{"messages": [{"content": "Find the rank of the matrix:\n[[16, -32, 0, 0, -40, 28],\n [-36, 72, 0, 0, 90, -63],\n [-16, 32, 0, 0, 40, -28],\n [0, 0, 0, 0, 0, 0],\n [12, -24, 0, 0, -30, 21],\n [-40, 80, 0, 0, 100, -70]]\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[[-31, 156, -128, 122, 28, -126],\n [-73, 18, 106, -124, 19, -63],\n [-81, -68, 214, -232, 26, 20],\n [-5, 48, -53, 55, 23, -7],\n [-27, 28, 5, -7, 35, 9],\n [18, -54, 23, -15, 12, 92]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[20, -16, -8, -11, 0, -10],\n [52, -52, -12, -28, -12, -28],\n [-45, -3, 51, 27, -45, 15],\n [-42, 70, -14, 21, 42, 28],\n [52, 0, -56, -31, 48, -18],\n [44, 48, -88, -29, 96, -6]]\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 6x6 matrix:\n[[-30, -6, 6, -12, -6, 30],\n [100, 20, -20, 40, 20, -100],\n [50, 10, -10, 20, 10, -50],\n [20, 4, -4, 8, 4, -20],\n [70, 14, -14, 28, 14, -70],\n [40, 8, -8, 16, 8, -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 6x6 matrix:\n[[-32, -24, 12, 32, 32, 40],\n [-16, -12, 6, 16, 16, 20],\n [-80, -60, 30, 80, 80, 100],\n [8, 6, -3, -8, -8, -10],\n [-24, -18, 9, 24, 24, 30],\n [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[[0, 40, -8, -28, -31, 37],\n [4, 8, 18, -49, -35, 41],\n [-89, -40, 20, -22, -120, 32],\n [-20, 84, -58, 34, -15, 6],\n [-2, -16, 72, -148, -116, 116],\n [41, -12, -42, -22, -54, 111]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-40, -100, -100, 90, 20, -20],\n [20, 50, 50, -45, -10, 10],\n [-4, -10, -10, 9, 2, -2],\n [-4, -10, -10, 9, 2, -2],\n [-36, -90, -90, 81, 18, -18],\n [0, 0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-36, -16, -72, -48, -32, 8],\n [-18, -6, -48, -27, -23, 2],\n [36, 36, -48, 18, -38, -28],\n [-162, -124, -12, -138, 38, 88],\n [-18, -14, 0, -15, 5, 10],\n [54, 40, 12, 48, -8, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[2, 18, 123, 59, 197, 83],\n [51, -83, -59, 76, -180, -63],\n [135, 65, 49, -73, -74, 150],\n [-67, -183, -111, 204, 5, -148],\n [-105, -33, 53, 123, 100, -80],\n [13, 16, -22, -101, 87, 16]]\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 6x6 matrix:\n[[72, 0, 48, -24, -56, -40],\n [45, 0, 30, -15, -35, -25],\n [45, 0, 30, -15, -35, -25],\n [-72, 0, -48, 24, 56, 40],\n [81, 0, 54, -27, -63, -45],\n [-90, 0, -60, 30, 70, 50]]\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 6x6 matrix:\n[[66, 111, -6, -6, -81, 24],\n [81, 125, 41, 60, -64, -50],\n [91, 143, 35, 52, -80, -38],\n [14, 33, -42, -58, -47, 72],\n [23, 18, 87, 122, 37, -138],\n [-45, -68, -29, -42, 31, 38]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-71, 148, 79, -103, 89, -85],\n [71, -11, -11, 31, -25, -35],\n [191, 72, -63, -67, -13, -45],\n [-6, 128, -46, 44, 182, 64],\n [120, 55, -185, -11, 106, 203],\n [77, 43, -77, -100, 7, 66]]\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 6x6 matrix:\n[[-80, 20, 106, 140, 79, -28],\n [14, -13, -10, -26, 16, 61],\n [94, -98, -118, -118, -15, 64],\n [60, -137, -148, -39, -32, -80],\n [50, 8, -54, -101, -50, 47],\n [9, -69, -102, -15, -26, -26]]\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, 80, 2, 62, 31, -66],\n [-102, 22, 86, 77, 10, -6],\n [4, 114, -50, 22, 94, -126],\n [-72, 21, 85, 28, 92, -45],\n [36, -94, 74, -118, 136, 6],\n [-40, -97, 97, -14, -21, 87]]\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[[-26, 24, 33, -55, 24, 47],\n [-25, 45, 90, -140, 30, 100],\n [13, -31, -67, 103, -18, -71],\n [-48, -20, -110, 154, 24, -74],\n [33, -29, -38, 64, -30, -56],\n [0, -38, -101, 151, -12, -95]]?\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, -96, -111, 47, -22, 34],\n [-56, 180, 66, -134, 100, -76],\n [11, 16, 61, -46, 12, 17],\n [76, -18, -44, -156, 84, 62],\n [-6, 28, -15, -29, 26, -14],\n [-10, -1, -3, 25, -12, -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[[-26, -102, -32, -3, -15, -94],\n [16, -30, -37, -60, -32, -4],\n [24, -36, -50, -84, -44, 0],\n [-8, -84, -42, -36, -28, -64],\n [-6, -72, -37, -33, -25, -54],\n [-40, -6, 43, 96, 44, -44]]\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[[140, 140, -62, 7, 30, -75],\n [-59, -10, -5, 74, 31, 16],\n [37, -10, -5, -10, -17, 4],\n [-19, 120, -30, 50, 74, -58],\n [-34, 90, -33, 90, 75, -36],\n [-78, -140, 50, -21, -50, 73]]\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, -4, 6, 2, 4, -14],\n [-3, -2, 3, 1, 2, -7],\n [3, 2, -3, -1, -2, 7],\n [18, 12, -18, -6, -12, 42],\n [-15, -10, 15, 5, 10, -35],\n [-12, -8, 12, 4, 8, -28]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-45, -18, 90, -81, -54, 36],\n [-30, -12, 60, -54, -36, 24],\n [-30, -12, 60, -54, -36, 24],\n [-25, -10, 50, -45, -30, 20],\n [40, 16, -80, 72, 48, -32],\n [-15, -6, 30, -27, -18, 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 6x6 matrix:\n[[-160, -16, -73, -2, 8, 11],\n [140, 5, 8, -14, 60, 50],\n [110, 77, 71, -26, -10, -40],\n [-20, 82, 4, -40, 12, -26],\n [140, -6, 101, 26, -60, -45],\n [-30, 14, -48, -22, 50, 35]]\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[[6, 34, -15, -14, 149, 26],\n [13, -37, 44, -53, -35, -33],\n [-49, 28, 90, -31, -4, -16],\n [200, -150, -192, -56, 90, -6],\n [-35, 15, 59, -13, -30, -13],\n [70, -61, -47, -38, 22, -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 6x6 matrix:\n[[44, 69, 61, 105, -205, 92],\n [-78, -95, 124, 57, 22, 36],\n [-74, -62, -35, -81, 151, -84],\n [250, 130, -65, 35, -34, 74],\n [112, -102, 38, 38, -10, 144],\n [-66, 88, 83, 93, -162, 2]]\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, -6, -8, -18, -16, 14],\n [-18, -6, -8, -18, -16, 14],\n [63, 21, 28, 63, 56, -49],\n [90, 30, 40, 90, 80, -70],\n [-54, -18, -24, -54, -48, 42],\n [27, 9, 12, 27, 24, -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 6x6 matrix:\n[[4, 4, -6, 10, 3, -9],\n [-40, -40, 60, -100, -30, 90],\n [4, 4, -6, 10, 3, -9],\n [-24, -24, 36, -60, -18, 54],\n [24, 24, -36, 60, 18, -54],\n [20, 20, -30, 50, 15, -45]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[84, 64, -48, -72, -60, 80],\n [-39, -61, 89, 86, -10, -85],\n [-75, -109, 5, 74, 122, -97],\n [153, 30, -76, -76, -61, 76],\n [114, -119, -33, 36, 29, -59],\n [-54, -17, -22, 5, 69, -14]]\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 6x6 matrix:\n[[112, -56, -56, -11, 22, -35],\n [3, -57, 30, 0, -8, 11],\n [-107, 34, 52, -2, -34, 48],\n [-76, 140, 32, 59, 42, -41],\n [144, -72, -32, 26, 60, -78],\n [-43, -37, 102, 52, 20, -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[[-92, 34, 59, -25, -6, -24],\n [16, -40, -104, 64, 82, -64],\n [88, -28, -44, 16, -5, 32],\n [44, -10, -11, 1, -12, 24],\n [-12, -30, -87, 57, 81, -72],\n [28, -2, 5, -7, -18, 24]]\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, 24, 8, 36, -28, -4],\n [-6, -36, -12, -54, 42, 6],\n [-1, -6, -2, -9, 7, 1],\n [-4, -24, -8, -36, 28, 4],\n [6, 36, 12, 54, -42, -6],\n [-4, -24, -8, -36, 28, 4]]\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[[-92, 48, -22, 66, 32, 82],\n [103, -9, 50, -111, -1, -56],\n [-54, -134, 21, 57, -81, -1],\n [-57, -15, -39, 78, -15, 15],\n [89, 73, -30, -53, 37, -60],\n [-78, -32, 66, 0, -3, 92]]\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[[2, 25, 56, -96, -59, 43],\n [-90, -45, -36, 0, 63, -99],\n [42, 35, 49, -56, -63, 70],\n [46, 25, 23, -8, -37, 54],\n [54, 25, 17, 8, -33, 56],\n [86, 45, 39, -8, -65, 98]]\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[[46, -55, -113, -88, 50, -68],\n [-41, 71, 78, -6, 18, 30],\n [2, -14, 41, 76, -42, 38],\n [-140, 12, 27, -10, -178, 65],\n [-19, -20, 25, 32, -52, 37],\n [-3, 68, 107, 44, 48, 39]]\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[[46, -62, 22, -28, 71, -57],\n [-154, -62, -110, -116, 145, -139],\n [132, -138, -16, 0, 116, -26],\n [-62, -47, -85, -40, 72, -50],\n [2, 36, 78, -20, -11, -5],\n [-84, 149, 31, 48, -172, 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[[-8, 13, 26, 0, 41, -43],\n [-15, 20, 40, -5, 60, -55],\n [-10, 18, 36, 2, 58, -64],\n [-1, 13, 26, 13, 49, -72],\n [-19, 16, 32, -17, 40, -15],\n [-35, 28, 56, -33, 68, -19]]\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, -44, -63, -19, 35, 11],\n [78, 58, 11, 70, -24, -45],\n [-45, -54, -60, -33, 33, 24],\n [24, 18, 17, 8, 10, -23],\n [31, 8, 28, -31, 88, -63],\n [-5, 8, -9, 31, -61, 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[[-24, -63, 49, 20, -58, -89],\n [10, -14, -12, 3, -17, -12],\n [38, -166, 101, -26, -105, -133],\n [2, 27, 70, -52, 75, 66],\n [16, -185, 119, -8, -130, -175],\n [-44, -12, 46, 20, -14, -46]]\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[[-246, -75, 32, -4, 35, -25],\n [57, -131, -210, 97, -200, -71],\n [-55, -99, -64, 41, 40, 23],\n [61, 71, -21, 125, -18, -154],\n [52, -168, -252, 48, -160, 62],\n [-27, -75, -86, 135, -92, -172]]\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[[-166, -2, 73, 29, 74, -82],\n [54, 0, -25, -49, 39, 71],\n [183, -43, -36, 52, 7, 118],\n [-17, 57, -41, -9, -87, -74],\n [76, 99, -53, -108, 75, 124],\n [94, -68, -89, -35, -159, -39]]\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, 38, 6, 0, 38, -44],\n [-18, -15, 3, 30, -3, 30],\n [-5, 39, 16, 55, 61, -22],\n [45, 93, 12, -15, 87, -114],\n [30, 25, -5, -50, 5, -50],\n [-67, -99, -4, 65, -73, 142]]?\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, -33, 27, -16, -2, -46],\n [-7, -142, -67, -10, 66, 90],\n [-131, 16, -75, 98, 50, 50],\n [-46, -70, -45, 92, 45, -52],\n [-52, 82, -71, 40, -157, -36],\n [81, 44, 84, -82, -13, -10]]\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[[-53, 61, -108, -100, 85, -33],\n [-103, -9, 36, -4, -73, -123],\n [17, 81, -93, -19, 102, 40],\n [-40, -27, 32, 148, -53, -78],\n [49, 80, 16, -4, 42, 31],\n [9, 22, 125, 181, -79, -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[[5, 30, -30, 52, 11, -45],\n [-1, -41, -20, 59, -39, -72],\n [-14, -74, 46, 39, -43, -78],\n [-22, -2, 128, -34, 38, -4],\n [-13, -58, 54, 0, -27, -31],\n [0, -75, -32, 42, -67, -55]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-108, 62, -82, 142, -12, 82],\n [-38, 27, -47, 57, 8, 27],\n [-32, 22, -37, 47, 5, 23],\n [32, -22, 37, -47, -5, -23],\n [-36, -12, 87, 3, -81, 39],\n [44, 10, -90, -10, 88, -46]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-54, -92, 0, 56, -50, -66],\n [-27, -43, -82, -44, -17, 50],\n [-24, -30, -68, -42, -8, 46],\n [-36, -67, -38, 10, -36, -11],\n [42, 125, 18, -74, 86, 75],\n [99, 171, 74, -42, 89, 50]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-15, -88, 11, -87, -111, 4],\n [-54, 78, 9, 22, -12, 27],\n [68, -64, -4, 0, 42, -34],\n [-28, 52, -2, 22, 9, 15],\n [-16, 42, -39, 28, 42, 13],\n [21, 66, -24, 75, 108, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[-6, 4, -103, -46, 29, 64],\n [-2, -7, 94, 43, -27, -62],\n [44, 24, -66, -36, 22, 64],\n [-76, -36, 30, 24, -14, -56],\n [-26, -6, -87, -36, 23, 44],\n [-96, -46, 46, 34, -20, -76]]\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[[-26, 55, -23, -67, 13, -18],\n [-18, 52, -48, -86, 26, -68],\n [7, -9, 85, 40, -34, -4],\n [10, -4, 82, 24, -30, -44],\n [2, -24, -83, 7, 28, 60],\n [-16, 53, -23, -81, 17, -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[[-65, 17, -31, -87, -12, -100],\n [116, -17, 48, 70, -66, 108],\n [17, 124, -135, -125, 22, -135],\n [-31, -5, -23, -59, -48, -39],\n [72, -87, 112, 100, -92, 143],\n [-113, -61, 35, -5, 20, -23]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[69, 19, -9, 1, 33, 31],\n [15, -101, -20, -23, 32, -98],\n [85, 42, -66, 53, 56, -18],\n [51, -64, -64, 15, 62, -108],\n [-125, -100, 78, -73, -72, -30],\n [-48, -137, -29, -68, 59, -125]]\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[[-21, -53, -28, 39, -91, 119],\n [7, 40, 20, -19, 75, -70],\n [11, -107, -36, 55, -201, 100],\n [-10, 21, 8, 4, 48, -5],\n [40, 9, 40, 38, 36, -148],\n [17, -47, 12, 85, -57, -23]]\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 6x6 matrix:\n[[-8, 36, 8, 1, -21, 2],\n [-68, 27, -25, -38, -39, 79],\n [-4, 171, 55, 26, -87, -33],\n [32, 108, 52, 38, -42, -64],\n [-48, 72, 0, -18, -54, 44],\n [28, -99, -19, 1, 60, -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[[-57, -154, -87, 52, 27, 38],\n [56, -118, 1, -82, -33, 26],\n [148, -30, -18, -140, -120, 15],\n [53, -70, -129, -38, -15, -19],\n [10, -98, -69, -27, -22, 34],\n [6, 90, 72, -17, 23, -33]]\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, -22, -65, -67, -163, -19],\n [37, -19, 104, 1, 218, 48],\n [119, 54, 79, 72, 13, -74],\n [-96, 79, -81, -89, -9, 83],\n [-118, -168, -5, -40, -75, -43],\n [138, 24, 33, 60, 143, 34]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-32, 90, 6, 91, -97, 90],\n [-65, -121, 43, 27, -56, 25],\n [-67, -35, 72, 118, -143, 160],\n [16, 20, 55, -1, -15, 129],\n [-4, 79, 22, 97, -109, 86],\n [176, 60, 74, -147, 93, 46]]?\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[[18, 63, 10, 36, -5, -71],\n [73, 24, 30, -33, 5, -26],\n [209, -21, -38, -21, -142, -171],\n [9, -74, -33, -24, -37, 29],\n [142, -40, -33, -27, -102, -97],\n [-60, -78, -65, 27, -50, 25]]\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 6x6 matrix:\n[[-18, 26, 10, 26, 64, 48],\n [3, -31, -35, 119, 46, -18],\n [-16, 24, 10, 19, 55, 43],\n [-26, 34, 10, 54, 100, 68],\n [16, -24, -10, -19, -55, -43],\n [26, -66, -50, 94, -32, -80]]\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[[-63, 17, 47, -57, -3, -7],\n [68, -110, -8, 86, 56, -44],\n [6, -98, 61, 31, 24, -56],\n [-94, 88, 46, -124, -2, 2],\n [36, -50, 28, 12, 34, -54],\n [55, 11, -55, 70, -66, 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[[10, 50, 0, 25, 20, 50],\n [-10, -50, 0, -25, -20, -50],\n [6, 30, 0, 15, 12, 30],\n [14, 70, 0, 35, 28, 70],\n [2, 10, 0, 5, 4, 10],\n [0, 0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[41, 5, 43, 61, -33, 31],\n [-24, 40, -8, -56, 56, -72],\n [41, 5, 43, 61, -33, 31],\n [44, 110, 88, 16, 54, -98],\n [67, 35, 81, 87, -31, 17],\n [36, -5, 34, 58, -37, 39]]\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 6x6 matrix:\n[[47, 28, 19, -69, -48, 47],\n [24, 58, -49, 14, -13, 3],\n [-65, -42, 19, 74, 14, -86],\n [-89, -6, -20, 155, -4, -158],\n [-51, -76, 57, 69, -50, -63],\n [-2, -82, 40, -73, 85, 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[[-40, 48, -32, 64, 32, 0],\n [5, -6, 4, -8, -4, 0],\n [-45, 54, -36, 72, 36, 0],\n [-50, 60, -40, 80, 40, 0],\n [50, -60, 40, -80, -40, 0],\n [30, -36, 24, -48, -24, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[10, 9, 34, -13, 7, 3],\n [207, 13, 60, 136, 173, 20],\n [-66, 13, 52, -9, -55, 7],\n [-38, 0, -28, 2, -26, 24],\n [-38, -32, -115, 8, -30, -23],\n [31, 10, 43, 3, 24, 2]]\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 6x6 matrix:\n[[61, -78, -100, -15, 54, 27],\n [-86, 78, -34, 3, -22, 172],\n [171, 33, -77, 47, -37, -37],\n [-62, 17, -31, -14, 3, 120],\n [-87, 47, 43, 3, -9, 31],\n [19, 28, 26, 23, -12, -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 6x6 matrix:\n[[61, 68, -11, 30, -61, 86],\n [91, 12, 0, 59, -135, 43],\n [90, -88, -58, 86, -121, -85],\n [50, 72, -38, 26, -21, 75],\n [10, -104, -57, 35, -5, -128],\n [53, 68, 19, 20, -73, 96]]\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[[50, -40, -45, -45, -40, 35],\n [-40, 32, 36, 36, 32, -28],\n [90, -72, -81, -81, -72, 63],\n [30, -24, -27, -27, -24, 21],\n [-20, 16, 18, 18, 16, -14],\n [40, -32, -36, -36, -32, 28]]\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[[62, -39, 177, -35, 75, -31],\n [-51, -92, -4, 6, 20, 5],\n [93, -40, 131, -13, 16, 59],\n [-183, 85, 48, 134, 182, 21],\n [129, -194, 33, -121, -139, -84],\n [-48, -19, 21, -35, 64, -96]]\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[[-9, -126, -105, -42, 66, 33],\n [18, -4, 20, 65, -4, 85],\n [75, -80, 45, -66, -96, -36],\n [-21, 196, 115, 79, -44, -31],\n [94, -26, 110, -19, -138, -14],\n [48, -64, 20, -70, -64, -50]]\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[[123, -74, -61, -50, -176, 44],\n [-106, 50, 64, -18, 136, -12],\n [121, 77, -78, -61, -106, 32],\n [13, -113, 26, -123, -85, 63],\n [55, 84, -57, 68, -11, -29],\n [106, -33, -51, -79, -143, 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[[3, 6, 9, 18, 63, -48],\n [57, -54, 45, -36, 84, 54],\n [36, -40, 24, -36, 14, 68],\n [58, -60, 42, -48, 52, 84],\n [26, -20, 24, -6, 69, -2],\n [-18, 28, -6, 36, 46, -80]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-24, 12, -24, -24, 0, 18],\n [24, -12, 24, 24, 0, -18],\n [-56, 28, -56, -56, 0, 42],\n [0, 0, 0, 0, 0, 0],\n [72, -36, 72, 72, 0, -54],\n [32, -16, 32, 32, 0, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-10, 64, 74, -63, -25, -17],\n [-68, -32, -34, -8, 40, 33],\n [116, 168, 96, -4, 47, 103],\n [13, 46, 19, -41, -104, -14],\n [-46, 165, 44, 65, 68, 41],\n [102, -7, 42, 47, -15, -95]]\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[[52, -10, 7, 47, -60, -5],\n [-5, 24, -20, -35, 28, 14],\n [-8, -28, 16, 3, -25, -282],\n [36, -39, -99, -12, -75, -37],\n [37, 59, 202, 89, 3, 99],\n [87, 10, 6, 67, -64, 16]]\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 6x6 matrix:\n[[-22, 181, 44, -86, -33, -43],\n [36, 152, 18, -102, -6, 34],\n [12, 68, -79, -79, 115, -11],\n [-102, -77, -1, 89, -2, -130],\n [36, -46, -77, -17, 95, 37],\n [64, 58, 50, -42, -64, 92]]\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[[-40, 42, 52, 183, 38, 9],\n [-90, -8, 60, -62, -100, 72],\n [-16, 68, -116, 143, 60, -6],\n [-6, -30, 204, 24, 60, -84],\n [-108, -18, -16, -112, -112, 38],\n [-80, 30, 94, 2, 41, -43]]\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[[-112, 70, -2, 8, -34, -26],\n [49, -55, -4, 3, 23, 39],\n [84, -15, 9, -16, 13, -23],\n [77, -5, 10, -17, 9, -31],\n [-21, 90, 15, -19, -32, -92],\n [126, -60, 6, -14, 32, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[37, 25, 5, 26, -28, 21],\n [-5, 15, -25, 70, 0, 35],\n [-29, -15, -10, -2, 21, -7],\n [-55, -39, -5, -46, 42, -35],\n [-38, -22, -10, -12, 28, -14],\n [-63, -49, 0, -70, 49, -49]]\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, -171, 1, -95, -14, -6],\n [-73, -108, -58, -99, 79, 24],\n [-32, 14, 2, 150, -7, -11],\n [-41, -147, 36, -110, -105, -58],\n [-51, -115, -128, -184, 58, -4],\n [-103, -33, 24, 58, 31, -170]]\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[[-153, 26, 92, 31, 83, -5],\n [90, -81, 18, -74, -96, 39],\n [-32, -1, -18, 57, -35, -37],\n [61, 8, -17, -37, 18, 24],\n [-116, -77, 92, 15, -51, 33],\n [143, -94, 135, -144, -73, 68]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[33, 137, 37, 66, -85, 122],\n [-39, 0, 2, 62, 27, -25],\n [133, 65, 128, 67, 84, -137],\n [13, 9, 11, 12, 53, -50],\n [119, 30, 66, -48, -25, -13],\n [-159, -34, -175, -99, -122, 224]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[64, -72, 72, 16, -64, -32],\n [-8, 9, -9, -2, 8, 4],\n [-40, 45, -45, -10, 40, 20],\n [-80, 90, -90, -20, 80, 40],\n [80, -90, 90, 20, -80, -40],\n [-80, 90, -90, -20, 80, 40]]\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[[15, 36, 78, -25, -6, -91],\n [22, -26, 87, -75, -75, -7],\n [-108, -64, -44, -56, 16, 24],\n [37, 106, -120, 181, 135, -27],\n [28, -98, -60, -18, -87, 200],\n [-53, -18, -59, 10, 37, 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[[4, 7, 8, -10, -5, -9],\n [24, 42, 48, -60, -30, -54],\n [-16, -28, -32, 40, 20, 36],\n [-8, -14, -16, 20, 10, 18],\n [-32, -56, -64, 80, 40, 72],\n [8, 14, 16, -20, -10, -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[[76, 142, 18, -143, -16, -58],\n [-12, 97, -75, -82, -53, -112],\n [45, 64, 57, -112, -29, -25],\n [-28, -19, 146, -79, -64, -21],\n [-74, -76, 81, -42, -91, -37],\n [-9, -2, 37, -103, -73, -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[[-42, -56, 7, -70, 70, -14],\n [-60, -80, 10, -100, 100, -20],\n [-60, -80, 10, -100, 100, -20],\n [36, 48, -6, 60, -60, 12],\n [-30, -40, 5, -50, 50, -10],\n [-54, -72, 9, -90, 90, -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 6x6 matrix:\n[[6, -4, -8, 6, -2, -2],\n [21, -14, -28, 21, -7, -7],\n [24, -16, -32, 24, -8, -8],\n [-18, 12, 24, -18, 6, 6],\n [27, -18, -36, 27, -9, -9],\n [30, -20, -40, 30, -10, -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[[-17, -48, -57, -5, -34, -36],\n [-30, 2, -10, 8, 28, -26],\n [-47, -113, -137, -10, -74, -91],\n [31, -78, -69, -23, -106, -6],\n [-61, 13, -11, 18, 66, -49],\n [-55, -108, -135, -7, -62, -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 6x6 matrix:\n[[-46, -101, 0, -78, 104, 100],\n [26, -67, -64, -12, -12, -24],\n [-62, -133, -60, -27, 34, 44],\n [-148, 8, 16, -43, 82, 68],\n [80, -73, 54, 1, 16, 66],\n [-26, -104, 0, -1, 22, 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[[7, -2, -42, -21, 39, -14],\n [4, -8, -12, -6, 6, 4],\n [-5, 22, -6, -3, 21, -26],\n [24, -88, -2, -1, -59, 94],\n [13, -22, -46, -23, 29, 6],\n [-9, 22, 20, 10, -4, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[-117, 84, 28, -69, 50, -18],\n [153, -85, 73, 164, -65, -9],\n [-1, -55, 37, -101, 66, 2],\n [-24, 103, 111, 172, -50, -42],\n [47, 26, 38, 148, -52, -34],\n [-3, -24, 26, -180, 151, 33]]\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[[-73, -149, 28, 66, 39, 114],\n [-23, 69, -34, 17, 27, 22],\n [19, -5, 195, 7, -99, -7],\n [-40, -72, -9, 34, 37, 59],\n [-103, -195, 52, 100, 87, 158],\n [1, -39, 151, 23, -23, 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[[52, -60, 65, -193, 2, 98],\n [-42, 98, 20, 48, 20, -33],\n [4, -76, -39, -101, -54, 105],\n [-22, 6, 43, -21, -124, -116],\n [-102, -118, -111, 208, -130, -147],\n [16, 20, -51, 18, -22, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-52, -61, 78, -45, -25, 25],\n [20, 65, -86, 24, 36, 2],\n [-32, 103, -34, -33, 39, 25],\n [17, -70, 62, 9, -38, -24],\n [50, -49, 66, 27, -43, -53],\n [30, -96, 12, 36, -30, -18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-20, 58, 74, 32, 112, 56],\n [40, 20, 39, 38, 31, 24],\n [146, -16, 39, 70, -31, 4],\n [-20, -105, -55, -100, -80, -80],\n [16, 84, 44, 80, 64, 64],\n [4, 69, 77, 56, 106, 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[[127, 47, 64, 8, 103, -66],\n [-71, 30, -27, -12, 31, -26],\n [41, -14, 20, 34, -43, 42],\n [-23, -118, -104, -27, -92, 24],\n [-8, 147, 76, 73, 54, -10],\n [86, 63, 47, 43, 15, -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[[27, -54, 81, 9, -45, 45],\n [-6, 12, -18, -2, 10, -10],\n [-24, 48, -72, -8, 40, -40],\n [15, -30, 45, 5, -25, 25],\n [-15, 30, -45, -5, 25, -25],\n [27, -54, 81, 9, -45, 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[[18, -144, -54, -144, -9, -81],\n [12, 52, 28, 44, 0, 16],\n [58, -94, -14, -114, -14, -86],\n [56, -78, -8, -98, -13, -77],\n [-62, -22, -38, 6, 10, 34],\n [-132, 20, -52, 76, 24, 104]]\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, 27, -66, -25, -16, -63],\n [82, -45, 34, -71, 54, 103],\n [34, -63, -24, -83, 34, 63],\n [107, -52, 63, 2, 27, 88],\n [-19, -50, -56, -31, -9, -9],\n [46, 27, 66, 37, 10, 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 6x6 matrix:\n[[58, -82, 114, -96, -43, -112],\n [-85, 11, -57, 54, 26, 56],\n [100, 66, 52, 10, -127, 50],\n [21, -64, -41, -17, 58, -57],\n [35, -82, 132, -7, 8, -181],\n [-60, -2, -86, -2, 87, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[-45, 38, 31, -13, -15, -84],\n [17, 41, -7, 32, 41, 113],\n [-18, 34, 14, 4, 6, -6],\n [-10, 45, 10, 15, 20, 35],\n [-69, 146, 55, 23, 33, 0],\n [18, -34, -14, -4, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[60, -57, 61, -36, 28, 95],\n [-160, 67, -91, 16, 32, -45],\n [72, -48, 56, -24, 8, 64],\n [-34, 34, -36, 22, -18, -58],\n [-100, 61, -73, 28, -4, -75],\n [-26, 23, -25, 14, -10, -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[[0, 56, 40, 80, -72, -40],\n [0, -28, -20, -40, 36, 20],\n [0, 35, 25, 50, -45, -25],\n [0, -42, -30, -60, 54, 30],\n [0, -7, -5, -10, 9, 5],\n [0, -63, -45, -90, 81, 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[[70, -40, 44, -6, 16, -4],\n [-25, 30, 22, -34, -1, -19],\n [95, -100, -50, 97, 8, 54],\n [30, -40, -36, 50, 0, 28],\n [-120, 90, -24, -39, -21, -21],\n [-70, 50, -20, -17, -13, -9]]\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[[70, 21, -14, 49, 21, 56],\n [-40, -12, 8, -28, -12, -32],\n [-80, -24, 16, -56, -24, -64],\n [20, 6, -4, 14, 6, 16],\n [0, 0, 0, 0, 0, 0],\n [30, 9, -6, 21, 9, 24]]\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 6x6 matrix:\n[[14, 6, 4, 12, -18, -14],\n [63, 27, 18, 54, -81, -63],\n [63, 27, 18, 54, -81, -63],\n [-14, -6, -4, -12, 18, 14],\n [-28, -12, -8, -24, 36, 28],\n [-7, -3, -2, -6, 9, 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[[0, -40, 24, 16, 36, -20],\n [-20, -54, 42, 38, 46, -30],\n [10, 37, -27, -23, -32, 20],\n [-10, 13, -3, 3, -13, 5],\n [20, -86, 42, 18, 80, -40],\n [0, -20, 12, 8, 18, -10]]\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[[-6, 49, -62, -56, 14, -14],\n [14, 45, -146, -172, 63, 80],\n [43, -32, -4, 55, -89, -11],\n [3, 16, -152, -17, -40, 31],\n [46, -17, -84, -40, -43, 50],\n [1, -9, 75, -37, 55, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[51, 47, -188, -26, -92, 87],\n [-45, -82, -9, -12, 22, 69],\n [-115, -22, 174, -77, 135, 90],\n [15, -60, -33, 66, 28, 27],\n [131, 3, -70, 132, -117, -39],\n [-66, -7, -97, -118, 0, 183]]\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 6x6 matrix:\n[[-40, -38, -12, -6, 142, -28],\n [-72, 9, 59, 192, 90, -81],\n [-44, -38, -40, 33, -42, -55],\n [-103, -65, -11, 191, 242, -128],\n [35, 6, -26, -90, -64, 42],\n [116, 157, 100, -160, -143, 179]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-19, 67, -61, 37, -8, 10],\n [26, -12, -64, 102, -72, 38],\n [-7, -14, -107, 63, -101, -57],\n [-18, -40, -68, 58, -101, -2],\n [61, 43, -12, -19, 62, -102],\n [164, 96, -113, 148, 31, -76]]\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[[6, -51, -25, -26, 103, -140],\n [-16, -110, -9, -65, -2, 8],\n [31, -45, -54, -3, 35, -57],\n [-50, 31, 79, 15, -86, 115],\n [-22, -44, 19, 14, 67, -113],\n [-16, -103, -15, -143, 50, -17]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[36, 27, -143, 33, 84, -28],\n [-32, 110, 8, -74, -30, -124],\n [24, -33, -50, 39, 39, 38],\n [20, 1, -67, 23, 42, 0],\n [8, -104, 66, 44, -18, 116],\n [24, -114, 22, 66, 12, 128]]\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[[18, -9, 24, 30, -30, -18],\n [-54, 27, -72, -90, 90, 54],\n [-42, 21, -56, -70, 70, 42],\n [48, -24, 64, 80, -80, -48],\n [-30, 15, -40, -50, 50, 30],\n [-60, 30, -80, -100, 100, 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[[-78, -23, -115, 10, 58, 87],\n [-16, 33, -51, 39, 43, -42],\n [6, 36, -5, 61, 7, 59],\n [46, 2, 81, -5, -51, 19],\n [-18, -23, -25, -44, 16, -75],\n [-98, -21, -148, 26, 76, 121]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[45, 45, 12, -20, -16, 95],\n [-71, 40, -93, -113, 58, -47],\n [173, -5, 104, 85, -15, 38],\n [-79, 4, 33, 51, -54, 53],\n [25, -14, 98, 112, -13, -46],\n [1, -44, -59, -42, 31, -68]]?\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[[-9, 2, -9, -1, -8, -9],\n [-45, 10, -45, -5, -40, -45],\n [0, 0, 0, 0, 0, 0],\n [-36, 8, -36, -4, -32, -36],\n [36, -8, 36, 4, 32, 36],\n [-45, 10, -45, -5, -40, -45]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[40, -32, 8, 16, 80, -40],\n [-20, 16, -4, -8, -40, 20],\n [45, -36, 9, 18, 90, -45],\n [-50, 40, -10, -20, -100, 50],\n [45, -36, 9, 18, 90, -45],\n [40, -32, 8, 16, 80, -40]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-47, 62, 57, -51, 49, -11],\n [-104, 143, 93, -55, 82, -11],\n [38, -56, -81, 105, -64, 2],\n [87, -113, -49, -7, -49, 18],\n [-63, 9, 12, 64, 39, -138],\n [-58, 80, -28, 112, -14, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-21, -26, 43, 63, 19, 61],\n [24, 18, -55, -31, 31, -58],\n [-30, -58, 51, 163, 121, 108],\n [-12, -24, 20, 68, 52, 44],\n [6, 22, -5, -69, -71, -32],\n [-18, -40, 28, 116, 96, 70]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[50, -60, 98, 0, -34, 108],\n [30, -33, 63, 3, -21, 69],\n [-25, 40, -35, 10, 15, -40],\n [15, -69, -42, -51, 0, -39],\n [-35, 56, -49, 14, 21, -56],\n [50, -120, 14, -60, -22, 24]]\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[[-77, 75, 106, 16, 58, -44],\n [1, -9, -57, -45, -41, -2],\n [22, 46, 18, 17, 67, -75],\n [-8, 142, 92, -130, -8, -40],\n [116, -41, -72, -96, -109, 93],\n [58, 55, 94, -59, -20, 56]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-85, 21, -80, -93, 40, -44],\n [-56, -92, -16, 36, -70, 12],\n [96, 131, 47, -14, 89, -80],\n [3, -103, 32, 114, -99, -8],\n [-9, 68, -53, -104, 74, 72],\n [20, 1, -1, 54, -14, -102]]\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[[25, 72, 31, -19, 25, -44],\n [-5, 18, -1, 10, 47, -52],\n [115, 104, 37, -6, 39, -50],\n [-38, -55, -5, -21, -90, 97],\n [-95, -91, -48, 34, 29, -15],\n [44, 10, -10, 27, 48, -40]]?\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[[12, -42, -100, -136, 60, -44],\n [-64, 20, 148, 170, -82, 8],\n [-66, -21, 74, 62, -36, -38],\n [-16, 14, 54, 67, -31, 12],\n [-28, -52, -50, -91, 35, -64],\n [38, -31, -124, -153, 71, -26]]\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 6x6 matrix:\n[[-164, -32, 8, -40, -72, -80],\n [68, 54, 26, -2, 0, -22],\n [176, 0, -108, 38, 232, 92],\n [22, -2, -78, 6, 136, -10],\n [25, 14, 66, -4, -96, 20],\n [129, 15, -53, 64, 124, 77]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[63, -14, -14, -28, -63, 7],\n [-36, 8, 8, 16, 36, -4],\n [-81, 18, 18, 36, 81, -9],\n [-54, 12, 12, 24, 54, -6],\n [-18, 4, 4, 8, 18, -2],\n [-63, 14, 14, 28, 63, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-41, 10, -138, -15, 104, -66],\n [-49, 26, -96, 55, 47, -61],\n [5, 33, 11, 20, 45, -59],\n [48, -52, 60, -98, 32, 8],\n [-47, 7, -33, 70, -93, 115],\n [47, 48, -41, -83, 81, -137]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, -5, -8, -10, 2, 10],\n [-64, -40, -64, -80, 16, 80],\n [-56, -35, -56, -70, 14, 70],\n [-48, -30, -48, -60, 12, 60],\n [40, 25, 40, 50, -10, -50],\n [-32, -20, -32, -40, 8, 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[[-30, 17, 23, -46, -1, -42],\n [66, -43, -47, 102, 5, 94],\n [30, 11, -41, 42, -13, 34],\n [-84, 70, 50, -132, -14, -124],\n [18, 71, -66, 16, -40, 2],\n [-24, -90, 85, -22, 51, -4]]?\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[[-48, 60, 117, 93, 16, 92],\n [32, 5, -6, 14, -78, 43],\n [-84, -75, 57, 133, -44, -27],\n [48, 35, 4, -48, -61, 73],\n [12, 110, 85, 37, 11, 128],\n [-52, -95, 4, 72, -60, -55]]?\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[[-10, 29, -97, -53, -66, 81],\n [-70, 17, -121, 1, -90, 71],\n [0, 24, -72, -48, -48, 64],\n [-10, -28, 74, 61, 48, -71],\n [90, 9, 63, -63, 54, -9],\n [80, 23, 11, -86, 18, 32]]?\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, 0, 90, 9, -54, -18],\n [-35, 0, -50, -5, 30, 10],\n [21, 0, 30, 3, -18, -6],\n [0, 0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0, 0],\n [49, 0, 70, 7, -42, -14]]\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, -48, -93, -85, 25, -36],\n [24, -8, 133, 91, -29, 78],\n [-66, 52, 34, 21, 70, 18],\n [6, 33, -9, 48, 53, -42],\n [54, -58, -212, -135, -36, -126],\n [-18, 7, -50, -63, -34, -12]]\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[[-69, -1, 35, 50, -72, 19],\n [25, -22, 133, 13, -9, 87],\n [11, 3, 43, -42, 36, 203],\n [40, -9, 43, -32, 39, 84],\n [7, -101, 42, -93, 45, 70],\n [-7, -73, -31, -116, 66, 121]]\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, -15, 42, -3, 6, -9],\n [9, 12, 24, -37, -19, 3],\n [39, 72, -84, -103, -31, -39],\n [71, 79, -134, -68, -33, -6],\n [60, 49, -74, -59, -38, -35],\n [-46, -4, -10, -8, 30, -41]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[96, -89, -4, 0, -153, -126],\n [33, 14, 22, -61, -15, -1],\n [8, -38, -11, 143, 32, -45],\n [84, -82, 37, 14, -59, -90],\n [-68, -11, -12, 7, 30, 41],\n [73, 21, -2, 53, -14, -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[[79, 86, 18, -56, -5, 95],\n [11, -54, -8, -54, -83, -88],\n [60, 4, -2, 74, 67, 22],\n [137, 34, -72, 74, 110, -20],\n [-112, -40, 100, -180, -223, 7],\n [53, 30, -24, -18, 10, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[54, 15, 9, -54, -6, -51],\n [72, -97, 77, -98, 44, -55],\n [36, 10, 6, -36, -4, -34],\n [81, -9, 31, -88, 5, -73],\n [9, -92, 54, -30, 41, 2],\n [81, 72, -14, -70, -31, -82]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[34, -10, -46, 90, -112, -96],\n [-3, 15, -3, -15, 48, 24],\n [9, -5, -11, 25, -36, -28],\n [40, 0, -60, 100, -100, -100],\n [15, 5, -25, 35, -24, -32],\n [-32, 0, 48, -80, 80, 80]]\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 6x6 matrix:\n[[-41, -38, 93, 121, -55, 69],\n [-102, -24, -86, 70, 20, -24],\n [-15, 109, -94, -117, 87, -90],\n [66, -69, 55, -5, 5, -3],\n [-49, -24, -93, -23, 110, -124],\n [-26, 93, -71, -51, 18, 4]]\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[[-72, 45, 54, 36, -72, 9],\n [24, -15, -18, -12, 24, -3],\n [8, -5, -6, -4, 8, -1],\n [-64, 40, 48, 32, -64, 8],\n [64, -40, -48, -32, 64, -8],\n [48, -30, -36, -24, 48, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-18, -2, 14, -10, -10, 20],\n [90, 10, -70, 50, 50, -100],\n [9, 1, -7, 5, 5, -10],\n [36, 4, -28, 20, 20, -40],\n [-81, -9, 63, -45, -45, 90],\n [63, 7, -49, 35, 35, -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[[-21, -39, -126, -27, -101, -26],\n [150, 41, 160, 43, 37, 43],\n [-21, -22, 103, -41, -100, -61],\n [184, -12, 11, 147, -16, 57],\n [-72, -25, 40, 51, 3, -94],\n [81, -14, -1, 97, 4, 60]]?\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 6x6 matrix:\n[[90, 0, 103, -164, 23, 65],\n [33, -131, 162, -62, 115, -5],\n [-51, 91, -1, -58, -93, -1],\n [103, 48, -36, -10, 53, 61],\n [-47, 3, 13, 20, 15, -21],\n [-36, 50, 11, -74, -87, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[17, -14, -5, 31, -46, -27],\n [-90, 44, -30, -38, 44, 94],\n [-104, 48, -40, -32, 32, 104],\n [103, -50, 35, 42, -48, -107],\n [-83, 42, -25, -41, 50, 89],\n [27, -10, 15, -2, 8, -23]]\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[[-38, -56, 13, -61, -25, 63],\n [8, 117, -97, 15, 92, -23],\n [62, -37, 27, 71, 27, -37],\n [24, -140, -23, 78, 56, 15],\n [-49, -67, 39, -29, -75, 17],\n [52, -47, 16, 72, -88, 54]]\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, -18, -14, 84, 18, -60],\n [22, 4, -13, 20, -62, -6],\n [36, 12, -14, 0, -96, 12],\n [-28, -1, 22, -50, 83, 24],\n [-4, -4, -2, 16, 8, -12],\n [18, 15, 5, -54, -39, 42]]\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[[-13, 1, 36, 2, 105, 148],\n [30, 25, 43, 38, -43, 39],\n [-131, 22, -38, -66, 150, 81],\n [-90, -41, -81, -79, 124, -62],\n [128, -2, 116, 90, -34, 156],\n [-108, -30, -93, -93, 111, -61]]\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[[-42, 26, -33, 132, 136, -8],\n [54, -30, -45, -36, -24, -24],\n [29, -18, 24, -93, -96, 6],\n [-23, 12, 39, -15, -24, 18],\n [-11, 8, -39, 81, 88, -14],\n [-5, 2, 24, -27, -32, 10]]?\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 6x6 matrix:\n[[7, 9, -5, -7, 6, 7],\n [-70, -90, 50, 70, -60, -70],\n [42, 54, -30, -42, 36, 42],\n [-63, -81, 45, 63, -54, -63],\n [-63, -81, 45, 63, -54, -63],\n [35, 45, -25, -35, 30, 35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[48, 88, -26, -66, 74, 64],\n [-64, -54, 41, 31, -67, -22],\n [-28, -63, 14, 49, -49, -49],\n [108, 153, -63, -108, 144, 99],\n [4, -31, -6, 29, -13, -33],\n [-32, -52, 18, 38, -46, -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[[-7, 165, 3, -68, 8, 35],\n [-69, -58, 10, -58, 91, -21],\n [39, -102, -66, 35, 83, 42],\n [-113, 112, 100, 34, -4, -79],\n [137, -70, -100, 33, -65, 78],\n [64, 25, 31, 65, -177, -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[[92, -101, -3, 49, -126, 3],\n [81, -63, 135, -124, 24, 244],\n [-41, 133, 7, -21, 92, -70],\n [-41, 76, -86, 52, 8, -143],\n [24, -86, -122, -26, -35, -5],\n [28, 54, 124, -1, 13, 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 6x6 matrix:\n[[-25, -13, -82, 97, -85, 38],\n [-121, -64, 0, -53, 38, -67],\n [86, 91, 130, -112, 71, -29],\n [56, 53, 92, -128, 86, -49],\n [-22, 9, -12, 138, -100, 69],\n [41, 9, -10, -53, 35, -18]]\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 6x6 matrix:\n[[-95, 139, -65, 58, 73, 92],\n [56, -149, 59, -36, -56, -66],\n [-47, 61, 97, 106, 34, 11],\n [-13, 33, -61, 13, 21, 44],\n [124, 79, 73, -59, -35, -25],\n [-42, -188, 80, 2, -44, -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[[-33, -83, -81, -94, -84, 63],\n [-13, -42, -43, -9, 17, 39],\n [-2, -28, -16, -46, -78, 18],\n [64, -123, -37, 67, -51, 126],\n [-40, -65, -76, -85, -49, 48],\n [29, -51, -12, 22, -38, 51]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 12, 16, 36, -4, 36],\n [28, 0, -24, 16, -12, 0],\n [35, -21, -64, -39, -11, -63],\n [9, -15, -32, -37, -1, -45],\n [-6, 3, 10, 5, 2, 9],\n [-118, 24, 140, 0, 46, 72]]\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[[22, 6, -16, -20, 4, 12],\n [-56, 35, 21, 63, 14, 28],\n [-8, 84, -28, 28, 40, 96],\n [59, -106, 5, -83, -48, -110],\n [-15, 39, -6, 24, 18, 42],\n [82, 8, -54, -78, 8, 28]]\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, -161, 10, 16, -79, -85],\n [-33, 26, -35, 33, 69, -100],\n [-32, 4, -29, 43, -8, 61],\n [53, -107, 92, -108, -53, -169],\n [151, 124, 119, -188, 42, -35],\n [10, 69, -49, 49, 40, 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[[106, -30, -38, -20, 83, -61],\n [44, -9, 46, 22, -99, 0],\n [-34, 0, 92, 41, -143, 55],\n [64, 66, -144, -42, -50, -104],\n [68, 9, -42, -12, -25, -52],\n [-68, 4, 86, 37, -112, 68]]?\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[[88, 60, -50, 99, 74, -61],\n [-111, -63, 63, -95, -95, 90],\n [37, 15, -34, 55, 52, -15],\n [-5, 87, 79, -13, -131, -28],\n [-23, 33, 43, 2, -71, 17],\n [-86, -120, -1, -97, 11, 78]]\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[[4, -16, 32, 20, -4, -16],\n [-4, 16, -32, -20, 4, 16],\n [4, -16, 32, 20, -4, -16],\n [-4, 16, -32, -20, 4, 16],\n [8, -32, 64, 40, -8, -32],\n [-8, 32, -64, -40, 8, 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 6x6 matrix:\n[[-12, 113, -21, -122, -23, -40],\n [-14, 194, 122, -36, 9, -26],\n [47, -89, -30, -23, -14, -19],\n [52, -20, -44, -45, -48, -52],\n [-44, -24, 44, 50, 86, 68],\n [18, -88, -102, 23, -55, -14]]\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[[-72, -27, -45, 45, 45, -36],\n [80, 30, 50, -50, -50, 40],\n [56, 21, 35, -35, -35, 28],\n [-24, -9, -15, 15, 15, -12],\n [72, 27, 45, -45, -45, 36],\n [-40, -15, -25, 25, 25, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[86, 45, -123, -94, 116, 33],\n [47, 24, -87, -159, -63, 90],\n [113, 28, -55, -107, 85, 31],\n [16, 65, 31, -58, 40, 27],\n [69, -98, -107, -42, -51, -99],\n [-38, 93, -27, -34, 54, 71]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[120, -52, -112, 16, 11, 40],\n [1, 26, -190, -18, -11, 86],\n [169, -18, 8, -98, -143, -137],\n [108, -8, -91, -119, -27, 21],\n [71, 38, -110, -204, -66, 7],\n [86, 4, -117, -80, -53, 10]]\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[[48, -60, -54, 30, 6, -18],\n [-37, 45, 91, -70, 41, 2],\n [-16, 18, 97, -85, 71, -13],\n [99, -125, -62, 15, 58, -49],\n [50, -62, -76, 50, -12, -14],\n [-87, 109, 88, -45, -20, 35]]\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, -14, -18, 4, -8, 14],\n [45, 35, 45, -10, 20, -35],\n [0, 0, 0, 0, 0, 0],\n [-36, -28, -36, 8, -16, 28],\n [-9, -7, -9, 2, -4, 7],\n [-9, -7, -9, 2, -4, 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, -19, -14, 11, -28, 13],\n [22, -69, -31, 28, -108, 18],\n [-3, 63, 30, -29, 86, -31],\n [33, -3, 6, -9, -36, -39],\n [-151, -31, 23, -3, -27, -13],\n [28, -61, -21, 18, -112, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 48, -5, 33, 7, 36],\n [-12, 24, -11, -1, 1, 4],\n [64, -18, 55, 97, 13, 74],\n [-80, 90, -71, -65, -5, -34],\n [-32, 54, -29, -11, 1, 2],\n [86, -87, 76, 78, 7, 45]]?\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[[15, -50, 74, 80, 161, -90],\n [-108, -28, -77, -40, 89, 17],\n [-98, 47, 96, -24, -1, -124],\n [-67, 94, 13, -95, -63, -84],\n [-98, -20, -87, -33, 76, 39],\n [-50, -70, -128, -13, 31, 137]]\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 6x6 matrix:\n[[112, 17, -57, 61, -100, -30],\n [-48, -122, -115, -3, -161, -103],\n [60, -25, -94, -59, -130, -25],\n [-31, -90, -48, 76, 51, 15],\n [112, -40, -23, 194, -105, -74],\n [-21, -1, -67, -36, 24, 27]]\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 6x6 matrix:\n[[-70, 40, 50, -30, 30, 90],\n [-63, 36, 45, -27, 27, 81],\n [28, -16, -20, 12, -12, -36],\n [7, -4, -5, 3, -3, -9],\n [21, -12, -15, 9, -9, -27],\n [-63, 36, 45, -27, 27, 81]]\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[[-114, -78, -15, -39, -6, -18],\n [-11, -55, 124, -146, -134, -84],\n [8, -20, -101, -1, 74, 66],\n [-9, -5, 90, -40, -78, -60],\n [9, 49, 85, 47, -48, -51],\n [161, 109, 42, 44, -10, 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[[-4, -45, 151, -56, 23, -5],\n [-50, 15, 23, 26, 7, 53],\n [-105, 35, 37, 59, 13, 112],\n [22, -50, 130, -66, 18, -32],\n [-20, -50, 190, -60, 30, 10],\n [-14, -35, 133, -42, 21, 7]]\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, -2, 12, 8, 14, 16],\n [-28, -7, 42, 28, 49, 56],\n [-8, -2, 12, 8, 14, 16],\n [-24, -6, 36, 24, 42, 48],\n [24, 6, -36, -24, -42, -48],\n [0, 0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-120, -186, 33, 41, 112, 28],\n [-142, 83, -136, -94, 130, 128],\n [91, -104, 193, -10, -69, -120],\n [127, 77, 18, 13, -83, -96],\n [26, 38, 65, -73, -22, 8],\n [6, -5, -70, 142, 24, 82]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[24, -86, 70, -2, 34, 48],\n [35, 105, -10, -40, 105, -185],\n [-13, 30, 6, -15, -17, -5],\n [-30, -68, 49, 4, -77, 138],\n [22, -10, 6, 0, 44, -34],\n [35, 6, 17, -13, 78, -77]]\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, 112, -34, 4, 145, 193],\n [-37, -64, 39, -73, -43, -24],\n [159, 60, -19, 37, 152, -4],\n [161, -4, -7, -4, 183, -1],\n [10, 48, 88, 146, -53, -188],\n [-121, -110, 77, 15, -130, -147]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[34, 11, -24, -42, 124, 64],\n [94, 76, 1, 48, -26, 54],\n [2, 28, -38, 52, 28, 84],\n [-27, 25, -27, 100, -70, 50],\n [-57, 8, -53, 90, -6, 86],\n [51, -30, 71, -130, 10, -130]]\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 6x6 matrix:\n[[38, 26, -17, -41, -9, 20],\n [45, -52, 70, 60, 43, 67],\n [14, -114, 125, 125, 97, 80],\n [78, 18, 10, 5, -35, 44],\n [46, 42, -26, -23, -55, 4],\n [63, 48, -23, -4, -83, 5]]\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[[-58, 48, -43, 22, 39, -1],\n [53, -32, -59, 69, -45, 37],\n [44, -95, -54, 63, 57, 92],\n [21, -27, 38, 0, -51, -44],\n [-31, 102, -21, -35, -9, -2],\n [-64, -57, 27, -5, 126, 4]]\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, 5, -7, -3, -9, -1],\n [-100, -50, 70, 30, 90, 10],\n [20, 10, -14, -6, -18, -2],\n [30, 15, -21, -9, -27, -3],\n [-90, -45, 63, 27, 81, 9],\n [10, 5, -7, -3, -9, -1]]\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, -12, 12, -28, 34, 40],\n [-166, -36, 149, -149, -123, 52],\n [-19, -14, 36, -36, -83, -20],\n [-102, -152, -17, -183, -53, 68],\n [-67, -13, 151, -41, -120, -16],\n [-9, -106, 38, -22, 21, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 40, 24, 8, 64, -24],\n [0, 25, 15, 5, 40, -15],\n [0, -30, -18, -6, -48, 18],\n [0, -50, -30, -10, -80, 30],\n [0, 15, 9, 3, 24, -9],\n [0, -50, -30, -10, -80, 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[[3, -40, 3, 37, -27, 23],\n [-43, 38, -13, -25, 41, -33],\n [3, 70, 30, -100, 51, -62],\n [48, 34, -36, 2, -6, 28],\n [67, -157, 79, 78, -116, 67],\n [43, -15, 70, -55, -14, -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[[1, 103, 13, 29, -48, 14],\n [-13, -65, -92, -106, -39, 45],\n [-39, -146, -3, 26, 64, -31],\n [63, 70, 8, -61, -7, 12],\n [-15, -26, 6, 23, 13, -10],\n [26, -115, 60, 25, 122, -63]]\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 6x6 matrix:\n[[-5, 140, -72, -29, -76, -184],\n [-128, -212, 147, -29, 90, 224],\n [-72, 22, 15, -67, 75, -58],\n [118, 62, -9, -77, -45, -90],\n [-65, -55, 0, 82, 51, 93],\n [-127, 87, -96, 110, -7, -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 6x6 matrix:\n[[-5, -83, 24, 18, -66, -23],\n [-80, -75, -93, 32, -56, -43],\n [-26, -53, 98, -1, 47, -4],\n [-91, -18, -71, -28, 192, -18],\n [42, 121, 63, -8, 8, 47],\n [34, -67, -68, 1, -63, -26]]\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[[28, 35, -49, 70, -35, -70],\n [16, 20, -28, 40, -20, -40],\n [-4, -5, 7, -10, 5, 10],\n [-16, -20, 28, -40, 20, 40],\n [-12, -15, 21, -30, 15, 30],\n [-32, -40, 56, -80, 40, 80]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-14, -14, -42, 28, 21, -14],\n [0, 0, 0, 0, 0, 0],\n [2, 2, 6, -4, -3, 2],\n [-12, -12, -36, 24, 18, -12],\n [20, 20, 60, -40, -30, 20],\n [10, 10, 30, -20, -15, 10]]\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[[-23, -102, -139, -90, 122, -12],\n [-85, -43, -10, 37, 43, 92],\n [-227, 26, -6, 35, 125, 162],\n [10, 83, 23, -2, -42, -3],\n [-27, -44, -62, -43, 65, -4],\n [50, -21, 51, 44, -85, -15]]\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 6x6 matrix:\n[[95, -12, 121, 2, -21, -20],\n [45, 34, 38, -47, 33, -32],\n [-49, -28, -83, 44, -15, 26],\n [-47, -2, -20, 5, -9, 18],\n [2, 84, 14, -107, 75, -43],\n [110, -20, 50, 19, -3, -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[[135, -13, -43, -70, -39, 2],\n [59, -4, -67, -27, -116, -19],\n [64, 22, -6, 49, 73, -20],\n [107, -11, -75, -74, -164, -16],\n [-39, -7, 34, -132, -106, 80],\n [19, 144, 159, -63, -54, 109]]\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, 147, 72, 54, -191, -46],\n [-9, 118, 174, -40, -75, 47],\n [71, 34, -40, -24, -41, 93],\n [33, -28, -159, 66, 20, -122],\n [52, 87, 10, 66, -109, -108],\n [-44, -47, -170, -4, 159, -92]]\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, -16, 4, -10, 4, 18],\n [24, 64, -16, 40, -16, -72],\n [3, 8, -2, 5, -2, -9],\n [-30, -80, 20, -50, 20, 90],\n [24, 64, -16, 40, -16, -72],\n [6, 16, -4, 10, -4, -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[[4, 81, 0, 40, 18, -80],\n [-11, -21, 108, -134, -111, 136],\n [49, -21, 118, -118, -122, 71],\n [-64, 74, 20, -16, -2, 30],\n [137, -50, -18, 58, 4, -141],\n [10, 44, -46, 76, 55, -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[[-10, -74, -44, 51, -62, 58],\n [-30, -70, 48, 47, 28, -62],\n [152, -20, 22, -95, -67, 94],\n [94, 12, -28, -64, -67, 100],\n [-46, 64, 28, -6, 73, -80],\n [-104, 90, -58, 34, 40, -32]]\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[[7, 28, -36, 57, -34, 9],\n [-44, 59, -49, 11, -28, 24],\n [-37, 17, -3, -42, 10, 9],\n [-63, 98, -86, 37, -54, 39],\n [2, -17, 19, -23, 16, -6],\n [75, -95, 77, -10, 42, -39]]\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 6x6 matrix:\n[[-49, -7, 91, -47, -77, -66],\n [88, 8, -41, -8, -58, 70],\n [-60, -26, 77, -28, -63, -59],\n [12, 4, 29, -28, -58, -6],\n [-38, 12, 42, -18, 7, -47],\n [43, 5, -11, -11, -41, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[-11, 3, -28, 45, -113, 10],\n [-26, 22, -112, -108, 16, -80],\n [-28, 90, -52, 24, 102, 80],\n [37, 87, -88, -72, -41, -122],\n [-41, 26, -138, -104, -5, -72],\n [58, 42, 100, 33, 120, 28]]\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[[75, -14, -87, 39, -60, -18],\n [-19, 6, 11, -43, 29, -12],\n [69, -10, -93, -3, -39, -36],\n [51, -14, -39, 87, -66, 18],\n [-86, 12, 118, 10, 46, 48],\n [-62, 12, 70, -38, 52, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[61, -22, -68, -68, -90, 36],\n [-28, 12, 30, 30, 42, -18],\n [-50, 96, 6, 6, 102, -90],\n [6, 14, -17, -17, -3, -9],\n [14, -6, -15, -15, -21, 9],\n [-38, -50, 83, 83, 33, 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, -4, -59, 14, 80, -56],\n [-101, 14, -125, 69, -95, 27],\n [28, -60, -4, 103, -65, -109],\n [10, 34, -23, 9, -96, 70],\n [52, 9, 25, -15, -83, 78],\n [-89, 96, -112, -8, -91, 133]]\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[[70, 40, 25, -55, 0, 25],\n [-27, 38, 113, -82, -68, -125],\n [-91, -30, 18, 29, -28, -80],\n [-43, -34, -37, 52, 12, 5],\n [-104, -72, -66, 106, 16, -10],\n [-46, -20, -2, 24, -8, -30]]\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[[-68, -106, -126, -106, 50, 24],\n [-54, 61, -137, -18, -64, 167],\n [-10, 215, -135, -15, -125, 160],\n [-59, -40, 47, -11, 111, -106],\n [-16, 125, -9, 62, -58, 94],\n [-100, 148, -78, -53, 49, -12]]\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, 70, -100, 75, 40, -48],\n [36, -4, 58, -35, -15, 38],\n [87, 80, -40, 76, 25, 44],\n [54, 79, -43, 20, 30, -41],\n [21, 91, -117, 75, 50, -75],\n [123, 130, -40, 39, 40, -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[[-21, -15, 6, -12, 3, -15],\n [56, 40, -16, 32, -8, 40],\n [70, 50, -20, 40, -10, 50],\n [63, 45, -18, 36, -9, 45],\n [-21, -15, 6, -12, 3, -15],\n [21, 15, -6, 12, -3, 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[[21, -35, 35, -35, 35, -21],\n [-27, 45, -45, 45, -45, 27],\n [-6, 10, -10, 10, -10, 6],\n [18, -30, 30, -30, 30, -18],\n [12, -20, 20, -20, 20, -12],\n [6, -10, 10, -10, 10, -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[[30, -10, 40, -180, 60, 150],\n [-6, 2, -8, 36, -12, -30],\n [-116, -22, 18, -18, -64, 50],\n [30, 3, 3, -27, 24, 15],\n [52, 13, -17, 45, 20, -55],\n [38, 9, -11, 27, 16, -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[[51, -125, 181, 23, 154, 53],\n [29, -108, 149, -39, 68, 61],\n [-18, 83, -16, 94, 62, 64],\n [40, -148, 220, -14, 148, 74],\n [50, -24, -62, -21, -68, -55],\n [7, -32, 95, 20, 80, 70]]\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[[-40, 37, 60, -63, -51, 49],\n [55, 36, 12, 123, -37, -99],\n [107, -67, -14, -23, -41, -4],\n [-51, 69, 8, 98, 22, -60],\n [166, -84, -52, 68, -24, -78],\n [76, -3, 66, -48, -118, 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[[-14, 2, -8, 8, -8, 20],\n [105, 39, 6, 39, -57, 30],\n [119, 43, 8, 42, -62, 30],\n [0, -42, 42, -77, 91, -140],\n [-112, -26, -22, -13, 27, 20],\n [21, 57, -48, 98, -118, 170]]\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[[-105, -8, -34, 64, 18, 89],\n [-62, -80, -28, 16, 76, 58],\n [-84, 24, -24, 60, -12, 69],\n [141, -24, 42, -96, 6, -117],\n [-135, -32, -46, 76, 42, 116],\n [-57, 0, -18, 36, 6, 48]]?\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[[-64, -56, 6, 43, -42, 89],\n [56, 47, 19, -30, 16, -44],\n [104, 74, 122, -44, -32, 16],\n [7, 3, 12, -6, -2, 0],\n [-64, -52, 0, 50, -44, 94],\n [46, 41, 53, 1, -30, 37]]\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, 0, 0, 0, 0, 0],\n [-15, 6, -3, 21, 27, 15],\n [40, -16, 8, -56, -72, -40],\n [-40, 16, -8, 56, 72, 40],\n [-35, 14, -7, 49, 63, 35],\n [5, -2, 1, -7, -9, -5]]\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 6x6 matrix:\n[[27, -5, 119, 28, 30, 35],\n [-81, 55, -185, -44, 22, -25],\n [-59, 13, 15, 4, 67, 46],\n [-12, -4, 134, 32, 71, 67],\n [-20, -16, 82, 20, 44, 48],\n [27, 85, 0, -2, 41, -10]]\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 6x6 matrix:\n[[-52, 92, 45, -124, -110, 35],\n [-93, 16, 27, -66, -28, 5],\n [-71, -102, -54, 49, 42, -7],\n [-106, 31, 33, -11, 109, -77],\n [106, -33, -30, 137, 147, -66],\n [-54, 8, 57, -54, -18, 9]]\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, -24, -5, -13, -70, -15],\n [-90, -6, -4, 42, 190, -8],\n [41, -15, -74, -37, 40, -62],\n [-142, 66, 28, 38, 160, 52],\n [142, -30, -2, -48, -240, -14],\n [74, -42, -32, -22, -50, -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[[-10, -18, 12, -10, 6, 14],\n [20, 36, -24, 20, -12, -28],\n [50, 90, -60, 50, -30, -70],\n [-25, -45, 30, -25, 15, 35],\n [50, 90, -60, 50, -30, -70],\n [-30, -54, 36, -30, 18, 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 6x6 matrix:\n[[33, -17, -50, -23, 21, 5],\n [-70, 17, 36, 39, -26, -41],\n [17, -11, -34, -13, 13, -1],\n [-83, 8, -2, 40, -19, -68],\n [-59, -1, -26, 25, -7, -59],\n [39, -10, -22, -22, 15, 22]]\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[[26, -42, -123, -96, 58, 65],\n [18, 22, -12, 25, 50, 29],\n [-48, 63, 198, 146, -127, -113],\n [18, 68, 12, 81, -28, 27],\n [32, -37, -129, -91, 77, 75],\n [-18, 26, 57, 46, -90, -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 6x6 matrix:\n[[25, 20, -5, -10, 0, 25],\n [-40, -32, 8, 16, 0, -40],\n [-35, -28, 7, 14, 0, -35],\n [0, 0, 0, 0, 0, 0],\n [15, 12, -3, -6, 0, 15],\n [-40, -32, 8, 16, 0, -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[[144, 36, -126, -1, -52, -85],\n [112, -47, 15, -142, 126, -71],\n [122, -5, -63, -43, -4, -59],\n [142, 60, -6, 22, -6, -37],\n [-250, -60, 15, 5, 0, 65],\n [98, 17, 21, 10, -12, 0]]\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[[10, 60, 105, 83, -100, 70],\n [-6, 16, 107, 51, -144, 104],\n [26, 164, 124, 134, 20, -68],\n [-4, -116, -178, -120, 108, -30],\n [-19, -166, -176, -151, 50, 22],\n [-37, -98, -34, -95, -26, 10]]?\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 6x6 matrix:\n[[97, -56, -15, -58, 9, -281],\n [218, 136, 42, 120, 19, -10],\n [64, 41, -82, -41, 120, -16],\n [81, 111, 23, 75, 34, 53],\n [85, 95, -25, 55, 49, 136],\n [43, 40, -65, -58, 94, -129]]\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, -80, 50, 80, 60, 90],\n [-24, -32, 20, 32, 24, 36],\n [-18, -24, 15, 24, 18, 27],\n [42, 56, -35, -56, -42, -63],\n [-12, -16, 10, 16, 12, 18],\n [-60, -80, 50, 80, 60, 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[[35, 146, 22, -41, -139, -213],\n [-31, -34, -77, 22, 32, 133],\n [16, 112, -33, 46, -95, -87],\n [69, -93, -37, 43, 108, 227],\n [-3, -79, 0, 21, 90, 148],\n [-27, 75, -160, 119, -94, -8]]\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, 69, -60, 60, -12, 38],\n [72, 218, -46, 78, -74, 96],\n [0, -54, -18, 0, -36, 42],\n [4, 62, 49, -23, 17, -36],\n [36, 29, -19, 15, -101, 108],\n [-24, 0, 60, -42, 66, -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[[125, 81, -98, -9, 37, 56],\n [-7, -73, 79, 54, -85, -57],\n [-41, -72, 126, 133, -21, -31],\n [-29, -32, -20, -125, -5, -79],\n [-119, -54, 62, -33, 29, -53],\n [-84, 58, -35, -49, 170, 48]]\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 6x6 matrix:\n[[-175, 98, 91, 69, 9, 159],\n [-100, -54, -76, -85, 20, -32],\n [-75, -22, -100, -73, -64, -42],\n [-125, 23, 31, 122, -23, 116],\n [-103, -37, 42, 6, 120, 57],\n [-153, 5, 2, -11, -29, 83]]\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, 19, -66, 62, 52, 71],\n [-5, 1, 61, -17, -12, -46],\n [-1, -25, -55, -37, -36, 16],\n [1, -11, -41, -11, -12, 20],\n [-4, -1, 44, -16, -12, -35],\n [-6, 0, 70, -22, -16, -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[[-82, -9, 44, -34, 5, -67],\n [-89, -22, -109, 99, -6, 89],\n [-68, -16, -13, -42, -92, 40],\n [-32, 19, -88, 58, 13, 41],\n [12, -19, -39, 64, 15, 55],\n [-254, -81, 54, -69, -117, -18]]\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 6x6 matrix:\n[[14, 40, 82, 27, 64, -62],\n [70, -70, -34, -78, -2, 26],\n [2, 36, 46, 19, 32, -34],\n [-68, 120, 32, 68, -10, -20],\n [-66, 126, 60, 81, 13, -42],\n [51, -75, -15, -48, 12, 9]]\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[[-64, 8, -48, 16, -32, -24],\n [-75, -83, 6, 51, 71, 40],\n [15, 24, 3, -45, -39, 36],\n [3, 90, -71, 11, -83, -132],\n [84, -34, 98, -80, 36, 152],\n [-15, -19, -12, 63, 43, -70]]\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 6x6 matrix:\n[[-74, 34, 94, -22, -20, -10],\n [8, 9, 0, 1, -15, -1],\n [6, 42, 30, -30, -60, -66],\n [30, -74, -87, 25, 90, 35],\n [-63, -2, 55, -12, 25, 4],\n [18, -59, -66, 49, 75, 95]]\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[[-26, 0, -54, 52, -42, 44],\n [-6, 0, -74, 76, -22, 20],\n [36, 10, -111, 107, -33, 2],\n [66, 10, -16, 13, 22, -54],\n [38, 14, -95, 85, -49, 10],\n [-62, -20, -13, 32, 31, 20]]?\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, -5, -8, -21, -19, -43],\n [-90, -10, 22, 20, 32, -6],\n [21, -34, -24, 64, 84, 86],\n [-57, -65, -47, 96, 134, 113],\n [-14, -13, 21, 46, 60, 41],\n [53, 0, 19, 31, 35, 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 6x6 matrix:\n[[-12, 10, -18, -20, -12, 10],\n [48, -25, 45, -22, -6, 20],\n [62, -35, 63, -10, 2, 15],\n [-15, 10, -36, -6, 3, 0],\n [-62, 40, -72, -24, -20, 5],\n [-64, 24, -36, 92, 38, -63]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[31, 55, 72, -61, -2, 27],\n [36, 72, 45, -81, 81, -54],\n [2, 14, -45, -17, 107, -108],\n [-13, -17, -59, 18, 63, -75],\n [-32, -60, -59, 67, -31, 6],\n [-21, -45, -12, 51, -78, 63]]\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[[90, 16, 83, -65, 94, -69],\n [-76, -13, -67, 65, -85, 55],\n [-53, 60, -88, 86, -119, 61],\n [-59, -32, -94, 38, -71, 39],\n [32, 73, -11, 61, -55, -17],\n [96, -50, 27, -136, 133, -80]]?\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 6x6 matrix:\n[[-83, 58, 68, 27, -38, -36],\n [37, -62, -2, -53, -18, 4],\n [-22, 92, -42, 94, 64, 16],\n [28, -8, -32, 4, 24, 16],\n [19, -14, -15, -7, 8, 8],\n [21, 54, -71, 71, 76, 32]]\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[[93, 45, -126, 74, -34, 74],\n [233, 9, -8, 32, 66, -84],\n [-77, 114, 4, 24, 9, 10],\n [-87, -90, 150, -129, -4, 19],\n [81, 122, 70, -2, 35, -109],\n [-5, 177, -86, 98, 0, 2]]\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 6x6 matrix:\n[[-6, -35, 88, -15, 7, 6],\n [-36, -46, 156, -18, -8, 41],\n [-53, 54, 31, 112, -75, -47],\n [6, 4, 126, -20, -46, 48],\n [201, 113, -45, -77, -80, 16],\n [-104, -34, 104, -16, -12, 112]]\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, 30, 27, 0, -27, -3],\n [6, 10, 9, 0, -9, -1],\n [6, 10, 9, 0, -9, -1],\n [0, 0, 0, 0, 0, 0],\n [36, 60, 54, 0, -54, -6],\n [-18, -30, -27, 0, 27, 3]]\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[[25, 28, 1, 45, -48, 57],\n [36, 51, 7, 71, -22, 56],\n [4, 34, -2, 9, -33, -6],\n [17, 77, 10, 46, 38, -35],\n [26, 8, 2, 45, -37, 72],\n [-15, -69, -8, -40, -26, 29]]\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 6x6 matrix:\n[[107, -69, 20, -34, -19, -31],\n [76, -55, 27, 39, 148, -70],\n [1, 50, -9, -26, 39, -9],\n [-98, -36, -94, 0, 18, 58],\n [48, 112, 167, 71, -54, -62],\n [100, 26, 139, 34, -86, -56]]\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[[-107, -89, -43, -83, -6, 177],\n [45, -18, 36, -23, 52, -33],\n [157, -65, -12, -87, 120, 20],\n [-122, 112, 2, 126, -126, -136],\n [120, -35, -38, -48, 81, -25],\n [161, -12, -17, -27, 86, -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[[-37, -12, 37, 15, 2, 63],\n [17, 46, 13, -41, 81, -127],\n [-71, 72, 77, 27, 75, -2],\n [-98, -12, 122, 6, 90, 82],\n [95, -54, -92, -38, -96, -32],\n [-65, 64, -103, 171, 47, 48]]?\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[[-12, 44, -14, -10, -32, -58],\n [111, -13, 35, -18, 20, -22],\n [-108, 56, -142, 134, 64, -138],\n [-3, 93, -68, 103, -29, -120],\n [-42, 82, -97, 205, -16, -59],\n [6, 35, -61, 137, 22, -45]]\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[[-58, -49, 145, -74, -27, 49],\n [-44, -138, -8, -98, -26, 63],\n [10, -208, -199, -141, 58, 80],\n [45, -10, -80, 39, -10, -67],\n [14, -111, -12, -73, 21, 20],\n [27, -109, 37, -53, 1, -13]]?\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[[160, -70, 10, 50, 150, 70],\n [68, -21, 21, 33, 65, 35],\n [-22, 49, 74, 46, -15, 14],\n [76, 28, 122, 106, 80, 70],\n [-36, 7, -19, -23, -35, -21],\n [36, -7, 19, 23, 35, 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 6x6 matrix:\n[[38, 82, -8, 4, -22, 42],\n [-38, -75, 24, -31, 28, -50],\n [-6, 52, -16, 62, -38, 30],\n [-107, -29, 49, 32, -20, -58],\n [-111, -50, 63, 1, -4, -76],\n [-30, -62, 54, -92, 44, -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[[-38, -127, -199, 58, -50, -79],\n [61, 28, -18, 52, -100, 49],\n [60, 38, 3, -36, -124, 124],\n [35, -5, -15, -93, -51, 98],\n [-81, 34, 94, -74, 55, 7],\n [-49, 131, 107, -29, -123, 34]]\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, -15, 12, 3, 15, 15],\n [0, 0, 0, 0, 0, 0],\n [-27, -45, 36, 9, 45, 45],\n [9, 15, -12, -3, -15, -15],\n [21, 35, -28, -7, -35, -35],\n [-3, -5, 4, 1, 5, 5]]\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[[114, -88, -16, 145, -9, 116],\n [-34, -34, -2, -66, 71, 17],\n [-22, 0, 72, -39, -13, -56],\n [12, -58, 6, -4, 48, 45],\n [-24, -28, 12, -49, 48, 6],\n [24, -104, -40, 0, 108, 116]]\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, -6, -63, 3, 130, -68],\n [60, 36, 0, 36, 48, -60],\n [-21, 18, 63, 9, -114, 48],\n [-79, -44, 7, -45, -74, 82],\n [95, 74, 35, 69, 22, -80],\n [35, 38, 35, 33, -26, -20]]\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, 12, 4, 0, 36, 32],\n [20, -12, -4, 0, -36, -32],\n [-20, 12, 4, 0, 36, 32],\n [-45, 27, 9, 0, 81, 72],\n [5, -3, -1, 0, -9, -8],\n [-15, 9, 3, 0, 27, 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[[-144, 27, 126, 54, 108, -99],\n [-69, -61, 88, 86, 29, -6],\n [41, -2, -38, -20, -29, 25],\n [-39, -78, 66, 84, 3, 21],\n [-62, 23, 50, 14, 50, -49],\n [31, 34, -42, -44, -11, -1]]?\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[[-21, 28, 27, -82, 80, -70],\n [60, 92, 82, -16, -34, 96],\n [11, -143, -19, 57, -36, -11],\n [23, -54, 97, -6, 2, -10],\n [-52, -47, -146, 48, -4, -63],\n [-148, -75, -34, 75, 22, -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[[14, 25, 46, 104, -15, -65],\n [-157, 54, -82, -42, -38, -16],\n [-123, -61, -73, -2, 36, 93],\n [36, -132, -24, -4, 74, 118],\n [-134, 75, -37, 8, -42, -41],\n [55, -59, -103, -124, -13, -20]]?\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[[-11, -87, 108, -26, -172, -25],\n [69, -7, 13, 120, 110, 18],\n [7, -16, 24, 76, -110, 59],\n [-22, 29, -66, -100, 77, -63],\n [-24, -1, 53, 18, -141, 18],\n [21, -71, -13, 6, -23, 33]]\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[[-37, 19, -38, 17, 131, 90],\n [-95, 95, -63, 6, -49, 52],\n [48, -36, -41, 50, -23, -44],\n [68, -70, 16, 0, -10, -40],\n [210, -226, -8, 28, 4, -88],\n [81, -140, 191, -170, 102, 40]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-42, 67, -26, -1, -70, 107],\n [6, 101, -4, -40, -87, 78],\n [-158, 128, -86, -103, -161, 77],\n [-39, -13, -63, -7, -23, -5],\n [26, 17, -6, 33, -14, 69],\n [153, -95, -9, 49, 83, -91]]\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[[-42, -48, -4, -50, -8, -42],\n [-76, -94, 8, -80, -24, -66],\n [68, 92, -24, 60, 32, 48],\n [-69, -81, -2, -79, -16, -66],\n [75, 90, -2, 83, 20, 69],\n [-28, -37, 8, -26, -12, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 6, 14, 0, 10, -20],\n [0, 0, 0, 0, 0, 0],\n [12, 6, 14, 0, 10, -20],\n [-12, -6, -14, 0, -10, 20],\n [-6, -3, -7, 0, -5, 10],\n [-42, -21, -49, 0, -35, 70]]?\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[[34, 20, 9, -19, 40, 29],\n [92, 10, -48, -32, 20, 22],\n [-58, -15, 16, 24, -30, -25],\n [24, 45, 57, -27, 90, 60],\n [10, -25, -48, 8, -50, -31],\n [-28, 35, 77, -7, 70, 42]]\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, -52, 63, -193, -149, 103],\n [-40, -8, -23, 13, -10, -20],\n [254, 198, -16, 42, 53, -27],\n [-230, -152, -66, 37, -28, -40],\n [186, 118, 66, -32, 12, 57],\n [-108, -108, -74, 30, -80, 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 6x6 matrix:\n[[21, -24, 0, 21, -21, 18],\n [-49, 56, 0, -49, 49, -42],\n [42, -48, 0, 42, -42, 36],\n [42, -48, 0, 42, -42, 36],\n [7, -8, 0, 7, -7, 6],\n [63, -72, 0, 63, -63, 54]]\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, -20, -11, 54, 16, 104],\n [-29, -7, 0, 20, 10, 32],\n [-30, -18, -26, 44, -4, 112],\n [-50, -10, 5, 30, 20, 40],\n [-85, -23, -6, 64, 26, 112],\n [-41, -19, -22, 48, 2, 112]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-26, -66, -110, -36, 80, 68],\n [62, 18, -35, 98, 23, 112],\n [-63, -30, -10, -85, 4, -57],\n [62, -112, -14, 18, 10, 22],\n [-47, -24, -76, -110, 100, -55],\n [1, 54, 43, 101, -91, 91]]\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 6x6 matrix:\n[[-102, -13, -11, -21, -146, -26],\n [21, -3, -9, 7, 18, 6],\n [-138, 5, 20, 37, -154, -72],\n [4, -16, 6, 42, 72, -32],\n [-99, 55, 72, 28, -102, -50],\n [160, 50, 25, -14, 160, 78]]\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 6x6 matrix:\n[[-37, 123, 186, -57, -55, 187],\n [-46, 5, -16, -105, 164, -130],\n [-3, -122, -177, 213, -118, -136],\n [-49, 37, -39, -27, -52, 40],\n [27, 63, -13, -124, 222, -90],\n [47, -153, -225, 74, 54, -218]]\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[[90, -60, -50, -106, -80, -64],\n [-80, 105, 4, 90, 2, 22],\n [62, -40, -60, -54, 28, -42],\n [-18, 95, -16, -16, -230, -48],\n [48, -45, -3, -66, -72, -27],\n [49, -70, 5, -57, -4, -10]]?\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 6x6 matrix:\n[[-62, -58, -78, -28, -28, -57],\n [140, 23, 226, 53, 81, 246],\n [-136, -44, 41, -126, -71, -43],\n [98, 54, 82, 124, 72, 82],\n [-237, -130, -44, -188, -173, -91],\n [-53, 28, -91, -63, -25, -130]]\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 6x6 matrix:\n[[-28, -2, 110, 150, -162, 195],\n [64, 113, 41, 64, -47, 69],\n [39, 8, -115, -117, 137, -160],\n [-28, -158, 126, -44, -38, -24],\n [-103, 31, -62, -43, 68, -42],\n [-136, -10, 8, 113, -93, 154]]\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[[2, 52, -49, -44, -82, -35],\n [85, -63, 32, 67, 21, 7],\n [-19, 17, -6, -43, 61, -15],\n [75, -73, -4, 91, 51, 91],\n [107, -99, 25, 93, 119, 68],\n [30, -30, 6, 11, 90, 21]]\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[[-58, -81, -15, -107, -94, 14],\n [-10, 33, 27, 92, -31, 14],\n [-108, 43, -52, 29, 12, -27],\n [38, 49, 67, -28, -27, 18],\n [-60, -100, -100, -45, 20, -25],\n [-60, -69, -52, -71, -29, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-14, -14, 2, 53, 24, 51],\n [-5, 6, -12, -28, 32, 18],\n [68, -64, -1, -1, -34, -28],\n [0, 6, 44, 83, -116, -77],\n [-40, 46, -40, -101, 116, 63],\n [-109, 112, 21, 26, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[76, -28, -66, -59, -3, -1],\n [80, -2, -39, 2, -12, -8],\n [4, -36, 2, -10, -42, -22],\n [-34, -64, 0, -59, -41, -19],\n [-98, -56, 28, -63, -21, -7],\n [26, 90, -37, 2, 118, 62]]\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[[18, -204, -186, -35, 107, -103],\n [-32, -157, -156, 36, 87, -98],\n [64, -52, -40, -100, 24, 10],\n [16, 98, 148, -1, -103, 72],\n [-66, -88, -22, 92, -38, -16],\n [-89, 26, -11, 118, 3, -20]]\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[[-51, 11, 29, 17, -41, 61],\n [-14, -21, -45, -17, 11, -42],\n [91, -21, 54, 61, 5, -42],\n [-29, 24, 9, -14, -10, 48],\n [-133, -62, -38, 36, -78, -7],\n [-50, 75, -135, -185, 95, 20]]?\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[[-49, 35, -49, -63, -35, -28],\n [-14, 10, -14, -18, -10, -8],\n [-35, 25, -35, -45, -25, -20],\n [-70, 50, -70, -90, -50, -40],\n [-7, 5, -7, -9, -5, -4],\n [21, -15, 21, 27, 15, 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[[-39, -16, -11, 34, -27, 7],\n [-12, -16, -2, 16, -12, -8],\n [42, -16, 16, -20, 18, -38],\n [-18, -120, 9, 72, -50, -100],\n [0, -48, 6, 24, -16, -44],\n [75, 40, 20, -70, 55, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-43, -12, 100, 73, -21, -18],\n [-43, 15, -14, 5, -30, 6],\n [-34, 31, -34, -34, 73, 10],\n [47, 14, -96, -79, 53, 17],\n [-210, 50, 92, 94, -28, -4],\n [-85, 1, 110, 85, -20, -17]]\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[[-206, 44, 47, 144, 102, -64],\n [19, -100, 212, -16, 73, -79],\n [-51, 4, -1, -28, 29, 91],\n [-51, -24, 24, -68, 41, -3],\n [10, -6, 68, -82, 57, 46],\n [62, -4, -44, 8, -60, 123]]\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[[-5, 2, -60, -63, 67, 20],\n [-3, 9, 29, 35, -43, -14],\n [5, -11, -15, -21, 29, 10],\n [0, 0, 0, 0, 0, 0],\n [9, -12, 38, 35, -31, -8],\n [21, -36, 22, 7, 13, 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[[-25, -32, -18, -32, -38, 72],\n [-75, -36, 36, -111, -24, 6],\n [-5, 12, 24, -11, 20, -50],\n [-10, 20, 42, -21, 34, -86],\n [-80, -28, 54, -121, -10, -30],\n [-70, -20, 54, -107, -2, -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[[60, 90, 55, -35, -55, -10],\n [8, 44, 50, -50, 14, -76],\n [40, -8, -54, 73, -82, 152],\n [-56, -44, 2, -24, 78, -84],\n [-56, -80, -46, 27, 54, 0],\n [0, -12, -16, 17, -8, 28]]\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, 20, -50, -20, -50, 30],\n [-32, 16, -40, -16, -40, 24],\n [-40, 20, -50, -20, -50, 30],\n [0, 0, 0, 0, 0, 0],\n [40, -20, 50, 20, 50, -30],\n [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[[27, 11, 102, -99, -71, 78],\n [-81, -50, -16, -43, -5, 49],\n [83, 38, -70, 133, 63, -111],\n [0, 22, 152, -137, -52, 147],\n [-29, -104, -43, -56, -69, 48],\n [-46, -88, -85, 7, -6, 9]]\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[[-24, -61, 8, -17, -139, -113],\n [22, 51, -70, 51, 58, 55],\n [-47, -14, 84, -6, -278, -155],\n [96, -68, 18, 83, -93, -93],\n [98, -22, -88, 50, 36, -24],\n [34, -57, -36, 9, 111, 31]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[118, -64, -117, 56, -22, 43],\n [36, 102, -7, -81, 32, -61],\n [-10, 32, 63, 38, -130, -9],\n [-56, -13, 79, 53, -117, -27],\n [125, 33, -101, -21, 28, 38],\n [33, 3, -78, -75, 114, -133]]\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[[-10, -86, 28, 1, -49, -33],\n [76, -40, 134, -130, 46, -96],\n [-36, 44, -76, 66, -10, 58],\n [44, 120, 6, -50, 94, 16],\n [-12, 26, -31, 24, 2, 25],\n [10, -84, 57, -31, -31, -52]]?\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 6x6 matrix:\n[[82, -15, -100, 99, 23, -101],\n [-37, 3, 58, -96, 43, 47],\n [117, -27, -108, 99, 27, -108],\n [137, -112, 25, 20, -143, 84],\n [43, -8, -33, -6, 63, -46],\n [131, -66, -52, -19, 86, -56]]\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 6x6 matrix:\n[[0, 0, 0, 0, 0, 0],\n [63, -70, -49, -21, -35, 0],\n [36, -40, -28, -12, -20, 0],\n [9, -10, -7, -3, -5, 0],\n [-72, 80, 56, 24, 40, 0],\n [63, -70, -49, -21, -35, 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[[-37, -66, -64, 103, -12, -50],\n [-49, -34, -33, -103, 111, -29],\n [-39, 1, -29, -42, 16, -43],\n [-176, -102, -98, 18, 92, -90],\n [55, -34, -40, 38, -2, -26],\n [-21, -12, -22, -112, 90, -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[[-40, 0, 24, 40, 80, 64],\n [-45, 0, 27, 45, 90, 72],\n [40, 0, -24, -40, -80, -64],\n [5, 0, -3, -5, -10, -8],\n [45, 0, -27, -45, -90, -72],\n [35, 0, -21, -35, -70, -56]]\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[[4, -96, -110, -12, -50, -108],\n [16, 40, -44, 8, 44, 32],\n [58, 12, 42, 92, -54, 28],\n [8, -81, -119, -10, -35, -95],\n [55, 15, 12, 80, -36, 25],\n [-30, 8, 144, -8, -28, 28]]?\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 6x6 matrix:\n[[-14, 48, 48, 86, 30, 72],\n [109, -172, 45, 9, 68, -142],\n [25, -26, 45, 63, 82, 14],\n [-31, -66, -157, -205, -26, -94],\n [-95, -8, -31, 89, -91, 42],\n [24, 15, 23, -7, -50, -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 6x6 matrix:\n[[-172, -10, -163, -47, 30, -104],\n [41, -73, 151, -8, -58, 157],\n [-90, 102, -124, 4, 104, -78],\n [-140, -48, -66, 39, -4, -84],\n [-185, 2, -138, -8, 40, -108],\n [-20, 2, 50, 72, 10, 7]]\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[[104, 68, -20, -76, -40, 0],\n [-101, -56, -28, 79, 16, 9],\n [72, 56, -56, -48, -48, 8],\n [17, 10, 2, -13, -4, -1],\n [10, 11, -23, -5, -14, 4],\n [98, 73, -61, -67, -58, 8]]?\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[[-24, 40, 3, -37, -4, -25],\n [-48, -16, 6, 22, -20, -26],\n [-56, 40, 7, -33, -16, -45],\n [-88, 72, 11, -61, -24, -73],\n [-104, -24, 13, 37, -42, -59],\n [24, -104, -3, 101, -4, 41]]\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[[25, 78, -6, 149, -16, -89],\n [114, 170, -120, 54, 51, 15],\n [20, 19, 82, 6, -13, 29],\n [6, 23, 74, 76, -28, -30],\n [100, 158, -16, 132, 3, -7],\n [-46, -70, 30, 4, -31, -5]]?\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, -30, 30, 54, 30, -30],\n [10, -5, 5, 9, 5, -5],\n [-50, 25, -25, -45, -25, 25],\n [80, -40, 40, 72, 40, -40],\n [0, 0, 0, 0, 0, 0],\n [-20, 10, -10, -18, -10, 10]]?\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[[6, 61, 48, 7, 40, -46],\n [-14, 60, -20, 16, -94, -72],\n [-2, -46, -32, -27, 82, 37],\n [-2, -75, -40, -7, -32, 64],\n [-2, -26, -24, -29, 106, 19],\n [-20, -75, -108, -33, 6, 38]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-90, -27, -58, 65, 76, -37],\n [115, 20, 58, -46, -81, 65],\n [90, 0, 28, 4, -46, 70],\n [85, 23, 52, -55, -69, 38],\n [-35, 17, 8, -45, -1, -48],\n [80, 19, 46, -45, -62, 39]]?\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 6x6 matrix:\n[[110, 60, -125, 45, -40, -25],\n [0, 18, 1, -69, -12, 75],\n [-36, -18, 41, -21, 12, 15],\n [1, 21, 0, -78, -14, 85],\n [24, 18, -27, -9, -12, 15],\n [-26, -24, 29, 27, 16, -35]]\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[[-3, -147, -132, 43, 54, 112],\n [-113, -12, 71, 17, 1, -58],\n [108, 100, -50, -22, 90, 42],\n [15, -116, -41, 31, 120, -70],\n [22, 11, -77, 8, -4, 34],\n [-117, 71, 83, -14, -95, 165]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[42, 0, -24, 84, 42, 72],\n [33, 31, -58, -26, -20, -38],\n [-17, 40, -20, -86, -49, -68],\n [63, 50, -44, 70, 33, 76],\n [96, 34, -79, 88, 40, 61],\n [89, 54, -80, -26, -17, -56]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-51, 105, 115, 16, -18, 68],\n [114, 89, -119, -55, -148, 115],\n [-41, -144, -91, -31, -44, -153],\n [-19, -35, -22, -48, -31, -31],\n [65, 47, -126, -68, -170, 42],\n [110, 136, -40, 74, -38, 124]]\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[[40, -10, -70, -20, 100, 90],\n [16, -4, -28, -8, 40, 36],\n [12, -3, -21, -6, 30, 27],\n [-4, 1, 7, 2, -10, -9],\n [4, -1, -7, -2, 10, 9],\n [20, -5, -35, -10, 50, 45]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-76, 60, 104, -36, 18, 94],\n [-18, 45, -18, -63, -81, 27],\n [32, -28, -40, 20, 0, -40],\n [-12, 43, -30, -65, -90, 20],\n [62, -77, -46, 79, 63, -81],\n [12, -30, 12, 42, 54, -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[[-71, -6, -22, -47, 21, 30],\n [70, -4, 28, 46, -10, -28],\n [-137, 38, -74, -89, -13, 50],\n [-8, -80, 48, -8, 88, 16],\n [74, -52, 60, 47, 41, -22],\n [-102, 36, -60, -66, -18, 36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-52, 80, 20, 28, -66, -26],\n [14, -154, -90, 50, 130, -44],\n [-24, -116, -60, 60, 90, -76],\n [7, 133, 105, -77, -118, 56],\n [-4, 18, -10, 10, -9, 6],\n [3, -17, -55, 35, 29, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-22, 59, 0, -112, 22, 68],\n [40, -38, -30, 65, -6, -70],\n [-69, 38, 66, -48, -2, 97],\n [18, -103, -30, -7, -72, -42],\n [-40, 152, 48, -32, 96, 88],\n [20, -38, -18, 27, -18, -38]]\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, 5, -103, -71, -64, -63],\n [-53, -127, 93, -33, 124, 109],\n [14, 140, -87, 49, -46, -8],\n [1, -87, 171, 46, 182, 165],\n [72, 53, 0, 35, -81, -98],\n [48, -33, 47, 23, 73, 98]]\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[[65, 74, 30, -2, 19, 15],\n [88, 56, -3, -1, -40, 50],\n [59, 65, 102, -14, 79, -45],\n [94, -11, 69, -21, -28, -10],\n [98, -32, 120, -32, -2, -50],\n [4, -65, -57, 1, -94, 40]]?\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[[38, 85, 93, 18, 27, 34],\n [33, 55, 93, 45, 21, 14],\n [11, -99, -9, -81, 15, -34],\n [2, 65, -3, -18, 3, 36],\n [33, 92, 78, 9, 24, 40],\n [-17, -78, -72, -81, -6, -20]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 94, 54, -56, -114, -74],\n [-52, 83, 67, -2, -75, -42],\n [143, -70, -58, -36, 43, -13],\n [-142, 71, 11, -36, -83, 17],\n [52, -120, -24, 120, 172, 64],\n [-109, 29, 49, 70, 12, 27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[44, -48, 72, -10, 144, -30],\n [-65, -43, -56, 51, 59, -4],\n [-68, -33, -15, -86, -55, 86],\n [33, 18, 3, 45, 34, -44],\n [129, -87, 243, -99, 85, -20],\n [-41, -146, 105, -38, 18, 31]]\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[[107, -5, 39, -22, 152, 106],\n [-83, -87, 69, -26, -8, -4],\n [-70, 33, 26, 2, -45, -60],\n [-182, 23, -42, 26, -83, 75],\n [-12, -55, 11, -54, -136, -179],\n [-25, -112, 69, -11, 61, 52]]\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, 32, 28, 99, -58, -81],\n [-4, -40, 22, 62, 14, -40],\n [-17, -20, -4, -19, 22, 20],\n [24, 48, 3, 27, -45, -39],\n [57, -16, 30, 83, -20, -41],\n [-51, 12, -18, -43, 12, 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[[-40, -40, 16, 20, 4, -20],\n [-20, -20, 8, 10, 2, -10],\n [-30, -30, 12, 15, 3, -15],\n [-60, -60, 24, 30, 6, -30],\n [-20, -20, 8, 10, 2, -10],\n [10, 10, -4, -5, -1, 5]]\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, 20, -45, 10, 10, 15],\n [1, -4, 9, -2, -2, -3],\n [4, -16, 36, -8, -8, -12],\n [-7, 28, -63, 14, 14, 21],\n [-7, 28, -63, 14, 14, 21],\n [-9, 36, -81, 18, 18, 27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[21, -27, 44, -5, 51, -87],\n [-33, 13, -25, -51, 67, -84],\n [21, -3, 8, 43, -69, 93],\n [-6, 20, -31, 26, -76, 117],\n [-45, 31, -54, -43, 25, -15],\n [-24, 14, -25, -28, 26, -27]]\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[[26, -89, 56, 47, -47, 3],\n [-68, 11, -112, -64, -10, -55],\n [93, -30, -11, 85, -15, 77],\n [-3, 48, -103, -74, 66, -2],\n [-42, -55, -30, -33, -124, -65],\n [63, 143, 11, 43, 71, 92]]\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[[20, 15, -10, 0, 10, -25],\n [-17, -18, 5, -21, -68, 23],\n [-6, -12, -2, -30, -88, 10],\n [-26, -27, 8, -30, -98, 35],\n [7, 6, -3, 3, 12, -9],\n [26, 21, -12, 6, 30, -33]]\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[[-142, 61, 98, 29, -28, -266],\n [-55, -144, -62, 33, 159, 90],\n [-188, -41, 64, 35, 44, -190],\n [73, -23, 24, 98, 26, 46],\n [-143, -65, -4, -24, 56, -66],\n [71, 32, 26, 83, 25, -26]]\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[[72, 189, 51, 239, 27, 4],\n [-25, 3, -70, 72, 85, 45],\n [-2, 9, 97, -31, -68, -25],\n [-30, 16, 50, 66, 17, 49],\n [80, 35, -15, -87, -66, -65],\n [-106, -123, 25, -43, 3, -52]]\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[[132, 68, -41, 69, -67, 91],\n [-136, -100, -10, -80, 70, -62],\n [-36, -36, -59, -150, -55, 1],\n [-20, -56, -67, -99, -45, 69],\n [128, 38, -53, 156, -9, 117],\n [-60, -60, 18, 82, 98, -6]]\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[[-25, 8, 33, -13, 10, 52],\n [-73, -25, 6, 44, 31, -11],\n [79, 13, -45, -20, -28, -40],\n [-59, 1, 11, 10, 38, 50],\n [-80, -28, 3, 50, 35, -15],\n [42, -26, 86, -8, -84, -68]]\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 6x6 matrix:\n[[-12, -29, -122, 43, -1, 47],\n [-93, 205, -22, 0, 25, -75],\n [-162, 83, -24, 75, 171, -53],\n [-49, 113, -31, 68, 114, -114],\n [-27, 55, 82, -32, 189, -91],\n [11, -4, -79, 61, 17, -19]]\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[[-80, -16, -16, 48, -72, -16],\n [-50, -10, -10, 30, -45, -10],\n [30, 6, 6, -18, 27, 6],\n [-20, -4, -4, 12, -18, -4],\n [-50, -10, -10, 30, -45, -10],\n [80, 16, 16, -48, 72, 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[[46, -32, 28, -42, 66, 60],\n [88, -104, 100, 24, 60, 14],\n [31, 16, -2, -105, 33, -22],\n [28, 4, -2, -78, 54, 43],\n [-14, -28, 10, 88, 0, 63],\n [97, -136, 130, 76, 45, -9]]\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[[8, 22, -88, 112, -98, -54],\n [-88, -84, 43, 152, 22, -109],\n [65, -13, -49, 10, -16, 25],\n [62, -121, -145, 76, -145, -66],\n [-21, -33, 75, -6, 90, 11],\n [48, -103, -55, -2, -75, 18]]\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 6x6 matrix:\n[[-2, -36, 60, 31, -30, -20],\n [-42, -104, 121, 91, 10, -86],\n [-47, 1, -20, -4, -8, -1],\n [-92, -80, 70, 66, -4, -68],\n [42, -8, 37, 9, -18, 2],\n [-52, -76, 71, 66, 28, -70]]\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[[-78, -99, -26, -98, 95, -27],\n [5, 17, -33, -78, 51, -12],\n [11, 15, 46, 124, -124, 23],\n [97, 67, 36, 72, 72, 21],\n [-62, -100, -1, -56, 109, -19],\n [57, 102, 2, 8, -71, 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[[91, 62, -115, -27, -6, -6],\n [-1, -30, 65, -15, 74, 74],\n [-14, 17, -40, 18, -66, -66],\n [-32, 6, -20, 24, -68, -68],\n [15, -10, 25, -15, 50, 50],\n [40, 4, 0, -24, 56, 56]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[130, 11, 30, -95, -41, 94],\n [43, -63, -8, -49, -67, 6],\n [67, 65, 38, 101, -63, -128],\n [-1, -23, 23, -68, 113, 161],\n [115, 86, 28, -132, -30, 90],\n [32, 29, -15, -78, -77, -23]]\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[[-8, 4, -28, 16, -40, -40],\n [18, -9, 63, -36, 90, 90],\n [-8, 4, -28, 16, -40, -40],\n [-6, 3, -21, 12, -30, -30],\n [10, -5, 35, -20, 50, 50],\n [-16, 8, -56, 32, -80, -80]]\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, 27, -11, -104, -2, 26],\n [52, -96, -8, -163, -103, -1],\n [-11, 105, 17, 187, 92, -9],\n [79, -47, -198, -38, -72, 186],\n [69, -46, -70, -2, -32, 56],\n [-114, -48, -7, -13, -49, 13]]\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[[-70, 24, -8, -60, -1, 50],\n [-62, -112, -46, -37, -14, 73],\n [-56, 97, -4, 25, 20, 65],\n [-48, 166, 21, -68, 49, 79],\n [198, 8, 0, -1, 46, -197],\n [16, 42, -94, -87, 82, -17]]\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 6x6 matrix:\n[[-111, 95, -10, 79, -17, 57],\n [16, -62, -100, -17, -67, -11],\n [-11, 14, -15, 30, 16, -35],\n [-28, 16, -40, 38, -6, -22],\n [84, -62, 20, -51, 31, -57],\n [-57, 32, -55, 52, -26, 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[[-33, 90, -82, 29, -22, -45],\n [-105, 165, -42, -69, 27, -9],\n [1, 28, 34, -80, 84, 3],\n [-78, 90, -4, -55, -16, 36],\n [-34, 68, -84, 54, -80, -18],\n [11, -70, 110, -76, 60, 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 6x6 matrix:\n[[-72, -48, -80, -8, 72, -8],\n [-36, -24, -40, -4, 36, -4],\n [90, 60, 100, 10, -90, 10],\n [72, 48, 80, 8, -72, 8],\n [-63, -42, -70, -7, 63, -7],\n [-63, -42, -70, -7, 63, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[32, 22, -33, -86, 176, 13],\n [15, 38, 1, -52, 56, 67],\n [-100, -134, -15, 22, 104, 67],\n [-14, -14, 25, 85, -171, -57],\n [-33, -62, -1, 65, -57, -63],\n [-103, -130, 17, 115, -107, -1]]\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, 84, 5, -35, 5],\n [-59, 22, 30, -119, -18, -93],\n [73, -168, -75, 73, -82, 70],\n [27, -134, -95, 84, -73, -6],\n [26, -38, -23, 2, -12, 11],\n [-6, 108, 49, -159, 75, -59]]?\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[[-36, 42, -12, 18, -48, 36],\n [-48, 56, -16, 24, -64, 48],\n [-48, 56, -16, 24, -64, 48],\n [48, -56, 16, -24, 64, -48],\n [18, -21, 6, -9, 24, -18],\n [30, -35, 10, -15, 40, -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[[4, 96, -52, 40, 66, -166],\n [-13, 11, -11, 15, -11, -24],\n [80, 28, -8, -60, 116, -52],\n [-8, 56, -16, 40, 34, -74],\n [-5, -83, 41, -35, -61, 138],\n [-31, 105, -41, 85, 39, -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[[-76, -60, 92, 62, -30, 28],\n [18, -98, 74, 77, -49, 18],\n [24, 88, -88, -76, 44, -24],\n [67, 68, -94, -67, 34, -28],\n [-82, 0, 44, 14, 0, 16],\n [1, 72, -62, -59, 36, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[-50, 32, 56, -4, -52, 40],\n [-91, 2, 146, 90, -122, 126],\n [75, -11, -113, -58, 96, -95],\n [-19, -13, 41, 42, -32, 39],\n [-42, 55, 25, -52, -30, 7],\n [4, 30, -30, -56, 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 6x6 matrix:\n[[-46, 20, 15, -9, -34, 11],\n [28, 82, 37, 96, 6, -4],\n [-56, 132, 66, 90, -64, 14],\n [-44, -100, -20, -111, 14, 19],\n [-62, 10, 92, 12, 50, 54],\n [2, -88, -3, -63, 62, 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[[-160, -32, -69, -172, -32, 70],\n [108, 50, 121, -12, -14, 48],\n [-48, 14, -62, -71, -27, 13],\n [94, 35, 88, 96, -33, -43],\n [86, 13, 39, -6, 67, 55],\n [138, 18, 115, 52, 61, 39]]?\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[[117, -97, 62, 24, -63, -80],\n [-72, -37, 52, 90, 20, 113],\n [45, 11, -48, 16, -15, -62],\n [-27, 87, -69, -102, 45, -33],\n [-120, 92, -80, 101, -20, 128],\n [21, 58, -124, 29, 49, -85]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[126, 79, 132, 84, 68, -28],\n [45, 88, 111, 184, 50, 21],\n [-106, 17, -94, 118, -124, 66],\n [105, 121, 122, 129, 65, -36],\n [18, 30, -32, 28, -71, 4],\n [-142, -47, -65, 45, 18, 79]]\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, -58, 34, 30, -95, 11],\n [-106, -37, 66, 36, -115, 52],\n [20, 23, 0, 30, -10, 61],\n [-15, 57, 27, 28, -10, 99],\n [46, 163, -6, -36, 145, 80],\n [50, 106, -10, 0, 80, 82]]\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, 36, -18, 36, 18, 24],\n [20, 60, -30, 60, 30, 40],\n [4, 12, -6, 12, 6, 8],\n [10, 30, -15, 30, 15, 20],\n [-18, -54, 27, -54, -27, -36],\n [8, 24, -12, 24, 12, 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[[14, 49, 18, -2, 1, -14],\n [56, 52, 102, 89, -63, -52],\n [-19, -10, 67, 38, -97, -111],\n [-8, 16, 34, 16, -24, -49],\n [-3, 116, -15, -84, 11, -36],\n [49, -60, 17, 87, 22, 83]]\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 6x6 matrix:\n[[52, -44, 1, -20, -24, -31],\n [50, 38, -11, 40, -110, 55],\n [118, 57, 107, -25, -61, 83],\n [113, 27, 129, -72, -22, 52],\n [-56, -23, -21, -63, -47, -19],\n [-55, 41, -81, 114, 2, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[107, 45, -104, 42, -47, 194],\n [-62, 109, -29, -108, -76, 68],\n [65, 25, -89, -46, -110, 186],\n [-75, -117, 172, -46, 15, -148],\n [-11, -105, 189, -154, -69, -50],\n [77, -126, 137, 2, 21, -40]]?\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[[-34, 37, 113, -61, -6, 17],\n [96, -78, -60, -66, 6, -3],\n [-13, -61, -61, 0, 7, 42],\n [-5, 75, -17, 104, -5, -64],\n [57, 9, 33, -48, -3, -30],\n [-76, 73, 59, 53, -6, -4]]\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, -39, 120, -126, -27, 86],\n [41, -38, -7, 31, -27, -82],\n [50, -152, 141, -89, -110, -87],\n [-44, -38, 126, -110, -42, 50],\n [-15, -18, 49, -30, -32, 3],\n [-82, 10, 125, -131, 6, 99]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-26, -42, 136, -26, -112, -125],\n [-65, 49, 32, 26, -21, -8],\n [-26, 2, 48, 0, -38, -38],\n [-1, -27, 56, -16, -47, -55],\n [-66, 22, 88, 10, -68, -63],\n [-99, 99, 0, 54, 9, 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[[-52, 0, 4, -108, -40, -8],\n [-38, 54, 68, -54, 22, 44],\n [-32, -51, -59, -90, -73, -52],\n [35, 18, 19, 81, 44, 22],\n [27, 15, 16, 63, 35, 18],\n [-16, 33, 41, -18, 19, 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[[-66, -22, 59, -103, -42, 72],\n [56, 98, 3, 88, -75, -84],\n [-26, -62, -112, -21, 63, 10],\n [-92, -47, 18, -133, -33, 87],\n [82, 103, -10, 126, -54, -107],\n [-26, 26, 10, -33, -63, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[-57, -60, 57, 11, 49, 65],\n [-10, 28, 50, 4, 36, 56],\n [-43, -71, 28, 11, 28, 31],\n [-71, 56, 21, -44, 6, 46],\n [-11, -40, -69, -17, -51, -71],\n [-13, -89, -12, 17, 0, -19]]\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 6x6 matrix:\n[[67, 60, 76, 118, -46, 65],\n [93, 18, 30, 82, -61, 67],\n [29, 96, -10, -19, 1, -77],\n [-10, 98, 72, 65, 10, -14],\n [28, -20, 30, 57, -27, 64],\n [160, 82, -66, -20, -73, -52]]\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 6x6 matrix:\n[[12, 3, -3, -18, 12, 9],\n [20, 5, -5, -30, 20, 15],\n [12, 3, -3, -18, 12, 9],\n [36, 9, -9, -54, 36, 27],\n [-32, -8, 8, 48, -32, -24],\n [-20, -5, 5, 30, -20, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[28, -91, -58, -106, -90, -96],\n [56, 16, 104, 8, 40, -16],\n [-28, -35, -82, -34, -50, -16],\n [14, 4, 26, 2, 10, -4],\n [-49, 139, 79, 163, 135, 150],\n [-35, -55, -115, -55, -75, -30]]\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, 39, 42, 5, -4, 11],\n [-16, -24, 0, 40, -32, 32],\n [-14, -3, -18, -25, 20, -23],\n [62, 45, 48, 5, -4, 12],\n [52, 48, 30, -30, 24, -19],\n [102, 99, 54, -75, 60, -51]]?\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 6x6 matrix:\n[[-31, 23, -103, -74, 138, 62],\n [-87, 41, 143, 32, -14, -72],\n [60, -5, -82, 15, 70, -92],\n [69, -7, -101, -4, -2, 64],\n [-11, 7, 79, 32, -105, 46],\n [-134, 34, 128, -42, -47, 136]]\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, 90, -30, 104, -4, 53],\n [50, -100, 62, -149, 14, -78],\n [50, -100, -40, -30, -20, -10],\n [-5, 10, 4, 3, 2, 1],\n [-10, 20, -58, 83, -18, 46],\n [15, -30, -48, 33, -18, 21]]?\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[[-25, 122, 77, -64, -23, 0],\n [-34, -84, 13, -10, 58, 65],\n [-39, -131, 71, -86, 141, 130],\n [78, 93, -43, 50, -92, -153],\n [-26, -62, -18, 46, 6, -4],\n [-18, 77, 90, -100, 28, 46]]?\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, 10, 5, 6, 10, -3],\n [12, 20, 10, 12, 20, -6],\n [6, 10, 5, 6, 10, -3],\n [6, 10, 5, 6, 10, -3],\n [42, 70, 35, 42, 70, -21],\n [-12, -20, -10, -12, -20, 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[[-36, -21, -57, -6, 27, 18],\n [-70, 97, 92, 91, -102, 104],\n [84, 24, 62, -30, 2, -36],\n [78, 8, 17, -53, 39, -30],\n [19, 42, -15, -41, 49, 55],\n [-15, -99, -10, 39, -46, -117]]\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[[-68, 0, 8, -11, -9, -44],\n [7, 81, 221, -121, -90, 199],\n [-141, 111, 65, -103, -8, 27],\n [58, -1, 39, 16, -10, 121],\n [93, -126, -69, 139, 12, 9],\n [38, 35, 34, 4, 6, 158]]\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 6x6 matrix:\n[[49, -12, -8, 39, 134, -21],\n [37, 34, -11, 11, 65, -35],\n [58, 68, -86, 70, 50, -166],\n [35, 210, 25, -115, -55, -25],\n [63, 60, -68, 61, 80, -137],\n [-16, 24, 76, -88, -16, 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[[-49, 5, 49, 7, -17, 84],\n [-14, -34, -24, -40, -34, -78],\n [-35, 3, 136, -16, -37, 99],\n [56, -36, -53, -51, -14, -169],\n [98, 70, -63, 91, 112, 42],\n [49, -17, -78, -18, 11, -125]]?\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 6x6 matrix:\n[[-26, 31, -12, -30, -33, 100],\n [30, -58, -68, 14, -77, -43],\n [48, -111, -110, -22, -104, -143],\n [29, 60, 11, 0, 28, 70],\n [-146, -6, -30, -109, -52, 3],\n [63, -7, 64, 117, 65, -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[[-66, 68, 32, 12, 34, -8],\n [6, 24, 30, -30, 72, 6],\n [11, -28, 23, -27, -4, -17],\n [4, 8, -5, 2, 13, 8],\n [22, 32, -65, 44, 19, 50],\n [9, 72, -132, 111, -3, 87]]?\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, -8, 34, -46, 92, 46],\n [-27, -175, -186, 74, -127, -61],\n [-94, -121, -38, 7, -20, -19],\n [-100, -118, 82, 19, 16, -10],\n [-110, -121, 93, 34, -21, -28],\n [-13, 70, 2, -75, -197, -12]]\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[[85, -64, 22, -36, 95, 18],\n [-5, -39, 0, 5, 31, 129],\n [20, 59, 11, 25, -59, -87],\n [-80, 21, -32, -23, -28, -105],\n [-10, 32, 2, 28, -44, 12],\n [-55, -69, -36, -89, 89, -93]]?\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[[-53, 44, 53, 3, -72, -126],\n [35, -7, -49, 26, 56, 55],\n [-70, -3, 24, 73, -74, -157],\n [20, -36, -92, 120, 64, 4],\n [62, 32, -6, -86, 59, 129],\n [50, -42, -54, 4, 70, 116]]\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, 0, 73, -14, -4, -16],\n [88, 78, 30, 20, -20, 58],\n [-72, -72, -48, 0, 0, -36],\n [-58, -21, 89, -82, 78, -89],\n [21, 102, -67, -46, 104, 16],\n [5, 42, -31, -22, 48, 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[[20, 28, -8, 4, 32, 28],\n [0, 0, 0, 0, 0, 0],\n [-50, -70, 20, -10, -80, -70],\n [35, 49, -14, 7, 56, 49],\n [-50, -70, 20, -10, -80, -70],\n [-15, -21, 6, -3, -24, -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[[4, 24, -21, 58, -116, -111],\n [3, -18, 34, 12, -13, 1],\n [-74, -28, 5, -20, 66, 123],\n [41, 2, 5, -40, 61, 18],\n [-7, 10, -29, -34, 57, 42],\n [80, 8, 22, -10, -4, -64]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 22, -75, -12, 2, -51],\n [-15, -39, -31, -11, 23, 41],\n [-80, -116, -9, -90, 59, 21],\n [143, -45, -73, -138, -132, -22],\n [-124, -38, 115, -3, 91, 80],\n [-33, -99, -55, -52, 37, 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[[-52, 60, 81, -8, -76, -74],\n [43, -54, -90, -8, 57, 78],\n [-23, 6, -72, -72, -61, 46],\n [-35, 18, -63, -80, -81, 36],\n [-64, 60, 27, -56, -112, -38],\n [-24, 24, 18, -16, -40, -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[[-52, 91, 83, 106, 177, -61],\n [54, -59, -68, -9, -151, 47],\n [60, -20, -37, -36, -77, 61],\n [102, 79, 33, -23, 96, 104],\n [-16, 103, 103, 5, 250, -10],\n [82, -89, -2, -132, 102, 78]]\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 6x6 matrix:\n[[69, -53, -174, -57, 75, -120],\n [1, -9, 76, -41, 27, 124],\n [-6, 18, 9, 23, -3, -17],\n [70, -118, -137, -103, 164, -23],\n [-28, 132, 107, 117, -34, -7],\n [-78, -34, 121, -51, -110, 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[[-220, -121, 63, -40, 150, 25],\n [-65, 5, 1, -68, 138, 25],\n [66, 38, -53, -47, -3, -92],\n [-92, 36, 151, -29, 39, 99],\n [24, 87, 157, -54, -66, -4],\n [-20, 83, -20, -7, 42, 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[[-4, 28, 32, 28, 8, 12],\n [-8, 56, 64, 56, 16, 24],\n [9, -63, -72, -63, -18, -27],\n [-6, 42, 48, 42, 12, 18],\n [-1, 7, 8, 7, 2, 3],\n [-6, 42, 48, 42, 12, 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[[-14, -4, 33, -84, -19, 115],\n [-97, 68, 134, 23, -42, 85],\n [30, -36, -63, 88, -19, -65],\n [-72, 94, 122, -50, 42, 10],\n [-58, 19, 72, 31, -60, 90],\n [105, -62, -139, -43, 65, -106]]\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[[110, 50, 94, 23, 12, 86],\n [-99, 39, -22, -4, -21, -47],\n [-61, 13, 20, -5, 11, 28],\n [-104, 24, 16, -8, 8, 20],\n [-37, -23, -32, -9, -1, -25],\n [66, -166, -110, -25, 20, -49]]\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[[52, 13, -41, 57, -56, 98],\n [6, -21, -32, -26, 35, 17],\n [37, -20, 27, 60, -52, 75],\n [-10, -25, -26, -48, 57, -13],\n [-28, -97, -1, -103, 134, -32],\n [-7, 77, 10, 45, -72, -31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-20, -37, -40, -43, -44, -42],\n [58, -117, 30, 101, -66, -139],\n [144, 5, -50, 48, -43, -30],\n [56, 55, 162, 26, 81, 10],\n [-7, 45, 141, 35, 126, -9],\n [-53, 31, 29, -17, -50, 158]]\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, 3, -58, -27, -1, -54],\n [-104, 10, 82, 54, 16, 88],\n [-68, 25, -5, -9, 30, 64],\n [-92, 43, 67, 117, 44, 52],\n [-48, 84, -28, 108, 80, 0],\n [-24, -63, 56, -81, -55, 60]]\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 6x6 matrix:\n[[-100, -50, -40, 80, 10, -100],\n [-100, -50, -40, 80, 10, -100],\n [90, 45, 36, -72, -9, 90],\n [70, 35, 28, -56, -7, 70],\n [100, 50, 40, -80, -10, 100],\n [-40, -20, -16, 32, 4, -40]]\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[[26, -60, -70, 56, 62, -24],\n [-18, -40, -8, -8, -23, 18],\n [-79, -130, -21, -56, -106, 74],\n [-9, 50, 37, -32, -26, 6],\n [5, 20, 75, 13, -19, 11],\n [13, 50, -7, -8, 21, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-46, 55, 58, 17, -28, 17],\n [72, 21, -48, -97, 65, 20],\n [-4, 17, 66, 63, -19, -162],\n [4, 51, 58, 53, -29, -94],\n [-26, -19, 1, 109, -79, 35],\n [-82, 41, 111, 85, -57, -89]]\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 6x6 matrix:\n[[9, -9, -18, 24, -21, 9],\n [12, -12, -24, 32, -28, 12],\n [-24, 24, 48, -64, 56, -24],\n [12, -12, -24, 32, -28, 12],\n [24, -24, -48, 64, -56, 24],\n [27, -27, -54, 72, -63, 27]]\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[[-52, -99, -98, 50, 41, -16],\n [46, 83, 83, -50, -37, 7],\n [-16, -88, -72, -96, -8, -120],\n [-60, -143, -130, -32, 27, -98],\n [-28, -35, -38, 50, 25, 20],\n [-18, -48, -25, -170, -38, -137]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-71, -87, 84, -5, -99, -107],\n [-110, 47, -11, 37, -90, -131],\n [-87, 31, -32, 3, -85, -91],\n [108, 63, -85, 109, 8, 81],\n [-10, -5, -19, -39, -6, 9],\n [-1, -70, 72, 50, -64, -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[[24, 59, -66, -24, -36, 24],\n [7, -18, -34, -4, -53, 18],\n [-15, 45, 68, 13, 104, -32],\n [-5, 100, 22, 21, 54, 4],\n [-37, -47, 28, 94, -103, 54],\n [13, 18, -14, -30, 27, -14]]\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, 4, -7, 10, 0, -6],\n [-25, 20, -35, 50, 0, -30],\n [35, -28, 49, -70, 0, 42],\n [30, -24, 42, -60, 0, 36],\n [15, -12, 21, -30, 0, 18],\n [50, -40, 70, -100, 0, 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[[65, -192, 46, 106, -147, -14],\n [-50, 60, 4, 73, -10, -115],\n [-31, 14, -10, 76, -39, -68],\n [54, -215, 32, 132, -174, 6],\n [83, -14, 18, -67, 21, 3],\n [80, -205, 36, 86, -146, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -80, -80, -24, 40, 40],\n [0, -60, -60, -18, 30, 30],\n [0, -20, -20, -6, 10, 10],\n [0, 80, 80, 24, -40, -40],\n [0, 20, 20, 6, -10, -10],\n [0, -50, -50, -15, 25, 25]]?\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, 42, 48, 44, 4, -2],\n [-18, 52, -40, 6, -78, -128],\n [-81, 29, 103, -68, 39, -69],\n [-45, 20, 50, 148, 106, 90],\n [-38, -12, -83, -26, -45, -76],\n [-60, -19, -82, 19, -5, -39]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[45, 195, -90, 127, -66, -90],\n [3, 15, 77, 135, -30, -60],\n [62, 28, -26, -74, 8, -66],\n [-146, -51, -46, -80, 120, 99],\n [-69, 58, -97, -5, 56, -45],\n [54, 17, -49, 9, -75, -9]]\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, -48, -49, 53, 55, -2],\n [-40, -82, -56, 92, 40, -18],\n [25, -68, -71, 75, 81, -2],\n [-50, 64, 78, -70, -98, -4],\n [35, -34, -45, 37, 59, 4],\n [-45, 72, 83, -79, -101, -2]]\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[[94, -63, 43, -33, -62, -24],\n [-50, 108, 16, 39, 17, -13],\n [17, 17, 30, -28, -44, -92],\n [69, 102, 64, 23, -88, -144],\n [149, 64, 59, 15, -144, -214],\n [-109, 34, -82, -39, 130, 262]]\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, 2, -3, -4, -3, 7],\n [-9, -2, 3, 4, 3, -7],\n [18, 4, -6, -8, -6, 14],\n [81, 18, -27, -36, -27, 63],\n [36, 8, -12, -16, -12, 28],\n [-72, -16, 24, 32, 24, -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 6x6 matrix:\n[[8, 4, 8, 4, -18, 2],\n [20, 10, 20, 10, -45, 5],\n [28, 14, 28, 14, -63, 7],\n [-16, -8, -16, -8, 36, -4],\n [24, 12, 24, 12, -54, 6],\n [24, 12, 24, 12, -54, 6]]\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 6x6 matrix:\n[[57, -11, 132, -105, 40, -35],\n [162, 70, 48, -86, -36, 34],\n [-66, 68, -60, 32, 72, 20],\n [-170, -82, -28, 54, -24, -116],\n [-108, -17, 58, -49, 29, -136],\n [25, -61, 176, -83, 158, 37]]\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 6x6 matrix:\n[[6, -86, -6, 70, 9, -53],\n [-148, -109, -44, 6, 79, -31],\n [123, -55, 26, 81, -60, -69],\n [-32, -35, 20, -40, 20, -123],\n [-52, 2, -46, 112, 85, 114],\n [114, -55, 83, 29, -123, -118]]\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 6x6 matrix:\n[[-68, -69, -50, 62, 68, 24],\n [-103, -93, 65, 76, 103, 21],\n [-78, -81, -80, 74, 78, 30],\n [-94, -84, 70, 68, 94, 18],\n [-81, -81, -45, 72, 81, 27],\n [79, 75, -5, -64, -79, -21]]\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[[-11, -18, 28, -11, 35, 2],\n [41, -10, 39, 62, -109, -19],\n [34, -33, -18, 126, -156, -76],\n [40, 17, 59, 13, -66, 21],\n [17, 31, -2, -25, -15, 30],\n [-38, 61, -36, -56, 112, 30]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-62, -40, 24, 18, 34, -14],\n [88, 61, -24, 28, -23, -31],\n [-49, 59, 24, 150, 62, -170],\n [-53, 94, 56, 188, 65, -151],\n [57, -8, -28, -127, -71, 143],\n [2, -102, 28, -50, 10, 111]]\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[[-78, -70, -89, -37, 76, -16],\n [-70, 138, -77, -122, 3, 110],\n [40, 28, -74, -84, -31, 107],\n [-70, -25, -122, -147, -17, 135],\n [-4, 123, 60, -17, -29, 47],\n [164, -168, 90, 106, -40, -36]]?\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 6x6 matrix:\n[[27, -42, -24, -48, 9, -39],\n [-11, 6, 52, -20, 35, 51],\n [34, -51, -40, -57, 3, -58],\n [33, -37, -50, 35, -16, -55],\n [-58, 82, 75, 64, 4, 101],\n [-56, 105, -39, 137, -95, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-68, -95, -4, -49, 141, -22],\n [-202, -70, 65, -144, 24, -98],\n [126, -6, 80, -50, -9, -6],\n [-216, 141, 80, 19, -156, 12],\n [98, -36, 16, 51, 145, 25],\n [14, 6, 96, -13, 22, -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[[19, -164, -75, 109, 186, 84],\n [39, -146, -213, 263, 83, -83],\n [219, -42, 187, -140, 50, 20],\n [-113, -30, -137, 91, 74, 99],\n [147, -66, -69, 40, 110, 20],\n [-62, 122, -60, -15, -105, -12]]\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, -75, -71, -11, -57, 81],\n [58, -47, -42, -1, -33, 63],\n [-16, 12, 14, 8, 12, 0],\n [-16, 12, 14, 8, 12, 0],\n [-46, 33, 44, 35, 39, 27],\n [2, 1, -8, -21, -9, -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[[123, -34, 17, 54, -19, -7],\n [90, 21, -23, -16, 18, 86],\n [11, 20, 64, 22, -12, -76],\n [41, -11, -1, 14, -4, 8],\n [98, -32, 37, 60, -25, -45],\n [52, -47, -43, 20, -6, 46]]\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[[-26, -9, -25, 25, -9, 51],\n [3, 12, 15, 0, 27, -33],\n [51, -5, 24, -55, -36, -44],\n [-52, 1, -29, 55, 27, 55],\n [100, -37, 17, -115, -135, -19],\n [9, 17, 24, -5, 36, -52]]\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 6x6 matrix:\n[[-6, 23, 8, -69, -13, -79],\n [12, -31, -16, 83, 11, 93],\n [-6, 23, 8, -69, -13, -79],\n [36, -42, -48, 62, -18, 58],\n [-6, 20, 8, -58, -10, -66],\n [-21, 16, 28, -5, 19, 3]]\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[[10, -60, 50, -40, -40, -50],\n [-3, 18, -15, 12, 12, 15],\n [-7, 42, -35, 28, 28, 35],\n [-2, 12, -10, 8, 8, 10],\n [3, -18, 15, -12, -12, -15],\n [3, -18, 15, -12, -12, -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[[9, -15, -12, -6, -27, -12],\n [-24, 40, 32, 16, 72, 32],\n [-27, 45, 36, 18, 81, 36],\n [-12, 20, 16, 8, 36, 16],\n [24, -40, -32, -16, -72, -32],\n [15, -25, -20, -10, -45, -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 6x6 matrix:\n[[31, 1, 13, 52, 16, 24],\n [216, 0, -91, 162, 103, -34],\n [233, -58, -17, 179, 54, -25],\n [19, -202, 10, 83, -27, -61],\n [99, -26, 55, 91, -2, 27],\n [140, 111, 2, 87, 60, 55]]\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[[165, -55, 6, -58, 64, -16],\n [-42, -8, 46, -59, -61, -23],\n [42, -3, -11, -15, -21, -30],\n [20, 43, -67, 38, -32, -9],\n [-2, 105, -113, 28, -17, 110],\n [52, -17, -41, 98, 63, -42]]\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, 5, -50, 50, 45, 45],\n [-18, -6, 60, -60, -54, -54],\n [-21, -7, 70, -70, -63, -63],\n [-3, -1, 10, -10, -9, -9],\n [6, 2, -20, 20, 18, 18],\n [-3, -1, 10, -10, -9, -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[[21, 6, -52, 19, -24, 4],\n [-25, -26, 7, 11, 11, -3],\n [-7, -55, -27, 120, 49, 70],\n [-5, 25, 95, -50, 35, 0],\n [80, 137, 183, -117, 55, 34],\n [67, 47, -95, 8, -59, 4]]\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[[-200, -2, 67, 147, 35, -149],\n [111, -1, -8, -72, -25, 127],\n [-116, 35, 36, 62, 104, -129],\n [-149, -67, 12, 104, -61, -87],\n [81, 22, 26, -64, 45, 116],\n [34, 81, 52, -18, 109, 21]]\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, -42, -12, -141, 21, -45],\n [-22, 14, 26, -52, 26, -40],\n [30, -70, -50, -100, -10, 0],\n [-29, 49, 43, 34, 19, -20],\n [-4, -14, 0, -65, 13, -25],\n [20, 0, -20, 90, -30, 50]]\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, 185, 118, 0, -95, -56],\n [47, 64, 77, 93, 122, -28],\n [-59, -33, -18, 56, -12, 57],\n [-126, 7, 4, 140, -6, 98],\n [46, -30, 27, 104, 7, -46],\n [71, 132, 101, -27, 15, -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[[-138, -218, 61, -76, 122, 7],\n [108, 190, -47, 62, -88, -23],\n [-42, 32, 20, 58, -32, -142],\n [-83, 114, 123, 1, -61, -4],\n [21, 4, -34, 27, 1, -57],\n [-10, 16, 54, -74, 13, 164]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[160, -63, -9, 116, -155, 27],\n [-227, 18, 58, -53, 135, -93],\n [-319, 71, -103, 32, 66, -80],\n [43, 40, -149, 39, -14, -136],\n [31, -13, -123, 37, -66, -56],\n [-88, -91, -78, -30, -48, -44]]\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[[-22, -24, -4, 24, -67, -24],\n [20, -60, 80, 0, -130, 0],\n [-28, 54, -84, 8, 112, -8],\n [-60, 0, -72, 48, -30, -48],\n [-42, -9, -42, 36, -42, -36],\n [8, 21, -10, -12, 53, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-27, 69, -15, -52, 71, -34],\n [19, 28, 40, -38, 58, -33],\n [64, -35, 85, -2, 13, -15],\n [32, -76, 20, 56, -76, 36],\n [1, 22, 10, -22, 32, -17],\n [41, -34, 50, 10, -8, -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[[20, 16, 20, -12, 12, -16],\n [10, 8, 10, -6, 6, -8],\n [80, 64, 80, -48, 48, -64],\n [-100, -80, -100, 60, -60, 80],\n [-30, -24, -30, 18, -18, 24],\n [-70, -56, -70, 42, -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 6x6 matrix:\n[[-84, -144, -60, 116, -38, -80],\n [-75, -75, -70, 70, -84, 26],\n [81, 18, 6, -46, 117, -32],\n [-15, 0, -60, 0, -46, 84],\n [-24, -33, 88, 40, 21, -142],\n [12, 30, 64, -16, 18, -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[[-67, -77, 102, 24, -51, 45],\n [70, -24, 9, 60, 155, 5],\n [-77, -29, 121, 85, -6, -35],\n [-28, -116, 29, -24, -49, 0],\n [-106, -142, 79, -20, -143, -60],\n [-67, 83, 2, -15, -110, -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[[-22, 91, -157, 59, 31, -40],\n [34, 158, -60, -11, -123, -238],\n [79, -59, 112, -89, -57, -51],\n [-13, 66, -149, 85, 17, 23],\n [27, 109, -135, 48, -49, -92],\n [-92, -48, 74, -12, 86, 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[[-10, -58, -31, 64, 71, 191],\n [49, -62, 4, 73, 65, 127],\n [190, -61, 96, 126, -4, -26],\n [191, -28, 56, 63, 55, -75],\n [127, 12, -13, 93, 16, 19],\n [-21, 50, -110, 63, 7, 144]]\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[[120, -72, 34, -10, -74, -158],\n [-134, 94, -63, 32, 9, 267],\n [-48, 46, 37, -12, 59, -13],\n [145, -110, 55, -32, -109, -138],\n [33, -36, -11, -1, -117, 116],\n [-66, -66, 51, -90, 118, 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 6x6 matrix:\n[[-55, 128, -24, -104, -47, 41],\n [-11, 1, -41, -35, -9, -113],\n [-118, -42, -12, 30, -81, -29],\n [12, 45, 193, -46, -29, 93],\n [74, -149, -49, 79, 145, -64],\n [-15, -10, -52, 6, 30, 19]]\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[[66, 61, -61, -118, 62, 4],\n [-26, 64, 159, 146, -148, 30],\n [-52, 68, -51, -24, 128, 86],\n [-67, -34, -18, 73, 97, 5],\n [58, -45, 55, -6, -162, -60],\n [44, 111, 17, -52, -8, 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 6x6 matrix:\n[[-40, 16, 28, 12, -32, 16],\n [50, -20, -35, -15, 40, -20],\n [-10, 4, 7, 3, -8, 4],\n [-70, 28, 49, 21, -56, 28],\n [-90, 36, 63, 27, -72, 36],\n [70, -28, -49, -21, 56, -28]]\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, 42, -6, -54, -42, 12],\n [32, 56, -8, -72, -56, 16],\n [16, 28, -4, -36, -28, 8],\n [20, 35, -5, -45, -35, 10],\n [40, 70, -10, -90, -70, 20],\n [-32, -56, 8, 72, 56, -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 6x6 matrix:\n[[-41, -121, -121, 1, 42, -103],\n [-32, 45, 46, 20, 34, 27],\n [-40, 19, -8, 68, 48, -17],\n [-11, 92, 85, 31, 14, 62],\n [171, 0, 32, -135, -187, 69],\n [-4, -111, -101, -32, 1, -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[[-103, 50, 25, 1, 32, 27],\n [67, 26, -63, -42, 48, 19],\n [61, -30, 5, -2, -54, -29],\n [-3, -82, -37, 68, 88, 17],\n [38, 124, -42, -108, 12, 26],\n [151, -10, -101, -45, 52, 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[[4, 20, -6, 4, 8, 18],\n [-2, -10, 3, -2, -4, -9],\n [10, 50, -15, 10, 20, 45],\n [4, 20, -6, 4, 8, 18],\n [-14, -70, 21, -14, -28, -63],\n [20, 100, -30, 20, 40, 90]]\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 6x6 matrix:\n[[28, -15, -61, -65, 111, -5],\n [7, 147, -116, 106, -51, -41],\n [-32, 75, 106, 110, -120, 53],\n [-14, -70, -39, -67, 45, -30],\n [15, 189, -262, 82, 24, -105],\n [-54, 145, -78, 88, -78, -124]]\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[[-5, -5, 10, -8, 8, 5],\n [35, 35, -70, 56, -56, -35],\n [35, 35, -70, 56, -56, -35],\n [-20, -20, 40, -32, 32, 20],\n [25, 25, -50, 40, -40, -25],\n [-25, -25, 50, -40, 40, 25]]\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, 11, 99, 38, 45, 32],\n [101, 158, 24, -26, -96, 2],\n [75, -1, -75, -72, -120, -73],\n [182, -4, 69, 1, -87, -7],\n [-150, 63, -119, -61, 14, -26],\n [-66, 69, 10, 6, 53, 43]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[136, -36, 11, 12, 69, -90],\n [72, -2, -1, 20, 57, -63],\n [-16, -14, 6, -16, -30, 27],\n [0, 100, -40, 80, 120, -90],\n [128, -38, 12, 8, 60, -81],\n [-56, -24, 11, -36, -75, 72]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[31, 56, -8, 79, 10, -98],\n [-78, -66, -38, -21, -64, 60],\n [14, 39, 184, -7, -95, 106],\n [95, 0, -20, 91, 114, -116],\n [6, -49, -3, -50, 32, 62],\n [46, -26, 65, 73, 19, -33]]?\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[[-23, 8, -20, -15, -22, 52],\n [-19, -18, -15, -47, -24, 41],\n [-174, 108, -166, -6, 80, 10],\n [-53, 18, -49, -25, 8, 23],\n [133, -76, 127, 12, -70, 10],\n [-35, -6, -30, -46, -24, 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[[61, 56, 91, 90, -53, 44],\n [13, 48, 165, 60, -63, 102],\n [-4, 29, -9, -50, -105, -94],\n [117, -67, -116, -107, -138, -126],\n [-2, 7, -238, -101, -48, -207],\n [-183, 40, 39, -55, 49, 12]]?\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[[98, 57, 126, -80, -9, -92],\n [-52, 49, -30, -117, 18, 63],\n [49, 110, -139, -67, -133, 127],\n [-61, -44, -147, 15, -26, 192],\n [30, -100, -10, 156, -14, 2],\n [-58, 46, 10, -44, 38, -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[[16, 51, 98, -66, 20, -31],\n [22, 91, 122, -94, 28, 125],\n [44, -13, -19, -22, 28, 10],\n [59, -6, -92, 149, 106, 51],\n [9, 53, 84, -93, -2, 86],\n [43, -67, -175, 195, 78, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-27, 142, -71, -26, 32, 60],\n [52, -98, 62, -17, 3, -66],\n [-70, 11, -43, 133, -85, 75],\n [53, -140, -9, 104, 21, -63],\n [109, -120, 11, 90, 20, -78],\n [49, 38, -99, -40, 164, -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[[32, -28, -13, -81, 22, -5],\n [25, 48, 6, -31, 76, 0],\n [-80, 55, 64, 51, -148, -16],\n [41, 43, -6, -36, 112, 4],\n [-59, 98, 61, 62, -62, -9],\n [7, 15, 11, -45, 2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-75, -15, -25, -40, -15, 10],\n [60, 12, 20, 32, 12, -8],\n [-26, 54, 2, 24, 30, 36],\n [94, -33, 22, 17, -12, -41],\n [-65, -87, -35, -82, -57, -32],\n [93, 63, 39, 78, 45, 12]]\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, 68, 23, -26, 48, 19],\n [48, -29, -15, 4, 71, 101],\n [-82, 79, -115, 46, -21, -3],\n [-28, 80, 91, -42, 5, -75],\n [114, -94, 65, -44, 51, 79],\n [2, -30, -94, 42, 10, 70]]?\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[[9, 28, 71, 6, -61, -55],\n [-87, 44, 109, 6, -113, -107],\n [-185, 100, 83, -86, 1, 59],\n [-127, 29, 46, -13, -49, -41],\n [184, -103, -78, 93, -14, -76],\n [42, -92, -71, 80, -36, -96]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-57, -102, 32, -49, -196, 86],\n [-135, -3, 48, -55, -65, 64],\n [-13, -96, -35, 119, -16, 45],\n [107, -31, -53, 63, -75, 31],\n [34, 143, 21, 6, 9, -37],\n [-28, -56, 33, -40, -32, -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, 2, -64, 84, -179, -49],\n [-20, -66, -60, 90, -86, 1],\n [23, 92, -56, 70, -153, -127],\n [79, 48, 79, -41, 134, -27],\n [-36, 1, -62, 9, -94, 1],\n [77, 40, -79, 129, -126, -127]]\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[[-1, 124, 50, 6, 14, 1],\n [-39, 66, -84, 63, -66, 30],\n [66, 70, 64, -50, 28, -12],\n [105, -59, -94, -46, -62, 11],\n [-39, -100, 10, 4, 26, -11],\n [66, 95, 6, -27, -16, 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[[-45, 97, -100, -117, -93, -100],\n [25, -64, 49, 73, 55, 56],\n [21, -75, 53, 82, 67, 63],\n [14, -40, 17, 43, 28, 27],\n [76, -13, 60, 47, -4, 41],\n [-18, -64, 22, 54, 66, 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 6x6 matrix:\n[[54, -14, -34, -56, 8, -38],\n [146, -156, -118, 32, -50, -28],\n [65, 87, 12, 39, 48, -24],\n [-30, 136, 88, -114, 24, 24],\n [-75, -15, 20, -65, -17, 15],\n [-54, 78, 76, 30, -1, 59]]\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 6x6 matrix:\n[[2, -6, 6, -8, -5, 3],\n [6, -18, 18, -24, -15, 9],\n [-10, 30, -30, 40, 25, -15],\n [-4, 12, -12, 16, 10, -6],\n [12, -36, 36, -48, -30, 18],\n [-6, 18, -18, 24, 15, -9]]\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[[22, 11, 26, 30, 15, 15],\n [-14, -62, 13, -40, 17, -14],\n [27, -140, -66, -34, 49, 10],\n [-72, -87, 164, -32, -39, -49],\n [-2, -82, -64, -90, 60, -12],\n [4, -11, 48, 165, -139, 22]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-20, 80, -100, -70, -80, -10],\n [6, -24, 30, 21, 24, 3],\n [2, -8, 10, 7, 8, 1],\n [2, -8, 10, 7, 8, 1],\n [-14, 56, -70, -49, -56, -7],\n [2, -8, 10, 7, 8, 1]]\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[[221, 1, 2, 87, 107, 235],\n [-54, -40, 68, 5, -54, -106],\n [-5, -132, -29, -4, -6, -106],\n [103, 64, -32, 19, 83, 155],\n [66, 81, 42, 63, 96, 132],\n [74, -89, -42, -2, 38, -10]]\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[[44, 82, 3, 69, -93, -105],\n [-45, -48, 105, 51, 79, 97],\n [30, 216, 13, 1, 74, -209],\n [21, 111, 4, -9, 49, -100],\n [-41, 86, 172, 223, -73, -86],\n [66, 128, -10, -4, 5, -92]]?\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, 73, -9, -41, 72, -40],\n [47, 133, 28, 12, 105, -41],\n [-33, 64, 7, 25, 33, -1],\n [38, -50, 20, -48, -42, -14],\n [-60, 40, -38, 47, 39, 21],\n [-37, -42, -20, 12, -33, 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[[25, -117, 135, -52, -43, -31],\n [22, -66, 74, -34, -16, -6],\n [93, -63, 51, -75, 60, 99],\n [-63, 15, -1, 42, -57, -83],\n [-35, -21, 35, 14, -49, -63],\n [-52, 48, -44, 46, -26, -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, -64, -28, -78, -26, -104],\n [-16, -67, 57, 153, 16, 111],\n [67, 19, -42, -55, 39, -55],\n [-66, 16, -15, -129, -75, -159],\n [102, -170, -69, 4, 84, -41],\n [-45, 84, 90, 90, -50, 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[[-50, -65, 80, 100, -55, 35],\n [115, 45, -142, 56, -27, -38],\n [88, 18, -94, 66, -42, 18],\n [6, 14, 6, -78, 22, 84],\n [-85, -7, 67, -39, 49, -120],\n [100, -5, -79, 97, -79, 119]]?\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[[-29, -91, -141, -31, 86, 18],\n [-113, 52, 24, 14, 24, -26],\n [165, -61, -81, 18, -11, 55],\n [97, 29, 93, 41, -106, -3],\n [-22, 30, -30, 78, -4, 4],\n [-9, -49, 15, -139, 52, -5]]\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 6x6 matrix:\n[[20, 36, 32, -12, 12, -20],\n [5, 9, 8, -3, 3, -5],\n [50, 90, 80, -30, 30, -50],\n [-50, -90, -80, 30, -30, 50],\n [35, 63, 56, -21, 21, -35],\n [-35, -63, -56, 21, -21, 35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-60, 10, -97, 98, -9, 45],\n [8, -21, 9, -17, 13, -65],\n [12, -34, 13, -26, 21, -105],\n [36, -32, 53, -64, 21, -105],\n [-44, -7, -74, 69, 2, -10],\n [-24, 28, -34, 44, -18, 90]]\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 6x6 matrix:\n[[-18, 70, 74, 75, -107, -58],\n [13, -21, 101, -18, -82, 32],\n [-5, -33, 10, -49, 8, 37],\n [-3, -69, -93, -93, 123, 60],\n [-109, -5, -54, -108, 47, 27],\n [51, -59, -87, -29, 115, 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 6x6 matrix:\n[[-14, 49, 7, -70, 28, 42],\n [16, -56, -8, 80, -32, -48],\n [-14, 49, 7, -70, 28, 42],\n [16, -56, -8, 80, -32, -48],\n [16, -56, -8, 80, -32, -48],\n [2, -7, -1, 10, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[134, -87, 87, 62, 5, 114],\n [0, -71, -24, -23, -48, -88],\n [152, -115, 109, -10, -50, 164],\n [-115, 130, -76, 68, 93, -104],\n [-10, -55, -102, -59, 11, -98],\n [-80, 59, -89, -104, 9, -34]]\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[[-72, 72, 56, 24, 56, -72],\n [-55, 54, 26, 13, 33, -40],\n [107, -99, 51, 7, -5, -13],\n [131, -126, -18, -17, -53, 56],\n [-135, 126, -46, -3, 17, 0],\n [-66, 63, 1, 6, 22, -21]]\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, -15, -86, -36, 61, 36],\n [-26, -124, -19, -129, -95, -59],\n [58, -18, 27, -1, -21, -69],\n [96, 47, 20, 68, 30, -2],\n [-10, -57, 57, -42, -89, -87],\n [12, -112, -142, -142, 0, 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[[28, -42, -32, 19, -15, 12],\n [21, -17, 5, -22, 25, 38],\n [-7, 17, 21, -21, 20, 10],\n [21, -31, -23, 13, -10, 10],\n [56, -52, 0, -42, 50, 88],\n [-35, 53, 41, -25, 20, -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 6x6 matrix:\n[[45, 45, 18, -99, -18, -45],\n [-52, -31, 20, -5, -2, 34],\n [1, -27, -41, 117, 25, 1],\n [42, 31, 1, -47, -7, -42],\n [9, -18, -8, 8, 10, -55],\n [33, 44, 3, -38, -13, 11]]\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[[-46, -8, 116, 0, -76, 26],\n [24, 23, -141, 22, 81, -12],\n [4, 12, -54, 15, 29, 1],\n [51, -10, -70, -31, 55, -42],\n [-45, -24, 0, -93, -9, -72],\n [-99, 18, 10, 5, -37, 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[[86, -98, -4, -31, 7, -18],\n [30, -62, 12, 12, -90, -48],\n [-79, 47, -28, -1, -50, -42],\n [-70, 76, 36, 45, 19, 40],\n [48, -1, 80, 53, 63, 89],\n [4, 4, -32, -17, -33, -26]]?\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, -7, -14, 0],\n [24, -56, 56, -32, 40, -20],\n [9, 45, -81, -9, -18, 0],\n [-33, 99, -111, 45, -66, 30],\n [-72, 80, -32, 92, -76, 50],\n [-24, 56, -56, 32, -40, 20]]?\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[[-1, 111, -4, -20, 98, -92],\n [-54, 187, 95, -7, 3, -105],\n [-9, 272, 166, -72, -16, -110],\n [17, -11, -1, -100, -8, 73],\n [53, 93, -10, -50, -43, -94],\n [-114, -202, -45, 35, 58, 195]]\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, -13, 9, -32, 35, -39],\n [-125, 92, 176, 163, 103, -201],\n [116, -107, -153, -148, -111, 203],\n [-24, 18, 3, -51, 10, 1],\n [-110, 130, 125, 65, 80, -135],\n [-22, 0, 67, 111, 19, -65]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[-35, -65, -17, -135, 2, 103],\n [-39, 26, -87, -156, -110, 186],\n [-104, -68, -15, 21, 4, -38],\n [45, 56, 16, 113, 141, -175],\n [-54, -56, -68, -160, -110, 140],\n [58, -61, -43, -201, 5, 61]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[15, -6, -25, 20, 24, -37],\n [-8, -28, -30, 37, 47, -34],\n [5, 22, 25, -30, -38, 29],\n [68, 76, 30, -67, -89, 10],\n [4, -4, -10, 9, 11, -14],\n [-3, 30, 45, -48, -60, 57]]\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, -47, 41, 21, -58],\n [-41, 35, 4, -113, -118, -24],\n [64, 106, -39, -192, -57, -40],\n [15, 113, -4, -262, -92, 2],\n [77, 25, -18, -1, 104, 20],\n [-12, 52, -18, -122, -122, -52]]?\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 6x6 matrix:\n[[3, 8, 25, 17, -17, -3],\n [-138, -62, -79, 22, -130, 141],\n [3, -28, 38, -4, -16, 13],\n [78, -2, 43, -42, 86, -65],\n [24, 16, 53, 21, -9, -22],\n [-111, -32, -108, 8, -76, 101]]\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[[74, 67, 71, -81, -84, 56],\n [-82, -48, -146, 68, 26, 40],\n [-87, -110, -50, 82, -11, 67],\n [71, 126, -20, -70, 47, -89],\n [-85, -101, -58, 81, 3, 50],\n [-25, -99, 127, 53, 41, -71]]\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[[-116, 65, -44, -131, -18, 61],\n [70, -15, 7, 89, -13, -22],\n [-92, 104, -60, -20, -108, 96],\n [118, -69, 7, -13, 119, -100],\n [-106, 74, -4, 60, -148, 108],\n [-13, -62, 56, -25, 54, -31]]\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 6x6 matrix:\n[[-41, 110, 4, -54, 31, -106],\n [33, 29, 60, 68, 28, 7],\n [-70, -37, -22, -35, -5, 65],\n [87, -3, -48, 103, -14, 42],\n [34, 68, 115, 66, 56, -44],\n [-15, -101, 33, 56, -16, 161]]\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[[142, 62, -110, -78, 83, 96],\n [59, -55, -107, 32, -1, 4],\n [-17, -131, -35, 108, -13, -80],\n [-22, 2, 74, -18, 41, -24],\n [130, 50, -2, -84, 185, 54],\n [157, 119, -95, -114, 104, 132]]\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 6x6 matrix:\n[[-17, -38, -21, -3, 32, 0],\n [44, -62, 1, -16, 47, 23],\n [-47, 20, -140, 142, 90, -87],\n [171, -14, -33, 58, 43, -60],\n [11, 66, 7, 1, -80, -64],\n [-106, 54, -87, 97, 32, -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[[27, -87, -144, -34, -2, -18],\n [2, -14, 76, -32, 94, 26],\n [-3, 75, 6, 24, -170, -40],\n [-42, 60, 45, -54, 9, 9],\n [33, 27, 121, 84, -42, -2],\n [96, -174, -115, 6, 41, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[-26, -55, 79, -49, 26, -46],\n [-115, -92, -50, 8, -103, 71],\n [-7, -34, 88, -46, 45, -49],\n [103, 91, 58, -4, 103, -52],\n [-5, 16, 20, 10, 15, 31],\n [-65, -40, -25, 13, -53, 58]]\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[[-136, 22, -130, -50, -1, 82],\n [165, 8, 81, -1, -67, -106],\n [-65, 6, -50, -5, -54, 102],\n [-165, -2, -103, 24, 0, 147],\n [57, -54, 68, 15, 48, -40],\n [-23, 32, 53, 80, -41, 81]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-34, 29, -41, -61, 59, -31],\n [34, -25, 30, -60, -22, 69],\n [84, -35, -5, 22, -33, -10],\n [0, 27, 18, 129, -22, -80],\n [105, -23, 10, 22, -35, -26],\n [-86, 77, 21, 27, 41, -57]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-84, -4, 2, -54, -56, 24],\n [-32, 32, -38, 36, 30, -16],\n [38, 14, -15, 45, 44, -20],\n [120, -40, 50, 0, 10, 0],\n [-48, 48, -57, 54, 45, -24],\n [-8, 24, -28, 36, 32, -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[[17, -62, 25, -2, -69, -30],\n [-29, 168, 75, 78, -29, -54],\n [-106, 24, 22, -38, -98, 21],\n [129, 111, -47, 70, 253, 65],\n [131, -148, -13, -28, -44, 3],\n [29, -18, -31, -40, 3, 57]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-36, -36, 104, 16, -60, 52],\n [-18, -4, -67, 29, 47, -16],\n [-135, -95, 50, 120, -5, 75],\n [36, 10, 117, -55, -83, 26],\n [9, 13, -60, 2, 37, -25],\n [72, 50, -21, -65, -1, -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[[40, -15, -50, -40, -30, 35],\n [32, -12, -40, -32, -24, 28],\n [56, -21, -70, -56, -42, 49],\n [-32, 12, 40, 32, 24, -28],\n [32, -12, -40, -32, -24, 28],\n [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[[-74, 56, 51, 105, -39, -117],\n [-27, 44, 43, 49, -48, -62],\n [6, 84, 95, 23, -101, -41],\n [32, -44, 92, -94, -2, 52],\n [66, 52, 42, -52, -66, 58],\n [-5, 42, 158, -17, -68, -25]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, 32, 27, 103, 71, 9],\n [87, -1, -5, 1, 6, 49],\n [-70, -67, -13, 36, -45, 74],\n [-72, 52, 71, -134, -120, -162],\n [85, -9, -42, -11, 40, 45],\n [-21, -16, -4, 107, 55, 61]]\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, 47, 19, -8, 22, 1],\n [-63, -75, -71, -66, -134, 103],\n [65, 64, 49, 52, 105, -85],\n [-80, -38, 21, 109, 80, -97],\n [98, 35, -35, 21, 21, -49],\n [89, 4, -85, 82, 28, -105]]\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 6x6 matrix:\n[[58, 27, 37, 84, 73, -38],\n [81, -59, 48, -10, 64, 62],\n [30, -95, 15, -100, -5, 110],\n [76, -30, 46, 24, 70, 28],\n [48, 6, 30, 48, 54, -12],\n [32, -75, 17, -72, 5, 86]]\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, 152, -74, -42, -94, 2],\n [68, -70, 134, 118, -78, -80],\n [-194, -157, -7, 32, -115, 147],\n [67, -31, 5, -15, 145, -56],\n [8, 22, -178, -64, 58, 24],\n [-69, -35, 117, 38, -41, 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[[20, 90, -80, 20, 0, 0],\n [-12, -54, 48, -12, 0, 0],\n [0, 0, 0, 0, 0, 0],\n [2, 9, -8, 2, 0, 0],\n [-4, -18, 16, -4, 0, 0],\n [20, 90, -80, 20, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[30, -100, 0, 20, -100, -90],\n [27, -90, 0, 18, -90, -81],\n [30, -100, 0, 20, -100, -90],\n [-12, 40, 0, -8, 40, 36],\n [18, -60, 0, 12, -60, -54],\n [15, -50, 0, 10, -50, -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[[74, -44, 36, 42, 8, -4],\n [-58, 80, -18, -40, -46, -14],\n [91, -12, 132, 5, 16, -42],\n [105, -42, 139, 14, 56, -34],\n [20, 47, 24, 2, -27, -21],\n [39, -30, -122, 95, -43, 41]]\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[[-44, -45, 14, -7, -56, -31],\n [31, 55, -49, 45, 32, 6],\n [-72, -110, 84, -74, -80, -26],\n [42, 35, 0, -7, 56, 35],\n [11, 5, 7, -9, 16, 12],\n [4, 20, -28, 28, 0, -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[[35, -23, -20, 9, -17, -18],\n [40, 32, -40, 24, 8, -24],\n [-25, 48, 5, 1, 27, 11],\n [-125, 53, 80, -39, 47, 66],\n [-50, 130, 0, 10, 70, 20],\n [70, 5, -55, 30, -10, -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[[-126, -55, 23, 17, -111, -35],\n [8, 52, 112, 16, 12, 29],\n [-10, 67, 29, -52, 19, -28],\n [-3, 107, 42, -48, 40, 37],\n [-25, -33, -116, -32, -14, -25],\n [130, 42, 80, 5, 92, -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 6x6 matrix:\n[[-3, -13, -4, -16, 37, -47],\n [10, 43, 53, -5, -27, 2],\n [31, -50, -28, 37, -30, 5],\n [19, -80, -54, 15, 32, -55],\n [2, 79, 109, -57, 33, -94],\n [-20, -30, -87, 52, -58, 150]]\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[[85, 38, -57, -78, -29, -24],\n [88, 6, -2, -107, 2, 104],\n [-3, 14, -26, 13, 47, 63],\n [21, 33, -43, -3, -3, -34],\n [80, 77, -35, -55, 24, 71],\n [35, -44, 8, -67, -55, -37]]\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 6x6 matrix:\n[[88, -11, -122, 21, -42, 82],\n [15, 6, 30, -3, 16, -9],\n [51, -72, -111, 87, -107, 18],\n [-78, 27, 105, -39, 55, -57],\n [57, -35, -161, 42, -81, 78],\n [-3, -98, -65, 111, -125, -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[[-78, 5, -10, -99, 38, -55],\n [-51, 15, -5, -62, 22, -33],\n [75, 23, -141, -34, 93, -91],\n [-111, -10, 73, -60, -17, 8],\n [55, 63, -65, -1, 19, -31],\n [7, -33, -83, -28, 100, -61]]\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 6x6 matrix:\n[[37, -8, -31, 26, -52, -27],\n [45, -228, 33, -72, 39, 15],\n [-72, 107, 78, -56, 12, 43],\n [98, -38, -94, 136, 58, -104],\n [90, 83, -56, 140, 20, -123],\n [4, -41, -16, -16, -40, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[-15, 10, -20, 5, -15, 25],\n [-27, 18, -36, 9, -27, 45],\n [-9, 6, -12, 3, -9, 15],\n [0, 0, 0, 0, 0, 0],\n [-24, 16, -32, 8, -24, 40],\n [27, -18, 36, -9, 27, -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[[42, -49, 63, -14, -42, 42],\n [48, -56, 72, -16, -48, 48],\n [-42, 49, -63, 14, 42, -42],\n [6, -7, 9, -2, -6, 6],\n [30, -35, 45, -10, -30, 30],\n [60, -70, 90, -20, -60, 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[[21, -54, -72, -78, -60, 12],\n [25, -98, -92, -99, -36, 60],\n [-44, -84, 18, 25, 4, 82],\n [49, 170, 26, 20, 24, -142],\n [-22, 76, 76, 82, 32, -44],\n [-57, -142, -1, 7, -22, 121]]\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[[-48, -18, 12, 30, 60, -6],\n [48, 18, -12, -30, -60, 6],\n [-24, -9, 6, 15, 30, -3],\n [32, 12, -8, -20, -40, 4],\n [16, 6, -4, -10, -20, 2],\n [-48, -18, 12, 30, 60, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-28, 56, -21, 42, 70, -28],\n [32, -64, 24, -48, -80, 32],\n [-4, 8, -3, 6, 10, -4],\n [-20, 40, -15, 30, 50, -20],\n [-28, 56, -21, 42, 70, -28],\n [-24, 48, -18, 36, 60, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-17, -4, 98, 121, -90, -87],\n [-59, -91, -27, -171, 16, 56],\n [128, 48, -2, 32, 111, 84],\n [46, 53, -49, -27, 60, 12],\n [-37, 46, -56, 29, -30, -45],\n [175, 165, -35, 144, 116, 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[[-165, -54, -121, 112, -133, 22],\n [-109, -81, -37, 98, -81, 27],\n [66, 74, 47, -21, 60, 126],\n [37, 32, 22, -21, 31, 32],\n [-12, -26, -13, -7, -14, -70],\n [172, 63, 121, -119, 138, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-60, 60, 60, 40, -20, -10],\n [30, -30, -30, -20, 10, 5],\n [24, -24, -24, -16, 8, 4],\n [30, -30, -30, -20, 10, 5],\n [54, -54, -54, -36, 18, 9],\n [-60, 60, 60, 40, -20, -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[[-70, -56, 35, -7, -21, -49],\n [-70, -56, 35, -7, -21, -49],\n [100, 80, -50, 10, 30, 70],\n [100, 80, -50, 10, 30, 70],\n [-50, -40, 25, -5, -15, -35],\n [40, 32, -20, 4, 12, 28]]\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[[9, 15, 26, 1, -82, -70],\n [-5, 13, -14, -3, 68, 38],\n [11, 26, -46, -6, 119, 70],\n [68, 14, -112, -6, 106, 88],\n [-115, -64, 130, 10, -63, -30],\n [16, 58, 20, -4, -40, -72]]\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[[30, -28, 8, 18, 44, 34],\n [88, 85, -18, -12, -105, 151],\n [-20, -235, 175, 70, 70, -55],\n [51, -85, 89, 50, -28, 59],\n [49, -100, 114, 50, -52, 62],\n [-6, -103, 131, -44, -34, 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 6x6 matrix:\n[[8, 25, -41, -79, 13, 22],\n [-24, 15, -63, -81, 3, -6],\n [20, -20, 68, 94, -6, 0],\n [76, 35, 29, -35, 29, 74],\n [6, 0, 8, 7, 1, 4],\n [56, 10, 54, 30, 14, 44]]\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 6x6 matrix:\n[[168, -17, -44, 40, 146, 96],\n [122, 9, 38, 134, 132, 62],\n [240, 20, -36, 212, 190, 60],\n [21, 74, 33, 177, -18, -93],\n [-96, 40, 71, 28, -79, -69],\n [-30, -66, -4, -168, 21, 96]]\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[[-55, -55, -25, 57, -23, 13],\n [55, -11, -53, -27, -25, 83],\n [40, 17, -9, -31, 0, 24],\n [10, 29, 27, -19, 18, -30],\n [-55, -55, -25, 57, -23, 13],\n [-10, 81, 103, -31, 62, -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[[84, 52, 76, -58, 80, -10],\n [-60, -8, -56, 38, -76, 14],\n [-44, -75, -37, 36, -11, -6],\n [72, 13, 67, -46, 89, -16],\n [-72, 4, -68, 44, -100, 20],\n [44, 58, 38, -34, 22, 2]]\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[[-8, -120, -81, -68, 30, 10],\n [47, 33, -54, -52, 8, -71],\n [49, -61, -200, -11, 110, 42],\n [-36, 105, 63, -4, -98, -10],\n [59, -50, -114, -92, 124, -66],\n [13, -76, 11, -76, 22, -66]]?\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[[-4, -50, 99, -47, 58, -48],\n [-177, 102, 84, 118, -137, 42],\n [-82, -60, 56, 19, -36, 12],\n [148, 27, -80, -95, 87, -12],\n [88, -100, 2, -56, 38, 20],\n [111, -5, -14, 72, -68, 90]]\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 6x6 matrix:\n[[84, -14, -96, -53, -72, 13],\n [40, -58, -22, 124, 6, -78],\n [77, -26, -63, -6, 23, -10],\n [-102, 17, 155, 75, 166, 22],\n [6, 38, -26, -119, 27, 33],\n [58, -19, -53, -7, -23, 2]]\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[[-90, 14, 162, -50, -91, 41],\n [-100, -40, 55, -125, 10, 115],\n [40, 24, -4, 60, -20, -56],\n [-40, 4, 67, -25, -36, 21],\n [90, -6, -144, 60, 75, -51],\n [60, 32, -15, 85, -22, -79]]\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[[120, -140, -9, 51, -60, 21],\n [24, 35, -64, 54, -48, 64],\n [34, 43, -5, -50, 38, -168],\n [-6, -9, 65, -41, -40, 15],\n [-156, 13, 118, -63, 30, 113],\n [143, 6, -128, 65, -20, -113]]\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, -115, 15, -56, 27, 58],\n [12, 53, 27, -74, 46, -88],\n [36, -116, 18, 67, -84, 149],\n [38, -156, 72, -47, 7, 91],\n [-58, 162, -65, 45, 5, -105],\n [182, -96, 140, -56, -119, 108]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-10, -2, -5, -9, -5, -2],\n [20, 4, 10, 18, 10, 4],\n [-70, -14, -35, -63, -35, -14],\n [90, 18, 45, 81, 45, 18],\n [-60, -12, -30, -54, -30, -12],\n [-100, -20, -50, -90, -50, -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 6x6 matrix:\n[[63, -15, 71, -45, -50, -23],\n [-1, -14, -15, 49, 75, 14],\n [80, -42, 111, 50, 120, -20],\n [-41, 34, -64, -81, -155, 4],\n [43, -29, 48, 45, 90, -3],\n [-7, 28, 2, -95, -155, -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[[-41, -6, -43, -8, -98, -11],\n [-3, 72, 39, -48, 114, -39],\n [3, 38, 25, -24, 70, -19],\n [-27, -12, -33, 0, -78, -3],\n [46, -4, 42, 16, 92, 18],\n [-61, 89, -7, -76, 18, -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[[124, 99, -12, -37, 106, 120],\n [54, 92, 26, -54, -7, 42],\n [-14, 11, 23, -5, -21, -7],\n [-36, -118, -28, 109, 89, -2],\n [-168, -54, 63, -32, 12, 25],\n [-148, -168, 9, 109, 17, -63]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-34, 47, 26, -42, 69, -14],\n [132, 52, -6, -87, 145, 114],\n [81, 149, 15, -81, 203, 110],\n [-44, 68, -34, 19, -29, 34],\n [-2, -118, -68, -57, -77, -12],\n [-49, 92, 49, 92, 3, -23]]\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[[31, -67, -37, 37, -22, 5],\n [-74, 136, -67, 15, 1, -91],\n [23, 18, 3, 18, -86, -20],\n [8, 11, -51, -53, 50, 51],\n [13, -71, -39, 103, -60, -61],\n [-33, -20, 77, -60, 134, 54]]\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[[-2, 51, -52, -35, -51, 60],\n [-108, 158, 64, 22, -72, 60],\n [-36, 64, -30, -34, -142, 100],\n [-20, 41, 6, -1, -73, 66],\n [-55, 109, 7, -5, -57, 61],\n [-19, 6, 3, -4, 18, -37]]\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, -56, 28, 52, -4, 20],\n [11, 40, -41, -47, -13, -7],\n [35, 91, -70, -96, -12, -24],\n [24, 30, 6, -18, 18, -18],\n [51, 90, -31, -77, 17, -37],\n [10, -19, 55, 39, 33, -9]]?\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[[5, -11, 35, 51, -66, 111],\n [-94, -24, 50, 32, 130, -86],\n [59, 120, 65, 116, -107, 58],\n [75, 24, -39, -19, -84, 66],\n [50, 18, -20, 4, -36, 61],\n [58, 40, -4, -2, -154, 43]]\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[[40, -23, -24, -13, 22, 63],\n [-72, -29, 8, -3, 66, 45],\n [160, 20, -40, -10, -80, 0],\n [16, -62, -36, -25, 88, 144],\n [-56, 13, 24, 11, -2, -45],\n [-80, -42, 4, -7, 88, 72]]?\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[[-113, -67, -55, -5, -102, 199],\n [-13, 4, -66, -5, 123, 27],\n [-66, 102, -116, 54, 100, 34],\n [-85, 18, 28, -71, -61, 87],\n [57, 32, 130, -72, -56, -73],\n [-11, -6, -58, 107, -113, 81]]\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[[-27, 126, 147, 63, 66, 2],\n [132, 172, -16, 28, -41, -133],\n [-2, -108, -84, -52, -45, 11],\n [5, 70, 61, 0, -7, -33],\n [-62, 81, 182, 6, 3, -8],\n [-128, -156, 22, -53, 39, 117]]\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[[80, -88, -136, 46, 148, 46],\n [114, -9, -115, -2, 70, 103],\n [108, -57, -113, 54, 119, 69],\n [0, 15, 43, 23, -25, -10],\n [10, 73, 15, -67, -78, 44],\n [-18, 78, -20, -131, -85, 49]]\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, 60, -108, 75, 81, -105],\n [76, -58, 31, -3, -10, -119],\n [-8, 71, -80, 21, 29, 28],\n [-60, 75, -46, 30, 46, 101],\n [-32, -31, 30, 54, 30, 27],\n [2, -125, 141, -75, -90, -30]]\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 6x6 matrix:\n[[14, 56, 49, 49, 0, -56],\n [0, 0, 0, 0, 0, 0],\n [6, 24, 21, 21, 0, -24],\n [16, 64, 56, 56, 0, -64],\n [-16, -64, -56, -56, 0, 64],\n [-6, -24, -21, -21, 0, 24]]\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 6x6 matrix:\n[[-25, -20, 15, 0, 5, 15],\n [-30, -24, 18, 0, 6, 18],\n [5, 4, -3, 0, -1, -3],\n [-30, -24, 18, 0, 6, 18],\n [-25, -20, 15, 0, 5, 15],\n [-45, -36, 27, 0, 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[[-28, -23, 22, -59, -1, 85],\n [-5, 111, -148, 85, -4, 56],\n [-28, -79, 119, -68, -26, -18],\n [-36, -67, -57, -119, -4, -99],\n [-47, -37, -5, -78, -21, 9],\n [98, 112, -6, 191, 46, 47]]\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 6x6 matrix:\n[[-3, 3, 5, -9, 14, -49],\n [-45, -29, -36, 13, -49, 5],\n [48, 22, 25, 4, 21, 84],\n [15, 15, 20, -15, 35, -55],\n [-39, -27, -34, 15, -49, 23],\n [-63, -37, -45, 11, -56, -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[[-49, -6, -10, -71, 88, 25],\n [62, 46, 131, -73, -104, 28],\n [-8, 12, 70, 132, -6, 142],\n [32, 0, -28, -78, -42, -106],\n [16, -10, -71, -161, -4, -166],\n [55, 10, -8, -118, -77, -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 6x6 matrix:\n[[-20, -30, 12, 0, 4, -24],\n [-26, -39, -15, -45, 25, -33],\n [-8, -12, 15, 15, -5, -9],\n [52, 78, -55, -35, 5, 61],\n [-6, -9, -10, -20, 10, -8],\n [-38, -57, 16, -10, 12, -46]]\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[[8, 24, -33, 19, -28, -25],\n [-44, 36, -21, 23, 16, 19],\n [78, -26, -72, 4, -98, -34],\n [-60, 136, -45, 75, 4, -72],\n [48, 24, -18, 14, -48, -80],\n [-114, 82, 90, 18, 130, 3]]\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[[35, 49, -28, -70, -70, 49],\n [-35, -49, 28, 70, 70, -49],\n [-15, -21, 12, 30, 30, -21],\n [35, 49, -28, -70, -70, 49],\n [45, 63, -36, -90, -90, 63],\n [30, 42, -24, -60, -60, 42]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-105, 49, -43, 35, 200, -52],\n [61, -40, 35, -3, -159, 42],\n [-41, 97, -15, 68, 52, -10],\n [85, 3, 19, -40, -100, 26],\n [-36, 86, -8, 73, 22, -2],\n [59, -34, 33, -2, -151, 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 6x6 matrix:\n[[-18, 72, 9, -63, 45, 45],\n [16, -64, -8, 56, -40, -40],\n [10, -40, -5, 35, -25, -25],\n [-16, 64, 8, -56, 40, 40],\n [10, -40, -5, 35, -25, -25],\n [20, -80, -10, 70, -50, -50]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[54, 33, -113, 18, 7, 35],\n [-83, 40, 75, 18, -95, 55],\n [-42, -8, 74, 4, -2, -22],\n [102, -106, -89, -151, -49, 40],\n [18, -89, 52, -77, 24, -51],\n [-88, 41, 137, 114, 109, -111]]\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, -5, 6, -5, 6, -6],\n [-9, 5, -6, 5, -6, 6],\n [-54, 30, -36, 30, -36, 36],\n [-27, 15, -18, 15, -18, 18],\n [-45, 25, -30, 25, -30, 30],\n [-54, 30, -36, 30, -36, 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[[-70, -78, -32, -60, 76, -86],\n [-66, -74, 67, -77, 126, -98],\n [-85, -57, -1, -123, 148, -133],\n [24, -28, 18, 80, -72, 60],\n [-39, -19, -58, -52, 42, -55],\n [86, 122, 42, 44, -68, 90]]?\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[[-39, -9, 3, -6, -3, 15],\n [66, 70, -58, -52, 42, -10],\n [-54, -33, 24, 15, -18, 15],\n [-26, -6, 2, -4, -2, 10],\n [57, 20, -11, 1, 9, -20],\n [69, 57, -45, -36, 33, -15]]\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 6x6 matrix:\n[[-14, 16, -47, 28, 68, -12],\n [-2, 43, -71, 34, 89, -21],\n [30, -18, 75, -48, -114, 18],\n [22, -17, 61, -38, -91, 15],\n [-26, 8, -53, 36, 84, -12],\n [-22, 17, -61, 38, 91, -15]]\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 6x6 matrix:\n[[85, 61, 75, 91, -137, -109],\n [71, 47, 57, 41, -91, -47],\n [35, 80, 22, 24, -67, -103],\n [174, 108, 116, -40, -132, 50],\n [34, 6, 44, 104, -91, -94],\n [-131, -65, -101, -37, 136, 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[[114, -59, -37, 83, -87, -33],\n [37, -9, 36, -47, 34, -44],\n [67, -75, 25, 25, -133, 7],\n [-22, -144, -122, -93, 13, -212],\n [30, -19, -116, 78, -103, 10],\n [52, 108, 91, 154, -29, 185]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-18, -21, -110, 43, -80, 24],\n [22, 22, 120, -46, 88, -26],\n [45, 3, 80, -19, 68, -15],\n [-86, 28, -20, -24, -40, -2],\n [-35, 16, 10, -18, -4, -5],\n [9, -6, -10, 8, -4, 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[[-43, -2, -19, -66, -16, -9],\n [39, 40, 41, 67, 51, -88],\n [-55, 82, 70, -73, -74, -61],\n [-24, -4, -54, -16, -50, -54],\n [15, 16, 38, 14, 47, -10],\n [6, 80, 103, 9, 14, -62]]\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, 37, -44, 35, -58, 52],\n [-159, -41, 102, -18, 130, -96],\n [74, 60, 35, 26, -92, 125],\n [29, 1, -42, 4, -18, 0],\n [25, 1, -2, -8, -18, 16],\n [-9, -35, 90, -66, 22, 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[[-96, -78, -4, 32, 4, -66],\n [-28, 98, 17, 61, 34, -100],\n [35, -27, 0, 45, -70, 85],\n [9, -8, 37, 47, -41, -4],\n [107, 33, 63, -84, 0, 27],\n [5, 207, 14, -25, 128, -157]]\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, -36, 54, -24, -12, 30],\n [-48, -18, 3, 84, 90, -9],\n [10, 24, -40, 32, 24, -24],\n [50, 48, -60, -16, -32, -28],\n [73, 60, -68, -48, -68, -28],\n [60, 36, -30, -72, -84, -6]]\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 6x6 matrix:\n[[-126, 77, -125, -21, -113, -22],\n [-18, -78, -93, 75, -16, 32],\n [112, 3, 106, -14, 63, 9],\n [6, -39, 141, -21, 137, -11],\n [54, -42, 15, 27, 24, 18],\n [-4, -12, -28, 5, -31, -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[[43, 60, 50, 54, 29, 20],\n [-89, -90, -62, -100, -31, 20],\n [8, 0, 7, 21, 19, -11],\n [55, 10, -27, 33, -40, -99],\n [107, 120, 78, 110, 25, -8],\n [-130, -150, -96, -130, -26, 4]]\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[[-126, 40, -23, 0, -28, 7],\n [-70, -27, -55, 63, -56, 70],\n [56, -69, -146, 24, 51, 19],\n [-52, -38, -50, -36, -50, -40],\n [28, 35, 102, 23, -6, 27],\n [121, -86, -81, 13, 35, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[-81, 71, 58, -34, 20, 58],\n [65, -117, -61, 35, 8, -45],\n [101, -5, -50, 54, -72, -70],\n [-74, 158, 84, 44, -72, 68],\n [-20, -90, -20, -80, 100, 0],\n [-58, 58, 49, 33, -24, 53]]\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, 30, 90, 90, -30, 0],\n [35, -15, -45, -45, 15, 0],\n [70, -30, -90, -90, 30, 0],\n [-70, 30, 90, 90, -30, 0],\n [-63, 27, 81, 81, -27, 0],\n [-70, 30, 90, 90, -30, 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[[28, -34, -3, 10, -22, -56],\n [35, -113, 0, -1, -80, -28],\n [63, -38, -26, 33, -74, -77],\n [-49, -34, 30, -39, 30, 71],\n [119, 31, -60, 83, -80, -184],\n [-35, 120, -4, 3, 74, 39]]\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[[-3, 28, -59, 109, -7, 85],\n [-13, -59, -29, 14, -59, 75],\n [-106, 14, -58, -46, -75, -7],\n [-70, 35, 10, 65, 41, 59],\n [53, 50, -56, -71, 2, 0],\n [34, -46, 46, 124, 55, 126]]?\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[[-25, 36, -59, 22, 44, 50],\n [43, 13, 16, -19, -49, -18],\n [-24, -89, 77, -3, -23, -76],\n [36, -9, 90, -72, 108, 54],\n [21, -1, 53, -46, 80, 44],\n [39, 93, -79, 4, -18, 56]]\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[[-37, -80, 19, 61, -38, -54],\n [30, 15, -42, -14, 43, 5],\n [-27, -135, -27, 99, -9, -99],\n [-28, -35, 28, 28, -35, -21],\n [-14, 95, 74, -66, -45, 77],\n [23, -50, -65, 33, 48, -44]]?\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 6x6 matrix:\n[[21, 12, -3, -6, -3, -15],\n [70, 40, -10, -20, -10, -50],\n [-14, -8, 2, 4, 2, 10],\n [-70, -40, 10, 20, 10, 50],\n [-14, -8, 2, 4, 2, 10],\n [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[[41, 117, -148, -122, 25, 110],\n [6, -53, 60, 39, -43, -55],\n [-66, -102, 89, 43, -6, -51],\n [-16, -27, -4, 79, -1, -39],\n [-48, -50, -11, -95, 35, -48],\n [32, 59, -43, -13, 39, -15]]\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[[110, 79, -98, -109, -89, 59],\n [94, 23, -74, -23, 6, 31],\n [42, -17, -12, 15, 69, -89],\n [112, 49, -79, -65, 46, 17],\n [-2, -44, -20, -159, -34, -113],\n [-116, 42, 121, 83, -167, -146]]\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, 48, -40, -56, -56, 64],\n [16, -48, 40, 56, 56, -64],\n [-2, 6, -5, -7, -7, 8],\n [-16, 48, -40, -56, -56, 64],\n [6, -18, 15, 21, 21, -24],\n [-6, 18, -15, -21, -21, 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[[-41, 26, -138, 86, 21, -29],\n [34, 31, 22, 29, 43, 73],\n [35, 76, -54, 108, 95, 113],\n [32, -64, 179, -113, -67, 2],\n [28, -9, 83, -70, -4, 13],\n [-28, 18, -89, 21, 15, -40]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 72, 72, 72, 8, -32],\n [0, 0, 0, 0, 0, 0],\n [0, 72, 72, 72, 8, -32],\n [0, -63, -63, -63, -7, 28],\n [0, -72, -72, -72, -8, 32],\n [0, -27, -27, -27, -3, 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[[4, 1, 5, -5, -9, -9],\n [0, 0, 0, 0, 0, 0],\n [24, 6, 30, -30, -54, -54],\n [28, 7, 35, -35, -63, -63],\n [12, 3, 15, -15, -27, -27],\n [24, 6, 30, -30, -54, -54]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 48, 68, 130, 113, -2],\n [-25, 165, 16, 126, 138, 44],\n [73, -44, -19, -49, -66, 67],\n [-35, -49, 58, 50, 41, -88],\n [-63, -63, -18, -72, -54, -90],\n [-1, -53, -18, -60, -58, -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[[40, -24, 24, 32, 40, 0],\n [-50, 30, -30, -40, -50, 0],\n [-5, 3, -3, -4, -5, 0],\n [5, -3, 3, 4, 5, 0],\n [-5, 3, -3, -4, -5, 0],\n [-45, 27, -27, -36, -45, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[86, -9, 11, -74, -15, -23],\n [37, -8, 65, -121, 34, 19],\n [-73, 7, 0, 49, 19, 24],\n [76, -4, -48, 20, -52, -48],\n [10, -5, 59, -94, 37, 25],\n [130, -10, -36, -34, -58, -60]]\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[[-18, 6, -48, 12, 12, -18],\n [28, -2, -61, 40, -4, 83],\n [-1, 1, -15, 6, 2, 4],\n [28, -4, -24, 24, -8, 68],\n [49, -7, -42, 42, -14, 119],\n [-18, 0, 63, -36, 0, -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[[0, -11, -31, 104, 53, -40],\n [80, 54, 53, 77, -32, -84],\n [-44, 14, -95, 68, 106, -44],\n [-35, 35, 0, -61, -37, -18],\n [18, -4, -2, 109, 22, -52],\n [46, 10, 22, -66, -6, 44]]\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[[41, -125, 89, 9, -54, 45],\n [27, 98, -15, -99, -114, -91],\n [47, -78, -81, -50, 95, 63],\n [-25, -14, -65, 3, 60, -11],\n [23, 33, 149, 19, -122, -7],\n [-22, 73, -150, -53, 43, -40]]?\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, -91, -15, 118, -18, 133],\n [71, -40, -51, 78, 77, 5],\n [31, 30, -54, -18, 112, -152],\n [196, -10, -45, 9, 46, 13],\n [120, -7, -56, 51, 2, 82],\n [-68, 15, 36, -10, -73, 70]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-130, -70, -25, 8, 64, -62],\n [107, 24, 46, -23, 102, 85],\n [-58, -48, -1, -104, -30, -148],\n [74, 14, -23, -24, 0, -18],\n [32, -2, -89, 96, 74, 44],\n [-88, -41, -40, -30, -61, -123]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[74, 76, 63, 25, -22, 101],\n [-48, -11, 73, -2, -111, 61],\n [52, -2, -58, 126, -9, 57],\n [95, 51, -17, 103, 7, 91],\n [-83, -95, -89, -5, 23, -111],\n [-2, -3, 44, -145, 65, -172]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-10, -7, 55, 113, -15, 70],\n [-49, -53, 185, 146, -4, 19],\n [14, 17, 67, 44, -48, 10],\n [-102, -86, -51, 19, 159, -7],\n [-84, -34, 31, 15, 95, -63],\n [-14, 47, -53, -99, 29, -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[[-27, 12, 18, 6, -12, -30],\n [-90, 40, 60, 20, -40, -100],\n [-63, 28, 42, 14, -28, -70],\n [45, -20, -30, -10, 20, 50],\n [36, -16, -24, -8, 16, 40],\n [-18, 8, 12, 4, -8, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-23, 81, -119, 31, 170, -49],\n [24, -36, 77, -31, -110, 8],\n [46, 54, 28, -56, -40, -94],\n [9, 45, -28, -10, 40, -49],\n [1, 45, -42, 0, 60, -41],\n [43, 63, 14, -52, -20, -99]]?\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[[20, 23, 37, 81, -16, -33],\n [-61, -3, 18, -43, -12, -8],\n [15, -23, -22, 104, 19, 7],\n [-2, 17, 37, -55, -32, -69],\n [5, -22, -25, 111, 25, 32],\n [53, -72, -87, 32, 38, -21]]\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[[-5, 54, -15, -38, 49, -1],\n [13, 57, -22, -120, -124, -43],\n [-58, 72, -30, -79, -49, 55],\n [-18, 32, -14, -51, -53, 11],\n [78, -64, 34, 105, 151, -73],\n [37, 33, -6, -44, 16, -55]]\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 6x6 matrix:\n[[-26, -51, -57, 29, -32, 20],\n [-10, 133, 165, -103, -13, -82],\n [-6, 117, 113, -77, -49, -90],\n [8, -1, -19, 10, -11, -6],\n [8, 30, 96, -44, 89, 22],\n [-6, 24, 78, -39, 54, 12]]\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[[142, -95, 41, -57, -132, 27],\n [-59, -42, 109, -17, 51, 120],\n [162, -59, -27, -34, -153, -50],\n [112, -93, 57, -62, -99, 52],\n [44, -8, -64, -113, 39, -5],\n [-50, 20, -18, -46, 90, 24]]\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[[-34, -6, -130, 75, -35, 84],\n [-74, 12, -124, 135, -15, 50],\n [72, 6, 158, -101, 15, -162],\n [19, -61, -67, -28, -32, 11],\n [89, -14, 74, -137, -15, -6],\n [181, -8, 18, -180, -109, -31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[90, -80, -28, -84, -58, 50],\n [45, -40, -27, -41, -32, 25],\n [90, -80, -80, -80, -70, 50],\n [81, -72, -7, -77, -48, 45],\n [27, -24, -50, -22, -27, 15],\n [-63, 56, 30, 58, 43, -35]]\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[[5, 51, 63, 114, -136, 129],\n [-176, -126, 30, -16, 98, -28],\n [45, 56, -112, -61, 34, -98],\n [-74, 27, -27, -15, 6, -65],\n [14, -60, 162, 31, -23, 91],\n [-104, -95, -41, -34, 103, -44]]\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 6x6 matrix:\n[[3, -33, -24, -60, -15, 90],\n [-57, -24, -48, 6, 54, -30],\n [16, -21, -8, -50, -25, 80],\n [12, -8, 0, -24, -16, 40],\n [-84, -37, -72, 6, 79, -40],\n [18, -12, 0, -36, -24, 60]]\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, -7, -56, -63, 56, -28],\n [-28, -7, -56, -63, 56, -28],\n [4, 1, 8, 9, -8, 4],\n [-24, -6, -48, -54, 48, -24],\n [-8, -2, -16, -18, 16, -8],\n [-12, -3, -24, -27, 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[[110, -129, -150, 26, 17, 129],\n [25, -18, -24, 35, 59, 47],\n [-71, 90, -23, -136, 62, -54],\n [40, -39, -86, -12, 57, 65],\n [52, -48, 23, 135, 45, 69],\n [80, -105, -63, 51, -60, 68]]\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 6x6 matrix:\n[[-45, -39, -27, 13, 33, 33],\n [33, -21, 57, -24, 13, 13],\n [-42, -30, -30, 14, 26, 26],\n [-3, 15, -15, 6, -11, -11],\n [-3, 39, -33, 13, -29, -29],\n [-18, -78, 36, -13, 60, 60]]\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[[14, 2, 23, 7, -32, -36],\n [18, 102, 42, 9, 21, 78],\n [18, 102, 42, 9, 21, 78],\n [18, 62, 37, 9, -4, 28],\n [12, 20, 22, 6, -16, -8],\n [12, -20, 17, 6, -41, -58]]\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[[6, -31, -57, -54, 86, 101],\n [18, -5, -119, -143, 80, 142],\n [135, -85, -34, 100, 18, 12],\n [-12, -21, -48, -66, 114, 96],\n [7, -102, -99, -61, 200, 108],\n [-52, 138, -27, -151, -160, 14]]\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, -2, -26, 74, -16, -117],\n [-41, 119, 13, -177, -62, -82],\n [60, -180, 211, 89, -91, 65],\n [-19, -71, -29, 6, 46, 202],\n [-236, 218, -56, -93, 2, -166],\n [-81, 160, 98, -17, 38, -133]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-15, -93, -21, 33, 24, 48],\n [11, 64, 14, -27, -33, -24],\n [14, 85, 19, -32, -29, -40],\n [-6, -51, -13, 4, -41, 56],\n [-17, -109, -25, 35, 14, 64],\n [7, 59, 15, -5, 46, -64]]\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 6x6 matrix:\n[[-115, 95, -85, -50, -5, 30],\n [48, -47, 1, 22, 10, -60],\n [-26, 13, -59, -10, 8, -48],\n [-44, 29, -67, -18, 6, -36],\n [-13, 0, -60, -4, 11, -66],\n [23, -6, 78, 8, -13, 78]]\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[[24, 18, 21, 3, -6, 15],\n [0, 0, 0, 0, 0, 0],\n [72, 54, 63, 9, -18, 45],\n [-40, -30, -35, -5, 10, -25],\n [-24, -18, -21, -3, 6, -15],\n [64, 48, 56, 8, -16, 40]]\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[[95, 60, 66, 46, 38, 41],\n [15, 64, -48, -20, -68, 61],\n [-90, -20, -102, -62, -86, -2],\n [40, 110, -63, -23, -99, 102],\n [-45, -24, -36, -24, -24, -15],\n [-60, 10, -93, -53, -89, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-45, -54, -20, 70, -84, -91],\n [-72, -97, -75, -26, 7, -141],\n [-46, -21, -36, 8, 8, -33],\n [128, 99, 47, -58, 46, 153],\n [-136, -90, -59, -3, 7, -146],\n [20, 44, -25, 1, 130, 134]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-14, -15, -3, -7, -29, -21],\n [21, -36, -2, 4, -54, 12],\n [-42, 63, 3, -9, 93, -27],\n [-7, -48, -6, -8, -82, -24],\n [21, 63, 9, 15, 111, 45],\n [119, -39, 7, 41, -31, 123]]\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[[0, 81, -90, -63, 63, 18],\n [0, 36, -40, -28, 28, 8],\n [0, -36, 40, 28, -28, -8],\n [0, 9, -10, -7, 7, 2],\n [0, -36, 40, 28, -28, -8],\n [0, -54, 60, 42, -42, -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[[24, -60, 48, 24, -12, -36],\n [24, -60, 48, 24, -12, -36],\n [24, -60, 48, 24, -12, -36],\n [20, -50, 40, 20, -10, -30],\n [36, -90, 72, 36, -18, -54],\n [-12, 30, -24, -12, 6, 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 6x6 matrix:\n[[-26, -22, 45, 53, -25, -25],\n [-30, -20, 25, 35, -25, -45],\n [-22, -3, -40, -31, -10, -68],\n [-42, -42, 105, 117, -45, -21],\n [48, 18, 30, 12, 30, 114],\n [48, 46, -110, -124, 50, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[60, -104, 79, 77, 7, 101],\n [6, 115, -116, 11, -134, -28],\n [-38, -59, 52, 29, -26, -20],\n [-92, -1, -9, 54, -177, -93],\n [-5, 74, -65, -28, -26, -30],\n [59, -87, 65, 67, 8, 94]]\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, 1, 42, 14, 86, 53],\n [-32, 39, 26, 50, 6, 21],\n [0, 5, -50, -10, -110, -65],\n [-28, 32, 44, 48, 52, 46],\n [10, -8, -50, -24, -94, -61],\n [26, -30, -38, -44, -42, -39]]\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[[21, -42, -49, -49, -7, 70],\n [-15, 30, 35, 35, 5, -50],\n [18, -36, -42, -42, -6, 60],\n [21, -42, -49, -49, -7, 70],\n [15, -30, -35, -35, -5, 50],\n [24, -48, -56, -56, -8, 80]]\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 6x6 matrix:\n[[-2, -10, -35, -61, 23, 55],\n [92, 8, 87, 35, -19, -125],\n [-70, -20, -85, -5, 25, 47],\n [6, 35, 15, 60, -59, -68],\n [-53, 46, -1, -15, -50, 119],\n [-9, -62, -103, -49, 80, -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[[5, -50, 40, 25, -20, 50],\n [3, -30, 24, 15, -12, 30],\n [2, -20, 16, 10, -8, 20],\n [10, -100, 80, 50, -40, 100],\n [-9, 90, -72, -45, 36, -90],\n [-9, 90, -72, -45, 36, -90]]\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[[-8, 78, 85, 125, -52, 48],\n [-165, -75, -114, -225, -40, 151],\n [-155, 19, -25, -61, 34, 178],\n [-23, -60, 10, -27, 42, 39],\n [-107, 115, 23, 40, -116, 135],\n [123, 35, 56, 128, 50, -126]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[-52, 7, 38, 32, -21, -45],\n [11, -50, -46, 74, -18, -51],\n [10, -41, -18, 36, -8, -20],\n [-38, 77, 94, -108, 21, 67],\n [27, 9, 120, -190, 57, 172],\n [-28, 47, -6, 16, -10, -32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-57, -17, 100, -89, 26, -3],\n [-31, -23, 92, -39, -111, -77],\n [-4, -76, -17, 127, 131, -54],\n [-113, 75, 48, 12, 134, -64],\n [104, -44, -66, -64, -62, 138],\n [-12, 30, 84, -162, -86, 62]]\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 6x6 matrix:\n[[110, 103, 15, 27, 14, -93],\n [77, 71, 85, -44, 28, -7],\n [-119, -55, -79, 62, -38, 73],\n [78, 98, 20, 64, -42, -80],\n [-84, -7, 101, -24, -52, 151],\n [130, 40, -51, 12, 41, -177]]\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 6x6 matrix:\n[[-45, 79, -6, 22, 31, -47],\n [36, -28, 18, -88, -16, 20],\n [-27, 81, 9, -54, 27, -45],\n [12, -44, -7, 40, -14, 24],\n [9, -35, -6, 34, -11, 19],\n [-42, 86, -1, -4, 32, -50]]\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 6x6 matrix:\n[[12, 36, -60, 18, -42, -12],\n [6, 18, -30, 9, -21, -6],\n [-12, -36, 60, -18, 42, 12],\n [16, 48, -80, 24, -56, -16],\n [-12, -36, 60, -18, 42, 12],\n [8, 24, -40, 12, -28, -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[[-44, -44, -46, -16, -24, -92],\n [-27, -4, 90, 76, 61, 51],\n [-19, -35, -80, -49, -56, -109],\n [21, 41, 83, 49, 64, 127],\n [-101, -61, 73, 91, 68, -31],\n [2, -12, -73, -54, -46, -62]]?\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[[0, 0, 0, 0, 0, 0],\n [6, 4, 9, -4, -1, -7],\n [-42, -28, -63, 28, 7, 49],\n [-12, -8, -18, 8, 2, 14],\n [36, 24, 54, -24, -6, -42],\n [30, 20, 45, -20, -5, -35]]\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[[-3, -27, -39, -6, -45, 45],\n [-25, -69, -126, 6, -119, 130],\n [28, 14, -14, 11, -87, 45],\n [139, -5, 64, -88, 89, 12],\n [49, 37, 65, -14, 60, -44],\n [56, 62, 85, -1, 81, -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[[-26, 11, -6, -142, -67, 109],\n [46, -28, 82, 32, 78, -66],\n [42, -8, 130, -2, 2, -22],\n [-128, -18, 104, -192, 86, 170],\n [27, -27, -41, -55, 56, -9],\n [21, -31, 163, 24, 104, -47]]\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[[-34, -22, 124, -6, 112, 153],\n [-51, 79, -58, 58, 134, 111],\n [-107, 73, -10, -72, -40, -9],\n [-32, -5, 144, -79, -65, -16],\n [109, -143, 22, 28, 0, 1],\n [-147, 85, 114, -159, -131, -55]]?\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[[-40, -80, -60, 50, -40, 50],\n [4, 8, 6, -5, 4, -5],\n [-32, -64, -48, 40, -32, 40],\n [-32, -64, -48, 40, -32, 40],\n [-16, -32, -24, 20, -16, 20],\n [-24, -48, -36, 30, -24, 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 6x6 matrix:\n[[100, -50, -84, 42, 132, -20],\n [-39, 49, 70, -39, -57, -27],\n [-67, 102, 64, -114, -63, 59],\n [58, -60, -48, 65, 63, -39],\n [28, 110, 44, -121, 57, -9],\n [-39, 38, 48, -34, -51, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[42, -56, 48, 18, -48, 26],\n [21, 0, -6, -18, -8, 2],\n [-18, -12, 18, 27, 0, 3],\n [54, -76, 66, 27, -64, 35],\n [-105, 0, 30, 90, 40, -10],\n [-108, 12, 18, 81, 48, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[30, -65, -10, 35, -65, -75],\n [0, -21, 12, 27, 3, 27],\n [-21, 91, -19, -83, 39, -6],\n [-6, 83, -38, -97, 3, -75],\n [0, -63, 36, 81, 9, 81],\n [-12, 89, -32, -95, 17, -51]]\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 6x6 matrix:\n[[184, -30, 205, 89, -99, -28],\n [7, -35, -55, 90, 25, -88],\n [-188, -7, -206, -108, 103, -17],\n [27, -67, 29, -46, 41, -33],\n [-105, 110, 20, -139, -145, 60],\n [-168, 104, -126, -194, 94, 185]]\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[[13, -158, 15, -47, 57, -10],\n [150, -138, 24, 80, -44, -36],\n [125, -65, 123, 25, 45, -91],\n [5, -121, 99, -96, 79, -48],\n [-109, -112, -114, -84, -49, 76],\n [174, -105, 153, 51, 59, -76]]\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 6x6 matrix:\n[[-20, 2, -10, 11, 48, 66],\n [-134, 0, -96, -93, 28, 32],\n [69, 7, -212, 18, 9, -38],\n [-12, 24, 20, -10, -28, 20],\n [177, 14, -79, 111, -3, -22],\n [43, -8, 43, 66, 61, 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[[151, -61, 131, 7, 0, -74],\n [5, 54, -21, -10, 65, 49],\n [48, 32, 78, -44, 36, -23],\n [85, -1, 132, -97, -17, -54],\n [-93, -20, 120, -48, 74, -4],\n [32, 111, -12, -105, -29, -2]]\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 6x6 matrix:\n[[-9, -22, -42, 13, 60, -108],\n [70, -179, 42, -69, -32, -75],\n [16, -155, 30, -85, -36, -15],\n [-70, 85, -66, 63, 88, -63],\n [70, -31, -11, -6, 8, -84],\n [44, 14, 71, 54, -34, 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[[-42, 128, -114, 58, 12, 89],\n [82, -86, 132, -125, 98, 113],\n [-107, 143, -101, 71, -122, -13],\n [-79, 137, -43, 22, -60, 125],\n [19, -17, -45, -124, -44, 95],\n [-40, -2, 10, -79, -122, 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[[-9, -9, -54, -63, -81, -36],\n [-8, -8, -48, -56, -72, -32],\n [5, 5, 30, 35, 45, 20],\n [1, 1, 6, 7, 9, 4],\n [-2, -2, -12, -14, -18, -8],\n [9, 9, 54, 63, 81, 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[[-147, -32, 75, -28, -89, 78],\n [-147, -153, 7, -44, 1, 92],\n [112, -34, -104, -70, 13, 76],\n [-96, -34, 42, -12, -23, 8],\n [4, -106, -114, -60, 82, 34],\n [32, 60, 62, 18, -132, 144]]\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, -41, -176, 4, 68, -53],\n [-55, 76, -20, 0, -26, -64],\n [56, -19, -68, 62, 30, 15],\n [149, -104, -124, 45, -39, -7],\n [-47, 57, 99, 78, 29, 80],\n [-111, 98, -4, -30, 84, -40]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[73, 8, 109, 97, -19, -29],\n [-15, -10, 1, -45, 161, -101],\n [49, 9, 63, 76, -81, 27],\n [-39, -9, -45, -66, 99, -45],\n [-43, -3, -69, -52, -21, 39],\n [-23, -8, -19, -47, 109, -61]]?\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[[-88, -98, -116, 11, -26, -92],\n [20, -242, -122, 74, 94, -146],\n [18, -75, -13, -9, 65, -21],\n [30, 59, 65, -34, 19, 61],\n [-58, 106, 11, -25, -88, 37],\n [-26, 232, 115, -78, -90, 141]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-44, -43, -46, -33, 13, 52],\n [-106, -100, -104, -100, -30, 60],\n [149, 18, 206, 58, 97, -62],\n [22, 17, 53, 31, -54, 6],\n [-131, -83, -102, -57, -122, 145],\n [-27, 63, -77, 57, 9, 63]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-54, 63, -72, 36, 0, -18],\n [-24, 28, -32, 16, 0, -8],\n [24, -28, 32, -16, 0, 8],\n [-30, 35, -40, 20, 0, -10],\n [0, 0, 0, 0, 0, 0],\n [54, -63, 72, -36, 0, 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[[-59, -193, -46, -73, -33, 143],\n [-102, -65, -34, -61, -8, 78],\n [-12, 106, 51, 20, 70, 5],\n [-51, -110, -64, -70, -61, 31],\n [63, 102, 27, 48, 11, -94],\n [92, 50, 57, 78, 39, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-108, 96, 54, -12, -70, 104],\n [87, 84, 195, -27, 26, -25],\n [-173, -29, -179, -13, -36, 51],\n [100, -32, 28, 44, 0, -12],\n [-179, 89, -18, 25, -137, 187],\n [135, -29, 68, -13, 79, -107]]\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, -48, -50, -40, 98, 8],\n [33, 32, 35, 30, -57, 3],\n [12, 40, 47, 44, -55, 20],\n [-54, 48, 64, 68, -28, 62],\n [60, 32, 32, 24, -72, -12],\n [69, 8, 2, -6, -48, -33]]?\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, 16, -56, 16, -24, -72],\n [-36, 18, -63, 18, -27, -81],\n [-40, 20, -70, 20, -30, -90],\n [-36, 18, -63, 18, -27, -81],\n [8, -4, 14, -4, 6, 18],\n [-20, 10, -35, 10, -15, -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[[-40, 8, 32, -8, -8, 8],\n [0, 0, 0, 0, 0, 0],\n [60, -12, -48, 12, 12, -12],\n [30, -6, -24, 6, 6, -6],\n [20, -4, -16, 4, 4, -4],\n [40, -8, -32, 8, 8, -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[[-107, 24, -11, -41, -14, 52],\n [94, -56, -27, 73, -151, 163],\n [133, -109, 52, 122, -107, -23],\n [-15, 16, -29, -11, -28, 75],\n [48, 40, -29, 11, 41, -31],\n [-70, 42, -34, -38, -4, 66]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-47, -17, -29, 14, 79, -27],\n [45, 45, 15, -140, -15, 45],\n [0, -3, 13, 61, -48, 3],\n [-61, -13, -30, 26, 80, -24],\n [4, 10, 15, 28, -47, 15],\n [-55, 29, -9, -8, 29, 21]]\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[[113, -63, 6, -80, 11, 9],\n [-107, 110, 132, 53, 50, -199],\n [234, -154, -124, -108, -120, 54],\n [-104, 106, 196, 4, 152, -136],\n [-24, 6, 40, -24, 100, 74],\n [-29, 23, -58, 46, 40, -77]]\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 6x6 matrix:\n[[77, 171, 7, 67, -114, -153],\n [-219, 36, -56, 1, 214, -30],\n [-41, 98, 5, -105, -73, -81],\n [-56, 110, 20, -143, -70, -120],\n [175, 52, -8, 104, -160, 0],\n [114, -106, 4, 8, -112, 162]]\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[[-41, -31, 186, -21, 98, -88],\n [-21, 17, -97, -42, 66, 34],\n [-65, 34, 10, 131, -152, -66],\n [69, -47, -34, -65, 100, 56],\n [60, 96, -180, 54, -43, 136],\n [-57, 9, 173, -13, 31, -84]]\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[[-7, 21, 35, -21, -70, 7],\n [4, -12, -20, 12, 40, -4],\n [-10, 30, 50, -30, -100, 10],\n [-8, 24, 40, -24, -80, 8],\n [2, -6, -10, 6, 20, -2],\n [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[[-12, 4, 94, -30, 28, -13],\n [21, 8, 53, -6, 47, 19],\n [-117, -5, 58, -60, -94, -100],\n [21, -74, -65, 18, -63, -37],\n [-91, 14, 35, -42, -63, -63],\n [35, -80, -5, 6, -31, -35]]?\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, 0, 0, 0, 0, 0],\n [20, 6, 20, -18, -16, 14],\n [70, 21, 70, -63, -56, 49],\n [20, 6, 20, -18, -16, 14],\n [-10, -3, -10, 9, 8, -7],\n [-50, -15, -50, 45, 40, -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[[49, -10, -13, 38, -28, 45],\n [0, 29, 30, -25, 88, 11],\n [-39, -13, 51, 2, 154, 15],\n [-146, -59, -30, -148, -11, -36],\n [4, 1, -23, -17, -46, 4],\n [-11, -93, -44, 59, 33, 119]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-17, -7, -85, 53, -55, 24],\n [-56, -18, 53, -26, -26, -36],\n [23, -34, -122, 73, -30, 43],\n [-6, -29, -153, 94, -73, 47],\n [-31, -15, -59, 39, -55, 10],\n [-5, -101, -16, 15, 3, -12]]\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 6x6 matrix:\n[[-66, -66, -58, -26, -43, 26],\n [-126, 95, -10, 27, 94, 8],\n [117, -77, 0, -56, -38, 15],\n [-165, 16, 98, 44, -20, -179],\n [-122, 7, -48, 10, -66, -16],\n [12, 79, 62, 50, 71, -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[[-20, 77, -3, -3, -1, -48],\n [25, -103, 3, 0, -1, 63],\n [-40, -17, -25, -101, -59, -20],\n [-40, 145, -7, -11, -5, -92],\n [40, -91, 13, 41, 23, 68],\n [35, -110, 8, 19, 10, 73]]\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, -4, -209, -51, -36, -33],\n [66, -23, -131, -81, -27, -22],\n [78, -28, -92, -39, 28, -14],\n [122, -88, -43, -63, 68, 13],\n [90, -14, -86, -105, 26, -42],\n [-70, -15, -14, 12, -113, 39]]\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[[-54, 30, -36, -30, 6, -36],\n [27, -15, 18, 15, -3, 18],\n [-63, 35, -42, -35, 7, -42],\n [-36, 20, -24, -20, 4, -24],\n [-36, 20, -24, -20, 4, -24],\n [54, -30, 36, 30, -6, 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[[3, 78, -75, -144, -57, 78],\n [18, -104, 28, -131, -85, 157],\n [-9, -112, -20, 103, 17, 38],\n [-69, -58, -58, 65, -87, 57],\n [53, -75, 92, 13, -4, -26],\n [-49, 103, -95, -9, 7, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[24, 8, 16, 80, 24, -48],\n [27, 9, 18, 90, 27, -54],\n [3, 1, 2, 10, 3, -6],\n [15, 5, 10, 50, 15, -30],\n [-18, -6, -12, -60, -18, 36],\n [18, 6, 12, 60, 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[[-34, 103, 104, 66, -99, 113],\n [34, 76, -10, 127, -21, 31],\n [-37, 108, 78, 10, -145, 88],\n [-76, -104, 8, 0, 1, -45],\n [-66, -20, -70, 10, 61, -105],\n [-72, -55, 2, 7, 80, -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 6x6 matrix:\n[[-63, -144, 59, 55, 45, 21],\n [47, 125, 62, -80, -43, -49],\n [73, -17, 105, -8, 35, -100],\n [9, -30, 85, -18, 7, -77],\n [3, -165, 51, 126, 117, 102],\n [47, 1, -11, 4, 13, -54]]\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 6x6 matrix:\n[[-21, -19, -47, 41, -66, -105],\n [1, -47, -53, -56, 33, 132],\n [115, -56, 18, 106, 31, 39],\n [-51, 27, -11, -12, -51, -66],\n [-26, 124, 114, -73, 67, 10],\n [119, -127, 69, 149, 6, 45]]\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[[146, -47, 76, 71, 37, 57],\n [52, 35, -11, -41, -21, 18],\n [77, 18, 2, 10, 7, 38],\n [-3, 6, -72, -30, -111, 93],\n [22, -149, 141, 109, 3, -6],\n [95, 71, 45, -56, 61, -63]]\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[[46, -55, -86, -124, -47, -16],\n [-15, 77, 74, 54, 37, -40],\n [-54, -58, -78, 0, 21, 0],\n [-91, -125, -144, -38, -11, -52],\n [6, -88, -132, -102, -43, 56],\n [-15, -160, -17, 44, -71, -10]]\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[[8, -8, -14, 18, 12, -14],\n [-40, 40, 70, -90, -60, 70],\n [-8, 8, 14, -18, -12, 14],\n [-32, 32, 56, -72, -48, 56],\n [-8, 8, 14, -18, -12, 14],\n [36, -36, -63, 81, 54, -63]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-139, -18, 44, -68, -18, 12],\n [4, 48, -32, 8, 120, -24],\n [23, -10, 100, 4, -70, 88],\n [-16, -49, -14, -11, -100, -17],\n [-41, -14, 104, -26, -62, 80],\n [108, 8, -82, 55, 20, -50]]\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[[1, -12, 23, -17, 57, 9],\n [36, 38, 9, 18, -121, -99],\n [-96, -54, -19, 73, -32, 5],\n [-36, -6, -19, 55, -98, -43],\n [-66, -38, -7, 52, -25, -7],\n [68, 24, 38, -71, 89, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-80, 16, -16, -32, -16, -48],\n [-40, 8, -8, -16, -8, -24],\n [-90, 18, -18, -36, -18, -54],\n [-40, 8, -8, -16, -8, -24],\n [60, -12, 12, 24, 12, 36],\n [20, -4, 4, 8, 4, 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 6x6 matrix:\n[[15, 20, -7, -38, 16, 12],\n [15, 5, 2, -42, 4, 23],\n [-42, -5, -11, 120, -4, -71],\n [-6, 70, -44, 36, 56, -62],\n [27, 15, 0, -74, 12, 37],\n [0, 90, -54, 24, 72, -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[[-35, -19, -24, 84, -5, 39],\n [42, 16, 60, -64, 68, -92],\n [37, -42, 88, 90, 148, -61],\n [-11, -6, -78, 44, -54, 115],\n [97, 28, -5, -19, 143, -14],\n [-63, 43, -28, -20, -27, -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[[-6, 17, -5, 0, 9, -1],\n [14, -89, 13, 24, -41, 17],\n [-22, -61, -15, 60, -17, 33],\n [-39, 55, -31, 27, 36, 10],\n [-24, 31, -19, 18, 21, 7],\n [5, 29, 3, -21, 10, -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 6x6 matrix:\n[[-30, -80, -10, -90, -70, 30],\n [21, 56, 7, 63, 49, -21],\n [30, 80, 10, 90, 70, -30],\n [-18, -48, -6, -54, -42, 18],\n [24, 64, 8, 72, 56, -24],\n [-18, -48, -6, -54, -42, 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[[9, 15, 24, -6, 18, -12],\n [-19, -21, -72, 2, -22, 46],\n [-36, -108, 0, 72, -144, -45],\n [-18, -30, -48, 12, -36, 24],\n [25, 31, 88, -6, 34, -54],\n [28, 100, -32, -72, 136, 66]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-15, 37, 99, 7, 150, -21],\n [-78, -38, -102, 42, -100, 70],\n [-54, 14, -16, 0, 15, -61],\n [42, -28, 31, 35, 10, 156],\n [75, -9, 36, 6, 60, 75],\n [21, -48, -56, 25, -115, 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[[0, -58, 64, 128, -2, 70],\n [42, -28, -26, -34, 90, 32],\n [32, 161, 34, -151, -36, -108],\n [6, 44, -44, -97, 9, -49],\n [27, 30, -57, -114, 54, -33],\n [-64, -22, -44, 26, -72, -24]]\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[[-123, 9, -244, 84, -33, 8],\n [-5, -65, -82, 118, -65, -72],\n [1, 61, -30, -78, 85, 72],\n [21, -51, -15, 73, -42, -56],\n [119, -7, 197, -72, 44, -4],\n [35, 11, 12, -26, 41, 16]]\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 6x6 matrix:\n[[49, -13, 90, 2, -32, -97],\n [100, -26, 84, 10, -64, -82],\n [58, -40, -18, 2, -86, 2],\n [87, -29, -18, 12, -68, 27],\n [-26, 3, 69, -9, 9, -88],\n [26, 28, -60, 18, 52, 112]]\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[[-75, -112, 39, -83, -73, -60],\n [15, 50, -44, 48, 34, -53],\n [-45, 52, -74, -34, -30, 49],\n [1, -183, 53, -139, -46, -70],\n [-28, -83, 106, 50, -7, -114],\n [-80, -159, 163, -34, -90, -114]]\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[[54, 24, -30, 0, 0, -6],\n [18, 8, -10, 0, 0, -2],\n [-18, -8, 10, 0, 0, 2],\n [18, 8, -10, 0, 0, -2],\n [-27, -12, 15, 0, 0, 3],\n [54, 24, -30, 0, 0, -6]]\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 6x6 matrix:\n[[47, -21, 8, -3, 18, -39],\n [-40, -35, -85, -25, 10, 60],\n [-118, 92, 38, 28, -64, 78],\n [63, -7, 42, 7, 14, -63],\n [-106, 67, 11, 17, -50, 78],\n [-152, 80, -8, 16, -64, 120]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 18, -15, -30, 12, 15],\n [0, 60, -50, -100, 40, 50],\n [0, 30, -25, -50, 20, 25],\n [0, 0, 0, 0, 0, 0],\n [0, 48, -40, -80, 32, 40],\n [0, -24, 20, 40, -16, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[14, -34, 26, -74, 10, 44],\n [-40, 13, -75, 84, -6, -38],\n [40, -37, 35, -116, -26, 102],\n [-89, -52, -82, 55, 91, -84],\n [-86, -61, -163, 46, 10, 12],\n [34, 47, 14, 22, -59, 21]]?\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[[-136, 48, 44, -47, 37, -44],\n [-24, 48, 87, -117, 52, -86],\n [-133, 101, 8, -99, 5, -94],\n [-99, 151, -30, -159, -41, -168],\n [54, 48, -126, -2, -88, -3],\n [-33, 93, -132, -32, -100, -60]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[136, 8, -58, 66, -151, 79],\n [-53, -109, -35, -6, -1, 69],\n [60, 108, 26, -42, 59, -19],\n [49, 111, -3, -20, 94, 16],\n [-160, 22, 74, -66, 233, -93],\n [124, -14, -60, -76, -100, 126]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-196, 62, 0, -17, -6, -72],\n [38, 179, 39, 82, 80, 60],\n [-42, 21, 65, 51, 66, -10],\n [123, -14, -14, 30, -131, -69],\n [331, 31, 14, 80, 19, 122],\n [97, 8, 15, 44, -45, -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 6x6 matrix:\n[[-6, 23, -90, 75, 80, 26],\n [-6, 13, -40, 40, 35, 16],\n [-30, 1, 120, -24, -113, 16],\n [-48, 40, 0, 96, -8, 64],\n [48, -12, -140, 2, 134, -36],\n [48, -40, 0, -96, 8, -64]]\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, 48, -42, 30, 30, 36],\n [-56, 56, -49, 35, 35, 42],\n [-48, 48, -42, 30, 30, 36],\n [56, -56, 49, -35, -35, -42],\n [16, -16, 14, -10, -10, -12],\n [-48, 48, -42, 30, 30, 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[[68, 31, 65, 28, -81, 12],\n [-25, -14, 109, -14, 59, 125],\n [-37, -27, 82, 24, 34, 101],\n [14, 51, -73, -20, -55, -46],\n [-90, -63, -27, 21, 81, 24],\n [-85, -73, -40, 44, 64, -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 6x6 matrix:\n[[24, 52, -70, -81, -13, 38],\n [-16, 0, 0, 4, 17, -9],\n [-60, -4, 76, 9, 52, -17],\n [48, -4, -14, -3, -49, 20],\n [62, -36, -27, 49, -63, -2],\n [-14, -68, -49, 125, 20, -77]]\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 6x6 matrix:\n[[-81, -120, -71, 85, 49, -68],\n [136, 95, 50, -1, -135, 59],\n [-36, -174, -72, 76, 121, 52],\n [-64, -143, -57, 31, 144, 39],\n [91, 14, 60, 17, 18, 128],\n [-27, -24, -66, 3, -57, -80]]\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, -91, -37, -33, 3, -40],\n [51, -3, -91, -123, 101, -121],\n [33, 122, 28, -3, -10, 58],\n [69, 15, -103, -141, 125, -142],\n [-57, 12, 92, 111, -118, 143],\n [38, 37, 5, 24, 51, -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[[-18, 70, -46, 38, -74, 6],\n [85, -29, 73, -68, 120, -48],\n [75, -31, 67, -62, 110, -42],\n [-11, -85, 33, -24, 52, 12],\n [63, 77, 7, -14, 14, -42],\n [-104, 16, -80, 76, -132, 60]]?\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[[27, 29, -29, 12, 34, -47],\n [-31, 24, -118, 139, 64, 40],\n [-41, -159, 152, -5, -111, 103],\n [116, 157, -25, -35, 112, -203],\n [51, 77, 46, -68, 112, -129],\n [123, 107, -66, 18, 46, -171]]\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, -35, 21, 70, 7, 63],\n [16, 10, -6, -20, -2, -18],\n [16, 10, -6, -20, -2, -18],\n [48, 30, -18, -60, -6, -54],\n [-40, -25, 15, 50, 5, 45],\n [0, 0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-54, -46, -72, 42, -83, 24],\n [8, 10, -18, 14, 37, -6],\n [-39, -25, -133, 84, 7, 5],\n [61, 57, 29, -14, 136, -37],\n [-60, -45, -42, 66, -87, 102],\n [-19, -21, -67, 2, -28, -61]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[110, 8, 39, -87, -32, 57],\n [-16, -30, -70, 67, 59, 15],\n [4, 14, 32, -29, -27, -9],\n [-24, 20, 40, -22, -34, -30],\n [-20, 8, 14, -2, -12, -18],\n [-38, 36, 73, -43, -62, -51]]\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[[-78, -134, -52, -66, 35, 42],\n [-84, -94, 19, -51, -5, 39],\n [-52, -89, -36, -46, 24, 28],\n [86, 51, -57, 69, 28, -35],\n [40, -20, -130, -30, 70, -10],\n [122, 30, -162, 60, 85, -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[[36, -20, 12, -32, 16, -40],\n [-63, 35, -21, 56, -28, 70],\n [9, -5, 3, -8, 4, -10],\n [-9, 5, -3, 8, -4, 10],\n [-81, 45, -27, 72, -36, 90],\n [-63, 35, -21, 56, -28, 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[[-99, 84, -11, 108, 60, -8],\n [-60, -63, -46, 195, -27, -82],\n [24, 93, 117, -91, 79, -46],\n [60, -30, 3, -104, -24, 24],\n [-18, -72, -69, 57, -24, -72],\n [-35, 40, -29, 29, -10, 116]]?\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, 21, -21, -12, 42, 126],\n [15, 18, -15, -18, 36, 75],\n [24, -5, -11, 44, -10, 146],\n [-17, -36, 23, 54, -72, -73],\n [-3, 51, -18, -114, 102, -57],\n [9, 55, -26, -106, 110, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[-25, 0, -9, 17, 9, -10],\n [84, -135, -130, -57, 31, 4],\n [-159, 20, 36, 56, -20, 50],\n [96, 36, -30, 4, -14, -104],\n [-45, 156, 77, 98, 27, -126],\n [-33, -39, -20, -6, -7, 38]]\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 6x6 matrix:\n[[40, 58, -20, -34, -46, -64],\n [-56, -68, 4, 44, 44, 80],\n [56, 68, -4, -44, -44, -80],\n [4, 52, -86, -16, -76, -40],\n [60, 43, 50, -39, -1, -64],\n [-92, -74, -62, 62, 14, 104]]\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[[-130, 139, -25, -93, 216, -2],\n [128, -6, 47, 13, -63, 11],\n [-136, 106, 8, -99, 201, -41],\n [-118, -16, -94, 116, -81, 54],\n [60, -25, -53, -88, 89, -105],\n [1, 56, 118, -69, 81, -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[[2, 12, 14, 8, -4, 2],\n [0, 0, 0, 0, 0, 0],\n [-3, -18, -21, -12, 6, -3],\n [9, 54, 63, 36, -18, 9],\n [-3, -18, -21, -12, 6, -3],\n [-8, -48, -56, -32, 16, -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[[-8, -10, 8, -4, -5, -3],\n [-56, -70, 56, -28, -35, -21],\n [40, 50, -40, 20, 25, 15],\n [32, 40, -32, 16, 20, 12],\n [80, 100, -80, 40, 50, 30],\n [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[[-60, -18, -54, -60, -54, -60],\n [60, 18, 54, 60, 54, 60],\n [70, 21, 63, 70, 63, 70],\n [80, 24, 72, 80, 72, 80],\n [-100, -30, -90, -100, -90, -100],\n [-20, -6, -18, -20, -18, -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[[0, 0, 0, 0, 0, 0],\n [-27, 0, -90, 18, -81, 27],\n [27, 0, 90, -18, 81, -27],\n [-18, 0, -60, 12, -54, 18],\n [12, 0, 40, -8, 36, -12],\n [3, 0, 10, -2, 9, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-32, -66, -58, 58, 17, 78],\n [-23, 15, -59, 81, 64, -30],\n [-7, 65, 94, 22, 68, -211],\n [2, 20, 36, -110, 35, -228],\n [45, -9, -120, -115, 88, 50],\n [59, 16, 15, -137, 72, -18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-133, 198, 95, -69, -73, 161],\n [93, -105, 39, 7, 1, -140],\n [77, -38, 29, -5, 3, -86],\n [-85, 39, -22, 8, 56, 102],\n [-82, 17, 102, -26, -44, 27],\n [79, -186, 60, 46, 38, -153]]?\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[[50, 18, -1, -27, 11, 40],\n [89, 45, -6, -20, 64, 12],\n [-1, 7, -20, -10, -57, 73],\n [-21, -1, -43, -19, -26, -1],\n [22, -20, 41, -29, 15, 10],\n [-24, -18, 20, 20, 61, -107]]\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[[-100, -20, 30, 50, 80, -90],\n [20, 4, -6, -10, -16, 18],\n [50, 10, -15, -25, -40, 45],\n [70, 14, -21, -35, -56, 63],\n [10, 2, -3, -5, -8, 9],\n [-60, -12, 18, 30, 48, -54]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-14, -56, 21, 21, -35, 0],\n [2, 8, -3, -3, 5, 0],\n [4, 16, -6, -6, 10, 0],\n [-18, -72, 27, 27, -45, 0],\n [16, 64, -24, -24, 40, 0],\n [-14, -56, 21, 21, -35, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[-126, -28, -21, 35, -7, -42],\n [-20, -120, 150, -110, 30, -40],\n [-94, -44, 15, 3, 1, -38],\n [70, 56, -42, 21, -7, 35],\n [20, 68, -81, 58, -16, 25],\n [2, -92, 123, -93, 25, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[56, -43, 5, -105, -33, -73],\n [-121, -181, 67, 150, -48, 34],\n [71, 39, 0, 30, 65, -11],\n [-5, 39, -7, -40, -51, 53],\n [84, 170, -69, -120, 58, -34],\n [-28, -17, 16, 75, 7, 39]]\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[[-1, -2, 1, -10, -9, 8],\n [-6, -12, 6, -60, -54, 48],\n [2, 4, -2, 20, 18, -16],\n [5, 10, -5, 50, 45, -40],\n [-1, -2, 1, -10, -9, 8],\n [-9, -18, 9, -90, -81, 72]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-10, 20, 60, 20, -20, -50],\n [5, -10, -30, -10, 10, 25],\n [5, -10, -30, -10, 10, 25],\n [7, -14, -42, -14, 14, 35],\n [7, -14, -42, -14, 14, 35],\n [2, -4, -12, -4, 4, 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 6x6 matrix:\n[[69, -15, -28, -27, 115, -103],\n [96, 8, 88, -72, 24, 0],\n [8, -53, 57, -14, -28, 98],\n [-15, 55, -14, 21, -41, -79],\n [49, -24, 21, -69, 95, 107],\n [10, 100, -30, -55, 65, 30]]\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 6x6 matrix:\n[[18, -24, -217, -4, 29, 13],\n [-7, -81, -32, -40, 81, 3],\n [-19, -134, -35, 38, 150, 57],\n [1, -54, -57, -34, 52, -1],\n [-119, -47, -75, 36, 158, 80],\n [-26, 34, 175, 24, -25, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[7, -3, -6, -6, -10, -5],\n [42, -18, -36, -36, -60, -30],\n [-35, 15, 30, 30, 50, 25],\n [42, -18, -36, -36, -60, -30],\n [-28, 12, 24, 24, 40, 20],\n [-35, 15, 30, 30, 50, 25]]?\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[[29, 67, -22, -4, -42, 13],\n [-67, 8, -8, -39, -82, 72],\n [-73, -36, 36, -59, -2, 26],\n [18, 84, -6, -39, -42, 15],\n [-6, -95, 4, 56, 58, -28],\n [-113, -1, -2, -68, -114, 107]]\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[[-44, 48, 42, -20, -52, -20],\n [52, -94, -86, 20, 76, 30],\n [-16, 10, 8, -8, -16, -6],\n [40, -107, -100, 12, 72, 29],\n [12, 13, 14, 8, 4, 1],\n [-12, -13, -14, -8, -4, -1]]\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[[-34, 22, -22, -5, 5, -36],\n [54, 126, 18, 135, -135, 36],\n [68, 32, 36, 70, -70, 62],\n [58, -4, 34, 35, -35, 57],\n [-38, 0, -22, -25, 25, -37],\n [-62, 20, -38, -25, 25, -63]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[88, 17, -59, 100, 107, -47],\n [76, 28, -68, 203, 144, 61],\n [91, 11, -66, 61, 72, -5],\n [-57, 134, 63, 128, 33, 11],\n [-121, -108, 20, -5, -35, 42],\n [-31, 30, 50, 166, 109, -34]]\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 6x6 matrix:\n[[107, 15, -55, -81, -126, -37],\n [-69, 45, -59, -5, 104, 139],\n [-63, -61, 75, 102, 40, -49],\n [24, 0, -56, 61, 14, 88],\n [134, -45, 25, 64, -126, -98],\n [81, 45, -73, -102, -94, -1]]\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[[69, -36, -48, 12, -78, 0],\n [30, -60, -60, 40, -40, 20],\n [53, 30, 14, -36, -52, -26],\n [-36, 21, 27, -8, 41, -1],\n [-66, -21, -3, 32, 67, 25],\n [-85, 0, 20, 20, 90, 20]]\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, 20, 58, 64, -24, 30],\n [61, -71, -42, -65, 45, -50],\n [-72, -27, 117, 82, -38, 90],\n [-93, 69, 14, -3, -73, 140],\n [-2, 55, 35, 92, 0, -60],\n [-18, -54, -25, -94, -14, 95]]\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[[5, -45, -50, 40, -25, 5],\n [29, -87, -110, 64, -31, 59],\n [19, -84, -100, 68, -38, 34],\n [33, -36, -60, 12, 6, 78],\n [-33, 36, 60, -12, -6, -78],\n [-22, -5, 10, 20, -23, -57]]\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[[18, -3, 28, 75, 90, -13],\n [44, 78, -24, 98, 92, -110],\n [20, -6, 34, 86, 104, -12],\n [-20, -78, 57, -2, 22, 89],\n [-28, -90, 59, -22, 2, 107],\n [-6, 45, -57, -69, -96, -36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[46, -100, 86, -9, -52, 33],\n [77, -66, 61, 46, -64, 8],\n [-56, 72, -64, -19, 52, -17],\n [-81, 2, -9, -89, 52, 23],\n [-25, -70, 55, -70, 0, 40],\n [-35, 78, -67, 8, 40, -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[[-21, -95, 33, 155, -57, -184],\n [0, -6, 86, -80, 45, 139],\n [-97, 85, -36, -15, 57, 42],\n [-44, -35, 103, -3, 48, 54],\n [-30, 160, -155, -105, 88, 251],\n [-42, -61, 39, 111, -22, -142]]\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[[-12, 18, 15, -9, 18, 6],\n [-32, 48, 40, -24, 48, 16],\n [0, 0, 0, 0, 0, 0],\n [24, -36, -30, 18, -36, -12],\n [-8, 12, 10, -6, 12, 4],\n [4, -6, -5, 3, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-69, -135, 145, -83, -102, -78],\n [-64, -114, 22, -70, -122, 13],\n [43, 11, -141, 15, -28, 157],\n [-75, 65, -1, 72, 46, 5],\n [-79, -33, 95, -33, -18, -140],\n [-105, 25, 77, 7, 28, -164]]?\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 6x6 matrix:\n[[38, 68, -105, -91, -1, 93],\n [-57, 1, 54, 107, -37, 146],\n [81, -176, 32, 55, 175, -55],\n [71, -52, -66, 19, 42, 94],\n [36, -24, -36, -56, 89, 55],\n [-8, -6, -1, -13, 21, 69]]\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 6x6 matrix:\n[[-41, 15, -28, -83, 58, -43],\n [167, -171, 4, 167, -3, 38],\n [10, -60, 172, 10, -112, -62],\n [7, -20, 2, -39, 35, -12],\n [147, -127, -52, 163, 20, 63],\n [-25, 55, -46, 40, -21, 28]]\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[[-127, 95, -113, -136, -30, 58],\n [1, 23, -87, 34, 0, 48],\n [25, -11, 12, -89, 55, -51],\n [-105, 9, -5, -81, 34, -20],\n [33, 40, -94, -41, 23, 49],\n [-26, -20, -69, 15, 57, -29]]\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, -43, -38, -11, 39, 59],\n [18, -79, -53, 42, 63, 78],\n [9, -21, -12, 13, 21, 23],\n [43, -75, -38, 55, 81, 83],\n [51, 27, 48, -1, 51, 19],\n [48, 149, 139, -32, -51, -118]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[16, 112, 21, 0, -62, 38],\n [60, -32, 1, -88, 0, -72],\n [-90, 15, -29, 88, -55, 64],\n [50, 23, 34, -54, 64, 73],\n [-102, -11, -11, 62, 60, 279],\n [-25, -147, -40, -51, 52, 23]]\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, 68, 74, 98, -78, -16],\n [143, 63, 37, -107, -45, -55],\n [-16, -100, -77, -38, 96, 38],\n [-221, -185, -14, 112, 54, 31],\n [121, -1, 59, -45, 17, -29],\n [-79, 28, -134, 47, 65, 95]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[84, 60, -78, -3, 3, -72],\n [-56, -45, 34, -32, 7, 56],\n [40, 105, -58, -79, 144, -72],\n [32, 47, -34, -21, 44, -40],\n [28, -12, -18, 30, -58, -8],\n [-32, -87, 2, -25, -78, 72]]\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[[107, -98, -136, 183, -63, -98],\n [-2, 92, -24, -182, 30, 50],\n [104, -116, -16, 76, 20, 7],\n [84, -38, -109, 2, -46, 9],\n [59, -24, -29, -51, -17, 49],\n [83, -92, 70, -54, 100, 92]]\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 6x6 matrix:\n[[-108, 36, 11, -108, -23, 10],\n [84, -24, -14, 72, -27, -64],\n [-19, -9, 7, 27, 89, -4],\n [1, -9, 4, 27, 59, 14],\n [109, -33, -17, 99, -21, -76],\n [41, -21, -3, 63, 47, -24]]\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, 4, -18, 16, 10, -12],\n [0, 20, -90, 80, 50, -60],\n [0, 20, -90, 80, 50, -60],\n [0, -20, 90, -80, -50, 60],\n [0, -12, 54, -48, -30, 36],\n [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[[11, 91, -47, 38, 3, -20],\n [-122, 89, -61, -22, -93, 12],\n [56, -56, -14, 46, -12, -70],\n [38, 32, 18, 42, 54, -6],\n [35, -6, -34, 54, -21, -68],\n [-132, 124, 35, 7, 9, 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[[21, 70, 35, -42, 63, 28],\n [-6, -20, -10, 12, -18, -8],\n [-6, -20, -10, 12, -18, -8],\n [-21, -70, -35, 42, -63, -28],\n [-24, -80, -40, 48, -72, -32],\n [9, 30, 15, -18, 27, 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[[104, -18, 20, -30, -70, 62],\n [45, 2, -2, -28, 0, 33],\n [-101, 42, -11, 78, 19, -125],\n [49, 85, -45, -41, 88, -20],\n [-81, -2, 10, 68, -24, -77],\n [-15, -38, 24, 24, -54, 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[[-100, 90, 90, -90, 10, -90],\n [-30, 27, 27, -27, 3, -27],\n [50, -45, -45, 45, -5, 45],\n [-60, 54, 54, -54, 6, -54],\n [-40, 36, 36, -36, 4, -36],\n [-80, 72, 72, -72, 8, -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 6x6 matrix:\n[[-67, 70, 60, 21, -4, 74],\n [56, 18, 12, 67, -66, -60],\n [65, -116, 39, -108, -9, -22],\n [-16, 100, 2, 43, -17, 90],\n [9, 8, -97, -8, -29, -22],\n [-182, 18, -242, 5, 156, -40]]\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[[101, 20, -117, -142, 78, 45],\n [-68, -78, -51, 21, -135, 136],\n [14, -62, -103, 46, 37, -25],\n [-194, -58, 9, -10, -157, 100],\n [-17, 72, 60, -90, -9, 16],\n [15, 53, -67, -118, 42, 9]]?\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 6x6 matrix:\n[[15, 7, -26, -38, 49, 23],\n [-109, -81, 214, -126, -127, -153],\n [91, 35, -73, 56, 29, 102],\n [35, 61, -96, 106, 35, 43],\n [41, 73, -11, -9, 34, 14],\n [7, -36, -4, 67, -53, 22]]\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[[-83, 102, 20, -15, -196, -72],\n [46, 126, 112, -164, -22, 124],\n [20, 199, -1, 57, -242, 34],\n [-105, -72, -101, 45, -79, -101],\n [118, -41, -139, -41, -12, 92],\n [-141, 4, 136, -105, 49, -35]]\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 6x6 matrix:\n[[-47, -38, -69, 9, -73, -11],\n [71, -93, 85, -133, 29, -45],\n [54, -41, 51, 38, -132, -25],\n [-50, 178, -37, 112, 8, 129],\n [59, 26, 83, -29, 25, 25],\n [-22, 19, -32, 77, 54, -39]]\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[[1, -2, -1, 6, 7, 5],\n [-61, 66, -59, 10, -11, -41],\n [49, -56, 41, 12, 31, 47],\n [25, -29, 20, 9, 19, 26],\n [-12, 17, -3, -25, -32, -27],\n [1, -9, -16, 53, 59, 38]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-20, 102, 34, 148, -133, 52],\n [-117, 160, -60, 67, -20, 114],\n [51, 26, -48, 74, -14, -16],\n [-26, 42, -100, -4, 70, 38],\n [16, 109, -119, -84, 129, 34],\n [43, -23, 39, 97, -87, -34]]?\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[[49, 117, 64, 167, 82, -68],\n [-17, 78, -13, 92, -32, -153],\n [-86, 92, 17, 46, 8, -32],\n [44, -163, -22, -174, 36, 207],\n [121, -23, 84, 63, -74, 8],\n [1, -13, 50, -14, -56, 54]]\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[[-8, -28, 12, 0, 4, 28],\n [-2, -7, 3, 0, 1, 7],\n [-14, -49, 21, 0, 7, 49],\n [-16, -56, 24, 0, 8, 56],\n [14, 49, -21, 0, -7, -49],\n [-20, -70, 30, 0, 10, 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[[-70, 56, -7, -49, -28, -21],\n [-70, 56, -7, -49, -28, -21],\n [10, -8, 1, 7, 4, 3],\n [-30, 24, -3, -21, -12, -9],\n [20, -16, 2, 14, 8, 6],\n [-30, 24, -3, -21, -12, -9]]\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 6x6 matrix:\n[[12, 4, -18, 16, 6, -20],\n [36, 12, -54, 48, 18, -60],\n [-24, -8, 36, -32, -12, 40],\n [18, 6, -27, 24, 9, -30],\n [48, 16, -72, 64, 24, -80],\n [-6, -2, 9, -8, -3, 10]]\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, -11, 5, -2, -23, -5],\n [-48, -32, 76, 58, 56, 80],\n [-48, -22, 62, 50, 58, 70],\n [-48, -27, 69, 54, 57, 75],\n [8, -33, 41, 21, -17, 25],\n [-16, 11, -5, 2, 23, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-81, -93, -41, -77, -88, -24],\n [48, 45, 9, 21, 48, -6],\n [62, 24, -40, -56, 48, -76],\n [78, 78, 22, 46, 80, 0],\n [-55, -15, 45, 65, -40, 80],\n [-81, -93, -41, -77, -88, -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 6x6 matrix:\n[[201, 114, 82, 234, -74, 82],\n [139, 8, -28, 112, -8, 37],\n [104, -80, -73, 11, 90, 87],\n [-4, -50, -79, -61, 60, -51],\n [78, 57, 11, 126, -97, -22],\n [28, 113, 161, 100, -53, 94]]\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 6x6 matrix:\n[[-84, 88, -32, -135, 6, 61],\n [-22, 58, 290, -91, -330, 1],\n [238, -202, -81, 18, 206, -99],\n [-104, 49, -176, 6, 214, 115],\n [-78, 29, -149, 9, 215, 145],\n [-80, 49, 64, -3, -44, 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[[126, -99, -18, 135, -90, 0],\n [62, -18, 14, 70, -50, -60],\n [20, 15, 20, 25, -20, -60],\n [95, -47, 7, 105, -73, -54],\n [-35, 6, -11, -40, 29, 42],\n [-44, 10, -12, -50, 36, 48]]\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[[-65, 21, -44, -14, -35, -47],\n [-43, -59, 12, -6, 69, -73],\n [30, -107, 16, 86, -7, -56],\n [-44, -32, -19, 12, -3, -64],\n [87, -14, 40, 32, 2, 67],\n [42, -63, 51, 18, 72, 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[[-62, -21, 38, 60, 20, 6],\n [0, -1, 32, -6, 18, -36],\n [-3, -36, -47, -33, -37, 13],\n [-36, -44, -94, 14, -62, 92],\n [136, 186, 158, 22, 162, -130],\n [13, 42, 128, 0, 62, -93]]?\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 6x6 matrix:\n[[-94, 38, 12, -104, 60, 16],\n [-47, 73, -44, -20, 36, 8],\n [-121, 7, -36, -100, 20, 62],\n [-53, -21, -52, -20, -28, 54],\n [22, 26, -52, 56, -20, 4],\n [-26, 84, -42, 0, 38, -6]]\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[[-49, 42, 63, 21, 49, -35],\n [-63, 54, 81, 27, 63, -45],\n [-42, 36, 54, 18, 42, -30],\n [-28, 24, 36, 12, 28, -20],\n [-21, 18, 27, 9, 21, -15],\n [-35, 30, 45, 15, 35, -25]]\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[[-18, 9, 15, -15, 30, 3],\n [-12, 6, 10, -10, 20, 2],\n [-60, 30, 50, -50, 100, 10],\n [12, -6, -10, 10, -20, -2],\n [-48, 24, 40, -40, 80, 8],\n [-30, 15, 25, -25, 50, 5]]\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 6x6 matrix:\n[[-49, 63, -63, -28, -28, -28],\n [-21, 27, -27, -12, -12, -12],\n [42, -54, 54, 24, 24, 24],\n [-42, 54, -54, -24, -24, -24],\n [-21, 27, -27, -12, -12, -12],\n [-49, 63, -63, -28, -28, -28]]\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[[-59, 13, 45, -17, -69, 95],\n [-52, -50, 118, -110, -45, -26],\n [-76, 33, 36, -105, -64, 48],\n [-8, 25, -17, 64, -55, 94],\n [93, -39, -29, 69, 5, -85],\n [56, -21, -36, 83, 73, -38]]\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 6x6 matrix:\n[[-57, 66, 0, -22, -132, -14],\n [9, -180, -73, 157, 70, -143],\n [40, 100, 19, -83, 22, 82],\n [52, 16, -2, -22, 76, 36],\n [-49, -154, -34, 128, -16, -124],\n [-42, -90, -5, 67, -22, -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[[15, -15, 18, -29, -12, -9],\n [48, -51, 63, -115, -57, -42],\n [36, -42, 54, -114, -66, -48],\n [-39, 43, -54, 105, 56, 41],\n [-6, 22, -36, 130, 104, 74],\n [-33, 21, -18, -25, -48, -33]]\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 6x6 matrix:\n[[12, -4, 10, -12, -8, 8],\n [24, -8, 20, -24, -16, 16],\n [6, -2, 5, -6, -4, 4],\n [-54, 18, -45, 54, 36, -36],\n [-18, 6, -15, 18, 12, -12],\n [60, -20, 50, -60, -40, 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[[-68, 127, 12, 40, 59, -13],\n [-20, 151, -33, 28, -7, -16],\n [-8, -130, 48, -16, 38, 14],\n [-76, -31, 69, 20, 103, 4],\n [-16, -92, 42, -8, 40, 10],\n [-28, 21, 15, 12, 31, -2]]\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[[102, 44, 8, 20, 5, -1],\n [53, 49, 51, 32, 121, -84],\n [-151, -57, -28, -8, -33, 17],\n [-92, -40, 4, -24, 18, -14],\n [135, 95, 70, 60, 160, -110],\n [86, 28, 18, -4, 19, -9]]?\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 6x6 matrix:\n[[-20, -102, 54, 10, -78, 28],\n [-30, -54, 48, 0, -46, 26],\n [-43, 48, 27, -19, 24, 17],\n [-11, 33, 0, -8, 21, 1],\n [37, -39, -24, 16, -19, -15],\n [-111, 18, 105, -33, -14, 61]]\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[[70, -90, -40, 70, 80, -100],\n [42, -54, -24, 42, 48, -60],\n [28, -36, -16, 28, 32, -40],\n [14, -18, -8, 14, 16, -20],\n [-21, 27, 12, -21, -24, 30],\n [14, -18, -8, 14, 16, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-76, -58, 232, 47, 35, -128],\n [-145, -169, 123, 29, 66, -11],\n [24, -53, -156, -17, 6, 75],\n [-58, -7, 222, 26, 29, -129],\n [25, 162, 42, -45, -29, -9],\n [64, -79, -18, 4, 13, -83]]?\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[[-70, 15, -87, -17, 85, -14],\n [6, -32, -95, -68, 42, 64],\n [28, -30, -44, -84, 36, 32],\n [-2, -10, -37, -32, 26, 16],\n [0, 8, 27, 9, -5, -22],\n [24, -8, 21, -21, -7, -2]]\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[[23, 19, -103, -26, 107, -113],\n [-123, -178, -75, 90, 17, -35],\n [-27, -17, -71, -40, 29, -23],\n [46, 93, 75, 79, -12, 26],\n [55, 150, 1, -16, 62, 37],\n [-26, 37, 37, 79, 24, 96]]\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 6x6 matrix:\n[[-34, 70, 44, -36, 14, -28],\n [48, -28, -51, 15, -7, 131],\n [-73, -12, -56, 60, -62, 19],\n [-46, -24, -58, 58, -46, -20],\n [11, -162, -67, 91, -55, -8],\n [10, -28, -14, 14, -6, 4]]\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[[-57, 15, -68, 208, 94, -83],\n [97, 6, 100, -30, -42, -30],\n [-59, 102, -76, 58, -50, 34],\n [-17, 117, -36, 92, -58, -1],\n [92, 39, 92, -70, -88, 7],\n [-90, -78, -82, -10, 86, 23]]\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[[-133, 106, -20, 196, 96, -17],\n [30, 8, 28, -20, -32, -6],\n [71, 43, 75, -27, -82, -26],\n [98, -133, 39, -201, -64, 61],\n [85, -52, 10, -110, -64, -1],\n [-65, 76, 26, 110, 36, -7]]\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[[-56, -24, 8, 80, 16, -56],\n [55, 10, 5, -65, 30, 110],\n [-29, -26, 17, 55, 54, 26],\n [-13, -11, 7, 24, 22, 9],\n [52, 6, 8, -58, 40, 118],\n [-25, -27, 19, 52, 62, 41]]\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[[-66, 40, 70, -36, -27, -43],\n [52, -22, -30, 32, 0, 12],\n [-78, -84, -58, -76, -25, 15],\n [-80, 72, 118, -37, -45, -73],\n [100, -18, -16, 69, -23, -7],\n [168, 2, 6, 124, -38, -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[[-58, -34, 49, -34, 0, -82],\n [-8, 144, -16, -32, 88, 16],\n [-10, 180, -20, -40, 110, 20],\n [56, 70, -53, 26, 22, 86],\n [28, 84, -34, 4, 40, 52],\n [25, 40, -25, 10, 15, 40]]\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[[142, -81, 62, -97, 170, 47],\n [-9, 81, 90, -36, -18, -9],\n [-108, 90, -12, 58, -132, -38],\n [126, -63, 66, -91, 150, 41],\n [-47, 45, 2, 22, -58, -17],\n [-20, -9, -34, 25, -22, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 2, 4, -2, 6, 4],\n [-2, -2, -4, 2, -6, -4],\n [-7, -7, -14, 7, -21, -14],\n [5, 5, 10, -5, 15, 10],\n [8, 8, 16, -8, 24, 16],\n [1, 1, 2, -1, 3, 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 6x6 matrix:\n[[-6, -60, 60, -60, -12, 54],\n [3, 30, -30, 30, 6, -27],\n [-7, -70, 70, -70, -14, 63],\n [-9, -90, 90, -90, -18, 81],\n [-6, -60, 60, -60, -12, 54],\n [5, 50, -50, 50, 10, -45]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[-100, -36, -137, 50, 46, -138],\n [-43, -17, -130, -126, -55, 23],\n [21, -73, -52, -60, 67, -98],\n [2, 26, -19, 28, -17, -7],\n [-12, -158, 87, -20, -83, 94],\n [17, 37, -51, -132, -1, 36]]\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[[20, 30, -5, 10, 0, 35],\n [-40, -60, 10, -20, 0, -70],\n [-12, -18, 3, -6, 0, -21],\n [-4, -6, 1, -2, 0, -7],\n [-28, -42, 7, -14, 0, -49],\n [-4, -6, 1, -2, 0, -7]]\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[[-76, -33, -95, -89, -11, -70],\n [-17, 77, 56, -39, -46, -23],\n [41, -53, 38, 95, 77, -9],\n [62, 18, 94, -34, -1, 86],\n [-44, 26, 20, -40, -85, 34],\n [33, 122, 135, -76, -92, 87]]\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[[-39, -85, 12, -22, 104, -25],\n [161, -5, -88, 101, 54, -102],\n [-89, -101, -36, 3, -84, 2],\n [32, 248, 60, 40, -26, 82],\n [-31, 119, 112, -86, 148, 62],\n [-76, -22, 80, -146, 188, 22]]?\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, -60, -31, -63, 37, 80],\n [-40, -3, 29, -9, 61, 56],\n [-41, 93, 88, 90, 20, -56],\n [30, 48, 6, 54, -66, -96],\n [-41, -29, 14, -36, 74, 88],\n [46, -24, -50, -18, -58, -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 6x6 matrix:\n[[-40, -68, -6, -100, -36, 36],\n [-22, -50, -9, -70, -24, 36],\n [-23, 26, 26, 20, 1, -63],\n [-45, -24, 17, -50, -23, -27],\n [25, -10, -20, 0, 5, 45],\n [51, 72, 1, 110, 41, -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[[24, 40, 4, -28, 12, -36],\n [64, 60, -46, -58, 22, -41],\n [22, 18, -19, -19, 7, -11],\n [96, 104, -52, -92, 36, -78],\n [-32, -16, 40, 24, -8, 4],\n [52, 68, -14, -54, 22, -56]]?\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[[-80, 8, -80, -40, 48, -72],\n [80, -8, 80, 40, -48, 72],\n [80, -8, 80, 40, -48, 72],\n [-90, 9, -90, -45, 54, -81],\n [60, -6, 60, 30, -36, 54],\n [50, -5, 50, 25, -30, 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[[-90, -58, -68, -15, 99, 112],\n [19, -4, 17, 108, -60, -4],\n [-68, -54, -65, -30, 93, 94],\n [-144, 86, 76, 3, -9, 4],\n [72, -46, -46, -29, 21, 0],\n [-8, 58, 38, -109, 9, -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 6x6 matrix:\n[[0, 70, 23, 55, -61, 21],\n [-54, -38, -30, 56, 62, -80],\n [-120, -25, -28, 63, 46, -53],\n [13, 45, -31, 42, -43, 16],\n [-120, 8, 98, 6, 2, 10],\n [-40, -48, -35, -63, 27, 29]]\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[[30, 64, -86, -1, -10, 6],\n [14, -13, 21, -51, -8, -4],\n [-4, -15, 25, -4, 10, -6],\n [-18, -22, -10, -11, -74, 36],\n [-8, 66, -97, 97, 6, 13],\n [46, 46, -39, -48, 20, -17]]?\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 6x6 matrix:\n[[43, 22, 20, -40, 19, -23],\n [-28, -20, -12, 20, -12, 20],\n [-61, -122, -12, -40, -21, 113],\n [-30, 57, -27, 105, -18, -48],\n [41, -23, 27, -85, 21, 17],\n [45, 67, 13, 5, 17, -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[[82, 0, -38, 3, 48, -69],\n [136, -20, -84, 14, 64, -122],\n [-14, 72, 82, -33, 48, 39],\n [-41, 41, 62, -20, 8, 50],\n [-43, -19, 0, 7, -40, 29],\n [11, -39, -46, 18, -24, -24]]\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[[41, 61, -146, -53, -121, -67],\n [30, -7, 46, -73, 115, -11],\n [-28, -6, -6, 62, -54, 11],\n [-3, -24, -38, -2, -88, 13],\n [40, 14, 4, -86, 74, -18],\n [36, 59, -162, -43, -159, -59]]\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 6x6 matrix:\n[[165, 37, -2, -40, -7, -84],\n [173, 15, 38, 34, -90, -105],\n [68, 28, -24, -24, -4, -24],\n [19, -5, 14, 52, -70, -15],\n [-34, -2, -12, 48, -58, 24],\n [23, 27, -34, -136, 158, 1]]\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[[-137, 32, -49, 128, 87, -169],\n [-33, 13, -7, 31, 19, -34],\n [-72, 15, -4, 81, -29, 29],\n [-139, 49, -115, 67, -37, 20],\n [-6, -17, 78, 73, -45, 71],\n [65, 16, 13, -80, 129, -167]]?\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, 36, 64, -112, -4, 152],\n [-21, -45, -31, 19, 12, -32],\n [-67, -87, -30, 111, 34, -66],\n [-46, -12, -88, 70, -14, -176],\n [-78, -50, -83, 132, 6, -186],\n [-5, -65, 42, 1, 38, 106]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[100, 25, 176, -22, -104, 64],\n [155, 41, -117, -73, -99, -191],\n [89, 59, 101, 49, -139, 56],\n [-6, 7, -80, 29, 55, -100],\n [0, 2, 127, 43, -24, 135],\n [-122, -22, 43, 69, 116, 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[[-199, -69, 132, -36, 65, -20],\n [10, -38, -6, 79, -4, 9],\n [92, -75, -48, -15, -56, -106],\n [4, 90, -5, 32, 26, 91],\n [41, 17, 29, 198, 47, 59],\n [-59, -15, 12, 24, 9, 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 6x6 matrix:\n[[8, -23, 11, 11, 18, -6],\n [-34, 36, -23, 53, -67, 54],\n [-28, 22, -16, 56, -54, 48],\n [-32, 27, -19, 61, -62, 54],\n [8, -62, 26, 74, 24, 12],\n [-22, -31, 6, 122, -35, 60]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[49, -70, 28, 28, 21, -70],\n [18, -40, 24, 12, 10, -40],\n [9, 30, -36, 0, -3, 30],\n [6, 20, -24, 0, -2, 20],\n [61, -130, 76, 40, 33, -130],\n [-67, 160, -100, -46, -39, 160]]\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[[-100, -80, 100, -70, 30, 30],\n [-20, -16, 20, -14, 6, 6],\n [10, 8, -10, 7, -3, -3],\n [-50, -40, 50, -35, 15, 15],\n [20, 16, -20, 14, -6, -6],\n [-60, -48, 60, -42, 18, 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 6x6 matrix:\n[[42, -30, 65, 21, -37, -42],\n [0, 35, -12, 35, -4, 11],\n [-65, 90, 62, -15, -16, 34],\n [8, -60, -5, -45, 13, -16],\n [-66, 55, 44, -47, 0, 31],\n [-30, 40, 26, -8, -6, 16]]\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 6x6 matrix:\n[[30, 54, 54, -6, 18, 54],\n [0, 0, 0, 0, 0, 0],\n [30, 54, 54, -6, 18, 54],\n [-5, -9, -9, 1, -3, -9],\n [40, 72, 72, -8, 24, 72],\n [10, 18, 18, -2, 6, 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[[14, 0, -20, -14, 12, 18],\n [-35, 0, 50, 35, -30, -45],\n [-28, 0, 40, 28, -24, -36],\n [-21, 0, 30, 21, -18, -27],\n [-63, 0, 90, 63, -54, -81],\n [49, 0, -70, -49, 42, 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[[36, 16, 32, 8, 20, 4],\n [0, 0, 0, 0, 0, 0],\n [54, 24, 48, 12, 30, 6],\n [45, 20, 40, 10, 25, 5],\n [36, 16, 32, 8, 20, 4],\n [-72, -32, -64, -16, -40, -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[[-13, 6, -55, 19, 10, 82],\n [121, -80, -39, -1, 86, -21],\n [-115, 52, -8, 55, -113, 74],\n [-41, 22, 57, -1, -58, -54],\n [-3, 48, 77, -101, 62, -89],\n [33, -50, -88, 69, -3, 91]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[76, 29, -45, -58, 122, 29],\n [-25, -1, -59, 17, 137, -35],\n [-28, 37, 48, 1, -14, 22],\n [-3, 35, 25, -16, 108, 59],\n [128, -18, -57, 41, -36, -62],\n [-75, 65, 13, -29, 159, 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[[-52, -74, 58, 24, 34, -26],\n [-122, -118, -9, -91, 7, -101],\n [93, 77, 70, 87, 38, 46],\n [-93, -78, -21, -33, -126, -57],\n [-44, -26, -103, -57, -49, 21],\n [84, 77, 31, 62, 20, 51]]\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, 31, -40, 36, 19, 31],\n [52, 73, 170, 29, -149, -109],\n [56, 50, 40, 36, -46, -22],\n [-80, -56, 20, -54, 4, -20],\n [20, -7, -110, 17, 83, 75],\n [92, 65, -20, 62, -7, 21]]?\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[[-115, 2, -66, -1, -60, 130],\n [108, -11, 13, -5, -16, -48],\n [63, 9, 68, 15, 74, -138],\n [-103, -8, -50, -29, -24, 154],\n [-12, -5, 12, -20, 34, 24],\n [-139, 38, -62, 83, -92, -14]]\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[[-75, -9, -66, -122, 161, -89],\n [-15, -23, -2, 18, -15, 13],\n [40, -16, -80, -80, -40, -64],\n [98, 94, 49, 59, 0, -90],\n [106, 78, 82, 92, -90, 30],\n [-9, 9, -73, -117, 89, -103]]\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 6x6 matrix:\n[[-146, -117, -54, -9, 42, 47],\n [-22, -27, 103, 49, -52, 77],\n [30, -53, -95, -141, -69, -78],\n [-73, 12, -60, -90, 48, -53],\n [-6, 72, 178, 40, -49, 61],\n [-127, -83, -66, 35, 88, 42]]\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[[47, 107, -30, 30, 85, 89],\n [5, -40, -18, -60, -38, -43],\n [27, 80, 26, 20, 106, 91],\n [13, -43, -50, -70, -65, -61],\n [40, 37, -24, -50, 41, 30],\n [-10, -69, -32, -50, -87, -80]]\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[[-159, 44, -76, 10, -5, 155],\n [-159, 144, 0, 67, -64, 90],\n [-93, 74, 2, -4, -45, 68],\n [-98, 110, 14, 107, -51, 62],\n [10, 204, 188, 154, -164, -54],\n [-170, 152, 0, 57, -69, 95]]\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, -75, 105, 69, 12, -32],\n [35, -44, 7, -98, -27, -41],\n [13, -38, 43, -68, 15, -75],\n [-15, 11, 17, 44, 24, -2],\n [86, -73, 17, -25, -66, 22],\n [-36, 52, 1, 163, 33, 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[[49, -56, -56, -49, -28, 14],\n [-7, 8, 8, 7, 4, -2],\n [-42, 48, 48, 42, 24, -12],\n [-70, 80, 80, 70, 40, -20],\n [21, -24, -24, -21, -12, 6],\n [35, -40, -40, -35, -20, 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[[20, -20, 2, 8, 8, 16],\n [80, -80, 8, 32, 32, 64],\n [-60, 60, -6, -24, -24, -48],\n [-40, 40, -4, -16, -16, -32],\n [10, -10, 1, 4, 4, 8],\n [-40, 40, -4, -16, -16, -32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, -20, -18, 16, -42, -10],\n [-48, -67, -46, 25, -90, -1],\n [12, 10, -2, 14, -18, -20],\n [-18, -22, -11, 0, -15, 9],\n [-24, -25, -6, -13, 6, 25],\n [-6, -9, -7, 5, -15, -2]]\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[[-4, -14, -10, -10, -20, 2],\n [-20, -70, -50, -50, -100, 10],\n [-16, -56, -40, -40, -80, 8],\n [0, 0, 0, 0, 0, 0],\n [-8, -28, -20, -20, -40, 4],\n [14, 49, 35, 35, 70, -7]]\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, -96, -60, 37, 45, 39],\n [-12, -11, -42, 29, 79, -31],\n [-7, 86, 7, -60, 74, 82],\n [-43, -13, -54, -61, 0, 68],\n [-22, -86, 25, 61, -72, -20],\n [-82, -161, 14, 98, -74, 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[[-48, 37, 38, 27, 70, 74],\n [87, 29, -15, -39, 57, -104],\n [5, 74, -44, 71, 106, -19],\n [99, -114, 137, -180, -13, -112],\n [67, 7, -2, -11, 77, -103],\n [54, 36, 50, -15, 163, -72]]?\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[[-14, -25, -40, 22, -168, -28],\n [-76, -44, 104, -117, 47, -86],\n [-110, -51, -138, -81, -25, -10],\n [-66, 71, 14, 55, -53, 102],\n [-68, -63, -49, -156, 32, -78],\n [2, -30, -39, -74, 172, -20]]\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[[80, 24, -32, -56, -16, 24],\n [90, 27, -36, -63, -18, 27],\n [50, 15, -20, -35, -10, 15],\n [50, 15, -20, -35, -10, 15],\n [-60, -18, 24, 42, 12, -18],\n [30, 9, -12, -21, -6, 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[[5, 28, -91, -115, 70, -80],\n [-61, 40, 10, -12, -7, -66],\n [-102, 8, 152, 152, -106, 20],\n [-3, 70, 39, 62, -97, 18],\n [141, -32, -54, -4, -1, 114],\n [-16, 70, 53, 74, -104, 16]]\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 6x6 matrix:\n[[21, 14, -37, 15, -110, -104],\n [-3, -15, -30, 9, 12, 0],\n [-22, 2, 84, -30, 120, 128],\n [10, 36, 62, -18, -44, -16],\n [-10, -36, -62, 18, 44, 16],\n [-2, -24, -58, 18, 4, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[81, 148, 128, 8, 93, -64],\n [-42, -129, -9, -22, -120, 94],\n [-63, -144, 10, 12, -26, 20],\n [64, 150, -72, 18, 52, -56],\n [70, -58, 101, -108, 32, -85],\n [5, 45, -91, -31, -56, 45]]\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, 62, -7, 18, -66, -62],\n [134, -79, -47, -88, 7, 3],\n [-125, 120, -1, 106, 8, 2],\n [-25, 36, -47, -58, -100, -118],\n [-4, 24, -66, 20, 32, 40],\n [-14, 34, -54, -38, -64, -77]]\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, 6, 54, -56, -46, 44],\n [71, 83, 25, 18, 36, -20],\n [-42, -33, 0, -16, 20, 35],\n [-91, -130, -47, -22, -100, 3],\n [-44, 17, -38, 52, 68, -33],\n [77, 61, 101, -72, 65, 106]]\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[[32, 34, 173, 27, -116, 15],\n [25, -13, -57, -37, 20, -1],\n [-24, 8, 16, 38, 2, 8],\n [73, 33, 10, 86, -54, 104],\n [-17, -25, -106, -35, 71, -20],\n [53, 27, 5, 76, -39, 85]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-15, -10, 15, 30, -10, 25],\n [-27, -18, 27, 54, -18, 45],\n [9, 6, -9, -18, 6, -15],\n [21, 14, -21, -42, 14, -35],\n [-15, -10, 15, 30, -10, 25],\n [24, 16, -24, -48, 16, -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 6x6 matrix:\n[[41, 71, 37, 79, -82, -44],\n [-90, 97, 110, -57, -4, -3],\n [161, -77, -51, 75, -34, -104],\n [86, 50, 42, 64, -60, -102],\n [-117, 164, 187, -46, -62, -19],\n [-68, -4, -22, -31, 32, 75]]\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[[-19, -24, -7, 30, 12, 12],\n [6, 8, 22, -3, -28, 51],\n [-158, -160, 169, -67, 62, -37],\n [22, 24, 4, 3, -78, 105],\n [-38, -32, 86, -64, -14, 8],\n [43, 48, -26, -23, -55, 23]]\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[[-90, 70, 40, 40, -10, 60],\n [90, -70, -40, -40, 10, -60],\n [-9, 7, 4, 4, -1, 6],\n [-90, 70, 40, 40, -10, 60],\n [45, -35, -20, -20, 5, -30],\n [36, -28, -16, -16, 4, -24]]?\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 6x6 matrix:\n[[-39, 31, 50, -38, 59, -103],\n [-120, 40, 58, -144, 166, 16],\n [15, -23, 124, -95, -14, -73],\n [-38, 52, -181, 149, -8, 55],\n [79, -26, -103, 152, -100, 39],\n [-118, 60, -20, -33, 25, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[12, 0, 12, 3, 30, -6],\n [-32, 0, -32, -8, -80, 16],\n [24, 0, 24, 6, 60, -12],\n [-12, 0, -12, -3, -30, 6],\n [12, 0, 12, 3, 30, -6],\n [8, 0, 8, 2, 20, -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[[18, -134, 116, -78, 66, 27],\n [-108, 94, 10, -19, -25, 48],\n [31, -75, 111, -87, -25, 63],\n [-59, -33, -59, 66, 150, -22],\n [-15, -36, -79, -20, 84, 47],\n [-81, 42, 71, 99, 27, -11]]\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, 62, 68, -66, 88, 66],\n [36, 18, 44, -46, 40, 46],\n [-30, -50, -70, 70, -80, -70],\n [-69, 95, 39, -29, 96, 29],\n [-96, 29, -44, 53, -4, -53],\n [-54, 57, 14, -7, 52, 7]]\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[[25, -68, -94, -65, 172, -16],\n [-37, -20, -16, 6, -2, -80],\n [174, -159, 85, 5, 75, 28],\n [-39, 30, 64, 55, -130, -48],\n [70, -93, -1, -13, 89, -36],\n [-65, 161, 26, 14, -142, 153]]\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, 154, 15, -21, 153, 106],\n [12, 160, 91, 12, 143, 146],\n [-71, -92, -27, 81, -36, -95],\n [-42, -128, 115, -2, -173, -120],\n [-27, -74, 24, 233, -25, 8],\n [135, -25, -28, -230, -81, -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 6x6 matrix:\n[[18, -96, -18, 90, 36, 9],\n [-40, 100, 20, -40, 0, -10],\n [16, -108, -20, 112, 48, 10],\n [12, -30, -6, 12, 0, 3],\n [-6, -36, -6, 66, 36, 3],\n [-21, 95, 18, -81, -30, -9]]\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[[56, -137, 39, 1, -120, 69],\n [-54, 125, -27, -25, 126, -102],\n [45, 105, -94, 51, 128, -9],\n [19, 13, -12, -4, 18, -32],\n [-142, -11, 101, -79, -46, -44],\n [154, 13, -93, 72, 6, 2]]\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 6x6 matrix:\n[[40, 5, 10, -45, -40, -20],\n [8, 1, 2, -9, -8, -4],\n [-8, -1, -2, 9, 8, 4],\n [-64, -8, -16, 72, 64, 32],\n [40, 5, 10, -45, -40, -20],\n [-24, -3, -6, 27, 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[[-79, -90, -11, 13, 9, -25],\n [162, 31, 57, -35, -61, 2],\n [-2, -3, 60, 67, -31, 29],\n [78, 13, -1, -49, -15, -14],\n [6, -42, -39, -60, 12, -39],\n [-61, -36, -33, -7, 25, -17]]\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 6x6 matrix:\n[[92, -52, 9, -47, 42, -11],\n [-5, -31, 73, 35, 11, 85],\n [-47, 16, -128, -21, -7, -83],\n [90, -67, -101, -52, 71, -55],\n [1, 96, -101, 43, 79, -115],\n [41, -128, -36, -139, -114, 16]]\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 6x6 matrix:\n[[43, -71, 47, 5, -43, -10],\n [-73, 92, -125, 118, -5, -152],\n [-56, 6, 19, 44, 83, -23],\n [-23, 102, -102, -22, -15, 11],\n [7, 87, -90, -43, -7, 53],\n [-35, -96, 97, 86, 11, -110]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, 94, 19, 76, 73, -11],\n [-20, 123, 75, 201, 37, 97],\n [80, 76, 37, 48, 188, -48],\n [-42, 43, 21, 103, -45, 19],\n [26, -143, 50, -23, -100, 84],\n [-35, 35, 18, 78, -36, 70]]\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[[-8, 54, 7, 35, -105, -16],\n [-22, -103, -4, 23, 23, -75],\n [100, 61, -2, -65, -71, -99],\n [30, 86, 17, -5, -80, 10],\n [-43, -34, 35, 62, -43, 0],\n [-58, -122, -13, 41, 56, -38]]?\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, 36, 36, -24, 40, -20],\n [24, -72, -72, 48, -80, 40],\n [-18, 54, 54, -36, 60, -30],\n [9, -27, -27, 18, -30, 15],\n [-3, 9, 9, -6, 10, -5],\n [-30, 90, 90, -60, 100, -50]]?\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[[35, -10, 40, 15, 53, -44],\n [-42, 77, -63, 49, -14, -63],\n [21, 30, 30, 7, 69, -52],\n [-17, -54, -49, 50, -100, 10],\n [-6, 33, -27, 65, 6, -83],\n [24, -96, 24, -16, -48, 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[[48, -16, -16, 80, -8, 72],\n [-24, 8, 8, -40, 4, -36],\n [-42, 14, 14, -70, 7, -63],\n [-36, 12, 12, -60, 6, -54],\n [-60, 20, 20, -100, 10, -90],\n [42, -14, -14, 70, -7, 63]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-48, -24, 24, -12, -12, -42],\n [-16, -8, 8, -4, -4, -14],\n [56, 28, -28, 14, 14, 49],\n [-56, -28, 28, -14, -14, -49],\n [-56, -28, 28, -14, -14, -49],\n [16, 8, -8, 4, 4, 14]]\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[[-76, 65, -11, -21, 4, -11],\n [-95, 25, -70, -30, 60, 25],\n [41, -25, 16, 12, -12, -1],\n [15, -30, -15, 3, 16, 14],\n [42, 15, 57, 15, -52, -29],\n [32, -25, 7, 9, -4, 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[[10, 40, 28, 16, 0, 40],\n [91, -93, -53, 44, 73, -23],\n [110, 9, -19, -112, 77, 90],\n [-143, 3, 65, 160, -171, -41],\n [-30, 30, -113, -102, 2, 22],\n [82, -93, 85, 32, 85, -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[[-27, -4, 11, -22, -22, -11],\n [22, 69, 29, 17, 17, -4],\n [-41, -35, 0, -33, -33, -11],\n [64, -51, -61, 53, 53, 38],\n [-52, -34, 6, -42, -42, -16],\n [62, 46, -4, 50, 50, 18]]\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 6x6 matrix:\n[[0, 24, 31, 54, -26, 27],\n [12, -126, -18, -111, 123, -75],\n [148, 80, 100, 26, -56, 26],\n [-76, 48, -61, 28, -54, 25],\n [80, 32, 75, 34, -22, 19],\n [-34, 24, -14, 31, -28, 19]]\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[[32, 96, -120, 28, 108, -24],\n [-72, 59, -3, 49, 64, 106],\n [-12, -92, 87, -38, -98, 1],\n [44, 90, -81, 36, 86, -49],\n [12, 52, -87, 8, 68, -1],\n [20, 17, -12, 7, 12, -27]]\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[[79, 15, 11, 53, 9, -65],\n [5, -23, 6, -78, 46, -8],\n [-74, -4, 60, -82, 64, 10],\n [108, -16, -77, 49, -50, -23],\n [17, -124, 32, 37, -30, -73],\n [-5, -10, 57, -32, 55, -42]]?\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[[3, 7, 46, -17, 8, 82],\n [-51, -35, -14, -23, -4, 22],\n [21, 14, 2, 11, 1, -16],\n [-15, -7, 26, -19, 4, 62],\n [80, 56, 32, 32, 8, -16],\n [53, 35, 2, 29, 2, -46]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-32, 0, -24, 80, -32, 40],\n [-4, 0, -3, 10, -4, 5],\n [24, 0, 18, -60, 24, -30],\n [-40, 0, -30, 100, -40, 50],\n [-36, 0, -27, 90, -36, 45],\n [4, 0, 3, -10, 4, -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[[25, -30, -40, 50, 10, -15],\n [15, -18, -24, 30, 6, -9],\n [20, -24, -32, 40, 8, -12],\n [45, -54, -72, 90, 18, -27],\n [-10, 12, 16, -20, -4, 6],\n [25, -30, -40, 50, 10, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-18, -18, 24, -54, -72, 90],\n [-55, -69, 50, 31, -52, 37],\n [-29, -33, 32, -31, -68, 77],\n [-26, -36, 18, 62, 16, -40],\n [19, 27, -12, -55, -20, 41],\n [31, 36, -33, 23, 64, -70]]\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, -90, 54, 4, 9, 35],\n [-30, 30, -50, -20, -35, -25],\n [-4, 84, -44, 0, -2, -30],\n [-28, 48, -56, -18, -32, -30],\n [16, -96, 64, 8, 16, 40],\n [-24, 84, -68, -14, -26, -40]]\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[[14, 15, -5, 1, -32, 41],\n [-5, -35, -5, -5, 80, -40],\n [-105, 15, -7, -31, -12, -50],\n [-87, 21, 12, -15, -39, -66],\n [9, -13, 5, 5, 24, -20],\n [-37, -35, 26, 5, 67, -128]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-120, -82, -67, -59, 2, -69],\n [-2, 113, -56, -3, -101, 29],\n [-29, 59, 71, 104, -145, 32],\n [132, 76, -101, -114, 113, 40],\n [50, 88, 79, 146, -32, -43],\n [7, -68, 25, 17, 104, -83]]?\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[[196, 32, 4, -31, -48, 23],\n [17, -7, -8, -86, -66, -61],\n [-114, -19, 62, -64, -61, -47],\n [-72, 58, -10, 4, -16, -57],\n [284, -10, -119, -89, 3, 23],\n [-202, 27, 157, 17, -80, -38]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[71, -36, -35, -18, -38, -47],\n [54, -74, -36, -28, 24, -50],\n [-16, -41, 48, 0, -49, -24],\n [-150, -90, 190, 20, -70, -10],\n [-52, 156, 11, 44, -27, 90],\n [180, -69, -126, -48, -27, -96]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -6, 30, 37, -46, 15],\n [0, 23, 3, -14, -40, -28],\n [0, -7, -3, 2, 16, 8],\n [0, 8, 24, 20, -56, -4],\n [0, 15, 15, 5, -50, -15],\n [0, 5, -3, -7, -2, -7]]\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, 108, -52, 64, -4, 26],\n [-93, -51, -46, -5, -87, -9],\n [-35, -63, 42, 19, -15, 27],\n [78, -69, 26, -113, 33, -69],\n [60, -45, -20, -121, 7, -86],\n [-51, 33, 18, 99, -7, 71]]\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[[77, 52, -41, 37, 52, 18],\n [-15, 0, 10, -7, -24, -102],\n [-17, 33, 85, 21, -30, -55],\n [147, 102, -58, 79, 108, 120],\n [53, 38, -10, 33, 44, 92],\n [20, 50, 67, 40, 8, 50]]\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[[20, -8, -16, -12, 12, -40],\n [-40, 16, 32, 24, -24, 80],\n [25, -10, -20, -15, 15, -50],\n [-25, 10, 20, 15, -15, 50],\n [-15, 6, 12, 9, -9, 30],\n [-5, 2, 4, 3, -3, 10]]\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[[-11, -10, 32, 145, -35, -57],\n [-42, -27, 51, 132, -38, -19],\n [-48, -96, -24, 4, 60, 90],\n [56, -17, 31, -24, -78, -94],\n [3, -54, 24, 61, -35, -40],\n [35, -13, -41, -145, 29, 29]]?\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[[-51, -115, -38, 62, -133, -149],\n [-96, -92, 38, -56, -131, -10],\n [43, 28, -4, 72, 67, 4],\n [-16, 5, 14, -48, -11, 29],\n [-39, -53, -21, -11, -87, -85],\n [86, 71, -23, 79, 124, 23]]?\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[[-26, -8, 127, 79, -31, -99],\n [-72, 12, -36, -19, -85, -33],\n [-46, -42, -40, -48, -70, -48],\n [-13, -75, -124, -119, -42, 3],\n [-7, -29, -22, -29, -18, -15],\n [-65, -57, -89, -88, -99, -48]]\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[[3, 5, 71, 121, -48, -110],\n [92, 7, 42, -12, -4, -91],\n [74, -57, 48, 93, -103, -148],\n [-18, -54, -9, 78, -82, -23],\n [-84, 63, -21, -15, 69, 117],\n [84, -55, 69, 135, -125, -181]]?\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 6x6 matrix:\n[[30, 34, -38, 20, 20, 8],\n [-8, 31, 31, 40, -3, 45],\n [-70, -34, 80, -34, -39, 9],\n [-81, 39, 27, -78, -24, 18],\n [-59, -20, 76, -14, -33, 21],\n [109, -68, -74, 52, 36, -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[[-139, 133, 54, 63, 124, -16],\n [40, -53, 2, -105, 31, 88],\n [17, -28, -4, 5, -53, 33],\n [-42, 1, 18, 112, -145, 77],\n [14, -55, 10, -6, -97, 131],\n [7, -4, 0, -30, 29, 4]]\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[[85, -82, -167, -85, 20, -92],\n [-2, -180, -86, -132, -8, -28],\n [-62, -78, 88, 0, 0, -43],\n [15, 152, 49, 91, 4, 99],\n [53, 103, 18, 84, 36, 39],\n [-7, -69, 54, 2, 28, 44]]\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 6x6 matrix:\n[[-56, -20, 26, 96, 18, -60],\n [-8, 26, 122, -38, -84, -100],\n [36, 39, 65, 6, 54, -36],\n [85, 71, -48, 6, 52, 64],\n [25, -2, -17, -42, 24, 36],\n [-28, -35, -71, 50, 36, 40]]\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 6x6 matrix:\n[[-108, 38, 14, -82, 72, -24],\n [92, 54, 6, 78, -76, -4],\n [66, 18, 0, 54, -51, 3],\n [40, 35, 5, 35, -35, -5],\n [-92, -1, 5, -73, 67, -11],\n [6, 98, 20, 14, -21, -27]]\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[[64, -190, -72, 14, -15, -123],\n [12, -5, -41, -20, 22, 1],\n [98, -60, -104, -100, -12, -21],\n [-102, 87, 43, 76, 68, 44],\n [-10, 59, 19, -16, -2, 40],\n [62, -1, -27, -74, -37, 11]]\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[[21, -6, -12, 21, -3, -27],\n [-7, 2, 4, -7, 1, 9],\n [35, -10, -20, 35, -5, -45],\n [-35, 10, 20, -35, 5, 45],\n [63, -18, -36, 63, -9, -81],\n [21, -6, -12, 21, -3, -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[[-17, 0, -17, 41, 0, -43],\n [-72, -78, -65, 86, 55, -65],\n [-38, -66, -33, 18, 47, 1],\n [-24, -50, -63, 26, 57, -79],\n [-3, -8, 25, -17, -8, 63],\n [54, 60, 40, -58, -38, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[64, -102, -61, -130, 45, 0],\n [0, 25, -81, -11, 93, -62],\n [24, -102, -19, -148, -31, 4],\n [32, 20, -50, 36, 90, -16],\n [64, -71, 37, -19, -25, 74],\n [4, -25, -20, -48, 5, -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[[-98, 30, -36, -60, 124, -45],\n [121, -247, 151, 131, -17, -48],\n [-84, 90, -70, -42, -80, 109],\n [-97, 113, -75, -59, -19, 81],\n [78, 80, 36, 64, -54, 141],\n [61, -70, 34, 36, -28, -35]]?\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[[-42, -80, -66, 68, 14, 28],\n [48, 40, 54, -22, 14, -32],\n [57, 88, 81, -70, -7, -38],\n [-57, -16, -51, -8, -35, 38],\n [42, -64, 6, 88, 70, -28],\n [-21, -64, -43, 60, 21, 14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 22, -16, 16, -80, -86],\n [68, 32, -12, -56, 16, -88],\n [76, 37, -21, -55, -10, -122],\n [-58, -5, 32, 48, 8, 93],\n [-114, -46, 2, 116, -104, 82],\n [26, 11, 3, -29, 34, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-27, -54, -63, 63, 72, 27],\n [-15, -30, -35, 35, 40, 15],\n [-24, -48, -56, 56, 64, 24],\n [-30, -60, -70, 70, 80, 30],\n [27, 54, 63, -63, -72, -27],\n [15, 30, 35, -35, -40, -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[[41, -73, 44, -79, 32, -29],\n [-54, -16, -67, 68, 64, 31],\n [128, -62, -51, 100, 40, -168],\n [68, -226, -27, -67, -5, -174],\n [53, -121, 38, -121, -22, -95],\n [-60, -18, 69, -113, -53, 93]]?\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[[30, 30, -4, 22, 70, -32],\n [-20, -72, 73, -44, -34, 31],\n [21, -39, 100, -43, 41, 2],\n [23, 159, -153, 55, -15, -29],\n [-6, -26, 44, -34, -26, 20],\n [-47, -161, 106, -37, -25, 38]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0, 0],\n [-8, 0, 20, 8, 8, 28],\n [10, 0, -25, -10, -10, -35],\n [0, 0, 0, 0, 0, 0],\n [18, 0, -45, -18, -18, -63]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[12, 131, -200, 108, 64, -140],\n [-1, 77, 14, -129, 98, 63],\n [-82, -76, -130, -48, -154, 0],\n [2, 0, -89, 117, -41, -91],\n [14, 135, -191, 99, 73, -133],\n [24, -67, 166, -18, -2, 70]]\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[[63, -78, -26, -85, -47, 23],\n [-1, 6, 2, 5, 9, 9],\n [22, -12, -4, -18, 10, 38],\n [27, 18, 6, 3, 69, 111],\n [47, -42, -14, -51, -7, 49],\n [-9, 54, 18, 45, 81, 81]]\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 6x6 matrix:\n[[-62, 13, -37, 8, -46, -10],\n [64, -8, 33, 1, 38, 25],\n [-30, -27, 14, -53, 36, -95],\n [0, 24, -23, 41, -42, 65],\n [94, -29, 65, -28, 86, -10],\n [-140, 34, -88, 26, -112, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-24, 24, -64, -18, 100, -70],\n [-20, 22, -58, -34, 118, -70],\n [4, -59, 68, 41, -57, 85],\n [4, 70, -103, 20, -62, -91],\n [22, 38, -99, 27, -82, -75],\n [18, 12, -23, -3, -36, -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[[78, 72, -39, 96, -27, -117],\n [110, 40, -95, 80, -35, -45],\n [-87, -18, 84, -51, 27, 9],\n [93, 42, -75, 75, -30, -54],\n [-54, -96, -3, -108, 21, 171],\n [-17, -58, -19, -59, 8, 108]]\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[[-15, -19, 5, -39, -27, -31],\n [-50, 30, 70, 70, 110, 30],\n [-80, 6, 88, 22, 86, -12],\n [30, -11, -38, -27, -51, -8],\n [70, 35, -54, 67, 11, 68],\n [90, 16, -86, 24, -48, 46]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 14, -2, -10, 70, 10],\n [-42, -15, -1, 23, 45, -21],\n [-81, -70, -37, 50, -115, -97],\n [-33, -64, 48, 101, -45, -39],\n [-24, -9, -85, -55, -135, -57],\n [18, 33, -65, -85, -55, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-32, -58, 12, -157, -102, -30],\n [-14, 69, -86, -129, 121, -74],\n [39, -24, 121, -91, -86, 59],\n [-2, 13, -57, 191, -67, -67],\n [-53, 9, -104, 143, 27, -34],\n [-57, 9, 39, 26, -175, 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[[57, 64, 36, -23, 16, -26],\n [-31, 31, 3, 7, 34, -23],\n [-10, 39, -14, -13, -1, -92],\n [62, 34, 11, 77, -19, -21],\n [-53, 33, -112, -118, 17, 88],\n [6, -101, 108, 131, -13, -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[[10, -88, -86, -46, 140, -94],\n [-4, -53, -65, -90, 53, -37],\n [6, 34, 12, 134, 42, 48],\n [17, -102, -73, -28, 144, -120],\n [-21, 136, 50, 22, -102, 123],\n [16, -135, -93, -54, 151, -125]]\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[[-24, 45, 92, -40, 20, 92],\n [39, -40, -4, 29, 50, -44],\n [-105, -46, -12, 57, 6, 116],\n [-57, 46, 36, -33, -36, 88],\n [-36, -61, 36, 57, 81, 74],\n [13, 124, 100, -115, -44, 48]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[-24, 18, 24, -36, -36, -42],\n [32, -24, -32, 48, 48, 56],\n [24, -18, -24, 36, 36, 42],\n [4, -3, -4, 6, 6, 7],\n [24, -18, -24, 36, 36, 42],\n [16, -12, -16, 24, 24, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[-82, -180, -16, -98, -61, -46],\n [15, 11, 10, -4, 20, 7],\n [-37, -23, -26, 14, -51, -17],\n [15, 11, 10, -4, 20, 7],\n [-68, -54, -44, 14, -89, -32],\n [-73, -37, -54, 36, -104, -33]]\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[[-112, -103, 100, 19, -48, -166],\n [20, -49, 40, 97, -60, 26],\n [-28, 15, -12, -59, 32, -38],\n [-77, -5, 44, -37, -6, -131],\n [-26, 44, -24, -80, 44, -42],\n [-35, -72, 11, -17, 13, -19]]?\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[[55, -62, -16, -80, -40, 48],\n [-54, 80, -10, 80, 11, -61],\n [-9, 42, -90, 20, -113, 59],\n [-17, 7, 8, 25, 11, 18],\n [38, -43, -14, -55, -32, 39],\n [62, -38, -36, -90, -56, -14]]\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[[52, -49, 100, -1, -63, 9],\n [33, 39, -30, 57, -54, 54],\n [-25, -5, -10, -23, 36, -24],\n [43, -76, 130, -30, -45, -17],\n [-17, -16, 10, -26, 27, -25],\n [-66, 57, -120, -3, 81, -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[[3, -10, 2, 9, 4, -6],\n [-12, 40, -8, -36, -16, 24],\n [21, -70, 14, 63, 28, -42],\n [-30, 100, -20, -90, -40, 60],\n [-6, 20, -4, -18, -8, 12],\n [-12, 40, -8, -36, -16, 24]]\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 6x6 matrix:\n[[18, 27, 69, -21, 33, 69],\n [-52, -70, 68, -20, 140, -92],\n [-72, -92, 87, 3, 139, -56],\n [-102, -80, 11, -27, 84, -34],\n [26, -5, 117, -1, 101, -5],\n [124, 69, 158, -34, 133, -51]]\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 6x6 matrix:\n[[-6, 89, 51, -57, 27, 63],\n [41, 134, 188, -43, -8, 122],\n [59, -94, 53, 113, -20, -16],\n [-16, 146, 99, -56, -2, 84],\n [93, 74, 201, -65, 8, 128],\n [38, -11, 81, 47, -45, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[45, 90, 45, 54, 36, 18],\n [-30, -60, -30, -36, -24, -12],\n [45, 90, 45, 54, 36, 18],\n [40, 80, 40, 48, 32, 16],\n [-45, -90, -45, -54, -36, -18],\n [-35, -70, -35, -42, -28, -14]]\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[[144, 197, 74, 137, 99, -124],\n [55, 99, 57, 120, 68, -46],\n [5, 19, 37, 133, 82, -25],\n [-63, -110, -41, -32, -9, 31],\n [-57, -104, -51, -82, -41, 37],\n [-108, -144, -48, -78, -60, 90]]?\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 6x6 matrix:\n[[38, -47, 22, 38, -3, 80],\n [28, 58, -33, -27, 102, 30],\n [6, -95, 50, 58, -99, 40],\n [18, 99, -54, -54, 135, 0],\n [22, -39, 19, 29, -15, 50],\n [-94, 91, -41, -79, -21, -190]]\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[[11, 18, 131, -10, -105, -96],\n [11, -23, -47, -8, 70, 42],\n [-36, -29, -94, 38, 55, 54],\n [38, 49, 88, -44, -65, -48],\n [-6, 37, -56, -3, 5, 41],\n [3, -6, -97, -5, 85, 77]]?\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, -35, -75, 20, -15, -65],\n [-4, 8, 12, 10, -12, 17],\n [-6, 33, 45, 54, -63, 72],\n [-16, 60, 84, 92, -108, 130],\n [-4, 50, 66, 88, -102, 110],\n [10, -27, -39, -38, 45, -58]]\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, 30, -18, -18, 18, -60],\n [55, 65, -25, -55, 55, -20],\n [-44, -5, -4, 11, -11, -45],\n [-21, 35, -21, -21, 21, -70],\n [-34, -100, 46, 76, -76, 90],\n [51, 56, -21, -48, 48, -13]]\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, -33, -18, -92, 6, -5],\n [35, -145, 2, -58, -26, -19],\n [31, -4, 108, -123, 60, 27],\n [19, -85, -5, -40, -16, -13],\n [-13, 5, -22, 73, -2, 80],\n [-61, 167, -71, 60, 20, 51]]\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[[-1, 6, -20, 55, 146, 54],\n [24, 42, 40, 2, 10, -18],\n [12, 64, 54, 56, 80, 48],\n [98, 34, -9, -53, 93, -153],\n [41, 40, -5, 39, -26, -30],\n [-69, -104, -48, -73, -86, 14]]\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, 32, 52, -36, -32, -24],\n [-34, -62, -18, -6, -88, 36],\n [21, 54, -4, 20, 86, -24],\n [-53, -86, -36, 4, -84, 48],\n [28, 72, -8, 24, 78, -24],\n [-33, -68, -10, -14, -102, 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 6x6 matrix:\n[[-9, 1, 1, -4, -10, 7],\n [45, -5, -5, 20, 50, -35],\n [-9, 1, 1, -4, -10, 7],\n [-36, 4, 4, -16, -40, 28],\n [-72, 8, 8, -32, -80, 56],\n [9, -1, -1, 4, 10, -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[[-16, 38, -108, 2, 176, 119],\n [70, 98, -126, 55, 25, 54],\n [-30, 85, -129, -49, 133, 110],\n [-84, -39, -41, 11, -11, -99],\n [-31, -16, -5, 45, -194, -187],\n [-11, -25, -38, 25, 4, -102]]\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[[-21, -75, 81, 105, 9, 69],\n [-43, -101, 108, 84, 5, 83],\n [1, -43, 51, 125, -29, 55],\n [-31, -58, 57, 6, 51, 35],\n [58, 119, -123, -56, -44, -86],\n [32, 39, -57, -36, 190, -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[[54, 54, -54, 30, -51, -27],\n [-27, -17, 12, 5, 13, 21],\n [-54, -42, 36, -6, 36, 36],\n [45, -5, 30, -75, 20, -60],\n [-18, -46, 60, -66, 52, -12],\n [-36, 28, -60, 108, -46, 66]]\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, 48, 134, 23, -38, 96],\n [16, 104, 33, 64, -27, 70],\n [-10, -6, 11, 72, 127, -83],\n [-48, -10, 69, -35, 25, -23],\n [34, -18, -118, -27, -22, -33],\n [66, 80, -9, 66, 95, -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[[0, -6, 9, -30, 18, 15],\n [0, 2, -3, 10, -6, -5],\n [0, -10, 15, -50, 30, 25],\n [0, -18, 27, -90, 54, 45],\n [0, -14, 21, -70, 42, 35],\n [0, -12, 18, -60, 36, 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[[13, -40, 17, 80, 50, -24],\n [-4, 32, -20, -32, -24, 0],\n [-9, -8, 15, -42, -19, 30],\n [-11, -24, 29, -46, -17, 42],\n [1, -8, 5, 8, 6, 0],\n [-18, 0, 18, -90, -45, 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[[4, -16, 153, 153, -195, -78],\n [19, -40, -78, -47, 119, 87],\n [-106, -80, 48, 26, -110, 16],\n [28, -32, 27, 57, -37, 11],\n [-52, -46, 135, 118, -183, -49],\n [19, 126, 15, -31, -22, -113]]\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 6x6 matrix:\n[[0, 3, 46, -10, 20, 12],\n [6, 4, 96, -12, 51, 6],\n [-9, 14, -154, -17, -92, -5],\n [-18, -40, 16, 56, 5, 46],\n [9, 104, 30, -183, -30, 13],\n [-24, -90, -52, 148, -8, 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[[63, 3, 14, -64, 60, -11],\n [108, 22, 87, 92, 28, 117],\n [-6, 91, 8, -127, -61, -125],\n [-49, -16, -1, -65, 87, -49],\n [-26, 53, 96, 181, -4, 122],\n [129, -32, 21, -121, 28, -36]]\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 6x6 matrix:\n[[-84, 38, -24, 47, 55, 7],\n [2, -46, -77, 33, 104, -84],\n [84, -69, -38, -26, 41, -97],\n [59, -42, -7, -23, 19, -43],\n [22, 15, 88, -40, 71, 25],\n [-106, 63, -10, 49, 16, 38]]\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 6x6 matrix:\n[[-100, -59, 33, 95, 112, 14],\n [38, 72, 40, 12, -10, -66],\n [84, 71, -5, -59, -80, -38],\n [8, 61, 57, 47, 28, -70],\n [13, 7, -5, -13, -15, -1],\n [-32, -110, -86, -58, -24, 116]]\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, -18, 0, 4, -20, -10],\n [56, 63, 0, -14, 70, 35],\n [16, 18, 0, -4, 20, 10],\n [-48, -54, 0, 12, -60, -30],\n [72, 81, 0, -18, 90, 45],\n [32, 36, 0, -8, 40, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[54, 9, -33, 51, -111, -27],\n [94, -20, -94, 54, -94, -26],\n [8, 0, -8, 8, -18, -12],\n [26, 42, 44, 40, -94, 72],\n [-43, -22, -13, -31, 57, -91],\n [63, 8, -21, 37, -62, 71]]?\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 6x6 matrix:\n[[-118, 94, -84, 71, 97, 9],\n [-49, 63, 1, 54, 48, 21],\n [208, -65, 57, -54, -182, 36],\n [-16, -92, 88, -74, -6, -66],\n [-101, 39, -38, 19, 50, -30],\n [88, 7, -11, 8, -60, 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[[3, 23, -31, -45, -31, -63],\n [3, -7, -41, -44, -45, -26],\n [-17, 24, 0, 20, 16, 11],\n [1, 77, -39, 82, 71, -8],\n [119, -7, 57, 121, 143, -41],\n [-140, -8, -84, -172, -200, 44]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-33, -22, -64, 14, 42, -123],\n [-19, -66, 138, 25, -5, 52],\n [-48, -13, -4, -42, 95, -134],\n [-33, -31, 34, -86, 131, -169],\n [-45, 13, -100, -4, 74, -84],\n [-93, 65, 69, -79, 60, -199]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[34, -42, 88, -66, 33, 36],\n [76, -48, 4, 36, -57, -48],\n [21, -23, 42, -29, 12, 14],\n [-33, 19, 6, -23, 30, 26],\n [-35, 25, -14, -5, 18, 14],\n [34, -22, 4, 14, -24, -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[[0, 32, -8, -8, -20, -4],\n [0, 64, -16, -16, -40, -8],\n [0, -24, 6, 6, 15, 3],\n [0, 16, -4, -4, -10, -2],\n [0, -8, 2, 2, 5, 1],\n [0, -72, 18, 18, 45, 9]]?\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 6x6 matrix:\n[[61, -25, 84, 26, 62, 29],\n [-23, 78, 16, 78, 36, -17],\n [-17, 10, -14, 17, -99, -7],\n [-36, 50, -26, 15, -23, -44],\n [27, 1, 54, 41, -81, -5],\n [93, -29, 154, 169, 19, 169]]\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[[106, 157, 66, -78, 47, 80],\n [47, -85, 106, 107, -88, 3],\n [112, -18, -120, 92, 56, 92],\n [-26, -5, -12, -12, 2, -16],\n [-106, 38, -96, -102, 58, -50],\n [-206, -52, 110, -88, -89, -162]]\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 6x6 matrix:\n[[-11, 8, 28, 109, 194, 92],\n [-19, 53, 30, -111, 6, 36],\n [-114, -154, 154, 155, -27, -140],\n [0, 4, 68, 137, 155, -11],\n [-44, -18, 26, -41, -17, 16],\n [-81, -130, -106, 84, 13, 43]]\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[[36, 12, 60, -36, 48, -54],\n [-25, -12, 17, 14, -15, -45],\n [-8, -4, 8, 4, -4, -18],\n [-4, -2, 4, 2, -2, -9],\n [50, 20, 30, -40, 50, 0],\n [33, 10, 71, -36, 49, -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 6x6 matrix:\n[[-40, -20, 54, 102, 40, -38],\n [-4, -65, -88, 7, -30, -97],\n [-93, 155, 170, 114, -85, 12],\n [-45, -45, 1, 54, 50, -113],\n [39, 22, 8, -25, -19, 101],\n [24, -80, -54, 0, 50, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-36, 18, -18, -81, -27, 27],\n [-24, 12, -12, -54, -18, 18],\n [-36, 18, -18, -81, -27, 27],\n [20, -10, 10, 45, 15, -15],\n [-28, 14, -14, -63, -21, 21],\n [-36, 18, -18, -81, -27, 27]]\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[[21, 83, 107, 17, -70, -22],\n [-61, 94, 107, -44, -51, -42],\n [-63, -97, -13, 125, -84, -18],\n [80, -44, -136, -144, 4, 50],\n [32, -46, -144, -74, -58, 158],\n [-88, -130, -72, 162, 0, 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[[-18, -27, 21, 22, 115, 20],\n [26, 25, -4, -9, -71, -8],\n [-118, -19, -22, -67, -33, 73],\n [-16, -30, -31, 9, 16, -52],\n [126, 27, 0, 57, -33, -102],\n [94, 33, -17, 24, -97, -86]]\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[[-30, -40, -45, -25, -40, -50],\n [96, 38, 132, 8, 140, 52],\n [-60, 40, -74, 46, -96, 44],\n [84, -23, 108, -38, 130, -22],\n [-18, -84, -35, -63, -16, -102],\n [0, -135, -18, -108, 18, -162]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[150, 35, -95, 105, -129, -37],\n [42, 45, -9, 3, -15, 9],\n [12, -10, -14, 18, -18, -10],\n [4, -10, -8, 11, -10, -7],\n [28, 50, 4, -13, 2, 17],\n [86, 35, -47, 49, -65, -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[[52, -70, -106, 34, -98, -2],\n [-20, -14, -11, -29, -70, -7],\n [-47, -78, -40, -3, -6, -35],\n [49, -241, -111, 125, 49, -94],\n [-30, -39, -88, 41, 3, 72],\n [-3, 21, 122, -42, 47, -89]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-14, 28, 14, 70, -70, -14],\n [-20, 40, 20, 100, -100, -20],\n [-10, 20, 10, 50, -50, -10],\n [16, -32, -16, -80, 80, 16],\n [2, -4, -2, -10, 10, 2],\n [-8, 16, 8, 40, -40, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[64, 138, 154, 36, 48, 146],\n [-80, 21, 1, -2, -60, 11],\n [80, 132, 152, 36, 60, 142],\n [56, -12, 2, 2, 42, -5],\n [-64, -129, -145, -34, -48, -137],\n [-8, -51, -53, -12, -6, -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, -87, -62, 41, -50, -17],\n [102, -33, -76, 7, -40, -73],\n [-52, -173, -102, 111, 80, 59],\n [15, 40, 17, -22, 10, -10],\n [-60, -54, -12, 42, 60, 54],\n [-18, 34, 34, -18, 0, 10]]\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 6x6 matrix:\n[[-89, -80, 25, -128, 90, -98],\n [-40, -40, 8, -64, 0, -40],\n [21, 38, 19, 24, -30, -12],\n [-88, -125, -36, -108, 130, -11],\n [124, 155, 24, 156, -190, 53],\n [-4, 15, 28, -22, -60, -43]]\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, 8, 19, 9, -2, -8],\n [-49, -15, -146, -27, -6, 88],\n [37, -18, 14, 54, 48, 33],\n [-37, 44, -46, -57, 0, -9],\n [-16, 15, 22, -33, -30, -55],\n [57, 86, -90, -25, 76, 51]]\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, 17, 87, -35, 84, -62],\n [-52, 2, -85, 27, -49, 22],\n [-72, -41, -117, -38, 31, 76],\n [24, 27, -40, 85, -54, -58],\n [12, -12, 60, 37, -77, 2],\n [78, 70, 124, -11, -25, -38]]\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 6x6 matrix:\n[[24, -120, -45, -98, 155, 43],\n [209, 23, -50, -29, -115, 99],\n [129, 1, 68, 89, -37, -16],\n [69, -140, 38, -43, 113, -4],\n [208, -78, 42, 25, 2, 17],\n [71, -28, 22, -28, -113, -10]]\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[[-10, 1, 150, 5, 37, -85],\n [-6, 3, -30, 15, -9, 9],\n [0, -1, 50, -5, 13, -25],\n [-34, 13, 30, 65, 1, -49],\n [-28, 9, 110, 45, 23, -83],\n [19, -7, -30, -35, -4, 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 6x6 matrix:\n[[-155, 98, -105, -91, 170, -14],\n [-133, 105, 82, -112, -49, -31],\n [83, -98, 41, 54, -54, -122],\n [3, 50, 27, 24, -81, 74],\n [-16, -5, 64, -16, -54, -72],\n [-55, 121, -105, -2, 17, 56]]\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 6x6 matrix:\n[[-17, 61, -49, 23, -85, 16],\n [-49, 3, 80, 2, -20, 69],\n [-19, -19, 56, -6, 20, 29],\n [47, 17, -81, -13, -45, -58],\n [-76, 26, 67, 37, -5, 89],\n [-85, 75, -20, 90, 0, 75]]\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[[-90, -60, -80, 90, -30, 30],\n [45, 30, 40, -45, 15, -15],\n [-45, -30, -40, 45, -15, 15],\n [27, 18, 24, -27, 9, -9],\n [0, 0, 0, 0, 0, 0],\n [-90, -60, -80, 90, -30, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-5, -5, 25, 35, -20, -20],\n [-2, -2, 10, 14, -8, -8],\n [-6, -6, 30, 42, -24, -24],\n [-6, -6, 30, 42, -24, -24],\n [7, 7, -35, -49, 28, 28],\n [3, 3, -15, -21, 12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}