, -4, -8, -12, 4, 4, 6],\n [10, 4, 8, 12, -4, -4, -6],\n [-55, -22, -44, -66, 22, 22, 33],\n [30, 12, 24, 36, -12, -12, -18]]\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[[24, -6, -214, 101, 225, -84, -223],\n [208, -28, 46, -136, -192, -6, 117],\n [-175, -85, -9, -169, -37, -16, 21],\n [70, 41, -36, -65, 142, 79, -160],\n [84, 157, -276, 64, 47, -61, -80],\n [187, 255, -165, -77, -39, 60, -134],\n [-32, 167, -283, 181, 170, -74, -203]]\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 7x7 matrix:\n[[21, -84, -14, 49, -77, 77, 35],\n [24, -96, -16, 56, -88, 88, 40],\n [-27, 108, 18, -63, 99, -99, -45],\n [9, -36, -6, 21, -33, 33, 15],\n [18, -72, -12, 42, -66, 66, 30],\n [18, -72, -12, 42, -66, 66, 30],\n [9, -36, -6, 21, -33, 33, 15]]\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[[63, 48, 122, -161, 14, 138, 4],\n [72, 90, 34, -102, 16, 64, 28],\n [45, 36, 82, -111, 10, 94, 4],\n [108, 168, -48, -76, 24, 8, 64],\n [-27, -9, -87, 96, -6, -90, 6],\n [9, -6, 56, -53, 2, 54, -8],\n [99, 102, 112, -191, 22, 146, 24]]?\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[[122, -37, 10, -78, 59, 124, 138],\n [-198, 46, -136, -27, -22, -129, -32],\n [-281, -2, -149, 40, 19, -210, -93],\n [86, 37, 52, -80, 1, 188, 250],\n [-2, -111, -88, -35, 127, -39, 0],\n [85, -33, -59, -52, 16, -44, -123],\n [-59, 187, 23, -15, -194, -1, -21]]?\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, 132, -79, -119, 48, 157, 40],\n [69, -147, 57, 63, -114, -25, -17],\n [-90, 210, -75, 45, 144, -81, -12],\n [101, 101, -100, 194, -138, 46, -29],\n [-3, -41, 26, -6, 0, -23, -2],\n [11, -59, 15, -181, -12, 162, 48],\n [-74, 132, -37, 37, 114, -90, -13]]\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[[-23, -21, -14, -4, 9, -152, -12],\n [-41, 48, -14, -17, -76, 122, 43],\n [48, -39, 6, 37, 109, -100, -37],\n [2, -1, -35, 55, 112, -103, 0],\n [70, -80, 59, -24, 21, -99, -73],\n [-43, 44, -71, 67, 97, -61, 42],\n [101, -83, 60, 6, 85, -78, -80]]\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[[-84, 208, -171, 173, -126, -184, -1],\n [-25, 62, -27, 98, 29, 11, -56],\n [176, 36, -59, -72, -171, -106, 53],\n [-186, 71, 31, 144, 51, 64, -106],\n [77, -1, -83, -44, 68, 84, 11],\n [35, -37, -49, 72, 240, 139, -50],\n [-6, 23, 145, 75, -132, -80, -76]]\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 7x7 matrix:\n[[-35, 0, 107, -32, -96, 18, 88],\n [-25, -25, 116, 132, -36, 1, -29],\n [112, -34, -16, 4, 86, 198, -23],\n [-36, -89, 48, 124, -10, 56, 35],\n [-66, -41, 46, -106, -120, 78, 235],\n [6, -90, -18, -144, -26, 150, 167],\n [97, -119, 4, -55, 51, 306, 104]]\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[[-56, -21, -14, 70, 84, 0, -63],\n [-32, -12, -8, 40, 48, 0, -36],\n [16, 6, 4, -20, -24, 0, 18],\n [96, 36, 24, -120, -144, 0, 108],\n [-48, -18, -12, 60, 72, 0, -54],\n [-40, -15, -10, 50, 60, 0, -45],\n [40, 15, 10, -50, -60, 0, 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[[-19, -37, -29, -39, 52, -51, 26],\n [-49, 33, -119, 11, 172, -121, 6],\n [33, 167, 15, 157, -60, 97, -94],\n [-24, 56, -72, 40, 96, -56, -16],\n [-45, 44, -114, 22, 162, -110, -1],\n [-45, -17, -93, -31, 144, -115, 28],\n [-26, 81, -85, 61, 110, -59, -27]]\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[[28, -48, 261, -13, 11, -22, 17],\n [184, 89, 48, 76, -5, 73, 128],\n [146, 98, -274, 23, 6, -12, 90],\n [-222, -170, 60, -81, 80, -25, -140],\n [224, 91, -192, 12, 22, -52, 135],\n [82, -44, 43, 46, 21, -35, 33],\n [-150, -47, -54, 107, -96, 16, -127]]\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[[37, -91, -12, -196, 24, -199, 118],\n [-82, -4, 140, 144, -14, 256, 8],\n [-53, -16, 188, -39, 182, 155, 133],\n [-58, -62, 50, -9, -83, 97, 118],\n [-5, 86, -104, 279, -104, 122, -245],\n [56, 31, 16, 77, 126, -80, -188],\n [-57, -58, 14, -162, -287, -6, 223]]\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[[63, 145, 48, -68, -92, 108, -126],\n [41, 40, 35, 76, -5, 5, 61],\n [-55, -22, -13, -82, 29, 35, -59],\n [-61, -207, -154, -66, -12, -196, -32],\n [-18, -14, -36, -92, -32, 0, -96],\n [23, -74, -52, 61, -23, -121, 58],\n [-35, -155, -47, 139, 88, -152, 191]]?\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[[-98, 6, -137, -38, 160, -61, 64],\n [315, -124, 41, -80, -57, 75, 94],\n [2, -244, -132, -136, -50, -213, 155],\n [132, -125, -24, -104, -81, -70, 67],\n [210, -234, 6, 146, -261, -4, 108],\n [97, -272, 28, 58, -253, -87, 103],\n [-3, 21, 35, -388, 219, -4, 43]]?\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 7x7 matrix:\n[[-127, -52, 118, 281, 51, -232, -1],\n [-79, 106, -174, -151, -79, 76, 149],\n [-129, -5, 111, 66, 169, -26, 30],\n [-66, 45, -115, 69, -138, -84, 51],\n [-35, 32, -92, 93, -134, -51, -38],\n [-107, 54, -64, 159, -79, 10, -149],\n [-91, -2, 37, 154, 17, -73, -52]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[113, -60, 79, 36, -179, -39, -22],\n [-204, 96, -42, 96, -90, 90, 51],\n [-218, 151, -75, 102, -160, 256, 90],\n [-65, 83, -107, 90, 70, 102, -19],\n [-30, -18, 27, 100, -75, -107, -36],\n [-30, -33, 75, 86, -178, -102, -9],\n [54, -34, 62, -108, -64, 36, 49]]?\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, 79, 177, 160, -14, -127, -106],\n [-29, -46, 13, 8, -30, 0, -47],\n [-56, -47, 87, 96, -6, -39, -100],\n [46, 15, -57, -80, -38, 23, 42],\n [71, 113, 70, 72, 46, -64, 22],\n [83, 113, -26, -24, 52, -7, 103],\n [99, 141, -30, -24, 72, -9, 129]]\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, 29, -5, -120, -117, 27, 6],\n [128, -94, 106, 121, 101, 79, -10],\n [174, -87, 223, -17, 31, 61, -20],\n [127, 30, 21, -106, -117, 45, 20],\n [-151, 62, -138, 103, 137, -118, 58],\n [62, 46, -57, 37, 67, -6, 106],\n [147, -93, 200, 74, 164, 52, 50]]\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[[150, 0, -50, -2, 36, 82, 78],\n [43, -11, -127, 161, 23, 158, -55],\n [-57, -21, 63, -96, 24, -105, 3],\n [-91, 56, 73, 9, -114, -57, -23],\n [162, -93, -162, 43, 190, 148, 18],\n [-54, -24, -126, 194, 20, 134, -126],\n [17, 2, -77, 114, -3, 102, -41]]?\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[[0, 30, -21, 0, -30, -30, -18],\n [0, 30, -21, 0, -30, -30, -18],\n [0, 50, -35, 0, -50, -50, -30],\n [0, -10, 7, 0, 10, 10, 6],\n [0, 0, 0, 0, 0, 0, 0],\n [0, 70, -49, 0, -70, -70, -42],\n [0, -80, 56, 0, 80, 80, 48]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 7x7 matrix:\n[[59, 177, 41, 122, -176, -93, 217],\n [-121, 151, 47, -49, -22, 296, 154],\n [57, 314, -28, 94, -189, 50, 314],\n [-79, 25, -8, -105, -66, 114, 60],\n [72, 67, 20, 123, -115, -166, 154],\n [-61, -189, 173, 105, -24, -52, 5],\n [46, -314, 100, 169, 121, -191, -160]]\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 7x7 matrix:\n[[-92, 148, 159, 40, -76, -60, 52],\n [91, -100, 108, 18, 202, 17, 40],\n [-43, 49, -24, -8, -83, -13, -5],\n [-2, 149, 12, 142, -45, -12, -141],\n [76, -228, -22, -48, 204, 68, 68],\n [-22, 130, 267, 72, 50, -68, 62],\n [-73, -54, -74, -138, -108, -5, 106]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 2, 202, 67, 114, -117, -237],\n [-46, -90, 210, 26, -47, -121, -9],\n [6, 56, 43, 27, -31, -2, 140],\n [-60, -56, 89, -77, 7, -130, -39],\n [-72, -9, 172, -37, 67, -158, -125],\n [114, 7, -199, 6, 95, 63, -230],\n [174, -83, -62, 154, -28, 150, -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[[50, 55, -40, -10, 0, -50, -60],\n [-70, -77, 56, 14, 0, 70, 84],\n [70, 77, -56, -14, 0, -70, -84],\n [110, 121, -88, -22, 0, -110, -132],\n [-40, -44, 32, 8, 0, 40, 48],\n [50, 55, -40, -10, 0, -50, -60],\n [-60, -66, 48, 12, 0, 60, 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 7x7 matrix:\n[[-72, 76, -13, -76, -74, 10, 3],\n [46, -119, -13, 175, -25, -48, -60],\n [-38, 44, -11, -102, 12, 22, 21],\n [-3, -13, 72, 51, 39, 80, -38],\n [-56, -215, -96, 257, -173, -90, -175],\n [54, 47, -94, -178, 64, -100, 128],\n [-170, -89, -30, 1, -73, 86, -151]]\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[[10, 16, 6, -10, -14, 18, 14],\n [-60, -96, -36, 60, 84, -108, -84],\n [10, 16, 6, -10, -14, 18, 14],\n [-55, -88, -33, 55, 77, -99, -77],\n [-45, -72, -27, 45, 63, -81, -63],\n [20, 32, 12, -20, -28, 36, 28],\n [15, 24, 9, -15, -21, 27, 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[[-171, 71, 59, 45, -90, -69, -7],\n [-108, 90, 72, -81, -36, -54, -27],\n [-15, 71, 55, -153, 22, -21, -33],\n [21, -63, -49, 126, -14, 21, 28],\n [144, -120, -96, 108, 48, 72, 36],\n [-15, 71, 55, -153, 22, -21, -33],\n [147, -51, -43, -63, 82, 57, 1]]\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[[40, -55, 20, 35, -15, 15, -15],\n [-46, 37, 54, 98, -65, -61, 47],\n [70, -85, 2, 2, 9, 45, -39],\n [-86, 92, 34, 63, -50, -76, 62],\n [104, -98, -80, -146, 102, 114, -90],\n [-142, 154, 50, 93, -76, -122, 100],\n [8, -11, 4, 7, -3, 3, -3]]\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, 137, 163, -17, -28, 41, 104],\n [90, 118, 120, 48, -84, -230, 70],\n [-6, 8, 26, 74, 122, -92, -54],\n [93, 28, -5, -29, -204, -138, 71],\n [-72, -34, -2, 70, 230, 38, -100],\n [18, 87, 97, -11, -49, -9, 72],\n [78, 42, 34, 58, -47, -230, 8]]\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[[-70, -96, -72, -182, -38, -32, 70],\n [-28, 48, -34, 42, 2, 58, 4],\n [-58, 68, -69, 43, -3, 95, 16],\n [104, 80, 70, -10, -34, 50, -176],\n [35, 98, -14, -70, -61, 119, -152],\n [-176, -102, -154, -101, 0, -13, 215],\n [-7, 10, -10, 0, -3, 15, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[24, -22, -20, -14, -6, -2, -8],\n [72, -66, -60, -42, -18, -6, -24],\n [24, -22, -20, -14, -6, -2, -8],\n [132, -121, -110, -77, -33, -11, -44],\n [132, -121, -110, -77, -33, -11, -44],\n [84, -77, -70, -49, -21, -7, -28],\n [120, -110, -100, -70, -30, -10, -40]]?\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[[-37, -56, -121, 122, -55, -65, 179],\n [-66, -35, -36, 167, -66, -64, -39],\n [163, -140, 104, 81, -49, 21, 146],\n [45, 26, 129, -63, 202, -262, 117],\n [299, -193, 125, -79, 49, 263, 17],\n [116, -160, -84, -80, 84, 104, 74],\n [176, -77, 244, 90, 107, -19, -98]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-15, 120, -23, 101, 42, 25, -73],\n [-120, 120, 16, 8, -24, -80, -64],\n [90, -69, -17, 14, 27, 67, 35],\n [70, 0, -26, 62, 44, 70, -6],\n [30, 54, -24, 78, 42, 48, -36],\n [-125, 132, 15, 15, -22, -81, -71],\n [-125, 69, 30, -45, -49, -102, -32]]\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 7x7 matrix:\n[[-14, -21, 9, -29, -23, 2, 7],\n [-86, 61, -101, -12, -8, -49, 101],\n [-44, -57, 51, 11, 23, 112, -51],\n [-20, 14, -11, 13, 5, 10, 7],\n [96, 67, -47, 97, 113, -44, -25],\n [131, -126, 41, -93, 38, -56, -41],\n [-172, 84, -386, -132, 100, -250, 346]]\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[[-7, 77, -13, -284, 80, -38, -222],\n [104, 4, 15, -35, 114, -38, -150],\n [-86, 7, 100, -271, -198, -151, 174],\n [-147, -145, 40, -121, -96, 82, -14],\n [105, -14, 42, -6, 20, -205, 106],\n [74, -221, 95, 2, 78, 81, -244],\n [-54, -167, 112, -143, -47, 18, -20]]\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 7x7 matrix:\n[[61, -216, 188, -161, 153, -46, -99],\n [103, -69, -163, -50, 120, 50, 114],\n [69, -152, 118, -26, 56, 62, -165],\n [-18, 164, -4, 280, -227, 97, -162],\n [-166, 114, 98, 64, -163, 177, -92],\n [184, -316, 94, -203, 265, -144, -60],\n [12, 166, -162, 154, -87, 75, 106]]\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[[186, -75, 157, 54, -180, -44, -17],\n [81, -217, 145, -1, -171, -128, -77],\n [-233, 36, 36, 248, 38, 189, -205],\n [122, -6, 86, 46, -79, -36, -11],\n [135, 127, -40, -47, -58, 28, -5],\n [-169, 6, 12, 27, 105, 146, 136],\n [2, -241, 111, 20, -157, -122, -159]]\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[[-100, -30, -60, -100, 60, 0, -90],\n [-70, -21, -42, -70, 42, 0, -63],\n [70, 21, 42, 70, -42, 0, 63],\n [10, 3, 6, 10, -6, 0, 9],\n [-50, -15, -30, -50, 30, 0, -45],\n [10, 3, 6, 10, -6, 0, 9],\n [-50, -15, -30, -50, 30, 0, -45]]?\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[[43, -92, -8, -109, 20, -5, -34],\n [-174, 225, 22, -55, 89, 3, -291],\n [204, -75, 66, -37, -23, -98, 156],\n [18, -183, 184, -79, -103, -69, 18],\n [-175, 45, -44, -102, 49, -23, -237],\n [-233, 129, -42, -58, 37, -19, -276],\n [-32, -3, 226, 31, -159, -100, 6]]\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[[-13, -49, 39, 22, 2, -27, -79],\n [9, -21, -15, -18, 30, -9, 66],\n [-87, -43, 133, 14, -62, -61, -43],\n [-136, 200, 156, -144, -196, -172, 216],\n [56, 98, -96, -22, 2, 46, 28],\n [-62, 46, 81, -26, -77, -55, 23],\n [-94, -160, 165, 50, -13, -71, -92]]\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[[21, -134, 66, -192, -219, 231, -8],\n [12, 90, -45, 104, 70, -160, -5],\n [81, 38, 87, 8, 37, -76, 132],\n [135, 4, 57, -92, -176, 2, 52],\n [-183, -36, -42, 76, 118, 5, -56],\n [72, -78, 78, -144, -130, 157, 45],\n [-66, 70, -72, 152, 290, -77, -21]]\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 7x7 matrix:\n[[-53, -135, 142, 155, -25, 32, 72],\n [-72, 50, 4, -18, -54, 28, -70],\n [148, -186, 88, 142, 114, -24, 202],\n [109, 7, 36, 35, 59, 58, 40],\n [-88, -129, 161, 166, -50, 49, 51],\n [9, -121, 13, 50, 28, -73, 96],\n [10, -180, 142, 174, 22, 10, 134]]\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 7x7 matrix:\n[[-34, -103, 54, 83, -83, 75, 44],\n [16, -69, -94, 51, -93, -34, 21],\n [74, -167, -206, 107, -55, -195, 34],\n [-40, 206, 218, -150, 52, 217, 5],\n [-49, 68, 18, -30, 26, 24, -72],\n [-18, 121, 101, -88, 70, 75, -21],\n [128, 41, -196, -65, 83, -224, 3]]\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[[-20, 58, 66, -131, 14, 45, -30],\n [-36, -91, -3, 20, -213, -100, 71],\n [-4, 34, -82, 27, -14, 37, 92],\n [2, 27, 29, -52, 19, 21, -20],\n [-11, -101, 23, 99, -7, -85, -66],\n [-39, 173, -27, -166, 75, 164, 74],\n [-121, -5, 189, -194, -5, -7, -145]]?\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, -12, 195, 129, -159, -132, 18],\n [60, 44, -159, -137, 127, 156, 14],\n [106, -41, -17, 93, 6, -84, -79],\n [22, 42, -62, -73, 47, 94, 24],\n [-120, 52, 69, -63, -51, 64, 90],\n [30, 28, -147, -136, 122, 138, 16],\n [46, -54, -41, 36, 36, -58, -58]]\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[[-42, -26, 82, 34, 132, 67, 65],\n [43, 34, -26, -63, 16, -44, 9],\n [106, 66, 10, -25, -51, -44, -56],\n [153, -262, 26, -23, 129, -127, -67],\n [-91, 200, -140, -33, -243, 10, -12],\n [36, -58, 90, 0, 170, 15, 45],\n [-105, 148, -64, 11, -145, 56, 16]]\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[[99, -18, 69, 78, -75, -81, 33],\n [-56, 4, -52, -44, 104, 0, -44],\n [196, 64, 94, 147, -14, -144, 36],\n [-47, -56, 5, -32, -97, 57, 21],\n [11, 8, 7, 8, -11, 3, 7],\n [-5, 112, -41, -12, 109, 51, -17],\n [42, 36, 18, 30, -6, -6, 14]]\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[[-100, -7, 104, -9, 34, -3, 63],\n [415, 30, -275, 167, -313, 277, -154],\n [-130, 152, 195, -35, 183, -34, 138],\n [-15, 111, 53, 52, -10, 67, 17],\n [-84, 46, -10, 6, -19, -11, -108],\n [191, -122, -86, 128, -226, 162, 65],\n [173, -97, -144, -7, -76, 23, -56]]?\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[[-197, -129, -50, -111, -90, 104, -77],\n [367, 38, 113, -219, -90, -125, 119],\n [129, 35, 93, 83, 23, -245, -299],\n [-24, 115, -115, 61, 77, -113, 48],\n [-318, 129, -110, 27, -109, -170, -247],\n [-10, -99, -19, 50, 93, 171, 123],\n [-32, -77, -18, 166, 87, 14, 166]]\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[[-8, -16, 32, -28, -44, -20, 36],\n [4, 8, -16, 14, 22, 10, -18],\n [14, 28, -56, 49, 77, 35, -63],\n [24, 48, -96, 84, 132, 60, -108],\n [-12, -24, 48, -42, -66, -30, 54],\n [-6, -12, 24, -21, -33, -15, 27],\n [-10, -20, 40, -35, -55, -25, 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[[6, 33, 15, -27, 15, 30, -24],\n [-10, -55, -25, 45, -25, -50, 40],\n [-10, -55, -25, 45, -25, -50, 40],\n [2, 11, 5, -9, 5, 10, -8],\n [-24, -132, -60, 108, -60, -120, 96],\n [-12, -66, -30, 54, -30, -60, 48],\n [-22, -121, -55, 99, -55, -110, 88]]\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 7x7 matrix:\n[[-32, -95, -62, 142, -25, -138, 3],\n [22, -235, 11, 126, -58, -82, -34],\n [-46, 25, 181, -120, 66, 231, 1],\n [-66, 159, -93, -48, 22, -35, 19],\n [-16, 63, -123, -8, -25, -96, -4],\n [0, 157, -11, -82, 35, 49, 23],\n [94, -74, 88, -56, -19, 93, -25]]\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 7x7 matrix:\n[[148, 21, -96, 35, 37, 180, 272],\n [93, 47, -191, 42, 60, -125, -65],\n [28, 14, -122, 108, 92, 44, -18],\n [-147, -42, 89, -26, -47, -105, -207],\n [-1, -52, -4, 42, -8, 229, 182],\n [-99, -25, 201, -40, -40, 59, -5],\n [188, 80, -191, 23, 69, -64, 89]]\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[[60, 20, 30, -45, 45, 55, -30],\n [-96, -32, -48, 72, -72, -88, 48],\n [96, 32, 48, -72, 72, 88, -48],\n [-72, -24, -36, 54, -54, -66, 36],\n [-96, -32, -48, 72, -72, -88, 48],\n [144, 48, 72, -108, 108, 132, -72],\n [72, 24, 36, -54, 54, 66, -36]]?\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[[-74, -72, 75, 37, -105, -136, 189],\n [-87, -143, 82, -57, 65, -38, 30],\n [9, -55, -43, 120, 60, 56, 49],\n [83, 73, -95, 32, 84, 134, -133],\n [-34, -48, 24, 68, -52, -62, 130],\n [52, 48, -66, 82, 6, 56, -6],\n [19, 21, -27, 64, -28, 2, 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[[69, -101, -52, 124, -65, -116, -131],\n [24, -21, 13, 29, 0, 19, -71],\n [57, -98, -75, 117, -77, -157, -82],\n [39, -76, -71, 89, -67, -145, -40],\n [27, -58, -61, 67, -55, -123, -18],\n [-3, 12, 19, -13, 15, 37, -8],\n [0, 30, 66, -30, 48, 126, -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[[67, 115, -46, -140, -114, -68, -97],\n [9, 90, 1, -116, -49, -13, -55],\n [134, 95, -105, -104, -167, -129, -118],\n [86, -70, -80, 104, -48, -76, -2],\n [-124, -100, 96, 112, 160, 120, 116],\n [53, -40, -49, 60, -31, -47, -3],\n [-194, -65, 159, 56, 209, 183, 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[[88, 37, -68, 6, -73, -114, -54],\n [-146, -7, -110, 156, 298, 190, -84],\n [-70, 70, 4, 264, 131, 292, -90],\n [-43, -3, -114, 32, 144, 18, -31],\n [-18, -33, -126, 100, 54, 130, -14],\n [-206, -163, 51, 75, 175, 194, -69],\n [21, -119, 51, -141, -142, -178, -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 7x7 matrix:\n[[-39, -54, 98, 37, 188, 112, -14],\n [-195, -222, -3, 40, -208, 309, 161],\n [-50, 76, -38, 76, -32, -6, -12],\n [133, 164, 60, -83, 44, -236, -108],\n [113, -37, -25, -76, 186, -139, -68],\n [-148, -205, -18, 88, -130, 384, 190],\n [-73, 129, 89, 80, -34, 43, -21]]\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[[-36, -96, 24, 48, -24, -132, 12],\n [128, 116, -68, 111, 120, 62, -125],\n [163, 140, -86, 151, 154, 65, -162],\n [132, 92, -68, 149, 128, 14, -139],\n [-68, -60, 36, -61, -64, -30, 67],\n [1, -32, 2, 42, 6, -59, -13],\n [16, 8, -8, 22, 16, -4, -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[[4, 84, 2, -85, -20, 224, 53],\n [2, 26, 44, -61, -26, 58, 1],\n [-9, -27, -33, -69, -10, 97, 44],\n [12, 42, 186, -75, -65, -88, -86],\n [31, 207, 155, -13, -37, 97, -51],\n [-4, -10, -4, -46, -11, 52, 19],\n [24, 166, 116, -16, -29, 96, -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[[34, 52, -17, 138, -20, 13, 26],\n [-32, -8, 16, -48, 70, 56, -62],\n [-8, 40, 4, 72, 70, 84, -54],\n [-34, -4, 17, -42, 80, 67, -70],\n [16, 16, -8, 48, -20, -8, 20],\n [48, -12, -24, 24, -135, -124, 115],\n [-38, -44, 19, -126, 40, 9, -42]]\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[[-5, -44, 101, 97, 58, -2, -61],\n [42, -120, -186, 78, 60, 132, 138],\n [3, 6, -33, -21, -12, 6, 21],\n [6, -56, 26, 82, 52, 28, -10],\n [42, -120, -186, 78, 60, 132, 138],\n [-9, -1, 76, 32, 17, -22, -50],\n [0, 0, 0, 0, 0, 0, 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[[-5, 30, -50, -55, -45, 25, 45],\n [148, 120, -4, 60, -40, 30, -16],\n [-112, -120, 46, 0, 70, -45, -26],\n [50, 60, -30, -10, -40, 25, 20],\n [-74, -60, 2, -30, 20, -15, 8],\n [-188, -168, 28, -52, 72, -50, 0],\n [131, 150, -68, -15, -95, 60, 43]]\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[[60, 46, 35, -88, 50, -80, 160],\n [181, 133, 138, -109, -178, -267, 118],\n [-103, -8, 119, 137, 247, 109, 34],\n [-144, -26, 49, -12, 299, 117, 85],\n [89, 35, 106, 11, 130, -41, 135],\n [-73, -40, 17, 175, 136, 134, -21],\n [118, 163, 167, -208, -114, -299, 196]]\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[[37, -2, 73, -46, -114, 134, -59],\n [-127, -81, -108, 23, 6, 140, 66],\n [-94, -43, -60, 104, -226, 87, -7],\n [-47, 160, -169, -106, -104, -55, 39],\n [-82, -68, -40, 290, -23, -59, 83],\n [48, -90, 134, 73, 114, -63, -53],\n [-23, -128, 6, 55, 54, 147, 67]]\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[[-3, -95, 89, 72, 94, 32, 95],\n [-3, -63, 45, 36, 66, 24, 51],\n [10, 146, -62, -48, -164, -64, -82],\n [-11, 41, -209, -174, 4, 20, -187],\n [-4, -36, -6, -6, 46, 20, 2],\n [5, -15, 90, 75, -5, -10, 80],\n [9, 93, -3, 0, -114, -48, -21]]?\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 7x7 matrix:\n[[53, 16, 12, 15, 22, -102, 109],\n [63, -32, -45, 0, -1, -82, 44],\n [120, -117, -55, 222, 78, -26, 40],\n [-24, 82, -4, -12, 78, -188, 154],\n [28, 54, 106, -12, -20, 4, 84],\n [-72, 91, 105, -63, -22, 62, 8],\n [-103, -21, -140, -27, 45, -32, -106]]\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[[-64, -144, -136, -48, 141, 7, 29],\n [-33, -84, -84, 177, 118, 62, 29],\n [236, 120, 182, -50, -48, 214, -160],\n [-58, -25, -97, -56, 148, -44, -34],\n [81, -58, -31, 124, 166, 189, -67],\n [88, 55, 21, -232, 38, 32, -138],\n [-150, -193, -129, 140, -54, -74, 202]]?\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 7x7 matrix:\n[[-41, 71, -132, -159, -203, 3, 10],\n [-63, -103, 46, 227, 122, 279, 327],\n [-55, 45, 69, -131, -51, -124, -163],\n [-86, -10, 0, -224, -131, -136, -125],\n [78, 82, -135, -24, -76, 33, 51],\n [50, 96, -78, -69, -59, 16, 45],\n [-111, -367, 232, -69, 96, -101, -81]]\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 7x7 matrix:\n[[10, -72, -128, -92, 105, 110, 146],\n [-71, 166, -67, 87, -130, -101, 72],\n [-22, -131, -33, 112, 110, 24, -25],\n [126, 124, 50, 7, -22, -210, 4],\n [-207, 195, -257, 215, -43, -35, 181],\n [164, -28, 121, -112, -97, -5, -56],\n [-116, 3, 51, 4, -67, 54, -73]]\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[[100, -32, 25, 1, 26, 36, -106],\n [20, -65, -53, -91, -109, -133, -91],\n [-64, 108, -5, 86, -38, 44, -30],\n [76, -147, -3, -125, 33, -79, 39],\n [32, 65, 62, 104, 103, 153, 1],\n [-80, -58, -80, -116, -126, -186, 46],\n [-60, 167, 33, 165, 23, 147, -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[[-72, 24, -96, 48, -6, -168, 168],\n [106, -83, 150, 42, -41, 178, -165],\n [-104, 64, -144, 0, 22, -200, 192],\n [-82, 53, -114, -6, 20, -154, 147],\n [-68, 30, -92, 28, 2, -148, 146],\n [-56, 26, -76, 20, 3, -120, 118],\n [32, -84, 56, 152, -74, -32, 52]]?\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[[70, -56, -70, 0, 77, 70, -49],\n [100, -80, -100, 0, 110, 100, -70],\n [-80, 64, 80, 0, -88, -80, 56],\n [0, 0, 0, 0, 0, 0, 0],\n [-40, 32, 40, 0, -44, -40, 28],\n [100, -80, -100, 0, 110, 100, -70],\n [-100, 80, 100, 0, -110, -100, 70]]?\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[[-136, -107, 73, 149, 174, 39, -59],\n [-29, -9, 47, 87, 187, 49, -73],\n [107, 90, 50, 54, 165, 128, 36],\n [60, 33, 59, 30, 47, 29, 12],\n [-48, -46, 92, 142, 178, 91, 3],\n [-132, -155, 129, 89, -50, -145, -95],\n [-55, -1, -67, 19, 119, 68, -26]]\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 7x7 matrix:\n[[136, 66, 101, 88, 130, -31, 47],\n [-42, -30, 1, -82, 14, -121, -1],\n [-117, 210, -74, 23, 104, 149, 44],\n [-58, 168, -10, -2, 148, 12, 54],\n [-138, 141, -71, -46, 77, 44, 29],\n [-103, -27, -57, -87, -45, -37, -19],\n [-131, 164, -72, -23, 86, 79, 34]]\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[[18, 36, -36, 12, -30, 15, 33],\n [12, 24, -24, 8, -20, 10, 22],\n [54, 108, -108, 36, -90, 45, 99],\n [0, 0, 0, 0, 0, 0, 0],\n [30, 60, -60, 20, -50, 25, 55],\n [-42, -84, 84, -28, 70, -35, -77],\n [-12, -24, 24, -8, 20, -10, -22]]\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[[-93, 178, -47, 108, -61, 75, -128],\n [214, -19, -84, -156, 100, -178, 127],\n [-18, 121, 71, 78, -33, 233, 17],\n [-110, -204, 24, 45, 11, -9, 7],\n [-91, 12, -6, 132, -50, 96, -46],\n [-209, 56, -79, 158, -103, -51, -224],\n [38, 231, -178, -84, 132, -47, -31]]\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[[116, -87, -148, -25, -115, 61, -14],\n [74, -50, -14, 117, -80, 8, 62],\n [-16, 37, 212, -1, 173, -169, 30],\n [142, -71, 94, -26, 79, -153, 28],\n [68, -19, 200, 125, 89, -165, 98],\n [54, -47, -146, -106, -65, 67, -60],\n [-86, 42, -74, -17, -44, 98, -34]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[55, -194, 39, -54, -2, 70, 87],\n [-51, 50, 131, 13, -53, 76, -76],\n [32, 164, -76, 46, -26, -8, -18],\n [-89, 231, 45, 20, -27, 55, -11],\n [52, -153, -36, -46, 30, 7, 100],\n [-151, 309, 263, 27, -127, 231, -84],\n [-33, -27, -69, 3, 66, -129, -24]]\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[[15, 21, -21, -6, 24, 12, -12],\n [-45, -63, 63, 18, -72, -36, 36],\n [50, 70, -70, -20, 80, 40, -40],\n [-40, -56, 56, 16, -64, -32, 32],\n [-15, -21, 21, 6, -24, -12, 12],\n [5, 7, -7, -2, 8, 4, -4],\n [-20, -28, 28, 8, -32, -16, 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[[160, -177, -25, -14, 91, 124, -82],\n [180, -30, -148, 68, 93, 85, 23],\n [-24, -193, 222, -65, 21, 55, -158],\n [88, 32, 37, 151, 94, 33, -4],\n [132, 78, -28, 200, 117, 37, 35],\n [48, 56, 90, 166, 84, 10, -8],\n [-164, 36, 68, -98, -107, -83, 5]]\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[[-56, -112, -33, 200, 185, -90, -110],\n [191, 237, 59, -38, -153, -169, -21],\n [-130, -190, -16, 140, 60, 14, -184],\n [-72, -214, 117, -1, -83, -95, -248],\n [64, -18, 128, -75, -66, -113, -30],\n [-29, -185, -93, 61, -99, 139, -58],\n [-5, -439, 119, -66, -189, -53, -206]]\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 7x7 matrix:\n[[-42, 24, 25, 188, -113, 104, 99],\n [-164, -5, -62, 211, -181, -17, 95],\n [7, 32, 47, 65, -36, 91, 110],\n [60, 134, -47, -276, 163, -248, 35],\n [67, 111, 186, 144, -2, 106, 210],\n [217, 206, 145, -72, 146, 71, 144],\n [-55, -81, -151, -231, 59, -170, -145]]\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[[16, 4, -60, 106, 70, 191, 5],\n [-35, 51, -166, 93, 271, 126, -13],\n [-57, 129, 161, 46, -146, 16, 62],\n [-7, 122, -12, 75, 19, 75, -19],\n [-36, -61, -121, -131, 109, -154, -58],\n [-62, 86, -76, 36, 136, 36, -8],\n [230, 134, 181, 141, -241, 22, -41]]?\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 7x7 matrix:\n[[152, -96, -136, -164, -24, 112, -4],\n [-84, 162, 107, 83, 93, -99, 113],\n [-66, -66, 23, 56, -39, -24, -79],\n [122, 60, -5, -25, 47, -15, -15],\n [-22, -188, -85, -53, -105, 85, -87],\n [36, -218, -93, -51, -111, 75, -167],\n [156, 0, -59, -54, -31, 65, -60]]\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, 9, -67, 59, 104, 52, 13],\n [23, -72, 104, -67, -115, -27, -2],\n [-9, 29, -11, 92, -88, -50, -101],\n [50, 4, -6, -48, 130, -29, 45],\n [114, -73, 123, -241, -25, -25, 85],\n [24, 97, -77, -11, 85, 14, 56],\n [55, -77, 93, -136, -15, -14, 46]]\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 7x7 matrix:\n[[-49, 77, 29, -121, 30, -84, -41],\n [104, -74, 6, 46, -92, 29, -9],\n [-51, 84, 115, 67, -20, 68, -136],\n [54, 181, 184, 72, -98, 26, -244],\n [29, -67, -101, -125, 26, -101, 119],\n [65, -31, 57, -93, -98, -49, -72],\n [27, -35, -103, 49, 50, 1, 121]]\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[[-46, -74, 159, 33, -100, 8, 37],\n [18, -107, -99, -118, 78, -77, 88],\n [-13, -114, 16, -12, 25, 273, -201],\n [0, 134, -309, -145, -7, 121, 50],\n [-15, 71, 186, 146, -50, -22, -73],\n [-48, -83, -88, -162, 47, 204, -56],\n [11, -93, -81, -147, 166, 99, 0]]\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 7x7 matrix:\n[[81, 10, 11, 18, 35, -53, -31],\n [45, -42, 41, 60, -16, -98, 20],\n [216, -60, -124, -12, 20, -128, -76],\n [30, 78, -34, -60, 69, 77, -65],\n [78, -31, -119, -51, -3, -8, -43],\n [195, -116, -41, 72, -27, -221, -13],\n [138, -66, -38, 36, -7, -135, -21]]\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 7x7 matrix:\n[[104, 39, -109, -35, -102, -41, 160],\n [7, -107, -115, 113, 158, 101, -35],\n [11, 133, -35, 13, -102, 17, 77],\n [153, 104, -24, -140, -232, -120, 207],\n [84, -118, -38, -57, 21, -61, 47],\n [70, 104, 108, -111, -161, -65, 51],\n [4, -107, -175, 137, 164, 107, -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[[-4, 76, -65, -89, -96, 65, -90],\n [44, -44, -23, 169, 192, -49, 90],\n [-20, 72, -38, -130, -144, 66, -100],\n [-22, 88, -50, -152, -168, 80, -120],\n [-10, -96, 104, 70, 72, -78, 100],\n [3, 108, -105, -102, -108, 90, -120],\n [-49, 40, 34, -179, -204, 47, -90]]\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[[20, 60, -89, 30, -155, 149, -78],\n [-32, 35, 290, 51, 4, 5, 45],\n [4, 135, -87, 76, 11, 85, -133],\n [-75, 100, -44, -150, -132, 29, 61],\n [-63, 120, -266, -174, -70, 3, 1],\n [38, 115, 53, 176, -81, 187, -159],\n [-23, -10, -107, -135, -187, 53, 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[[-117, 18, 9, -3, -30, -51, 30],\n [169, -19, 49, -26, -19, 29, 11],\n [72, -24, 155, -31, -111, -140, 152],\n [105, -57, -52, 77, 108, 13, -31],\n [-30, 78, -62, -88, -26, 178, -126],\n [-291, 117, -45, -92, -89, 65, -61],\n [24, 21, -1, -36, -20, 54, -29]]\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[[-118, 168, -70, -87, -52, -198, 37],\n [-222, 108, -42, -81, -5, -195, 58],\n [-141, 36, -210, -29, 165, -113, 148],\n [-7, -128, -74, 50, 250, 210, 108],\n [-71, -10, 15, 1, 106, 149, 22],\n [-183, -82, -94, -1, 154, -87, 124],\n [-131, 74, -52, -38, -59, -186, 2]]\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[[15, 30, 27, -27, 9, -6, 15],\n [-50, -100, -90, 90, -30, 20, -50],\n [-5, -10, -9, 9, -3, 2, -5],\n [5, 10, 9, -9, 3, -2, 5],\n [35, 70, 63, -63, 21, -14, 35],\n [-60, -120, -108, 108, -36, 24, -60],\n [-30, -60, -54, 54, -18, 12, -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[[140, -2, -277, -184, 27, -214, -297],\n [117, -82, -186, -36, -177, -140, -118],\n [-95, 92, 131, 97, -137, 81, 76],\n [-155, -46, 70, 194, -267, -156, -84],\n [146, 78, -283, -276, -69, 46, 7],\n [123, 58, -111, -138, -208, -25, 13],\n [124, 28, 29, 0, 91, 178, 98]]?\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 7x7 matrix:\n[[78, -18, 32, -54, -153, -66, 0],\n [-171, -76, 78, 18, -14, -53, -210],\n [-108, 23, -10, -91, 132, 92, -72],\n [52, -17, -28, 196, 9, -64, 95],\n [-33, 13, -18, 10, 75, 37, 3],\n [-177, -83, 102, 82, -54, -47, -213],\n [31, 11, -54, -76, 75, -27, 35]]\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 7x7 matrix:\n[[82, -107, -21, 102, -36, -249, -120],\n [-5, 145, 44, -125, -24, 75, 67],\n [-82, -51, -177, -98, 151, -54, 249],\n [28, -27, 50, 102, 148, -39, 28],\n [-87, -124, -191, -11, 56, -174, 89],\n [-73, 94, -59, -149, -48, 12, 83],\n [-21, 74, -29, -101, 144, 18, 209]]\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[[58, -16, -77, -20, -59, 78, 50],\n [44, -22, -75, 5, -60, 78, 33],\n [-78, -24, 27, 120, 9, -18, -90],\n [48, 8, -28, -60, -16, 24, 52],\n [-74, 50, 148, -35, 121, -156, -49],\n [-104, -32, 36, 160, 12, -24, -120],\n [78, 24, -27, -120, -9, 18, 90]]\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[[98, 140, -51, 20, 36, -164, 133],\n [-5, -94, 93, -79, -100, 139, -113],\n [68, 148, -122, -52, -24, -92, 214],\n [-27, -32, 8, 3, 0, 33, -30],\n [74, 52, 28, 2, 0, -74, 16],\n [152, 16, 144, -104, -128, 8, -64],\n [80, -56, 172, -16, -48, 16, -164]]\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[[77, 153, 156, -91, -67, -1, 58],\n [49, 69, -24, 69, -209, 5, 94],\n [163, -102, 99, -140, 196, 25, -211],\n [9, -136, -103, 48, 79, -10, -89],\n [20, -73, -9, -22, 83, 13, -81],\n [-162, 104, 50, -12, -92, 74, 118],\n [47, 9, -34, 52, -135, 18, 32]]?\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 7x7 matrix:\n[[-19, -140, -19, 72, 192, -30, -62],\n [29, 46, 14, -81, -84, 15, 106],\n [-28, -98, -5, 81, 120, -81, -100],\n [2, 124, -18, -12, -94, 150, 2],\n [40, -220, 50, -90, 120, -270, 160],\n [1, -10, 35, -18, -63, -153, 1],\n [3, -240, 6, 21, 241, -156, 25]]\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[[-12, 12, 8, 18, 14, -20, 6],\n [60, -60, -40, -90, -70, 100, -30],\n [18, -18, -12, -27, -21, 30, -9],\n [6, -6, -4, -9, -7, 10, -3],\n [60, -60, -40, -90, -70, 100, -30],\n [12, -12, -8, -18, -14, 20, -6],\n [42, -42, -28, -63, -49, 70, -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[[-120, 20, -70, -120, 0, 70, 80],\n [96, -16, 56, 96, 0, -56, -64],\n [-144, 24, -84, -144, 0, 84, 96],\n [-84, 14, -49, -84, 0, 49, 56],\n [-96, 16, -56, -96, 0, 56, 64],\n [120, -20, 70, 120, 0, -70, -80],\n [24, -4, 14, 24, 0, -14, -16]]\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 7x7 matrix:\n[[66, -99, -11, 66, 44, -11, -88],\n [-24, 36, 4, -24, -16, 4, 32],\n [-66, 99, 11, -66, -44, 11, 88],\n [6, -9, -1, 6, 4, -1, -8],\n [6, -9, -1, 6, 4, -1, -8],\n [-54, 81, 9, -54, -36, 9, 72],\n [-6, 9, 1, -6, -4, 1, 8]]\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[[30, -38, -154, -105, 22, -72, 13],\n [-98, 117, 146, 162, 2, 98, 1],\n [72, -8, 64, -234, 310, -246, 138],\n [66, -155, 22, -16, -2, 122, 115],\n [5, 123, 84, -35, 145, -189, -57],\n [14, 161, -58, 160, 54, -60, -138],\n [-2, -72, 74, 162, -135, 195, -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[[-71, -7, 91, 58, 79, -10, -51],\n [12, 164, -80, -132, 8, -72, 110],\n [84, 48, -21, 99, 78, -163, -99],\n [78, 94, -52, 30, 58, -154, -38],\n [116, -48, -42, 110, -2, -84, -103],\n [78, 46, -103, -69, -62, -25, 58],\n [147, -69, -57, 132, -15, -92, -123]]\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 7x7 matrix:\n[[-136, -183, -30, 207, 192, -20, -170],\n [-12, 170, 145, -58, 80, 70, -111],\n [-31, 123, 199, -45, -44, -165, -7],\n [1, 295, 102, 73, -12, -51, -148],\n [26, -5, 62, -268, -122, 104, 110],\n [-97, 64, 81, 124, 145, -34, -154],\n [20, -217, -139, -126, -126, 102, 121]]\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[[-28, 63, -16, -55, 27, 31, 16],\n [-74, 27, -60, -59, 109, -31, 60],\n [66, 90, 68, -18, -128, 120, -68],\n [42, 63, 44, -15, -83, 81, -44],\n [74, 99, 76, -19, -143, 133, -76],\n [-28, -63, -32, 23, 61, -71, 32],\n [-40, 81, -24, -73, 41, 37, 24]]\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 7x7 matrix:\n[[-10, -70, 50, -40, 50, 80, 10],\n [7, 49, -35, 28, -35, -56, -7],\n [1, 7, -5, 4, -5, -8, -1],\n [-5, -35, 25, -20, 25, 40, 5],\n [-10, -70, 50, -40, 50, 80, 10],\n [5, 35, -25, 20, -25, -40, -5],\n [10, 70, -50, 40, -50, -80, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[158, -25, 183, 154, 61, -41, -66],\n [72, 19, 24, 168, 193, -13, -12],\n [-2, 18, -53, 119, 143, -77, -43],\n [-8, -12, 33, 173, 204, -72, -172],\n [55, 0, 44, -150, -200, 106, 160],\n [119, -43, 137, -107, -113, 105, 74],\n [-355, 75, -361, -152, -36, -22, 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[[40, -102, -61, 59, -24, 28, 45],\n [-40, 46, 54, -44, 39, -67, -35],\n [-64, 117, -48, -102, -129, -57, 136],\n [-80, 169, 52, -118, -27, -71, 10],\n [-48, -33, -57, -45, -72, -126, 132],\n [80, -85, 32, 106, 99, 119, -130],\n [40, -4, 9, 41, 24, 88, -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[[138, -40, 85, 81, -108, -27, -101],\n [-187, 55, 114, 4, -40, 164, 24],\n [-70, 22, 119, 5, 51, 95, 10],\n [-140, 129, -54, -21, -225, 55, -220],\n [-1, -264, 213, 64, 192, -104, -14],\n [99, 105, 1, 21, -138, 42, -100],\n [-34, -32, 108, 90, 211, 84, 203]]?\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 7x7 matrix:\n[[-57, 11, 80, 115, 12, -105, -15],\n [45, 18, 21, -21, 9, 9, 57],\n [81, 48, 87, 3, 27, -27, 129],\n [-39, 0, 31, 59, 3, -51, -23],\n [-96, -2, 70, 140, 6, -120, -60],\n [-63, -33, -54, 9, -18, 9, -93],\n [-42, -48, -118, -62, -30, 78, -106]]\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[[265, 129, -75, -165, 94, -32, -31],\n [237, 110, 9, 18, 110, 101, 163],\n [163, -111, -313, -230, 13, 20, -171],\n [-218, -62, 138, 239, -95, 48, 43],\n [-144, -21, 54, 206, 81, 114, 24],\n [314, 96, -136, -326, -48, -125, -87],\n [-81, -53, 49, 143, 78, 109, 160]]\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 7x7 matrix:\n[[-10, 124, 166, -54, -48, -8, 134],\n [3, 82, 143, -7, -56, 60, 107],\n [6, -102, -156, 26, 56, -32, -120],\n [-5, -119, -198, 20, 72, -68, -151],\n [29, 79, 34, -123, 60, -152, 62],\n [-64, 95, 3, -139, 40, -248, 28],\n [-51, 42, 21, -31, -16, -68, 15]]\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[[85, 94, -10, -54, -49, 60, -21],\n [109, 55, -129, -167, 53, 71, 77],\n [130, -38, 58, 32, -4, -134, 184],\n [32, 55, -62, -43, -197, 125, -41],\n [20, 80, 158, 66, 184, -96, -76],\n [61, -171, -294, -202, -13, 29, 309],\n [54, -149, -205, -145, 54, -27, 270]]\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 7x7 matrix:\n[[192, -86, -62, 50, 74, -49, 127],\n [-144, 42, 78, -78, -78, 57, -111],\n [168, -34, -112, 118, 106, -80, 140],\n [72, -86, 52, -78, -26, 30, 10],\n [24, 98, -160, 202, 118, -104, 92],\n [-156, 83, 32, -17, -47, 28, -94],\n [-96, 98, -46, 74, 18, -25, -25]]\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[[-54, -63, 81, 54, -27, 90, -63],\n [-6, -7, 9, 6, -3, 10, -7],\n [-30, -35, 45, 30, -15, 50, -35],\n [30, 35, -45, -30, 15, -50, 35],\n [-42, -49, 63, 42, -21, 70, -49],\n [72, 84, -108, -72, 36, -120, 84],\n [-18, -21, 27, 18, -9, 30, -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[[-49, -172, 6, -199, -50, -49, 257],\n [122, -41, -16, -248, 199, -79, 117],\n [-167, 104, 10, 15, -118, 64, 46],\n [54, -100, 93, 177, 81, -74, -71],\n [-121, 248, 59, 25, -29, 100, 38],\n [65, 107, 32, 133, -73, 106, -52],\n [-117, -99, -83, 88, -194, 10, -87]]\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[[12, -5, 9, -7, -1, 7, 3],\n [24, -10, 18, -14, -2, 14, 6],\n [96, -40, 72, -56, -8, 56, 24],\n [-12, 5, -9, 7, 1, -7, -3],\n [72, -30, 54, -42, -6, 42, 18],\n [-24, 10, -18, 14, 2, -14, -6],\n [-144, 60, -108, 84, 12, -84, -36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[40, 44, 24, -33, -65, -40, -56],\n [-113, 34, 73, 11, -84, 46, 63],\n [35, 96, 75, -63, -158, -62, -83],\n [-175, 68, 61, 107, -66, 126, 75],\n [19, -9, -22, 10, 29, 0, -10],\n [114, -13, 21, -135, -55, -126, -61],\n [75, 37, 52, -109, -110, -100, -68]]\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[[-90, 6, -64, 70, 74, -96, 102],\n [-78, 66, -112, -62, 62, 48, 66],\n [31, -16, 35, 4, -25, 3, -30],\n [77, 43, 10, -157, -65, 186, -105],\n [135, -9, 96, -105, -111, 144, -153],\n [-1, -62, 57, 126, 3, -135, 24],\n [91, -1, 60, -81, -75, 108, -105]]\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[[3, 72, 65, -39, -16, 39, 5],\n [-2, 135, -126, -1, -232, 66, -140],\n [91, 81, -137, -57, -48, -12, -45],\n [169, 0, -255, -46, 50, -84, 1],\n [142, 162, -38, -152, 28, 2, 10],\n [167, 108, -69, -140, 91, -33, 44],\n [-23, 108, -39, -6, -168, 62, -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[[110, -128, -10, -30, 82, -84, -106],\n [121, -157, -11, -42, 74, -105, -131],\n [-121, 229, 11, 82, -2, 161, 195],\n [33, -51, -3, -16, 12, -35, -43],\n [110, -74, -10, 0, 136, -42, -58],\n [22, 14, -2, 16, 56, 14, 14],\n [-66, -15, 6, -33, -141, -21, -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[[-86, 44, -36, -76, -40, 56, 82],\n [3, 66, 42, 6, -12, 60, 39],\n [89, 22, 78, 82, 28, 4, -43],\n [3, -176, -104, -6, 36, -162, -111],\n [0, -242, -146, -12, 48, -222, -150],\n [-90, -44, -92, -84, -24, -24, 30],\n [-29, -33, -41, -28, -4, -25, -2]]\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[[-111, -30, -8, -25, 82, -201, -121],\n [106, -60, -81, 107, -74, 226, 49],\n [-92, -90, -73, 42, 72, -146, -157],\n [65, -40, -66, 86, -36, 93, -55],\n [81, 10, -42, 77, -34, 23, -147],\n [-77, 10, 13, -30, 64, -195, -138],\n [-20, 110, 127, -130, 0, -34, 147]]\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 7x7 matrix:\n[[-127, 159, 20, 65, 187, -172, -99],\n [44, -9, -142, -68, -67, 15, 234],\n [-24, 33, 108, 30, 81, -60, -123],\n [27, 114, 236, -9, 134, -129, -79],\n [200, -72, 110, -110, -242, 234, 119],\n [-99, -63, 84, 101, 141, -92, -295],\n [46, -75, -244, -38, -255, 238, 226]]\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 7x7 matrix:\n[[-100, -41, 111, -91, 146, -129, -194],\n [-30, -120, -92, -288, -58, 43, 244],\n [99, -20, 139, 49, 246, -53, -159],\n [106, 78, -155, 111, -103, 119, 159],\n [149, 29, -90, 189, 100, -9, -32],\n [202, 70, 107, 128, 267, 64, -158],\n [-78, -52, -125, -42, 21, -123, -40]]\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[[-42, -60, -54, 36, -54, 6, 66],\n [49, 70, 63, -42, 63, -7, -77],\n [63, 90, 81, -54, 81, -9, -99],\n [-70, -100, -90, 60, -90, 10, 110],\n [-56, -80, -72, 48, -72, 8, 88],\n [-7, -10, -9, 6, -9, 1, 11],\n [-7, -10, -9, 6, -9, 1, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[40, 91, -114, -92, -5, -170, 97],\n [67, -109, -34, -119, -202, -84, -29],\n [-46, -74, 24, -4, -127, 118, -153],\n [-12, 31, -164, -82, -166, -36, -20],\n [-48, 86, 21, 60, 144, 26, 52],\n [-157, -48, -24, -253, -335, -2, -148],\n [264, -210, 3, 169, -13, 22, 25]]\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[[102, 21, -71, 92, 54, 186, 82],\n [-48, -3, -3, 24, -75, -80, -47],\n [-114, 274, 136, -116, -197, 34, -87],\n [13, 143, -58, -1, -109, 83, 72],\n [-166, -99, 160, -54, -41, -274, -224],\n [-162, 69, 10, 102, -107, -22, -74],\n [-194, 42, 133, 10, -130, -150, -201]]?\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[[-77, 77, 14, -14, 0, -63, 77],\n [8, -38, -11, 32, -12, 18, -74],\n [43, -53, -11, 18, -4, 39, -65],\n [64, 26, 17, -80, 36, 18, 134],\n [18, -58, -16, 44, -16, 30, -106],\n [-157, 127, 19, 2, -12, -117, 91],\n [-47, 17, -1, 22, -12, -27, -19]]\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 7x7 matrix:\n[[-30, 93, 132, -27, -24, 108, -66],\n [24, 31, 99, 34, 44, 19, 59],\n [18, 36, 99, 27, 36, 27, 45],\n [38, -26, 11, 45, 52, -45, 89],\n [-34, -17, -88, -45, -56, 0, -82],\n [48, -6, 66, 60, 72, -30, 114],\n [-20, 62, 88, -18, -16, 72, -44]]\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[[3, -104, -138, -1, -117, 68, 47],\n [-11, 24, 42, 9, 29, -36, -7],\n [-46, -125, -117, 41, -131, -16, 75],\n [85, 113, 63, -74, 110, 100, -84],\n [6, -7, -15, -5, -9, 16, 1],\n [78, 43, -21, -67, 33, 128, -49],\n [-78, -43, 21, 67, -33, -128, 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[[-99, 99, -54, -99, -63, -63, 99],\n [110, -110, 60, 110, 70, 70, -110],\n [-77, 77, -42, -77, -49, -49, 77],\n [-11, 11, -6, -11, -7, -7, 11],\n [22, -22, 12, 22, 14, 14, -22],\n [66, -66, 36, 66, 42, 42, -66],\n [99, -99, 54, 99, 63, 63, -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[[166, 106, -42, 45, -27, -21, -35],\n [230, 17, -111, -51, 87, -69, 23],\n [154, 29, -13, -32, 133, -161, 35],\n [-84, 43, 67, 60, -68, 26, -32],\n [-30, 148, 136, 123, -53, -79, -53],\n [-46, -139, -9, -114, 153, -81, 83],\n [40, 126, 82, 86, -16, -88, -36]]\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 7x7 matrix:\n[[108, 86, 78, 37, -60, 35, -105],\n [-100, -48, -46, 19, -20, -33, 89],\n [2, 143, 113, -118, 62, -15, -131],\n [36, 170, 82, -174, 68, -67, -208],\n [-74, -181, -113, 108, -14, 31, 209],\n [26, 27, 77, 4, 38, 67, -5],\n [110, 107, 139, -18, 34, 82, -113]]\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[[130, -82, 44, -2, 114, 80, 112],\n [-60, 17, -21, 116, -12, 68, -46],\n [-146, 100, -48, -50, -159, -145, -139],\n [140, -104, 48, 76, 138, 150, 114],\n [-140, 87, -51, 36, -72, -32, -86],\n [-97, 73, -32, -67, -114, -125, -91],\n [-95, 86, -39, -85, -30, -87, -15]]?\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 7x7 matrix:\n[[-132, 88, 99, 22, -99, -77, 88],\n [-21, 4, 19, -2, 2, -16, 14],\n [156, 16, -156, 40, -96, 136, -104],\n [-189, 36, 171, -18, 18, -144, 126],\n [198, -72, -168, 0, 42, 138, -132],\n [84, -56, -63, -14, 63, 49, -56],\n [-252, 48, 228, -24, 24, -192, 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[[80, 0, -10, 0, -60, -10, 40],\n [56, 0, -7, 0, -42, -7, 28],\n [-172, 72, -121, 72, 198, 35, 100],\n [-65, 42, -75, 42, 89, 16, 76],\n [35, -30, 55, -30, -55, -10, -60],\n [48, -48, 89, -48, -82, -15, -100],\n [1, -42, 83, -42, -41, -8, -108]]\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[[-17, 56, 75, -158, 252, 41, 44],\n [-11, -61, 14, 43, -28, 85, 104],\n [-41, 148, 21, -131, 176, -135, -69],\n [30, -176, -30, 104, -232, 102, 128],\n [32, -26, -48, 121, -140, -4, -89],\n [-39, -26, 17, -51, 0, -5, 137],\n [-6, -19, -61, 36, -188, -120, -11]]\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 7x7 matrix:\n[[-26, -40, 28, -5, -14, -21, -5],\n [39, 64, -76, -70, 90, -86, 47],\n [-49, -50, 42, -40, 104, -119, 108],\n [56, 52, -120, -115, -34, -89, -99],\n [7, -12, 16, 60, -134, 122, -113],\n [-21, -36, 4, -45, 0, -71, -8],\n [-17, -14, 30, 20, 28, 3, 42]]\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[[-6, 53, 27, -102, -12, 56, -88],\n [-165, 6, 126, 121, 198, -56, 30],\n [-4, 48, -64, 48, -108, 120, -40],\n [148, -6, -152, -37, -195, 62, 22],\n [70, 72, -55, -105, -8, 30, 47],\n [-78, 6, 55, 14, -65, 92, -173],\n [101, 93, -178, -7, -207, 176, 11]]?\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[[-177, 29, -3, -26, 61, 19, -69],\n [62, 143, -64, 130, 68, -61, 60],\n [-210, 32, 23, -22, 72, 49, -116],\n [140, 22, 83, 98, -18, 69, -66],\n [-236, 35, -32, -50, 78, -3, -54],\n [206, -85, 97, 20, -98, 68, -26],\n [44, 68, 50, 100, 32, 50, -72]]?\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 7x7 matrix:\n[[-69, -76, -26, -150, -99, 74, 135],\n [-212, -46, -24, -10, -139, 180, 64],\n [-325, -3, -14, 42, -87, 140, -8],\n [183, -73, 16, -68, -35, 32, 16],\n [21, -64, 70, 298, 124, -22, -167],\n [-9, 98, -7, 42, -77, 112, -101],\n [155, -63, -8, -36, 29, -68, 118]]\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[[50, 13, -158, -77, -100, 18, 89],\n [-46, 112, 170, -91, -66, -56, 220],\n [71, -40, -221, -61, -66, 57, 32],\n [-24, -29, 104, -134, 100, 152, 181],\n [-127, 195, 177, 17, -9, -4, -54],\n [-150, 421, 122, 4, -266, -172, 1],\n [91, -176, -177, 76, 54, 13, -138]]\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 7x7 matrix:\n[[-18, 30, 2, 48, -178, 62, -26],\n [-14, -18, 5, -97, 175, -93, -34],\n [-7, 33, -1, 88, -231, 97, -3],\n [-56, 36, 11, -37, -119, -3, -100],\n [22, -6, -5, 41, -15, 29, 42],\n [-35, 33, 6, 11, -154, 34, -59],\n [32, -24, -6, 10, 94, -10, 56]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[60, 24, -24, 0, 60, -54, -54],\n [134, 8, 76, -84, -10, 45, -75],\n [-76, -76, 160, -84, -220, 234, 114],\n [-66, 4, -60, 56, 30, -51, 29],\n [88, 39, -46, 7, 100, -93, -83],\n [-104, -72, 128, -56, -200, 204, 124],\n [28, 15, -22, 7, 40, -39, -29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[49, 70, -49, 56, -49, 28, -42],\n [14, 20, -14, 16, -14, 8, -12],\n [77, 110, -77, 88, -77, 44, -66],\n [77, 110, -77, 88, -77, 44, -66],\n [84, 120, -84, 96, -84, 48, -72],\n [14, 20, -14, 16, -14, 8, -12],\n [56, 80, -56, 64, -56, 32, -48]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 7x7 matrix:\n[[108, 23, 39, 193, -95, -76, -74],\n [54, 11, -31, 4, 4, 4, 19],\n [42, 75, -3, 70, 14, 28, -7],\n [24, 92, 12, 86, 18, 36, -18],\n [99, -83, -16, 38, -85, -93, -13],\n [99, -21, -2, 90, -69, -65, -27],\n [-69, 7, -90, -233, 138, 117, 120]]\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 7x7 matrix:\n[[60, -30, -48, -18, -66, -54, 54],\n [60, -30, -48, -18, -66, -54, 54],\n [80, -40, -64, -24, -88, -72, 72],\n [-20, 10, 16, 6, 22, 18, -18],\n [-70, 35, 56, 21, 77, 63, -63],\n [-50, 25, 40, 15, 55, 45, -45],\n [-120, 60, 96, 36, 132, 108, -108]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[132, -132, -84, 108, 12, -96, 132],\n [-121, 121, 77, -99, -11, 88, -121],\n [22, -22, -14, 18, 2, -16, 22],\n [77, -77, -49, 63, 7, -56, 77],\n [-33, 33, 21, -27, -3, 24, -33],\n [88, -88, -56, 72, 8, -64, 88],\n [121, -121, -77, 99, 11, -88, 121]]\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[[-22, -110, 110, 11, 77, -66, -44],\n [2, 10, -10, -1, -7, 6, 4],\n [0, 0, 0, 0, 0, 0, 0],\n [-22, -110, 110, 11, 77, -66, -44],\n [20, 100, -100, -10, -70, 60, 40],\n [-8, -40, 40, 4, 28, -24, -16],\n [-20, -100, 100, 10, 70, -60, -40]]\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[[17, -5, -8, 77, 41, 30, 8],\n [0, -69, 18, -83, 17, 36, -53],\n [6, 94, 78, 6, 226, 10, -127],\n [14, -22, -2, 42, 38, 34, -7],\n [-2, 41, -34, 71, -69, -36, 77],\n [-7, -74, -74, 2, -214, -18, 125],\n [-6, 175, 54, 57, 157, -56, -55]]?\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[[-158, -2, 107, 240, -117, 192, 226],\n [41, 70, 6, 126, 31, 244, -48],\n [146, 147, -182, -42, 162, 113, -223],\n [278, -2, 91, -190, 50, -34, -99],\n [-104, -61, -61, -62, 27, -157, -67],\n [-185, -122, 144, 114, -130, -15, 165],\n [91, 13, -178, -170, 57, -204, -199]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-118, -50, 56, 41, 25, -83, -48],\n [-94, -99, 79, -51, 81, 28, 116],\n [78, 176, -78, -51, -165, 87, -202],\n [-38, 13, -141, 65, -23, -76, -100],\n [-2, 0, 85, -32, 0, 31, 19],\n [68, -3, -51, -98, 18, 135, 128],\n [24, 90, -16, -47, -88, 63, -105]]\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[[-12, -48, -48, 98, 124, -76, -76],\n [-52, 54, 54, -12, -74, -111, -111],\n [-44, 72, 72, -54, -124, -72, -72],\n [76, -72, -72, 6, 92, 168, 168],\n [52, -54, -54, 12, 74, 111, 111],\n [-32, -18, -18, 78, 74, -111, -111],\n [52, -42, -42, -8, 46, 121, 121]]?\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[[10, 226, -24, 81, 183, 76, -9],\n [142, -25, 157, -3, 11, -29, -101],\n [140, -15, -4, -261, -105, 148, 138],\n [-192, 64, -132, 156, 76, -44, 8],\n [136, -83, 154, -33, -41, -42, -88],\n [-4, 152, 21, 135, 159, -1, -72],\n [168, 16, 61, -183, -43, 111, 58]]\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[[210, -3, 238, 137, 156, 26, 50],\n [120, -14, -3, -19, -128, 159, 56],\n [-221, 70, -157, -65, 16, -74, -13],\n [148, -99, 184, 111, 90, -82, -86],\n [-58, 61, -1, 36, 97, -27, 15],\n [-150, 206, -45, -29, 167, 15, 181],\n [53, 121, 21, -34, 19, 152, 200]]\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 7x7 matrix:\n[[32, -223, 91, 145, -188, -170, -7],\n [-189, -22, 41, -35, -5, -105, 123],\n [83, -35, -7, 34, -35, 26, -85],\n [90, -137, 66, 136, -107, -119, 60],\n [-24, 156, -65, -112, 112, 125, -31],\n [106, 62, 5, 47, 57, -3, 149],\n [-19, -37, 44, 37, -46, -87, 90]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 0, 24, 152, -80, 120, 24],\n [-5, 0, 50, 170, 110, -90, -120],\n [-14, 8, 84, 268, 87, -58, -143],\n [-43, 34, 74, 47, -8, -38, -79],\n [-50, 42, 72, 5, -77, 18, -36],\n [-76, 58, 92, -103, 37, -158, -130],\n [-27, 18, 58, 63, 86, -114, -117]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-26, 185, -155, -73, 24, -81, -89],\n [102, 16, -65, 81, 67, 15, 255],\n [99, 46, -38, -54, 115, 10, 39],\n [-211, 55, -125, 132, -226, -31, -29],\n [-65, 73, -80, -30, -36, -10, -115],\n [38, -4, 48, -155, 91, 44, -223],\n [-28, 49, -113, 45, -28, 33, 31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-38, 32, -44, -3, 19, -21, 50],\n [-60, 90, -100, 110, 120, -90, 80],\n [24, -56, 56, -89, -89, 63, -36],\n [62, -58, 72, -117, -81, 57, -54],\n [-82, -77, 42, 160, -85, 84, -52],\n [-10, -50, 40, -13, -73, 57, -30],\n [124, 29, 26, 43, 118, -75, -66]]\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[[-88, -48, -32, -32, 8, -24, 24],\n [-33, -18, -12, -12, 3, -9, 9],\n [-33, -18, -12, -12, 3, -9, 9],\n [-11, -6, -4, -4, 1, -3, 3],\n [22, 12, 8, 8, -2, 6, -6],\n [-66, -36, -24, -24, 6, -18, 18],\n [22, 12, 8, 8, -2, 6, -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[[-121, -99, 110, -77, 99, -99, 55],\n [-55, -45, 50, -35, 45, -45, 25],\n [132, 108, -120, 84, -108, 108, -60],\n [-121, -99, 110, -77, 99, -99, 55],\n [121, 99, -110, 77, -99, 99, -55],\n [-77, -63, 70, -49, 63, -63, 35],\n [99, 81, -90, 63, -81, 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[[88, 20, -96, -58, -82, 8, -46],\n [0, -100, -40, -10, -10, 120, -110],\n [-66, 40, 94, 49, 67, -72, 95],\n [22, -10, -30, -16, -22, 20, -28],\n [-88, -150, 44, 45, 69, 148, -97],\n [-99, -25, 107, 65, 92, -6, 49],\n [-99, -95, 79, 58, 85, 78, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[108, -12, -84, 72, -108, -132, -24],\n [90, -10, -70, 60, -90, -110, -20],\n [-81, 9, 63, -54, 81, 99, 18],\n [-99, 11, 77, -66, 99, 121, 22],\n [-18, 2, 14, -12, 18, 22, 4],\n [72, -8, -56, 48, -72, -88, -16],\n [72, -8, -56, 48, -72, -88, -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[[5, -76, 49, -12, -32, -8, 33],\n [-129, -43, -33, 104, -44, 79, 3],\n [-188, -121, -272, 42, 130, -121, 35],\n [62, 55, -60, 16, 16, 23, 40],\n [-211, 61, -96, 202, -50, 176, -50],\n [-58, -176, 8, -72, 32, -134, 22],\n [-91, -70, 42, 110, -102, 121, 34]]\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[[-168, 76, -37, -1, 87, 87, -78],\n [-77, 104, -23, 19, 216, 35, 100],\n [-3, 48, 211, -223, -33, 105, -72],\n [-98, 1, -162, 245, 106, 55, -76],\n [12, -83, -9, -14, -20, -192, -106],\n [95, -128, -165, 153, -30, -253, 0],\n [202, -184, -67, 69, -290, -138, -48]]?\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 7x7 matrix:\n[[135, 100, 164, -167, -95, -25, 109],\n [7, 67, 60, -114, -33, 54, -32],\n [-68, 209, 87, -119, -348, 23, 215],\n [22, 7, 32, -45, 4, 33, 4],\n [-155, -151, -192, 238, 57, 62, 17],\n [73, -21, -4, 104, -31, -180, 115],\n [19, 50, 29, 13, -125, -73, 137]]\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[[27, 33, -6, -33, 0, 9, -12],\n [9, 11, -2, -11, 0, 3, -4],\n [-72, -88, 16, 88, 0, -24, 32],\n [90, 110, -20, -110, 0, 30, -40],\n [54, 66, -12, -66, 0, 18, -24],\n [-81, -99, 18, 99, 0, -27, 36],\n [99, 121, -22, -121, 0, 33, -44]]\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[[15, 21, 30, -33, -15, -9, -9],\n [-30, -42, -60, 66, 30, 18, 18],\n [15, 21, 30, -33, -15, -9, -9],\n [0, 0, 0, 0, 0, 0, 0],\n [-40, -56, -80, 88, 40, 24, 24],\n [10, 14, 20, -22, -10, -6, -6],\n [-30, -42, -60, 66, 30, 18, 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[[42, -16, 52, 38, 14, -60, -18],\n [-87, 37, -46, -71, -29, 51, -36],\n [-18, 9, 12, -12, -6, -15, -33],\n [-57, 23, -50, -49, -19, 57, 0],\n [-33, 16, 14, -23, -11, -18, -51],\n [15, -6, 14, 13, 5, -16, -1],\n [57, -25, 18, 45, 19, -19, 38]]\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 7x7 matrix:\n[[13, 251, -268, 21, 116, 179, -142],\n [-66, 102, 64, 2, 26, 20, -89],\n [25, 71, 25, -56, -73, -53, -78],\n [-13, -86, 234, 50, 21, 132, 2],\n [-7, 199, -163, 148, 59, 161, -84],\n [83, 2, -114, 14, 99, 232, -11],\n [28, -30, -30, -40, -50, -85, 26]]\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[[-219, 24, 138, -40, -224, -272, 48],\n [212, 78, 18, 58, 36, -3, 70],\n [174, 176, 182, -75, -15, -34, -131],\n [75, 43, 119, -208, 28, 63, -298],\n [172, -125, -143, 48, 80, 37, 126],\n [17, -18, 64, -80, -150, -209, 28],\n [-59, -110, 24, -163, -54, -63, -125]]?\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[[0, 0, 0, 0, 0, 0, 0],\n [66, -55, 11, -77, 132, -66, 11],\n [0, 0, 0, 0, 0, 0, 0],\n [48, -40, 8, -56, 96, -48, 8],\n [48, -40, 8, -56, 96, -48, 8],\n [-48, 40, -8, 56, -96, 48, -8],\n [-66, 55, -11, 77, -132, 66, -11]]\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[[96, -41, 96, 37, 13, 8, 19],\n [15, -102, 84, 87, -3, -39, -84],\n [-126, -21, -72, 15, -21, -42, -93],\n [142, -8, 104, 10, 22, 34, 76],\n [209, -38, 172, 37, 31, 39, 88],\n [12, -55, 48, 47, -1, -20, -43],\n [22, -123, 104, 105, -3, -46, -99]]\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[[-8, 88, 8, -96, -32, -32, 56],\n [-5, 55, 5, -60, -20, -20, 35],\n [8, -88, -8, 96, 32, 32, -56],\n [-3, 33, 3, -36, -12, -12, 21],\n [4, -44, -4, 48, 16, 16, -28],\n [-9, 99, 9, -108, -36, -36, 63],\n [10, -110, -10, 120, 40, 40, -70]]\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[[-35, -20, 50, 30, 50, -20, -50],\n [-7, 10, -18, -26, -6, 6, 16],\n [7, -17, 32, 42, 14, -11, -29],\n [105, 18, -66, 6, -102, 30, 72],\n [-56, -11, 38, 0, 56, -17, -41],\n [70, 54, -128, -92, -116, 50, 126],\n [49, 63, -140, -122, -110, 53, 135]]?\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 7x7 matrix:\n[[17, -9, 63, 58, -296, 176, 178],\n [124, 137, 118, -105, 67, -155, -32],\n [-133, -206, -108, 49, -76, 36, 122],\n [-27, -89, 21, 229, -163, 34, 266],\n [-55, -202, 3, -65, -276, -42, 332],\n [30, 94, -95, 98, 170, 22, -94],\n [-18, 5, -8, 208, -4, 3, 144]]\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[[-125, 237, -52, -201, 151, 180, 65],\n [51, 0, 47, 112, -40, -35, -6],\n [110, -86, 163, -148, -163, -122, 236],\n [-81, -19, 16, 255, -17, 88, -271],\n [138, -255, 197, 92, -265, -187, 52],\n [-4, -131, -66, 105, -8, -43, -139],\n [101, -256, 142, 162, -223, -155, -52]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, -10, 2, 0, -2, 1, -6],\n [-9, 30, -6, 0, 6, -3, 18],\n [21, -70, 14, 0, -14, 7, -42],\n [-9, 30, -6, 0, 6, -3, 18],\n [6, -20, 4, 0, -4, 2, -12],\n [-15, 50, -10, 0, 10, -5, 30],\n [-6, 20, -4, 0, 4, -2, 12]]?\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 7x7 matrix:\n[[-14, 16, -18, 127, 2, -13, 22],\n [70, -147, -61, -54, 40, 6, -46],\n [-20, -162, 12, -220, -112, 98, -178],\n [80, 4, -9, -106, 76, -25, 23],\n [106, 40, -46, 131, 122, -41, 62],\n [-6, -52, -18, 3, 18, -17, 30],\n [-65, 210, 14, 81, 87, -178, 271]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 7x7 matrix:\n[[12, 42, 42, -12, 60, -54, -72],\n [-22, -77, -77, 22, -110, 99, 132],\n [-12, -42, -42, 12, -60, 54, 72],\n [6, 21, 21, -6, 30, -27, -36],\n [-12, -42, -42, 12, -60, 54, 72],\n [4, 14, 14, -4, 20, -18, -24],\n [20, 70, 70, -20, 100, -90, -120]]\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[[47, -133, 17, 64, 324, 68, 96],\n [-106, 5, 3, 38, -186, 64, -56],\n [-104, 84, -166, 140, 133, 100, 132],\n [62, -29, 107, -146, -209, -130, -96],\n [137, -227, 145, 5, 238, 34, -50],\n [90, 123, 17, -157, -199, -183, -72],\n [-27, -50, -18, 62, 130, 66, 60]]\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[[30, 178, 66, 28, -82, -162, 164],\n [59, -9, -190, 147, 20, 31, -92],\n [312, -26, 102, 251, -17, 58, -22],\n [178, 51, 91, -33, -101, 24, 41],\n [-60, -166, -138, -177, 138, 31, -47],\n [-104, 154, -148, -63, 5, -230, 148],\n [19, 332, -91, -1, -231, -168, 204]]\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[[-6, 96, 66, 36, -45, 78, -60],\n [-111, 144, 60, 36, -19, 139, -131],\n [44, 22, -34, -54, 39, -2, -178],\n [56, 118, 104, 54, -84, 82, -52],\n [11, -161, -130, -81, 96, -134, 47],\n [49, -209, -146, -89, 98, -180, 101],\n [73, 116, 124, 72, -107, 79, -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 7x7 matrix:\n[[-35, 56, -21, 14, -77, 42, -7],\n [55, -88, 33, -22, 121, -66, 11],\n [-15, 24, -9, 6, -33, 18, -3],\n [40, -64, 24, -16, 88, -48, 8],\n [-50, 80, -30, 20, -110, 60, -10],\n [45, -72, 27, -18, 99, -54, 9],\n [60, -96, 36, -24, 132, -72, 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[[46, 27, 18, 49, 13, -34, 39],\n [-39, -189, 17, -41, -49, 137, -23],\n [46, 149, 26, 55, 75, -130, 17],\n [-68, -219, 52, -63, -13, 144, -67],\n [31, 49, -147, 2, -149, 37, 95],\n [-23, -137, 169, 7, 131, 17, -83],\n [70, 176, -44, 65, 2, -116, 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[[-23, -8, 67, -49, 18, 58, 74],\n [-206, 211, -222, 166, -107, 86, 195],\n [17, -59, 131, 94, 124, -46, -37],\n [74, -146, 239, -258, 98, -76, -160],\n [100, -43, 194, -45, 42, 252, 109],\n [-35, -73, 52, 6, 92, -197, -75],\n [267, -171, -4, -135, -61, 19, -25]]?\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[[77, -12, 121, 45, 53, 95, -52],\n [-77, -30, -65, -59, 10, -32, 17],\n [-110, -102, -14, -104, 103, 43, -25],\n [-22, -36, 18, -26, 44, 32, -18],\n [11, -42, 71, -7, 68, 74, -41],\n [99, -12, 151, 59, 63, 117, -64],\n [-55, 6, -83, -33, -34, -64, 35]]\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[[-55, -15, -28, 37, 72, -44, 74],\n [-146, 151, 340, 36, -197, -53, -109],\n [132, -40, 242, 60, -50, -74, -40],\n [-114, 97, -218, -286, 68, 253, -55],\n [39, -52, -81, 39, 59, -28, 55],\n [-47, 49, -229, -217, 76, 201, -28],\n [73, 55, 86, 118, -122, -67, -39]]\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 7x7 matrix:\n[[-45, -36, 90, 18, -36, 45, -99],\n [50, 40, -100, -20, 40, -50, 110],\n [-40, -32, 80, 16, -32, 40, -88],\n [40, 32, -80, -16, 32, -40, 88],\n [20, 16, -40, -8, 16, -20, 44],\n [25, 20, -50, -10, 20, -25, 55],\n [-40, -32, 80, 16, -32, 40, -88]]\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 7x7 matrix:\n[[54, 210, 49, -26, 98, 160, -14],\n [-13, 84, 70, -147, 186, -42, 68],\n [3, 93, 56, -38, 53, 37, 31],\n [6, -57, -32, 83, -112, 60, -11],\n [48, -72, 25, 132, -19, -37, 76],\n [-6, -141, -17, 46, -31, -76, 53],\n [53, -57, -65, 133, -77, 48, -47]]\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 7x7 matrix:\n[[17, -8, 73, -16, 181, -62, -61],\n [81, 174, 9, 151, -72, -21, 132],\n [326, 276, 182, 52, -294, -128, 164],\n [-49, -122, 19, 157, 106, -29, 92],\n [90, -78, 124, 53, 7, -161, 42],\n [2, 157, -87, -34, -117, 57, -14],\n [54, -167, 101, 57, -50, -114, 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[[60, 12, 24, 132, 132, -132, 132],\n [35, 7, 14, 77, 77, -77, 77],\n [30, 6, 12, 66, 66, -66, 66],\n [-40, -8, -16, -88, -88, 88, -88],\n [35, 7, 14, 77, 77, -77, 77],\n [-55, -11, -22, -121, -121, 121, -121],\n [60, 12, 24, 132, 132, -132, 132]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[16, -130, -97, -40, 185, -21, 108],\n [-6, 103, -239, 9, 100, 170, -21],\n [-45, 76, -201, 4, 118, 126, -8],\n [-17, 20, 150, -26, -121, -43, 89],\n [-113, -63, -115, -27, 217, -11, 74],\n [-103, -98, 2, -36, 151, -79, 101],\n [-148, 15, 35, -7, 50, -44, 24]]\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[[-45, 57, 7, 80, 25, -256, -140],\n [-314, 164, 41, 159, 122, -70, -122],\n [-103, 66, 3, -28, -14, 56, 47],\n [-4, 225, -122, 189, -127, 158, 16],\n [98, -60, -82, -64, 66, -56, 128],\n [8, -123, 43, -78, 36, 136, 51],\n [25, -244, 69, -15, 196, 150, 10]]?\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[[-140, 36, 130, 59, 4, 86, 0],\n [-22, 24, -12, 14, -28, 33, 4],\n [124, -66, -36, -47, 61, -93, 14],\n [-4, 20, -44, -4, -38, 8, -12],\n [-8, 30, -28, 21, -35, 49, 22],\n [6, 36, -44, 28, -42, 65, 40],\n [-94, 32, -44, -46, -80, -55, -132]]\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[[36, 95, -38, -87, 103, -76, 83],\n [189, 120, -123, -177, 16, -134, 166],\n [150, -16, -123, 45, 41, -37, -3],\n [-60, 20, 85, 122, -73, 113, -114],\n [-91, -40, -18, 77, 158, 50, 16],\n [33, -151, -102, 169, 53, 90, -24],\n [76, 57, -78, -9, 48, -91, -103]]\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, 71, 134, -8, 96, -83, 85],\n [-20, -22, -74, -56, -80, 53, 19],\n [-94, -16, -205, -71, -198, 88, -20],\n [78, -42, 126, 2, 116, -4, 40],\n [-35, 35, -2, 74, 20, -48, -66],\n [-128, -188, -161, 83, -66, 149, -205],\n [-111, -183, -168, 34, -92, 163, -157]]\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[[41, 83, -73, -4, 70, -19, 60],\n [-24, -51, 10, -52, 1, -49, -98],\n [-122, 37, -104, 52, 35, 7, 18],\n [-81, -84, 95, 82, -121, 94, 8],\n [3, 11, -67, -85, 79, -98, -89],\n [-165, -102, -29, -43, -8, -67, -185],\n [-130, -47, -4, 57, -48, 38, -25]]\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[[20, 209, -125, -24, 25, -96, -70],\n [97, -75, 98, -49, -155, -33, -86],\n [-65, -129, 99, 149, -70, 77, -122],\n [19, -99, 88, -85, -13, 23, 80],\n [-190, 31, 68, 131, -181, -125, -113],\n [23, -201, 132, 7, -4, 134, 49],\n [135, -16, -26, -85, 40, 44, 77]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-162, 221, -65, -163, 26, -255, 33],\n [60, 88, 138, -21, 161, 31, -75],\n [-113, -63, -155, -16, 55, 47, 202],\n [-68, -32, 125, -4, 142, 126, 77],\n [11, 147, 62, -92, -25, -47, -73],\n [101, 1, 68, 18, -81, 59, -100],\n [13, -64, 46, 21, -49, 120, 17]]\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[[-18, 33, -30, 18, 21, -3, 18],\n [-28, 54, -84, -20, 38, -18, 108],\n [2, -5, 22, 22, -5, 7, -42],\n [-18, 32, -16, 36, 19, 2, -12],\n [-28, 49, -14, 70, 28, 7, -42],\n [-44, 76, -8, 128, 42, 16, -96],\n [-28, 50, -28, 52, 30, 2, -12]]\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 7x7 matrix:\n[[14, 35, 29, -34, -3, 18, -4],\n [35, 40, 3, -97, -80, -33, 30],\n [-21, -5, 8, 45, 47, -21, -4],\n [-11, 58, 70, 16, 79, -3, -15],\n [-46, -172, -124, 152, 14, 66, -30],\n [8, -37, -58, -25, -74, -48, 31],\n [-40, -43, -13, 98, 73, -12, -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[[-38, -1, 85, -34, 41, -41, 104],\n [36, -29, -88, -75, -137, -44, -70],\n [-48, 5, -7, -130, -139, -87, -46],\n [-99, 54, 11, -98, -117, -52, -115],\n [-33, 30, 18, 21, 21, 21, -33],\n [129, -62, -140, 37, -53, 33, -47],\n [137, -93, -56, 36, 36, 5, 123]]\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[[-232, -203, -299, -147, -204, 233, -158],\n [4, -77, -64, -136, -140, 269, 14],\n [-73, -41, 32, -184, -54, 29, -121],\n [-203, -39, -200, 24, 38, -149, -155],\n [174, -132, 195, 291, 96, -242, 131],\n [-31, 180, 169, -176, -22, -50, 9],\n [192, 61, 170, -8, -76, 179, 229]]?\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, -44, -154, 187, 80, -70, -95],\n [139, -204, 309, -126, -99, -52, 50],\n [45, -81, -123, 61, 74, 35, 14],\n [77, -77, 28, -54, 70, 7, 28],\n [6, 0, 153, -98, -90, 26, 41],\n [220, -106, -256, -22, -84, -158, 162],\n [139, -108, -144, -29, 34, -28, 100]]?\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[[-51, 291, 139, 109, -66, 335, 198],\n [98, 71, -75, 203, 160, 18, -150],\n [119, -96, -98, 74, 46, -135, 20],\n [221, 12, 223, 18, -53, 224, 37],\n [-8, -137, 141, -97, -84, 90, 79],\n [-196, -78, -208, 17, 33, -162, 41],\n [81, -23, -119, 184, 191, -269, -43]]\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[[-24, -60, 108, -144, -132, 84, -108],\n [29, -130, 36, -141, -25, 38, 27],\n [-66, 60, 112, -46, -158, 76, -182],\n [30, 30, -98, 110, 124, -74, 112],\n [-40, 80, 32, 40, -56, 16, -88],\n [2, -40, 28, -58, -30, 24, -14],\n [-55, 20, 118, -85, -159, 84, -167]]\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[[-76, 134, 381, -212, 280, 367, -255],\n [73, -14, 133, 74, 36, -114, 58],\n [-24, 213, -161, -112, 155, 33, 171],\n [91, -119, 239, 64, -103, -114, -224],\n [43, 131, 41, 72, -17, -92, -66],\n [49, 17, 121, 20, -97, 54, 83],\n [-125, 10, 78, -133, 194, 233, -220]]?\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[[6, 10, -18, -10, -18, -6, 14],\n [-36, -60, 108, 60, 108, 36, -84],\n [-15, -25, 45, 25, 45, 15, -35],\n [30, 50, -90, -50, -90, -30, 70],\n [-27, -45, 81, 45, 81, 27, -63],\n [27, 45, -81, -45, -81, -27, 63],\n [-9, -15, 27, 15, 27, 9, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-30, 90, 84, 42, 27, 84, -36],\n [0, 10, 26, 18, 43, 36, 16],\n [38, -120, -122, -64, -60, -128, 36],\n [-36, 110, 106, 54, 41, 108, -40],\n [24, -100, -140, -84, -142, -168, -16],\n [6, 10, 56, 42, 115, 84, 52],\n [13, -40, -39, -20, -16, -40, 14]]\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[[32, 123, 44, 103, 114, -27, -26],\n [28, 17, -24, 37, 106, -133, 46],\n [-18, -71, -26, -59, -64, 13, 16],\n [8, 9, -4, 13, 30, -33, 10],\n [26, 51, 2, 55, 96, -81, 16],\n [-21, 38, 53, 2, -83, 161, -73],\n [-19, 4, 27, -16, -73, 109, -43]]\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[[34, -74, -42, -10, 16, 28, -38],\n [13, 17, -51, -75, -12, -10, 45],\n [-42, -2, 54, 6, 88, 132, -122],\n [-29, -15, 48, 26, 66, 97, -102],\n [-207, 217, 261, 45, 172, 246, -191],\n [-87, 82, 81, -45, 112, 171, -116],\n [22, -34, -51, -57, 18, 35, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, -61, 29, 131, 117, -25, 63],\n [97, -12, 3, 17, 107, 90, -41],\n [-22, 25, 92, 87, -124, -194, 157],\n [-118, 11, 67, 50, -117, -202, 114],\n [100, -3, -12, -62, -70, 35, 99],\n [106, 108, 55, -162, -191, -37, 13],\n [-99, -28, -15, -24, 115, 29, -117]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[65, -181, 98, -154, -113, 134, -124],\n [4, 32, 5, 40, -15, 86, -140],\n [-44, -116, -64, 16, -70, -32, 124],\n [-112, -100, -136, 138, -70, 26, 70],\n [-98, 28, -189, 209, -17, 13, 55],\n [-44, 124, -101, 158, 38, 10, -34],\n [55, -79, 169, -186, -69, -157, 105]]?\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[[-24, 30, -12, 37, -27, 22, -15],\n [89, 65, 224, -21, 184, -103, 225],\n [75, -64, -106, -62, -116, 21, -167],\n [43, -101, -80, -87, -40, -5, -93],\n [-190, 45, -102, 129, -72, 96, -40],\n [35, 50, 194, -8, 184, -87, 225],\n [-32, -17, -14, 0, 11, 4, 9]]\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[[-84, -251, -63, -33, 258, -95, 303],\n [-93, 16, -217, 33, -4, -1, -40],\n [169, -95, 198, -62, -98, -165, -127],\n [-239, 169, -117, 40, 75, 263, 45],\n [-140, -54, -54, -77, 131, 52, -15],\n [-18, -121, -173, -84, 75, -38, -58],\n [-17, -14, -81, 25, 8, -96, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[20, 35, 116, -31, 118, -188, -35],\n [48, -136, -88, -180, 12, 116, 72],\n [33, -27, 68, -100, 112, -108, 0],\n [14, -9, -124, 31, -142, 92, 19],\n [15, -29, 2, -53, 29, -5, 12],\n [-10, -101, 58, -142, 151, 75, 43],\n [-34, -94, 78, -117, 165, 103, 40]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-42, 18, -30, 60, 0, 0, 18],\n [-77, 33, -55, 110, 0, 0, 33],\n [-7, 3, -5, 10, 0, 0, 3],\n [77, -33, 55, -110, 0, 0, -33],\n [28, -12, 20, -40, 0, 0, -12],\n [77, -33, 55, -110, 0, 0, -33],\n [-56, 24, -40, 80, 0, 0, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[52, -33, 103, -115, 24, -58, -22],\n [-42, -52, -148, 30, 36, 38, -48],\n [-56, -15, -66, 50, 65, -12, 31],\n [26, 101, 209, 13, -32, -64, 122],\n [47, 6, -5, -26, -85, 53, -63],\n [-119, 83, -35, 194, 64, -21, 168],\n [91, -88, 17, -172, -25, 5, -143]]\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, -7, 26, -132, -48, 13, 76],\n [81, 90, -245, -32, -50, 60, -235],\n [45, 47, -109, -60, -57, 49, -95],\n [-122, -72, 230, 72, 27, -28, 188],\n [8, 72, -140, -24, -87, 88, -158],\n [3, 34, -103, 64, 16, 8, -125],\n [109, -39, 11, -84, 69, -85, 89]]?\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[[-166, -79, 64, 83, 123, 109, 21],\n [-135, 67, 17, 155, 50, 64, 93],\n [109, 174, -116, 101, -106, 62, -25],\n [-6, 195, -68, 129, -45, 141, -24],\n [187, 217, -161, 61, -146, 144, -139],\n [-190, -80, 130, 0, 104, -116, 161],\n [32, 78, -33, 49, -53, -65, 70]]?\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[[167, 56, -111, 5, -71, 170, -48],\n [6, 16, -130, -184, 115, 112, 171],\n [-72, 99, 67, -32, 286, -76, -18],\n [-31, 11, -42, -169, 151, 20, 168],\n [128, 30, -34, -96, 4, 80, 84],\n [-42, 93, -33, -6, 204, 24, -54],\n [76, 97, -17, 64, 68, 59, -126]]\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[[0, 128, 142, 36, 66, 108, 70],\n [35, 1, -76, 67, -58, -79, -35],\n [-6, 62, 82, 6, 42, 66, 40],\n [66, 22, -121, 132, -99, -132, -55],\n [-54, -146, -43, -144, 15, 0, -25],\n [81, 123, -42, 189, -72, -81, -15],\n [-63, 11, 151, -117, 111, 153, 70]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}