{"messages": [{"content": "Determine the rank of the following matrix:\n[[59, 8, 18, -23, 14],\n [62, 22, 31, -20, -2],\n [53, -30, 4, -14, 30],\n [-11, 56, 25, 26, 24],\n [0, -44, -34, -27, -3]]\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, 35, 9, -10, 16],\n [-30, -43, -1, 28, -36],\n [-6, -41, -11, 11, -18],\n [30, 19, -7, -24, 28],\n [-36, -54, -2, 34, -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 5x5 matrix:\n[[-24, -2, 0, -38, 48],\n [12, -2, 0, 25, -42],\n [-12, 0, 0, -21, 30],\n [-16, -3, 0, -22, 22],\n [-4, -3, 0, -1, -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[[12, 14, 11, 22, 3],\n [-2, 15, 25, 18, 19],\n [-12, 37, -2, -10, 35],\n [46, -38, 2, 26, 9],\n [-48, 14, -17, -42, -27]]\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 5x5 matrix:\n[[-28, -35, 13, 22, 26],\n [4, 45, 11, 4, -8],\n [6, 39, 9, 3, -6],\n [-10, -64, -18, -9, 4],\n [36, 14, -30, -38, -36]]\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[[11, -11, 15, 20, -13],\n [-15, 25, -15, -30, 25],\n [-9, -29, -33, -6, -17],\n [-24, 18, -36, -42, 24],\n [-8, -16, -24, -8, -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[[6, 2, -4, -3, -1],\n [12, 4, -8, -6, -2],\n [-12, -4, 8, 6, 2],\n [36, 12, -24, -18, -6],\n [-24, -8, 16, 12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-3, 18, -9, 18, -12],\n [5, -30, 15, -30, 20],\n [-3, 18, -9, 18, -12],\n [-6, 36, -18, 36, -24],\n [-5, 30, -15, 30, -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[[-30, 3, -2, 14, 2],\n [0, 13, 3, -11, -3],\n [-24, -23, -13, 37, 1],\n [-18, -12, 15, 5, 27],\n [-66, 12, -17, 37, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0, 0],\n [-18, -12, 0, -12, 6],\n [30, 20, 0, 20, -10],\n [6, 4, 0, 4, -2],\n [30, 20, 0, 20, -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[[2, -8, 0, -4, 10],\n [-3, 12, 0, 6, -15],\n [-4, 16, 0, 8, -20],\n [-1, 4, 0, 2, -5],\n [-1, 4, 0, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-61, 55, 2, -21, -67],\n [58, -43, -25, 15, 28],\n [-4, 40, 27, -33, -27],\n [-18, 6, -31, -5, -11],\n [-27, 12, 45, 6, 5]]\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[[-5, 10, 25, -20, 25],\n [1, -2, -5, 4, -5],\n [-4, 8, 20, -16, 20],\n [2, -4, -10, 8, -10],\n [-4, 8, 20, -16, 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[[-2, 45, -15, 19, -13],\n [-35, 25, -2, 46, -9],\n [8, 32, 0, 8, 6],\n [43, 29, -12, -32, 1],\n [2, -5, 27, 5, 32]]\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 5x5 matrix:\n[[-9, -12, -15, -18, 0],\n [-16, -16, 52, 7, 2],\n [12, -3, -35, -31, -22],\n [-26, -2, -12, 19, 42],\n [-44, -36, -4, -21, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-15, 38, 10, 50, -17],\n [-9, 0, -14, -15, 57],\n [-12, -26, 29, 10, -10],\n [-15, 16, -15, 0, 61],\n [9, 34, -23, 5, -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[[-25, 5, -5, -10, -10],\n [-10, 2, -2, -4, -4],\n [15, 30, -20, -20, 20],\n [16, 10, -6, -4, 12],\n [17, -10, 8, 12, 4]]\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, -7, 18, 2, -5],\n [21, -24, 10, 19, -11],\n [-5, 14, -22, -46, -4],\n [-8, -1, 22, 46, 13],\n [10, -20, -12, 1, -13]]\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[[7, 3, -4, 12, -4],\n [-3, -11, 4, 12, -8],\n [-30, -25, 20, -30, 5],\n [22, 24, -16, 12, 2],\n [33, 19, -20, 48, -14]]\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, 10, 2, 6, -4],\n [10, -25, -5, -15, 10],\n [2, -5, -1, -3, 2],\n [8, -20, -4, -12, 8],\n [12, -30, -6, -18, 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[[-3, -15, 18, 5, -20],\n [-8, 4, 10, -42, 26],\n [28, 1, 22, 34, -32],\n [-9, -29, 23, 18, -39],\n [-16, -38, 18, 30, -50]]\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, -10, 10, 10, -10],\n [12, -6, 6, 6, -6],\n [0, 0, 0, 0, 0],\n [20, -10, 10, 10, -10],\n [20, -10, 10, 10, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-10, 0, 12, -12, -12],\n [-23, -13, 1, 21, 12],\n [19, 13, -14, -26, 21],\n [45, 10, -43, -45, 51],\n [-4, 55, 32, -12, -15]]\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, 50, 41, 14, -28],\n [-24, 16, 41, 38, 62],\n [-69, -55, -71, 3, -10],\n [-29, 29, -25, -15, 10],\n [23, -11, -47, -41, -72]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[16, 1, 23, 1, -6],\n [16, 2, 22, 2, 0],\n [8, -2, 14, -2, -18],\n [0, 3, -3, 3, 18],\n [-24, -9, -27, -9, -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[[30, 18, 45, -24, -21],\n [-25, -42, -15, 29, 31],\n [-30, -66, -5, 40, 45],\n [30, 24, 40, -26, -24],\n [-20, 0, -40, 12, 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 5x5 matrix:\n[[-3, -6, -9, 0, -6],\n [1, 2, 3, 0, 2],\n [4, 8, 12, 0, 8],\n [4, 8, 12, 0, 8],\n [-5, -10, -15, 0, -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[[42, -32, -23, 4, -35],\n [-22, 39, 16, 36, 8],\n [30, 24, -28, 4, -32],\n [40, -9, -29, 18, -34],\n [-26, -12, 22, -12, 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[[-5, 14, -4, -7, -7],\n [-2, 20, -4, 2, -22],\n [-4, 22, -5, -2, -20],\n [-13, 22, -8, -23, 1],\n [2, 10, -1, 8, -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 5x5 matrix:\n[[1, -7, -5, -1, 0],\n [-18, -6, -24, -24, 6],\n [26, 46, -12, 33, -15],\n [26, 5, -7, 16, -13],\n [29, -14, -5, -12, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[13, -39, 41, 25, 7],\n [12, -2, -4, -7, 13],\n [-38, 2, 18, 26, -42],\n [15, -35, 35, 20, 10],\n [-2, -30, 38, 28, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[13, -7, 19, 16, -6],\n [-21, 34, -8, 53, 17],\n [-11, 25, -23, 36, 24],\n [3, -4, 20, 7, -11],\n [1, -7, 0, -18, -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[[-1, 12, 17, 21, -4],\n [21, -27, -7, 9, 9],\n [10, -21, -16, -12, 7],\n [-4, 3, -2, -6, -1],\n [-30, 36, 6, -18, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-15, -12, -15, 15, 18],\n [-24, -6, 24, 36, 24],\n [14, 20, 46, -6, -20],\n [9, -6, -39, -21, -6],\n [-3, 2, 13, 7, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-20, 34, 13, 0, -16],\n [35, -29, 6, -19, 4],\n [-5, 8, 29, -46, -35],\n [0, -58, -51, 15, 89],\n [5, 13, -12, 47, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-19, 55, -12, -33, -9],\n [-31, -11, -56, 25, -8],\n [-52, 66, 32, -2, -22],\n [-41, 39, -34, -14, -1],\n [-8, -21, 50, 40, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-7, 11, -5, 12, 2],\n [3, 1, 5, 0, -6],\n [-11, 23, -5, 24, -2],\n [-10, 20, -5, 21, -1],\n [15, -15, 15, -18, -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[[-27, 54, -34, -25, -6],\n [21, -42, 30, 23, 2],\n [21, -42, 26, 19, 5],\n [-30, 60, -40, -30, -5],\n [36, -72, 48, 36, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 19, 21, 10, 18],\n [18, 28, -17, 17, 33],\n [-10, -25, 13, -20, 4],\n [-12, -32, 6, -18, -40],\n [14, 12, -33, 5, 41]]?\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[[-30, -30, -20, -30, -10],\n [-6, -6, -4, -6, -2],\n [-6, -6, -4, -6, -2],\n [-18, -18, -12, -18, -6],\n [-30, -30, -20, -30, -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[[-23, 60, -25, -11, 72],\n [-16, 51, -34, -4, 42],\n [-5, 12, 55, -53, 12],\n [-4, 7, 47, -42, 12],\n [-14, 66, 10, -62, 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[[-30, 0, 30, 30, 24],\n [-10, -5, 21, 13, 16],\n [-40, 10, 18, 34, 16],\n [5, 20, -49, -17, -36],\n [-20, 30, -46, 2, -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[[0, 1, -1, -2, 3],\n [-9, -40, -5, -10, 6],\n [-9, -41, -4, -8, 3],\n [2, 5, 5, 10, -13],\n [7, 33, 2, 4, 1]]\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, -15, -12, 9, -18],\n [-6, 30, 24, -18, 36],\n [-5, 25, 20, -15, 30],\n [0, 0, 0, 0, 0],\n [4, -20, -16, 12, -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[[-21, 29, -19, -5, -13],\n [0, -10, -20, -20, 25],\n [-33, 43, -35, -13, -14],\n [6, -14, -6, -10, 18],\n [-6, 16, 10, 14, -23]]\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[[-4, -17, -13, -33, -45],\n [24, -2, 26, 16, 10],\n [16, 4, 20, 20, 20],\n [-8, -6, -12, -17, -20],\n [4, 17, 13, 33, 45]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, -15, -12, -9, 18],\n [-6, 30, 24, 18, -36],\n [5, -25, -20, -15, 30],\n [4, -20, -16, -12, 24],\n [-3, 15, 12, 9, -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[[24, -4, 12, -30, -10],\n [28, -2, 10, -39, -13],\n [12, -12, 21, 0, 0],\n [4, -6, 10, 3, 1],\n [-32, 8, -20, 36, 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[[90, 54, 56, 23, -10],\n [-9, -23, 11, 20, 10],\n [-54, -30, -21, -21, 7],\n [39, 33, 13, -15, -10],\n [42, 22, 3, -11, -8]]?\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[[17, 16, 9, -15, 19],\n [28, 25, 13, -24, 31],\n [-7, -12, -11, 9, -9],\n [24, 5, -11, -12, 23],\n [-9, 24, 39, -9, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 14, -6, -32, -12],\n [28, 2, 6, 36, 28],\n [-40, -8, -2, -36, -42],\n [28, 10, 16, 40, 14],\n [-34, -4, -6, -40, -34]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 16, -26, 22, 18],\n [-10, 20, 30, 10, -10],\n [-14, 34, 26, 24, -4],\n [0, 12, -32, 20, 20],\n [1, -5, 5, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[44, 7, -43, -31, 8],\n [16, -36, 32, -2, 38],\n [13, -15, 8, -5, 17],\n [-14, 10, -24, 10, -66],\n [6, -42, 48, 6, 42]]\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, 0, 0, 0, 0],\n [5, -1, 3, 1, 3],\n [-20, 4, -12, -4, -12],\n [-10, 2, -6, -2, -6],\n [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[[28, -20, -40, -1, 3],\n [-26, -6, -41, -10, -8],\n [10, -6, -86, 8, 28],\n [2, 6, 71, -2, -16],\n [2, 6, 71, -2, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, 8, 8, 5, -21],\n [-20, -25, -18, -13, 49],\n [10, 11, 6, 5, -17],\n [15, 20, 16, 11, -43],\n [5, 2, -4, -1, 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[[-20, 20, 25, -30, 15],\n [4, -4, -5, 6, -3],\n [-24, 24, 30, -36, 18],\n [4, -4, -5, 6, -3],\n [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[[4, 12, -16, 24, 20],\n [2, 6, -8, 12, 10],\n [-1, -3, 4, -6, -5],\n [4, 12, -16, 24, 20],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-27, 21, 7, 38, 40],\n [29, -30, -12, -21, -34],\n [-34, -4, 8, 26, 52],\n [-36, 36, 12, 42, 48],\n [12, 6, -2, -10, -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[[-18, 14, -28, 20, 2],\n [0, 6, -10, -16, 22],\n [18, -30, -12, 6, 6],\n [-45, 46, -19, 38, -24],\n [-18, 12, -14, 28, -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 5x5 matrix:\n[[10, -3, 33, -30, -18],\n [-8, 2, -26, 24, 12],\n [-6, 3, -21, 18, 18],\n [4, -3, 15, -12, -18],\n [6, -3, 21, -18, -18]]\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, -1, 1, -12, -9],\n [19, 6, 20, -4, -2],\n [-21, -7, -25, -7, -4],\n [-18, -11, -23, 37, 16],\n [-3, 0, -6, -24, -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[[3, -12, -33, -21, 19],\n [20, -31, 21, 34, 16],\n [-22, 52, 9, -11, -29],\n [21, -40, 14, 27, 18],\n [-28, 13, 4, 22, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-38, -4, -28, -2, -17],\n [36, -2, 26, -1, 14],\n [14, 20, 12, 10, 13],\n [-24, 60, -12, 30, 12],\n [34, -8, 24, -4, 11]]\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, 22, -8, -36, 0],\n [31, 39, 20, -18, -38],\n [12, 18, -6, -3, -6],\n [26, -18, -16, 52, 14],\n [-33, 13, 10, -51, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-20, -10, -52, -15, 19],\n [-12, 1, -28, -19, 17],\n [12, 6, 36, 15, -17],\n [-16, 28, 4, -27, 10],\n [16, -15, 16, 26, -16]]\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[[-16, -15, 2, -4, 24],\n [-26, -20, 4, -6, 36],\n [18, -40, -12, -2, 12],\n [18, -5, -6, 2, -12],\n [-36, 10, 12, -4, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 10, 30, 15, -10],\n [0, -10, -30, -15, 10],\n [0, 2, 6, 3, -2],\n [0, -8, -24, -12, 8],\n [0, -8, -24, -12, 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[[-5, -20, -10, -20, 10],\n [-14, -8, -28, 16, -20],\n [6, -8, 12, -24, 20],\n [11, 20, 22, 8, 2],\n [0, 8, 0, 12, -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[[15, 20, 10, 30, 25],\n [-9, -12, -6, -18, -15],\n [6, 8, 4, 12, 10],\n [-3, -4, -2, -6, -5],\n [-18, -24, -12, -36, -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 5x5 matrix:\n[[-2, -26, 2, 18, 18],\n [-19, 52, -18, -62, 9],\n [-26, 43, 11, -39, 9],\n [17, -36, -9, 32, -10],\n [27, -2, 23, 18, 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[[-3, 5, -1, 5, -2],\n [-18, 30, -6, 30, -12],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [18, -30, 6, -30, 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 5x5 matrix:\n[[-7, 7, 15, -23, 24],\n [13, -11, -29, 41, -44],\n [4, 2, -12, 8, -12],\n [6, -18, -6, 30, -24],\n [-7, 0, 19, -17, 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[[-18, 6, -12, 18, 30],\n [-7, 11, -6, 11, 15],\n [-13, 26, -12, 23, 30],\n [5, -19, 6, -13, -15],\n [5, -45, 10, -25, -25]]\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[[-42, 47, 4, 34, -11],\n [16, -35, 9, -37, 16],\n [-5, -10, -7, 5, -12],\n [-20, 5, -14, 12, 25],\n [-26, 20, -2, 22, -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[[-13, 7, 5, 3, -8],\n [-7, 1, 7, -3, 0],\n [12, -3, -10, 3, 2],\n [-3, 12, -15, 18, -18],\n [13, -16, 9, -18, 22]]?\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, -15, -6, -6, -6],\n [-1, 5, 2, 2, 2],\n [3, -15, -6, -6, -6],\n [-10, 26, 32, 26, 32],\n [0, -8, 4, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-4, 0, 20, 44, 4],\n [4, 0, -8, 7, -13],\n [2, 0, -10, -22, -2],\n [-10, 0, 34, 42, 22],\n [-7, 0, 19, 9, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -36, -30, -6, 18],\n [0, 0, 0, 0, 0],\n [0, -36, -30, -6, 18],\n [0, 6, 5, 1, -3],\n [0, 6, 5, 1, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[14, -28, 35, -14, 39],\n [-15, 30, -25, 10, -30],\n [-2, -8, 25, 2, 33],\n [-13, 6, -25, 30, -12],\n [-9, 20, -10, 2, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[24, -2, 19, -21, -3],\n [-35, 5, -25, 30, 5],\n [15, 5, 20, -15, 0],\n [-18, 14, 2, 12, 6],\n [-9, 7, 1, 6, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, 12, -54, -12, -12],\n [41, 10, 30, 25, 35],\n [-6, -18, 54, 34, 20],\n [-25, -10, 0, -55, -45],\n [40, 6, 48, -26, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 20, 24, -24, -4],\n [-10, -25, -30, 30, 5],\n [-8, -20, -24, 24, 4],\n [-4, -10, -12, 12, 2],\n [-6, -15, -18, 18, 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[[-8, 0, 8, -8, -2],\n [-12, 0, 12, -12, -3],\n [-16, 0, 16, -16, -4],\n [4, 0, -4, 4, 1],\n [-4, 0, 4, -4, -1]]\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, -24, -28, 58, -8],\n [9, -14, 9, 6, 19],\n [-50, -48, -22, 76, 14],\n [10, -12, -16, 34, -4],\n [22, 24, 24, -54, 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[[-49, -14, 17, 4, 3],\n [25, 31, 13, -7, 13],\n [1, 20, 13, 2, 24],\n [-19, 3, -33, 13, 70],\n [24, 35, 36, -25, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1, 6, 15, -6, 10],\n [-2, 12, -24, -12, -4],\n [12, -72, -18, 72, -48],\n [-9, 54, 9, -54, 34],\n [0, 0, -27, 0, -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[[14, 12, 0, 18, 10],\n [16, 0, 12, 0, -4],\n [-28, -24, 0, -36, -20],\n [34, 36, -6, 54, 32],\n [-18, -28, 11, -42, -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[[6, 2, -8, 5, 3],\n [36, -10, -15, -14, -48],\n [30, 2, -28, 9, -9],\n [-36, -2, 33, -10, 12],\n [-30, -6, 34, -17, -3]]\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 5x5 matrix:\n[[12, 8, 0, 6, -6],\n [30, 20, 0, 15, -15],\n [-12, -8, 0, -6, 6],\n [-12, -8, 0, -6, 6],\n [-36, -24, 0, -18, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[5, 10, 5, 0, 5],\n [-1, -2, -1, 0, -1],\n [0, 0, 0, 0, 0],\n [5, 10, 5, 0, 5],\n [-6, -12, -6, 0, -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[[-23, 11, -7, -12, 42],\n [6, -15, 12, 0, -18],\n [27, -21, 15, 12, -54],\n [18, 48, -42, 24, 0],\n [25, -16, 11, 12, -48]]\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, -57, 5, 47, -106],\n [8, 13, -15, -11, 52],\n [-9, 9, 2, -3, 27],\n [-22, 22, 26, -4, 1],\n [-18, 45, 37, -20, 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 5x5 matrix:\n[[-2, 5, 8, 21, 1],\n [8, -6, 12, 5, 62],\n [5, -19, 26, 4, 27],\n [-58, 42, 39, -10, 10],\n [-34, 52, -2, -12, 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[[-10, 20, -5, 6, 23],\n [8, -5, 4, 15, 8],\n [-30, 25, -15, -45, -15],\n [18, -15, 9, 27, 9],\n [0, -15, 0, -27, -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[[1, 5, 1, -6, -4],\n [-1, -5, -1, 6, 4],\n [6, 30, 6, -36, -24],\n [-4, -20, -4, 24, 16],\n [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[[-4, -14, 32, 18, 36],\n [-8, -4, 32, 12, 24],\n [-4, 22, -16, -18, -36],\n [15, -24, -18, 9, 18],\n [8, -2, -24, -6, -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[[-24, 25, 10, -18, 46],\n [6, -12, 38, 6, 6],\n [25, -24, 36, -24, -4],\n [6, -3, -2, -18, 4],\n [-4, 28, -4, -36, -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[[0, 0, 0, 0, 0],\n [-8, 4, -8, 6, 6],\n [-20, 10, -20, 15, 15],\n [-12, 6, -12, 9, 9],\n [8, -4, 8, -6, -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, 15, 6, -3, -24],\n [-11, -45, -3, -1, -3],\n [0, -7, 11, -4, 22],\n [-11, -25, -11, 3, -11],\n [-8, 5, -21, 8, -26]]\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 5x5 matrix:\n[[33, 0, -37, 38, 3],\n [-43, 3, 13, -46, 11],\n [14, -42, 15, 10, -19],\n [15, -36, -15, 24, -12],\n [-25, 7, 18, -32, 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[[13, -19, -46, 35, -46],\n [7, 12, -27, -4, -23],\n [38, 0, 10, 20, 38],\n [15, -15, 0, 55, 0],\n [22, -18, -2, -5, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-5, 2, -23, 42, -29],\n [-4, -38, 10, 15, -4],\n [11, -6, -54, 60, -12],\n [-7, -38, 12, 18, -10],\n [-8, 6, -6, 21, -24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-8, -14, -18, 8, -48],\n [-18, 4, -6, 4, 23],\n [-7, -36, 35, 31, -51],\n [45, 26, 23, -31, 27],\n [-39, -21, 32, 35, 19]]\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, 10, -1, -9],\n [-13, -36, -18, -30, -26],\n [0, 6, -10, 5, 13],\n [8, 12, -10, 8, 20],\n [-15, 10, 20, 15, -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[[-20, 21, -17, 2, -21],\n [30, -35, 15, 4, 21],\n [15, -16, 12, -1, 15],\n [-15, 13, -21, 7, -24],\n [-15, 19, -3, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[17, 24, 18, -40, 2],\n [6, -20, -48, 26, 24],\n [34, 26, -6, -49, 22],\n [-9, -14, -12, 23, 0],\n [-14, -12, 0, 22, -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 5x5 matrix:\n[[10, -2, -4, 4, 0],\n [-5, 1, 2, -2, 0],\n [-20, 4, 8, -8, 0],\n [15, -3, -6, 6, 0],\n [-15, 3, 6, -6, 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[[0, 0, 0, 0, 0],\n [-2, -1, 6, 0, -3],\n [-12, -6, 36, 0, -18],\n [0, 0, 0, 0, 0],\n [-2, -1, 6, 0, -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[[-6, -30, 0, 6, -6],\n [0, 0, 0, 0, 0],\n [2, 10, 0, -2, 2],\n [3, 15, 0, -3, 3],\n [5, 25, 0, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 0, 8, 2, 12],\n [18, 0, 12, 3, 18],\n [30, 0, 20, 5, 30],\n [-30, 0, -20, -5, -30],\n [-12, 0, -8, -2, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-24, 58, 1, 32, 23],\n [4, 46, 36, 2, 16],\n [-48, 13, 15, -21, 15],\n [-17, -71, -45, -13, -17],\n [-40, -24, -6, -2, 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[[-6, -5, 2, 14, 13],\n [-9, -26, 34, 1, 11],\n [12, 3, -2, 4, 5],\n [-27, 47, -8, -59, -52],\n [24, -31, -2, 22, 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[[16, 24, -8, 4, 8],\n [-20, -30, 10, -5, -10],\n [12, 18, -6, 3, 6],\n [-16, -24, 8, -4, -8],\n [12, 18, -6, 3, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, -8, 8, -20, 18],\n [8, 56, 24, 14, 42],\n [1, -2, 8, 25, -8],\n [15, 0, 30, 26, 46],\n [18, 0, 4, 16, 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 5x5 matrix:\n[[-8, 16, -16, 0, -8],\n [8, -16, 16, 0, 8],\n [-12, 24, -24, 0, -12],\n [8, -16, 16, 0, 8],\n [6, -12, 12, 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 5x5 matrix:\n[[4, -25, 13, -1, 34],\n [10, -35, 27, -21, 10],\n [-8, -29, 17, 23, 30],\n [4, 3, 5, -17, -32],\n [-3, -2, 6, 1, -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[[3, -22, -43, -30, -7],\n [14, -7, -3, 27, 8],\n [-17, 9, 26, 6, 25],\n [43, -9, -4, 24, -59],\n [-71, 35, -12, -81, 47]]\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, -24, 0, 16, -12],\n [24, -4, -8, -14, 4],\n [4, -14, -8, 16, -16],\n [-46, 38, 16, -6, 16],\n [9, -42, -16, 46, -42]]\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 5x5 matrix:\n[[-40, -41, -8, -36, 20],\n [-14, -10, 0, -18, -1],\n [36, 39, 13, -1, -32],\n [9, 0, -1, 60, -18],\n [-81, -45, -3, -36, -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[[8, 20, 41, -7, 19],\n [-12, 20, -26, -50, -32],\n [-16, -38, 12, -22, 1],\n [-31, 33, 24, -10, 13],\n [-1, -39, -12, -8, -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[[-3, -29, 5, -44, 8],\n [-2, -12, 4, -18, 4],\n [6, -32, -3, -45, 8],\n [5, -3, -13, -6, -4],\n [30, -23, 43, 5, 38]]?\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 5x5 matrix:\n[[3, 7, 2, -3, -16],\n [-2, -18, 0, 6, 44],\n [-16, -22, -4, 8, 30],\n [-4, -33, 12, 6, 55],\n [-1, -5, 16, -5, -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[[10, 5, 6, -1, 6],\n [7, 15, -1, 4, -7],\n [-2, -2, 18, -8, -18],\n [-8, -7, 22, -11, -26],\n [-4, 20, -9, 8, -27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[33, 31, 21, 13, 26],\n [-8, -53, 50, 11, -21],\n [17, 16, 17, -12, -13],\n [20, 15, 6, 23, 43],\n [-23, -29, -3, -18, -35]]\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, -12, -9, 12, 9],\n [15, -21, 20, 32, -20],\n [-38, 1, 17, 4, -17],\n [12, 21, -33, -36, 33],\n [7, 19, -28, -32, 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[[20, -11, -6, -20, -6],\n [6, -15, -18, 12, 18],\n [9, -3, 0, -12, -6],\n [-14, 22, 24, -8, -20],\n [27, -35, -36, 4, 26]]\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[[-46, -40, 32, 42, 10],\n [16, 12, 17, -21, 30],\n [25, 24, -3, -51, 86],\n [-4, -4, -19, 24, -71],\n [18, 16, -10, -21, 11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[22, -10, 0, -22, 15],\n [39, 27, 0, 18, -9],\n [-14, -38, 0, -32, 6],\n [-4, -20, 0, -16, 0],\n [2, 34, 0, 30, -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[[28, 28, -10, 23, -24],\n [-24, 12, 42, -21, 36],\n [30, 48, 6, 24, -18],\n [28, 28, -10, 23, -24],\n [-16, -20, 2, -13, 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 5x5 matrix:\n[[-18, -30, -18, 0, -18],\n [-9, -15, -9, 0, -9],\n [0, 0, 0, 0, 0],\n [12, 20, 12, 0, 12],\n [-15, -25, -15, 0, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-25, 6, 33, -27, -31],\n [-2, 31, -22, 21, 35],\n [-2, -17, -52, 27, -3],\n [6, -21, -41, 23, -10],\n [5, 23, -17, 27, -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[[23, -27, -25, 25, 6],\n [26, 6, -10, 18, 0],\n [19, -31, -25, 21, 9],\n [36, -24, -30, 34, 6],\n [29, 29, 0, 18, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -24, 0, -4, 24],\n [0, 0, 0, 0, 0],\n [-6, 36, 0, 6, -36],\n [-1, 6, 0, 1, -6],\n [-4, 24, 0, 4, -24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-20, 10, 11, 53, -63],\n [7, -10, 27, -10, 3],\n [-7, -18, 2, 13, -34],\n [6, 6, 30, 0, 20],\n [-18, -18, 9, 45, -57]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-9, 7, 29, -10, 40],\n [-5, 8, -19, 6, -3],\n [33, 36, -23, -8, 27],\n [39, 4, -4, -36, -75],\n [22, -5, 5, -26, -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[[10, 8, 2, 10, 8],\n [-20, -16, -4, -20, -16],\n [20, 16, 4, 20, 16],\n [5, 4, 1, 5, 4],\n [20, 16, 4, 20, 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[[-43, -73, -20, 35, 16],\n [-1, 11, 16, 7, 8],\n [-16, -10, -20, 62, -20],\n [-9, -30, 6, -34, 25],\n [-17, -26, -34, 50, -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[[-15, 15, -18, 0, 12],\n [30, -30, 36, 0, -24],\n [-20, 20, -24, 0, 16],\n [-10, 10, -12, 0, 8],\n [-30, 30, -36, 0, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 57, -3, 21, -37],\n [18, -47, 31, -10, 48],\n [-2, -22, 7, 18, 9],\n [-16, -33, -8, 19, 12],\n [6, 17, 17, 46, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 32, 9, -27, -2],\n [13, 8, -16, -7, -24],\n [-23, 6, 7, 1, 13],\n [-46, 6, 40, 1, 55],\n [27, -14, 7, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[14, 15, -5, 6, -17],\n [14, 15, -5, 6, -17],\n [6, 3, 1, -2, -5],\n [-10, -9, 2, -2, 11],\n [-34, 3, -24, 38, 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 5x5 matrix:\n[[12, -15, 15, 9, 6],\n [5, -22, 19, 21, 1],\n [9, -6, 7, 1, 5],\n [-35, 28, -31, -9, -19],\n [-12, 15, -15, -9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[36, 18, 0, -12, 36],\n [30, 15, 0, -10, 30],\n [24, 12, 0, -8, 24],\n [6, 3, 0, -2, 6],\n [24, 12, 0, -8, 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 5x5 matrix:\n[[25, 30, 54, 20, 65],\n [-6, 40, 50, 35, 23],\n [8, -10, 8, 52, 32],\n [-53, 28, 11, 55, -56],\n [-11, 53, 44, 41, 6]]\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, -8, -20, -24, -36],\n [41, -6, -16, 0, -22],\n [-4, 13, 19, 29, 11],\n [25, 4, 0, -28, -32],\n [23, -7, -13, 41, 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[[31, 6, 3, 31, 29],\n [-67, 19, -11, -4, -11],\n [-10, 8, 6, -27, -10],\n [-14, -9, -13, 49, 1],\n [31, 14, 17, 1, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-19, 21, 2, 14, -18],\n [36, -54, 42, -36, 72],\n [24, -36, 28, -24, 48],\n [17, -15, -14, -10, 6],\n [16, -21, 9, -14, 24]]\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[[-2, 5, -20, 34, -24],\n [24, 0, 0, 12, -12],\n [-22, -2, 8, -25, 21],\n [50, -5, 20, -10, 0],\n [-14, -1, 4, -14, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[15, -3, -6, -15, 6],\n [-25, 5, 10, 25, -10],\n [0, 0, 0, 0, 0],\n [30, -6, -12, -30, 12],\n [15, -3, -6, -15, 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[[-25, -24, -4, -28, -24],\n [-1, -32, -20, -30, -26],\n [-11, -4, 28, 12, 4],\n [-8, -22, 4, -12, -14],\n [-33, 19, 10, -2, 3]]\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[[33, 39, -10, -7, -3],\n [-31, -22, -26, -28, -6],\n [-56, -64, 2, 2, -2],\n [-4, 14, 23, -27, 27],\n [4, 11, -14, 31, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-23, 9, -23, -23, 8],\n [26, 14, 38, -22, 16],\n [36, 24, 12, 6, -6],\n [6, -27, 5, 43, -19],\n [-35, -36, -28, 30, -15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-18, 4, -15, -52, 51],\n [20, -12, 10, 40, -54],\n [20, -4, 14, 40, -42],\n [16, 2, 6, -16, 12],\n [-8, -8, -13, -32, 15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0, 0],\n [-5, -5, 5, 0, 1],\n [20, 20, -20, 0, -4],\n [25, 25, -25, 0, -5],\n [-10, -10, 10, 0, 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[[28, 34, -50, -27, 29],\n [31, 31, -46, -53, 36],\n [-27, 0, 22, 7, -20],\n [-23, 14, 18, -36, -11],\n [18, 19, -13, -14, 4]]?\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, 50, -21, -15, -18],\n [-30, 57, 13, -36, 12],\n [-20, 35, 2, -25, 18],\n [4, 64, 8, -24, -42],\n [-28, 96, 29, -59, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-50, -52, 38, -54, -39],\n [-18, 25, 2, 27, -12],\n [-24, 22, -52, -9, 51],\n [-50, 13, -42, -21, 38],\n [12, 40, -48, 24, 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 5x5 matrix:\n[[-25, -14, -25, 4, -6],\n [-25, -20, -33, 6, 7],\n [17, 8, 2, 5, -4],\n [-14, 14, -19, -29, 10],\n [39, 24, 10, -5, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-9, -10, 40, -4, 14],\n [35, 15, 10, 50, 15],\n [22, 4, -32, 32, 4],\n [-10, -1, 6, -16, -5],\n [-9, -2, 32, -11, 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[[-8, 18, -18, 30, -21],\n [-20, 30, 16, -38, 12],\n [-60, 8, 28, -24, 19],\n [-4, -6, 54, 27, 22],\n [10, 27, -20, 4, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0, 0],\n [-4, 3, 6, -4, -1],\n [24, -18, -36, 24, 6],\n [-24, 18, 36, -24, -6],\n [12, -9, -18, 12, 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[[21, 8, -19, -14, -4],\n [23, 4, -7, -12, -2],\n [-8, -4, 10, 6, 2],\n [28, -6, 23, -7, 3],\n [3, 4, -11, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[30, -34, -30, 0, 22],\n [5, -55, -45, 10, 30],\n [-18, 34, 26, -18, -11],\n [-17, 24, 25, 20, -28],\n [33, 11, 7, -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[[20, -1, 3, 19, 8],\n [20, -13, -11, -3, 4],\n [31, -2, 33, 63, 48],\n [8, -28, -10, -18, 20],\n [28, -2, 14, 38, 24]]\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[[-17, 20, -43, -2, 11],\n [66, -39, -3, -78, 24],\n [16, -31, 25, -12, 3],\n [-29, 26, 10, 36, -18],\n [8, -12, 3, -20, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-28, -16, -41, -23, 25],\n [14, 17, 16, 10, 1],\n [24, 24, 30, 18, -6],\n [-22, -13, -32, -18, 19],\n [-8, -14, -7, -5, -7]]\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 5x5 matrix:\n[[-11, 17, -12, 2, 9],\n [-6, 0, 4, 4, 28],\n [53, -51, 16, 14, -47],\n [20, -11, -7, 21, 2],\n [-5, 5, 0, -10, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-16, 30, 16, -7, 11],\n [-15, 27, 15, -15, 12],\n [16, -28, -16, 22, -14],\n [0, 4, 0, 30, -6],\n [-7, 13, 7, -4, 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[[-2, 16, 15, -6, -15],\n [-18, 24, 0, -24, 0],\n [25, -44, -12, 36, 12],\n [-16, 32, 12, -24, -12],\n [12, -24, -9, 18, 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[[-28, 46, -8, 67, -8],\n [-46, -14, 12, 23, -20],\n [-26, -40, 0, -18, -14],\n [-33, 27, 24, 47, -4],\n [42, -41, 16, -71, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[30, -12, -18, -30, 12],\n [-21, 7, 10, 25, -15],\n [-6, 8, 14, -10, 24],\n [25, -17, -28, -5, -23],\n [3, -4, -7, 5, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-11, -49, -11, 30, -31],\n [5, 23, -3, -14, 9],\n [5, 39, 1, -22, 17],\n [9, 31, 19, -20, 29],\n [4, 8, -14, -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[[54, 18, -6, -29, -35],\n [-18, -33, 23, -11, -1],\n [60, 5, 5, 4, -34],\n [-12, -10, 6, 2, 5],\n [-18, 21, -19, 1, 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[[-6, 3, 8, 5, 3],\n [3, -33, -49, 59, 21],\n [0, -40, -28, 2, -54],\n [24, 12, -8, -40, 0],\n [0, 27, 18, 1, 39]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[26, -28, -11, 19, 10],\n [-32, -28, 17, 19, -28],\n [12, 16, -37, -13, 18],\n [-13, 24, 4, -16, -3],\n [14, 2, 57, -15, 33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -2, 5, 1, 5],\n [0, -8, 20, 4, 20],\n [0, -8, 20, 4, 20],\n [0, 6, -15, -3, -15],\n [0, -8, 20, 4, 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 5x5 matrix:\n[[-3, -21, 27, 15, -18],\n [-18, 26, -42, -34, 12],\n [-56, -12, -6, -30, -36],\n [32, -4, 18, 26, 12],\n [-51, -15, 0, -24, -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[[0, 0, 0, 0, 0],\n [10, 0, -20, 25, 5],\n [12, 0, -24, 30, 6],\n [12, 0, -24, 30, 6],\n [-8, 0, 16, -20, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-20, 2, -2, -9, 9],\n [-4, 14, -6, -5, -23],\n [12, -32, 14, 13, 50],\n [4, 6, -6, -11, 11],\n [-8, 20, -12, -18, -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[[-28, 18, 26, 20, -30],\n [-18, -3, -3, -6, -15],\n [10, 13, 17, 18, 5],\n [15, -6, -9, -6, 15],\n [5, 15, 20, 20, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-30, -30, 12, -30, 0],\n [-20, -20, 8, -20, 0],\n [10, 10, -4, 10, 0],\n [10, 10, -4, 10, 0],\n [20, 20, -8, 20, 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[[10, 10, -13, 42, -23],\n [8, -2, 8, 11, -6],\n [-1, -15, 23, -8, 4],\n [3, -1, 5, -7, 4],\n [-11, -11, 15, -51, 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[[-18, -26, 53, 8, -21],\n [11, 6, 5, -12, 4],\n [-20, -16, -4, 40, -28],\n [17, 6, -9, 24, -30],\n [18, 22, -54, 14, -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[[-14, 66, 12, 4, -38],\n [12, -16, 2, -17, -18],\n [-2, 34, 6, -43, -21],\n [-1, 26, -10, 27, -28],\n [-6, -9, 8, 29, 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[[-2, -12, 22, -35, 14],\n [8, 28, -8, 40, -16],\n [10, 31, 6, 30, -12],\n [-10, -33, 2, -40, 16],\n [12, 30, 36, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-72, -52, 38, 6, 8],\n [3, 10, 5, -3, 2],\n [-6, -18, 3, 5, 10],\n [69, 42, -43, -3, -10],\n [51, 28, -40, -1, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-8, 30, -11, 10, -29],\n [-34, -4, 10, -60, 6],\n [46, -30, 13, 56, 15],\n [3, 0, -24, 0, 24],\n [-34, 20, 1, -41, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, -6, 0, 14, 11],\n [4, 11, 13, 9, 21],\n [-12, 18, 12, -10, 5],\n [-16, 16, 8, -16, -4],\n [4, 5, 7, 7, 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[[12, -11, 7, -11, 32],\n [10, -10, 0, -16, 24],\n [10, 45, 25, -15, -10],\n [20, 20, 28, -19, 29],\n [0, 30, 18, 6, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 3, 21, -12, -30],\n [17, 14, -10, 16, 16],\n [42, 21, 3, 24, 2],\n [39, 15, -3, 24, 10],\n [53, 20, -16, 38, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[36, 41, 46, 0, 7],\n [-10, -32, -10, 17, 9],\n [6, -41, 31, 4, 13],\n [20, 4, 40, 12, 8],\n [-14, 37, 16, -15, -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[[8, -50, -36, -14, 23],\n [-5, 23, 18, 8, -11],\n [9, 29, 6, -8, -9],\n [16, 10, -12, -18, 1],\n [-13, 7, 18, 16, -7]]?\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 5x5 matrix:\n[[-14, -34, 9, -8, -1],\n [52, -29, -55, -17, 43],\n [-6, 30, -15, 3, 15],\n [-38, 40, 36, 8, -26],\n [30, -30, -51, 3, 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[[2, 3, 0, 3, 2],\n [-8, -12, 0, -12, -8],\n [6, 9, 0, 9, 6],\n [-7, -4, -1, -10, 0],\n [8, 25, -2, 13, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, -4, -8, 2, -2],\n [-3, -6, -12, 3, -3],\n [5, 10, 20, -5, 5],\n [2, 4, 8, -2, 2],\n [2, 4, 8, -2, 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 5x5 matrix:\n[[-4, -5, 0, 5, -6],\n [-44, -9, -2, 37, -62],\n [-22, 27, 47, 11, 2],\n [66, 15, -28, -39, 54],\n [12, -15, -34, 7, -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[[23, 12, -2, 10, -2],\n [42, -8, 20, 28, 20],\n [-10, 6, -8, -8, -8],\n [-39, -11, -4, -20, -4],\n [-19, -23, 12, -4, 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[[-18, -10, 8, -22, 7],\n [10, 4, -2, 12, -1],\n [2, -9, 15, 1, 18],\n [8, -8, 16, 8, 20],\n [-10, -25, 35, -15, 40]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[16, 0, 34, -22, 11],\n [39, -30, 72, 20, -15],\n [17, -30, 24, 32, -15],\n [29, -12, 33, -41, 49],\n [-1, 18, 10, -2, -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[[-18, -30, -6, -30, -24],\n [14, 26, -6, 32, 16],\n [-10, -14, -14, -8, -16],\n [-4, -4, -12, 2, -8],\n [-12, -20, -4, -20, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-19, 2, -1, -21, -3],\n [27, 2, 5, 11, 7],\n [8, 12, 16, -46, 0],\n [7, -8, 0, 32, -10],\n [-22, 8, 0, -44, 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[[14, -8, 14, -48, 39],\n [5, -19, -11, -53, 1],\n [-22, 26, 6, 84, -4],\n [19, 24, 39, 8, 23],\n [28, 2, 16, -4, 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[[-38, 9, 6, 17, 5],\n [-16, -35, -30, 9, -7],\n [26, 4, 15, -7, 4],\n [-57, -61, -47, 28, -1],\n [-7, -22, -15, -3, 10]]\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 5x5 matrix:\n[[-8, -6, -8, 2, -8],\n [7, 11, 9, 0, 7],\n [26, -15, 14, -17, 26],\n [-36, -4, -28, 16, -36],\n [-28, 2, -20, 14, -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[[20, 6, 30, 40, -58],\n [4, -1, -15, 8, -11],\n [-13, -15, -18, -34, 39],\n [-7, -26, -27, -21, 29],\n [10, -24, -6, -33, -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 5x5 matrix:\n[[-5, -6, -12, -28, -8],\n [3, -18, -9, -39, -18],\n [-13, 6, -20, -52, -8],\n [9, -36, -9, -39, -26],\n [15, -45, 1, 7, -18]]\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 5x5 matrix:\n[[-24, 0, 0, 24, -24],\n [36, 0, 0, -36, 36],\n [24, 0, 0, -24, 24],\n [24, 0, 0, -24, 24],\n [-6, 0, 0, 6, -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[[-4, -24, -2, -8, -18],\n [-44, 42, -7, -13, 18],\n [22, -9, -20, -33, 27],\n [-28, -42, 7, 1, -54],\n [-26, 57, 3, 10, 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[[5, 6, 3, 4, 3],\n [0, 0, 0, 0, 0],\n [20, 24, 12, 16, 12],\n [-30, -36, -18, -24, -18],\n [-15, -18, -9, -12, -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[[-32, -36, 4, -20, -24],\n [0, -3, -13, 1, -18],\n [-40, -42, 18, -26, -12],\n [10, 9, -11, 7, -6],\n [-10, -15, -15, -5, -30]]\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 5x5 matrix:\n[[3, 0, 3, 4, -5],\n [2, -2, 0, 6, -10],\n [-8, -7, -15, 1, -10],\n [-11, -13, -24, 7, -25],\n [3, 6, 9, -6, 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 5x5 matrix:\n[[23, -7, 0, 1, 3],\n [-3, 3, 0, 3, 9],\n [13, -11, 0, -10, -30],\n [10, -8, 0, -7, -21],\n [9, 3, 0, 9, 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[[15, -15, 6, -36, 24],\n [-22, 7, -1, 12, -25],\n [4, 4, -4, 28, 8],\n [-12, -22, 10, -32, 18],\n [-4, -15, 9, -50, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[3, -18, 9, 27, -36],\n [-24, -27, -18, 9, 18],\n [-24, -31, -37, 19, 28],\n [26, 25, 33, -7, -36],\n [-21, -21, -49, 12, 46]]\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[[27, 19, 55, 47, -13],\n [-11, -26, -54, -58, -13],\n [-1, -5, -22, 14, 14],\n [-10, 17, 43, 64, 26],\n [10, -20, -24, -10, -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[[-1, -30, 11, -20, 6],\n [55, -2, 20, -25, -14],\n [-27, -15, -9, 15, 16],\n [-5, 13, 4, 20, -15],\n [26, 11, 1, -2, -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[[14, 5, 2, 12, 18],\n [8, 0, -6, -6, 6],\n [14, 13, 22, 48, 30],\n [-6, -9, -18, -36, -18],\n [-6, -9, -18, -36, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-5, -18, 12, -4, 29],\n [10, 13, -24, -17, -8],\n [-46, -1, 33, -34, 29],\n [-29, 24, 0, -42, -3],\n [-38, 56, -6, -42, -48]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[24, -24, 16, -4, -20],\n [-36, 36, -24, 6, 30],\n [-18, 18, -12, 3, 15],\n [-36, 36, -24, 6, 30],\n [-12, 12, -8, 2, 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[[-18, -15, -21, -23, 21],\n [-8, 5, -70, -46, 0],\n [0, -5, 11, 5, 1],\n [-18, -20, -10, -18, 22],\n [-11, -40, 35, 3, 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, 35, 12, 8, 6],\n [7, 1, -47, 3, 28],\n [-15, -25, -36, 9, 24],\n [-51, -38, -30, 35, 10],\n [-51, -38, -30, 35, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, 12, -12, 0, -12],\n [-2, -45, 9, -6, 9],\n [-10, -1, -11, -2, -11],\n [12, 6, 12, 3, 12],\n [-16, 0, -18, -3, -18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[16, 16, 20, -28, -8],\n [-24, 16, 10, 2, 42],\n [-12, -24, -27, 33, -3],\n [-4, -20, -21, 23, -10],\n [12, 24, 27, -33, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-17, 18, 16, -31, 1],\n [26, 1, -16, 41, -3],\n [-19, 48, 20, -48, 4],\n [8, -23, 14, 15, 5],\n [-32, -56, 46, 46, -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 5x5 matrix:\n[[1, 4, 4, 1, 5],\n [-6, -24, -24, -6, -30],\n [-6, -24, -24, -6, -30],\n [3, 12, 12, 3, 15],\n [-4, -16, -16, -4, -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 5x5 matrix:\n[[-39, 20, -17, 33, 7],\n [2, -48, -24, 60, 16],\n [-26, -10, -2, 18, 9],\n [-37, 28, 1, 12, -3],\n [23, -8, 9, -42, 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 5x5 matrix:\n[[-3, 44, 22, -35, 47],\n [9, -52, 4, -29, -20],\n [14, -33, 0, 4, -25],\n [-50, 79, 2, 40, -48],\n [-15, 9, -26, 47, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-7, -10, -1, -9, 7],\n [25, 10, 25, 0, 20],\n [7, 9, 6, -11, 6],\n [-10, 20, -20, -15, -23],\n [8, -10, 14, 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 5x5 matrix:\n[[6, -3, 2, 4, -3],\n [36, -18, 12, 24, -18],\n [36, -18, 12, 24, -18],\n [0, 0, 0, 0, 0],\n [-24, 12, -8, -16, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, -15, 18, -15, 9],\n [10, -25, 30, -25, 15],\n [10, -25, 30, -25, 15],\n [10, -25, 30, -25, 15],\n [-2, 5, -6, 5, -3]]?\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[[2, 18, 10, -21, 2],\n [14, 6, 34, -22, 0],\n [6, 42, 22, 44, -16],\n [4, 60, 48, 71, -42],\n [-7, -42, -50, -80, 43]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[0, 27, 1, -3, -47],\n [-1, 23, 12, -28, 0],\n [-26, -18, 4, 0, 5],\n [-62, -12, 12, -30, -8],\n [-45, 30, 25, -39, -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[[19, 17, 21, -6, 16],\n [6, -6, 18, 12, 24],\n [-18, -18, -18, 8, -12],\n [-4, 4, -12, -8, -16],\n [-21, -24, -18, 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[[1, 12, -12, -17, -6],\n [-28, -24, 34, 40, 20],\n [15, -16, -5, 21, -17],\n [-9, 16, 7, -23, 21],\n [4, -20, 11, 28, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[13, -41, -6, 7, -13],\n [25, -15, -10, -30, 15],\n [12, 23, 10, -31, 27],\n [-30, 9, -42, 27, -27],\n [-43, 34, -68, 22, -26]]\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[[4, -16, 0, -24, 16],\n [-4, 16, 0, 24, -16],\n [4, -16, 0, -24, 16],\n [-2, 8, 0, 12, -8],\n [-4, 16, 0, 24, -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 5x5 matrix:\n[[15, 15, -3, -9, -9],\n [20, 20, -4, -12, -12],\n [-5, -5, 1, 3, 3],\n [25, 25, -5, -15, -15],\n [-5, -5, 1, 3, 3]]\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, 0, 0, 0, 0],\n [-30, 30, 18, 18, 36],\n [-5, 5, 3, 3, 6],\n [0, 0, 0, 0, 0],\n [15, -15, -9, -9, -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 5x5 matrix:\n[[0, -2, -3, 2, 2],\n [6, -33, 53, -25, -47],\n [10, -36, 38, -20, -45],\n [36, -7, 18, -23, -8],\n [-4, 25, -46, 21, 36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[16, 62, 0, -13, -7],\n [-12, 2, 5, 30, 14],\n [-1, -17, 30, 38, 4],\n [8, -25, -35, -44, 32],\n [-21, 12, 35, 44, -62]]\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[[-1, -1, -6, -6, 4],\n [1, 1, 6, 6, -4],\n [0, 0, 0, 0, 0],\n [2, 2, 12, 12, -8],\n [-1, -1, -6, -6, 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[[-24, -8, 0, -16, -4],\n [-6, -2, 0, -4, -1],\n [6, 2, 0, 4, 1],\n [6, 2, 0, 4, 1],\n [-6, -2, 0, -4, -1]]\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[[-25, 30, -15, 15, -5],\n [0, 0, 0, 0, 0],\n [-30, 36, -18, 18, -6],\n [-30, 36, -18, 18, -6],\n [15, -18, 9, -9, 3]]\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[[3, 6, -6, 3, -3],\n [1, 2, -2, 1, -1],\n [1, 2, -2, 1, -1],\n [4, 8, -8, 4, -4],\n [-4, -8, 8, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-6, -27, -15, -12, -9],\n [6, 32, 14, 12, 6],\n [-8, 9, -29, -16, -39],\n [8, -14, 30, 16, 42],\n [-8, 4, -28, -16, -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[[13, 7, 0, -2, 7],\n [26, 9, 25, -34, 34],\n [-10, -14, -13, 8, -9],\n [30, 20, -13, 12, 5],\n [7, 10, 0, 4, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[9, 7, -26, 8, -38],\n [-23, -36, -25, -3, -11],\n [17, 0, -18, -16, -50],\n [-7, -38, 19, -39, 17],\n [-4, 15, 13, 21, 35]]\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[[-12, 5, 7, 19, 12],\n [-10, 5, 5, 20, 5],\n [-8, 10, -2, 46, -32],\n [10, -5, -5, -20, -5],\n [2, -6, 4, -29, 29]]\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 5x5 matrix:\n[[28, 24, -18, -34, 34],\n [30, 24, -45, -9, 9],\n [16, 17, -15, -16, 10],\n [-38, -46, 39, 37, -13],\n [2, 5, 21, -27, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[30, -30, 0, 24, 18],\n [0, 0, 0, 0, 0],\n [-20, 20, 0, -16, -12],\n [10, -10, 0, 8, 6],\n [20, -20, 0, 16, 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[[30, 22, -24, 17, -31],\n [-68, 25, 85, -14, 47],\n [10, 10, -4, 7, -13],\n [-2, 42, 6, 11, -3],\n [-38, 18, 46, -7, 27]]\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[[-16, -16, -8, -12, 24],\n [-16, -16, -8, -12, 24],\n [-12, -12, -6, -9, 18],\n [12, 12, 6, 9, -18],\n [-16, -16, -8, -12, 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[[-15, 11, 34, -36, -18],\n [-29, -14, 10, 35, 45],\n [22, -8, -37, 16, -1],\n [-44, -7, 34, 7, 17],\n [-60, -27, 18, -9, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[20, 16, 20, 4, 0],\n [10, 8, 10, 2, 0],\n [-20, -16, -20, -4, 0],\n [-30, -24, -30, -6, 0],\n [-30, -24, -30, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[11, -1, 14, -9, -19],\n [-3, -3, -6, 1, 7],\n [-17, -5, -26, 11, 33],\n [20, -10, 20, -20, -30],\n [8, -4, 8, -8, -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[[-11, 17, -13, 1, -29],\n [12, -4, -4, -12, 8],\n [-25, -5, 25, 35, 5],\n [-5, -1, 5, 7, 1],\n [-4, 12, -12, -4, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[38, 4, -50, 22, -28],\n [-5, -41, -15, -6, -51],\n [13, 12, -5, -5, 20],\n [0, 39, 15, 15, 39],\n [12, 23, -15, 31, -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[[-20, -6, -28, 8, 16],\n [-20, -6, -28, 8, 16],\n [-16, -16, -28, -16, -4],\n [-4, 10, 0, 24, 20],\n [4, -8, 1, -20, -17]]\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, -10, 14, 7, 0],\n [40, 12, -26, -36, -14],\n [-12, 28, -6, 2, 20],\n [12, -26, 0, 2, -19],\n [28, 26, -26, -30, -1]]\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, 15, 21, -3, -3],\n [-32, 4, -16, -2, -36],\n [-20, -8, -52, -5, -36],\n [6, -16, -25, 2, 6],\n [-32, 11, -9, -4, -39]]\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 5x5 matrix:\n[[13, -28, 18, 40, -12],\n [-10, 20, -14, -34, 8],\n [-5, 11, 3, 19, 15],\n [18, -30, 6, 6, -30],\n [-14, 29, -3, 11, 29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-5, 1, -5, 0, 2],\n [-10, 2, -10, 0, 4],\n [-25, 5, -25, 0, 10],\n [-15, 3, -15, 0, 6],\n [15, -3, 15, 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 5x5 matrix:\n[[-18, 18, 15, 0, 18],\n [24, -24, -20, 0, -24],\n [-6, 6, 5, 0, 6],\n [-6, 6, 5, 0, 6],\n [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[[-10, -8, -6, -4, -6],\n [-17, -20, -3, -20, -15],\n [2, 8, -6, 14, 6],\n [-21, -20, -9, -15, -15],\n [34, 24, 24, 7, 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[[-5, -4, -5, 6, -5],\n [-30, -24, -30, 36, -30],\n [25, 20, 25, -30, 25],\n [-25, -20, -25, 30, -25],\n [5, 4, 5, -6, 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[[14, 9, 20, 9, 29],\n [14, 15, 10, 1, 11],\n [-6, -3, -10, -5, -15],\n [-22, -27, -10, 3, -7],\n [-2, 0, -5, -3, -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 5x5 matrix:\n[[3, 0, 5, -5, 6],\n [18, 0, 30, -30, 36],\n [-9, 0, -15, 15, -18],\n [0, 0, 0, 0, 0],\n [-18, 0, -30, 30, -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[[22, 2, -4, -6, -40],\n [3, -3, -3, -18, 15],\n [24, 0, -6, -18, -30],\n [14, -2, -5, -21, -5],\n [-10, -2, 1, -3, 25]]\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, 28, -24, -22, 42],\n [-54, -34, -4, 34, -5],\n [-6, 28, -18, -14, 65],\n [-18, -5, 41, 7, -21],\n [-36, -49, -23, 38, -33]]\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 5x5 matrix:\n[[-30, 24, -12, -30, -12],\n [-5, 4, -2, -5, -2],\n [10, -8, 4, 10, 4],\n [-30, 24, -12, -30, -12],\n [-25, 20, -10, -25, -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[[-2, 4, 12, -12, 2],\n [0, 0, 0, 0, 0],\n [-5, 10, 30, -30, 5],\n [-2, 4, 12, -12, 2],\n [4, -8, -24, 24, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-7, 19, 14, 1, -2],\n [-26, -3, -29, 37, 3],\n [14, 2, 38, -36, -10],\n [36, -32, -34, -10, 14],\n [-31, 17, -26, 45, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[16, -24, -16, -8, 20],\n [-20, 30, 20, 10, -25],\n [-12, 18, 12, 6, -15],\n [-12, 18, 12, 6, -15],\n [-20, 30, 20, 10, -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[[-15, 25, -10, -20, 25],\n [9, -7, -1, 13, -10],\n [-27, 5, 17, -41, 20],\n [15, -33, 17, 19, -30],\n [27, -21, -3, 39, -30]]\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 5x5 matrix:\n[[-8, 20, -20, 0, -4],\n [14, 41, -25, -8, 19],\n [10, -25, 25, 0, 5],\n [34, 29, -5, -12, 35],\n [-18, -31, 15, 8, -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 5x5 matrix:\n[[-3, -35, -23, 8, 5],\n [-6, -14, -11, 5, 8],\n [-23, 4, -11, 35, 56],\n [-38, -63, -51, 12, 35],\n [-3, 8, 2, 10, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[5, 27, -17, 22, -2],\n [13, 20, -28, -1, 26],\n [9, 3, -17, -14, 26],\n [29, 14, -18, -15, 38],\n [18, 12, -10, -4, 19]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-16, -18, -16, 32, -32],\n [-25, -31, -25, 0, 35],\n [-22, -12, -22, 8, -14],\n [-22, -19, -22, 30, -34],\n [-6, 0, -6, 3, -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[[12, 4, 8, -12, 0],\n [-19, 22, -6, -1, 25],\n [-5, -13, -6, 13, -10],\n [-14, 1, -8, 10, 5],\n [7, -26, -2, 13, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[0, 6, 6, 0, 6],\n [0, -5, -5, 0, -5],\n [0, 2, 2, 0, 2],\n [0, 0, 0, 0, 0],\n [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[[-10, 0, 12, 6, 10],\n [-25, 0, 30, 15, 25],\n [-30, 0, 36, 18, 30],\n [0, 0, 0, 0, 0],\n [-15, 0, 18, 9, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[0, 0, 0, 0, 0],\n [-4, -1, -4, -5, 3],\n [12, 3, 12, 15, -9],\n [-12, -3, -12, -15, 9],\n [20, 5, 20, 25, -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[[34, 16, -27, 35, -41],\n [50, -3, -19, 4, 6],\n [26, -1, 4, 33, -28],\n [28, 6, -6, 34, -31],\n [24, 4, -20, -4, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-13, -5, 27, 24, -14],\n [-6, 18, 0, 8, 6],\n [32, -5, -54, -54, 22],\n [-7, -2, 12, 10, -5],\n [-9, -12, 18, 10, -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[[-39, 27, 34, 42, 32],\n [18, 4, -8, -8, -14],\n [16, -27, 9, -11, -8],\n [-27, 44, -3, 66, 46],\n [37, 0, -46, -16, -19]]\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[[-22, -28, -18, -22, -30],\n [-60, -52, -26, 56, -16],\n [-28, -4, -34, 8, -32],\n [-38, -48, -7, 30, -5],\n [-47, -52, -15, 35, -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[[10, -24, -36, 11, 8],\n [12, -26, -22, -10, 3],\n [46, 5, -28, -22, 41],\n [-28, -34, 12, -48, -20],\n [24, -35, -18, -53, 11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-44, -60, -10, 11, 16],\n [-20, -29, -33, -15, 2],\n [8, 13, 49, 28, 0],\n [8, 15, -24, 3, 35],\n [24, 32, -32, -26, -4]]\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 5x5 matrix:\n[[36, -62, 18, -54, -19],\n [1, -24, -66, -31, 53],\n [-23, 20, 22, 41, -33],\n [29, 8, 26, -17, -4],\n [-10, 2, 26, 16, -25]]\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[[-3, -4, -22, -6, 1],\n [-6, 0, -24, -6, 0],\n [3, -8, -8, -3, 2],\n [15, -16, 20, 3, 4],\n [-9, 20, 14, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[7, 26, 79, -6, -84],\n [29, -46, 0, 19, 11],\n [-9, 56, -1, -46, -30],\n [-20, 32, -47, 9, 24],\n [-50, 78, -6, -50, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[16, 0, 24, -12, -24],\n [28, -12, 12, 12, 12],\n [7, -3, 3, 3, 3],\n [18, -2, 22, -8, -18],\n [-14, 6, -6, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, -8, -8, 8, 0],\n [18, 12, 12, -12, 0],\n [3, 2, 2, -2, 0],\n [0, 0, 0, 0, 0],\n [-18, -12, -12, 12, 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[[-15, -13, -11, -13, 13],\n [-20, -20, -22, -16, 40],\n [-15, -15, 21, 33, -45],\n [-5, -3, 10, 7, -27],\n [-20, -21, 4, 19, -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[[16, 20, -24, 16, -12],\n [24, 30, -36, 24, -18],\n [4, 5, -6, 4, -3],\n [4, 5, -6, 4, -3],\n [-12, -15, 18, -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 5x5 matrix:\n[[0, 0, -5, -20, 10],\n [0, 0, -6, -24, 12],\n [0, 0, -5, -20, 10],\n [0, 0, -1, -4, 2],\n [0, 0, -6, -24, 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[[14, -12, 20, -2, 2],\n [-23, 6, -42, 5, -1],\n [-22, -39, -15, 6, 4],\n [30, -39, 1, 0, 8],\n [30, -15, 17, -3, 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[[-27, 19, 27, -38, 5],\n [10, 25, -20, 26, 63],\n [7, -40, -12, 29, -38],\n [29, -20, -26, 29, -6],\n [4, -2, -17, 17, 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 5x5 matrix:\n[[-30, -18, 0, -36, 12],\n [-30, -18, 0, -36, 12],\n [5, 3, 0, 6, -2],\n [15, 9, 0, 18, -6],\n [-5, -3, 0, -6, 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 5x5 matrix:\n[[-2, -31, -17, 3, 9],\n [20, -10, -14, -6, 14],\n [-10, -20, -13, 3, 18],\n [18, 14, 4, -6, -5],\n [-16, -3, 6, 6, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, -23, 9, 21, -14],\n [-34, -35, 25, 36, -13],\n [-20, -31, 21, 11, 0],\n [-4, 28, 18, -18, 40],\n [6, 36, -2, -9, 19]]\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[[19, -30, 9, 73, 74],\n [19, -26, 2, 46, 55],\n [-41, 54, -24, -30, -29],\n [11, -22, 19, 50, 41],\n [-8, 12, -24, 43, 53]]?\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 5x5 matrix:\n[[-50, -41, 0, -10, -45],\n [-65, -64, -66, -17, -21],\n [-18, -23, 18, -26, 0],\n [11, 23, -12, 35, -21],\n [-21, -12, -72, 27, -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[[10, -39, -3, 6, 8],\n [5, 21, 3, -6, -2],\n [21, -30, 22, -5, 12],\n [1, 48, 28, -17, -4],\n [-5, 27, 11, -7, -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[[18, 36, 30, 24, -36],\n [6, 12, 10, 8, -12],\n [9, 18, 15, 12, -18],\n [-12, -24, -20, -16, 24],\n [6, 12, 10, 8, -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[[2, 1, 3, 5, 5],\n [-15, 0, -19, -28, -29],\n [-21, 12, -21, -24, -27],\n [19, -13, 18, 19, 22],\n [20, -5, 23, 31, 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[[-5, 1, 18, -12, -2],\n [7, -47, -27, 4, 4],\n [36, -40, 6, -21, -10],\n [5, 43, 21, -10, -12],\n [33, -55, -15, -14, -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[[-49, -14, -40, -5, -40],\n [-21, -19, -41, 18, 17],\n [61, -7, 24, 18, 52],\n [-46, -5, -48, -1, -4],\n [-25, 10, -10, -21, -28]]\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[[-3, 3, -12, -15, 0],\n [4, -4, 16, 20, 0],\n [-2, 2, -8, -10, 0],\n [0, 0, 0, 0, 0],\n [3, -3, 12, 15, 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[[-9, 27, -45, 30, 18],\n [10, -6, 6, 0, -8],\n [-23, 21, -27, 10, 22],\n [36, 0, -18, 30, -18],\n [-4, 6, -9, 5, 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[[32, 7, -39, 44, -7],\n [-39, -6, 6, -42, -33],\n [6, -6, 46, -11, 52],\n [-28, 34, -2, 12, -30],\n [5, 38, 18, 41, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-10, 10, 2, 14, 1],\n [10, -10, 0, -30, 0],\n [18, -18, -10, 26, -5],\n [28, -28, -8, -20, -4],\n [-2, 2, 4, -26, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, -15, 9, 0, 3],\n [-20, -25, 15, 0, 5],\n [-20, -25, 15, 0, 5],\n [16, 20, -12, 0, -4],\n [-24, -30, 18, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-25, -10, 25, -20, 20],\n [-25, -10, 25, -20, 20],\n [25, 10, -25, 20, -20],\n [0, 0, 0, 0, 0],\n [-30, -12, 30, -24, 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[[-34, 4, 0, 27, -15],\n [16, -11, -6, -28, 7],\n [40, -35, 29, -40, 50],\n [9, -18, 23, -9, 10],\n [-49, 27, -24, 46, -23]]\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 5x5 matrix:\n[[-20, 12, -19, -1, -18],\n [-16, 18, 16, -16, 12],\n [20, 3, 29, -17, -8],\n [44, -33, 8, 16, 4],\n [16, 3, 27, -15, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, -16, -26, -20, 26],\n [36, -24, 24, 24, -24],\n [-36, 24, -24, -24, 24],\n [-9, 10, -3, -4, 3],\n [15, 2, 19, 16, -19]]?\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[[-6, -30, 30, 30, -30],\n [-6, -30, 30, 30, -30],\n [-3, -15, 15, 15, -15],\n [3, 15, -15, -15, 15],\n [1, 5, -5, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1, 27, 6, -2, -17],\n [-11, 42, -18, -20, 21],\n [11, 15, 4, -10, -64],\n [-15, 21, 16, 27, 26],\n [18, -30, 18, 7, -49]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[16, -18, 8, -37, 15],\n [-15, 9, -3, 33, -9],\n [-5, 17, -9, 14, -12],\n [19, -3, -1, -40, 6],\n [-7, 7, -3, 16, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-53, -18, -30, -34, -24],\n [-22, -29, 13, -19, -30],\n [-18, -29, 48, -23, -22],\n [27, -6, 49, 14, -8],\n [4, -8, 9, 4, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[0, 20, 22, 13, 14],\n [-32, -4, -86, -31, -28],\n [-28, 16, -72, -6, -18],\n [-60, 0, -48, -102, -6],\n [42, 0, 28, 74, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -8, 4, 6, 23],\n [-13, -17, 17, 24, -1],\n [-4, -6, 1, -58, 23],\n [34, 34, -25, 16, -38],\n [-8, -16, 15, -52, 4]]\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, 0, 0, 0, 0],\n [-8, -10, 10, 12, 2],\n [-24, -30, 30, 36, 6],\n [8, 10, -10, -12, -2],\n [12, 15, -15, -18, -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[[21, -22, -14, 8, -32],\n [6, -32, -4, 10, -4],\n [-12, -36, 8, 10, 28],\n [24, 2, -16, 1, -42],\n [9, 32, -6, -9, -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[[15, 6, -15, 12, -15],\n [10, 4, -10, 8, -10],\n [30, 12, -30, 24, -30],\n [5, 2, -5, 4, -5],\n [-20, -8, 20, -16, 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 5x5 matrix:\n[[-12, -74, 36, 15, -16],\n [-4, -36, -36, -62, 38],\n [-9, 72, -2, -16, 25],\n [-19, 40, -12, 14, 14],\n [9, 40, -32, -66, 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[[-20, -30, -30, 0, 5],\n [20, 30, 30, 0, -5],\n [-16, -24, -24, 0, 4],\n [4, 6, 6, 0, -1],\n [24, 36, 36, 0, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[20, 10, -25, -15, -25],\n [-8, -4, 10, 6, 10],\n [20, 10, -25, -15, -25],\n [-12, -6, 15, 9, 15],\n [12, 6, -15, -9, -15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, 16, 24, -6, 30],\n [-13, 6, 16, 2, 13],\n [35, 4, 14, -17, 62],\n [12, -27, -18, 27, 0],\n [0, -13, -8, 16, -5]]\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[[-17, 22, 26, 31, 4],\n [15, 2, 14, 34, -8],\n [51, -24, 0, 33, -16],\n [53, -22, 4, 39, -10],\n [-3, 2, 23, 25, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[15, 15, -12, -6, -3],\n [-20, -20, 16, 8, 4],\n [-25, -25, 20, 10, 5],\n [5, 5, -4, -2, -1],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[2, -42, 8, -18, 16],\n [4, 27, 35, 17, -11],\n [-16, 45, -23, 31, -10],\n [15, 17, 24, -3, -14],\n [-34, 60, -30, 56, -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 5x5 matrix:\n[[-30, -46, 23, 41, 42],\n [2, 7, -21, -28, -24],\n [66, 6, -18, -54, -22],\n [-27, -58, 14, 23, 43],\n [-52, 5, -5, 5, 12]]\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, 0, 10, -22, 6],\n [-11, -19, -68, 29, -15],\n [10, -4, -30, 42, -12],\n [-30, 6, 24, -30, 0],\n [-24, 13, 45, -32, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-26, 10, 22, 11, 0],\n [-34, 10, 28, 24, 0],\n [0, 0, 0, 0, 0],\n [17, -13, -16, 13, 0],\n [27, -7, -22, -22, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[18, 18, -20, 12, -3],\n [0, 0, 0, 0, 0],\n [-36, -15, 5, -3, -15],\n [0, 15, -25, 15, -15],\n [6, 5, -5, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 30, 12, -18, 24],\n [-4, -10, -4, 6, -8],\n [-4, -10, -4, 6, -8],\n [12, 30, 12, -18, 24],\n [6, 15, 6, -9, 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[[8, -16, -5, 22, -29],\n [24, -20, -28, -10, -52],\n [48, 58, 70, 57, -6],\n [27, 30, 22, 2, -4],\n [24, 36, 30, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[11, 52, -32, 64, 38],\n [-20, -4, 41, 5, 29],\n [58, 28, -8, -1, 0],\n [38, 46, 26, 18, 44],\n [-33, -48, 11, -26, -27]]\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[[49, 54, -44, -25, 12],\n [-42, -10, 3, -35, 39],\n [66, 72, -60, -30, 12],\n [-22, 8, -16, -46, 14],\n [-19, -8, 4, 3, 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 5x5 matrix:\n[[-16, -4, -12, -16, -20],\n [-20, -5, -15, -20, -25],\n [-8, -2, -6, -8, -10],\n [-24, -6, -18, -24, -30],\n [20, 5, 15, 20, 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[[-17, 64, 64, -14, 47],\n [8, -12, -33, -9, -16],\n [-26, 6, 36, 3, 19],\n [-7, -6, 23, 16, 6],\n [4, 16, -4, -12, 4]]\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 5x5 matrix:\n[[27, 1, -33, -13, 21],\n [-45, -27, -13, 7, -15],\n [54, 15, 12, -27, 27],\n [-33, -27, -15, 3, -9],\n [-2, -10, 22, 2, -6]]\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 5x5 matrix:\n[[-18, 5, -26, -2, 40],\n [21, -30, 39, -22, -53],\n [24, -25, -1, 3, -39],\n [-29, 0, -13, 36, 28],\n [20, 25, 2, 16, -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[[12, 20, -4, 8, 24],\n [6, -18, 36, -12, -66],\n [-7, 7, -23, 6, 38],\n [-8, -18, 9, -8, -29],\n [-22, -32, 1, -12, -31]]?\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[[2, -16, -2, -31, 14],\n [6, 32, 6, -12, 36],\n [-1, 21, 38, 55, 17],\n [0, -26, 54, 26, 34],\n [19, 35, -20, -30, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, 34, -6, 34, -33],\n [-4, 20, 3, 10, -17],\n [14, -19, 0, -12, 23],\n [-2, 16, -9, -36, -8],\n [-16, -20, -18, -64, 12]]\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[[-5, -1, -6, 4, 4],\n [20, 4, 24, -16, -16],\n [-20, -4, -24, 16, 16],\n [0, 0, 0, 0, 0],\n [-5, -1, -6, 4, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[30, 25, -15, -25, -5],\n [-24, -20, 12, 20, 4],\n [-12, -10, 6, 10, 2],\n [-30, -25, 15, 25, 5],\n [-12, -10, 6, 10, 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[[0, 0, 0, 0, 0],\n [-12, 20, 12, 0, 24],\n [-9, 15, 9, 0, 18],\n [15, -25, -15, 0, -30],\n [-12, 20, 12, 0, 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[[0, -30, 47, 2, -50],\n [-26, -40, 27, 14, -48],\n [22, -13, -38, -20, 69],\n [-26, -43, 14, 12, -45],\n [-61, -32, 27, 36, 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[[-9, 38, 11, 32, -8],\n [-24, -5, 1, -9, 6],\n [29, -2, 4, -2, 14],\n [1, 9, -9, 17, -32],\n [0, -19, -10, -13, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-27, 12, -6, 8, 2],\n [21, -9, 6, -6, -2],\n [-3, -3, -18, -2, 6],\n [-15, 15, 30, 10, -10],\n [-54, 36, 36, 24, -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[[-12, 0, -8, 4, -8],\n [15, 0, 10, -5, 10],\n [15, 0, 10, -5, 10],\n [-12, 0, -8, 4, -8],\n [12, 0, 8, -4, 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[[1, -7, 59, -34, 36],\n [-16, 0, -10, -30, 20],\n [-5, -2, 22, -15, 28],\n [-2, -4, 52, -8, 54],\n [-10, 0, -37, 0, -1]]\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, -27, -20, 27, 33],\n [0, -55, 1, -15, 12],\n [-54, -40, 34, -28, -31],\n [8, 3, -2, 17, 9],\n [10, -20, 16, 28, 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[[20, -30, 30, 20, 5],\n [-16, 24, -24, -16, -4],\n [24, -36, 36, 24, 6],\n [-16, 24, -24, -16, -4],\n [-4, 6, -6, -4, -1]]\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[[3, 16, -27, 35, -6],\n [-18, 0, 2, -50, 4],\n [-12, 14, -22, -10, -2],\n [-12, 5, -7, -25, 1],\n [6, -13, 21, -5, 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[[2, 2, -8, 2, 10],\n [6, 6, -24, 6, 30],\n [-2, -2, 8, -2, -10],\n [-4, -4, 16, -4, -20],\n [4, 4, -16, 4, 20]]\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, 16, 42, 62, -44],\n [2, -5, 6, 23, -6],\n [-4, -23, -2, 17, 18],\n [7, -31, -8, 25, 15],\n [-40, 42, 33, -5, 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 5x5 matrix:\n[[15, -12, 6, -15, 9],\n [20, -16, 8, -20, 12],\n [5, -4, 2, -5, 3],\n [15, -12, 6, -15, 9],\n [25, -20, 10, -25, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[30, 0, 5, 20, 15],\n [36, 0, 6, 24, 18],\n [-24, 0, -4, -16, -12],\n [-18, 0, -3, -12, -9],\n [24, 0, 4, 16, 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[[14, -24, -6, -24, 8],\n [23, 15, -18, -34, 18],\n [-41, -15, 16, 48, -36],\n [-13, -6, 1, 11, -13],\n [-13, 42, -7, 15, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, -18, -12, 0, -36],\n [-4, -12, -8, 0, -24],\n [6, 18, 12, 0, 36],\n [1, 3, 2, 0, 6],\n [2, 6, 4, 0, 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[[-51, -9, -18, 5, -30],\n [-41, 20, -33, -3, -9],\n [27, -45, 54, 15, -36],\n [-5, 35, -3, -2, -36],\n [10, -28, 6, 20, 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[[12, 7, 10, -2, -6],\n [6, -40, 11, 18, 24],\n [4, 20, -6, -8, -44],\n [24, -26, 16, 14, -30],\n [-26, 85, -25, -40, -2]]\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, 26, -24, -8, -2],\n [-1, 9, 36, -5, -30],\n [17, 0, 45, 1, -36],\n [-30, 7, -45, -6, 36],\n [13, -17, 18, 5, 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[[-18, 0, 24, 36, 36],\n [27, -36, 16, 6, 0],\n [6, 0, -8, -12, -12],\n [-16, 12, 4, 12, 14],\n [-19, 12, 8, 18, 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[[-18, -18, 33, -39, -8],\n [0, -26, 30, 10, -32],\n [16, 16, 2, 22, -24],\n [-24, -38, 24, -32, 8],\n [-18, -37, -21, -1, 44]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, -3, 4, -5, -2],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [-8, -12, 16, -20, -8],\n [-12, -18, 24, -30, -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[[-14, -2, 4, 29, 38],\n [-22, -18, 8, 21, 62],\n [12, -2, -3, -31, -32],\n [1, -2, -6, -1, -2],\n [-11, -18, -20, 15, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-20, -6, 0, 0, 4],\n [27, 9, 2, 2, -7],\n [27, 9, 2, 2, -7],\n [13, 3, -2, -2, -1],\n [-4, -3, -4, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[2, -33, -15, -14, 22],\n [0, -28, -46, -26, 18],\n [28, 4, -36, -47, -14],\n [16, 34, -1, -26, -17],\n [42, 9, 23, -21, -32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[18, -15, 9, 9, -18],\n [6, -5, 3, 3, -6],\n [-6, 5, -3, -3, 6],\n [18, -15, 9, 9, -18],\n [-24, 20, -12, -12, 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[[8, 16, 2, 8, -4],\n [-8, -8, -24, -12, 8],\n [-4, -24, 43, 4, -6],\n [-2, -26, 60, 9, -10],\n [-4, 12, -56, -14, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[20, 13, -10, 20, -28],\n [-10, 24, 58, 96, -24],\n [12, 5, -24, -24, 44],\n [-13, 11, 42, 58, -62],\n [-5, 6, 24, 38, -92]]\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, -18, 5, 24, -1],\n [-2, 10, -3, -12, 3],\n [-42, -14, 1, 36, 31],\n [48, 12, 0, -36, -36],\n [-22, -16, 3, 30, 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[[15, -24, 60, 9, 12],\n [11, -20, 15, -14, -20],\n [-10, -16, 15, 11, 8],\n [16, 30, -15, -9, 0],\n [-20, 14, -6, 26, 32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[25, -28, 8, 0, 42],\n [46, -40, 32, 0, 59],\n [-21, 34, -47, -24, -1],\n [-59, 16, -38, 24, -64],\n [6, -64, 0, 36, 34]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-15, -9, 3, -18, 9],\n [-5, -3, 1, -6, 3],\n [-30, -18, 6, -36, 18],\n [25, 15, -5, 30, -15],\n [10, 6, -2, 12, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 2, -2, -17, 18],\n [-18, -18, 2, 61, -66],\n [9, 0, -4, -23, 24],\n [9, 12, 0, -33, 36],\n [6, 26, 6, -37, 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[[-26, 36, 6, 32, -18],\n [38, -36, 30, -26, 18],\n [18, -24, -2, -21, 12],\n [18, -24, -2, -21, 12],\n [0, 0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-20, 20, -15, 0, -5],\n [-10, 8, 3, -2, 1],\n [11, -10, 3, 1, 1],\n [-6, 8, -15, 2, -5],\n [-9, 10, -12, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-20, 2, -14, 18, 4],\n [36, -7, 24, -31, -5],\n [-14, -19, -17, 21, 16],\n [-4, 14, 2, -2, -8],\n [-14, 15, -5, 7, -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[[30, -24, 12, -4, 16],\n [-2, -24, 52, -72, -12],\n [-14, 36, -44, 48, -12],\n [-5, -22, 24, -21, 19],\n [24, -17, 4, 5, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 5, 3, -6, -1],\n [24, 20, 12, -24, -4],\n [24, 20, 12, -24, -4],\n [6, 5, 3, -6, -1],\n [-30, -25, -15, 30, 5]]?\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, 36, 46, 28, 22],\n [12, -6, 28, 90, 54],\n [16, -16, -12, 20, 16],\n [-10, -2, -5, -17, -16],\n [5, -26, -41, -38, -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 5x5 matrix:\n[[0, 0, 0, 0, 0],\n [-15, 6, -9, 18, 3],\n [-30, 12, -18, 36, 6],\n [15, -6, 9, -18, -3],\n [25, -10, 15, -30, -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, -30, 10, 20, -15],\n [6, -36, 12, 24, -18],\n [5, -30, 10, 20, -15],\n [1, -6, 2, 4, -3],\n [-2, 12, -4, -8, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[73, -6, -13, 46, 5],\n [-14, -50, -14, -32, 1],\n [-15, -66, -14, -31, -4],\n [9, 20, -71, 24, 22],\n [-10, 24, 0, -20, 12]]\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 5x5 matrix:\n[[-5, 1, 1, 6, -6],\n [-36, 18, 24, 33, -45],\n [15, -21, -31, -1, 21],\n [-28, 2, 0, 37, -33],\n [22, -8, -10, -23, 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[[-50, -1, -32, 30, 4],\n [15, -33, 46, -26, -13],\n [-46, 19, -56, 38, 24],\n [-13, -6, 16, 4, -51],\n [8, -11, 7, -10, 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[[-23, -17, -22, 17, 35],\n [1, 7, 8, -7, -25],\n [-29, -19, -25, 19, 35],\n [-20, -12, -16, 12, 20],\n [15, 1, 3, -1, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-21, 28, -18, 72, -58],\n [-8, 36, -25, 59, -11],\n [-21, -32, 13, -25, -35],\n [-4, -26, 2, -32, 23],\n [-30, 11, -16, -2, -7]]?\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 5x5 matrix:\n[[5, -6, 2, -5, 6],\n [-30, 36, -12, 30, -36],\n [2, -4, 0, 18, -12],\n [26, -32, 10, -16, 24],\n [21, -24, 9, -36, 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[[5, -5, 0, 3, 5],\n [5, -5, 0, 3, 5],\n [-5, 5, 0, -3, -5],\n [-10, 10, 0, -6, -10],\n [-20, 20, 0, -12, -20]]\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[[17, 1, -16, 18, -11],\n [-32, 5, 2, -30, 14],\n [-9, 17, -18, -24, -21],\n [6, -13, -20, 36, 24],\n [31, -4, 16, 18, -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[[-8, -4, -2, -2, 6],\n [20, 10, 5, 5, -15],\n [4, 2, 1, 1, -3],\n [-12, -6, -3, -3, 9],\n [-12, -6, -3, -3, 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[[-2, -3, -50, -9, -36],\n [12, -13, -5, 21, -17],\n [-46, 14, 25, 2, -9],\n [6, 5, 52, 3, 46],\n [-10, 12, 58, -2, 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[[12, -18, 12, 6, 12],\n [-8, 12, -8, -4, -8],\n [-8, 12, -8, -4, -8],\n [12, -18, 12, 6, 12],\n [10, -15, 10, 5, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, -16, 4, 16, 12],\n [4, 8, -2, -8, -6],\n [-6, -12, 3, 12, 9],\n [10, 20, -5, -20, -15],\n [2, 4, -1, -4, -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[[15, 25, -25, 10, 25],\n [9, 15, -15, 6, 15],\n [12, 20, -20, 8, 20],\n [15, 25, -25, 10, 25],\n [-3, -5, 5, -2, -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[[-85, 50, -5, 0, -50],\n [66, -36, 0, 0, 42],\n [5, 5, 48, -35, -17],\n [-63, 40, 9, -10, -42],\n [-1, 1, -9, 5, 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[[-24, -22, -20, -11, -15],\n [-44, 18, -38, 43, 55],\n [-31, 20, -42, -17, 24],\n [25, -8, 24, -13, -24],\n [-31, -22, -24, 0, -7]]\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, 12, -39, 36, -9],\n [8, -8, 26, -24, 6],\n [19, -19, 13, -5, -15],\n [22, -22, 34, -26, -6],\n [-6, 6, 3, -6, 9]]\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 5x5 matrix:\n[[16, 24, 8, 12, 12],\n [12, 18, 6, 9, 9],\n [16, 24, 8, 12, 12],\n [-8, -12, -4, -6, -6],\n [-20, -30, -10, -15, -15]]\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, -66, -33, -11, 57],\n [2, -12, 9, 13, -11],\n [-18, 60, 30, 6, -60],\n [-26, 32, 13, -19, -67],\n [-2, -24, 3, 3, -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[[6, -24, 12, 12, -18],\n [-6, 24, -12, -12, 18],\n [-1, 4, -2, -2, 3],\n [2, -8, 4, 4, -6],\n [-4, 16, -8, -8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[21, 40, 26, 20, 7],\n [5, -19, -25, 1, -15],\n [-16, -38, -26, -18, -12],\n [-18, 20, 44, -16, 18],\n [19, -17, -38, 14, -21]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-40, 30, 35, 33, 27],\n [-14, 26, -11, 10, 11],\n [-34, 26, 29, 28, 23],\n [22, -8, -32, -19, -14],\n [34, -26, -29, -28, -23]]\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 5x5 matrix:\n[[22, -4, 38, -24, -28],\n [16, 16, 17, -34, 8],\n [8, 16, 4, -24, 16],\n [-14, 4, -25, 14, 20],\n [18, 4, 27, -26, -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[[-8, -13, 2, 44, -3],\n [14, 16, 10, 4, -6],\n [-14, -16, -10, -4, 6],\n [-26, -31, -16, 8, 9],\n [-7, -8, -5, -2, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, 8, -4, 8, 6],\n [6, -15, 0, -12, -13],\n [36, 18, 36, 0, 24],\n [16, 2, 14, -4, 5],\n [60, -6, 48, -24, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-13, -14, 2, -18, -23],\n [-17, 8, 4, 0, -19],\n [-4, 7, -7, 6, 4],\n [13, 36, 32, 32, 7],\n [-20, 1, 7, -8, -28]]\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, -18, 0, -10, 4],\n [2, -21, -3, -14, 8],\n [2, -6, 12, 6, -12],\n [3, 3, 30, 25, -34],\n [4, -24, 12, -4, -8]]\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, 18, 30, -12, 26],\n [12, 42, 60, 0, 42],\n [-24, -12, 0, -48, 20],\n [-18, -9, 0, -36, 15],\n [10, -10, -25, 30, -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[[-6, -6, 18, -18, 66],\n [-2, 5, 0, 4, -16],\n [-2, 5, 0, 4, -16],\n [1, -6, 3, -7, 27],\n [-22, 20, 30, -6, 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[[-5, 19, -6, 22, -21],\n [7, 2, 15, 0, 3],\n [0, -13, -3, -14, 12],\n [28, -31, 51, -42, 48],\n [-6, 15, -9, 18, -18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -24, -8, -20, 8],\n [0, 0, 0, 0, 0],\n [3, 18, 6, 15, -6],\n [0, 0, 0, 0, 0],\n [5, 30, 10, 25, -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[[-8, -20, 16, 16, 20],\n [4, 10, -8, -8, -10],\n [12, 30, -24, -24, -30],\n [-10, -25, 20, 20, 25],\n [-2, -5, 4, 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[[-5, -10, -23, -8, 18],\n [3, -38, -27, 14, 14],\n [2, -7, -29, -20, 2],\n [-10, -27, 3, 36, 34],\n [-24, 43, 59, 20, 26]]\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 5x5 matrix:\n[[1, -1, -4, 0, -1],\n [-5, 5, 20, 0, 5],\n [-4, 4, 16, 0, 4],\n [1, -1, -4, 0, -1],\n [5, -5, -20, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-17, 44, -28, 32, -56],\n [-55, 17, 6, 11, -28],\n [-9, -20, 26, -19, -2],\n [7, 7, 8, 18, -2],\n [32, -3, 2, 1, -6]]\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[[-35, 33, 40, 22, 39],\n [8, -58, -30, 12, -12],\n [15, 69, 32, 12, 0],\n [-43, -14, 9, -8, 42],\n [-13, -69, -38, -34, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-8, 31, 72, 37, -21],\n [28, -14, -34, -16, 0],\n [-10, 1, -1, 7, -33],\n [-24, -10, 4, 6, -24],\n [16, 10, -24, -6, -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[[3, 3, 3, -9, 0],\n [2, 2, 2, -6, 0],\n [4, 4, 4, -12, 0],\n [2, 2, 2, -6, 0],\n [-2, -2, -2, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, -32, -24, 40, -34],\n [-2, -32, -14, 18, -17],\n [-6, -31, -12, 19, -16],\n [24, -8, -6, -14, 2],\n [-34, -21, -7, 38, -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[[34, -14, -33, -30, -24],\n [-23, -3, 58, -36, -46],\n [16, -5, -54, 51, 63],\n [-9, 1, 21, -12, -16],\n [-34, 29, 35, 21, 11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -6, -2, 4, 6],\n [0, -6, -2, 4, 6],\n [0, 0, 0, 0, 0],\n [0, -36, -12, 24, 36],\n [0, -30, -10, 20, 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 5x5 matrix:\n[[10, 0, -45, 30, 5],\n [10, 20, 15, -14, 13],\n [-18, -35, -24, 23, -23],\n [8, 25, 39, -31, 14],\n [16, 10, -42, 26, 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[[5, 7, 17, 35, 28],\n [-15, -5, -19, -9, -4],\n [20, 3, 18, -10, -13],\n [-20, 0, -12, 28, 28],\n [15, 6, 21, 15, 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[[24, -1, 40, -23, 1],\n [-29, -10, -31, 34, 17],\n [-33, 20, 1, -20, -35],\n [8, -29, -35, 46, 36],\n [26, 6, 47, -41, -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[[18, 25, 0, -14, 19],\n [-36, -29, 9, 13, -35],\n [12, -23, -17, 19, 7],\n [30, 16, -11, -5, 28],\n [60, 18, -28, 0, 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[[8, 8, -8, -2, 0],\n [12, 12, -12, -3, 0],\n [16, 16, -16, -4, 0],\n [0, 0, 0, 0, 0],\n [-12, -12, 12, 3, 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[[21, 0, -6, 24, 3],\n [-11, 8, -14, -20, 19],\n [-21, 0, 6, -24, -3],\n [-7, 0, 2, -8, -1],\n [-6, -16, 36, 8, -42]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-27, -42, 60, 39, -39],\n [-29, -39, 55, 36, -37],\n [1, -49, -35, -50, 17],\n [-12, -20, 25, 18, -17],\n [12, -25, -70, -65, 37]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 4, 4, -1, -4],\n [12, -8, -8, 2, 8],\n [12, -8, -8, 2, 8],\n [0, 0, 0, 0, 0],\n [-6, 4, 4, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[5, 1, -3, -23, -3],\n [-4, 6, -27, 43, 27],\n [10, 9, 7, 57, 17],\n [47, 13, -18, -44, 12],\n [-89, -20, 46, 2, -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 5x5 matrix:\n[[2, -23, -1, 27, -18],\n [14, 21, 9, -3, 26],\n [16, -6, -7, -13, 36],\n [-21, -4, 9, 32, -59],\n [-3, -6, -16, -37, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[20, 30, 5, -20, -10],\n [-12, -18, -3, 12, 6],\n [16, 24, 4, -16, -8],\n [-12, -18, -3, 12, 6],\n [-16, -24, -4, 16, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[33, -3, 29, -23, 24],\n [-26, -54, 8, -23, -26],\n [19, 15, -7, 0, 18],\n [-17, -33, -1, -13, -16],\n [5, 3, -11, 0, 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 5x5 matrix:\n[[38, -36, -45, 33, 20],\n [6, 19, 11, 5, 10],\n [-21, 8, 17, -27, -30],\n [15, 6, -13, -2, -13],\n [13, 21, 13, 16, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[20, -4, 1, -25, -17],\n [35, 16, 5, -16, 28],\n [16, 6, 9, -5, 23],\n [-20, 7, 26, -58, 68],\n [-48, -24, 15, -1, -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 5x5 matrix:\n[[24, 36, -12, 6, -36],\n [-20, -30, 10, -5, 30],\n [24, 36, -12, 6, -36],\n [-24, -36, 12, -6, 36],\n [4, 6, -2, 1, -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[[46, -16, 64, 14, -40],\n [-37, 31, -17, 24, 6],\n [12, -27, 5, 11, -19],\n [38, -41, 23, -5, -23],\n [29, -48, 16, 13, -33]]\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, -25, 10, 5, -5],\n [-6, 5, -2, -1, 1],\n [-36, 30, -12, -6, 6],\n [-36, 30, -12, -6, 6],\n [24, -20, 8, 4, -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[[-28, -2, -10, 10, -12],\n [-8, 36, -8, 0, -8],\n [-42, -40, 2, 0, -4],\n [-1, -36, -13, 30, -10],\n [-32, -42, -20, 36, -20]]\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 5x5 matrix:\n[[-50, 75, 78, -3, 18],\n [32, 23, 5, 10, -14],\n [30, -1, -16, 15, -2],\n [-14, 5, 20, 17, -38],\n [-58, 33, 48, -3, 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[[-16, 20, 24, -2, 8],\n [9, 8, 3, 8, 12],\n [-3, 2, 3, -1, 0],\n [-4, 26, 24, 7, 20],\n [11, 16, 9, 12, 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[[-26, 37, 16, 6, -12],\n [-34, 64, 8, 24, -6],\n [-17, 36, 18, 6, -13],\n [-14, -30, -2, -18, 0],\n [-4, -40, -3, -21, 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 5x5 matrix:\n[[-12, 54, -30, -3, -36],\n [-4, -12, 24, -8, 4],\n [-32, 54, 8, -27, -34],\n [-1, -3, -8, 0, 15],\n [-10, 24, 10, -9, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[78, 42, 18, 12, 62],\n [4, 13, -3, -2, 3],\n [-40, 14, -14, -60, -34],\n [0, -45, 10, 46, 2],\n [25, 16, 4, 8, 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[[-12, -10, 15, 6, 11],\n [-46, -36, 49, 22, 27],\n [-27, -15, 45, 36, 12],\n [-32, -30, 35, 6, 35],\n [-3, -7, -12, -18, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-60, 0, -14, 16, -14],\n [-48, -7, -13, 9, -19],\n [30, 26, 29, 31, 13],\n [12, 17, 25, 35, -5],\n [18, 41, 36, 52, 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[[-5, 8, -1, 12, 0],\n [-25, 8, 19, 20, 24],\n [-30, -8, 36, 2, 42],\n [-10, -16, 22, -16, 24],\n [15, 16, -27, 14, -30]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-38, -22, -8, 14, 6],\n [-35, -27, -32, -33, 37],\n [-37, -25, -22, -19, 28],\n [13, 8, 4, -5, -2],\n [47, 32, 26, 5, -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[[-33, -3, 49, 36, 14],\n [-36, -5, 51, 6, -65],\n [-17, -10, 26, 38, 67],\n [-25, 3, 7, -7, 5],\n [-22, 4, 20, -4, -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[[0, 0, 0, 0, 0],\n [12, -12, -30, -12, -12],\n [12, -12, -30, -12, -12],\n [6, -6, -15, -6, -6],\n [6, -6, -15, -6, -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[[0, -20, 24, -16, -16],\n [0, 0, 0, 0, 0],\n [0, -25, 30, -20, -20],\n [0, -30, 36, -24, -24],\n [0, 15, -18, 12, 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[[48, 44, -26, -20, -56],\n [50, 34, 20, -12, -4],\n [-9, -13, 16, 6, 20],\n [31, 21, 9, -8, -8],\n [51, 29, 19, -12, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0, 0],\n [-6, -6, -4, -8, 10],\n [-3, -3, -2, -4, 5],\n [12, 12, 8, 16, -20],\n [-18, -18, -12, -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 5x5 matrix:\n[[-12, -22, 12, -30, -22],\n [18, -25, -9, -11, 2],\n [-6, 24, -24, 5, 9],\n [40, -11, -3, 32, 27],\n [6, 11, -6, 15, 11]]\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 5x5 matrix:\n[[17, -12, 34, 34, -42],\n [-4, 5, -10, -14, 14],\n [33, 25, -2, -23, -20],\n [20, 33, -30, -40, 6],\n [3, -1, 6, 1, -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[[-16, -20, 20, -4, 4],\n [-12, -15, 15, -3, 3],\n [8, 10, -10, 2, -2],\n [24, 30, -30, 6, -6],\n [12, 15, -15, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[10, 5, 20, 10, 30],\n [4, 2, 8, 4, 12],\n [-10, -5, -20, -10, -30],\n [2, 1, 4, 2, 6],\n [2, 1, 4, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-44, -58, -78, -16, 46],\n [23, 30, 75, 10, 9],\n [-5, 0, 41, 16, 53],\n [-10, -16, -16, 2, 18],\n [-28, -41, -56, -6, 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[[0, 34, -38, -38, 26],\n [-13, -15, -2, -8, 6],\n [41, 10, -22, -28, -13],\n [21, -17, -6, -16, -14],\n [-18, 1, -15, -19, 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[[-5, -3, 2, 43, 0],\n [-30, -46, 75, -14, 16],\n [30, 24, -42, 8, -24],\n [-18, 4, -2, 38, 22],\n [32, 36, -62, 12, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[6, 6, 12, 36, 18],\n [0, 0, 0, 0, 0],\n [-6, -6, -12, -36, -18],\n [5, 5, 10, 30, 15],\n [-2, -2, -4, -12, -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[[25, 1, 38, -20, -6],\n [-31, 17, -4, -7, 10],\n [-18, 7, 10, 5, 11],\n [38, 6, -20, 4, -26],\n [-49, 11, 20, -1, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-23, -21, 17, 15, -10],\n [21, 6, -4, -25, 19],\n [-42, 36, 12, 12, 18],\n [-26, 3, 19, 0, 15],\n [-20, 54, -6, 2, 22]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, -19, 21, 0, 16],\n [-24, 19, 25, -15, -35],\n [54, 21, -69, 36, 24],\n [48, 37, -41, 39, 11],\n [16, 6, -4, 15, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[32, -24, 0, -16, 12],\n [-14, 2, -9, -6, -9],\n [-5, 57, -3, 25, 27],\n [-9, -29, -39, -45, -27],\n [0, 23, -9, 3, 12]]\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 5x5 matrix:\n[[7, 20, -6, -17, 12],\n [-6, -24, 12, -36, 24],\n [-47, 23, 49, 38, 57],\n [-32, -23, 27, 32, 11],\n [23, -1, -22, -67, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-17, -8, 6, 6, -24],\n [22, -30, 0, 48, -10],\n [44, -17, 0, 36, 20],\n [-29, 40, 30, -66, 0],\n [15, -1, -6, 6, 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[[37, 2, 53, -19, 38],\n [-16, 14, -21, 20, -4],\n [-25, 34, -26, 22, 2],\n [8, 48, -36, -33, -32],\n [23, 42, 8, -3, 18]]\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, -24, -24, -24, -6],\n [6, 18, 3, 30, -15],\n [-15, 18, 33, 6, 24],\n [-13, -32, -2, -56, 31],\n [13, 4, -16, 20, -25]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[5, -1, 2, -5, -6],\n [40, 58, 6, -35, -26],\n [-39, -92, -10, 37, 9],\n [10, 13, 26, 24, -10],\n [22, 77, 8, -38, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[10, 0, -25, -10, 10],\n [-28, -18, 25, 28, -16],\n [12, 12, 0, -12, 4],\n [12, 12, 0, -12, 4],\n [8, 12, 10, -8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-46, 32, -66, 16, 12],\n [-17, 35, -21, 66, -55],\n [37, -22, 38, -6, -10],\n [-38, 7, -40, -28, 40],\n [0, -35, -8, -56, 36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -3, 27, 24, 0],\n [16, -27, 3, 0, 12],\n [-8, 20, -20, -16, -8],\n [8, -20, 20, 16, 8],\n [-28, 44, 4, 8, -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, 12, 28, -15, 6],\n [44, -20, -10, -19, -54],\n [10, 20, 55, -35, 0],\n [-48, 12, -12, 33, 54],\n [-50, 20, 5, 25, 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[[15, -9, 5, -1, -8],\n [14, 1, 15, -3, -4],\n [-16, -23, -45, -9, 8],\n [8, 22, 38, 20, -12],\n [-26, 2, -24, 3, 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[[-36, 8, -24, -24, 23],\n [-27, -9, -11, -11, 14],\n [-18, -4, -10, -10, 18],\n [-30, -8, -10, -10, 1],\n [-27, -5, -15, -15, 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 5x5 matrix:\n[[27, -7, 7, -5, 12],\n [-34, 10, -9, 21, -6],\n [60, -36, 42, 8, 11],\n [-43, 31, -39, -8, -2],\n [35, -23, 23, 18, 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[[7, -12, 20, 6, -15],\n [-46, 10, -2, -22, -50],\n [44, -4, 1, 13, 45],\n [11, 0, 7, -3, 0],\n [47, 3, 22, -12, 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[[26, -22, 7, -22, -20],\n [18, 76, 2, 4, -16],\n [-5, 26, 2, 3, 10],\n [-9, 35, -32, 29, -62],\n [11, 36, -26, 24, -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[[2, 70, 61, -16, 24],\n [-3, -75, -66, 16, -26],\n [-46, -20, -38, 52, -22],\n [26, -35, -18, -18, -3],\n [-32, -40, -49, 40, -24]]\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[[3, -9, -16, 2, 2],\n [-1, 1, 12, 18, -12],\n [-1, -3, 13, 27, -18],\n [-11, -1, 17, 5, 0],\n [-7, -7, -12, -20, 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[[-22, 10, 30, -18, 3],\n [24, -16, -6, -2, -9],\n [-17, 11, 6, 0, 6],\n [2, 10, -60, 48, 12],\n [8, -8, 12, -12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-18, -43, -42, 23, -20],\n [16, 39, 4, -15, 41],\n [2, -12, -34, 24, 13],\n [-8, 5, 8, 44, 81],\n [7, 20, 11, -29, -8]]?\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 5x5 matrix:\n[[-32, 3, 2, 2, -27],\n [-14, 20, 36, -56, 3],\n [-20, -21, 1, 12, -12],\n [22, 26, 24, 24, -20],\n [30, 34, 28, -64, 36]]\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[[66, -39, -76, -27, -27],\n [51, -27, -78, 4, -39],\n [-12, -5, 29, -39, 59],\n [24, -11, -18, -20, -20],\n [0, 0, -40, 18, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-5, 4, -2, -5, 6],\n [20, -16, 8, 20, -24],\n [15, -12, 6, 15, -18],\n [10, -8, 4, 10, -12],\n [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[[-10, -3, 15, -12, 1],\n [4, 4, -20, -12, 36],\n [18, 3, -15, 36, -33],\n [-4, 1, -5, -18, 29],\n [30, 9, -45, 36, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-32, -11, -12, 13, 17],\n [13, 32, 20, -2, -2],\n [2, 10, 21, -14, -1],\n [-20, -32, 18, -32, 2],\n [3, -11, -3, -5, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, 15, 9, -6, 16],\n [30, 47, -6, -28, 41],\n [-1, 47, -20, 2, 17],\n [13, 38, -8, -18, 13],\n [-29, -12, -16, 18, -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[[-7, 0, -36, 27, 41],\n [6, 0, 32, -14, -34],\n [0, 0, -6, -48, -6],\n [-3, 0, -13, 31, 20],\n [0, 0, -2, -16, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[21, -14, 40, -9, -11],\n [-12, 9, -17, -24, 4],\n [20, -15, 28, 28, -5],\n [-69, 58, -52, 9, -37],\n [27, -20, 39, 21, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, -7, 0, -5, -6],\n [23, 21, 21, 11, 9],\n [4, 3, 6, 1, 0],\n [24, 18, 36, 6, 0],\n [-15, -5, -45, 5, 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[[27, 12, -10, 16, -7],\n [26, 36, 9, 18, 36],\n [-53, -5, 27, 4, 14],\n [-41, -11, 19, -30, 18],\n [4, 3, 5, -17, 26]]\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[[-22, 23, -7, -27, -12],\n [4, 15, 25, 45, 44],\n [-42, 26, -27, -76, -63],\n [-49, -40, 45, -24, 1],\n [-18, -47, 48, 15, 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[[1, 0, 0, -5, 7],\n [1, 15, -15, -11, 19],\n [3, -10, 10, -11, 13],\n [-6, 50, -50, 10, -2],\n [-3, 0, 0, 15, -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[[42, 36, 24, 16, 24],\n [51, 18, 24, -20, 12],\n [-43, 30, -3, 67, -21],\n [-12, 0, 6, -54, 30],\n [36, 54, 28, 46, 15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-16, -16, -4, -4, 20],\n [4, 4, 1, 1, -5],\n [-24, -24, -6, -6, 30],\n [-24, -24, -6, -6, 30],\n [-4, -4, -1, -1, 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 5x5 matrix:\n[[-36, 48, -3, -15, 0],\n [-33, 34, 6, -18, -26],\n [-21, 14, 24, -12, -70],\n [57, -14, 0, 60, 38],\n [24, 9, 19, 38, -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 5x5 matrix:\n[[-9, -7, -1, 25, 28],\n [-29, -19, 11, 1, -24],\n [55, 31, -41, -28, 13],\n [7, 9, 15, 11, 18],\n [1, 3, 9, 15, 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[[-12, 1, 57, -42, 4],\n [15, -6, -2, -14, 0],\n [-60, 52, 32, 26, 2],\n [-3, -31, 13, 10, -2],\n [15, -23, -39, 45, -7]]\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 5x5 matrix:\n[[-28, -34, 23, 28, -23],\n [0, -2, 3, 28, -3],\n [23, 26, -16, 4, 16],\n [23, 28, -19, -24, 19],\n [-9, -12, 9, 24, -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, -30, 19, -12, -1],\n [22, -1, -27, 30, 19],\n [-39, -23, 14, 66, 56],\n [8, 1, 6, -30, -22],\n [48, 11, -23, -42, -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 5x5 matrix:\n[[-1, -14, -5, 50, 31],\n [1, -1, 0, -5, -1],\n [-2, 20, 6, -44, -34],\n [2, 7, 3, -37, -20],\n [-1, -2, -1, 14, 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[[71, -50, -2, 35, 13],\n [-89, 55, 8, -31, -10],\n [34, -35, 2, 29, 5],\n [-30, 5, 10, 11, 5],\n [9, -28, 2, 24, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[15, 9, 0, 18, -15],\n [-30, -18, 0, -36, 30],\n [25, 15, 0, 30, -25],\n [0, 0, 0, 0, 0],\n [-20, -12, 0, -24, 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 5x5 matrix:\n[[3, -4, 29, -3, 31],\n [-12, -26, 10, -9, 2],\n [6, 0, 34, -2, 38],\n [3, -2, 23, -2, 25],\n [12, 20, 8, 6, 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 5x5 matrix:\n[[8, -22, -22, -2, -28],\n [12, 30, -42, -30, -24],\n [8, 20, -28, -20, -16],\n [-16, -26, 54, 34, 36],\n [7, 14, -24, -16, -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 5x5 matrix:\n[[-9, -18, 15, -3, 12],\n [0, 0, 0, 0, 0],\n [15, 30, -25, 5, -20],\n [-3, -6, 5, -1, 4],\n [-18, -36, 30, -6, 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[[6, -31, 17, 47, 55],\n [51, -5, 60, 1, 12],\n [15, 3, 17, -1, -11],\n [-9, -27, -1, 43, 43],\n [-51, 11, -60, -27, -40]]\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, 0, 3, 0],\n [-10, -8, 12, 4, 2],\n [9, 2, -18, -3, -3],\n [17, -2, -42, -5, -7],\n [-24, 12, 72, 6, 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[[30, 25, -20, -15, -15],\n [-18, -15, 12, 9, 9],\n [36, 30, -24, -18, -18],\n [30, 25, -20, -15, -15],\n [-36, -30, 24, 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 5x5 matrix:\n[[38, 12, 44, -20, -14],\n [-26, -48, -32, 44, 20],\n [3, -30, 2, 22, 7],\n [-2, 48, 0, -36, -12],\n [-12, -48, -16, 40, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[48, -15, 36, 2, -22],\n [60, -30, 36, -2, -32],\n [-12, 20, 4, 6, 12],\n [-30, 10, -22, -1, 14],\n [24, 5, 28, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[25, -25, 52, -19, 19],\n [14, -6, -10, -3, -28],\n [-17, -41, -1, -18, 32],\n [5, -31, -9, -7, 6],\n [-27, 5, -34, 2, -7]]\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 5x5 matrix:\n[[-38, 0, 59, 4, 21],\n [-56, 0, 28, 40, 62],\n [50, 0, -15, -40, -60],\n [-42, 0, 0, 36, 55],\n [34, 0, -13, -20, -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 5x5 matrix:\n[[2, -12, -8, -4, 6],\n [-13, 42, 24, 22, -39],\n [8, -12, -4, -12, 24],\n [-12, 18, 6, 18, -36],\n [-7, 33, 21, 13, -21]]\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[[-6, 28, -27, 14, -7],\n [-16, 38, 17, 24, 29],\n [8, -31, 5, 7, -18],\n [8, 18, -15, -48, 13],\n [19, -42, 48, 0, 5]]\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[[-28, 0, 40, 10, 2],\n [-14, -5, -24, -19, 14],\n [32, 17, 10, -6, -27],\n [4, 3, 1, -3, -4],\n [-20, -6, 0, -2, 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 5x5 matrix:\n[[20, -36, 40, -14, 14],\n [-20, 45, -43, 20, -29],\n [12, -29, 19, -24, 7],\n [44, -36, -16, 32, -62],\n [18, -18, -28, 14, -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[[5, -14, -14, -7, -12],\n [-14, 40, 44, 20, 29],\n [18, 22, -15, -46, 25],\n [-15, -40, 5, 45, -45],\n [6, 40, 16, -24, 33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-30, 8, -16, -11, 0],\n [-24, -20, -20, -4, 0],\n [6, 27, 11, -3, 0],\n [18, -51, -3, 15, 0],\n [42, 2, 26, 13, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, 3, -6, -3, -4],\n [-6, -11, -48, 11, -37],\n [8, -12, 24, 12, 16],\n [6, 15, 54, -15, 42],\n [6, -29, -12, 29, -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[[-24, -17, -2, 20, -7],\n [25, -34, 12, -2, -45],\n [10, -8, 8, 2, -8],\n [6, -21, 14, 14, -15],\n [-8, -25, -2, 8, -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 5x5 matrix:\n[[41, -8, 27, 26, 0],\n [1, -55, -44, -27, -23],\n [56, -50, 6, -6, -46],\n [32, -1, 25, 25, 23],\n [22, -37, -11, -27, -53]]\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 5x5 matrix:\n[[-22, 30, -26, 20, -38],\n [-10, 12, -8, 2, -2],\n [9, -12, 10, -7, 13],\n [-18, 21, -13, 1, 2],\n [2, -6, 10, -16, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, -37, -14, 70, -1],\n [29, -6, 15, -46, 3],\n [25, -12, -4, -27, 10],\n [-19, 32, 36, -31, -18],\n [-23, 10, -27, 16, 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[[4, 0, 20, -12, -16],\n [-6, 0, -30, 18, 24],\n [5, 0, 25, -15, -20],\n [-4, 0, -20, 12, 16],\n [-5, 0, -25, 15, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[30, -45, -9, -24, -12],\n [-25, 42, 15, 17, 16],\n [-25, 30, -5, 25, 0],\n [-25, 36, 5, 21, 8],\n [15, -24, -7, -11, -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[[-9, 6, -33, -6, -12],\n [-2, -2, -12, 2, -8],\n [-2, -5, -36, 14, -65],\n [-1, 13, 18, -15, 30],\n [0, -18, -12, 12, 6]]?\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[[31, -6, 32, 14, -41],\n [-12, -16, -16, -22, 2],\n [17, -18, 4, -20, -37],\n [1, -38, 6, -17, -26],\n [-32, 20, -17, 16, 57]]?\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, 4, -32, 20],\n [26, -13, 0, 36, -21],\n [27, -29, 31, 4, 8],\n [25, -10, -5, 40, -25],\n [20, -21, 22, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[22, 38, 6, 4, -8],\n [17, 3, 21, 14, -18],\n [10, 12, 6, 4, -6],\n [20, 24, 12, 8, -12],\n [17, 32, 3, 2, -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[[-47, -18, 24, -7, -21],\n [7, 8, -1, -13, -1],\n [53, 10, -30, -11, 3],\n [15, -24, -17, -33, -41],\n [3, -2, -2, -15, -11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, -16, -12, -16, 8],\n [-10, -20, -15, -20, 10],\n [-10, -20, -15, -20, 10],\n [-6, -12, -9, -12, 6],\n [4, 8, 6, 8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[15, 4, -13, 2, -3],\n [3, 37, 11, 23, -48],\n [-7, -1, 9, -3, 0],\n [11, 4, -15, 8, -3],\n [18, 1, -33, 16, 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[[-7, -15, -16, -4, 29],\n [-30, -22, 12, -6, 26],\n [-3, -8, 7, -3, -6],\n [-9, -26, 7, -9, 0],\n [3, -8, -3, -3, -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[[-8, 20, 16, 20, -16],\n [8, -20, -16, -20, 16],\n [6, -15, -12, -15, 12],\n [-6, 15, 12, 15, -12],\n [10, -25, -20, -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[[31, -13, 0, 14, -10],\n [-9, -3, 0, -6, 30],\n [12, -10, 0, 4, 16],\n [44, -18, 0, 20, -16],\n [34, -12, 0, 16, -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[[8, 13, 15, 4, 8],\n [-20, -36, -34, 18, -34],\n [8, 10, 18, 28, -4],\n [0, -3, 3, 24, -12],\n [-14, -24, -25, 3, -19]]\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, -12, -6, 31, -34],\n [-1, 14, 18, -27, 36],\n [-44, 4, -24, -32, 20],\n [-3, -12, -18, 21, -30],\n [14, 2, 12, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, 19, 21, -15, -17],\n [39, 15, 11, 7, 3],\n [0, -67, -19, 7, 7],\n [42, -49, -11, 9, -19],\n [-3, -30, 7, -20, -38]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[18, 18, 24, -6, 24],\n [-18, -18, -24, 6, -24],\n [18, 18, 24, -6, 24],\n [-15, -15, -20, 5, -20],\n [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[[-13, -8, -7, 4, -5],\n [17, -22, 2, -30, -11],\n [46, 28, 34, 2, -4],\n [0, 19, 15, 0, -13],\n [-5, 22, 10, -4, -3]]\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, -24, 6, 6, 6],\n [15, 20, -5, -5, -5],\n [18, 24, -6, -6, -6],\n [18, 24, -6, -6, -6],\n [12, 16, -4, -4, -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[[24, -20, 33, -29, -18],\n [16, 46, -58, 50, 39],\n [1, -22, -10, -13, 65],\n [1, -26, 19, -8, -27],\n [-41, -86, 64, -68, -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[[-29, 23, 5, 11, -16],\n [15, -20, -5, -35, 20],\n [-3, 25, 19, 13, 8],\n [6, -12, -12, 24, -18],\n [7, -1, 7, -27, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[42, 0, 33, 25, 22],\n [-30, -22, -22, -32, 0],\n [33, -15, 27, 10, 28],\n [-15, 3, -12, -7, -10],\n [24, 26, 17, 31, -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[[18, 11, -2, 2, -24],\n [21, -15, 15, -3, -6],\n [-9, -7, 13, -3, 23],\n [-14, -40, -2, -4, 23],\n [-24, -4, -8, 0, 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[[11, 7, -16, 11, -15],\n [-14, -22, 28, -14, 30],\n [7, 11, -14, 7, -15],\n [-8, -16, 18, -8, 20],\n [25, 5, -30, 25, -25]]\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, -60, 0, 30, 10],\n [38, -18, -19, 28, -16],\n [8, 12, -4, -2, -6],\n [-50, 0, 25, -25, 25],\n [36, -36, -18, 36, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[12, -24, 6, 4, -46],\n [51, -9, -9, -11, 17],\n [-72, 54, -45, -12, 9],\n [-15, -6, 36, -2, 39],\n [21, 36, -36, 32, 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[[-6, -4, -2, -10, 10],\n [-12, -6, 42, 66, -48],\n [17, 10, -25, -29, 17],\n [37, 23, -26, -10, -5],\n [7, 3, -36, -60, 45]]\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 5x5 matrix:\n[[25, -34, 34, -32, -49],\n [7, -24, 8, -35, -24],\n [4, -6, -29, -6, 33],\n [25, 8, 5, 11, 26],\n [45, -6, -10, -7, 51]]\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[[-9, 0, 5, 14, 5],\n [-20, -4, 12, 16, 0],\n [13, 8, -9, 10, 15],\n [-28, -2, 16, 36, 10],\n [16, 5, -10, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-13, 19, 27, 7, 0],\n [-11, 23, -3, 9, -30],\n [-35, -11, 37, -9, 46],\n [-10, -27, -26, -20, 5],\n [-48, 11, 16, 14, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-32, 28, -28, -8, 42],\n [12, -33, 22, 33, -6],\n [-10, 68, -35, -48, 7],\n [-7, -43, 12, 5, -3],\n [10, -32, 21, 36, -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[[-9, -12, 19, -41, 18],\n [-12, 14, -18, 17, -6],\n [51, -38, 41, -15, 4],\n [12, -35, 15, -23, 27],\n [3, 13, -26, 44, -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[[3, 0, 9, 18, 9],\n [0, 0, 0, 0, 0],\n [6, 0, 18, 36, 18],\n [-1, 0, -3, -6, -3],\n [4, 0, 12, 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[[44, 20, 5, -33, 32],\n [9, -12, -19, -17, 11],\n [-27, -6, -25, 2, -10],\n [-22, -34, 14, 11, -31],\n [-20, 4, 10, 18, -17]]\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[[-13, -21, -40, -1, 8],\n [29, -37, 52, -47, -42],\n [-19, 31, -12, 33, 18],\n [19, 0, -30, -45, 5],\n [-42, -13, -30, 30, 1]]\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[[-8, 12, -12, -8, -16],\n [4, -6, 6, 4, 8],\n [8, -12, 12, 8, 16],\n [8, -12, 12, 8, 16],\n [-4, 6, -6, -4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[24, 24, 30, -24, -12],\n [-8, -8, -10, 8, 4],\n [-8, -8, -10, 8, 4],\n [-8, -8, -10, 8, 4],\n [4, 4, 5, -4, -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[[32, -32, -13, -69, 3],\n [6, -5, -3, -12, 1],\n [-39, 9, 34, 57, -14],\n [-43, -12, 42, 36, -42],\n [43, -5, -35, -54, 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 5x5 matrix:\n[[-25, 15, 30, -30, 30],\n [5, -3, -6, 6, -6],\n [10, -6, -12, 12, -12],\n [-15, 9, 18, -18, 18],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-11, 8, 27, 24, -10],\n [3, 38, -6, -1, 35],\n [-13, -23, 36, 27, -41],\n [3, -30, 39, 18, -48],\n [-9, 22, 8, 13, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 0, 12, 2, -8],\n [20, 0, -30, -5, 20],\n [-4, 0, 6, 1, -4],\n [-24, 0, 36, 6, -24],\n [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[[-2, -6, 4, -8, -4],\n [-20, 7, 8, -21, -17],\n [-26, -23, 30, 11, 39],\n [48, 7, -34, -5, -29],\n [4, 26, -16, 30, 10]]\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 5x5 matrix:\n[[-34, -9, -1, 32, -4],\n [-12, 8, 22, 18, 12],\n [2, 7, 13, 2, 8],\n [24, 14, 16, -18, 12],\n [-6, 4, 11, 9, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-24, -28, 11, 15, 13],\n [12, 12, -15, -3, -9],\n [17, 20, -7, -11, -9],\n [10, 12, -3, -7, -5],\n [-9, -4, 35, -9, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-24, 16, -4, 12, -37],\n [-33, -26, -15, -11, -19],\n [16, 67, 66, 32, 10],\n [63, -11, -10, -19, 17],\n [-13, -43, -12, -31, -25]]\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[[18, 16, -4, -8, -18],\n [-30, 4, 5, 19, -3],\n [-22, -4, 12, 18, 8],\n [-18, -10, 5, 10, 12],\n [2, 40, 24, 24, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, 0, -18, 15, -12],\n [-15, 0, 30, -25, 20],\n [-9, 0, 18, -15, 12],\n [-3, 0, 6, -5, 4],\n [12, 0, -24, 20, -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 5x5 matrix:\n[[-3, 0, 6, 0, 6],\n [12, 0, -24, 0, -24],\n [18, 0, -36, 0, -36],\n [6, 0, -12, 0, -12],\n [-9, 0, 18, 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[[16, 9, -4, -12, -28],\n [-72, -7, 12, 50, 10],\n [50, -32, 16, -68, 18],\n [20, 21, -20, 12, 8],\n [34, 7, -4, -29, -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[[-7, -22, -8, -23, 30],\n [18, 30, 6, 27, -48],\n [35, 32, -10, 36, -64],\n [-3, 8, 2, 20, -6],\n [-21, -28, 2, -34, 48]]\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, 13, 69, 58, -44],\n [17, 22, 1, -1, -22],\n [-27, -17, -11, -12, 28],\n [38, 23, 14, 17, -40],\n [14, 13, -6, -7, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-36, -11, -7, -39, 23],\n [-6, 9, -12, 0, 6],\n [24, -26, 38, 6, -22],\n [24, 4, 8, 24, -16],\n [-18, -33, 24, -36, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[15, 30, -15, -25, 5],\n [-18, -36, 18, 30, -6],\n [18, 36, -18, -30, 6],\n [15, 30, -15, -25, 5],\n [-9, -18, 9, 15, -3]]?\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[[-12, 8, -14, 26, -16],\n [22, -35, -8, -29, 30],\n [24, -11, 3, -17, 2],\n [-62, 34, 3, 37, -4],\n [0, 11, 3, 8, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[15, 6, -1, -5, 6],\n [-9, -3, 0, 4, -3],\n [0, -3, 3, -5, -3],\n [-12, 3, -7, 17, 3],\n [-9, -3, 0, 4, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-35, -42, -27, -34, 15],\n [-18, 30, -24, -30, -6],\n [-27, -33, -66, -66, -4],\n [-20, -36, -18, -22, 15],\n [34, 20, 32, 45, -32]]\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[[18, 65, 22, 14, -41],\n [-15, -25, 25, 5, -5],\n [10, 42, -14, -6, -6],\n [18, 3, -57, -15, 33],\n [-11, -1, -4, -10, 7]]\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 5x5 matrix:\n[[18, -15, 3, 3, 18],\n [21, 6, -7, 6, 19],\n [-15, -33, 6, -3, -9],\n [25, 16, 37, -10, 13],\n [-5, 6, -47, 16, 3]]\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[[-5, 11, 24, -11, 26],\n [6, -16, 15, -6, -9],\n [24, 9, -20, 0, 0],\n [-39, 9, 15, -1, 1],\n [-14, -11, 21, 0, 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[[13, -13, 10, 29, 12],\n [-22, -25, 5, -10, -3],\n [48, 14, -20, 28, 7],\n [-58, 20, 38, -34, -6],\n [23, 20, -7, 11, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-54, 36, 14, 4, -40],\n [-31, 20, 27, 17, -27],\n [30, -28, 0, 3, 7],\n [34, -28, -10, -4, 16],\n [-32, 22, 18, 10, -24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[6, -6, -24, 18, 24],\n [-3, 21, 30, -15, -30],\n [14, 25, -17, 29, 17],\n [-10, -5, 25, -25, -25],\n [-6, -12, 6, -12, -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 5x5 matrix:\n[[4, -12, 24, 8, 20],\n [-6, 18, -36, -12, -30],\n [2, -6, 12, 4, 10],\n [16, -12, 8, 8, 40],\n [3, -9, 18, 6, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[40, 18, 51, -2, -28],\n [20, 12, 14, -16, -2],\n [-19, -49, 22, 32, -71],\n [15, 7, -6, -22, 4],\n [28, -8, 24, -48, -36]]\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 5x5 matrix:\n[[0, 0, 0, 0, 0],\n [8, -12, 4, -24, -24],\n [4, -6, 2, -12, -12],\n [2, -3, 1, -6, -6],\n [12, -18, 6, -36, -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[[-11, -9, 4, 15, -13],\n [40, -10, -38, -4, -36],\n [19, -9, -23, 0, -49],\n [38, 18, -37, -11, -48],\n [-59, -17, 52, 15, 35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[18, 12, -5, -13, -3],\n [9, 7, 2, -2, -1],\n [-31, -23, -8, 7, 4],\n [-11, -5, -2, 6, 3],\n [17, 9, -3, -13, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, -12, -30, -15, -26],\n [-39, 54, -48, 19, 54],\n [-9, -52, -30, -20, -25],\n [-26, -60, -36, -12, 20],\n [18, 16, -42, -15, -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[[-18, 0, 0, 6, -3],\n [-36, 0, 0, 12, -6],\n [12, 0, 0, -4, 2],\n [-36, 0, 0, 12, -6],\n [6, 0, 0, -2, 1]]\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 5x5 matrix:\n[[6, 5, 4, 2, 0],\n [-36, -30, -24, -12, 0],\n [-6, -5, -4, -2, 0],\n [18, 15, 12, 6, 0],\n [6, 5, 4, 2, 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 5x5 matrix:\n[[36, -18, 24, -24, -16],\n [-19, 6, -8, 22, 10],\n [-13, 6, -8, 10, 6],\n [3, 0, 0, -6, -2],\n [-13, -3, 4, 34, 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[[-2, 16, 2, 20, -7],\n [-14, -18, 14, -55, 3],\n [-34, 42, 34, -5, -27],\n [14, 8, -14, 40, 1],\n [-34, 42, 34, -5, -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[[-2, -38, 6, -42, -10],\n [6, 9, -23, 11, -12],\n [-6, -9, 43, -6, 5],\n [-7, 26, 16, 24, 33],\n [0, 0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-20, -20, 0, 0, 15],\n [21, 0, 9, 0, -3],\n [-6, -48, 18, 0, 30],\n [-13, 8, -9, 0, -3],\n [11, 32, -9, 0, -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, -18, 9, 12, 6],\n [-12, 18, -9, -12, -6],\n [-24, 36, -18, -24, -12],\n [-20, 30, -15, -20, -10],\n [4, -6, 3, 4, 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 5x5 matrix:\n[[25, -9, 20, -13, 20],\n [10, -12, 8, 20, -34],\n [15, -13, 12, 15, -26],\n [20, -15, 16, 13, -23],\n [20, -11, 16, 1, -3]]\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 5x5 matrix:\n[[12, -30, 18, 6, -36],\n [13, 59, 17, 24, 13],\n [9, -54, 14, -10, -33],\n [-3, 30, -4, 29, -15],\n [-11, 2, -16, -15, 25]]\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, -4, 40, -50, -9],\n [-14, -2, -10, 10, 17],\n [-60, -30, 21, -39, 60],\n [1, 7, 29, -36, 0],\n [1, 1, 20, -25, -2]]?\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 5x5 matrix:\n[[46, 32, 50, 50, 15],\n [16, -12, -12, 88, -69],\n [-13, 44, 40, -57, 54],\n [-25, 10, 8, -29, -12],\n [13, -40, -32, -7, 12]]\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 5x5 matrix:\n[[10, -30, 15, -25, -15],\n [6, -18, 9, -15, -9],\n [6, -18, 9, -15, -9],\n [0, 0, 0, 0, 0],\n [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[[0, -7, -33, 24, 21],\n [8, -39, 31, -8, 29],\n [-2, -25, 33, -16, 9],\n [-18, 5, 26, -24, -26],\n [54, 44, -30, 24, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-18, 32, -32, -2, 4],\n [4, -29, 10, -13, 3],\n [-29, 35, 12, -32, -31],\n [28, -19, -7, 38, 23],\n [3, 9, -6, 12, 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[[15, 30, -30, 25, 15],\n [-6, -12, 12, -10, -6],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [12, 24, -24, 20, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 0, -10, 10, 6],\n [18, 0, -15, 15, 9],\n [-30, 0, 25, -25, -15],\n [-18, 0, 15, -15, -9],\n [6, 0, -5, 5, 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[[31, -5, 26, -34, -8],\n [-5, -2, 17, 30, -13],\n [-7, -26, -47, -28, 35],\n [40, -40, -5, -37, 41],\n [6, 39, 72, 35, -64]]?\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 5x5 matrix:\n[[29, 18, 31, 42, -22],\n [24, -2, 0, 15, 5],\n [-7, 11, -20, -30, 30],\n [-9, -3, 18, 15, -27],\n [18, 31, 15, 13, 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[[18, -27, 5, 4, -2],\n [20, -14, 6, 8, -24],\n [36, -26, 18, 20, 20],\n [-20, 21, -9, -9, -13],\n [-54, 34, -22, -27, 21]]\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, -34, -7, 10, -7],\n [-2, 6, 2, -1, 2],\n [10, -10, 1, 6, 1],\n [4, -12, -4, 2, -4],\n [18, 46, 37, 14, 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[[-12, -6, 0, 12, -4],\n [-12, -6, 0, 12, -4],\n [18, 9, 0, -18, 6],\n [-24, -12, 0, 24, -8],\n [6, 3, 0, -6, 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 5x5 matrix:\n[[-61, 18, -15, 25, -2],\n [-20, 15, 6, -10, 23],\n [9, 3, 9, -15, 15],\n [1, 12, 15, -25, 32],\n [-24, 12, 0, 0, 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[[-40, -42, 26, -68, 8],\n [-30, 33, 14, 30, 10],\n [30, 39, -23, 60, -10],\n [-12, -45, 18, -60, 12],\n [-2, -27, 8, -34, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-24, 12, 24, -40, -4],\n [-16, -6, 23, -29, 9],\n [-20, 60, -5, -25, -45],\n [-8, 18, 1, -11, -13],\n [0, 18, -9, 3, -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[[1, 24, -3, 2, 19],\n [18, -5, -13, 13, 62],\n [-17, 6, 11, 4, -1],\n [10, -17, -18, 19, 0],\n [-6, -25, 5, 9, 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[[30, -12, -9, -24, -6],\n [-4, -8, 50, 8, 8],\n [20, 14, -37, -17, -18],\n [-26, 4, 8, 20, 9],\n [2, 36, -26, 0, -23]]\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[[-7, 20, -4, 13, -15],\n [30, -2, 15, 9, -53],\n [10, 28, -29, -62, 54],\n [42, 12, 12, -46, 22],\n [-3, 20, -27, -13, -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[[-4, 6, 2, 0, 4],\n [8, -12, -4, 0, -8],\n [12, -18, -6, 0, -12],\n [-4, 6, 2, 0, 4],\n [6, -9, -3, 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 5x5 matrix:\n[[-53, 14, 19, -4, -60],\n [18, -5, -37, 29, 7],\n [16, -33, -21, 38, 33],\n [6, 1, 0, -39, 30],\n [26, -23, 49, 13, 33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-43, -48, -5, -12, 39],\n [-26, -72, -68, 28, 4],\n [17, -12, -5, 6, -9],\n [16, 30, 26, -9, -6],\n [33, -6, -29, 25, -33]]\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 5x5 matrix:\n[[-19, 12, -2, -5, 15],\n [-19, 5, -3, -8, 9],\n [16, -36, 4, -2, -39],\n [24, 12, 4, 16, 6],\n [-29, -7, 21, 4, -18]]\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[[23, -15, 24, 21, 29],\n [17, 30, -21, 12, 5],\n [3, -5, 6, 3, 5],\n [19, 15, -6, 15, 13],\n [-3, 5, -6, -3, -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[[8, -17, 0, 3, -6],\n [18, 3, 0, 3, -36],\n [27, -12, 0, 6, -45],\n [-18, 30, 0, -6, 18],\n [-25, 16, 0, -6, 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[[10, -30, -5, 20, 30],\n [12, -36, -6, 24, 36],\n [8, -24, -4, 16, 24],\n [-4, 12, 2, -8, -12],\n [-4, 12, 2, -8, -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[[11, 4, 2, 6, -13],\n [-15, 10, -16, -31, 13],\n [3, -21, 10, 28, 9],\n [30, 33, -34, -15, -8],\n [10, -38, 38, 60, -10]]\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 5x5 matrix:\n[[-12, 16, 25, -4, -18],\n [-36, 6, -26, 13, 44],\n [-4, 4, 7, 21, -16],\n [22, -1, 22, -13, -31],\n [40, -12, 16, -12, -36]]\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[[-17, 17, 16, 7, -5],\n [-9, 11, 8, 3, -5],\n [4, -20, 0, 4, 20],\n [33, -12, -36, -21, -15],\n [12, 8, -16, -12, -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[[-50, 37, -25, -10, -37],\n [-64, 56, -10, -18, -28],\n [48, -51, -15, 18, 3],\n [22, -35, -25, -10, 35],\n [-66, 48, -30, -24, -24]]\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[[-68, 54, 25, -5, 29],\n [9, -2, -9, -44, 29],\n [-2, 23, -9, -32, -12],\n [29, -42, -3, 14, 15],\n [-43, 41, 3, -9, 8]]?\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[[33, 33, -66, -12, 45],\n [14, 34, -58, -1, 50],\n [42, -2, 0, -33, -20],\n [21, 25, -27, -17, 24],\n [-22, -34, 59, 7, -47]]?\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[[-12, 12, -8, -8, 24],\n [3, 12, -11, 4, 21],\n [-12, -3, 5, -10, -3],\n [15, 0, -3, 12, -3],\n [-5, -15, 14, -6, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[68, -34, -2, -20, -10],\n [-6, 2, 0, -7, 22],\n [-52, 32, 0, 20, -11],\n [-42, 27, -1, 4, 17],\n [-12, -28, 12, 32, -17]]?\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, -10, 0, -20, 20],\n [0, 0, 0, 0, 0],\n [5, 10, 0, 20, -20],\n [-3, -6, 0, -12, 12],\n [-6, -12, 0, -24, 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[[21, -9, 30, -21, -6],\n [66, -18, 48, 6, -60],\n [-42, 10, -24, -14, 44],\n [9, -1, 0, 11, -14],\n [-45, 13, -36, 1, 38]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-8, -2, -6, 54, 48],\n [4, 4, 6, -22, -20],\n [10, 22, 27, -35, -34],\n [12, 27, 33, -41, -40],\n [-4, 2, 0, 32, 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[[2, -54, -26, 26, -8],\n [37, 0, 14, -46, -2],\n [-2, 24, -20, -10, -3],\n [-8, -18, 30, -16, 59],\n [-34, -17, -23, 27, 35]]\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, 0, 0, 0, 0],\n [-36, -18, 30, -24, 18],\n [-36, -18, 30, -24, 18],\n [18, 9, -15, 12, -9],\n [24, 12, -20, 16, -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[[-15, -24, 6, 3, 12],\n [-25, -46, 0, 5, 18],\n [-31, -53, 9, 5, 25],\n [32, -19, -55, -46, -5],\n [-29, 6, 40, 37, 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 5x5 matrix:\n[[3, 0, -9, 12, -12],\n [0, 0, 0, 0, 0],\n [2, 0, -6, 8, -8],\n [-6, 0, 18, -24, 24],\n [-1, 0, 3, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[19, 26, -10, -4, 12],\n [4, 44, -4, 8, 12],\n [-12, 51, 3, 18, 9],\n [11, -1, -5, -6, 3],\n [11, 60, -8, 8, 18]]\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, -25, 10, -15, 15],\n [-1, -5, -2, -13, 15],\n [21, 25, -6, 25, -27],\n [15, 15, -6, 9, -9],\n [1, 5, 2, 13, -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[[-13, -7, 6, -6, -8],\n [-3, 33, -8, -51, 54],\n [6, 6, 34, 39, -24],\n [10, -14, 32, 66, -52],\n [-2, 34, -14, -57, 60]]\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, 19, -12, 29, 39],\n [52, -6, -10, 48, 38],\n [21, -10, -21, -17, -20],\n [-14, 17, -25, 4, 7],\n [50, -29, -17, -22, -24]]\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[[22, -11, -4, 2, 2],\n [6, 1, 4, 2, -14],\n [24, -7, 2, 4, -16],\n [21, -13, -7, 1, 11],\n [-9, 4, 1, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-32, -20, 16, -26, 15],\n [4, -20, -2, -8, -30],\n [-16, -20, 8, -18, -5],\n [8, 24, -4, 16, 20],\n [32, 12, -16, 22, -25]]\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[[56, -14, 12, 35, 22],\n [34, 7, 18, 26, 36],\n [23, 1, 27, 51, 48],\n [-31, -8, -7, -24, -27],\n [-15, 12, -39, -36, -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[[20, 4, -12, 0, -4],\n [5, 1, -3, 0, -1],\n [-20, -4, 12, 0, 4],\n [-25, -5, 15, 0, 5],\n [10, 2, -6, 0, -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 5x5 matrix:\n[[6, 5, 6, 4, -3],\n [-6, -5, -6, -4, 3],\n [-30, -25, -30, -20, 15],\n [6, 5, 6, 4, -3],\n [-36, -30, -36, -24, 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 5x5 matrix:\n[[-9, 3, 12, 0, 18],\n [-3, 1, 4, 0, 6],\n [-6, 2, 8, 0, 12],\n [-15, 5, 20, 0, 30],\n [-6, 2, 8, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 2, -6, -6, -8],\n [0, 0, 0, 0, 0],\n [-12, -2, 6, 6, 8],\n [-6, -1, 3, 3, 4],\n [18, 3, -9, -9, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-27, -15, -24, -9, 30],\n [5, -5, -2, -5, 0],\n [-18, -10, -16, -6, 20],\n [-12, 5, -1, 6, 5],\n [22, 20, 26, 14, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-47, -28, -47, 39, -45],\n [47, 50, 31, -47, 15],\n [-13, 7, -7, -14, -24],\n [-18, -3, -1, 27, 21],\n [46, 26, 35, -81, -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[[36, 9, -26, -18, 37],\n [-1, 4, -1, -19, 11],\n [-36, -27, 13, -9, -23],\n [29, 28, -7, 11, 17],\n [-51, -30, 20, -24, -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 5x5 matrix:\n[[-28, -50, 12, 45, -43],\n [-12, 9, 0, 2, 12],\n [12, 54, 12, -51, 51],\n [32, 43, -12, -43, 35],\n [0, -30, 0, 20, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-29, 31, -22, -6, 13],\n [12, 13, 27, -22, 2],\n [13, -21, 36, 10, -18],\n [-17, -15, 32, 34, -10],\n [13, -12, 25, 10, 16]]\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, 10, -5, 15, 20],\n [18, 10, 33, -39, -12],\n [0, 12, 15, -39, -12],\n [-17, 11, -41, 33, 29],\n [16, 24, 15, -25, 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[[6, 8, 43, 35, 61],\n [1, 15, 10, 16, -35],\n [2, -6, 34, 24, -2],\n [1, 33, -29, -8, 7],\n [-2, -10, -10, -12, -10]]\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[[22, -24, -28, 26, 12],\n [-1, 12, -6, 1, -2],\n [2, 6, -8, 4, 0],\n [4, -3, -6, 5, 2],\n [18, -21, -22, 21, 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 5x5 matrix:\n[[-6, 12, 6, -36, -24],\n [4, -8, -4, 24, 16],\n [0, 0, 0, 0, 0],\n [4, -8, -4, 24, 16],\n [3, -6, -3, 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 5x5 matrix:\n[[-11, 43, -9, 15, -37],\n [5, -17, 7, -7, 14],\n [-1, -18, -23, -6, 20],\n [-9, 2, -31, -30, 2],\n [12, -11, 40, 15, 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[[5, -26, 24, -7, -22],\n [-18, 41, 22, 7, 53],\n [-66, 25, 28, 5, -5],\n [-10, 18, 3, -9, 10],\n [-5, -3, 5, -11, -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[[0, 0, 0, 0, 0],\n [0, -10, -10, 12, -6],\n [0, -15, -15, 18, -9],\n [0, 0, 0, 0, 0],\n [0, -10, -10, 12, -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 5x5 matrix:\n[[12, 6, -27, 39, 17],\n [7, -14, -28, -39, -29],\n [24, 12, -12, -6, 6],\n [10, 26, 34, 23, 33],\n [6, -18, -57, 3, -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 5x5 matrix:\n[[2, -22, -2, -12, 4],\n [30, 4, 9, 40, 38],\n [3, 6, -39, -3, -6],\n [-18, -27, -72, -57, -36],\n [32, -22, -29, 16, 34]]\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 5x5 matrix:\n[[-30, 7, 21, 13, 31],\n [-7, -14, 10, -29, -5],\n [-30, -13, 24, -1, 32],\n [-13, 13, 15, -44, -22],\n [-1, 22, -3, 19, 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[[10, 0, 0, -5, -15],\n [10, 0, 0, -5, -15],\n [-10, 0, 0, 5, 15],\n [10, 0, 0, -5, -15],\n [-4, 0, 0, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0, 0],\n [-2, 0, -3, 5, 0],\n [10, 0, 15, -25, 0],\n [2, 0, 3, -5, 0],\n [6, 0, 9, -15, 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[[18, 24, 7, 33, -37],\n [16, 3, 16, 11, -6],\n [-2, 9, -7, 8, -13],\n [30, -15, 41, 0, 19],\n [2, 21, -9, 22, -31]]\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[[6, -10, 12, 37, 30],\n [36, 28, -12, 2, 24],\n [-8, -16, 12, 24, 12],\n [-14, 21, 9, -21, 6],\n [12, -65, -21, 36, -42]]?\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[[5, -27, 30, 29, -14],\n [7, -31, 52, 47, -22],\n [25, 48, 1, -32, 43],\n [1, 29, -29, -44, 39],\n [12, -48, 36, 30, -6]]\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[[31, -22, -49, 1, -35],\n [-4, -19, 37, -7, -9],\n [0, 8, -29, -14, 19],\n [-15, 26, 27, 0, 46],\n [-24, 13, -34, -7, -10]]\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 5x5 matrix:\n[[2, -23, 5, -1, -7],\n [-19, 18, 25, 9, -11],\n [-14, -28, 4, -17, -8],\n [-7, -19, -18, -26, 6],\n [-18, -43, 15, -16, -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 5x5 matrix:\n[[0, 36, -42, 10, 8],\n [-34, 26, 43, -2, -29],\n [-26, -4, 61, -4, -24],\n [-16, 32, -5, -31, -39],\n [-6, 8, 4, 7, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -2, 12, 4, -12],\n [-12, 4, -24, -8, 24],\n [-6, 2, -12, -4, 12],\n [-9, 3, -18, -6, 18],\n [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[[-9, -28, -9, -23, -24],\n [-17, 0, -17, -3, -36],\n [3, 15, 3, 12, 9],\n [-16, -12, -16, -12, -36],\n [3, -36, 3, -27, 0]]\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, 6, 6, 30, 30],\n [0, -2, -2, -10, -10],\n [0, 6, 6, 30, 30],\n [0, 2, 2, 10, 10],\n [0, 6, 6, 30, 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 5x5 matrix:\n[[-3, -6, 4, -1, -4],\n [-15, -30, 20, -5, -20],\n [9, 18, -12, 3, 12],\n [18, 36, -24, 6, 24],\n [-18, -36, 24, -6, -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 5x5 matrix:\n[[-18, -36, 36, 12, 6],\n [-15, -30, 30, 10, 5],\n [-15, -30, 30, 10, 5],\n [0, 0, 0, 0, 0],\n [-18, -36, 36, 12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[26, 30, -18, 10, -13],\n [-5, 25, -10, 25, -10],\n [-13, 1, 2, 9, 0],\n [0, 0, 0, 0, 0],\n [-27, -25, 16, -5, 11]]\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[[23, 14, -5, -35, 28],\n [-34, -10, -44, 18, 11],\n [20, 18, 26, 0, -21],\n [10, 54, -15, -12, 16],\n [53, 12, 3, -37, -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[[20, -8, -20, -20, -4],\n [-25, 10, 25, 25, 5],\n [25, -10, -25, -25, -5],\n [-10, 4, 10, 10, 2],\n [-15, 6, 15, 15, 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[[-31, -30, 20, -42, -2],\n [41, 4, -30, 33, 30],\n [3, 28, -46, 21, -22],\n [-21, 30, -36, -19, -22],\n [5, -42, 41, 4, 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[[59, -1, 43, 59, 57],\n [-15, 21, -16, -20, -23],\n [-16, -28, -10, -10, -14],\n [-20, 10, -14, -26, -10],\n [35, 5, 3, 15, 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[[-30, -12, 30, 12, 18],\n [20, 8, -20, -8, -12],\n [15, 6, -15, -6, -9],\n [-25, -10, 25, 10, 15],\n [-25, -10, 25, 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[[2, -10, -14, -13, 17],\n [-6, 7, 27, 32, 26],\n [20, -11, -20, -36, -9],\n [28, 8, 44, 18, 18],\n [-14, 3, -12, -1, -22]]\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 5x5 matrix:\n[[0, 0, 0, 0, 0],\n [5, -1, 2, -6, 5],\n [-10, 2, -4, 12, -10],\n [0, 0, 0, 0, 0],\n [-5, 1, -2, 6, -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 5x5 matrix:\n[[-12, -18, -36, 12, 6],\n [0, 0, 0, 0, 0],\n [-6, -9, -18, 6, 3],\n [6, 9, 18, -6, -3],\n [8, 12, 24, -8, -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[[0, 0, 0, 0, 0],\n [-2, 8, 12, -10, 8],\n [1, -4, -6, 5, -4],\n [-3, 12, 18, -15, 12],\n [-5, 20, 30, -25, 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[[-37, -10, -20, 25, -12],\n [-30, -17, -16, 2, -57],\n [11, 18, 24, 1, -10],\n [-3, -29, -37, -12, 29],\n [1, 1, -7, 10, 43]]?\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, 39, -8, -22, -46],\n [-27, -53, 44, -23, 14],\n [35, -34, 3, 3, 25],\n [24, -36, -2, 32, 40],\n [42, -19, 8, -14, -18]]\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, -4, 32, -10, 20],\n [63, 70, 12, -7, 9],\n [-26, -40, -24, 32, -22],\n [-50, -54, -40, 18, -34],\n [19, 17, -32, 8, -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[[-12, 10, -10, -10, 2],\n [-24, 20, -20, -20, 4],\n [36, -30, 30, 30, -6],\n [-6, 5, -5, -5, 1],\n [30, -25, 25, 25, -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 5x5 matrix:\n[[-7, -9, -18, 31, -19],\n [1, 16, 19, 22, -19],\n [56, 14, -4, -20, -39],\n [-5, 4, 12, 11, -1],\n [41, -21, -32, -11, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-22, 36, -10, 44, -6],\n [10, -40, 1, -42, 11],\n [24, -21, 6, -24, -27],\n [59, -3, 41, -16, -27],\n [4, -20, -14, -4, -46]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[34, -53, -2, 16, 31],\n [22, 22, 0, 18, -2],\n [9, 36, 30, -24, -9],\n [-38, -25, -2, -12, -1],\n [0, -1, 46, -40, 5]]\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, 0, 24, -8, 4],\n [-14, -15, -24, -22, -24],\n [18, 3, -18, 12, 1],\n [14, 3, -12, 10, 2],\n [-16, 6, 42, -2, 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[[56, -84, -12, -32, 28],\n [19, -28, -23, 16, -21],\n [-21, 24, 5, -10, 13],\n [-5, 20, -15, 60, -65],\n [2, -16, -2, -36, 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[[18, 12, 24, 18, -36],\n [-19, -11, -2, 21, -32],\n [-16, -10, -12, 0, 4],\n [28, 17, 14, -12, 14],\n [7, 5, 14, 15, -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[[-10, -25, 15, 0, 30],\n [18, -9, -29, -20, -42],\n [1, 43, 0, 15, -12],\n [15, -30, -25, -25, -30],\n [-13, 35, 22, 25, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[10, 30, -27, 19, 0],\n [10, 20, -34, 8, 13],\n [-25, -16, -4, -39, 22],\n [25, 16, -52, 11, 27],\n [-5, -6, -37, -28, 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[[30, -5, -10, -25, -10],\n [36, -6, -12, -30, -12],\n [36, -6, -12, -30, -12],\n [36, -6, -12, -30, -12],\n [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[[10, -10, 25, 10, -20],\n [16, 12, 6, 20, -12],\n [7, -42, 60, 2, -39],\n [-4, 32, -44, 0, 28],\n [16, 12, 6, 20, -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 5x5 matrix:\n[[10, -12, 4, 10, 8],\n [25, -30, 10, 25, 20],\n [30, -36, 12, 30, 24],\n [-5, 6, -2, -5, -4],\n [-30, 36, -12, -30, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[30, -36, 24, 12, -30],\n [15, -18, 12, 6, -15],\n [-20, 24, -16, -8, 20],\n [-25, 30, -20, -10, 25],\n [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[[-9, 12, -7, 5, 9],\n [-4, 18, -20, 31, 28],\n [-20, 28, 6, -28, -16],\n [-39, 8, -17, 53, 15],\n [-5, -30, -14, 45, 27]]?\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, -3, 6, 2, 20],\n [18, -30, 36, -12, 24],\n [6, -18, 21, -8, 10],\n [-18, -2, 0, -4, -16],\n [6, 22, -24, 12, 0]]\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, 10, 33, -31],\n [29, -3, 6, -7, -7],\n [36, 11, 14, -7, 0],\n [-21, 6, -14, -24, 27],\n [-19, 7, -21, -45, 41]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 0, -1, 4, -1],\n [24, 0, -4, 16, -4],\n [-18, 0, 3, -12, 3],\n [-24, 0, 4, -16, 4],\n [18, 0, -3, 12, -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[[24, 24, 8, 9, -21],\n [0, 24, -24, -9, -3],\n [-15, 10, -30, -15, 10],\n [-36, -32, -16, -15, 31],\n [-3, -6, 2, 0, 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[[13, -1, -4, 7, -8],\n [-27, 23, 20, -33, 32],\n [7, 23, 11, -17, 13],\n [3, 39, 21, -33, 27],\n [-7, -23, -11, 17, -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[[5, -11, 1, 51, 26],\n [65, -8, 43, -12, 23],\n [-49, 5, -32, -10, -11],\n [31, 3, 13, 52, 28],\n [9, -13, 12, -30, -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[[3, 6, 5, 5, 1],\n [-9, -18, -15, -15, -3],\n [0, 0, 0, 0, 0],\n [18, 36, 30, 30, 6],\n [15, 30, 25, 25, 5]]\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[[-25, -20, -25, -15, 25],\n [25, 20, 13, 11, -27],\n [-15, -12, 21, 3, 21],\n [-20, -16, -26, -14, 19],\n [15, 12, -39, -9, -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[[37, -7, 17, -11, 15],\n [-22, 61, -74, -22, 0],\n [30, 1, -33, 18, -25],\n [1, 33, -12, -27, 24],\n [-13, 7, 33, 39, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, -4, -12, 4, -8],\n [10, -5, -15, 5, -10],\n [-12, 6, 18, -6, 12],\n [-4, 2, 6, -2, 4],\n [-4, 2, 6, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, 4, 24, 0, -8],\n [-24, 6, 36, 0, -12],\n [16, -4, -24, 0, 8],\n [8, -2, -12, 0, 4],\n [20, -5, -30, 0, 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[[-3, 0, 43, 29, -16],\n [7, -3, -21, -24, -7],\n [36, -6, -66, 0, 42],\n [-5, -1, 1, -24, -21],\n [29, -10, -33, -29, -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[[-14, 23, 6, 32, 34],\n [10, 5, 0, 20, -20],\n [0, -10, -2, -20, -2],\n [4, 7, 1, 18, -7],\n [-12, 14, 4, 16, 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[[-50, -36, 3, 5, -22],\n [-33, -1, 1, -17, -39],\n [0, -14, -40, 2, 0],\n [-30, -54, -39, 21, 6],\n [-63, -51, -5, 9, -25]]\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[[14, 10, 16, -20, 27],\n [0, 0, 0, 0, 0],\n [2, 3, -15, 16, -15],\n [-20, -18, 18, -16, 6],\n [-6, -7, 23, -24, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-36, -24, -12, -6, 18],\n [-36, -24, -12, -6, 18],\n [-24, -16, -8, -4, 12],\n [24, 16, 8, 4, -12],\n [30, 20, 10, 5, -15]]\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, 1, -30, -56, 20],\n [-4, 10, 12, 25, -21],\n [-30, -18, 36, 30, 8],\n [-22, -8, 0, -17, 15],\n [38, 31, -18, 13, -39]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-10, -4, -24, 6, 20],\n [24, 20, -36, -56, 30],\n [-8, -8, 24, 24, -20],\n [-10, -10, 30, 30, -25],\n [-12, -8, 0, 20, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, 5, 6, 3, 3],\n [2, -10, -12, -6, -6],\n [-6, 30, 36, 18, 18],\n [-2, 10, 12, 6, 6],\n [3, -15, -18, -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[[-10, 33, 9, 11, -3],\n [-2, -15, -19, -33, -7],\n [-18, -24, -21, -12, -14],\n [-24, 51, -2, -47, 17],\n [-28, 39, -2, -21, 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[[0, 10, -10, 12, -2],\n [0, -10, 10, -12, 2],\n [0, -20, 20, -24, 4],\n [0, -20, 20, -24, 4],\n [0, 0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-11, 14, -13, -23, 4],\n [-11, -28, 9, 1, 44],\n [-1, 16, -7, -7, -15],\n [-10, 57, -23, -24, -47],\n [-23, 36, -1, 3, -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 5x5 matrix:\n[[-36, -18, 12, 12, 24],\n [12, 6, -4, -4, -8],\n [-36, -18, 12, 12, 24],\n [-36, -18, 12, 12, 24],\n [-30, -15, 10, 10, 20]]\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, -2, 10, -6, 2],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [-15, -5, 25, -15, 5],\n [-9, -3, 15, -9, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[8, -6, 53, 6, -4],\n [-10, -24, -4, -24, -28],\n [-6, -24, -5, -38, -32],\n [4, -6, 43, 7, -4],\n [-6, -9, 9, -39, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-8, -18, -18, 28, -20],\n [-30, -26, 44, -22, 2],\n [65, 61, -56, 41, -2],\n [-9, -2, 38, -16, 9],\n [-64, -63, 58, -29, -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[[-18, 36, -30, -3, -24],\n [-6, 20, -2, 3, -4],\n [14, -42, -14, 7, 5],\n [-12, 24, -20, -2, -16],\n [4, 6, -54, 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[[40, -32, -30, 24, 14],\n [-15, 12, 18, 0, 15],\n [-25, 20, 30, 0, 25],\n [-10, 8, -3, -20, -35],\n [-15, 12, 21, 4, 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[[-32, -22, 6, 20, 16],\n [-14, -7, -3, 26, 4],\n [23, 18, -9, 0, -14],\n [-7, 0, -9, 36, -2],\n [-10, -6, 0, 12, 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[[40, 14, -18, 34, -11],\n [-12, 3, -6, 6, -4],\n [40, 0, 12, 26, -19],\n [-32, -6, 6, -16, 4],\n [-56, 4, -18, -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[[-59, 8, -10, 17, 2],\n [-11, 28, 62, -29, -58],\n [-13, 6, -6, 1, 8],\n [-4, 8, -8, -24, 0],\n [-22, 2, -8, 9, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, -8, -10, -6, 12],\n [10, 44, 7, 45, -6],\n [31, -4, -29, 3, 36],\n [14, -32, -24, -28, 28],\n [-49, 4, 45, -7, -56]]?\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[[6, 2, -18, 4, -12],\n [-3, 25, -4, -15, 6],\n [-18, 18, 42, -24, 36],\n [15, -9, -38, 17, -30],\n [0, 20, -10, -10, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, 8, 8, -4, -22],\n [15, -6, -6, 3, 5],\n [-36, 12, 12, -6, -6],\n [24, -6, -6, 3, -1],\n [-3, -10, -10, 5, 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[[0, -18, -10, 2, 18],\n [18, 18, 24, 12, -18],\n [-3, 24, 11, -5, -24],\n [3, -15, -6, 4, 15],\n [24, -3, 17, 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[[-36, 6, 30, 30, -24],\n [6, -1, -5, -5, 4],\n [40, 4, -8, -28, 20],\n [28, 6, 2, -18, 12],\n [-32, 0, 14, 24, -18]]\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, -1, 15, -27, -30],\n [12, -11, 9, -27, -18],\n [-24, -4, 51, -42, 13],\n [-9, 4, 15, -24, -35],\n [12, -5, -1, -21, -38]]?\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[[-4, -18, -16, 42, -34],\n [6, 33, 0, -9, 9],\n [1, 9, -14, 30, -23],\n [-2, -13, 8, -15, 11],\n [-8, -42, -8, 30, -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 5x5 matrix:\n[[57, 50, -33, 17, 47],\n [20, 11, -23, 27, 3],\n [19, 7, -6, 2, 20],\n [-53, -33, 45, -23, -29],\n [58, 35, -24, 35, 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[[19, -4, -4, -29, -25],\n [5, 0, -2, -7, -5],\n [31, 4, -16, -41, -25],\n [35, 20, -32, -37, -5],\n [-24, 4, 6, 36, 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[[-5, -15, -25, 20, -30],\n [0, 0, 0, 0, 0],\n [4, 12, 20, -16, 24],\n [1, 3, 5, -4, 6],\n [-1, -3, -5, 4, -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 5x5 matrix:\n[[22, -14, -31, -24, 12],\n [32, -12, -46, -28, 2],\n [2, 34, 21, 4, -22],\n [-4, -2, 35, 33, 67],\n [8, -4, -19, 16, -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 5x5 matrix:\n[[-12, 0, -10, 8, -6],\n [6, -3, 8, -19, 3],\n [-30, -1, -24, 15, -15],\n [0, 6, -6, 30, 0],\n [-24, 2, -22, 26, -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 5x5 matrix:\n[[6, 74, 28, 50, 4],\n [-6, -39, 27, -48, -57],\n [-1, -21, -22, -4, 21],\n [3, 8, -29, 20, 40],\n [-4, -43, -1, -43, -30]]\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[[-12, -36, -34, 58, -14],\n [17, 29, 10, -45, -25],\n [-11, -5, 1, -14, 14],\n [-8, -24, -29, 31, -21],\n [-6, -14, -2, 32, 16]]\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[[-54, 3, 24, 69, 6],\n [9, -1, 1, -41, 41],\n [18, 21, 33, -30, 6],\n [-45, 12, 42, 33, 39],\n [-18, -21, -24, -15, 58]]\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[[25, 0, -30, 29, 31],\n [17, 2, -22, 21, 19],\n [13, 3, -18, 17, 13],\n [9, -21, 6, -3, 33],\n [18, 8, -28, 26, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 8, -12, 10],\n [0, 0, 8, -12, 10],\n [0, 0, 0, 0, 0],\n [0, 0, 4, -6, 5],\n [0, 0, 24, -36, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -12, 4, 14, 12],\n [17, -23, 1, 19, 21],\n [-20, 8, 24, 5, -2],\n [1, 5, -19, -16, -9],\n [-28, 4, 12, -6, -2]]\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[[-8, -2, 40, 30, -8],\n [28, 7, -5, -24, -26],\n [24, 6, 30, 0, -36],\n [16, 4, -40, -36, 0],\n [-8, -2, 30, 24, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[15, 9, 6, -18, 3],\n [10, 6, 4, -12, 2],\n [-20, -12, -8, 24, -4],\n [20, 12, 8, -24, 4],\n [-5, -3, -2, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-19, 23, 11, -3, -24],\n [7, 10, 2, 12, -1],\n [68, -13, -36, -27, 29],\n [-18, 0, 16, 36, 2],\n [16, -28, -9, 10, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, 8, 20, -16, -16],\n [-9, -6, -15, 12, 12],\n [-6, -4, -10, 8, 8],\n [-9, -6, -15, 12, 12],\n [12, 8, 20, -16, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[34, 49, 14, -17, -6],\n [-2, 13, -22, 1, -12],\n [-24, -29, -14, 13, 8],\n [-3, 7, -8, 4, 12],\n [1, 13, -10, 1, 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[[2, -17, 44, 20, -2],\n [-18, 25, -34, -16, 3],\n [10, -15, -32, 16, 11],\n [-32, 16, 20, 8, 2],\n [-10, 14, 9, -12, -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[[-46, -18, 56, -2, -10],\n [-29, -30, 22, 0, 24],\n [7, -5, -40, 15, 59],\n [18, 48, 0, 2, -50],\n [-1, 11, 28, -11, -51]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-31, -3, -25, -20, 19],\n [50, -2, -2, 16, -18],\n [-5, 11, 29, 8, -3],\n [-18, 6, -30, -20, 22],\n [18, -24, -18, 4, -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 5x5 matrix:\n[[0, 30, -25, -15, 15],\n [0, 6, -5, -3, 3],\n [0, 36, -30, -18, 18],\n [0, 36, -30, -18, 18],\n [0, -18, 15, 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[[2, 6, -34, -19, 48],\n [5, -39, 13, -17, 10],\n [1, -33, 5, -10, 12],\n [-8, 24, -34, -8, 39],\n [-11, 54, -5, 32, -32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-36, 30, -12, -12, 0],\n [0, 0, 0, 0, 0],\n [-36, 30, -12, -12, 0],\n [30, -25, 10, 10, 0],\n [24, -20, 8, 8, 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[[52, 2, -20, -6, 14],\n [-46, 3, 45, 6, 15],\n [-32, -24, -18, -36, -12],\n [44, 10, -2, 8, 18],\n [14, -3, -15, -6, -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[[0, -3, 5, 7, 7],\n [10, 6, 5, -4, 16],\n [8, 12, -8, -20, -4],\n [10, 6, 5, -4, 16],\n [-28, -12, -22, 0, -56]]\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, 0, -54, 12, 18],\n [6, 34, -26, -26, 24],\n [-12, 12, 12, -8, -18],\n [-23, 0, 3, 6, -23],\n [-41, -19, -1, 27, -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[[10, 20, -5, -15, -20],\n [12, 24, -6, -18, -24],\n [-6, -12, 3, 9, 12],\n [-2, -4, 1, 3, 4],\n [-12, -24, 6, 18, 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[[15, 12, 15, 15, -6],\n [10, 0, 22, 10, -4],\n [15, 14, 12, 15, -6],\n [-10, -12, -4, -10, 4],\n [15, 22, 0, 15, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, -6, 4, -8, -12],\n [-5, -13, 14, 0, 30],\n [-2, -36, 32, -22, 12],\n [7, 14, -16, -3, -42],\n [-4, -9, 10, 1, 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[[-19, -43, -7, 10, -11],\n [1, -23, 13, -10, 5],\n [13, 21, 9, -10, 9],\n [-12, 36, -36, 30, -18],\n [-8, -16, -4, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[25, -25, 7, 46, -36],\n [-8, 9, -5, -18, 16],\n [-8, 34, -22, -44, 32],\n [-10, 38, -26, -52, 40],\n [28, -12, -2, 36, -32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-18, 30, 24, 30, -12],\n [18, -30, -24, -30, 12],\n [18, -30, -24, -30, 12],\n [-9, 15, 12, 15, -6],\n [-3, 5, 4, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[43, 13, -14, -3, -17],\n [-12, 22, 27, -12, 27],\n [23, 21, -3, -41, -44],\n [26, -64, -6, 89, -34],\n [45, 15, -13, -13, -32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-7, 18, -17, 7, 34],\n [-29, 14, -38, 4, -24],\n [-15, -49, 55, -25, -29],\n [33, 12, 9, 6, 36],\n [-29, -44, 39, -21, -32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[13, 33, 3, 16, 24],\n [-15, -27, -3, -12, -12],\n [-2, 6, 0, 4, 12],\n [-31, -27, -5, -8, 16],\n [13, 9, 2, 2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[18, -10, -2, -14, 0],\n [9, -5, -1, -7, 0],\n [-6, 2, 6, 10, 4],\n [6, 0, -14, -18, -10],\n [3, 2, -15, -17, -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 5x5 matrix:\n[[-10, 22, 36, 12, -16],\n [-30, -39, -18, 15, -27],\n [-10, -13, -6, 5, -9],\n [-25, 10, 36, 21, -31],\n [25, 0, -24, -19, 29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -36, 16, -24, 8],\n [36, -4, 0, -16, -24],\n [24, -7, 2, -13, -14],\n [18, -28, 12, -22, 0],\n [9, -27, 12, -18, 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[[-28, 5, 3, 16, -31],\n [12, 10, 16, -11, -3],\n [6, 20, 8, 2, 24],\n [53, -5, 23, -45, 5],\n [-19, 20, 26, 5, -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[[6, -18, -9, -18, -3],\n [-2, 6, 3, 6, 1],\n [6, -18, -9, -18, -3],\n [-10, 30, 15, 30, 5],\n [-6, 18, 9, 18, 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[[24, -9, 10, -32, -27],\n [41, -39, -16, -22, 16],\n [-16, -9, -16, 36, 40],\n [22, 8, 2, -4, 1],\n [-49, 54, 40, -8, -68]]\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 5x5 matrix:\n[[-12, -9, 3, 12, -9],\n [8, 6, -2, -8, 6],\n [-8, -6, 2, 8, -6],\n [-8, -6, 2, 8, -6],\n [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[[-25, -2, -20, 12, -16],\n [22, -1, 20, -8, 10],\n [-47, -51, 19, 43, -2],\n [-24, -70, 72, 44, 32],\n [21, 21, -27, -33, 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[[12, -24, 0, -8, -4],\n [-18, 36, 0, 12, 6],\n [-15, 30, 0, 10, 5],\n [-3, 6, 0, 2, 1],\n [-12, 24, 0, 8, 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[[7, 1, -7, -78, -18],\n [12, 25, -26, 10, 36],\n [-7, -31, 23, 12, -33],\n [7, -25, 5, -26, -30],\n [39, 7, -47, -8, 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[[7, -2, 21, 34, 35],\n [-20, 19, 33, 18, 24],\n [33, -30, -45, -18, -27],\n [24, -21, -27, -6, -12],\n [0, -3, -21, -26, -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[[-20, -15, 22, -22, 10],\n [-4, 14, 12, 36, -32],\n [26, -56, 20, -52, -2],\n [6, -26, 28, -8, -24],\n [-19, 4, 2, -10, 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 5x5 matrix:\n[[-12, -6, 36, 15, -21],\n [-34, -12, 12, 30, -12],\n [35, 12, -6, -30, 9],\n [-32, -12, 24, 30, -18],\n [-24, -10, 36, 25, -23]]\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, 1, 11, 7, 5],\n [5, 13, 15, 20, 14],\n [11, -19, -23, 2, -14],\n [15, -37, -25, 12, -20],\n [2, -36, -36, -22, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1, -19, 18, -12, 11],\n [41, 10, 5, -24, 23],\n [-12, -46, 18, -29, 14],\n [22, 29, -3, 6, 2],\n [23, 2, -4, -23, 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[[-12, 4, -4, -6, -6],\n [-36, 12, -12, -18, -18],\n [0, 0, 0, 0, 0],\n [-12, 4, -4, -6, -6],\n [-6, 2, -2, -3, -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[[5, 2, -14, 33, -42],\n [48, -35, -20, -26, 24],\n [33, -24, -8, -36, 62],\n [-46, 39, -8, 16, -44],\n [-8, 4, 22, 40, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[19, -27, 31, -10, 58],\n [-15, 16, -37, 12, -3],\n [-9, 3, -35, 18, 1],\n [-23, -20, -11, 20, -32],\n [-20, -8, 4, 8, -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[[8, 72, -16, 16, 48],\n [12, 18, 6, -32, 38],\n [0, -5, -13, -8, 3],\n [2, 43, -26, 15, 26],\n [10, -20, 15, -49, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-20, -24, -30, -9, 15],\n [25, 30, 15, 45, -30],\n [-20, -24, -32, -6, 14],\n [-30, -36, -42, -18, 24],\n [10, 12, 18, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-20, -3, 13, -1, 22],\n [2, 7, 2, 15, 18],\n [16, 19, -60, 33, -10],\n [-8, -4, -13, -8, -12],\n [18, 5, -23, 5, -22]]\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[[22, -40, -10, -8, -24],\n [2, -10, -6, 12, -20],\n [0, -15, -12, 30, -42],\n [-14, 30, 10, -4, 28],\n [18, -30, -6, -12, -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[[1, -10, -35, 47, 35],\n [35, -25, 22, -13, 29],\n [34, 33, 1, -16, -54],\n [-2, -23, 5, 4, 46],\n [21, 21, -22, 13, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, -14, -27, 34, -16],\n [-7, 22, 35, -33, 27],\n [2, -8, -12, 10, -10],\n [-2, 2, 5, -8, 2],\n [0, 12, 14, -4, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [-15, -6, -18, -3, -18],\n [-30, -12, -36, -6, -36],\n [30, 12, 36, 6, 36]]\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 5x5 matrix:\n[[30, -30, 20, 25, -5],\n [-6, 6, -4, -5, 1],\n [0, 0, 0, 0, 0],\n [6, -6, 4, 5, -1],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[7, -9, -12, -30, 15],\n [-5, 51, 4, -22, -52],\n [32, -17, 1, 28, 25],\n [-63, 56, 9, -34, -75],\n [76, -35, -19, 14, 49]]\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[[21, 15, -8, 1, -3],\n [-30, -15, -5, -20, 15],\n [15, 3, 14, 23, -15],\n [-36, -18, -6, -24, 18],\n [50, 31, -7, 16, -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[[6, 4, -12, -2, -8],\n [12, 8, -24, -4, -16],\n [-15, -10, 30, 5, 20],\n [18, 12, -36, -6, -24],\n [6, 4, -12, -2, -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[[-45, -22, 14, 42, -17],\n [-14, -22, -20, 4, 2],\n [-8, -14, -24, 4, -26],\n [10, -8, -12, -20, 42],\n [-25, -6, 22, 26, -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 5x5 matrix:\n[[24, -16, 0, -8, 20],\n [-36, 24, 0, 12, -30],\n [18, -12, 0, -6, 15],\n [6, -4, 0, -2, 5],\n [-12, 8, 0, 4, -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[[2, 16, -3, -7, -23],\n [4, -3, 9, -4, -1],\n [0, 42, -18, -12, -54],\n [-2, -37, 12, 13, 50],\n [-2, -30, 9, 11, 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[[6, 4, -10, -4, -8],\n [12, 8, -20, -8, -16],\n [-6, -4, 10, 4, 8],\n [-12, -8, 20, 8, 16],\n [-18, -12, 30, 12, 24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, -21, 3, -12, -42],\n [16, -4, 4, -8, 8],\n [5, 26, 10, 14, 6],\n [37, 21, 33, 2, -40],\n [31, 30, 24, 8, 2]]\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 5x5 matrix:\n[[20, 16, -4, 8, -4],\n [0, 0, 0, 0, 0],\n [5, 4, -1, 2, -1],\n [15, 12, -3, 6, -3],\n [30, 24, -6, 12, -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 5x5 matrix:\n[[-8, -12, 9, -8, 3],\n [60, -19, -5, 8, 36],\n [-31, 19, 1, 6, -30],\n [-17, -1, 20, 18, -33],\n [30, 4, 1, 28, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[24, -12, -8, -8, 24],\n [6, -3, -2, -2, 6],\n [0, 0, 0, 0, 0],\n [-36, 18, 12, 12, -36],\n [18, -9, -6, -6, 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[[32, -21, -14, -6, -50],\n [-17, 1, 9, -14, 25],\n [-19, 8, 9, -4, 29],\n [30, -27, -12, -18, -48],\n [1, -10, 1, -16, -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[[13, -10, -14, -13, -15],\n [25, -10, -30, -15, -20],\n [17, 22, -30, 21, 14],\n [-15, 6, 18, 9, 12],\n [28, -16, -32, -22, -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[[18, -36, -30, -18, -12],\n [-3, 6, 5, 3, 2],\n [15, -30, -25, -15, -10],\n [-12, 24, 20, 12, 8],\n [-6, 12, 10, 6, 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[[3, 1, 6, -1, -6],\n [15, 5, 30, -5, -30],\n [-6, -2, -12, 2, 12],\n [9, 3, 18, -3, -18],\n [-3, -1, -6, 1, 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[[6, 24, 12, 12, 12],\n [6, 24, 12, 12, 12],\n [6, 24, 12, 12, 12],\n [-5, -20, -10, -10, -10],\n [-6, -24, -12, -12, -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[[-19, 14, 12, 23, 13],\n [1, -11, -6, -7, 2],\n [5, -16, -18, -13, 4],\n [-10, -7, 12, 4, 4],\n [-22, 8, -6, 22, 25]]\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, -8, 15, -53, 0],\n [-36, -25, -9, 7, -34],\n [-5, -6, -4, 8, -19],\n [49, 38, 31, -5, 33],\n [23, -20, 26, -70, -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[[-12, -15, 3, -3, -6],\n [-4, -5, 1, -1, -2],\n [4, 5, -1, 1, 2],\n [0, 0, 0, 0, 0],\n [-16, -20, 4, -4, -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[[-6, -8, 24, -16, 28],\n [17, -27, 6, -34, 10],\n [0, -21, 54, -6, -12],\n [25, -36, -9, -59, 35],\n [4, 18, -62, -2, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-36, 36, -12, 18, -24],\n [-36, 36, -12, 18, -24],\n [-30, 30, -10, 15, -20],\n [12, -12, 4, -6, 8],\n [-6, 6, -2, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-18, 15, -15, -24, -33],\n [19, -34, -18, 7, 16],\n [-50, -51, 52, -12, -27],\n [-55, -46, 17, -31, -56],\n [-22, 25, 36, -4, -7]]?\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[[2, -6, -4, -2, 7],\n [15, -23, -1, -10, 18],\n [1, 19, -35, 10, 31],\n [-18, 22, -40, 14, 21],\n [45, -21, 18, -15, 21]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-12, -8, 1, 0, -15],\n [-24, -22, 13, -20, -9],\n [-15, 11, -29, 28, -9],\n [-1, -5, -2, -4, -10],\n [5, -12, 22, -14, -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[[-59, -1, -29, -7, 30],\n [12, 14, -21, -7, 8],\n [-17, -9, -43, -2, 26],\n [44, 9, -11, -1, -5],\n [47, 32, -8, -28, -25]]\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, 21, -66, 2, 46],\n [-34, -27, 38, -11, 18],\n [-39, -18, 9, -11, 1],\n [10, 0, 10, 3, 46],\n [4, 24, -60, 5, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-35, -4, -8, -4, 29],\n [-13, 2, 8, 2, 13],\n [-35, -8, -26, -8, 8],\n [-3, 14, 34, 14, -24],\n [8, 6, 20, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-23, -17, 32, 4, 30],\n [10, 17, -25, 16, -16],\n [-16, 4, 4, 32, 16],\n [21, 24, -39, 12, -30],\n [-1, -16, 19, -28, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0, 0],\n [4, 0, -4, -6, 10],\n [2, 0, -2, -3, 5],\n [6, 0, -6, -9, 15],\n [2, 0, -2, -3, 5]]\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, -34, 38, 1, 22],\n [-36, -5, 28, -39, -21],\n [-24, -16, 5, 32, 44],\n [12, -21, -9, 11, 15],\n [-50, -3, 28, 10, 19]]?\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[[-9, 12, -34, 6, 34],\n [-12, 0, 8, 24, -8],\n [-3, 6, -18, 0, 18],\n [20, -10, 20, -30, -20],\n [-22, 2, 8, 42, -8]]\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, 13, 22, -9, -6],\n [-28, 31, -2, 26, 5],\n [3, -32, -17, 29, 15],\n [15, -20, 13, -9, 5],\n [9, -25, -6, 3, 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 5x5 matrix:\n[[-4, -20, -40, -24, 36],\n [9, 39, -37, -9, 34],\n [-13, 31, 24, 31, -15],\n [-23, 13, -72, -45, 58],\n [12, -14, 29, 52, -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 5x5 matrix:\n[[-36, 28, -35, 34, -28],\n [54, -12, 39, 2, 20],\n [36, -22, 9, -18, 14],\n [-31, 34, -57, 38, -39],\n [-16, 31, -28, -10, -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[[34, 24, 25, -11, 0],\n [-16, -3, 36, -32, 39],\n [-46, 9, -27, 25, 23],\n [-3, 46, -20, -5, 30],\n [-33, 0, 5, -2, 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 5x5 matrix:\n[[-4, 12, -12, -8, 8],\n [-6, 18, -18, -12, 12],\n [6, -18, 18, 12, -12],\n [1, -3, 3, 2, -2],\n [3, -9, 9, 6, -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[[-1, -14, 12, 12, -9],\n [-12, 54, -36, -54, 36],\n [-12, 17, -6, -21, 12],\n [-28, -22, 36, 6, -12],\n [-14, 26, -12, -30, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 0, 12, 6, 6],\n [-8, 0, 8, 4, 4],\n [-2, 0, 2, 1, 1],\n [8, 0, -8, -4, -4],\n [2, 0, -2, -1, -1]]\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, -3, -5, 6, 1],\n [-18, -9, -15, 18, 3],\n [-18, -9, -15, 18, 3],\n [30, 15, 25, -30, -5],\n [-6, -3, -5, 6, 1]]?\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 5x5 matrix:\n[[6, 16, -4, -12, 3],\n [2, -28, -3, 11, -9],\n [22, -28, -19, -5, -15],\n [-8, -28, 5, 19, -6],\n [-22, 8, 18, 14, 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[[-36, 38, 5, -11, 18],\n [-67, 16, 12, -17, 2],\n [-60, 10, 13, -1, -14],\n [44, -36, -5, -15, 10],\n [-15, 28, -10, -8, 18]]\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, 20, -4, -6, -12],\n [9, -24, 2, 3, 8],\n [-15, 35, 0, 0, -5],\n [-3, 22, -10, -15, -26],\n [-18, 21, 14, 21, 29]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[18, -50, -2, -5, 44],\n [-17, 36, -10, 11, -24],\n [-16, -7, -30, -9, 59],\n [-24, 26, -9, -21, 20],\n [-12, 2, 22, -8, -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 5x5 matrix:\n[[4, 46, -58, 12, -16],\n [24, -42, 72, -42, 24],\n [-6, -1, 14, 40, 22],\n [-48, -63, 42, 15, -4],\n [6, -27, 24, -48, -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 5x5 matrix:\n[[-2, -5, -5, 4, 6],\n [6, 15, 15, -12, -18],\n [-8, -20, -20, 16, 24],\n [8, 20, 20, -16, -24],\n [8, 20, 20, -16, -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[[12, -12, -6, 12, 3],\n [11, -6, -33, 16, -16],\n [25, 10, -25, 33, -17],\n [-14, -44, -14, -21, 10],\n [12, 4, -34, 19, -21]]?\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, -14, -16, 30, -24],\n [2, -6, -32, -2, -4],\n [-16, -3, 16, 37, -19],\n [22, -17, -36, -37, 5],\n [-26, 24, 26, 40, -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[[-25, 15, -25, 10, -30],\n [42, -15, 18, -30, 33],\n [-44, 6, 4, 44, -18],\n [54, -12, 6, -48, 30],\n [-5, 3, -5, 2, -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 5x5 matrix:\n[[4, -12, 0, -4, 0],\n [-1, 3, 0, 1, 0],\n [-4, 12, 0, 4, 0],\n [5, -15, 0, -5, 0],\n [4, -12, 0, -4, 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 5x5 matrix:\n[[14, -36, -8, -16, 15],\n [-20, -4, -16, -36, 42],\n [-32, 24, -8, -24, 36],\n [-43, 34, -13, -32, 42],\n [-9, 20, 25, 18, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-30, 36, 0, -6, 6],\n [30, -36, 0, 6, -6],\n [0, 0, 0, 0, 0],\n [25, -30, 0, 5, -5],\n [30, -36, 0, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, -3, 6, -5, 6],\n [25, -15, 30, -25, 30],\n [15, -9, 18, -15, 18],\n [-20, 12, -24, 20, -24],\n [5, -3, 6, -5, 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, 20, -30, 23, 34],\n [-12, -60, 54, 24, -27],\n [-14, 0, -6, -13, 2],\n [-18, -48, 36, 15, -15],\n [2, -4, -4, 13, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[19, -8, -24, -4, 16],\n [-17, -5, 18, 3, -34],\n [-6, -3, -24, -14, -9],\n [2, -13, 0, 2, -19],\n [-12, 15, -6, -9, 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 5x5 matrix:\n[[-18, -12, -30, -18, -24],\n [15, 10, 25, 15, 20],\n [-12, -8, -20, -12, -16],\n [-3, -2, -5, -3, -4],\n [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[[-12, 31, 67, -36, 57],\n [2, 34, 49, -24, 39],\n [48, 38, -30, 48, -42],\n [12, -18, -30, -18, -18],\n [16, 42, 43, -27, 33]]\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 5x5 matrix:\n[[24, -1, 8, -39, -17],\n [24, 2, 12, -34, -18],\n [18, 9, 19, -13, -16],\n [6, 17, 25, 19, -10],\n [-6, -14, -21, -14, 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[[-33, 16, -3, 38, -14],\n [33, -16, 3, -38, 14],\n [-28, 8, 4, 40, -8],\n [27, -34, 27, -2, 26],\n [6, 18, -24, -36, -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[[-6, -26, 46, 10, 32],\n [-15, -6, -27, -9, -48],\n [5, 19, -12, -14, 27],\n [-18, 2, -41, -21, -45],\n [25, 18, 13, 15, 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[[0, 0, 0, 0, 0],\n [12, 3, 9, 6, -3],\n [0, 0, 0, 0, 0],\n [-4, -1, -3, -2, 1],\n [-20, -5, -15, -10, 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[[-3, 3, 3, 5, 3],\n [-9, 9, 9, 15, 9],\n [-18, 18, 18, 30, 18],\n [12, -12, -12, -20, -12],\n [-12, 12, 12, 20, 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 5x5 matrix:\n[[48, -30, 14, -32, -32],\n [12, -3, -19, -8, -8],\n [-30, 19, -10, 20, 20],\n [36, -21, 3, -24, -24],\n [36, -22, 8, -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[[0, -12, 2, 12, 12],\n [-4, 27, -6, -25, -24],\n [32, 6, 11, -22, -30],\n [12, 27, 0, -33, -36],\n [-40, 6, -16, 14, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[18, 30, 18, 0, -36],\n [9, 15, 9, 0, -18],\n [12, 20, 12, 0, -24],\n [15, 25, 15, 0, -30],\n [-12, -20, -12, 0, 24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[15, 58, 17, -24, 11],\n [28, 14, -4, 18, 36],\n [-2, -48, -17, 30, 5],\n [1, -34, -21, 24, 9],\n [18, 78, 57, -36, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[6, -2, -2, -4, 6],\n [-18, 6, 6, 12, -18],\n [3, -1, -1, -2, 3],\n [-15, 5, 5, 10, -15],\n [-12, 4, 4, 8, -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[[-30, -29, 3, -32, 4],\n [5, 5, -1, 6, 0],\n [10, 11, -5, 16, 4],\n [-15, -16, 6, -22, -4],\n [-25, -21, -7, -14, 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 5x5 matrix:\n[[-3, -21, -15, 24, -9],\n [-14, -21, 13, -4, 9],\n [12, 6, -28, 26, -18],\n [-18, -19, -8, 21, -3],\n [-14, 4, -13, 19, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-18, 12, -18, -24, 30],\n [6, 21, 0, -15, 30],\n [-22, -2, -18, -14, 10],\n [40, 15, 30, 15, 0],\n [-5, 20, -9, -22, 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[[20, -5, 15, 0, 25],\n [8, -2, 6, 0, 10],\n [-20, 5, -15, 0, -25],\n [-12, 3, -9, 0, -15],\n [8, -2, 6, 0, 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 5x5 matrix:\n[[-3, -18, 15, 18, 12],\n [-6, -36, 30, 36, 24],\n [0, 0, 0, 0, 0],\n [6, 36, -30, -36, -24],\n [-6, -36, 30, 36, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-51, -16, -55, -45, -41],\n [51, 36, 67, 19, 31],\n [10, -37, -61, 9, -10],\n [25, 40, 84, 11, 29],\n [-57, 0, -29, -41, -33]]\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 5x5 matrix:\n[[59, 3, 57, -39, 3],\n [-15, 7, -3, 0, -17],\n [-34, -30, -24, 15, 20],\n [-9, 35, 19, -40, 29],\n [1, 31, 39, -51, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -24, 10, 12, 34],\n [1, 7, 22, -10, -24],\n [5, -17, 32, 2, 10],\n [-5, 37, -2, -22, -60],\n [-6, 22, -36, -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 5x5 matrix:\n[[-32, -6, 2, 36, -34],\n [-20, -9, 2, 23, -19],\n [16, 8, 14, -14, 40],\n [8, -1, -8, -11, -3],\n [0, -31, -27, -6, -37]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 24, -8, -24, -16],\n [3, 6, -2, -6, -4],\n [-12, -24, 8, 24, 16],\n [12, 24, -8, -24, -16],\n [18, 36, -12, -36, -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[[66, 16, 49, -20, 58],\n [4, -23, 0, -20, -15],\n [58, 25, 45, -8, 57],\n [-44, -5, -33, 16, -30],\n [-28, -18, -22, 0, -34]]?\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, -21, -23, -19, 59],\n [-70, -33, -5, 2, 1],\n [-64, -31, -9, -14, 18],\n [16, -10, -8, 22, -26],\n [54, 37, 13, 25, -13]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, -1, -15, 35, -5],\n [-17, -5, -5, 36, -10],\n [43, 9, -15, -15, 13],\n [-6, 56, 26, 19, 1],\n [-65, 35, 25, -2, -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[[3, 3, 9, -9, -3],\n [-3, -3, -9, 9, 3],\n [-5, -5, -15, 15, 5],\n [4, 4, 12, -12, -4],\n [-3, -3, -9, 9, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-30, -61, -16, 66, -17],\n [-84, -61, 38, 66, 1],\n [30, 9, 39, -36, 8],\n [6, -42, 27, 24, 9],\n [18, -11, 61, -12, 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 5x5 matrix:\n[[-20, 8, 20, 20, 24],\n [5, -2, -5, -5, -6],\n [-20, 8, 20, 20, 24],\n [-30, 12, 30, 30, 36],\n [15, -6, -15, -15, -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[[29, -19, -5, -17, 20],\n [-40, -16, 16, 4, 8],\n [58, 2, 30, 16, -20],\n [-22, 50, 38, -14, 56],\n [-1, -17, -7, 15, -32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, -33, 30, 3, -24],\n [-5, 18, -33, 9, 30],\n [48, -21, -12, 24, -12],\n [-22, 13, -50, 22, 64],\n [26, -32, -6, 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[[-7, 42, 54, 46, -45],\n [-22, -4, -9, -22, -7],\n [6, -84, -73, -14, 32],\n [-4, 24, 12, -24, -21],\n [-53, 33, 25, -17, -26]]\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, -56, -15, 58, -32],\n [-6, -12, 24, 2, 2],\n [6, 14, 6, -7, 8],\n [5, -44, -11, 31, -17],\n [5, 29, -8, -31, 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[[-1, 5, -3, -5, 1],\n [-2, 10, -6, -10, 2],\n [3, -15, 9, 15, -3],\n [-4, 20, -12, -20, 4],\n [-4, 20, -12, -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[[42, 5, 10, -27, 16],\n [-27, -17, -26, 26, -35],\n [-13, 21, 16, -24, 21],\n [-8, -16, 22, -2, 2],\n [-17, 3, -1, -15, -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[[-3, 6, -2, -4, -3],\n [-18, 36, -12, -24, -18],\n [-3, 6, -2, -4, -3],\n [-3, 6, -2, -4, -3],\n [3, -6, 2, 4, 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[[-12, 12, 3, 6, 6],\n [-16, 16, 4, 8, 8],\n [-24, 24, 6, 12, 12],\n [-24, 24, 6, 12, 12],\n [-12, 12, 3, 6, 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 5x5 matrix:\n[[-10, -22, 24, -81, -3],\n [12, 28, -16, 71, -19],\n [-16, 8, 8, -2, 2],\n [0, -3, -5, -19, -40],\n [-10, -42, 12, -83, 35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-21, 0, -12, 1, 1],\n [-25, 8, -24, -15, -23],\n [9, -12, 24, 36, 33],\n [-8, -6, -1, 2, 21],\n [0, 8, -4, 0, -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 5x5 matrix:\n[[14, -30, -22, 22, 44],\n [1, -15, 19, 17, -2],\n [0, 15, -24, -18, 6],\n [-3, 20, -17, -21, -4],\n [0, 15, -24, -18, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[10, -4, -26, 45, -29],\n [15, -34, -27, 13, 16],\n [17, 26, -13, 14, -9],\n [11, 0, 5, -41, 45],\n [41, 6, -37, 7, 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[[0, 0, -30, -36, 24],\n [0, 0, -5, -6, 4],\n [0, 0, -5, -6, 4],\n [0, 0, -10, -12, 8],\n [0, 0, 15, 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 5x5 matrix:\n[[-34, 28, -17, -14, 13],\n [-44, 52, 10, 20, -14],\n [-70, 64, -29, 2, -3],\n [-34, 11, -52, -54, 45],\n [-37, 38, -1, -2, 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[[10, -15, 30, -3, 3],\n [-20, -5, 22, -9, -9],\n [11, -27, 3, 9, -6],\n [-18, 1, 37, -15, -3],\n [-2, 69, 21, -27, 33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, -12, -12, -7, 31],\n [-11, -9, 8, 46, -26],\n [21, -18, -6, -33, 21],\n [5, 12, -12, -43, 35],\n [-4, 18, -14, -34, 38]]\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 5x5 matrix:\n[[20, -4, -12, 8, -16],\n [32, 0, -6, 4, -4],\n [12, -12, -27, 18, -42],\n [-39, -5, -3, 2, -12],\n [2, 6, 12, -8, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[20, -7, -14, -2, 10],\n [20, 26, 7, -12, 8],\n [-10, 11, -13, 10, 32],\n [16, -42, -46, -60, -12],\n [-40, -4, -3, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-35, -1, -16, -37, -5],\n [29, -4, 14, 34, -7],\n [-20, -8, -8, -16, -20],\n [-1, -3, 0, 1, -7],\n [3, -4, 2, 6, -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[[-20, 0, -5, -5, 25],\n [0, 0, 0, 0, 0],\n [-24, 0, -6, -6, 30],\n [-24, 0, -6, -6, 30],\n [4, 0, 1, 1, -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 5x5 matrix:\n[[11, 19, 1, 12, -12],\n [-9, -7, -1, 8, 6],\n [-20, -27, -6, -17, 15],\n [-22, -19, -3, 14, 15],\n [-12, 2, 2, 44, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 24, 20, 0, -16],\n [15, -30, -25, 0, 20],\n [12, -24, -20, 0, 16],\n [-18, 36, 30, 0, -24],\n [12, -24, -20, 0, 16]]?\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[[-26, -36, 31, 34, 11],\n [26, 36, -31, -34, -11],\n [28, 24, -32, -8, -16],\n [-9, -15, 23, -28, -33],\n [4, 14, 1, -46, -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[[-13, -47, -21, -39, -31],\n [-46, -23, -31, -29, -42],\n [11, -32, -25, 13, -3],\n [-35, 23, -31, -3, -19],\n [-11, -36, -41, -15, -25]]\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, -22, 14, 29, 0],\n [10, 10, -30, 25, 0],\n [4, -8, 11, 1, 0],\n [42, -18, -11, 60, 0],\n [-10, 14, -16, -7, 0]]?\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, -12, -15, 15],\n [24, -8, 16, -2, -38],\n [-5, 20, -7, 16, 29],\n [2, 16, -2, 14, 16],\n [29, 12, 15, 16, -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[[-5, -2, 0, 5, -6],\n [-5, -2, 0, 5, -6],\n [-5, -2, 0, 5, -6],\n [30, 12, 0, -30, 36],\n [5, 2, 0, -5, 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[[12, 7, 51, -28, 44],\n [-36, 12, 36, 12, -48],\n [-18, -60, 9, 0, -39],\n [22, -10, -41, 0, 21],\n [20, -26, -4, -16, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-32, 2, -22, -6, -24],\n [1, 30, -27, 18, -25],\n [30, 24, -3, 17, 1],\n [-6, 16, -17, -21, -13],\n [53, -1, 35, -2, 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 5x5 matrix:\n[[-5, -20, 15, 10, -5],\n [-19, 4, 17, 18, 11],\n [33, -12, -27, -6, -9],\n [36, -8, -32, -14, -11],\n [-43, 12, 37, 4, 8]]\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[[2, -16, 12, -20, -4],\n [-28, 9, -6, 34, -12],\n [-28, 4, -25, 16, 34],\n [-27, 22, -27, 42, 16],\n [27, -35, 31, -60, -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[[-35, -39, -26, 25, -20],\n [11, 12, -41, 13, 14],\n [-40, -19, -1, 25, -30],\n [1, 17, 26, -5, -4],\n [-28, -13, 2, 18, -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[[15, 7, 17, -16, -11],\n [15, 7, 17, -16, -11],\n [15, 39, -15, 24, -3],\n [-20, -28, -4, -2, 10],\n [10, 2, 14, -14, -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 5x5 matrix:\n[[18, -3, -15, 15, 6],\n [24, -4, -20, 20, 8],\n [24, -4, -20, 20, 8],\n [-12, 2, 10, -10, -4],\n [6, -1, -5, 5, 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 5x5 matrix:\n[[-6, 15, 24, 18, -50],\n [23, 29, -8, 66, -70],\n [-1, -37, 6, -4, 6],\n [-32, 0, -4, -40, 40],\n [36, -6, 4, 52, -52]]\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, 3, -65, 63, 31],\n [-38, -39, 48, -67, 11],\n [-16, -5, 34, -19, -19],\n [-25, 21, 31, 0, -62],\n [-7, -70, -11, -14, 48]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, 51, -42, 18, -12],\n [20, -18, 22, -12, 6],\n [37, 46, -72, -15, -1],\n [-62, -22, 56, 36, -8],\n [15, 44, -39, 6, -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[[39, 6, 19, 30, 9],\n [14, -4, -11, 15, -11],\n [16, 4, -39, 33, -31],\n [-16, -10, -4, -18, -2],\n [-1, 20, -19, 18, -11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, -8, 0, -2, 12],\n [-4, -4, 0, -1, 6],\n [4, 4, 0, 1, -6],\n [16, 16, 0, 4, -24],\n [-20, -20, 0, -5, 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[[-12, -10, -10, -4, -10],\n [0, 0, 0, 0, 0],\n [30, 25, 25, 10, 25],\n [24, 20, 20, 8, 20],\n [6, 5, 5, 2, 5]]?\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, -2, -37, 16, 32],\n [17, 1, 27, 11, -14],\n [-27, 4, 13, -32, -18],\n [-9, -13, -13, -19, -18],\n [32, -7, 25, 21, -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[[-5, -6, 3, -1, 2],\n [15, 18, -9, 3, -6],\n [-5, -6, 3, -1, 2],\n [-10, -12, 6, -2, 4],\n [25, 30, -15, 5, -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[[19, -11, -4, 19, 41],\n [28, 53, -2, -39, 0],\n [17, 43, 5, -12, -30],\n [12, 9, 0, 3, 6],\n [-13, -24, -6, -10, 25]]?\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[[-8, 0, -8, 48, -42],\n [8, -12, 2, 8, -16],\n [12, 0, 12, -32, 28],\n [-4, -12, -10, 32, -37],\n [24, 12, 30, -40, 44]]?\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, -34, 26, -16, -6],\n [25, -15, 47, -14, -1],\n [-23, -1, -7, -24, 27],\n [50, -33, 35, -15, 44],\n [8, 30, 46, -4, 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 5x5 matrix:\n[[15, -9, 9, -3, 15],\n [30, -18, 18, -6, 30],\n [-30, 18, -18, 6, -30],\n [-15, 9, -9, 3, -15],\n [-10, 6, -6, 2, -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 5x5 matrix:\n[[-43, 6, 1, 23, -8],\n [-3, -12, -24, -16, 9],\n [-43, 24, 25, 15, -2],\n [2, -13, -12, 20, -13],\n [49, -21, -22, -26, 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, -36, 22, -6, 14],\n [18, 15, -26, 16, -4],\n [-6, -6, 17, -1, 4],\n [-30, -39, 40, -38, 8],\n [48, -15, -31, 29, 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[[5, 49, -35, 61, -37],\n [8, 25, -5, 19, -13],\n [3, 15, -7, 15, -9],\n [-15, 13, -42, 43, -10],\n [3, 37, -29, 49, -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[[6, -3, 30, 27, 6],\n [12, 60, 5, 10, -54],\n [10, 7, 40, 37, -2],\n [4, 4, 15, 14, -2],\n [2, -13, 20, 17, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-15, -38, 29, 4, 38],\n [-31, 1, 16, 5, 20],\n [19, -6, 27, -20, 2],\n [10, 22, -22, -32, -25],\n [-29, -23, -52, 7, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[15, 20, -5, -5, 15],\n [-9, -12, 3, 3, -9],\n [6, 8, -2, -2, 6],\n [15, 20, -5, -5, 15],\n [6, 8, -2, -2, 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 5x5 matrix:\n[[15, 0, -18, 5, -17],\n [-18, 13, 30, -7, 22],\n [18, 9, -18, 9, -22],\n [30, 20, -12, -10, -18],\n [0, 7, 3, 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 5x5 matrix:\n[[6, -3, 0, -12, 0],\n [8, -4, 0, -16, 0],\n [-12, 6, 0, 24, 0],\n [6, -3, 0, -12, 0],\n [-8, 4, 0, 16, 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[[14, -15, 8, 19, -5],\n [6, -55, 4, 19, -1],\n [-16, -29, -11, 28, -15],\n [-42, -22, -29, 53, -36],\n [-2, 30, -5, 49, -32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -4, 1, -5, 1],\n [16, 16, -4, 20, -4],\n [-16, -16, 4, -20, 4],\n [-20, -20, 5, -25, 5],\n [8, 8, -2, 10, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[38, -39, 26, -40, 9],\n [-22, 15, -15, 22, -12],\n [4, 36, -31, 8, -27],\n [14, -3, 15, -14, 24],\n [32, 6, 1, -24, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, 6, -33, -12, 5],\n [-19, 32, 35, 4, -12],\n [6, 24, 3, -3, 8],\n [20, 18, -16, -7, 19],\n [22, -18, -5, 4, 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[[-18, -29, 2, -22, 9],\n [-9, -3, -6, -1, -2],\n [24, 8, -5, 19, 3],\n [9, 26, -26, 35, -13],\n [58, 4, -2, 32, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 0, 0, 8, 2],\n [0, 0, 0, 0, 0],\n [-6, 0, 0, 8, 2],\n [12, 0, 0, -16, -4],\n [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[[0, 4, -8, 12, 24],\n [0, 6, -12, 18, 36],\n [0, 5, -10, 15, 30],\n [0, -4, 8, -12, -24],\n [0, -5, 10, -15, -30]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, 5, 2, 6, 5],\n [36, -34, -10, 18, -10],\n [4, 2, 2, 22, 10],\n [15, -12, -3, 15, 0],\n [-6, -3, -3, -33, -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[[-5, -5, -14, -17, 63],\n [22, -39, -35, -31, -64],\n [-15, 40, 36, 47, 28],\n [9, -12, -25, -20, 31],\n [-35, -9, 15, -21, 54]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-23, 5, 49, 17, 2],\n [13, -38, 3, -11, 37],\n [32, -5, -46, -8, -3],\n [-29, -8, -39, -53, 9],\n [-14, 84, -34, 18, -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[[-15, -20, -10, -5, -5],\n [-9, -12, -6, -3, -3],\n [6, 8, 4, 2, 2],\n [0, 0, 0, 0, 0],\n [-3, -4, -2, -1, -1]]\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 5x5 matrix:\n[[-2, 23, 19, 44, 21],\n [-10, -27, 44, -62, -57],\n [-42, -2, 26, -1, -53],\n [-32, 25, -18, 61, 4],\n [26, 27, 12, 17, 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[[-3, -35, -3, -4, 1],\n [-95, 8, -9, 38, -23],\n [1, -48, 51, 10, 29],\n [5, -38, -21, 4, -3],\n [-11, 47, -72, 5, -38]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -10, 4, 0, -2],\n [26, -30, 26, 45, -25],\n [-25, 10, -36, -40, 9],\n [-16, 9, 6, -32, 11],\n [-14, 8, -48, -36, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-20, -12, 0, -12, -16],\n [-20, -12, 0, -12, -16],\n [-25, -15, 0, -15, -20],\n [20, 12, 0, 12, 16],\n [15, 9, 0, 9, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, 36, 3, -24, 18],\n [-8, -16, -6, 27, -29],\n [-12, 16, -4, 8, -16],\n [-1, -4, -1, 5, -5],\n [-18, 24, -6, 12, -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[[30, 9, 0, -18, -54],\n [10, 13, -8, -10, -6],\n [-15, -42, 30, 24, -18],\n [10, -22, 20, 4, -48],\n [0, 30, -24, -12, 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[[-30, 0, -24, 30, -18],\n [-30, 0, -24, 30, -18],\n [5, 0, 4, -5, 3],\n [-25, 0, -20, 25, -15],\n [30, 0, 24, -30, 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[[-18, 6, 6, -24, 36],\n [9, -3, -3, 12, -18],\n [9, -3, -3, 12, -18],\n [18, -6, -6, 24, -36],\n [3, -1, -1, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-15, 45, -55, 25, 15],\n [10, 2, -2, 14, -2],\n [6, 30, -36, 36, 6],\n [-21, 39, -48, 12, 15],\n [-11, 41, -50, 26, 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[[-10, 32, -30, 18, 21],\n [16, -8, 8, -48, -28],\n [15, 17, -7, -14, -12],\n [-1, 41, -38, -15, 7],\n [5, 37, -24, 19, 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 5x5 matrix:\n[[6, -36, 12, 12, 18],\n [1, -6, 2, 2, 3],\n [-2, 12, -4, -4, -6],\n [3, -18, 6, 6, 9],\n [3, -18, 6, 6, 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 5x5 matrix:\n[[-25, -15, -36, -2, 10],\n [32, 29, 10, 4, 24],\n [11, -27, 50, 23, -38],\n [40, 21, 18, -40, 12],\n [12, 14, -12, 16, 28]]\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 5x5 matrix:\n[[34, 3, 10, 28, -9],\n [-21, -3, -12, -6, 27],\n [5, 0, -4, 14, 18],\n [6, -8, 8, 4, -12],\n [-38, -10, -4, -36, -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 5x5 matrix:\n[[10, 24, 4, -10, 24],\n [16, 44, -16, -16, 30],\n [-6, -12, -12, 6, -18],\n [3, 4, 14, -3, 12],\n [-3, 0, -30, 3, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -32, -18, -9, -26],\n [0, 20, 6, 0, 8],\n [0, -30, -9, 0, -12],\n [2, -24, -10, -3, -14],\n [6, 48, 6, -9, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, 40, 20, 22, 4],\n [-12, -15, -12, 3, 12],\n [8, -20, -4, -26, -20],\n [-8, -5, -6, 6, 10],\n [12, 25, 16, 5, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-15, 15, 18, -3, 15],\n [0, 0, 0, 0, 0],\n [-20, 20, 24, -4, 20],\n [-10, 10, 12, -2, 10],\n [20, -20, -24, 4, -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[[-9, -10, 34, -8, 0],\n [-9, -11, -1, -7, 19],\n [24, 5, -69, 17, 6],\n [18, -31, 7, 5, 28],\n [6, -15, -1, 1, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[44, 3, 1, -29, 19],\n [-18, -10, 0, -14, 16],\n [-4, -10, 22, -2, 6],\n [26, 24, -26, 20, -27],\n [-44, -13, 17, 19, -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[[2, -4, -12, -2, -6],\n [0, 10, 36, 11, 24],\n [47, -28, 6, 46, 27],\n [35, -18, -6, 29, 23],\n [9, -8, -18, 2, -3]]\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[[36, -10, -44, -5, 7],\n [-56, 35, -4, 36, 12],\n [36, 29, 11, -31, 16],\n [-14, 9, 16, -19, -55],\n [16, -29, 20, 13, 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 5x5 matrix:\n[[-52, 24, -34, 44, 24],\n [-20, 15, 0, 35, 10],\n [-22, -3, -1, 23, -6],\n [12, -27, 6, -28, -24],\n [70, -12, 27, -64, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[15, -49, 1, -36, 54],\n [21, -10, -20, -12, 18],\n [27, -13, 13, -27, -48],\n [-32, 7, 23, 16, 0],\n [38, 20, -56, 5, 6]]\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, 7, 39, 49, 29],\n [-22, -8, -34, -42, -12],\n [0, -19, 23, 31, 18],\n [-51, -22, 20, 0, -16],\n [-21, 9, 3, -15, -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[[-20, 20, 24, 24, 0],\n [-15, 15, 18, 18, 0],\n [25, -25, -30, -30, 0],\n [-25, 25, 30, 30, 0],\n [15, -15, -18, -18, 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 5x5 matrix:\n[[-17, -23, 2, -23, -33],\n [-1, -9, -6, -9, -18],\n [17, 23, -2, 23, 33],\n [-17, -13, 10, -13, -12],\n [14, 26, 4, 26, 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[[11, -30, -48, -3, -2],\n [14, 5, -11, 51, -11],\n [-2, -22, 3, -7, -14],\n [-3, -13, 2, 12, -16],\n [-24, 6, 36, -28, -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[[0, 8, 0, 8, -12],\n [0, -12, 0, -12, 18],\n [0, 4, 0, 4, -6],\n [0, 8, 0, 8, -12],\n [0, 12, 0, 12, -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[[-56, -9, 48, -1, -8],\n [1, -61, 23, -12, 12],\n [15, -7, -7, 3, -6],\n [-6, 53, 10, 14, -18],\n [1, -42, 11, 0, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-23, 40, 16, -12, 25],\n [-41, 40, 5, -35, -3],\n [-28, 35, 10, -20, 11],\n [-25, 47, 2, -24, 2],\n [-28, 26, 6, -22, 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[[-26, 23, 7, -12, -14],\n [1, -14, -8, -10, 9],\n [-22, -19, -18, -14, 11],\n [-27, 26, 11, -64, -12],\n [-28, 21, 7, -52, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-30, -10, 14, -2, 16],\n [-38, -26, 10, -12, 30],\n [-4, -16, 14, -23, 17],\n [-15, -18, 36, -24, 24],\n [-37, -15, 18, 5, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-5, -5, 0, 2, -2],\n [25, 25, 0, -10, 10],\n [0, 0, 0, 0, 0],\n [-25, -25, 0, 10, -10],\n [15, 15, 0, -6, 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[[-12, -12, 2, 6, -12],\n [30, 30, -5, -15, 30],\n [-36, -36, 6, 18, -36],\n [-12, -12, 2, 6, -12],\n [24, 24, -4, -12, 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[[-24, 15, -24, 27, -30],\n [16, -25, -8, -5, 10],\n [15, -15, 6, -12, 15],\n [-3, 30, 42, -21, 15],\n [6, -15, -12, 3, 0]]\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, -12, 34, -39, 12],\n [13, -1, 29, 51, -10],\n [44, -32, -8, 22, 40],\n [-64, 12, 32, -23, -38],\n [33, 13, -37, 18, -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[[33, -4, 12, 3, -8],\n [12, 8, -20, 13, 10],\n [6, 17, -27, 27, -2],\n [-48, -6, 22, -17, -18],\n [8, 1, -11, 1, 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[[-4, 2, -4, -10, -2],\n [0, 0, 0, 0, 0],\n [-10, 5, -10, -25, -5],\n [6, -3, 6, 15, 3],\n [-6, 3, -6, -15, -3]]\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[[1, -8, -40, -48, -24],\n [8, -10, 14, 3, 9],\n [7, 10, 9, 21, 10],\n [15, 24, 7, 36, 15],\n [9, 18, -50, -27, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[7, 9, 8, 5, 17],\n [9, 6, 3, 9, 18],\n [12, 8, 4, 12, 24],\n [-16, -15, -11, -14, -35],\n [5, 25, 30, -5, 25]]\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, 25, -37, -3, -23],\n [-24, 13, -24, -7, -14],\n [6, -28, 42, 4, 26],\n [-54, -12, 6, -12, 6],\n [-12, -43, 60, 1, 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[[25, 15, 20, 5, 30],\n [-15, -9, -12, -3, -18],\n [30, 18, 24, 6, 36],\n [15, 9, 12, 3, 18],\n [-30, -18, -24, -6, -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[[-15, -3, -3, 18, 18],\n [-30, -6, -6, 36, 36],\n [15, 3, 3, -18, -18],\n [0, 0, 0, 0, 0],\n [15, 3, 3, -18, -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[[38, 6, -1, 11, 19],\n [-34, 12, 9, -11, -17],\n [34, -12, -9, 11, 17],\n [-34, -3, 2, -10, -17],\n [52, -6, -8, 16, 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[[34, -21, -21, -9, 12],\n [-64, 32, -8, 27, -49],\n [-24, 18, 4, 3, -19],\n [-22, 27, -9, -9, -36],\n [36, -3, 22, -33, 26]]\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 5x5 matrix:\n[[-3, -1, -2, 4, 6],\n [-3, -5, -13, 35, 39],\n [18, 6, 12, -24, -36],\n [0, -4, -11, 31, 33],\n [-5, -3, -7, 17, 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 5x5 matrix:\n[[-14, 2, -4, 28, 48],\n [-11, -13, 14, 10, 33],\n [-7, -21, 20, -6, 13],\n [-17, -21, -20, -6, 8],\n [13, 25, 9, 14, 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[[27, 14, -9, -38, -10],\n [41, 6, -25, -38, -8],\n [-10, 16, 18, -38, 22],\n [45, -42, -25, 10, -44],\n [-15, -70, 33, 6, 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[[-5, 3, -3, 6, 7],\n [-2, 40, -9, 1, 22],\n [0, -1, -11, 41, 19],\n [13, -21, 6, -42, -35],\n [-36, -16, 62, -31, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -4, -4, 16, -4],\n [2, 2, 2, -8, 2],\n [-5, -5, -5, 20, -5],\n [6, 6, 6, -24, 6],\n [4, 4, 4, -16, 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[[25, 39, 53, 2, 33],\n [56, 12, 58, -20, 6],\n [-13, -45, -34, 11, -39],\n [-21, -1, -16, 13, 1],\n [-4, -34, 9, 50, -29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 18, 6, -36, 24],\n [2, -6, -2, 12, -8],\n [0, 0, 0, 0, 0],\n [5, -15, -5, 30, -20],\n [-2, 6, 2, -12, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, -19, 9, -28, 5],\n [34, 5, -12, -4, -34],\n [-2, 13, 30, -16, 15],\n [33, -29, -13, -35, -40],\n [-14, -22, -3, -10, 8]]\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 5x5 matrix:\n[[-20, 0, -25, -30, -10],\n [14, -6, 26, 30, 12],\n [-13, -3, -12, -15, -4],\n [-1, -3, 3, 3, 2],\n [25, 15, 10, 15, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[11, 32, 13, 12, 11],\n [49, 57, -25, -8, -3],\n [9, 28, 24, -4, -7],\n [-26, -30, 26, -38, -18],\n [6, -10, -24, 34, -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[[30, 21, -1, -3, 12],\n [-4, -21, -11, 25, -18],\n [24, -17, -20, 30, -12],\n [-42, -6, 13, -3, -12],\n [-17, 18, 13, 14, -15]]\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[[8, 8, -20, 24, -8],\n [-4, -4, 10, -12, 4],\n [-10, -10, 25, -30, 10],\n [0, 0, 0, 0, 0],\n [6, 6, -15, 18, -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[[-12, 36, -27, -15, 21],\n [-21, 9, 18, -6, 12],\n [-25, 45, -20, -20, 30],\n [-19, 39, -21, -17, 25],\n [-28, 36, -5, -17, 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[[8, -4, 4, -8, 16],\n [-10, 5, -5, 10, -20],\n [6, -3, 3, -6, 12],\n [-10, 5, -5, 10, -20],\n [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[[-18, -9, -35, -6, 31],\n [-21, 40, 21, -17, -30],\n [16, -22, -21, 24, 28],\n [-30, -18, -23, -41, 14],\n [-3, 0, 12, -14, -14]]\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[[25, 0, 30, -25, 25],\n [5, 0, 6, -5, 5],\n [5, 0, 6, -5, 5],\n [-25, 0, -30, 25, -25],\n [20, 0, 24, -20, 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[[-18, 26, 22, -29, 42],\n [-10, -14, 14, -9, 2],\n [18, -31, -16, 27, -42],\n [6, -33, 34, -7, -6],\n [-36, -18, 37, -34, 24]]\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, -5, 20, -30, 30],\n [-10, -31, 4, -46, 21],\n [12, 24, 48, -24, 54],\n [12, 31, 20, 18, 12],\n [4, 5, 28, -26, 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[[10, -11, 11, -1, -9],\n [-1, 18, -40, -15, -31],\n [18, -29, 25, 23, 25],\n [-7, 4, -8, -2, -25],\n [5, -9, -13, 12, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-37, 28, -13, 21, 19],\n [-12, 28, 27, 21, 9],\n [15, -4, 45, 11, -3],\n [2, 10, -1, -3, -2],\n [-32, 68, -8, 16, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, 30, -6, 12, 18],\n [-4, -20, 4, -8, -12],\n [-1, -5, 1, -2, -3],\n [4, 20, -4, 8, 12],\n [6, 30, -6, 12, 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 5x5 matrix:\n[[3, 0, -2, 1, -6],\n [6, 0, -4, 2, -12],\n [-6, 0, 4, -2, 12],\n [-3, 0, 2, -1, 6],\n [-3, 0, 2, -1, 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[[5, 1, 34, 51, -2],\n [38, 22, -44, -44, 31],\n [15, 11, -26, -29, 13],\n [55, 35, -46, -37, 41],\n [50, 26, -42, -36, 39]]\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[[54, 3, 2, 13, -34],\n [17, -4, -9, -16, -26],\n [11, 36, -7, -18, 13],\n [-43, 21, -30, -32, 68],\n [-34, -8, -27, -43, 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[[-16, 20, -20, -8, -4],\n [-4, 5, -5, -2, -1],\n [24, -30, 30, 12, 6],\n [8, -10, 10, 4, 2],\n [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[[17, 37, 1, -26, -31],\n [3, 24, -34, 26, -14],\n [12, 0, -20, 14, -53],\n [41, 16, 11, -6, 0],\n [-33, 4, 6, -18, 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[[26, -14, -6, 24, 20],\n [26, -14, -6, 24, 20],\n [2, -2, 3, -3, -1],\n [15, -13, 15, -12, -2],\n [-2, 2, -3, 3, 1]]\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[[-6, -1, 1, 1, -3],\n [18, 3, -3, -3, 9],\n [12, 2, -2, -2, 6],\n [0, 0, 0, 0, 0],\n [-12, -2, 2, 2, -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 5x5 matrix:\n[[-20, -30, 18, 24, 4],\n [-2, -6, 2, 6, 2],\n [31, 18, -26, -3, 9],\n [7, 6, -6, -3, 1],\n [-23, -24, 20, 15, -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[[25, 25, 10, -5, 20],\n [25, 25, 10, -5, 20],\n [-30, -30, -12, 6, -24],\n [-30, -30, -12, 6, -24],\n [-10, -10, -4, 2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[27, -4, 24, -11, 1],\n [-8, 4, -15, -2, -4],\n [27, -7, 3, -5, 16],\n [-20, -16, 4, 44, 36],\n [10, -8, 35, 8, 6]]\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[[-9, 0, -9, -6, -3],\n [0, 0, 0, 0, 0],\n [6, 0, 6, 4, 2],\n [15, 0, 15, 10, 5],\n [15, 0, 15, 10, 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[[14, -16, -6, -22, -20],\n [55, 26, 16, -41, 5],\n [-48, 14, -22, 33, 24],\n [20, 12, 28, 2, 34],\n [29, 22, 35, 2, 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[[27, -19, 18, -36, -24],\n [-71, 5, 26, 28, -24],\n [63, -25, -14, -3, -19],\n [6, -19, 38, -28, -42],\n [-28, -15, 14, 18, -36]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, -18, -9, 3, 0],\n [-2, -12, -6, 2, 0],\n [5, 30, 15, -5, 0],\n [2, 12, 6, -2, 0],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-10, -24, -24, 6, 18],\n [-29, -31, -29, -54, 10],\n [-14, -36, -15, -36, -6],\n [-32, 10, -7, -12, -26],\n [-25, -11, -28, 34, 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[[-2, 7, 10, -9, 0],\n [-8, 26, 8, -28, 20],\n [-24, 5, -19, -2, -5],\n [-8, -23, -26, 28, -20],\n [0, 28, -2, -28, 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[[-29, 11, 19, -24, -21],\n [-20, -20, -5, -20, 20],\n [6, -10, -9, 4, 14],\n [-10, 38, 29, -4, -50],\n [-13, 27, 23, -8, -37]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[23, 10, 26, -1, -3],\n [34, 2, 36, -10, -30],\n [-16, 4, -16, 8, 24],\n [-11, -13, -14, -5, -15],\n [-32, -13, -36, 2, 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 5x5 matrix:\n[[-12, 2, -6, -6, 2],\n [2, 9, -7, -3, -7],\n [36, -6, 18, 18, -6],\n [24, -18, 24, 18, 6],\n [4, -24, 22, 12, 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 5x5 matrix:\n[[-11, 7, -43, -7, -27],\n [-2, 0, 66, 14, -16],\n [18, 23, -14, -25, -43],\n [-43, -18, 12, 37, 8],\n [33, -5, 23, -25, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -1, -6, 5, -6],\n [-16, 4, 24, -20, 24],\n [-16, 4, 24, -20, 24],\n [-24, 6, 36, -30, 36],\n [20, -5, -30, 25, -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[[-2, 8, -4, -4, 2],\n [-5, 20, -10, -10, 5],\n [4, -16, 8, 8, -4],\n [-5, 20, -10, -10, 5],\n [1, -4, 2, 2, -1]]?\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 5x5 matrix:\n[[28, 17, 19, 2, -18],\n [4, 21, 27, 26, 6],\n [36, -6, -12, -36, -36],\n [-18, -23, -28, -18, 6],\n [-30, -8, -7, 12, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[14, 10, 23, 35, 33],\n [-5, -20, 25, 5, -5],\n [5, -14, 2, 2, -54],\n [5, -4, 7, 9, -14],\n [-15, 12, -21, -27, 42]]\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[[29, 21, 27, 16, 11],\n [20, 31, -21, 4, -12],\n [-6, -18, 36, 8, 20],\n [19, -2, 60, 20, 29],\n [-19, 2, -60, -20, -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[[13, 12, -16, -36, 15],\n [30, 42, 30, -4, 30],\n [35, 19, -11, 26, 15],\n [12, 5, 34, 0, -10],\n [-16, -13, -14, -44, -6]]\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, -25, 7, 24, 28],\n [-10, 26, -6, -24, -36],\n [30, 12, -12, -18, 33],\n [25, -11, -3, 6, 45],\n [-25, -49, 23, 54, 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[[33, 0, -9, 49, -31],\n [20, 28, 48, -14, 16],\n [10, -19, -22, 10, -27],\n [17, 4, 3, 19, -11],\n [7, 17, -5, 56, 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[[0, 14, -4, 14, 62],\n [-2, 8, -4, 4, 12],\n [41, -32, 27, 52, -5],\n [-8, 8, 5, 19, 6],\n [48, -25, -8, -11, 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 5x5 matrix:\n[[-12, -9, 12, -21, 27],\n [10, -31, -13, -22, 15],\n [-11, 22, 12, 15, -18],\n [-31, -35, 27, -59, 51],\n [2, 4, -6, 16, -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[[-18, -54, -12, -50, 40],\n [6, 30, 36, 30, -36],\n [7, 26, 18, 25, -25],\n [-9, -27, -6, -25, 20],\n [7, 17, -6, 15, -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[[18, -18, -33, 21, -12],\n [58, 35, -34, 39, 46],\n [24, -27, -54, 27, -24],\n [-4, 0, 54, -30, -12],\n [4, 2, 54, -38, -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 5x5 matrix:\n[[-6, -36, 8, 12, -21],\n [10, -22, 10, -13, -15],\n [27, 18, -18, -45, 9],\n [9, -25, 18, 11, 1],\n [5, 13, 10, 7, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[17, 1, -22, -4, -14],\n [-6, 2, 36, -3, 32],\n [14, -12, -27, -1, -14],\n [26, -22, -16, -7, 8],\n [-17, 15, 34, 1, 18]]\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, -4, 4, 16, -20],\n [-3, -3, 3, 12, -15],\n [5, 5, -5, -20, 25],\n [3, 3, -3, -12, 15],\n [2, 2, -2, -8, 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[[-11, 53, -57, -5, -35],\n [34, 2, -18, -38, -14],\n [-33, 35, -25, 26, -19],\n [32, -32, 18, -31, 44],\n [7, -29, 31, 2, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 36, 24, 36, -6],\n [6, 18, 12, 18, -3],\n [10, 30, 20, 30, -5],\n [-8, -24, -16, -24, 4],\n [-10, -30, -20, -30, 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[[13, 14, -8, -8, -18],\n [-13, -30, -17, 22, -28],\n [18, 0, 13, -42, -14],\n [39, 12, 8, -30, 2],\n [0, -14, 24, -2, 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 5x5 matrix:\n[[-14, -8, -8, 6, -22],\n [22, 4, -32, 17, 18],\n [-15, -28, 11, -23, -12],\n [21, 0, -45, 24, 12],\n [24, 8, -25, 14, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, -10, 25, 23, -12],\n [13, -8, 17, 18, -4],\n [14, -6, 12, 14, 0],\n [-6, -6, 0, -2, -16],\n [-17, 6, 6, 1, 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[[4, 2, 5, -5, -2],\n [12, 6, 15, -15, -6],\n [-24, -12, -30, 30, 12],\n [-24, -12, -30, 30, 12],\n [-12, -6, -15, 15, 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[[20, -12, 16, 20, 8],\n [10, -6, 8, 10, 4],\n [-30, 18, -24, -30, -12],\n [-20, 12, -16, -20, -8],\n [-5, 3, -4, -5, -2]]\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[[-12, -37, 3, -29, -12],\n [3, -23, -9, -16, -21],\n [46, -2, 17, -32, 27],\n [9, 19, -15, 24, -13],\n [-6, 4, 15, -6, 23]]\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 5x5 matrix:\n[[0, 1, 5, 2, 3],\n [15, 2, 30, -11, -19],\n [-9, -1, -17, 7, 12],\n [-12, 3, -1, 18, 29],\n [-18, -3, -39, 12, 21]]\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, 15, -15, -21, 24],\n [-3, -15, -15, 3, -12],\n [-7, 9, -29, -5, 20],\n [13, 4, 57, -18, -12],\n [7, -3, 30, -9, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, 2, 1, 0, 1],\n [-2, 2, 1, 0, 1],\n [12, -12, -6, 0, -6],\n [-12, 12, 6, 0, 6],\n [-4, 4, 2, 0, 2]]\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, 5, 25, -25, 5],\n [0, -3, -15, 15, -3],\n [0, -5, -25, 25, -5],\n [0, -6, -30, 30, -6],\n [0, -2, -10, 10, -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[[-13, -11, 7, 6, -14],\n [-14, -38, 6, 18, -32],\n [-25, -29, 13, 15, -32],\n [3, -21, -3, 9, -12],\n [28, 8, -16, -6, 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[[15, 27, 6, 0, 6],\n [20, 36, 8, 0, 8],\n [15, 27, 6, 0, 6],\n [1, 15, -2, -12, -20],\n [22, 22, 12, 16, 36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[20, -49, -48, -16, 24],\n [6, -12, -10, -12, -14],\n [-10, 8, 4, 21, 28],\n [24, -42, -38, -29, -2],\n [18, -45, -42, -24, -6]]\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[[-10, 4, -14, 8, 2],\n [23, 2, 33, -24, -13],\n [21, 42, 33, -42, -42],\n [6, 20, 10, -16, -18],\n [29, -6, 41, -26, -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[[-1, 3, 4, -1, 3],\n [-6, 18, 24, -6, 18],\n [2, -6, -8, 2, -6],\n [4, -12, -16, 4, -12],\n [5, -15, -20, 5, -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[[16, -1, -5, 21, 7],\n [-30, 17, 19, -27, -9],\n [15, -14, -13, 9, 3],\n [34, -9, -15, 39, 13],\n [17, -10, -11, 15, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-20, -12, -20, -20, -8],\n [-10, -6, -10, -10, -4],\n [-15, -9, -15, -15, -6],\n [-10, -6, -10, -10, -4],\n [20, 12, 20, 20, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[36, 36, -6, 36, 24],\n [-30, -30, 5, -30, -20],\n [18, 18, -3, 18, 12],\n [-24, -24, 4, -24, -16],\n [30, 30, -5, 30, 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[[-11, 4, -42, 41, 23],\n [-3, 3, -21, 22, 12],\n [22, 4, 24, -14, -10],\n [15, 6, 0, 9, 3],\n [-19, -4, -18, 9, 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[[0, -8, -16, -5, -27],\n [0, -34, 13, -28, 0],\n [0, 32, -20, 27, -11],\n [0, 12, 42, 6, 66],\n [0, -10, -11, -7, -21]]\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, -15, -6, 3, 3],\n [-15, -15, -6, 3, 3],\n [-20, -20, -8, 4, 4],\n [-20, -20, -8, 4, 4],\n [5, 5, 2, -1, -1]]\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 5x5 matrix:\n[[-37, -25, 10, -19, -36],\n [28, 20, -14, -16, 4],\n [63, 30, -27, -10, 49],\n [-13, -30, 3, -2, 21],\n [-9, 0, 3, -4, -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[[13, 25, -29, 39, -8],\n [-30, -8, 48, -34, -22],\n [-5, 56, -36, 37, -41],\n [-9, -11, -21, -51, 0],\n [-3, -23, 55, 1, 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[[4, 7, 1, -8, -6],\n [-56, 47, -47, 8, 26],\n [1, 24, -5, -18, -10],\n [24, -9, 15, -12, -10],\n [-16, 43, -25, -20, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[5, 12, -14, 18, 2],\n [25, 24, 32, 6, -26],\n [21, 30, -1, 28, -12],\n [-27, -30, -23, -16, 24],\n [32, 36, 26, 20, -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 5x5 matrix:\n[[8, -12, 12, 20, -16],\n [10, -15, 15, 25, -20],\n [10, -15, 15, 25, -20],\n [-12, 18, -18, -30, 24],\n [-12, 18, -18, -30, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, 26, 26, -22, 4],\n [-18, -10, -23, 7, -19],\n [-20, 3, 9, -23, -56],\n [6, -7, -20, 22, 35],\n [-36, 23, -47, 1, -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[[-25, -28, 17, 7, 3],\n [-23, -23, 32, -27, 4],\n [-20, -6, 47, 7, -8],\n [-39, -36, 36, -24, 3],\n [13, 24, 1, 36, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-23, -30, 5, -20, -11],\n [-14, 24, -4, 16, 25],\n [-24, -36, 6, -24, -15],\n [-5, 6, -1, 4, 7],\n [30, 0, 0, 0, -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[[15, 0, -3, -9, 12],\n [-25, 0, 5, 15, -20],\n [-15, 0, 3, 9, -12],\n [-20, 0, 4, 12, -16],\n [-10, 0, 2, 6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -8, 2, -17, -3],\n [-36, 24, -6, 66, 6],\n [-24, 16, -4, 24, 8],\n [-30, 20, -5, 20, 12],\n [36, -24, 6, -56, -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[[2, 5, -2, 5, -5],\n [-8, -20, 8, -20, 20],\n [-8, -20, 8, -20, 20],\n [-6, -15, 6, -15, 15],\n [4, 10, -4, 10, -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 5x5 matrix:\n[[6, 16, -2, 23, -19],\n [0, -4, -6, -19, 1],\n [-34, -26, 8, -15, -17],\n [-10, -18, 0, -29, 33],\n [-3, -4, 11, 17, -52]]\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 5x5 matrix:\n[[-10, -12, 6, 2, 4],\n [-20, -24, 12, 4, 8],\n [-15, -18, 9, 3, 6],\n [15, 18, -9, -3, -6],\n [-15, -18, 9, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, -11, 13, 2, -5],\n [-2, 1, -7, 2, 15],\n [6, 24, -24, -6, 0],\n [-8, -26, 22, 8, 10],\n [-2, -11, 13, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[20, -24, -4, 12, -4],\n [-15, 18, 3, -9, 3],\n [0, 0, 0, 0, 0],\n [30, -36, -6, 18, -6],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-45, -13, -3, 6, 14],\n [25, -30, -15, -21, -45],\n [60, 18, 0, -18, -18],\n [15, 17, 15, 24, 8],\n [-20, -17, -24, -45, -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[[-11, 3, -21, 10, -29],\n [-22, 30, 10, -32, 18],\n [4, -12, -16, 20, -24],\n [-4, 0, -10, 6, -14],\n [-7, -3, -24, 17, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 10, -6, -10, 4],\n [3, -15, 9, 15, -6],\n [-2, 10, -6, -10, 4],\n [-1, 5, -3, -5, 2],\n [-5, 25, -15, -25, 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[[-44, 17, 31, 18, -16],\n [-68, -2, 16, -6, 8],\n [-26, 2, 7, -3, -4],\n [-2, 22, 47, 65, 12],\n [26, 3, 2, 15, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-14, -3, 31, -22, -7],\n [33, -6, 9, 45, 27],\n [-8, -2, -28, 28, -23],\n [-17, 1, -28, 7, -27],\n [-3, -4, 5, 13, -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[[12, -24, -8, 0, 8],\n [6, -12, -4, 0, 4],\n [18, -36, -12, 0, 12],\n [6, -12, -4, 0, 4],\n [12, -24, -8, 0, 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 5x5 matrix:\n[[6, 5, 4, 4, -2],\n [36, 30, 24, 24, -12],\n [18, 15, 12, 12, -6],\n [24, 20, 16, 16, -8],\n [-6, -5, -4, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-54, -24, 27, 12, -15],\n [55, 5, -13, 20, -39],\n [24, 4, -8, -12, 12],\n [30, -21, 9, 21, -48],\n [63, 5, -16, -6, -6]]\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[[-27, 20, -66, 23, 30],\n [-14, 31, -48, -5, 35],\n [7, -34, 50, 36, -73],\n [0, 3, 4, 8, -24],\n [-22, -58, -4, 78, -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 5x5 matrix:\n[[-26, -27, -6, 10, -21],\n [26, 27, 6, -10, 21],\n [2, 6, 24, -6, -18],\n [-16, -12, 24, 0, -36],\n [16, 12, -24, 0, 36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-20, -15, 19, 19, 11],\n [18, -63, -17, -24, -16],\n [0, 35, 21, 23, 7],\n [-16, -39, -28, -28, -2],\n [34, -29, -32, -37, -23]]\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, 5, -30, -5, 10],\n [36, -6, 36, 6, -12],\n [-36, 6, -36, -6, 12],\n [6, -1, 6, 1, -2],\n [24, -4, 24, 4, -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 5x5 matrix:\n[[11, -63, -52, -21, 33],\n [-24, 0, -40, 4, 12],\n [30, -10, 38, -7, -3],\n [-29, -2, -47, 1, -7],\n [36, -9, 45, -16, -4]]\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[[-28, -48, 6, 2, -14],\n [-24, -16, -20, -44, 8],\n [16, -9, 33, 41, 26],\n [14, -13, 34, 44, 21],\n [-4, 0, -6, 6, -32]]\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 5x5 matrix:\n[[6, 30, -10, -40, 6],\n [-25, -10, 6, 6, -25],\n [-8, -17, -45, -30, -8],\n [-4, -20, 4, 24, -4],\n [-11, -32, 32, 62, -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[[0, 0, 0, -12, 2],\n [-25, -5, 12, 16, -24],\n [-54, 30, 34, 16, 6],\n [22, -40, -20, 31, -45],\n [-10, -20, 0, 13, -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[[3, -9, -9, 68, -30],\n [-14, 13, 0, 69, -19],\n [18, -18, 19, -22, 15],\n [-2, 11, 6, 57, -19],\n [11, 9, -12, 21, -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[[2, 12, -10, 10, -2],\n [4, 24, -20, 20, -4],\n [-3, -18, 15, -15, 3],\n [-1, -6, 5, -5, 1],\n [5, 30, -25, 25, -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 5x5 matrix:\n[[8, -16, -12, 20, -8],\n [6, -12, -9, 15, -6],\n [10, -20, -15, 25, -10],\n [2, -4, -3, 5, -2],\n [12, -24, -18, 30, -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[[-16, -16, 24, 12, -20],\n [20, 20, -30, -15, 25],\n [0, 0, 0, 0, 0],\n [-20, -20, 30, 15, -25],\n [12, 12, -18, -9, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[6, 12, 10, -20, -24],\n [41, 3, -39, 25, 16],\n [31, -24, -31, 10, -4],\n [-33, 24, 29, -4, 12],\n [-6, -27, 12, -27, -36]]\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, -18, 42, 40, 35],\n [10, 12, 75, 63, 55],\n [8, 47, -21, 5, -9],\n [32, 1, 39, 9, 23],\n [-18, -2, -24, 0, -6]]\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 5x5 matrix:\n[[6, -5, 6, -6, -6],\n [-30, 25, -30, 30, 30],\n [36, -30, 36, -36, -36],\n [30, -25, 30, -30, -30],\n [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[[-18, -18, -6, 6, -20],\n [18, 15, 9, 0, 15],\n [3, 22, -18, -39, 35],\n [0, -9, 9, 18, -15],\n [-9, -3, -9, -9, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 15, -12, 9, 6],\n [-24, -30, 24, -18, -12],\n [-8, -10, 8, -6, -4],\n [4, 5, -4, 3, 2],\n [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[[14, -7, -24, -5, -4],\n [-22, -28, 6, -55, 39],\n [0, 44, 10, 48, -46],\n [-34, -28, 0, -65, 35],\n [-46, 4, 32, -36, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-28, 8, -18, 12, 30],\n [16, -6, 8, -4, -24],\n [28, -8, 18, -12, -30],\n [-24, -1, -28, 26, -12],\n [24, -9, 12, -6, -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[[44, -3, -18, -7, 39],\n [33, -16, -19, -17, 7],\n [43, -9, -12, -8, 36],\n [-12, 43, -8, 23, 29],\n [12, 9, 12, 13, 39]]\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 5x5 matrix:\n[[0, 0, 0, 0, 0],\n [5, -15, -20, 20, -10],\n [-6, 18, 24, -24, 12],\n [-1, 3, 4, -4, 2],\n [4, -12, -16, 16, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-71, -18, -2, -21, -26],\n [-37, -21, 13, 16, -16],\n [-13, 37, -26, -63, 9],\n [-18, 1, -9, -10, 1],\n [-43, 5, -50, -44, 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[[-3, 6, -9, 6, 15],\n [-1, 2, -3, 2, 5],\n [-6, 12, -18, 12, 30],\n [-4, 8, -12, 8, 20],\n [1, -2, 3, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, 2, -7, 16, 14],\n [-24, 31, 5, -25, -19],\n [1, 0, -8, 14, 18],\n [24, -29, -1, 19, 13],\n [70, -69, 19, 42, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, -6, 48, -10, -14],\n [44, -4, 4, 42, 22],\n [24, 15, -36, 25, 38],\n [-22, 48, 0, -22, -26],\n [-25, 2, 42, -22, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-20, -12, 30, 28, 2],\n [-2, 18, -5, -2, 13],\n [8, 24, -20, -16, 12],\n [2, 6, -5, -4, 3],\n [10, -18, -5, -8, -17]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, -8, 25, 16, 35],\n [3, 21, 1, 6, -31],\n [-16, 1, 27, 31, 13],\n [8, 36, -4, -11, -43],\n [42, -16, -22, -24, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, 49, 13, 20, -11],\n [48, 12, 39, 24, -21],\n [-1, -49, -13, -20, 11],\n [-44, 4, -32, -16, 16],\n [-39, 9, -27, -12, 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[[8, -6, 10, 12, -8],\n [4, -3, 5, 6, -4],\n [8, -6, 10, 12, -8],\n [-8, 6, -10, -12, 8],\n [24, -18, 30, 36, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[22, 22, -6, 24, 14],\n [26, 34, -4, 31, 21],\n [33, 39, -8, 40, 23],\n [-2, 16, -7, 26, -6],\n [18, -42, -36, 12, -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 5x5 matrix:\n[[0, 15, 5, 30, 30],\n [0, -18, -6, -36, -36],\n [0, 18, 6, 36, 36],\n [0, -18, -6, -36, -36],\n [0, 9, 3, 18, 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[[1, 3, 2, -4, 2],\n [2, 6, 4, -8, 4],\n [0, 0, 0, 0, 0],\n [-5, -15, -10, 20, -10],\n [6, 18, 12, -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[[-30, -55, 41, -7, -30],\n [-14, -2, -26, -46, -46],\n [-12, -6, 6, -36, -31],\n [9, 9, -16, 20, 15],\n [-3, 15, -12, -42, -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[[-4, 8, 20, 0, 4],\n [49, -33, 20, -34, -35],\n [-26, 16, -12, -10, -33],\n [-19, 33, -10, 48, 36],\n [38, -41, 15, -44, -29]]\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[[-15, 27, -12, 18, 36],\n [-30, 30, -32, 20, 32],\n [24, 0, 28, 5, 5],\n [-19, 25, -22, 20, 24],\n [21, -5, 24, 0, -2]]\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, -8, 41, -12, 13],\n [30, 29, 41, 2, 13],\n [12, 4, -2, 34, -25],\n [-12, 9, 4, -30, 26],\n [26, 20, 29, 12, 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 5x5 matrix:\n[[-4, 10, -6, 0, 4],\n [12, -30, 18, 0, -12],\n [-8, 20, -12, 0, 8],\n [0, 0, 0, 0, 0],\n [12, -30, 18, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-12, 0, 0, 0, -2],\n [-30, 0, 0, 0, -5],\n [-18, 5, -25, -10, -3],\n [30, 0, 0, 0, 5],\n [12, -3, 15, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-3, 3, 5, 0, 6],\n [3, -3, -5, 0, -6],\n [-3, 3, 5, 0, 6],\n [12, -12, -20, 0, -24],\n [-3, 3, 5, 0, 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[[5, -6, -3, 4, 0],\n [20, -24, -12, 16, 0],\n [5, -6, -3, 4, 0],\n [20, -24, -12, 16, 0],\n [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[[-15, 3, 6, 6, 9],\n [-15, 3, 6, 6, 9],\n [-20, 4, 8, 8, 12],\n [-10, 2, 4, 4, 6],\n [-5, 1, 2, 2, 3]]?\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, 15, -44, -4, 16],\n [27, -39, 20, 60, 56],\n [19, 24, -4, 3, -1],\n [-21, 21, -14, -42, -32],\n [0, -4, 6, -13, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-15, -5, 30, 25, 25],\n [6, -20, -60, -2, 16],\n [7, -16, -54, -5, 10],\n [21, 29, 6, -43, -61],\n [12, 26, 24, -28, -46]]\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, 32, -12, 32, 24],\n [40, -20, 48, -20, -42],\n [-5, 10, -6, 10, 9],\n [25, 10, 30, 10, -15],\n [-15, -6, -18, -6, 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[[5, 0, -12, -18, 18],\n [0, 18, 54, 72, -72],\n [-30, -24, 0, 12, -12],\n [5, 6, 6, 6, -6],\n [-5, -18, -42, -54, 54]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, -3, 18, -8, -12],\n [1, 32, 26, 27, 25],\n [-3, -4, 10, -7, -9],\n [-27, -28, -38, -17, -27],\n [11, 26, 42, 15, 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[[-42, -24, 40, 14, -21],\n [-29, 39, 17, -66, -17],\n [-17, -57, 29, 63, -2],\n [5, -37, 5, 46, 4],\n [-24, -14, 26, 17, 7]]?\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, -12, -7, -30, 32],\n [17, 26, 0, 23, -29],\n [-15, -36, -2, -15, 37],\n [4, 26, -29, 50, 8],\n [-33, -16, 9, -38, 8]]?\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[[15, -18, -5, -42, 50],\n [12, -16, 0, -32, 36],\n [18, -28, 10, -44, 44],\n [-6, 10, -5, 14, -13],\n [-12, 20, -10, 28, -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[[30, 34, -21, -40, -6],\n [8, 12, 16, -4, 12],\n [5, 15, -49, 23, -62],\n [-14, -22, -51, 4, -38],\n [-7, -5, 38, -11, 52]]\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 5x5 matrix:\n[[1, 19, -26, -14, 6],\n [42, -28, 15, 15, 40],\n [7, -1, 7, -5, 38],\n [-1, -36, 44, 29, -24],\n [-34, 18, 2, -10, 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[[-30, -40, 2, 19, 10],\n [27, 14, 36, 32, 20],\n [-7, 0, -24, -24, -8],\n [-17, 4, 26, 15, -46],\n [-11, -30, 18, 33, 26]]\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 5x5 matrix:\n[[61, 13, 55, 9, 25],\n [42, -27, 58, -17, -39],\n [-105, -8, -63, 45, -2],\n [17, -14, -10, -52, -35],\n [31, 16, 11, -11, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-17, -27, 38, 10, 16],\n [-40, -23, 45, 31, 18],\n [15, -38, 8, -1, 46],\n [-48, 1, 7, 55, 34],\n [4, 23, -17, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, -30, 18, 12, -12],\n [0, 0, 0, 0, 0],\n [-8, -20, 12, 8, -8],\n [10, 25, -15, -10, 10],\n [12, 30, -18, -12, 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[[8, -2, -4, -4, -8],\n [-2, -8, -10, -4, -2],\n [-7, 23, 31, 16, 17],\n [-21, 18, 27, 18, 27],\n [-22, -3, 0, 6, 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 5x5 matrix:\n[[18, -6, 12, -24, 18],\n [3, -1, 2, -4, 3],\n [-15, 5, -10, 20, -15],\n [0, 0, 0, 0, 0],\n [18, -6, 12, -24, 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[[-3, 7, 4, 12, 12],\n [-3, -21, -10, -23, -16],\n [3, 21, 10, 23, 16],\n [0, 24, 12, 30, 24],\n [15, 17, 6, 5, -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 5x5 matrix:\n[[8, 6, 9, 8, -11],\n [24, -22, 2, 4, -33],\n [2, 15, 21, 25, -14],\n [8, -6, 18, 28, -29],\n [2, 11, 2, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, 6, -20, -22, 4],\n [8, -33, 22, 19, 46],\n [-10, 3, -39, -27, -8],\n [-18, 21, -29, -13, -48],\n [-4, -6, -12, -6, 4]]?\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 5x5 matrix:\n[[3, -6, 0, -12, -21],\n [-14, 9, 12, -26, -28],\n [-9, 5, -1, 12, 26],\n [7, 20, 8, 16, 19],\n [-12, -10, -8, 4, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[21, -11, -54, -14, 32],\n [-9, 18, 18, -24, -42],\n [12, 8, 36, 8, -32],\n [8, 9, -18, -30, -18],\n [10, -16, -72, -16, 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[[4, 6, -12, 2, -12],\n [-10, -15, 30, -5, 30],\n [-6, -9, 18, -3, 18],\n [0, 0, 0, 0, 0],\n [4, 6, -12, 2, -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[[-18, -38, 14, 12, 0],\n [-49, -9, 40, 27, 0],\n [-22, -2, 18, 12, 0],\n [6, -4, -5, -3, 0],\n [0, 0, 0, 0, 0]]\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[[37, -11, 24, 36, 42],\n [30, -28, 10, 36, 32],\n [-6, 30, 18, 6, 18],\n [-48, 45, 0, -69, -39],\n [33, -10, 35, -30, 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 5x5 matrix:\n[[4, -8, -8, 5, -2],\n [-8, 28, 34, -36, 42],\n [0, -12, -18, 22, -30],\n [6, -24, -30, 34, -42],\n [-40, 44, 26, -38, 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[[-12, 7, -38, -18, -25],\n [-4, -1, 0, 54, 19],\n [14, 5, -36, 87, 2],\n [12, 13, -74, 18, -43],\n [14, 11, -66, 51, -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 5x5 matrix:\n[[2, -12, -12, -2, 2],\n [2, -12, -12, -2, 2],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [2, -12, -12, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-36, -13, -4, -66, 22],\n [18, 21, 9, 20, -19],\n [21, -25, -1, -30, 24],\n [18, -8, 21, -38, -14],\n [30, 1, 4, -2, 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[[-17, -37, 18, 41, 27],\n [-58, -32, 36, 18, 58],\n [61, 3, 6, -17, -30],\n [-10, 5, -66, 36, -18],\n [-30, -12, 36, -26, 44]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[32, 9, -44, -12, 2],\n [-6, 12, 14, -15, 18],\n [12, -9, -24, 16, -20],\n [-20, -9, 26, 8, -2],\n [52, -12, -54, -16, -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[[30, 25, -20, -15, -10],\n [6, 5, -4, -3, -2],\n [-12, -10, 8, 6, 4],\n [12, 10, -8, -6, -4],\n [-12, -10, 8, 6, 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[[32, 28, -26, -36, 28],\n [33, 30, -24, -36, 33],\n [-22, -14, 31, 30, 0],\n [-6, 0, 18, 12, 14],\n [18, 18, -9, -18, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[7, -18, 16, 6, 9],\n [-37, -30, -18, -27, 19],\n [-19, -26, -10, -11, 9],\n [-19, 49, 31, 44, -32],\n [-2, 27, 35, 32, -13]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[46, -29, 2, -2, 46],\n [10, -3, -12, -35, 5],\n [-28, 12, -18, -16, -26],\n [-18, -1, 4, 46, -6],\n [64, 1, 65, -10, 57]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-7, 17, 44, -20, 5],\n [18, -10, 51, -32, -14],\n [-9, -29, 1, 41, -8],\n [5, -55, -5, 51, -28],\n [2, -10, -51, 25, -5]]?\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[[-18, 32, -14, 44, -54],\n [-48, 6, -21, 10, -18],\n [12, -26, 8, -36, 42],\n [12, 36, 9, 50, -48],\n [33, 18, 3, 22, -27]]\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[[-12, 4, 16, -12, 24],\n [18, -6, -24, 18, -36],\n [6, -2, -8, 6, -12],\n [15, -5, -20, 15, -30],\n [6, -2, -8, 6, -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[[-6, 1, 6, 15, -33],\n [-44, -21, 46, 1, -25],\n [52, 44, 2, 18, 18],\n [36, 30, -7, -49, 53],\n [12, -13, -40, 19, 29]]\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, -3, 12, -15, 6],\n [-4, -1, 4, -5, 2],\n [12, 3, -12, 15, -6],\n [8, 2, -8, 10, -4],\n [-24, -6, 24, -30, 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 5x5 matrix:\n[[-10, -10, 12, -10, -10],\n [5, 5, -6, 5, 5],\n [-25, -25, 30, -25, -25],\n [10, 10, -12, 10, 10],\n [20, 20, -24, 20, 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[[-6, 3, 9, -12, 6],\n [-6, 3, 9, -12, 6],\n [-12, 6, 18, -24, 12],\n [-2, 1, 3, -4, 2],\n [-10, 5, 15, -20, 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 5x5 matrix:\n[[19, -14, 11, -15, 32],\n [-1, -4, 1, 0, 2],\n [-21, -12, -3, 12, -14],\n [22, -2, 8, -15, 26],\n [26, -4, 10, -18, 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[[-3, 5, 16, -12, -18],\n [1, -6, -1, -22, -7],\n [6, -16, -26, -12, 18],\n [0, -5, 5, -30, -15],\n [-6, 21, 21, 42, -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[[-7, -3, 9, -3, -3],\n [-7, -3, 9, -3, -3],\n [30, 12, -40, 9, 16],\n [13, 3, -21, -6, 15],\n [-5, 3, 15, 21, -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[[1, 6, 0, -10, -9],\n [-16, -8, 0, 20, 20],\n [7, -2, 0, 0, -1],\n [2, 34, 0, -55, -49],\n [-18, 24, 0, -30, -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, 7, -14, 10, -15],\n [-2, -31, 52, -23, 3],\n [20, 29, -24, 37, 27],\n [21, 11, 12, 32, 27],\n [6, -2, 14, 9, 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[[-10, 25, 20, -25, 30],\n [10, -25, -20, 25, -30],\n [4, -10, -8, 10, -12],\n [-4, 10, 8, -10, 12],\n [-10, 25, 20, -25, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[41, -31, -5, -15, 20],\n [-13, -5, 14, -37, 20],\n [19, -25, 1, -15, 8],\n [-39, 18, 3, 35, -34],\n [-17, -34, 13, 11, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0, 0],\n [-12, 6, 18, 12, 0],\n [-20, 10, 30, 20, 0],\n [-24, 12, 36, 24, 0],\n [-12, 6, 18, 12, 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[[-16, -14, -33, 16, 28],\n [4, 9, 33, -15, -29],\n [-12, -5, 0, 1, -1],\n [-4, -13, -51, 23, 45],\n [8, 10, 30, -14, -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[[12, -24, -24, -18, -30],\n [8, -16, -16, -12, -20],\n [6, -12, -12, -9, -15],\n [12, -24, -24, -18, -30],\n [10, -20, -20, -15, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-18, 8, 25, -30, -25],\n [-18, -12, 0, 30, 30],\n [24, -4, -25, 20, 15],\n [-15, 10, 25, -35, -30],\n [-45, -10, 25, 15, 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[[-9, 8, -25, -29, -35],\n [-15, 13, -63, 20, -37],\n [-1, 28, 51, -34, 30],\n [-19, 50, 13, -44, -13],\n [-15, 35, 13, -62, -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[[6, 2, 4, -6, -5],\n [-28, -1, -24, 24, -11],\n [-10, 2, -12, 6, -5],\n [4, 4, -4, -9, 8],\n [10, 14, -8, -21, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, -27, 39, -14, 18],\n [-30, 9, 6, -12, -34],\n [-28, -12, -7, 1, -30],\n [-21, 9, -3, 6, -14],\n [-11, -11, 34, -37, -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, 33, 20, 15, 34],\n [-45, -21, -24, -25, 0],\n [5, -11, 3, -15, 11],\n [69, -23, 15, 4, -22],\n [58, -28, -17, -5, -60]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[14, -42, 13, 50, 25],\n [45, -42, -3, -14, -13],\n [-31, 40, -3, -8, 1],\n [-69, 96, -9, -44, 3],\n [-15, 12, 3, 22, 19]]\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 5x5 matrix:\n[[-5, -1, -8, 13, -2],\n [15, 9, -8, -11, 39],\n [-38, 12, 26, -12, -14],\n [-14, -12, -6, 28, -38],\n [-1, 13, -16, 5, 41]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-36, -40, -34, 0, 6],\n [-22, -32, -20, -12, 24],\n [19, 26, 18, 0, 28],\n [-36, -1, -29, 38, -25],\n [19, 23, 8, 14, 6]]\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, -2, -20, -53, 5],\n [-16, 26, -29, 10, 37],\n [-27, 15, 30, -43, -52],\n [24, -10, -2, 29, 17],\n [11, -15, 51, -19, -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 5x5 matrix:\n[[28, 0, -17, 4, -60],\n [7, -33, 20, 4, 31],\n [-8, 20, -34, 8, -42],\n [1, 15, 41, -36, 63],\n [-17, 21, 11, -8, 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[[10, -22, -6, -4, 6],\n [1, 2, 3, 2, 3],\n [-7, 21, 9, 6, -1],\n [0, -21, -18, -12, -12],\n [5, 3, 9, 6, 11]]\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, 4, 6, 4, -35],\n [-4, -3, 24, -3, -26],\n [0, 5, 0, 5, -30],\n [6, 17, -36, 17, -36],\n [-3, -12, 18, -12, 39]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-13, -3, 5, -35, -19],\n [-3, -21, 27, -45, 3],\n [-15, 5, -5, -25, -25],\n [-8, 21, -26, 20, -20],\n [9, -3, 3, 15, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[28, -24, 2, -16, 28],\n [-19, -6, -55, -3, -39],\n [-34, -1, -44, -1, -42],\n [-7, -16, -15, 3, -9],\n [-44, 20, -14, 4, -37]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, -12, 0, 36, 18],\n [-3, -16, -4, 20, 21],\n [17, 10, 8, 26, -9],\n [-9, -37, -10, 41, 48],\n [-9, -4, -4, -16, 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[[30, -30, -20, 25, -30],\n [12, -12, -8, 10, -12],\n [6, -6, -4, 5, -6],\n [-12, 12, 8, -10, 12],\n [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[[-10, 9, 6, -9, 15],\n [8, 18, -9, 24, -12],\n [12, -12, -7, 10, -18],\n [24, 0, -18, 36, -36],\n [-8, 0, 6, -12, 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[[-15, -25, -10, 25, -5],\n [0, 0, 0, 0, 0],\n [9, 15, 6, -15, 3],\n [12, 20, 8, -20, 4],\n [3, 5, 2, -5, 1]]?\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, 2, 3, 1, 3],\n [-26, -8, -26, 24, 44],\n [26, 12, 26, -10, -14],\n [-27, -10, -27, 19, 33],\n [2, 2, 2, 3, 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, -15, -10, 5, 10],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [-20, 12, 8, -4, -8],\n [25, -15, -10, 5, 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[[-30, 15, 10, 5, -30],\n [-6, 3, 2, 1, -6],\n [24, -12, -8, -4, 24],\n [36, -18, -12, -6, 36],\n [30, -15, -10, -5, 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 5x5 matrix:\n[[-10, 5, 15, 25, -5],\n [4, -2, -6, -10, 2],\n [-2, 1, 3, 5, -1],\n [12, -6, -18, -30, 6],\n [8, -4, -12, -20, 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[[-12, -30, 36, 12, 0],\n [-4, -10, 12, 4, 0],\n [-6, -15, 18, 6, 0],\n [-2, -5, 6, 2, 0],\n [4, 10, -12, -4, 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[[20, -6, 70, -48, -10],\n [-24, -54, 42, 12, -30],\n [-19, -21, -11, 25, -8],\n [20, 24, 4, -20, 4],\n [1, -9, 23, -11, -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[[23, -25, -28, -9, 22],\n [11, -15, -26, -3, 14],\n [31, -27, -10, -15, 22],\n [-16, 18, 22, 6, -16],\n [1, 5, 24, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-19, -6, 37, 4, 5],\n [29, -33, 50, -8, -14],\n [33, -10, -12, -43, -62],\n [-31, 40, -6, 45, 16],\n [-10, -16, 20, 10, 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 5x5 matrix:\n[[12, 15, 9, -6, -9],\n [-8, -30, -6, 24, -14],\n [20, 15, 15, 0, -25],\n [-24, -15, -18, -3, 33],\n [4, 25, 3, -22, 17]]\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, 12, 12, 0, 20],\n [25, 15, 15, 0, 25],\n [-15, -9, -9, 0, -15],\n [-25, -15, -15, 0, -25],\n [-20, -12, -12, 0, -20]]\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, 25, -6, -12, -30],\n [-6, -5, 4, 2, 6],\n [-24, 10, 34, -10, -12],\n [12, -20, -26, 14, 24],\n [30, 25, -20, -10, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 4, -12, -8, -8],\n [-4, -14, 18, -16, -8],\n [4, 16, -24, 12, 4],\n [-7, -24, 30, -29, -15],\n [4, 12, -12, 20, 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[[21, -27, -15, -27, 36],\n [-20, -10, 9, 14, 31],\n [-34, -2, 15, 28, 26],\n [32, -24, -22, -36, 24],\n [-38, -4, 21, 32, 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 5x5 matrix:\n[[6, -5, -2, 1, 4],\n [-36, 30, 12, -6, -24],\n [12, -10, -4, 2, 8],\n [18, -15, -6, 3, 12],\n [-24, 20, 8, -4, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[14, 18, -28, -12, 14],\n [16, 24, -29, -12, 16],\n [9, 15, -15, -6, 9],\n [-8, -24, 4, 0, -8],\n [17, 31, -26, -10, 17]]\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[[6, 6, -18, -18, 36],\n [3, 3, -9, -9, 18],\n [5, 5, -15, -15, 30],\n [2, 2, -6, -6, 12],\n [-1, -1, 3, 3, -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[[-24, 21, -12, -27, -15],\n [-12, -6, -24, -18, -6],\n [28, -19, 20, 33, 17],\n [-7, 2, -8, -9, -4],\n [-40, 13, -44, -51, -23]]\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, 4, -17, -5, -18],\n [32, 8, -44, 14, 12],\n [13, 2, -3, -11, -26],\n [10, 1, -11, 7, 12],\n [-8, -3, 21, -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[[-3, -4, -2, 5, 3],\n [30, 3, -19, -37, 10],\n [-10, -42, -54, 8, 30],\n [-40, -24, -18, 32, -6],\n [8, 1, -4, -9, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[23, 59, 80, 42, 48],\n [-54, -24, -21, -28, -31],\n [-17, -21, -6, 12, 0],\n [64, 60, 68, 19, 39],\n [18, 19, 7, -5, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 24, -24, 36, -24],\n [-3, 12, -12, 18, -12],\n [-3, 12, -12, 18, -12],\n [-4, 16, -16, 24, -16],\n [2, -8, 8, -12, 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[[-15, -16, 0, -55, 35],\n [-11, -14, -17, 5, 3],\n [-3, -6, -21, 45, -21],\n [-26, -32, -32, -10, 18],\n [-1, 0, 8, -25, 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[[-6, 18, 0, 12, 3],\n [-14, 2, 8, 36, 7],\n [-12, 26, 2, 26, 6],\n [2, -46, 8, 4, -1],\n [-8, 24, 0, 16, 4]]\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, 16, -4, -20, 8],\n [-16, -16, 4, 20, -8],\n [-8, -8, 2, 10, -4],\n [8, 8, -2, -10, 4],\n [24, 24, -6, -30, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-5, -15, 30, -30, -10],\n [-5, -15, 30, -30, -10],\n [3, 9, -18, 18, 6],\n [-4, -12, 24, -24, -8],\n [-4, -12, 24, -24, -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[[11, -12, -21, 8, -8],\n [10, 0, -6, 8, -16],\n [-29, 3, 21, -23, 44],\n [16, 3, -6, 13, -28],\n [21, 3, -9, 17, -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[[2, 32, 24, -6, 22],\n [21, -28, 68, -35, 41],\n [-54, 26, -68, 30, -10],\n [42, 1, -6, 8, -22],\n [-19, 41, 4, 3, 9]]?\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 5x5 matrix:\n[[4, -12, -2, -6, -8],\n [-10, 30, 5, 15, 20],\n [4, -12, -2, -6, -8],\n [8, -24, -4, -12, -16],\n [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[[4, -2, 12, -12, -10],\n [7, -6, 35, -31, -28],\n [-8, 4, -24, 24, 20],\n [34, -2, 18, -42, -22],\n [-2, 6, -34, 26, 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[[-4, 26, 2, -28, -32],\n [-6, 21, -3, -22, -28],\n [2, -31, -7, 34, 36],\n [-4, 17, -1, -18, -22],\n [0, -18, -6, 20, 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[[-16, -21, 34, 12, -6],\n [18, 31, -20, 32, -22],\n [21, -4, -39, -12, 1],\n [13, -5, -24, 5, -6],\n [7, 31, -7, 36, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 22, 22, -11, -33],\n [-25, -20, -41, -37, 22],\n [-8, 16, 2, -21, -11],\n [-4, 18, 32, 1, -43],\n [3, 4, -3, -2, 7]]\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, -6, 2, 12, -4],\n [15, -15, 5, 30, -10],\n [0, 0, 0, 0, 0],\n [-6, 6, -2, -12, 4],\n [9, -9, 3, 18, -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 5x5 matrix:\n[[46, 23, 46, -16, 20],\n [32, 26, 6, 12, 1],\n [0, -16, 20, -14, 0],\n [8, 8, -32, 38, -30],\n [-8, -24, 6, -3, -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[[18, -18, 30, -24, -6],\n [9, -24, 27, -27, -15],\n [9, -4, 11, -7, 1],\n [9, 11, -1, 8, 13],\n [3, 27, -19, 26, 23]]\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[[-26, -6, 20, 10, -34],\n [32, 1, -4, -8, -3],\n [-44, -16, 30, -22, -30],\n [0, -14, -3, -43, 29],\n [-26, 9, -2, 34, -1]]?\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, 15, -6, 15, -6],\n [12, -20, 8, -20, 8],\n [9, -15, 6, -15, 6],\n [0, 0, 0, 0, 0],\n [-18, 30, -12, 30, -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[[4, 20, 24, 4, -12],\n [-2, -9, -10, -1, 3],\n [-4, -14, -12, 2, -6],\n [5, 29, 38, 9, -27],\n [4, 17, 18, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, 12, -20, 16, -24],\n [-8, 12, -20, 16, -24],\n [8, -12, 20, -16, 24],\n [6, -9, 15, -12, 18],\n [-10, 15, -25, 20, -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 5x5 matrix:\n[[-11, 14, -19, -22, -16],\n [6, -44, 24, 37, -14],\n [0, 48, -18, -33, 30],\n [3, -14, 9, 13, -2],\n [-16, -16, -14, -7, -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[[9, 18, -6, 15, 18],\n [-15, -30, 10, -25, -30],\n [9, 18, -6, 15, 18],\n [6, 12, -4, 10, 12],\n [-9, -18, 6, -15, -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[[-20, -20, 14, 11, -9],\n [-15, 18, 15, 18, 9],\n [-30, -2, 18, 20, 1],\n [-5, 50, 11, 19, 24],\n [55, -10, -61, -59, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-21, 11, 18, -34, 14],\n [15, -16, -18, 29, -16],\n [6, -35, 6, 13, 0],\n [-18, -44, 39, -26, 23],\n [-18, 18, 0, -24, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[5, 1, -1, 3, -5],\n [-5, -1, 1, -3, 5],\n [-15, -3, 3, -9, 15],\n [-15, -3, 3, -9, 15],\n [5, 1, -1, 3, -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[[-12, -24, 36, 0, 12],\n [36, 8, -12, 24, -36],\n [-42, -4, 6, -30, 42],\n [-60, 0, 0, -45, 60],\n [-42, -12, 18, -27, 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[[-10, 7, -17, -10, -29],\n [41, 55, -5, 5, 19],\n [14, 65, -4, 16, -17],\n [0, 10, -33, -18, -36],\n [-63, -11, 28, 31, -44]]\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, 15, -9, 18, 12],\n [8, 20, -12, 24, 16],\n [0, 0, 0, 0, 0],\n [2, 5, -3, 6, 4],\n [-12, -30, 18, -36, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-15, -15, 12, 12, -3],\n [-5, -5, 4, 4, -1],\n [-30, -30, 24, 24, -6],\n [-10, -10, 8, 8, -2],\n [-30, -30, 24, 24, -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[[-4, 5, 7, 6, 14],\n [32, -19, -19, 32, -1],\n [-24, 27, 47, -32, -9],\n [-12, 6, 6, -21, -12],\n [20, -13, -15, 22, 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[[2, -8, -32, 55, -22],\n [-1, 16, 32, 14, 39],\n [-8, -3, 3, 65, -6],\n [-14, 11, -3, -45, 14],\n [-4, 18, 14, -16, 36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, -6, -2, 6, -6],\n [-4, 3, 1, -3, 3],\n [0, 0, 0, 0, 0],\n [-12, 9, 3, -9, 9],\n [16, -12, -4, 12, -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[[20, -9, 26, -5, 8],\n [-28, -9, -4, -20, 5],\n [12, 21, -24, 30, -15],\n [-8, -14, 16, -20, 10],\n [40, 6, 16, 20, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-4, 10, 9, -6, 10],\n [24, -6, 9, 9, -24],\n [-16, 16, 8, -12, 24],\n [-24, 24, 12, -18, 36],\n [-24, -12, -30, 0, 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[[8, -4, -12, -16, 24],\n [-13, -36, 33, 19, -34],\n [6, 60, 20, 14, 0],\n [-14, -42, 30, -4, -8],\n [-6, -31, -17, -7, -4]]\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, -5, -5, 10, 30],\n [20, -4, -4, 8, 24],\n [-5, 1, 1, -2, -6],\n [-10, 2, 2, -4, -12],\n [30, -6, -6, 12, 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[[10, -4, 0, -14, -28],\n [0, 8, 10, -6, 0],\n [-20, -12, -25, 43, 56],\n [55, -10, -26, -4, 10],\n [-10, 8, 21, -21, -36]]\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, -18, -24, 5, 8],\n [0, -29, -23, 5, 7],\n [56, 55, -23, -12, 21],\n [20, 50, 33, 7, 2],\n [-10, 16, 20, 1, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[34, -10, 12, 10, -30],\n [-12, 0, -8, -2, 12],\n [-36, 0, -24, -6, 36],\n [-7, -5, -10, 1, 9],\n [36, 0, 24, 6, -36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[34, 13, -28, -1, -50],\n [37, 29, -4, 6, -38],\n [-3, 3, 14, 1, 12],\n [-14, 13, 10, 18, 16],\n [-15, -3, 24, 0, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, 33, 18, 13, -61],\n [-9, -19, -10, 19, 41],\n [-32, 15, 4, 49, -26],\n [34, 1, 8, 35, 24],\n [-37, 2, -2, 46, -15]]\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[[13, -7, 8, -30, 3],\n [-9, -1, -12, -8, -6],\n [17, 9, 36, 20, 12],\n [5, 29, 60, 24, 6],\n [2, -30, -56, -8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-27, -15, 21, 39, 0],\n [45, -10, -4, -37, -9],\n [-28, -7, 17, 22, -9],\n [28, -7, -6, -5, 11],\n [55, -20, -5, -10, 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[[-46, 7, -5, 52, 1],\n [52, 33, 42, -10, -10],\n [-6, -7, 6, 13, -1],\n [6, -23, -11, -24, 3],\n [20, 21, 6, -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[[16, -4, 27, -9, 42],\n [25, 13, 32, 20, 18],\n [-4, -6, -16, -40, 9],\n [27, 42, 29, 42, 9],\n [-16, 2, -10, 4, 6]]\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, 33, 27, 33, 15],\n [-25, -11, 14, 27, 68],\n [-23, 27, -2, -3, 10],\n [4, -33, 26, -17, -15],\n [-19, -15, 2, -9, 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 5x5 matrix:\n[[0, -30, -30, 24, -30],\n [0, -5, -5, 4, -5],\n [0, 15, 15, -12, 15],\n [0, -25, -25, 20, -25],\n [0, -15, -15, 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[[-4, 20, -18, 24, 38],\n [-14, 12, 12, 9, 9],\n [-42, 2, 28, 35, 11],\n [22, -6, -4, -29, -21],\n [-8, 6, 11, 1, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-18, -26, -6, 2, 8],\n [12, 9, 14, -3, -2],\n [6, -28, 46, -8, 12],\n [12, 24, -4, 0, -8],\n [-9, -13, -3, 1, 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[[-15, 1, 18, -1, -3],\n [-29, -5, 14, 5, -37],\n [-19, 5, 34, -5, 13],\n [-24, -4, 12, 4, -30],\n [-16, 0, 16, 0, -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 5x5 matrix:\n[[-3, 48, 21, 45, -7],\n [3, -48, -21, -45, 7],\n [-1, 42, 33, 41, 2],\n [-3, 42, 15, 39, -8],\n [-4, 24, -12, 20, -16]]\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[[-6, -6, -21, 2, -15],\n [-24, -6, -9, 11, -3],\n [-11, -24, -2, -7, 22],\n [21, 6, -37, -5, -43],\n [-50, -30, 47, 7, 77]]\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, -6, 18, -30, 36],\n [-25, -5, 15, -25, 30],\n [-25, -5, 15, -25, 30],\n [25, 5, -15, 25, -30],\n [25, 5, -15, 25, -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[[29, -20, 28, -10, 7],\n [-12, 28, -4, 36, 32],\n [-2, 22, 6, 34, 36],\n [5, -16, 0, -22, -21],\n [17, -5, 19, 5, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 0, 16, 40, -16],\n [29, -13, 41, 35, 1],\n [0, 9, -12, -48, 30],\n [10, 0, -6, -26, 14],\n [-39, 16, 5, 19, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-15, 3, 6, 3, 15],\n [-25, 5, 10, 5, 25],\n [20, -4, -8, -4, -20],\n [10, -2, -4, -2, -10],\n [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[[-32, -30, -1, -8, 10],\n [-22, -25, -9, -9, 13],\n [10, 25, 30, 15, -25],\n [-30, -25, 5, -5, 5],\n [-8, -20, -24, -12, 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[[-24, 18, -15, 9, -3],\n [-11, 29, 7, -9, -2],\n [37, -13, 50, -35, 0],\n [-2, 42, -8, 9, -23],\n [13, 1, 3, 5, -19]]\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 5x5 matrix:\n[[-4, -16, 16, 16, 24],\n [3, 12, -12, -12, -18],\n [5, 20, -20, -20, -30],\n [-4, -16, 16, 16, 24],\n [5, 20, -20, -20, -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[[0, -1, 10, -16, 4],\n [23, 19, 9, -3, 16],\n [11, 10, -7, 17, 2],\n [-20, -22, 10, -20, -26],\n [-10, -12, -10, 18, -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[[-28, -37, 26, 45, 31],\n [-2, -30, -33, -28, 7],\n [-2, -15, -31, -33, 0],\n [-4, -2, 4, 26, 20],\n [8, -28, -7, -30, -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[[-20, -30, 20, -22, 34],\n [-1, 3, 4, 4, -1],\n [-19, -33, 16, -26, 35],\n [-29, -3, 56, 14, 25],\n [16, -3, -34, -13, -11]]\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[[7, -18, -12, 16, -7],\n [-46, -20, -28, -36, -20],\n [-6, -60, -48, 24, -30],\n [-5, 38, 28, -24, 17],\n [31, 2, 10, 30, 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[[-28, -24, -28, 0, -24],\n [30, 23, 31, -1, 27],\n [45, -36, -17, -60, 34],\n [14, 2, -24, -6, 46],\n [10, 14, 20, 6, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, -16, 0, -8, 0],\n [6, 30, -6, 15, 6],\n [-6, -22, -2, -11, 2],\n [4, 4, 12, 2, -12],\n [-4, -12, -4, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, 23, 28, 9, 14],\n [4, 19, 23, 9, 13],\n [6, 26, 32, 6, 12],\n [4, 22, 26, 18, 22],\n [-4, -22, -26, -18, -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[[-8, 10, -17, -7, -5],\n [-26, 28, -38, -10, -8],\n [2, 2, -13, -11, -7],\n [34, -32, 32, 0, 2],\n [33, -30, 27, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[9, 44, -1, 1, 13],\n [33, -2, -27, 27, 1],\n [3, -32, -7, 7, -9],\n [39, 4, -31, 31, 3],\n [21, 28, -13, 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[[3, 9, 3, 12, 12],\n [2, 6, 2, 8, 8],\n [-2, -6, -2, -8, -8],\n [1, 3, 1, 4, 4],\n [5, 15, 5, 20, 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[[27, 1, -18, 5, 55],\n [-22, 7, 6, -12, -39],\n [11, -12, -13, -7, 5],\n [24, -39, -79, -60, -16],\n [-2, 22, -13, -8, 19]]\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[[-30, -26, 28, -29, 30],\n [-22, -9, 32, 1, 10],\n [59, -25, -101, 18, 1],\n [1, -2, -7, -6, 3],\n [-29, -9, 43, 14, 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[[14, 20, -4, 6, 22],\n [5, 4, 2, 5, 5],\n [9, 16, -6, 1, 17],\n [15, 1, 18, 25, 5],\n [30, 35, 0, 20, 40]]?\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, 27, 22, 8, 24],\n [-3, -23, -1, -4, -14],\n [-2, -22, 2, -4, -16],\n [-50, 3, 16, 8, 36],\n [52, -23, -30, -12, -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[[0, 0, 0, 0, 0],\n [-5, 25, 20, -30, -15],\n [-4, 20, 16, -24, -12],\n [2, -10, -8, 12, 6],\n [-6, 30, 24, -36, -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[[3, 4, -3, 28, 25],\n [-13, 32, -13, 26, 34],\n [8, -47, 3, -56, -54],\n [13, -33, 14, -30, -38],\n [4, -33, -3, -36, -32]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 2, 3, -5, 5],\n [0, -4, -6, 10, -10],\n [0, 12, 18, -30, 30],\n [0, -10, -15, 25, -25],\n [0, -6, -9, 15, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[7, -11, 49, -13, 48],\n [38, -10, 32, 6, 16],\n [0, -38, 23, 22, 9],\n [17, -5, 3, 9, -6],\n [-41, 5, -39, 1, -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 5x5 matrix:\n[[12, -4, -8, -4, 24],\n [-6, 2, 4, 2, -12],\n [-15, 5, 10, 5, -30],\n [-12, 4, 8, 4, -24],\n [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[[-16, -2, -20, 32, -26],\n [29, 9, 19, 8, -31],\n [20, -10, 30, -46, 7],\n [8, 2, 4, 8, -18],\n [-14, -11, -2, -26, 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 5x5 matrix:\n[[53, -18, -23, -5, -56],\n [59, -14, -40, -33, -37],\n [-5, 41, -13, 12, 19],\n [37, -7, -17, -1, -38],\n [-23, -4, 40, 6, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[19, 13, -28, -23, 43],\n [-4, -24, -6, 8, -16],\n [6, 26, 22, -18, 18],\n [4, 25, -32, 4, 32],\n [-10, 0, 7, 0, 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[[19, 11, 6, 46, -32],\n [12, 8, 4, 32, -24],\n [-11, -4, -3, -20, 10],\n [-18, -2, -4, -20, 0],\n [11, -1, 2, 6, 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[[-24, -31, -18, -25, 10],\n [12, 17, 0, 14, 7],\n [24, 35, -6, 29, 22],\n [-24, -32, -12, -26, 2],\n [4, 9, -20, 8, 29]]\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 5x5 matrix:\n[[8, 5, 4, -16, 9],\n [12, -5, 4, -35, 4],\n [5, -25, 37, 29, -15],\n [-48, 87, -61, 2, 53],\n [20, -12, 25, 26, -6]]\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[[11, -11, 9, 12, -5],\n [2, 46, -8, -12, 6],\n [6, -6, -13, 10, -2],\n [11, 25, 27, 0, -23],\n [-14, -84, 48, 2, 16]]\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[[15, -34, -32, -9, -36],\n [-12, 7, 19, 9, 22],\n [33, 16, 17, -3, -12],\n [51, -23, -4, 14, -32],\n [-6, -30, 36, 28, 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[[5, 2, 20, -33, 8],\n [-15, -31, 15, -15, -6],\n [-2, 15, -27, 8, 32],\n [31, 38, 16, -3, -20],\n [9, 1, 29, -31, -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[[-28, 8, -3, -18, 8],\n [4, -14, 4, 14, -4],\n [-12, -12, 3, 6, 0],\n [-42, -15, 3, -3, 6],\n [54, 9, -1, 13, -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[[-12, -18, -18, 21, 67],\n [-15, -22, -23, 4, 57],\n [-6, 16, 14, 2, -24],\n [-7, 6, 4, -9, -17],\n [32, 4, 9, -7, -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[[6, 18, -15, 0, 9],\n [-8, -24, 20, 0, -12],\n [8, 24, -20, 0, 12],\n [4, 12, -10, 0, 6],\n [6, 18, -15, 0, 9]]\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[[17, 26, -31, 10, 3],\n [-39, 6, 9, -3, 2],\n [-20, -70, 54, -36, -14],\n [9, -2, -19, -51, -16],\n [57, -14, -7, 1, -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 5x5 matrix:\n[[30, -46, -30, -4, 36],\n [-15, 13, 9, 4, -18],\n [-30, 61, 39, 1, -36],\n [-20, 29, 19, 3, -24],\n [30, -26, -18, -8, 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[[0, 0, 0, 0, 0],\n [-20, 0, -12, 8, 12],\n [20, 0, 12, -8, -12],\n [-10, 0, -6, 4, 6],\n [25, 0, 15, -10, -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[[-68, -1, 2, -6, -60],\n [-20, 40, 0, 40, 35],\n [-42, 15, -1, 12, -13],\n [-4, -18, -4, -20, -19],\n [20, -15, 0, -14, -3]]?\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[[-8, 23, -6, -7, 3],\n [-4, 7, 0, -1, 3],\n [14, -2, -15, -9, -18],\n [22, -7, -21, -12, -27],\n [-24, 42, 0, -6, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[21, 6, -3, 3, 24],\n [20, -2, 16, 10, 16],\n [24, 4, 4, 4, 20],\n [-4, -4, 8, 0, -12],\n [-12, -3, 0, 1, -6]]?\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, -16, -15, -3, -10],\n [4, 30, -10, 6, 19],\n [0, 40, -24, 24, 46],\n [-34, -22, 28, -36, -30],\n [-41, -20, 1, 5, 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[[-4, -10, 8, -12, 4],\n [32, 60, -9, 41, -2],\n [-14, -27, 6, -20, 2],\n [0, 12, -33, 33, -18],\n [20, 30, 15, 5, 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 5x5 matrix:\n[[30, 0, 30, -6, -9],\n [22, -12, 1, 31, 72],\n [-20, 8, -19, 9, 16],\n [-2, 4, 8, -18, -40],\n [17, -10, 5, 14, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-48, -54, -6, -6, 12],\n [-32, -36, -4, -4, 8],\n [16, 18, 2, 2, -4],\n [23, 21, -8, 4, 7],\n [-21, -9, 30, -6, -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[[19, 16, 13, 41, 32],\n [-3, 33, 2, 36, -8],\n [-9, -18, -3, -32, -15],\n [27, -13, 18, 19, 51],\n [-27, 50, -18, 62, -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[[-15, 12, 27, 39, 3],\n [-8, 2, 6, 10, -4],\n [21, -8, -21, -33, 7],\n [-32, -3, 3, 13, -30],\n [23, 8, 9, 5, 29]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-11, -39, -2, -5, 29],\n [-60, -24, -10, 56, -25],\n [31, 39, -1, -13, -15],\n [-18, -6, -1, 16, -8],\n [-11, -3, 4, 7, -4]]\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 5x5 matrix:\n[[-30, -11, -8, 12, -7],\n [-44, -15, -30, 24, -9],\n [12, 38, 8, -12, 34],\n [12, -3, -4, -1, -4],\n [42, 27, -24, -6, 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[[-1, -29, -22, 6, 34],\n [25, 16, -25, -14, 34],\n [-32, -42, -16, 39, 34],\n [17, 9, -8, -15, 8],\n [19, 0, -15, -16, 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[[5, 1, -6, 1, 5],\n [15, 3, -18, 3, 15],\n [-30, -6, 36, -6, -30],\n [0, 0, 0, 0, 0],\n [20, 4, -24, 4, 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[[7, -16, -8, -14, 14],\n [-12, 12, 2, 8, -12],\n [66, -12, 30, 12, 24],\n [2, -20, -14, -20, 16],\n [34, -16, 8, -4, 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[[-3, 50, 13, -4, 21],\n [6, 41, 8, 6, 26],\n [-36, -4, 42, 50, 24],\n [-30, -48, 22, 36, -6],\n [-6, 45, 16, 2, 22]]\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[[5, -8, 0, -8, 14],\n [-15, -18, -21, -4, -14],\n [-30, 12, -18, 24, -60],\n [30, 24, 36, 0, 36],\n [-30, -12, -30, 8, -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[[16, 3, 45, -25, 37],\n [40, -17, 14, -35, -12],\n [17, 15, 14, -23, 14],\n [34, 30, -30, -34, -26],\n [-9, 18, 15, 0, 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[[48, -18, 32, -12, 34],\n [11, 56, -9, 34, 5],\n [1, 9, -3, -4, -18],\n [-24, 3, -2, 6, -7],\n [-10, 19, -16, 16, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-41, -32, 45, 14, -50],\n [4, 6, -8, 24, 2],\n [-12, -9, 5, 38, 5],\n [-21, -12, 2, -10, -25],\n [11, 22, -34, 54, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[33, -22, -40, -12, -16],\n [-53, -68, 14, 59, 45],\n [35, 29, -36, -38, -33],\n [20, 82, 6, -53, -41],\n [-69, 9, 38, 15, 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[[-45, -36, 5, 28, 6],\n [32, 14, -9, 13, 26],\n [-14, 10, 3, 25, -10],\n [-48, -12, 31, 35, -42],\n [-20, -8, 24, 9, -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[[33, -42, -27, -11, 36],\n [0, -1, -1, 56, 6],\n [-2, -9, -29, 26, -4],\n [36, -41, 1, -32, 62],\n [-28, 40, 21, 2, -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 5x5 matrix:\n[[-11, -2, -11, -2, -8],\n [30, 21, 30, 3, 30],\n [19, 0, 19, 4, 12],\n [-6, -8, -6, 0, -8],\n [-18, 14, -18, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-20, 20, -24, 20, -20],\n [-5, 5, -6, 5, -5],\n [-20, 20, -24, 20, -20],\n [-15, 15, -18, 15, -15],\n [-25, 25, -30, 25, -25]]\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 5x5 matrix:\n[[22, 10, 15, 19, -2],\n [22, 10, 15, 19, -2],\n [-24, -6, 45, 21, 12],\n [6, 4, 20, 16, 2],\n [24, 6, -45, -21, -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[[30, 6, -42, 5, 20],\n [49, -34, 34, 50, 66],\n [-12, -29, 3, -21, -24],\n [12, 0, -82, -38, -24],\n [-1, 9, -25, -12, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-30, -4, -6, -58, 23],\n [14, 7, -1, 60, -18],\n [-11, -14, 21, 5, -19],\n [51, -9, 22, 5, -19],\n [14, 30, -42, 50, 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[[-21, 26, -12, -1, -2],\n [-66, -12, -24, 30, 48],\n [-5, -22, 12, -21, 0],\n [8, -14, 10, -12, -4],\n [35, 12, 6, -1, -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[[-13, -30, -4, 6, -33],\n [32, 0, -42, -16, 10],\n [-29, 6, 24, -2, -16],\n [-34, 48, 32, -13, 4],\n [-19, -6, -14, -24, -36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, -18, 48, 31, -26],\n [-21, 41, -28, -22, -10],\n [34, -30, -42, -17, 44],\n [4, -11, -36, -14, 10],\n [-29, 23, -38, -19, -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[[-8, 25, 11, -46, 19],\n [-12, -32, -14, 15, 39],\n [-18, -33, 3, 27, 17],\n [4, 26, 10, 42, 6],\n [4, 13, 15, 24, -29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, 6, 8, 10, -12],\n [0, 0, 0, 0, 0],\n [30, -15, -20, -25, 30],\n [18, -9, -12, -15, 18],\n [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[[30, -40, -18, 23, 4],\n [-40, 11, 18, 21, -25],\n [-19, 29, -42, 13, 18],\n [26, -27, 32, -10, -7],\n [30, 10, 14, -29, 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[[-2, -6, -8, 10, -12],\n [1, 3, 4, -5, 6],\n [0, 0, 0, 0, 0],\n [2, 6, 8, -10, 12],\n [5, 15, 20, -25, 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[[19, -8, 39, 26, 17],\n [5, 8, -11, 12, 7],\n [11, -7, 31, 19, 12],\n [-2, -8, 22, 4, 2],\n [3, 3, -5, 3, 2]]\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 5x5 matrix:\n[[-1, 4, 7, 6, 7],\n [50, 6, 4, -13, 29],\n [0, 20, -15, -25, -20],\n [2, 34, 11, -4, 9],\n [-8, -36, -6, 12, -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[[0, 0, 0, 0, 0],\n [-15, 25, 0, -25, 10],\n [3, -5, 0, 5, -2],\n [18, -30, 0, 30, -12],\n [-18, 30, 0, -30, 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[[-6, 12, 0, 7, -16],\n [-4, 8, -10, 3, -4],\n [4, -8, 10, -3, 4],\n [-5, 10, 13, 8, -22],\n [-6, 12, 18, 10, -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[[-35, -15, 36, -3, 10],\n [34, -10, 0, 2, -2],\n [21, 31, 1, 34, -29],\n [0, 30, -24, 12, -15],\n [13, 33, -20, 21, -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[[-8, 8, 4, -12, -12],\n [4, -4, -2, 6, 6],\n [10, -10, -5, 15, 15],\n [-6, 6, 3, -9, -9],\n [2, -2, -1, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[61, -32, 10, 26, -20],\n [-13, -16, -28, 41, -30],\n [-29, -26, -6, 15, 16],\n [55, 31, 9, -31, -9],\n [12, 53, 11, -54, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[41, 10, 7, 21, 16],\n [-12, 1, -38, -30, -32],\n [10, -16, 40, 45, 36],\n [7, 0, 35, 24, 28],\n [41, 24, 11, 9, 16]]\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, -12, 24, -6, 60],\n [30, 39, -16, 3, 6],\n [4, -10, 3, 15, -18],\n [24, -6, -8, 29, -54],\n [42, 11, 19, 28, -18]]\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, -7, -21, -13, 13],\n [0, 7, -6, 37, -13],\n [37, -11, -57, 7, -33],\n [-21, -11, 20, -1, -41],\n [-23, -2, 34, -24, 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[[26, -6, -24, 12, 18],\n [-41, 6, 12, 0, -18],\n [35, -1, -12, 2, 19],\n [23, -16, -36, 20, 16],\n [33, 21, -12, 6, 33]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[16, -4, 0, -30, -16],\n [-8, 2, 0, 15, 8],\n [24, -6, -36, -15, -12],\n [-16, 4, 36, 0, 4],\n [20, -5, -3, -35, -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[[-9, -46, -9, 7, 56],\n [-12, -48, -12, 6, 60],\n [5, -30, 5, 10, 30],\n [0, 20, 0, -5, -22],\n [-18, 8, -18, -11, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-9, 34, 9, -16, 39],\n [-20, 4, 16, 0, -16],\n [-1, 13, -60, -48, -12],\n [-50, 40, -10, -40, 40],\n [-36, -13, 3, 4, -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 5x5 matrix:\n[[15, 5, -15, -15, 30],\n [12, 4, -12, -12, 24],\n [0, 0, 0, 0, 0],\n [9, 3, -9, -9, 18],\n [-9, -3, 9, 9, -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[[-43, 7, 42, 25, 17],\n [-16, 6, 4, -1, 25],\n [28, 58, -24, 30, -48],\n [-16, 33, 8, 32, -5],\n [-47, -19, 12, 10, 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 5x5 matrix:\n[[8, 0, 8, -8, 8],\n [8, 0, 8, -8, 8],\n [-8, 0, -8, 8, -8],\n [-12, 0, -12, 12, -12],\n [-12, 0, -12, 12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-20, -1, 0, 26, -53],\n [10, -11, -50, 23, 15],\n [20, 48, -2, 43, -94],\n [45, 13, -40, 15, 24],\n [-5, -26, 4, -31, 65]]?\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[[3, 2, 1, 5, -5],\n [-9, -6, -3, -15, 15],\n [-6, -4, -2, -10, 10],\n [-12, -8, -4, -20, 20],\n [-12, -8, -4, -20, 20]]\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[[-25, 40, 20, -20, 20],\n [-9, 0, 0, 6, 6],\n [10, -4, -2, -3, -7],\n [-27, 36, 18, -15, 21],\n [18, -24, -12, 10, -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 5x5 matrix:\n[[-18, 34, 0, 48, 42],\n [2, -14, 4, -20, -26],\n [-11, 4, 23, 8, 8],\n [5, -27, 10, -38, -45],\n [14, -4, -26, -8, -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[[35, 5, -15, 27, -16],\n [19, -35, 45, -25, 25],\n [1, 49, -54, 26, -41],\n [9, -20, -21, 49, 11],\n [-26, 19, -9, 41, -26]]\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, -20, -20, -4, 8],\n [0, -5, -5, -1, 2],\n [0, -10, -10, -2, 4],\n [0, -25, -25, -5, 10],\n [0, -5, -5, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-36, -24, -12, -24, 30],\n [18, 2, 8, 20, -18],\n [-6, 4, -2, -20, 17],\n [-12, -34, 0, 20, -5],\n [24, -6, 14, 24, -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[[-12, -33, -10, 12, 36],\n [-3, 10, -25, 6, -29],\n [42, 30, -29, 46, 1],\n [-21, -19, 20, -24, 8],\n [39, 23, 42, 4, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-15, 30, 0, 20, 30],\n [-6, -30, 36, -16, -54],\n [-9, 11, 6, 8, 7],\n [3, -34, 24, -20, -50],\n [18, -29, -6, -20, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[7, 24, 7, 12, 8],\n [-14, -19, -1, -16, -13],\n [-23, -4, 11, -20, -18],\n [1, 20, 2, 24, -5],\n [-12, -26, -1, -28, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[16, -24, -20, 24, -15],\n [16, -34, -19, 31, -15],\n [-56, 14, 61, -29, 42],\n [3, 18, 12, -18, 9],\n [6, 6, 27, -15, 18]]?\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 5x5 matrix:\n[[0, 0, 0, 0, 0],\n [16, -4, 16, 4, 0],\n [24, -6, 24, 6, 0],\n [8, -2, 8, 2, 0],\n [4, -1, 4, 1, 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[[-10, 10, 30, 20, 10],\n [4, -4, -12, -8, -4],\n [4, -4, -12, -8, -4],\n [-2, 2, 6, 4, 2],\n [2, -2, -6, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[11, -16, 14, 11, -3],\n [12, -12, 9, 6, -6],\n [2, 8, -10, -10, -6],\n [2, 8, -10, -10, -6],\n [-16, 16, -12, -8, 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[[-35, -39, 3, 10, 2],\n [30, 32, -14, 0, 4],\n [-20, -22, 4, 4, 0],\n [15, 17, 1, -6, -2],\n [10, 6, -42, 28, 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[[12, -2, 33, -3, 59],\n [-10, -7, -16, 12, -65],\n [-6, -22, -18, 12, 28],\n [24, -30, -8, 12, -52],\n [40, -38, -2, 10, -40]]\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[[-5, -5, -1, 1, 4],\n [25, 25, 5, -5, -20],\n [-20, -20, -4, 4, 16],\n [0, 0, 0, 0, 0],\n [15, 15, 3, -3, -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[[40, -26, -14, 34, -4],\n [-26, 22, 10, -26, 8],\n [0, 34, 6, -26, 36],\n [45, -25, -15, 35, 0],\n [29, -35, -13, 37, -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[[3, -18, -3, 15, -2],\n [38, -28, -18, 30, -32],\n [26, -16, -12, 18, -22],\n [2, -22, -3, 18, -1],\n [-1, 26, 3, -21, 0]]?\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[[-13, -12, -9, -10, 7],\n [2, -18, -10, 21, 24],\n [21, -23, -19, 40, 31],\n [9, 17, 6, -17, -28],\n [-2, -25, 12, 29, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-29, -6, 33, 23, -24],\n [1, 0, 3, 5, 0],\n [-29, -5, 13, -5, -20],\n [-7, -1, -1, -7, -4],\n [1, 0, 3, 5, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-4, -35, 45, -2, 15],\n [16, -20, 20, -12, 20],\n [0, -32, 40, -4, 16],\n [0, 32, -40, 4, -16],\n [-28, 3, 5, 17, -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[[-6, -3, -3, 4, 3],\n [12, 6, 6, -8, -6],\n [18, 9, 9, -12, -9],\n [0, 0, 0, 0, 0],\n [6, 3, 3, -4, -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[[10, -32, -48, -18, -38],\n [-30, 16, -16, 22, -14],\n [10, -27, -38, -16, -30],\n [-15, 3, -18, 9, -15],\n [-15, 8, -8, 11, -7]]\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 5x5 matrix:\n[[26, -27, 51, 54, 9],\n [-24, -9, -12, -23, 23],\n [-44, 53, -73, -66, -12],\n [46, -23, 48, 47, -18],\n [28, 3, -21, -28, -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 5x5 matrix:\n[[-18, 1, 40, 26, -12],\n [15, -30, -10, -10, -25],\n [6, -7, -8, -6, -4],\n [-9, -27, 42, 24, -39],\n [18, -11, -32, -22, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[5, 1, -1, 7, 31],\n [26, 19, 5, -19, 9],\n [39, -7, 3, -9, -61],\n [-26, 41, -3, -31, -21],\n [-3, 24, -2, -14, 4]]\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[[8, 16, -4, -24, 20],\n [-2, -4, 1, 6, -5],\n [2, 4, -1, -6, 5],\n [-2, -4, 1, 6, -5],\n [2, 4, -1, -6, 5]]\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[[-20, 11, 17, -9, 34],\n [1, -3, -4, 5, -8],\n [19, -8, -13, 4, -26],\n [12, -15, -21, 21, -42],\n [15, 4, 3, -16, 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[[0, 0, 0, 0, 0],\n [12, 0, 0, 18, 18],\n [12, 0, 0, 18, 18],\n [4, 0, 0, 6, 6],\n [12, 0, 0, 18, 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[[9, 36, -5, 2, -7],\n [12, -60, -18, -6, -6],\n [-23, -9, 27, 3, 22],\n [-28, -18, 28, 2, 22],\n [-21, 42, 27, 6, 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[[0, 0, 0, 0, 0],\n [12, 12, 20, 8, 24],\n [-6, -6, -10, -4, -12],\n [9, 9, 15, 6, 18],\n [9, 9, 15, 6, 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[[-15, -6, -1, 8, -3],\n [-7, -21, -10, 15, -17],\n [14, 0, -2, -4, -2],\n [14, 42, 20, -30, 34],\n [-5, -30, -15, 20, -25]]\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, -41, -59, 19, -14],\n [-8, 37, 46, -30, -3],\n [9, 16, 25, -13, 2],\n [20, -11, 4, 32, 32],\n [-27, -8, -17, 17, 5]]\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, 10, 5, 20, -15],\n [-8, 4, 2, 8, -6],\n [-24, 12, 6, 24, -18],\n [8, -4, -2, -8, 6],\n [-24, 12, 6, 24, -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[[-11, -36, 33, -19, 27],\n [29, 49, -21, 11, -49],\n [-12, -14, 10, -15, 3],\n [-21, 2, -18, 5, -53],\n [13, -36, 48, 6, 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[[-12, -13, 16, 24, 24],\n [-1, 45, -1, 26, -10],\n [2, -60, 14, 16, 32],\n [29, 32, -33, -2, -36],\n [-8, -42, 28, -8, 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[[-4, 24, -24, -16, 4],\n [3, -18, 18, 12, -3],\n [4, -24, 24, 16, -4],\n [-4, 24, -24, -16, 4],\n [-2, 12, -12, -8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-10, -4, -2, 12, 4],\n [5, 2, 1, -6, -2],\n [-5, -2, -1, 6, 2],\n [-5, -2, -1, 6, 2],\n [-30, -12, -6, 36, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-40, -14, 8, -32, 36],\n [-30, -15, 12, -18, 24],\n [-20, -10, 8, -12, 16],\n [0, -12, 16, 16, -8],\n [30, 21, -20, 10, -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[[4, 2, 6, 6, 6],\n [-4, -2, -6, -6, -6],\n [24, 12, 36, 36, 36],\n [-24, -12, -36, -36, -36],\n [20, 10, 30, 30, 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 5x5 matrix:\n[[-5, 9, -9, -8, 2],\n [12, -25, 24, 18, -5],\n [-16, -12, 0, -40, 4],\n [-5, 26, -21, -2, 3],\n [-13, 37, -33, -16, 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[[-12, -3, -18, 15, -6],\n [20, 5, 30, -25, 10],\n [-16, -4, -24, 20, -8],\n [-4, -1, -6, 5, -2],\n [-16, -4, -24, 20, -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 5x5 matrix:\n[[5, -8, -6, 6, -33],\n [9, -24, 18, 30, -21],\n [0, -3, 9, 6, 12],\n [-12, 39, -45, -54, 0],\n [4, -4, -12, 0, -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[[0, 24, 20, -12, -24],\n [0, -36, -30, 18, 36],\n [0, -18, -15, 9, 18],\n [0, 12, 10, -6, -12],\n [0, -30, -25, 15, 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, -22, -6, -14, -10],\n [2, 36, 11, 9, -30],\n [-13, 2, 4, 8, -17],\n [-16, 12, 21, -20, -35],\n [-3, -62, -29, 10, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[42, 15, 32, 5, 18],\n [33, 21, 23, -5, 3],\n [3, 3, 1, 1, -45],\n [-1, -15, 3, 13, 36],\n [26, -9, 24, 21, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-47, 9, -49, -10, -23],\n [31, -27, 28, -38, 18],\n [-32, 5, -39, 18, -19],\n [-30, -12, -27, 0, -6],\n [2, 57, 26, -18, 0]]\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[[-7, -13, 4, 10, -10],\n [9, -10, 7, -25, -26],\n [-12, -27, 9, 15, -24],\n [-12, -27, 9, 15, -24],\n [4, 9, -3, -5, 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[[-4, 0, 24, 20, 15],\n [24, -32, -16, 40, 6],\n [-12, 19, -4, -35, -12],\n [-12, 11, 28, 5, 12],\n [-4, 4, 8, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, 6, -18, 15, 12],\n [8, -4, 12, -10, -8],\n [-24, 12, -36, 30, 24],\n [-16, 8, -24, 20, 16],\n [-12, 6, -18, 15, 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[[0, -4, -24, -12, -4],\n [0, -4, -24, -12, -4],\n [0, 3, 18, 9, 3],\n [0, -4, -24, -12, -4],\n [0, -1, -6, -3, -1]]\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[[-17, -23, -24, 27, 5],\n [-3, -5, 8, -7, -1],\n [19, 31, -42, 36, 5],\n [2, 4, -14, 13, 2],\n [-6, -8, -10, 11, 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[[33, -6, 19, -22, 10],\n [-5, -24, -28, 17, -15],\n [5, -16, 23, -14, 3],\n [-16, -3, 1, 13, -27],\n [49, 61, -17, 2, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-29, 9, 2, -18, 19],\n [0, 0, 0, 0, 0],\n [-17, 5, -2, -12, 9],\n [10, -6, -34, -9, -29],\n [28, -8, 6, 21, -13]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-25, 0, 7, -24, 11],\n [5, -35, -35, -5, 30],\n [-18, 1, 6, -17, 7],\n [28, 4, -4, 28, -16],\n [11, -27, -29, 3, 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[[-20, 0, 22, 22, 8],\n [-10, 8, 44, 5, 6],\n [34, 0, 23, -43, 8],\n [10, 6, -24, -12, -16],\n [20, -24, 30, -18, 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[[8, 12, 12, 16, -6],\n [14, 0, 6, 7, 0],\n [-8, -12, -12, -16, 6],\n [14, 0, 6, 7, 0],\n [-36, 2, -14, -16, -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, 4, 16, -8, 8],\n [30, 6, 24, -12, 12],\n [-10, -2, -8, 4, -4],\n [-25, -5, -20, 10, -10],\n [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[[1, 1, -5, 5, -6],\n [-1, -1, 5, -5, 6],\n [4, 4, -20, 20, -24],\n [-2, -2, 10, -10, 12],\n [-2, -2, 10, -10, 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[[6, -1, 3, 3, -5],\n [0, 0, 0, 0, 0],\n [-30, 5, -15, -15, 25],\n [-24, 4, -12, -12, 20],\n [-36, 6, -18, -18, 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[[8, -11, -15, -7, -2],\n [-12, -3, 15, 15, -18],\n [-6, 5, 10, 6, -2],\n [6, -5, -10, -6, 2],\n [-8, 11, 15, 7, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[21, -4, 9, -12, -10],\n [-27, 12, -9, 0, -6],\n [-25, 20, -5, -20, -30],\n [-14, 8, -4, -4, -8],\n [-1, 4, 1, -8, -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[[14, 7, -15, -28, -4],\n [20, 24, -32, 12, -20],\n [-22, -13, -9, -8, -4],\n [-9, 3, -5, -2, 19],\n [32, 60, -52, 24, 24]]\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, 0, 0, 0, 0],\n [8, 12, 2, 6, 6],\n [4, 6, 1, 3, 3],\n [-16, -24, -4, -12, -12],\n [-8, -12, -2, -6, -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[[-25, 4, -3, 13, -9],\n [56, 8, 16, -38, 22],\n [-31, -8, -9, 22, -18],\n [50, 32, 22, -44, 40],\n [-72, -24, -24, 54, -42]]\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, -28, -9, -32, -36],\n [27, 20, 7, 24, 28],\n [19, 14, 5, 17, 20],\n [-10, -6, -4, -11, -16],\n [-9, -8, -1, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[32, 22, -18, 10, -10],\n [0, 9, 23, -18, -55],\n [-53, -29, 8, -27, -51],\n [-12, 16, 23, -29, -74],\n [26, 42, -7, 2, 4]]\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[[-18, -27, -12, 6, -18],\n [36, 6, 36, -36, 12],\n [0, 0, 0, 0, 0],\n [-60, -34, -54, 48, -32],\n [-42, -31, -36, 30, -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[[-12, 10, -10, 8, 12],\n [-36, 30, -30, 24, 36],\n [-36, 30, -30, 24, 36],\n [-30, 25, -25, 20, 30],\n [30, -25, 25, -20, -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[[-8, 6, -15, -23, 35],\n [45, -15, 14, 10, -26],\n [3, 35, -15, -52, 3],\n [36, 14, 24, 29, -69],\n [29, -5, -5, -25, 12]]\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[[-31, -1, -9, -3, -32],\n [25, -9, -11, -13, 22],\n [39, 33, 33, 3, 0],\n [-23, -33, -21, 9, 28],\n [-40, -24, -4, 28, 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[[-15, -12, 6, -12, -3],\n [-10, -8, 4, -8, -2],\n [15, 12, -6, 12, 3],\n [25, 20, -10, 20, 5],\n [25, 20, -10, 20, 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[[-23, 32, 10, -4, -32],\n [15, 8, -4, 25, -1],\n [-34, -22, 13, -36, -10],\n [7, 7, 20, 1, -51],\n [55, 23, -12, 43, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-24, 42, 1, 38, 38],\n [-15, 24, 13, 27, 19],\n [-2, -18, -28, -14, -36],\n [15, -24, -44, -64, -41],\n [-6, 0, 21, 39, 12]]\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 5x5 matrix:\n[[-2, 20, 18, -22, -2],\n [3, -32, -33, 31, 25],\n [1, 22, 21, -23, -21],\n [1, -4, -3, 5, -5],\n [-6, 46, 42, -50, -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[[0, 6, 9, -15, 18],\n [8, -10, -12, 2, -24],\n [0, 10, 15, -25, 30],\n [20, -13, -12, -25, -24],\n [-20, 17, 18, 15, 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[[0, 0, 0, 0, 0],\n [5, 0, 0, -20, 10],\n [-4, 0, 0, 16, -8],\n [0, 0, 0, 0, 0],\n [-1, 0, 0, 4, -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 5x5 matrix:\n[[-10, 12, 10, 8, -6],\n [-10, 12, 10, 8, -6],\n [20, -24, -20, -16, 12],\n [0, 0, 0, 0, 0],\n [-20, 24, 20, 16, -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[[-58, -61, -68, -12, 7],\n [10, 36, 6, -9, 7],\n [-41, -17, -41, -17, 11],\n [49, 33, 33, 5, 1],\n [8, 6, -12, -10, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-30, 20, 22, 8, -30],\n [33, -22, -20, -7, 33],\n [54, -36, -6, 0, 54],\n [-30, 20, -6, -4, -30],\n [6, -4, 18, 8, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -2, -6, 6, 2],\n [-16, -8, -24, 24, 8],\n [20, 10, 30, -30, -10],\n [24, 12, 36, -36, -12],\n [4, 2, 6, -6, -2]]\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[[-9, 9, 12, 0, -15],\n [18, -18, -24, 0, 30],\n [-12, 12, 16, 0, -20],\n [-18, 18, 24, 0, -30],\n [15, -15, -20, 0, 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[[-3, 4, 5, 1, 1],\n [-26, 24, -4, 4, 8],\n [28, -26, 8, -5, -13],\n [-30, 36, 6, 12, 36],\n [-16, 18, 18, 3, -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 5x5 matrix:\n[[-18, -24, 36, -24, -6],\n [-15, -20, 30, -20, -5],\n [-15, -20, 30, -20, -5],\n [-9, -12, 18, -12, -3],\n [15, 20, -30, 20, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[24, -18, -6, 18, -12],\n [12, -9, -3, 9, -6],\n [20, -15, -5, 15, -10],\n [20, -15, -5, 15, -10],\n [4, -3, -1, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[10, 10, -4, -10, 8],\n [30, 30, -12, -30, 24],\n [-15, -15, 6, 15, -12],\n [-25, -25, 10, 25, -20],\n [30, 30, -12, -30, 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 5x5 matrix:\n[[-27, -20, 39, -3, -24],\n [-5, -5, 15, 15, 15],\n [-13, -9, 15, -9, -21],\n [26, 19, -36, 6, 27],\n [-15, -12, 27, 9, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-21, 21, 3, -9, -21],\n [8, -4, 20, -12, 24],\n [-17, 19, 13, -15, -9],\n [10, -5, 25, -15, 30],\n [16, -15, 3, 3, 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[[29, -14, 10, 21, -11],\n [20, -4, -2, -6, -16],\n [31, -14, 11, 12, -11],\n [57, -21, 3, 42, -39],\n [38, -16, 11, 13, -16]]\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, -6, -12, -36, 0],\n [-15, -29, 14, -12, 30],\n [-6, -26, 20, 6, 30],\n [0, 0, 0, 0, 0],\n [15, 29, -14, 12, -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[[3, -31, -14, 26, 21],\n [-15, 22, 14, -3, -15],\n [5, -14, -36, 17, 15],\n [21, -2, 31, -33, -36],\n [-13, 7, -3, 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[[2, 6, 1, 6, -3],\n [8, 24, 4, 24, -12],\n [2, 6, 1, 6, -3],\n [6, 18, 3, 18, -9],\n [-10, -30, -5, -30, 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[[30, 12, -6, -18, -10],\n [1, -22, -10, -2, 37],\n [-12, 30, 33, -27, -54],\n [12, 23, 8, -10, -36],\n [-35, 50, 53, -56, -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[[61, -9, 6, -54, 56],\n [-27, -12, -51, 11, -29],\n [39, 3, 24, -32, 38],\n [2, -18, -63, -23, -3],\n [-30, 7, -3, 23, -27]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[24, -12, 18, 6, -6],\n [-16, 8, -12, -4, 4],\n [24, -12, 18, 6, -6],\n [-8, 4, -6, -2, 2],\n [24, -12, 18, 6, -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[[15, 5, -15, 30, -5],\n [-9, -3, 9, -18, 3],\n [-15, -5, 15, -30, 5],\n [-6, -2, 6, -12, 2],\n [-6, -2, 6, -12, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[8, -10, 4, 12, 2],\n [-8, 10, -4, -12, -2],\n [-24, 30, -12, -36, -6],\n [-4, 5, -2, -6, -1],\n [8, -10, 4, 12, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-33, 2, 12, -22, 18],\n [27, 45, -16, 34, -33],\n [45, 26, -18, 42, 10],\n [33, -2, -19, 12, -51],\n [12, -49, 3, -6, -27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[38, -27, -42, -20, 54],\n [29, -5, -22, -10, 28],\n [-1, -10, 1, -3, 5],\n [32, -36, -42, -23, 45],\n [-25, 18, 15, 16, -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[[27, -3, -24, 27, 0],\n [-26, 2, 26, -22, 4],\n [4, 0, -5, 2, -2],\n [5, -5, 10, 25, 20],\n [11, 1, -17, 1, -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[[14, 3, -14, -39, -7],\n [18, -7, -12, 61, 7],\n [6, 5, 3, 40, 1],\n [18, 33, 9, 21, -15],\n [-26, -17, 8, -19, 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[[-51, -3, 27, 21, 36],\n [-41, 3, 33, 27, 32],\n [14, 13, 18, 17, -3],\n [0, -23, -48, -43, -13],\n [32, 10, 0, 2, -18]]\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[[-9, 26, 14, 21, 24],\n [-18, -5, -38, -30, -15],\n [-11, 17, 0, 7, 13],\n [-6, -8, -20, -18, -12],\n [-2, -9, -14, -14, -11]]?\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[[12, -20, -18, 3, 24],\n [-12, -30, -14, 0, -4],\n [-12, -2, 14, -12, -20],\n [-15, -15, 20, -25, -25],\n [-30, -37, -9, -4, -26]]\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 5x5 matrix:\n[[-24, 36, -14, 64, -25],\n [7, 51, 44, -9, -11],\n [-4, 45, 23, 17, -16],\n [3, 6, 9, -2, -5],\n [-12, 18, -6, 42, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[11, 0, 2, 13, -18],\n [-11, -24, -10, 11, 5],\n [-5, -4, -92, -19, 59],\n [26, 15, -7, 12, 17],\n [28, 37, 28, -2, -24]]\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[[46, -64, 5, -13, -63],\n [-17, -27, 38, 36, -32],\n [27, 2, -30, -33, 7],\n [11, -18, 7, 0, -18],\n [35, -65, 16, 0, -66]]\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[[2, 15, 5, -24, 21],\n [8, -24, -1, 37, -28],\n [-18, 33, -3, -50, 35],\n [14, -27, 2, 41, -29],\n [18, -33, 3, 50, -35]]?\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 5x5 matrix:\n[[22, 26, -27, -43, -49],\n [19, 29, -20, 24, -16],\n [-5, -11, 7, 7, 1],\n [-10, -18, 15, 38, 15],\n [1, -1, 1, 21, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[10, -10, 19, -14, -5],\n [-50, 11, -39, 15, 61],\n [20, 40, -82, 56, 26],\n [-12, -14, -29, -13, 39],\n [-18, 54, 3, 60, -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 5x5 matrix:\n[[47, -14, 23, -26, 56],\n [3, -21, 7, -22, 12],\n [-20, -10, -20, 15, -50],\n [5, 10, -3, 12, -4],\n [-17, -1, -5, 1, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-10, -2, -4, 12, 4],\n [-10, 4, -2, 10, -6],\n [5, -11, -2, -2, 18],\n [-5, -1, -2, 6, 2],\n [-5, 5, 0, 4, -8]]\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, 2, 0, 3, -2],\n [20, 10, 0, 15, -10],\n [4, 2, 0, 3, -2],\n [12, 6, 0, 9, -6],\n [-4, -2, 0, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-32, 39, -17, -17, -29],\n [-22, 58, -14, -28, -32],\n [-3, 19, 21, -3, -14],\n [15, -22, -20, 0, 43],\n [9, 42, 2, -22, -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[[15, -10, 15, -10, -30],\n [12, -8, 12, -8, -24],\n [12, -8, 12, -8, -24],\n [15, -10, 15, -10, -30],\n [15, -10, 15, -10, -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[[26, 39, 10, 54, 30],\n [1, 4, 0, 35, 28],\n [35, 52, 16, 53, 16],\n [-42, -61, -54, -59, -31],\n [4, 5, 0, -14, -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[[-9, -24, 8, 6, 17],\n [-12, 8, 24, 8, 16],\n [-18, -54, 14, 12, 35],\n [-9, 6, 18, 6, 12],\n [-9, -18, 10, 6, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[30, -30, -1, 10, 28],\n [-4, 36, -35, -30, 3],\n [38, -22, -8, -8, 40],\n [24, 7, 1, -37, -12],\n [70, -44, 46, -38, -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 5x5 matrix:\n[[-12, 18, -3, 18, 15],\n [-20, 30, -5, 30, 25],\n [12, -18, 3, -18, -15],\n [16, -24, 4, -24, -20],\n [-24, 36, -6, 36, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, 20, 7, -6, -3],\n [-15, 23, 24, 1, 47],\n [56, 62, -38, -10, -30],\n [36, 57, -39, -3, 6],\n [64, 85, -49, -9, -12]]\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[[-21, -23, -10, -27, 60],\n [-15, 5, -5, 15, -30],\n [-34, -17, -13, -26, 32],\n [4, 16, 4, 12, -48],\n [-12, 0, -3, -12, -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[[-12, 14, -58, 29, 21],\n [-6, 36, 12, 7, 30],\n [12, 2, 56, -22, -12],\n [10, 42, 18, 10, 11],\n [6, 28, -20, 21, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[15, -18, -3, -6, 3],\n [-7, 21, 11, 4, 16],\n [-36, 18, -12, 12, -42],\n [-23, 15, -5, 8, -22],\n [-24, 12, -8, 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 5x5 matrix:\n[[-20, 6, -17, 13, 11],\n [12, 18, 25, 5, -7],\n [8, -30, -21, -18, -11],\n [-20, 54, 2, 47, -1],\n [20, -54, -42, -31, -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 5x5 matrix:\n[[-16, -20, 10, 26, -22],\n [-41, -60, -12, 22, -24],\n [-29, -30, -9, -4, -7],\n [-32, -34, -19, -17, 1],\n [56, 70, 19, -8, 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[[0, 10, 6, 8, 8],\n [0, 20, 12, 16, 16],\n [0, -30, -18, -24, -24],\n [0, -15, -9, -12, -12],\n [0, -20, -12, -16, -16]]\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, 25, 25, 15, -5],\n [10, 0, -14, -35, -15],\n [17, -20, -30, -31, -23],\n [-18, 8, -4, -18, -34],\n [-18, 15, 15, 9, -3]]?\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[[10, -12, -8, -6, -4],\n [-31, 30, 60, 45, 2],\n [-11, -4, 0, -11, -18],\n [-18, 12, 36, 24, -6],\n [10, 10, -48, -28, 26]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[25, -25, 15, 15, 30],\n [-25, 25, -15, -15, -30],\n [10, -10, 6, 6, 12],\n [-30, 30, -18, -18, -36],\n [-15, 15, -9, -9, -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[[20, 16, 4, -20, 8],\n [3, 16, 19, -3, -6],\n [-10, -25, -25, 10, 5],\n [-18, -28, -22, 18, 0],\n [14, 1, -11, -14, 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 5x5 matrix:\n[[-24, -6, 24, 36, 12],\n [16, 4, -16, -24, -8],\n [24, 6, -24, -36, -12],\n [-24, -6, 24, 36, 12],\n [-20, -5, 20, 30, 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[[8, 18, -8, -8, 48],\n [-20, 25, 15, 10, 5],\n [36, -19, -31, -14, 49],\n [-8, 6, 12, -16, -36],\n [16, -13, -15, 0, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-50, 14, -10, 36, 34],\n [-35, 13, -5, 25, 42],\n [24, 0, -22, -30, -32],\n [38, -10, 24, -13, 5],\n [20, -16, 46, -13, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-15, 0, -25, -40, -20],\n [-11, -15, -28, -32, 25],\n [-90, -72, 6, -24, 0],\n [-17, -3, -18, -32, -19],\n [47, 45, 0, 12, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[16, 17, -32, -44, -17],\n [14, -8, 2, -5, -10],\n [-28, 12, -5, -23, -14],\n [12, -15, -9, 5, 21],\n [24, -10, 2, 24, 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[[34, -81, -47, 26, 8],\n [-27, 39, 19, 0, -10],\n [-18, -53, -38, 4, 1],\n [-11, -29, -18, 102, -15],\n [4, -8, -9, 6, -5]]\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, 0, -26, 8, -51],\n [63, 10, -2, 14, -20],\n [13, 40, -26, 8, 23],\n [-53, -2, -9, -24, -16],\n [17, 26, -8, -34, -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 5x5 matrix:\n[[-12, 6, -2, 6, -4],\n [24, -12, 4, -12, 8],\n [-18, 9, -3, 9, -6],\n [-6, 3, -1, 3, -2],\n [6, -3, 1, -3, 2]]\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[[1, 1, 1, -4, -18],\n [-2, 8, -10, -36, 39],\n [1, -21, 12, 31, -34],\n [0, -12, 11, 21, -54],\n [-25, 41, -11, -14, 41]]\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, 16, 29, -28, -10],\n [5, -18, -7, 14, 30],\n [0, -2, -2, 16, -10],\n [8, 15, 13, 22, -55],\n [-37, -13, -37, 41, -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[[-5, 0, -6, -8, -27],\n [-73, -13, -2, -23, 0],\n [8, 13, 28, 5, -19],\n [-54, 33, -24, 9, 27],\n [-52, -25, 12, -25, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[52, 24, -32, -18, -7],\n [-22, -16, 0, -12, 2],\n [-7, -12, 26, 6, -38],\n [7, 4, -18, -12, 13],\n [-28, 4, 38, 52, 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[[36, -12, -24, -6, -36],\n [30, -10, -20, -5, -30],\n [-6, 2, 4, 1, 6],\n [0, 0, 0, 0, 0],\n [-18, 6, 12, 3, 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 5x5 matrix:\n[[-35, 21, -14, 76, -34],\n [-14, 18, -27, -8, -7],\n [20, -27, 38, 46, 5],\n [-39, 36, -15, 35, -27],\n [-45, 21, 3, 28, -35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 8, 12, 0, 24],\n [0, -2, -3, 0, -6],\n [0, -6, -9, 0, -18],\n [0, -10, -15, 0, -30],\n [0, 6, 9, 0, 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 5x5 matrix:\n[[0, 0, 24, 4, -20],\n [15, -10, -50, -20, 45],\n [-15, 10, 20, 15, -20],\n [6, -4, 4, -4, -2],\n [3, -2, -4, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-10, -12, 0, 1, -1],\n [-29, -11, -27, 43, 20],\n [-1, -23, 25, -41, -28],\n [-36, -36, -8, 13, -1],\n [-10, -12, 0, 1, -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[[-29, 12, -30, -6, -18],\n [25, -9, -3, 17, -28],\n [-34, 21, 24, 59, 2],\n [-16, 9, 41, 21, 42],\n [-21, 9, 12, -27, 36]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[14, 10, -21, -31, 7],\n [36, 20, -34, -14, 38],\n [-22, -12, 20, 6, -24],\n [38, 22, -39, -25, 37],\n [1, -2, 8, 29, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-60, 26, 55, -30, -11],\n [-24, -6, 27, 17, -57],\n [28, 8, -42, -2, 39],\n [-30, 16, 14, 16, -58],\n [-16, 0, 28, -36, 46]]?\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, 6, 12, 20, 0],\n [-12, -3, -9, -15, -6],\n [-12, 3, 0, 0, -12],\n [24, -2, 6, 10, 20],\n [-8, 2, 0, 0, -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 5x5 matrix:\n[[0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [24, -24, -8, 4, -12],\n [-36, 36, 12, -6, 18],\n [-30, 30, 10, -5, 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[[-5, 20, -20, 5, -20],\n [-1, 4, -4, 1, -4],\n [1, -4, 4, -1, 4],\n [2, -8, 8, -2, 8],\n [4, -16, 16, -4, 16]]\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, 40, -18, 11, -6],\n [-1, -7, 6, 1, -3],\n [-43, -37, -6, 20, 2],\n [32, 18, 14, 20, -29],\n [12, -2, 14, -10, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-24, 12, -6, 18, -8],\n [-24, 12, -6, 18, -8],\n [20, 10, 23, -21, -12],\n [-23, 29, 10, 12, -24],\n [-24, 42, 21, 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[[-16, -36, -40, 16, 0],\n [-17, -28, -23, 15, -26],\n [-19, -17, -18, 22, -8],\n [44, 24, 32, -56, 0],\n [-23, -17, -20, 28, -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[[-8, -10, 12, 4, -2],\n [26, 15, -30, -14, -1],\n [-20, 10, 12, 12, 10],\n [-4, -40, 24, 0, -16],\n [-19, 20, 6, 12, 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 5x5 matrix:\n[[-24, -16, -8, 44, -32],\n [56, -56, -52, 16, 39],\n [-53, -6, -4, -12, -55],\n [-34, -12, -4, 30, -20],\n [41, -10, -12, 5, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 15, -35, 0],\n [0, 0, -6, 14, 0],\n [-2, -5, 18, -39, -1],\n [-8, -20, -3, 19, -4],\n [-4, -10, 0, 6, -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[[-30, 25, -15, -15, -10],\n [36, -30, 18, 18, 12],\n [12, -10, 6, 6, 4],\n [-12, 10, -6, -6, -4],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-6, 36, -12, -6, 12],\n [6, -36, 12, 6, -12],\n [0, 0, 0, 0, 0],\n [5, -30, 10, 5, -10],\n [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[[-25, 1, 2, 5, -2],\n [-23, 4, 8, -1, 6],\n [-20, 3, 6, 0, 4],\n [-3, 12, 24, -21, 30],\n [17, 9, 18, -21, 26]]?\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[[53, 21, 79, 37, -74],\n [-9, -55, -25, 10, 12],\n [30, -6, 36, -48, -42],\n [-12, 36, -36, -32, 38],\n [14, -36, 6, -25, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-30, 0, -15, -10, 15],\n [24, 0, 12, 8, -12],\n [36, 0, 18, 12, -18],\n [-12, 0, -6, -4, 6],\n [12, 0, 6, 4, -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 5x5 matrix:\n[[20, 0, -5, 20, -5],\n [0, 0, 0, 0, 0],\n [-16, 0, 4, -16, 4],\n [-24, 0, 6, -24, 6],\n [-20, 0, 5, -20, 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[[-8, 20, -12, 24, 8],\n [6, -15, 9, -18, -6],\n [12, -30, 18, -36, -12],\n [12, -30, 18, -36, -12],\n [-6, 15, -9, 18, 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 5x5 matrix:\n[[-26, -14, 12, 14, -4],\n [27, 27, 22, 19, 7],\n [-14, 3, 34, 3, -17],\n [13, 6, -8, 6, 10],\n [-9, 10, 44, 20, -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[[0, -3, 15, -15, -15],\n [0, -5, 25, -25, -25],\n [0, -4, 20, -20, -20],\n [0, 2, -10, 10, 10],\n [0, 2, -10, 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[[-40, -10, -32, -50, 44],\n [-12, 1, -11, 12, 8],\n [24, 15, 12, 5, -13],\n [9, 9, 25, -15, -24],\n [-13, -48, 23, 22, -29]]\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 5x5 matrix:\n[[0, 0, 0, 0, 0],\n [-15, -15, 3, 6, -3],\n [15, 15, -3, -6, 3],\n [-30, -30, 6, 12, -6],\n [10, 10, -2, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, -9, 12, 0, 9],\n [-4, 6, -8, 0, -6],\n [4, -6, 8, 0, 6],\n [12, -18, 24, 0, 18],\n [-10, 15, -20, 0, -15]]\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[[-36, 30, 0, 12, 18],\n [30, -25, 0, -10, -15],\n [12, -10, 0, -4, -6],\n [0, 0, 0, 0, 0],\n [-36, 30, 0, 12, 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 5x5 matrix:\n[[20, 15, -20, -10, -5],\n [8, 6, -8, -4, -2],\n [4, 3, -4, -2, -1],\n [24, 18, -24, -12, -6],\n [-16, -12, 16, 8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-11, -53, -3, -21, 11],\n [12, -24, -24, 12, -12],\n [-10, 17, 19, -8, 10],\n [8, 14, -6, 12, -8],\n [-12, 24, 24, -20, 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[[-1, 22, -9, 28, 0],\n [-25, -2, -38, 11, -14],\n [27, 2, -11, 32, 30],\n [-39, -24, -71, 7, -17],\n [-37, 14, 0, -15, -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[[0, 25, 20, -5, 0],\n [0, 15, 12, -3, 0],\n [0, 30, 24, -6, 0],\n [0, -30, -24, 6, 0],\n [0, 25, 20, -5, 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[[0, 0, 0, 0, 0],\n [-12, -4, 12, -2, -10],\n [18, 6, -18, 3, 15],\n [-12, -4, 12, -2, -10],\n [18, 6, -18, 3, 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[[-4, 48, 25, -40, -6],\n [2, 33, 17, -26, 1],\n [10, 45, 33, 14, -11],\n [-4, -57, -34, 23, 7],\n [16, -21, -1, 71, -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[[5, 24, 6, -1, 1],\n [18, 0, 47, -2, 30],\n [-17, 20, 47, 23, -9],\n [1, -8, 35, 5, 13],\n [63, 23, -43, -17, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, 2, 4, 6, 2],\n [-18, -12, -24, -36, -12],\n [-3, -2, -4, -6, -2],\n [0, 0, 0, 0, 0],\n [12, 8, 16, 24, 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[[44, 14, -45, 32, -18],\n [-27, -25, 23, -16, 21],\n [13, 41, -14, 8, -33],\n [20, -25, 21, -9, 35],\n [-32, -38, 0, -2, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -24, 19, -32, -31],\n [18, 0, -15, 12, 15],\n [24, -16, -4, -8, -4],\n [-6, -12, 17, -22, -23],\n [18, -12, -3, -6, -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[[-2, 13, -10, 0, 9],\n [-11, -17, 18, -6, -10],\n [-45, 27, -6, -18, 24],\n [2, -22, 16, -12, -12],\n [17, -40, 31, 38, -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[[6, 32, -44, 0, 15],\n [10, 18, -26, -24, -15],\n [8, -18, 22, -8, -20],\n [-9, 16, -19, 3, 15],\n [-10, -35, 49, 0, -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[[-18, -3, -12, 3, 3],\n [6, 1, 4, -1, -1],\n [-18, -3, -12, 3, 3],\n [-36, -6, -24, 6, 6],\n [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[[6, 6, -15, -15, -18],\n [-10, -10, 25, 25, 30],\n [4, 4, -10, -10, -12],\n [-12, -12, 30, 30, 36],\n [-8, -8, 20, 20, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 10, 30, 0, 30],\n [0, 12, 36, 0, 36],\n [0, 2, 6, 0, 6],\n [0, 2, 6, 0, 6],\n [0, -6, -18, 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[[-2, 47, -5, -50, 64],\n [-2, -19, -9, 13, -24],\n [0, -45, 3, 45, -60],\n [6, 45, -31, -48, 56],\n [15, 24, -17, -12, 22]]\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, 1, 0, -1, 1],\n [-3, -3, 0, 3, -3],\n [6, 6, 0, -6, 6],\n [1, 1, 0, -1, 1],\n [1, 1, 0, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[15, 11, 23, 25, 24],\n [15, 19, 3, -21, -10],\n [-9, -6, -51, -21, 6],\n [33, 38, 7, -25, 0],\n [-33, -34, -31, 1, -8]]?\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, -1, 0, -3, -3],\n [4, -10, -30, -6, 6],\n [-4, -2, -10, 2, 6],\n [-24, 9, 10, 19, 15],\n [-6, -6, -25, 2, 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[[1, 23, 0, 12, -1],\n [26, -32, 67, -24, -15],\n [14, -60, -61, -24, 24],\n [41, -16, -87, 30, 33],\n [21, -47, -57, -12, 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[[-25, -5, 15, -5, 25],\n [10, 12, -8, -6, -8],\n [-15, 2, 8, -7, 16],\n [-30, 24, 12, -30, 36],\n [-30, 14, 14, -22, 34]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-30, -62, 27, 23, -10],\n [-53, -4, -26, 54, 41],\n [-41, 12, -38, 50, 49],\n [15, 10, -6, -8, 2],\n [2, -2, -13, 11, 16]]\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, -6, 20, -34, 8],\n [-30, -15, 25, -55, 5],\n [-22, -3, 25, -35, 13],\n [-6, -3, 5, -11, 1],\n [6, -3, -10, 7, -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[[11, -9, -5, 3, -19],\n [-31, 7, 4, 34, -4],\n [-33, 25, 25, 18, -9],\n [10, -10, -11, 4, 11],\n [-44, 26, 13, -16, 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[[9, 9, 22, 27, -56],\n [-16, -1, -8, -24, -5],\n [17, 20, 2, 11, -9],\n [-35, 1, -34, -60, 14],\n [25, -22, 36, 60, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, 27, 8, -6, 6],\n [20, 7, -3, 30, 29],\n [-14, 17, 10, -11, -9],\n [18, -4, -19, 19, 38],\n [4, -3, -1, 16, -3]]\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[[52, -32, 12, -6, -30],\n [-23, -8, -13, 5, 40],\n [-41, 28, 23, 15, 63],\n [37, -31, -11, -20, -41],\n [21, 33, 39, -44, -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[[-15, 14, 34, -7, -1],\n [19, 23, 14, 7, 18],\n [-9, 16, 43, 38, -1],\n [1, 12, -13, 12, -13],\n [-21, -39, -28, -7, -22]]?\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, -36, 6, -24, 0],\n [3, -18, 3, -12, 0],\n [0, 0, 0, 0, 0],\n [-3, 18, -3, 12, 0],\n [-1, 6, -1, 4, 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[[-20, 11, -31, -23, -11],\n [-13, -21, -10, 22, -19],\n [4, -9, 9, 9, -3],\n [-7, -9, -7, 19, -4],\n [17, 16, 19, -37, 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[[-3, -6, 9, -3, -18],\n [0, 0, 0, 0, 0],\n [-1, -2, 3, -1, -6],\n [5, 10, -15, 5, 30],\n [4, 8, -12, 4, 24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[23, 45, 9, 57, 57],\n [29, -15, 10, 8, -26],\n [-6, -36, -18, -22, -57],\n [38, -23, -42, -26, -71],\n [50, 48, 0, 64, 45]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, 39, -4, -20, -35],\n [-3, 51, 16, -49, -50],\n [10, 38, 24, -46, -36],\n [-10, -2, -4, 38, 20],\n [21, -42, 40, -31, 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 5x5 matrix:\n[[-15, -15, -10, -25, 25],\n [0, 0, 0, 0, 0],\n [3, 3, 2, 5, -5],\n [-18, -18, -12, -30, 30],\n [6, 6, 4, 10, -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 5x5 matrix:\n[[-8, 16, -8, -1, -33],\n [1, 16, -20, 8, -48],\n [10, 4, -14, 8, -30],\n [-18, -4, 14, -6, 48],\n [-18, 4, 2, 0, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[15, 1, 5, 6, 14],\n [10, -45, -55, 12, -3],\n [-17, 25, 25, 6, 14],\n [1, 32, 18, 10, 23],\n [-17, 19, 12, 8, 12]]?\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 5x5 matrix:\n[[-42, 0, -42, -34, 53],\n [-1, 52, 16, -13, 11],\n [-17, -31, -28, -6, 12],\n [-51, 33, -42, -48, 63],\n [26, 1, 26, 21, -34]]\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 5x5 matrix:\n[[46, -1, -7, -45, 44],\n [-8, -10, 38, 0, 8],\n [31, 25, -29, -4, 13],\n [-10, 19, 25, 33, -8],\n [-47, 2, -4, 46, -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[[-16, -1, 20, 45, -42],\n [3, -15, -8, -4, 3],\n [-4, 8, 8, 4, -12],\n [7, 19, -2, -36, 15],\n [1, 10, 0, 5, 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[[-24, -58, 37, -24, -6],\n [64, 43, -27, 7, 48],\n [-13, -24, 3, 1, 12],\n [-67, -23, 49, 10, -102],\n [50, -15, 18, -10, 42]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, -8, 3, 6, -11],\n [12, 16, -3, -6, 19],\n [-24, 0, 6, 12, -6],\n [12, 0, -3, -6, 3],\n [-4, -12, 1, 2, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-26, -30, 4, 10, -22],\n [17, 24, 12, 11, 29],\n [19, 30, 24, 25, 43],\n [11, 12, -4, -7, 7],\n [13, 12, -12, -17, 1]]\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 5x5 matrix:\n[[6, -6, -6, 24, 0],\n [5, -5, -5, 20, 0],\n [-5, 5, 5, -20, 0],\n [3, -3, -3, 12, 0],\n [6, -6, -6, 24, 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[[2, 7, -20, 7, -27],\n [6, -13, 8, -13, 4],\n [8, -24, 24, -24, 22],\n [0, -6, 12, -6, 15],\n [18, -37, 20, -37, 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[[-40, 52, -41, -22, -8],\n [10, 16, 1, 9, -1],\n [-28, 14, -22, -54, 0],\n [-18, -8, -5, -53, 8],\n [42, -34, 23, 53, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[58, -18, -4, 12, 36],\n [-54, 14, 22, 4, -8],\n [66, 0, -36, 18, 18],\n [-29, 22, -32, -19, -55],\n [25, 19, -40, 14, -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 5x5 matrix:\n[[-16, -21, -4, 14, 52],\n [-33, -45, -51, 6, 24],\n [-47, -43, -47, -19, 48],\n [38, 26, 30, 38, -40],\n [-3, 6, 3, -22, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, 1, 5, 5, 3],\n [24, 4, 20, 20, 12],\n [-30, -5, -25, -25, -15],\n [12, 2, 10, 10, 6],\n [-12, -2, -10, -10, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 12, 36, -18, -6],\n [-4, -8, -24, 12, 4],\n [-3, -6, -18, 9, 3],\n [5, 10, 30, -15, -5],\n [1, 2, 6, -3, -1]]?\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, -24, 6, 17, 9],\n [0, 0, 0, 0, 0],\n [16, 24, -24, -20, -12],\n [-12, -6, -12, 2, 0],\n [56, 48, 6, -31, -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 5x5 matrix:\n[[-36, 9, 26, -40, 6],\n [32, 14, -17, 14, -45],\n [10, -41, -28, 36, -12],\n [20, 35, 10, 0, 30],\n [27, 3, -14, 24, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 15, -29, 7, -13],\n [-1, 25, -43, -7, -18],\n [-1, -4, 7, 27, -8],\n [1, 41, -15, -51, 4],\n [-3, -39, -25, 47, -14]]\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 5x5 matrix:\n[[-40, 6, -56, 0, -18],\n [8, -1, 16, 8, 11],\n [-1, 1, 19, 34, 31],\n [38, -6, 46, -12, 6],\n [-15, 3, -3, 30, 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 5x5 matrix:\n[[30, -6, 36, 0, 6],\n [-25, 5, -30, 0, -5],\n [-10, 2, -12, 0, -2],\n [-30, 6, -36, 0, -6],\n [-30, 6, -36, 0, -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[[-18, 15, 18, -12, -18],\n [-18, 15, 18, -12, -18],\n [6, -5, -6, 4, 6],\n [-12, 10, 12, -8, -12],\n [12, -10, -12, 8, 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[[-20, -33, -35, 4, -21],\n [-4, -27, -22, 5, -3],\n [-20, -10, -45, -9, -36],\n [16, 22, -7, -15, 8],\n [-12, 4, -35, -13, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-21, 6, 17, -28, -1],\n [-32, 13, 16, -36, 24],\n [29, -21, 5, 0, 32],\n [-24, 20, -10, 8, -33],\n [-26, 12, 10, -24, 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 5x5 matrix:\n[[-18, -9, -6, -3, -15],\n [-12, -6, -4, -2, -10],\n [-6, -3, -2, -1, -5],\n [-12, -6, -4, -2, -10],\n [18, 9, 6, 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[[-2, -8, 12, -8, 0],\n [-15, 10, 20, 30, -40],\n [-3, -12, 18, -12, 0],\n [-5, -20, 30, -20, 0],\n [6, -4, -8, -12, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, 0, 5, -2, -5],\n [-24, 0, -20, 8, 20],\n [6, 0, 5, -2, -5],\n [-12, 0, -10, 4, 10],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[4, 3, 25, -12, 30],\n [-33, 65, -9, -58, 8],\n [-32, 57, -14, -43, -5],\n [24, -30, 39, -3, 51],\n [19, -33, -30, -4, -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 5x5 matrix:\n[[-6, 28, 3, -34, 2],\n [18, -12, -21, 6, 18],\n [-6, -20, 11, 30, -14],\n [-9, 27, 7, -31, -2],\n [9, 3, -12, -9, 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[[-49, -17, 13, -59, -37],\n [-16, 25, -20, 1, -40],\n [-5, -7, 5, -25, -11],\n [8, 32, -26, 8, -37],\n [-15, 19, -15, 5, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, -30, 20, -34, -28],\n [0, 45, -30, 25, 40],\n [0, -9, 6, -5, -8],\n [30, -15, 10, 35, -10],\n [-6, 30, -20, 8, 26]]\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, 18, -12, -22, -12],\n [-16, -8, 3, 16, -4],\n [-12, -3, 0, 9, -6],\n [0, -8, 6, 8, 8],\n [-20, 11, -12, -1, -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 5x5 matrix:\n[[-4, 8, -4, -8, 4],\n [-2, -8, 2, -28, 14],\n [-5, 1, -2, -28, 14],\n [-6, 30, -12, 24, -12],\n [-2, 4, -2, -4, 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[[6, -5, -2, -4, 5],\n [-6, 5, 2, 4, -5],\n [18, -15, -6, -12, 15],\n [6, -5, -2, -4, 5],\n [6, -5, -2, -4, 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[[7, -19, -1, -22, 39],\n [6, -12, 0, -9, 18],\n [-7, 19, 1, 22, -39],\n [9, -3, 3, 21, -27],\n [2, 6, 2, 20, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[10, -15, 10, -20, 0],\n [-10, 15, -10, 20, 0],\n [2, -3, 2, -4, 0],\n [2, -3, 2, -4, 0],\n [12, -18, 12, -24, 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[[-8, 20, 4, 8, 12],\n [-6, 15, 3, 6, 9],\n [-6, 15, 3, 6, 9],\n [-6, 15, 3, 6, 9],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-36, -14, -30, -3, -21],\n [0, -6, 0, -9, -9],\n [0, -6, 0, -9, -9],\n [-12, -12, -10, -12, -18],\n [36, 14, 30, 3, 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 5x5 matrix:\n[[-21, -84, -66, 6, -93],\n [14, -17, -8, 16, -5],\n [3, -28, -45, -24, -45],\n [-16, -4, 16, 10, -2],\n [8, 40, 19, -56, 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[[4, -4, 2, -6, -8],\n [-4, 4, -2, 6, 8],\n [10, -10, 5, -15, -20],\n [-12, 12, -6, 18, 24],\n [2, -2, 1, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[37, 8, 16, -2, 11],\n [28, 4, 28, -6, -2],\n [21, 8, 14, -5, 10],\n [9, -23, 0, 16, -38],\n [27, 2, -22, 13, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[16, 16, -12, -16, 4],\n [8, 8, -6, -8, 2],\n [0, 0, 0, 0, 0],\n [20, 20, -15, -20, 5],\n [16, 16, -12, -16, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-45, -10, -85, -35, -10],\n [23, 26, 51, 30, -1],\n [-13, -32, 43, 47, 35],\n [30, 16, -42, -44, -16],\n [-26, -36, 22, -30, -20]]\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, -5, 12, 1, -4],\n [13, 16, -30, 29, -18],\n [1, 4, -6, 13, -10],\n [-27, -18, 42, -1, -10],\n [-9, -9, 18, -12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-24, -20, 8, -20, -12],\n [12, 10, -4, 10, 6],\n [12, 10, -4, 10, 6],\n [-36, -30, 12, -30, -18],\n [24, 20, -8, 20, 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[[15, -15, -12, 0, 12],\n [-20, 20, 16, 0, -16],\n [5, -5, -4, 0, 4],\n [-30, 30, 24, 0, -24],\n [5, -5, -4, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-66, 6, -6, -18, 6],\n [9, -11, -9, -7, 21],\n [-9, 11, 9, 7, -21],\n [30, -18, -12, -6, 30],\n [-34, -2, -8, -14, 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 5x5 matrix:\n[[-46, 45, -29, -3, -31],\n [10, -6, 8, 22, 24],\n [-7, 15, 22, 19, 23],\n [14, -6, 64, -16, 23],\n [27, -21, 48, -1, 31]]\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, -4, 50, 10, -14],\n [-13, -2, -24, 11, 36],\n [-23, 10, 4, 49, 32],\n [-19, -4, -34, 14, 52],\n [13, -4, 5, -24, -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[[0, -6, -2, 2, 12],\n [0, -3, -1, 1, 6],\n [0, 12, 4, -4, -24],\n [0, -12, -4, 4, 24],\n [0, -15, -5, 5, 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[[-12, 5, 9, -26, -24],\n [1, 6, -6, 8, 9],\n [-7, 2, 6, -16, -15],\n [-15, 20, 0, -20, -15],\n [-24, 54, -18, -12, 0]]\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, -11, 7, -18, 11],\n [6, -33, -13, -22, 16],\n [10, 21, 17, 16, -7],\n [-28, 3, -23, 0, -5],\n [20, -63, -7, -50, 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 5x5 matrix:\n[[-8, 0, -8, 4, 6],\n [16, 0, 16, -8, -12],\n [-16, 0, -16, 8, 12],\n [-24, 0, -24, 12, 18],\n [-4, 0, -4, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-15, -9, -39, 3, -33],\n [-10, 30, 28, -25, 23],\n [30, -50, -24, 45, -19],\n [10, -2, 14, 4, 12],\n [5, -5, 1, 5, 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[[7, 19, -18, 13, -18],\n [26, -38, -28, 6, -4],\n [-10, -23, 12, -9, 20],\n [-22, -23, -2, 3, 23],\n [-8, 21, 28, -13, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 20, 16, 29, -16],\n [22, -8, 12, 5, 8],\n [8, -44, -46, -54, 4],\n [17, -37, -31, -32, -6],\n [-10, 18, 16, 8, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-26, -48, -22, 32, -7],\n [-38, -14, 1, 16, 36],\n [22, 8, -18, -32, -19],\n [18, 26, 37, 16, -4],\n [24, 34, 5, -36, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, -6, 18, -23, 14],\n [20, -8, 4, 7, 26],\n [-7, -3, 15, -26, 0],\n [-30, -2, -26, 27, -22],\n [-17, 3, -15, 14, -18]]\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],\n [30, -5, 25, -5, 15],\n [30, -5, 25, -5, 15],\n [-6, 1, -5, 1, -3],\n [30, -5, 25, -5, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-17, 7, 5, -42, 2],\n [10, 25, 50, -15, 20],\n [-1, 3, 5, -6, 2],\n [16, 18, 40, 6, 16],\n [4, -1, 0, 9, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 6, -18, -6, 0],\n [41, -35, 39, 29, 36],\n [-4, 3, 2, -2, -6],\n [37, -31, 27, 25, 36],\n [-5, 5, -15, -5, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[10, -10, -12, 8, -12],\n [-25, 25, 30, -20, 30],\n [5, -5, -6, 4, -6],\n [-30, 30, 36, -24, 36],\n [-30, 30, 36, -24, 36]]?\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 5x5 matrix:\n[[0, 2, -2, 4, -5],\n [0, -8, 8, -16, 20],\n [0, -2, 2, -4, 5],\n [0, 2, -2, 4, -5],\n [0, -8, 8, -16, 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 5x5 matrix:\n[[-8, -2, -26, 17, 25],\n [-16, 22, 22, -38, -36],\n [18, -22, -28, 1, 9],\n [28, -16, 56, 3, -1],\n [-17, 17, 62, 8, 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 5x5 matrix:\n[[16, -36, 41, 7, -1],\n [44, -42, -7, -27, 63],\n [62, -56, 0, -74, 40],\n [-25, 24, 76, 43, 8],\n [66, -60, 0, -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[[8, -12, -2, 0, -2],\n [8, -12, -2, 0, -2],\n [-12, 18, 3, 0, 3],\n [8, -12, -2, 0, -2],\n [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[[17, -8, -2, 7, 24],\n [6, -16, -2, 12, 4],\n [-21, 16, 5, -12, -30],\n [-25, 2, -12, -11, -21],\n [2, 22, 16, -8, -7]]\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[[-31, 57, 45, 0, -49],\n [-1, 16, 18, -10, -10],\n [32, -67, -63, -32, 68],\n [-4, 26, 6, 12, -18],\n [-11, 21, -3, 14, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, -2, -4, 4, 8],\n [6, 1, 2, -2, -4],\n [36, 6, 12, -12, -24],\n [36, 6, 12, -12, -24],\n [-18, -3, -6, 6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[66, 12, 30, -36, -42],\n [79, 15, 22, -10, 25],\n [63, 31, 31, -19, 4],\n [-42, -30, -52, 25, 28],\n [-70, -39, 16, 30, -5]]?\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, 0, 16, 4, -12],\n [-15, 0, 12, 3, -9],\n [15, 0, -12, -3, 9],\n [30, 0, -24, -6, 18],\n [-10, 0, 8, 2, -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 5x5 matrix:\n[[-24, 24, 24, -42, 38],\n [24, 6, 42, -6, 14],\n [-11, -36, -81, 36, -46],\n [-18, 24, 18, -18, 18],\n [7, 36, 69, -24, 34]]\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 5x5 matrix:\n[[10, 20, -5, 0, -5],\n [-8, -16, 4, 0, 4],\n [2, 4, -1, 0, -1],\n [-10, -20, 5, 0, 5],\n [6, 12, -3, 0, -3]]\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[[20, -20, -15, -5, 0],\n [-4, 4, 3, 1, 0],\n [-4, 4, 3, 1, 0],\n [4, -4, -3, -1, 0],\n [-16, 16, 12, 4, 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[[20, -8, 4, -32, -10],\n [-32, 10, -4, 52, 18],\n [12, -23, 18, -14, 7],\n [22, -20, 14, -32, -3],\n [-26, 9, -4, 42, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0, 0],\n [18, -6, 0, -15, -3],\n [-12, 4, 0, 10, 2],\n [12, -4, 0, -10, -2],\n [-18, 6, 0, 15, 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[[9, 22, 4, -19, 21],\n [-10, -6, 8, 12, 9],\n [24, 26, 6, -8, -32],\n [-14, -36, -42, -36, -28],\n [14, -22, -12, 40, -55]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-29, -21, -36, -24, -51],\n [-40, -37, 43, -46, 18],\n [14, 11, -65, 29, -45],\n [22, -15, 1, 13, -9],\n [-14, 11, -8, -17, -18]]\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[[18, -23, -3, -11, 10],\n [48, -21, 21, -9, 9],\n [-26, 21, -19, 19, -24],\n [4, 11, 1, 12, -15],\n [10, -10, 40, -30, 45]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-2, 4, -2, 4, -6],\n [8, -16, 8, -16, 24],\n [-10, 20, -10, 20, -30],\n [0, 0, 0, 0, 0],\n [10, -20, 10, -20, 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[[0, -1, 8, 0, -9],\n [-9, 8, -28, -9, 9],\n [-2, 1, 0, -2, -5],\n [-11, 6, -4, -11, -23],\n [-10, 6, -8, -10, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, -12, -4, 12, -24],\n [-10, 15, 5, -15, 30],\n [-10, 15, 5, -15, 30],\n [-12, 18, 6, -18, 36],\n [-2, 3, 1, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, -4, 20, 4, -2],\n [9, 3, -5, -13, 4],\n [23, 4, 8, -32, 9],\n [10, -1, 19, -13, 3],\n [-5, -4, 16, 8, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[26, -39, 11, -24, 15],\n [30, 0, -15, 5, 40],\n [0, -45, 24, -33, -21],\n [2, 18, 7, 15, 3],\n [-16, -24, 0, -22, -23]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-11, 9, 12, -3, 11],\n [15, -33, 0, 3, -27],\n [-11, 9, 12, -3, 11],\n [22, -18, -24, 6, -22],\n [5, 27, -30, 3, 13]]?\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, -33, 24, 12, -12],\n [-32, 18, -8, -24, -16],\n [36, -17, 6, 28, 22],\n [-30, -1, 9, -28, -37],\n [22, -14, 7, 16, 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[[15, -3, 6, -15, -9],\n [-30, 6, -12, 30, 18],\n [20, -4, 8, -20, -12],\n [-20, 4, -8, 20, 12],\n [-5, 1, -2, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[39, 15, -1, 1, 3],\n [-5, -9, -28, 15, -9],\n [57, 14, -22, -32, 68],\n [-56, -18, 0, 14, -26],\n [-4, -6, 14, 5, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[0, -3, -6, 2, 6],\n [0, 12, 24, -8, -24],\n [0, 0, 0, 0, 0],\n [0, -6, -12, 4, 12],\n [0, 3, 6, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[31, 48, 36, -20, 3],\n [5, -23, 25, -43, -38],\n [27, 20, -13, 9, 35],\n [14, 42, 6, 14, 24],\n [43, -41, -28, 0, 28]]?\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 5x5 matrix:\n[[-10, 30, 10, -25, -30],\n [2, -6, -2, 5, 6],\n [10, -30, -10, 25, 30],\n [2, -6, -2, 5, 6],\n [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[[4, 4, 2, 1, 0],\n [-10, -34, 10, -25, -18],\n [14, 22, 2, 11, 6],\n [10, 34, -10, 25, 18],\n [-4, -4, -2, -1, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[21, -24, -7, -25, 42],\n [-24, -35, 9, 0, 30],\n [11, -32, -4, -24, 48],\n [-6, -4, 5, 11, -6],\n [17, -9, 2, 9, 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[[-20, -10, -25, -30, -25],\n [12, 6, 15, 18, 15],\n [8, 4, 10, 12, 10],\n [-8, -4, -10, -12, -10],\n [16, 8, 20, 24, 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[[-6, 28, -10, -12, 30],\n [-4, 5, -5, -4, 6],\n [36, -4, 40, 24, -12],\n [8, -10, 10, 8, -12],\n [-33, -10, -35, -18, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, -28, 4, -32, 4],\n [2, -11, -2, -13, -3],\n [-16, 31, -8, 35, -9],\n [-15, 35, -5, 40, -5],\n [-15, -3, -21, -6, -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[[4, -18, 9, -18, -12],\n [-8, 0, 12, 6, 18],\n [-20, 28, 20, 15, 13],\n [16, -6, -31, 4, -4],\n [20, -24, -30, 0, 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 5x5 matrix:\n[[38, -37, -46, -5, 11],\n [-7, 7, 8, 1, -1],\n [2, -6, 8, -2, -22],\n [2, -6, 8, -2, -22],\n [1, 4, -14, 2, 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[[-24, -25, 4, 22, 22],\n [8, 11, 26, -21, -46],\n [36, 30, -30, -21, -30],\n [30, 20, -50, -5, -5],\n [-6, -13, -8, 10, -17]]\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, -31, -4, -40, -22],\n [-15, 0, -14, 13, 17],\n [-54, 24, 3, 15, 36],\n [-18, 33, 3, 42, 27],\n [30, -45, -12, -45, -33]]\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 5x5 matrix:\n[[20, -30, 15, 25, 10],\n [-4, 6, -3, -5, -2],\n [24, -36, 18, 30, 12],\n [20, -30, 15, 25, 10],\n [20, -30, 15, 25, 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, -8, 4, -13, -2],\n [-12, -16, 8, -23, -4],\n [12, 16, -8, 21, 4],\n [-12, -16, 8, -21, -4],\n [15, 20, -10, 24, 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[[-6, 48, -36, 48, -24],\n [-15, -20, 10, -32, 28],\n [16, 12, -4, 24, -24],\n [33, -19, 23, 2, -22],\n [7, 14, -8, 20, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-13, 11, -14, -4, 11],\n [-18, 18, -24, -24, 30],\n [27, -21, 26, -4, -13],\n [13, -8, 9, -16, 5],\n [-8, 4, -4, 16, -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[[-8, 10, 42, -19, 64],\n [2, 4, -7, -2, 0],\n [-12, 6, 40, -1, 33],\n [38, -42, 37, -37, 15],\n [-14, -2, 21, 15, -3]]\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, -28, -11, -28, 15],\n [25, 2, 34, 37, -50],\n [-30, 40, 20, 46, 4],\n [35, -32, -24, -47, -20],\n [-35, 35, -10, 6, 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[[30, 51, 39, -44, 45],\n [-3, -18, -20, 21, -5],\n [24, 4, 6, 24, 2],\n [0, -13, -7, 22, -15],\n [27, 21, 19, 1, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, -8, -16, -1, -18],\n [-16, 16, 16, 15, 30],\n [13, -13, -28, 0, -30],\n [11, -11, -4, -16, -18],\n [-15, 15, 36, -3, 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[[0, 0, 0, 0, 0],\n [16, 0, -16, 12, 0],\n [-16, 0, 16, -12, 0],\n [12, 0, -12, 9, 0],\n [16, 0, -16, 12, 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[[19, 31, 17, -14, -72],\n [53, -34, -46, -3, 5],\n [11, 16, 13, -13, -73],\n [74, 6, -29, 11, -13],\n [67, -5, -28, 19, -27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-21, 31, 33, 18, -31],\n [24, -32, -30, -12, 26],\n [0, 8, 18, 20, -22],\n [-30, 34, 24, 0, -16],\n [18, -14, 0, 16, -8]]\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, 0, 0, 0, 0],\n [1, 5, 0, 3, -1],\n [3, 15, 0, 9, -3],\n [6, 30, 0, 18, -6],\n [-4, -20, 0, -12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-24, -15, -3, 2, 5],\n [-11, -25, 24, -45, 18],\n [-26, -10, -12, 18, 0],\n [-33, -30, 9, -21, 15],\n [-12, -15, 9, -18, 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[[-24, 75, -48, 79, -30],\n [-12, -13, 6, -8, 17],\n [0, -34, 32, -4, -18],\n [-30, -6, 3, 41, -27],\n [-50, 39, -27, 108, -67]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-15, -2, -12, 7, 17],\n [-11, -4, 11, -9, -12],\n [-38, -12, -22, 34, 28],\n [-10, -2, -17, 18, 21],\n [-8, -8, 17, 2, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[5, -30, 10, 10, -5],\n [-1, 6, -2, -2, 1],\n [4, -24, 8, 8, -4],\n [0, 0, 0, 0, 0],\n [-3, 18, -6, -6, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[4, -4, 5, -2, 2],\n [4, -4, 5, -2, 2],\n [20, -20, 25, -10, 10],\n [-24, 24, -30, 12, -12],\n [4, -4, 5, -2, 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 5x5 matrix:\n[[-22, -64, 72, -14, 32],\n [37, 2, 36, 11, 39],\n [66, 18, -9, 51, 34],\n [26, 29, -15, 5, 10],\n [-43, -35, 33, -30, -7]]\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 5x5 matrix:\n[[4, 4, 0, -10, -12],\n [-4, -4, 0, 10, 12],\n [8, 8, 0, -20, -24],\n [-12, -12, 0, 30, 36],\n [-12, -12, 0, 30, 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[[15, 36, 8, -6, 32],\n [-19, -24, -49, 2, -5],\n [-16, -40, -42, 0, -22],\n [-12, 24, 10, 12, 16],\n [52, -20, 7, -36, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-26, -22, -35, -19, 51],\n [66, 4, -25, 24, 19],\n [-12, 16, -35, -28, 32],\n [-30, -30, 20, 5, -5],\n [-24, -26, 26, 9, -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[[-8, -4, -6, 0, 2],\n [16, 8, 12, 0, -4],\n [8, 4, 6, 0, -2],\n [24, 12, 18, 0, -6],\n [20, 10, 15, 0, -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 5x5 matrix:\n[[52, -20, 52, 28, 7],\n [40, -27, 24, 41, -4],\n [14, -48, 22, 19, -12],\n [-14, 50, -22, -15, 9],\n [-56, 57, -38, -52, 4]]\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, -12, -6, 0, 9],\n [-30, -24, -12, 0, 18],\n [15, 12, 6, 0, -9],\n [-30, -24, -12, 0, 18],\n [30, 24, 12, 0, -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[[12, -18, 0, -36, -30],\n [-6, 9, 0, 18, 15],\n [-8, 12, 0, 24, 20],\n [0, 0, 0, 0, 0],\n [12, -18, 0, -36, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[18, 4, -2, 0, -12],\n [-20, 22, 38, 28, -24],\n [12, 14, 14, 12, -24],\n [18, -13, -25, -18, 12],\n [-3, -12, -15, -12, 18]]\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[[-4, 3, 9, 19, 0],\n [0, 2, 4, 8, -2],\n [8, -4, -14, -30, -2],\n [8, -4, -14, -30, -2],\n [-24, -1, 16, 38, 19]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 6, -2, 30, 32],\n [9, 14, 4, 6, 7],\n [27, -26, -18, -7, -6],\n [11, -29, 24, 12, -16],\n [76, -4, -36, 4, 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[[2, 12, 10, 8, 8],\n [-4, -24, -20, -16, -16],\n [5, 30, 25, 20, 20],\n [3, 18, 15, 12, 12],\n [5, 30, 25, 20, 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[[-15, 10, 4, 9, -22],\n [20, -18, -2, -14, -34],\n [15, -16, -10, -19, -40],\n [13, -1, 43, 33, 25],\n [13, 0, 32, 26, 58]]\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 5x5 matrix:\n[[0, -17, -31, -45, 42],\n [17, -17, -13, -26, 22],\n [-2, -12, -24, -34, 32],\n [39, -21, 3, -12, 6],\n [-18, -6, -30, -36, 36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[30, -30, -30, -15, 10],\n [0, 0, 0, 0, 0],\n [12, -12, -12, -6, 4],\n [-12, 12, 12, 6, -4],\n [-36, 36, 36, 18, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -12, -6, -2, -4],\n [0, 36, 18, 6, 12],\n [0, -6, -3, -1, -2],\n [0, -30, -15, -5, -10],\n [0, -30, -15, -5, -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[[-5, -1, 3, -1, -1],\n [-20, -4, 12, -4, -4],\n [0, 0, 0, 0, 0],\n [-15, -3, 9, -3, -3],\n [5, 1, -3, 1, 1]]\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, 24, -12, 28, 28],\n [30, -24, -18, -18, -48],\n [-8, 4, -6, 6, 2],\n [2, 0, 6, -2, 4],\n [-9, 8, 9, 5, 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 5x5 matrix:\n[[-30, -36, 30, -12, -18],\n [25, 30, -25, 10, 15],\n [-30, -36, 30, -12, -18],\n [-10, -12, 10, -4, -6],\n [-5, -6, 5, -2, -3]]\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, 30, 5, -75, -46],\n [20, 2, -34, 4, -2],\n [6, 38, -9, -96, -27],\n [-18, 10, 9, -4, -23],\n [8, 8, 44, -34, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-7, -14, 26, -15, -30],\n [0, 14, 16, -20, 2],\n [-13, 0, 26, -7, 8],\n [-20, -8, 44, -14, -4],\n [4, -10, -28, 26, 6]]\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, -11, 14, 15, -1],\n [-15, -23, 14, 9, -3],\n [65, 5, -18, 9, -9],\n [-44, 4, -24, -36, 0],\n [35, -24, 32, 42, -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[[21, -27, -51, -18, -44],\n [35, 35, -5, -15, -5],\n [31, -11, -49, -30, -38],\n [29, 8, -23, -9, -24],\n [-3, -23, -27, -28, -10]]\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, 1, 22, 3, -21],\n [-8, 2, -16, 6, -2],\n [-32, -4, -16, -12, 36],\n [-2, 2, -10, 6, -6],\n [4, -1, 8, -3, 1]]?\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, -19, 8, -6, -5],\n [-10, 22, -20, -38, 38],\n [-8, -24, 12, 13, -22],\n [25, 23, 8, 13, 7],\n [-24, -15, -27, -19, -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[[6, -12, -18, -30, -24],\n [5, -10, -15, -25, -20],\n [-4, 8, 12, 20, 16],\n [-4, 8, 12, 20, 16],\n [3, -6, -9, -15, -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 5x5 matrix:\n[[30, 18, -18, -12, 0],\n [-30, -18, 18, 12, 0],\n [10, 6, -6, -4, 0],\n [-5, -3, 3, 2, 0],\n [10, 6, -6, -4, 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[[-6, -21, -21, 36, 39],\n [18, 10, -10, -42, -20],\n [-13, 13, 31, -27, -28],\n [-1, 16, 22, -29, -31],\n [36, 7, -34, -37, -11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, 4, 2, 3, 1],\n [6, -12, -6, -9, -3],\n [12, -24, -12, -18, -6],\n [0, 0, 0, 0, 0],\n [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[[-6, -11, 24, -22, -6],\n [-36, -42, 48, -36, 12],\n [36, 39, -36, 24, -18],\n [-12, -17, 28, -24, -2],\n [0, -4, 16, -16, -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[[-2, 11, -5, -10, 15],\n [5, 29, 1, 7, 20],\n [14, 5, 13, 16, 5],\n [7, -15, -3, -55, 50],\n [1, 15, 3, 23, -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[[16, 16, 24, 20, 0],\n [20, 20, 30, 25, 0],\n [12, 12, 18, 15, 0],\n [-8, -8, -12, -10, 0],\n [4, 4, 6, 5, 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[[20, 20, -25, 20, -30],\n [16, 16, -20, 16, -24],\n [4, 4, -5, 4, -6],\n [-16, -16, 20, -16, 24],\n [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[[-9, -30, 54, -6, 38],\n [-16, -72, 32, 58, 33],\n [-6, 30, -24, 16, 15],\n [16, 36, -68, 8, -30],\n [-9, -30, 42, -6, 2]]\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, 15, 1, -10, -24],\n [-1, 50, 6, -13, -18],\n [1, 45, -15, 13, -30],\n [48, 10, 78, -64, 24],\n [-19, 25, -21, 9, -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[[6, 12, 14, 0, 8],\n [-4, -6, -10, 0, -10],\n [-3, 0, -9, 0, -18],\n [11, 18, 27, 0, 24],\n [17, 33, 40, 0, 25]]?\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[[-48, -42, 30, 24, -36],\n [16, 24, -12, 8, 8],\n [4, -19, 2, -38, 12],\n [16, 24, -12, 8, 8],\n [-20, 0, 9, 38, -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[[-20, 14, 22, -28, -14],\n [-18, 30, 8, 0, 30],\n [-7, -6, -1, -18, -9],\n [-13, 12, 23, 34, 10],\n [-10, 16, -12, -22, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-19, -36, -22, -15, 11],\n [22, 54, 34, 24, -8],\n [-4, 2, 2, 2, 6],\n [8, 35, 23, 17, 3],\n [-14, -6, -2, 0, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-21, -10, -24, -2, 29],\n [-18, 37, 3, -19, -5],\n [-19, 2, -16, -6, 19],\n [-22, 42, 2, -22, -4],\n [-14, 32, 4, -16, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, 0, 0, 4, 2],\n [-5, 0, 0, -20, -10],\n [-5, 0, 0, -20, -10],\n [1, 0, 0, 4, 2],\n [1, 0, 0, 4, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -20, -20, -4, 16],\n [3, -15, -15, -3, 12],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [2, -10, -10, -2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-9, -9, 3, -8, -2],\n [5, -9, 18, -3, 12],\n [45, -22, 0, 0, -15],\n [-2, 21, -8, 33, -29],\n [4, 0, -23, -37, 36]]\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[[-22, 6, 12, 12, 14],\n [24, 4, -28, 4, 0],\n [25, 22, -45, 11, 1],\n [18, 18, -34, 8, 0],\n [-30, 1, 40, -27, -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 5x5 matrix:\n[[26, 7, -5, -20, 2],\n [-48, 4, 0, 30, 14],\n [-36, -5, 13, 31, -4],\n [32, 42, -14, -32, 30],\n [-28, 31, -7, 11, 32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[7, 21, 5, -26, 0],\n [-4, -52, -17, 42, 5],\n [0, 28, -2, -12, -28],\n [-14, -22, 8, 32, 20],\n [9, 51, -5, -38, -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[[-21, 12, 27, 15, 33],\n [-18, 6, 42, 24, 48],\n [13, -6, -23, -13, -27],\n [-14, 13, -4, -3, -1],\n [1, 3, -17, -10, -18]]\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[[-6, -24, 24, -6, -36],\n [2, 8, -8, 2, 12],\n [0, 0, 0, 0, 0],\n [-2, -8, 8, -2, -12],\n [2, 8, -8, 2, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[61, 19, -47, -28, -28],\n [-29, -40, 15, 5, 25],\n [24, -36, -55, -9, -8],\n [31, 58, 1, -31, -61],\n [-48, -41, 26, 25, 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 5x5 matrix:\n[[38, 9, -42, 13, -36],\n [-29, 5, 44, -8, 16],\n [29, -7, -22, 31, -18],\n [18, -19, 8, 14, -6],\n [-48, 35, 68, -63, 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[[12, 24, -16, -36, -15],\n [-2, -21, 14, 6, 11],\n [10, 39, -26, -30, -22],\n [8, -18, 12, -24, 7],\n [0, -6, 4, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[9, 2, -2, 17, 4],\n [15, 6, 6, 15, 12],\n [12, 4, 2, 16, 8],\n [3, 6, 18, -21, 12],\n [-14, -12, -28, 18, -24]]\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, -27, 0, -9, -21],\n [8, 1, 16, -2, -1],\n [-17, 5, -1, -10, 39],\n [-8, -10, -34, 5, -14],\n [20, -32, -14, -3, -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 5x5 matrix:\n[[-8, -29, 15, -12, 1],\n [-31, -22, 31, -25, 9],\n [35, -7, -29, 2, 0],\n [22, 22, 5, 1, 0],\n [3, -11, 16, -11, 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[[-7, 3, -9, 6, -1],\n [29, -22, 71, -37, -18],\n [-31, 3, -20, 19, -2],\n [14, 50, -38, -17, 10],\n [10, 51, -47, -14, 24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-36, 6, 3, 36, -18],\n [-5, 17, 2, -1, 4],\n [-5, -17, 42, -37, 19],\n [36, -28, 34, -36, 35],\n [-5, 1, 51, -37, 31]]\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, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [3, 2, 3, 1, -5],\n [-6, -4, -6, -2, 10],\n [3, 2, 3, 1, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 0, 13, -14, -12],\n [-13, -6, -11, 23, 5],\n [-5, 9, 1, 0, -12],\n [-16, 48, 2, -8, -28],\n [-29, 24, -22, 31, 43]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[44, -14, -18, 10, 34],\n [22, 4, 24, 7, -52],\n [-9, 26, -43, -60, 6],\n [-7, 19, -32, -59, -1],\n [24, -17, -19, -6, 43]]\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[[5, -78, -61, 18, -23],\n [40, -27, 8, 29, 6],\n [45, -54, -15, 18, 0],\n [-5, 39, 33, 19, -8],\n [10, 18, 8, -34, -36]]\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[[7, -9, 4, -8, -6],\n [-9, 31, -28, 0, 34],\n [-10, 8, 0, 14, 2],\n [24, -9, -12, -39, 9],\n [6, -15, 12, -3, -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[[0, 54, -20, -4, 38],\n [0, -5, 35, 3, -3],\n [0, 15, 11, 3, 9],\n [0, 17, -21, 28, -8],\n [0, 31, -36, -56, 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[[-4, 10, -30, -21, -32],\n [-28, 2, 58, 29, 16],\n [13, -36, -30, 2, 23],\n [-15, -60, 2, -2, 15],\n [-4, 32, -8, -14, -32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[24, -18, 6, 18, 0],\n [-16, 6, -14, -2, 12],\n [-10, 15, 10, -20, -15],\n [-12, 18, 12, -24, -18],\n [34, -15, 26, 8, -21]]\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, 29, 4, 30, 14],\n [-10, 8, -29, -29, 1],\n [12, 17, -26, 6, 26],\n [25, 11, 21, -1, -12],\n [15, 19, -10, -25, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1, -4, 4, -1, 3],\n [-5, -20, 20, -5, 15],\n [1, 4, -4, 1, -3],\n [6, 24, -24, 6, -18],\n [5, 20, -20, 5, -15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-3, -13, 11, -30, -23],\n [13, 9, 24, 11, 13],\n [4, 12, 27, -7, 0],\n [19, -1, 2, 35, 27],\n [-15, 33, 15, -12, -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[[-13, -13, 15, 5, -5],\n [-37, 8, -12, -4, 20],\n [-5, -15, 13, 15, -15],\n [7, 17, -7, -31, 25],\n [7, -38, 48, 13, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -36, 6, 30, 6],\n [3, 18, -3, -15, -3],\n [4, 24, -4, -20, -4],\n [-4, -24, 4, 20, 4],\n [-6, -36, 6, 30, 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 5x5 matrix:\n[[10, 24, 50, 26, -43],\n [-10, -2, -20, 2, 25],\n [30, -2, 20, -22, -35],\n [-10, 30, 40, 46, -20],\n [10, 0, -10, -10, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 1, 6, 5, -6],\n [6, -1, -6, -5, 6],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [24, -4, -24, -20, 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[[-54, 4, -39, 14, -3],\n [42, 12, 35, -15, 8],\n [-36, 36, 38, -38, 39],\n [18, 16, 73, -50, 36],\n [54, 12, 15, -10, -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[[-2, -2, -4, 3, 4],\n [-4, -4, -8, 6, 8],\n [2, 2, 4, -3, -4],\n [6, 6, 12, -9, -12],\n [-10, -10, -20, 15, 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 5x5 matrix:\n[[-32, -33, -22, -47, 47],\n [8, 25, 16, 10, -26],\n [-7, -29, 0, -4, 19],\n [-17, -26, -10, -15, 32],\n [25, 13, 40, 26, -51]]\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[[19, -8, 10, 29, 5],\n [21, 6, -6, 31, 7],\n [3, 36, -24, -22, 11],\n [26, -1, 8, 31, 10],\n [-19, -17, 20, -29, -7]]\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 5x5 matrix:\n[[-35, -2, -18, -13, -16],\n [-1, 47, 36, -47, 7],\n [-17, 0, 14, -7, -18],\n [48, -18, 31, 14, 23],\n [11, 33, 39, -39, 13]]\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, -5, 1, 21, 25],\n [-84, 28, 43, 46, -22],\n [-40, 7, 26, 27, -2],\n [12, 2, 70, -18, 7],\n [-10, -4, 67, 26, 32]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-10, 0, 10, 2, 10],\n [30, 0, -30, -6, -30],\n [-30, 0, 30, 6, 30],\n [15, 0, -15, -3, -15],\n [-15, 0, 15, 3, 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[[3, -5, 0, 5, 6],\n [-6, 10, 0, -10, -12],\n [12, -20, 0, 20, 24],\n [12, -20, 0, 20, 24],\n [6, -10, 0, 10, 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[[10, 5, 15, 0, 20],\n [2, 1, 3, 0, 4],\n [8, 4, 12, 0, 16],\n [6, 3, 9, 0, 12],\n [-12, -6, -18, 0, -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[[-6, -3, -3, 18, -3],\n [2, 1, 1, -6, 1],\n [-8, -4, -4, 24, -4],\n [8, 4, 4, -24, 4],\n [-8, -4, -4, 24, -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[[26, -21, -11, 13, -10],\n [8, 19, -37, -3, 22],\n [-19, 11, 3, -14, 11],\n [2, 5, 9, 9, -8],\n [17, -16, -12, 5, -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[[-30, -6, 26, 11, -29],\n [45, -55, 35, 15, -13],\n [54, -70, 26, 51, 3],\n [33, 4, -27, -4, 40],\n [42, -41, 19, 1, -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[[-6, 3, -2, -5, -1],\n [-24, 12, -8, -20, -4],\n [30, -15, 10, 25, 5],\n [6, -3, 2, 5, 1],\n [-6, 3, -2, -5, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-50, 26, -24, 36, -14],\n [9, -21, -12, -33, -24],\n [33, -13, 20, -17, 16],\n [-7, -5, -12, -9, -16],\n [-18, -6, -24, -12, -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[[12, -18, 17, -18, 3],\n [42, 4, -40, -29, -12],\n [-26, 5, 24, 26, 9],\n [-17, 26, 30, 44, 6],\n [19, -7, -31, -28, -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[[23, 21, 18, 4, -12],\n [-37, -21, -41, -3, 11],\n [-30, -52, -28, -46, -2],\n [-30, -45, -25, -30, 10],\n [-34, -69, -15, -52, 0]]\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 5x5 matrix:\n[[-2, 2, 0, -5, 0],\n [8, -8, 0, 20, 0],\n [-4, 4, 0, -10, 0],\n [0, 0, 0, 0, 0],\n [-10, 10, 0, -25, 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 5x5 matrix:\n[[-12, -10, 37, 18, -27],\n [13, -20, -14, 7, 42],\n [-12, 22, 4, -12, -38],\n [14, 24, -30, -34, -2],\n [-3, 18, 20, -9, -38]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -20, -12, 19, -1],\n [-10, 20, 18, -16, -6],\n [14, 24, 6, -27, 11],\n [18, -12, -18, 6, 12],\n [-16, -16, 0, 20, -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[[-20, -12, 12, 8, -8],\n [15, 9, -9, -6, 6],\n [-10, -6, 6, 4, -4],\n [-25, -15, 15, 10, -10],\n [-5, -3, 3, 2, -2]]?\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[[3, 15, -9, 12, -3],\n [2, 10, -6, 8, -2],\n [6, 30, -18, 24, -6],\n [0, 0, 0, 0, 0],\n [-3, -15, 9, -12, 3]]\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[[44, 7, 53, 23, 18],\n [-20, -15, -11, -45, 0],\n [9, 10, 0, 32, 0],\n [4, 3, -11, 31, 22],\n [-9, -23, 6, -56, 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[[-1, -6, -2, 1, -3],\n [-2, -12, -4, 2, -6],\n [-3, -18, -6, 3, -9],\n [6, 36, 12, -6, 18],\n [-4, -24, -8, 4, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[38, 0, -21, 17, -15],\n [-33, 2, 18, -4, 7],\n [18, -4, -6, -22, 10],\n [-28, 8, 18, 22, -8],\n [8, -12, -25, -7, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-15, 12, -34, 2, -9],\n [10, 6, 8, -4, 8],\n [-15, 12, -34, 2, -9],\n [6, 12, -4, -4, 6],\n [-10, -27, 14, 8, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-72, 18, 12, 0, -48],\n [-18, 5, -1, -3, -13],\n [-6, 5, -27, -21, -11],\n [54, -13, -13, -3, 35],\n [-30, 11, -23, -21, -27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-13, -66, -26, 13, -39],\n [31, -53, 20, -25, -27],\n [-39, 6, -42, 26, -8],\n [-32, 26, -40, 4, -14],\n [-33, 45, -12, 35, 19]]\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 5x5 matrix:\n[[-19, -7, 1, -15, 8],\n [0, 13, -28, -3, -25],\n [37, -17, 11, 21, -10],\n [3, 13, 38, 18, 40],\n [-21, -3, 21, -9, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, -7, 17, -4, 48],\n [-66, -12, -26, 12, 0],\n [-37, -26, -69, -23, -45],\n [-38, -7, -1, 8, 24],\n [53, 7, 10, -14, -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[[-8, 17, -6, 13, -3],\n [-25, 43, 2, -12, 51],\n [14, -12, -7, 36, -54],\n [-9, 14, 18, 3, 51],\n [6, 32, 8, 34, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-39, 9, -31, -4, -42],\n [-24, -30, -34, -37, -78],\n [2, 25, 17, 16, 36],\n [-29, 40, 10, 6, 9],\n [-27, 24, 6, -3, -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[[-3, -5, 10, 13, -12],\n [0, 30, -24, -6, 18],\n [2, -10, 4, -6, 0],\n [-4, -5, 12, 17, -15],\n [-3, 5, 2, 11, -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 5x5 matrix:\n[[2, 28, -5, -14, 19],\n [-6, -18, -33, 24, 39],\n [-18, -13, -1, 9, 35],\n [4, -20, -22, 20, 2],\n [22, 6, -17, 2, -29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[22, 20, 8, 56, -10],\n [-23, -34, 8, 2, 17],\n [10, 20, -10, -25, -10],\n [-4, 0, -6, -27, 0],\n [19, 18, 6, 45, -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[[22, 15, 5, 11, 11],\n [-22, -16, 13, -22, 11],\n [-6, -6, 33, -24, 39],\n [-26, -17, -19, -5, -29],\n [-36, -25, 0, -23, -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[[-10, 0, 10, -25, 0],\n [2, 0, -2, 5, 0],\n [2, 0, -2, 5, 0],\n [2, 0, -2, 5, 0],\n [-2, 0, 2, -5, 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[[19, 43, 8, -27, 52],\n [38, 34, -47, 10, 16],\n [27, -1, 25, 29, -4],\n [-49, -49, 49, -6, -31],\n [-18, -66, -12, 54, -84]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, -3, 29, 48, -10],\n [-12, -3, -7, -21, 5],\n [-9, -1, 7, 6, 10],\n [-54, -7, -3, -43, 55],\n [45, 10, -34, -27, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-22, 12, 32, 56, 18],\n [-12, -18, 6, -30, -18],\n [12, 3, -13, -7, 1],\n [15, 0, -18, -18, -3],\n [-21, 6, 28, 40, 11]]\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[[11, -5, -22, 2, 28],\n [-2, 2, 8, 4, -12],\n [4, -4, -16, -8, 24],\n [3, 6, 21, 30, -39],\n [-18, 3, 17, -24, -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[[0, 30, 0, -30, 30],\n [0, 12, 0, -12, 12],\n [0, -6, 0, 6, -6],\n [0, 24, 0, -24, 24],\n [0, 12, 0, -12, 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[[-2, -22, 27, 4, -22],\n [-18, 12, 12, -6, -30],\n [-2, -12, 16, 2, -14],\n [0, 0, 0, 0, 0],\n [11, 6, -22, 1, 29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[49, 15, 18, -50, -4],\n [-34, -18, -3, 29, 11],\n [-1, -15, 18, -10, 16],\n [34, 6, 18, -38, 2],\n [-9, -15, 12, 0, 14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -24, 16, -12, 8],\n [-2, 12, -8, 6, -4],\n [-6, 36, -24, 18, -12],\n [-4, 24, -16, 12, -8],\n [6, -36, 24, -18, 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[[0, 4, 1, 14, -2],\n [30, -14, -23, 2, -32],\n [-26, 15, 21, 5, 26],\n [-15, -11, 0, 2, 31],\n [36, -21, -29, -9, -36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-20, -12, -8, 24, 12],\n [-25, -15, -10, 30, 15],\n [25, 15, 10, -30, -15],\n [10, 6, 4, -12, -6],\n [-25, -15, -10, 30, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-12, 18, 32, -31, 42],\n [36, 22, 2, -22, 2],\n [-42, -5, -7, 2, 11],\n [28, 4, 0, -1, -10],\n [6, 27, 47, -43, 51]]\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[[9, 22, 1, -16, -4],\n [21, 38, 17, -8, -8],\n [0, 20, -22, -44, -2],\n [0, 0, 0, 0, 0],\n [9, 32, -10, -38, -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[[-36, -36, 30, 30, 36],\n [24, 24, -20, -20, -24],\n [30, 30, -25, -25, -30],\n [30, 30, -25, -25, -30],\n [24, 24, -20, -20, -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[[-9, -11, -8, 41, 15],\n [-37, -25, -34, 9, 11],\n [-15, 2, -32, -33, 12],\n [-22, -21, -6, 10, -7],\n [30, -6, 66, 24, -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[[29, -24, 10, -9, -16],\n [1, 27, -31, -6, 34],\n [5, -30, -32, 54, -10],\n [28, -26, -62, 48, 20],\n [37, -23, -9, -4, -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[[10, -25, 0, -10, 30],\n [0, 0, 0, 0, 0],\n [-4, 10, 0, 4, -12],\n [4, -10, 0, -4, 12],\n [-10, 25, 0, 10, -30]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[32, -20, 22, -24, -6],\n [19, -2, -5, 21, -9],\n [40, -17, 16, -24, 0],\n [48, -9, 0, 0, 0],\n [8, -7, 14, -48, 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[[3, 7, -6, -5, 0],\n [3, 5, -18, -25, 0],\n [4, 7, -22, -30, 0],\n [-11, -27, 14, 5, 0],\n [3, 9, 6, 15, 0]]\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, 10, -2, 4, 5],\n [6, -4, -14, 6, -14],\n [8, -16, -4, -10, 4],\n [-24, 30, -6, 21, -7],\n [27, -34, -5, -18, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[20, 12, -4, 4, 16],\n [30, 18, -6, 6, 24],\n [-20, -12, 4, -4, -16],\n [-15, -9, 3, -3, -12],\n [5, 3, -1, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, -12, -12, 0, -6],\n [15, -20, -20, 0, -10],\n [-6, 8, 8, 0, 4],\n [-12, 16, 16, 0, 8],\n [12, -16, -16, 0, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[38, -10, -60, -50, 6],\n [-58, -28, 20, 42, -36],\n [-35, 23, 50, 63, -19],\n [-20, 5, 15, 30, -16],\n [-2, 6, -5, 30, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[19, 30, 33, -15, 30],\n [5, 8, -1, 27, -8],\n [30, 60, 64, 6, 24],\n [14, 15, -9, 28, 21],\n [19, -16, -33, 21, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[18, 8, 15, -4, -22],\n [-2, -2, -1, 2, 8],\n [38, -7, 53, 32, -25],\n [30, -15, 51, 42, -21],\n [28, -22, 54, 52, -2]]?\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 5x5 matrix:\n[[30, 29, -22, 33, -34],\n [-15, 11, 21, 9, -1],\n [-14, 35, 6, 25, 18],\n [-18, 42, 14, 45, 15],\n [-40, -51, 28, -32, 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[[-46, -15, -3, -8, -11],\n [0, 36, -30, -18, 43],\n [18, 13, 1, -68, -15],\n [-3, 19, -10, -19, -18],\n [4, 25, -17, 15, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, -18, 22, -6, 2],\n [18, 24, 44, -7, -14],\n [34, 22, 78, -13, -36],\n [-2, 80, 26, 15, 6],\n [-42, -12, 33, 2, 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[[-31, -2, -40, -14, -27],\n [82, 12, 14, 23, 0],\n [-78, 36, 3, -9, 9],\n [-44, 32, 14, -8, -12],\n [-56, 48, -22, -14, -42]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -6, -6, -4, 8],\n [6, -3, -3, -2, 4],\n [0, 0, 0, 0, 0],\n [-6, 3, 3, 2, -4],\n [6, -3, -3, -2, 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[[4, -10, 0, 6, -10],\n [8, -20, 0, 12, -20],\n [-10, 25, 0, -15, 25],\n [6, -15, 0, 9, -15],\n [-2, 5, 0, -3, 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 5x5 matrix:\n[[-10, -6, 2, -5, 9],\n [10, 6, -2, 5, -9],\n [30, 26, -14, 19, -23],\n [30, 24, -12, 18, -24],\n [-5, -10, 8, -6, 1]]\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, -17, -29, -7, 10],\n [19, -26, -33, -17, 5],\n [-17, 23, 27, 47, 4],\n [-11, 19, 13, 50, 13],\n [13, -24, -19, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[23, -17, 10, -6, 7],\n [23, -45, 2, -21, 27],\n [-30, 70, 0, 35, -45],\n [-16, -4, -12, -3, 5],\n [3, 7, 6, -1, 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[[5, 10, 25, 30, -5],\n [6, 12, 30, 36, -6],\n [2, 4, 10, 12, -2],\n [-5, -10, -25, -30, 5],\n [4, 8, 20, 24, -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[[-30, 15, 15, -15, 5],\n [-6, 3, 3, -3, 1],\n [18, -9, -9, 9, -3],\n [-36, 18, 18, -18, 6],\n [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[[56, -2, -14, 6, 26],\n [5, -7, -6, 10, -9],\n [-46, 6, -31, -21, 23],\n [36, -34, -49, 25, 9],\n [17, 12, -5, 9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 6, -10, -10, 4],\n [-4, -12, 20, 20, -8],\n [-6, -18, 30, 30, -12],\n [-1, -3, 5, 5, -2],\n [6, 18, -30, -30, 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[[-14, 0, 4, 8, 3],\n [-15, -3, -6, -5, -14],\n [-25, 55, 30, -20, -45],\n [-54, 26, 20, 4, -26],\n [2, 4, 12, 15, 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[[-1, 5, 4, 2, -3],\n [-6, 0, -21, -23, -13],\n [-6, 24, 15, 5, -17],\n [-11, 19, -10, -20, -27],\n [8, -10, 13, 19, 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[[0, 0, 0, 0, 0],\n [18, -12, 12, -18, 15],\n [30, -20, 20, -30, 25],\n [12, -8, 8, -12, 10],\n [-24, 16, -16, 24, -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[[9, -3, -12, -12, 24],\n [17, -36, -11, -11, -27],\n [42, -66, -36, -36, -12],\n [-21, 33, 18, 18, 6],\n [-22, 42, 16, 16, 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[[-2, 5, -24, -22, 2],\n [9, 14, -33, -33, 4],\n [0, -15, 24, 18, -4],\n [8, -34, 24, 4, -8],\n [22, 5, -9, -19, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[18, 5, 17, 22, 6],\n [10, 4, 18, 11, -4],\n [-18, -6, -24, -21, 0],\n [-4, 4, 32, -10, -32],\n [0, -3, -21, 3, 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 5x5 matrix:\n[[12, -16, -24, 8, -16],\n [12, -16, -24, 8, -16],\n [0, 0, 0, 0, 0],\n [-6, 8, 12, -4, 8],\n [-3, 4, 6, -2, 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[[0, 0, 0, 0, 0],\n [20, -8, 20, -12, -12],\n [-15, 6, -15, 9, 9],\n [20, -8, 20, -12, -12],\n [10, -4, 10, -6, -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 5x5 matrix:\n[[-13, 26, 30, -25, -28],\n [-7, -10, -6, -19, -4],\n [-8, 9, 12, -17, -14],\n [1, -6, -6, 1, 4],\n [15, -25, -30, 30, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[16, 14, 16, 7, -13],\n [2, -2, -8, -11, -1],\n [-34, -32, -40, -22, 28],\n [1, -4, -12, -15, 0],\n [-16, -20, -32, -26, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[7, -10, -13, -18, 40],\n [-13, 0, 17, 12, -20],\n [28, 12, -32, -12, 8],\n [3, -8, -7, -12, 28],\n [-13, -13, 12, -3, 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 5x5 matrix:\n[[-30, 20, 14, 8, -4],\n [21, 11, 8, 2, 5],\n [33, 0, 9, -2, 6],\n [3, 33, 36, 10, 3],\n [-16, -3, -11, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-16, 22, 4, 41, 9],\n [58, 18, 42, -18, -33],\n [9, -18, 14, 17, -30],\n [4, -12, -28, -70, -40],\n [20, 2, 40, 51, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-36, -24, -30, -24, 18],\n [18, 12, 15, 12, -9],\n [30, 20, 25, 20, -15],\n [-24, -16, -20, -16, 12],\n [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[[30, 24, 0, -6, -36],\n [-30, -24, 0, 6, 36],\n [-30, -24, 0, 6, 36],\n [0, 0, 0, 0, 0],\n [10, 8, 0, -2, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 18, 3, 3, -15],\n [14, 21, 11, -19, -10],\n [6, 9, 9, -21, 0],\n [0, 0, 0, 0, 0],\n [14, 21, 11, -19, -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[[-3, -12, -33, -27, -38],\n [1, -2, -9, -7, -10],\n [-9, 9, 51, 39, 56],\n [-30, -21, 0, -6, -6],\n [-18, 0, 42, 30, 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[[-19, -9, -18, -3, -18],\n [-4, -18, 0, -21, -9],\n [14, -22, 20, -34, 4],\n [16, 4, 16, -2, 14],\n [30, -18, 36, -36, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-24, 2, 2, 0, -38],\n [-36, -2, -33, 35, -19],\n [-27, 18, -34, 23, -21],\n [11, -12, 30, -21, -3],\n [3, 3, -17, 13, 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[[8, 16, -24, 12, 20],\n [6, 12, -18, 9, 15],\n [-12, -24, 36, -18, -30],\n [-4, -8, 12, -6, -10],\n [4, 8, -12, 6, 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 5x5 matrix:\n[[-7, 1, -26, 6, 2],\n [6, -20, -20, -4, 34],\n [31, -12, 32, -25, 34],\n [11, 50, 6, -10, -35],\n [-41, -69, -44, 35, 33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, -12, -6, -9, -21],\n [23, 38, 19, 15, -19],\n [-10, -10, -5, 0, 30],\n [-27, -42, -21, -15, 31],\n [-9, -6, -3, 3, 37]]\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, -27, 36, -26, 12],\n [41, 29, -33, 35, -20],\n [12, -23, -5, 7, 1],\n [29, 21, -37, 35, -25],\n [-71, -28, 9, -21, 18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[25, 60, 41, -5, 64],\n [-20, -24, -18, -2, -22],\n [-33, 12, -1, -11, 24],\n [-20, 21, 0, 3, 25],\n [-20, -18, -26, 16, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[9, 5, -1, 20, -32],\n [-24, -6, -8, -34, 21],\n [51, 3, 5, 44, -10],\n [5, 11, 20, 36, -27],\n [2, 8, 8, 20, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-13, -3, -13, -26, -19],\n [5, 14, 32, 34, 42],\n [-1, -8, -39, -35, -49],\n [-64, -37, -24, 4, -14],\n [-12, 6, -6, -3, -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 5x5 matrix:\n[[-40, -15, -53, -27, 25],\n [25, -78, -28, 24, -32],\n [0, -14, -1, -2, 36],\n [-8, -5, -23, -17, 7],\n [20, -14, -3, 4, -27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[15, 0, -25, 15, 15],\n [15, 0, -25, 15, 15],\n [-15, 0, 25, -15, -15],\n [15, 0, -25, 15, 15],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[0, 0, 0, 0, 0],\n [0, 0, 8, -10, -6],\n [0, 0, -20, 25, 15],\n [0, 0, -20, 25, 15],\n [0, 0, 8, -10, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 18, -18, 0, 15],\n [0, 12, -12, 0, 10],\n [0, -6, 6, 0, -5],\n [0, 24, -24, 0, 20],\n [0, -18, 18, 0, -15]]?\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, 30, -50, -30, 25],\n [-6, -22, 1, 2, 3],\n [-42, -30, 39, -24, 51],\n [62, -13, 53, 31, -55],\n [39, -29, 11, 43, -38]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -11, -24, 2, -22],\n [0, -3, -10, 2, -8],\n [0, 11, -14, 14, 0],\n [0, -1, 3, -2, 1],\n [0, -4, -7, 0, -7]]\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, -10, -20, 25, -5],\n [0, 0, 0, 0, 0],\n [0, 2, 4, -5, 1],\n [0, 12, 24, -30, 6],\n [0, -4, -8, 10, -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[[0, 9, 7, -16, 9],\n [9, 0, -4, -14, 9],\n [-9, 0, 4, 14, -9],\n [-21, 15, 21, 6, -6],\n [20, -4, -12, -24, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-36, -54, 7, 16, -15],\n [4, 6, 21, 20, 18],\n [-8, -12, 14, 16, 6],\n [-8, -12, 14, 16, 6],\n [24, 36, 2, -4, 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 5x5 matrix:\n[[-2, -14, 12, 12, -12],\n [-13, -7, -20, -54, 36],\n [-24, -9, -28, 22, -8],\n [-39, -27, -14, -15, -3],\n [-14, 1, 2, 23, -25]]\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[[-3, -9, 4, 1, 15],\n [-10, 2, 0, -6, 6],\n [-11, 31, -12, -15, -33],\n [28, -44, 16, 28, 36],\n [-12, 36, -14, -17, -39]]\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[[13, 8, 17, -61, 25],\n [-34, -16, 18, -18, 54],\n [-30, -5, 9, 23, 19],\n [-37, -16, 11, 9, 39],\n [-1, 15, 8, 8, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-24, -8, 0, 3, 10],\n [-15, 2, 0, -13, -6],\n [27, 6, 0, 3, -6],\n [42, 4, 0, 16, 0],\n [33, 18, 0, -19, -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 5x5 matrix:\n[[8, 24, 12, -8, -16],\n [6, 18, 9, -6, -12],\n [8, 24, 12, -8, -16],\n [0, 0, 0, 0, 0],\n [-8, -24, -12, 8, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, 18, 9, -3, 9],\n [0, 0, 0, 0, 0],\n [-12, -24, -12, 4, -12],\n [-12, -24, -12, 4, -12],\n [18, 36, 18, -6, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-42, 16, -16, -26, -12],\n [13, -26, 8, -14, 25],\n [-59, -11, -22, -59, 16],\n [22, -29, 2, 19, 25],\n [31, 42, 24, 18, -41]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 6, -6, 9, 0],\n [0, -6, 6, -9, 0],\n [0, 6, -6, 9, 0],\n [0, 0, 0, 0, 0],\n [0, 10, -10, 15, 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[[-20, -16, -8, 12, -12],\n [15, 12, 6, -9, 9],\n [-5, -4, -2, 3, -3],\n [-30, -24, -12, 18, -18],\n [-20, -16, -8, 12, -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 5x5 matrix:\n[[30, 12, 30, -9, -33],\n [-6, 12, -15, 27, 21],\n [24, 16, 20, 4, -20],\n [18, 20, 10, 17, -7],\n [-28, -16, -25, 0, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[19, 37, -25, 17, 17],\n [7, -15, -7, -13, -31],\n [-10, -18, 1, -6, 34],\n [-24, 16, 54, 24, 24],\n [37, -19, -16, -12, -23]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-60, -10, 25, -37, 10],\n [-28, -16, -8, -28, 2],\n [-22, -8, 35, 1, -27],\n [-66, -19, 34, -30, -9],\n [-68, -20, 62, -18, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[13, 7, -11, -10, 7],\n [64, 2, 15, -28, -33],\n [-15, 2, 20, 16, -5],\n [-24, -1, -7, -4, 7],\n [-37, -17, 21, 58, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[20, -5, -55, 10, 30],\n [12, -15, -3, -20, -8],\n [-4, 37, -7, 28, 24],\n [20, 21, -4, -11, 9],\n [-16, 6, 59, -17, -33]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1, -33, 37, -21, 8],\n [-11, -20, 17, 18, 10],\n [10, -16, 20, 16, -16],\n [-2, -21, 20, -10, 6],\n [-40, -32, 10, -1, 52]]\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[[9, -4, -22, -10, -31],\n [48, -32, -4, 62, -24],\n [-21, 20, -6, -24, 11],\n [18, -19, -48, -12, -66],\n [35, -3, -70, 58, -41]]\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[[31, 11, 9, -20, 25],\n [63, 25, 3, -56, 62],\n [-3, -48, -9, 30, 12],\n [33, 40, 21, -36, 14],\n [34, -39, -18, -6, 57]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[7, 14, -2, -2, 2],\n [9, 9, 13, 15, 0],\n [4, 2, 11, 0, -27],\n [-13, -41, 31, 25, -28],\n [-9, -36, 36, 24, -42]]\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, 11, -1, -3, 8],\n [19, -19, 11, -15, -16],\n [19, -19, 11, -15, -16],\n [-5, 5, -2, 2, 4],\n [39, -39, 2, 14, -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[[30, -36, -24, 6, -24],\n [19, -12, -20, 29, 16],\n [25, -39, -16, -16, -46],\n [20, -33, -12, -17, -42],\n [3, -9, 0, -12, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[26, -24, 40, -54, 14],\n [5, 14, 34, -19, 3],\n [17, 20, 50, -55, 3],\n [21, 2, 68, -67, 11],\n [-22, 31, 46, -5, -3]]\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[[-8, -8, -16, -20, 20],\n [0, 0, 0, 0, 0],\n [-8, -8, -16, -20, 20],\n [4, 4, 8, 10, -10],\n [4, 4, 8, 10, -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 5x5 matrix:\n[[7, 22, -10, 16, -17],\n [38, 30, 3, -2, -14],\n [9, 12, -15, -26, 11],\n [-33, -26, -10, -16, 23],\n [75, 18, 36, -36, 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[[-3, -6, -18, 5, -34],\n [-13, -17, 24, 1, 52],\n [9, 13, -12, -3, -30],\n [26, 24, -36, 14, -40],\n [15, 17, -24, 3, -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[[17, -15, 19, -1, -18],\n [3, 3, 6, 11, 12],\n [8, 6, 9, 50, -26],\n [-11, 10, -22, -11, 2],\n [1, -16, 30, -17, 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[[-13, 53, 46, 26, 18],\n [-6, 33, 30, 20, 5],\n [-2, 18, 7, 5, 1],\n [-20, 10, 18, 28, 70],\n [9, -16, -23, -25, -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[[30, -7, -25, -9, -3],\n [-8, 20, 31, 2, 11],\n [34, 34, 3, -16, 11],\n [3, 56, 29, -22, 12],\n [-19, 36, 16, 28, 13]]\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[[-21, 0, -30, 16, 15],\n [-18, 15, -39, -28, -22],\n [-50, 10, -78, 22, 22],\n [-7, -37, -9, -45, -3],\n [-25, -13, -39, -16, 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 5x5 matrix:\n[[18, -61, 38, 0, -7],\n [-4, -25, 22, 12, 10],\n [16, 2, 18, 24, -51],\n [-16, -1, 45, 72, -22],\n [13, -51, 47, 18, -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[[6, -26, 36, 22, 22],\n [-31, -16, -15, -4, -29],\n [-23, -14, 9, 34, 21],\n [-43, -8, -21, 16, -11],\n [1, -8, -6, -26, -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[[-53, -13, 34, -26, 10],\n [13, -17, -9, 58, 19],\n [59, 1, -44, 18, -26],\n [48, 20, -31, 16, -11],\n [-35, 8, 11, -72, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -21, 13, 28, -23],\n [-22, 33, 39, -14, -5],\n [-7, 18, 6, 1, -26],\n [-3, -3, 17, 19, -29],\n [-5, 15, -5, -35, 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[[0, -9, -6, -6, 18],\n [0, -6, -4, -4, 12],\n [0, 12, 8, 8, -24],\n [0, -6, -4, -4, 12],\n [0, -15, -10, -10, 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, 18, 3, 6, 3],\n [1, -6, -1, -2, -1],\n [3, -18, -3, -6, -3],\n [-3, 18, 3, 6, 3],\n [-4, 24, 4, 8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, 36, 23, -44, 14],\n [0, 30, 22, -22, 4],\n [27, -19, -26, 8, 17],\n [-43, -19, 0, 4, -11],\n [33, -29, -32, 35, 24]]\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[[-30, -18, -36, 24, 30],\n [-15, -9, -18, 12, 15],\n [-15, -9, -18, 12, 15],\n [0, 0, 0, 0, 0],\n [10, 6, 12, -8, -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[[-21, -62, 5, 8, -8],\n [-8, 11, 12, -49, -25],\n [-2, 8, 52, -26, -72],\n [37, 39, -37, -10, 46],\n [-20, 23, 41, -19, -54]]\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, 15, 5, 0, -30],\n [6, 18, 6, 0, -36],\n [-12, -14, -11, -3, 35],\n [-2, 16, -1, -3, -25],\n [4, -10, 3, 3, 13]]\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[[9, -1, -33, 19, 15],\n [-32, 1, 60, -32, -26],\n [-29, -42, 33, 17, -41],\n [-26, 2, 54, -30, -23],\n [14, -16, -26, 26, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-24, 2, 22, 15, 12],\n [-8, 3, -38, 4, -14],\n [28, -55, 38, -25, 8],\n [10, -9, -23, -30, -12],\n [4, -24, 10, -4, 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[[2, -1, 69, -52, 82],\n [51, -40, -27, 3, -66],\n [13, -15, -30, 25, -50],\n [37, -30, 11, -19, -12],\n [23, -10, 3, -19, -6]]?\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 5x5 matrix:\n[[-21, 23, -11, -17, 16],\n [-19, 19, -17, -7, 14],\n [-10, 11, -15, -2, 7],\n [-18, 27, 9, -42, 15],\n [-20, 14, 35, -28, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 0, -18, 3, 6],\n [21, -6, 36, 3, -18],\n [-36, 16, -36, -18, 28],\n [-1, -2, -12, 5, 2],\n [3, -6, -18, 12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-45, 13, -11, -43, 0],\n [-9, 32, 14, -11, -39],\n [21, -27, -32, 46, 46],\n [-51, -10, -35, -9, 22],\n [-6, 48, 21, -48, -35]]\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[[3, -18, -9, -6, 3],\n [-21, -18, -33, -2, 7],\n [28, -24, 12, -12, 0],\n [-3, 18, 9, 6, -3],\n [-30, 36, -6, 16, -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[[24, 0, 16, -8, 8],\n [-30, 0, -20, 10, -10],\n [6, 0, 4, -2, 2],\n [-18, 0, -12, 6, -6],\n [-12, 0, -8, 4, -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[[-14, 12, -11, 17, -16],\n [2, -12, -19, -5, -8],\n [-6, 16, 17, 10, 4],\n [-18, 20, -5, 23, -16],\n [-4, -8, -26, 2, -16]]\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[[-6, -3, 18, 0, 0],\n [-4, -2, 12, 0, 0],\n [2, 1, -6, 0, 0],\n [12, 6, -36, 0, 0],\n [-6, -3, 18, 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[[-8, -10, -20, -16, 6],\n [-27, 8, -28, 8, 5],\n [-5, 42, -32, 8, 21],\n [-29, 26, -36, 16, 11],\n [7, 13, -8, -4, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[48, 60, 24, 72, -66],\n [40, 10, 18, 2, -2],\n [-2, 3, 4, 7, -15],\n [-6, -11, -10, -17, 28],\n [58, 17, 32, 9, -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[[15, -1, -6, -8, 1],\n [-30, 2, 12, 16, -2],\n [9, 19, 2, 12, -5],\n [3, 4, 0, 2, -1],\n [-30, -12, 8, 4, 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[[0, 7, 5, 12, -13],\n [4, 9, 17, 9, -21],\n [42, -42, 9, 9, 6],\n [-24, 22, -2, -18, 2],\n [-8, -1, -15, -3, 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 5x5 matrix:\n[[-25, -10, 20, -30, 15],\n [-15, -6, 12, -18, 9],\n [10, 4, -8, 12, -6],\n [-10, -4, 8, -12, 6],\n [30, 12, -24, 36, -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[[-36, 6, -12, -6, 36],\n [-6, 1, -2, -1, 6],\n [-12, 2, -4, -2, 12],\n [0, 0, 0, 0, 0],\n [12, -2, 4, 2, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-7, -25, 14, -37, -33],\n [-1, -35, 25, -29, -39],\n [-30, -9, 9, -24, -13],\n [9, -58, 20, -64, -25],\n [-27, 51, 6, 66, -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[[4, -10, -60, -7, -6],\n [3, -3, -33, -6, -6],\n [-12, -42, -12, 33, 42],\n [-3, 3, 33, 6, 6],\n [5, 13, -7, -13, -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 5x5 matrix:\n[[-44, -4, -34, -42, 14],\n [4, 19, 7, 5, -33],\n [39, -21, 15, 18, 3],\n [-14, -11, -14, -16, 18],\n [7, 0, -3, -8, -23]]\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[[-3, -16, 7, 9, -1],\n [-8, -42, 17, 23, -4],\n [-4, -24, 16, 16, 4],\n [2, 10, -3, -5, 2],\n [0, -10, 25, 15, 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[[4, 0, 20, -8, 24],\n [5, 0, 25, -10, 30],\n [1, 0, 5, -2, 6],\n [-6, 0, -30, 12, -36],\n [-2, 0, -10, 4, -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[[-12, -6, 52, 30, 44],\n [12, 10, 11, -11, 7],\n [-8, -5, 60, 28, 52],\n [10, -8, -62, -29, -42],\n [12, 5, -75, -37, -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[[22, -64, 8, -42, -4],\n [20, -28, -24, -34, -4],\n [-35, 24, 2, 47, 36],\n [-43, -44, 47, 38, 57],\n [-10, -44, 46, 8, 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 5x5 matrix:\n[[14, 28, 1, -15, -2],\n [14, 10, 19, 39, 16],\n [20, 6, -16, -12, 26],\n [-40, -26, 6, -6, -42],\n [0, -16, -4, 12, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-25, 13, 28, -13, -36],\n [9, -6, -16, 49, 21],\n [30, -12, -16, 35, -11],\n [-37, 19, 8, -1, 40],\n [6, 51, 0, 8, -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[[24, -4, 37, -16, 63],\n [-17, -5, 38, 18, 59],\n [33, -9, 4, -4, 23],\n [-41, 7, 11, 12, 0],\n [69, -9, -30, 15, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[13, 3, -3, -18, -17],\n [2, 6, 6, -8, -6],\n [-26, 12, 27, 19, 23],\n [-1, -3, -3, 4, 3],\n [30, -18, -36, -18, -24]]\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, -7, 14, 38, -40],\n [14, 26, 14, -16, 42],\n [4, -26, 43, 28, 13],\n [-35, -71, 22, -20, 34],\n [-6, 22, -18, -24, -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[[-18, -3, -18, 12, 6],\n [18, 3, 18, -12, -6],\n [-36, -6, -36, 24, 12],\n [-18, -3, -18, 12, 6],\n [-12, -2, -12, 8, 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[[-8, 12, 24, 16, -20],\n [8, -12, -24, -16, 20],\n [12, -18, -36, -24, 30],\n [-12, 18, 36, 24, -30],\n [-6, 9, 18, 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[[5, -4, -5, 3, -4],\n [12, -8, -12, 1, -5],\n [27, -12, -27, -21, 6],\n [-4, 8, 4, -21, 17],\n [-42, 24, 42, 12, 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 5x5 matrix:\n[[12, 5, 44, -2, -31],\n [10, 2, -12, 14, -28],\n [-6, -14, 4, -25, 37],\n [24, -29, -4, -23, -10],\n [9, -11, -14, -4, -5]]\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 5x5 matrix:\n[[-12, 4, 4, -24, 4],\n [-12, 4, 4, -24, 4],\n [18, -6, -6, 36, -6],\n [-18, 6, 6, -36, 6],\n [12, -4, -4, 24, -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[[-18, -4, 18, -6, -8],\n [-4, -6, 12, -6, -10],\n [-2, -3, 6, -3, -5],\n [-5, 4, -3, 3, 6],\n [-22, 13, -6, 9, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, 7, -1, 4, -2],\n [-4, 19, -10, -78, 5],\n [-3, -4, -1, -26, 3],\n [4, 22, -7, -14, 1],\n [-6, -26, 14, 56, -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 5x5 matrix:\n[[4, 8, -6, 0, -12],\n [0, 19, 17, -32, -16],\n [-2, 34, 5, -25, -16],\n [14, -36, 11, -1, -16],\n [10, 36, 1, -29, -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[[1, 30, 42, 2, -19],\n [67, -23, 2, 28, -43],\n [24, -62, -26, -41, -24],\n [-41, 11, 13, -36, 12],\n [-7, 42, 37, 17, 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[[2, 24, -20, 32, -30],\n [6, -4, -2, -10, -36],\n [5, 24, -20, 26, -21],\n [18, 32, -28, 14, -9],\n [8, -12, 6, -28, -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[[-31, 25, 4, 32, 6],\n [37, 5, 6, -10, -10],\n [15, 15, 6, 30, 18],\n [12, -50, -14, -46, 0],\n [-39, 5, -3, 11, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[23, 16, 2, -10, 23],\n [20, -24, 20, -22, -12],\n [29, -20, 8, -19, -13],\n [2, -20, -10, 3, -28],\n [5, 4, -16, 7, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -8, -4, 0, -11],\n [-8, -24, 0, 0, -24],\n [-6, -42, -12, 0, -51],\n [-14, -10, 16, 0, 2],\n [4, -12, -12, 0, -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[[-60, 44, 11, 0, 17],\n [12, -4, -38, -26, 38],\n [65, -7, -71, -11, -5],\n [50, -22, -3, 20, -29],\n [-58, 22, 16, -16, 18]]\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, 33, 5, 3, 19],\n [4, 32, -41, 11, -21],\n [26, -15, -42, 18, -35],\n [23, 16, 2, 38, 5],\n [-46, -8, 2, -26, 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 5x5 matrix:\n[[9, -19, -9, -12, -6],\n [43, -7, -47, -30, -26],\n [22, -29, -24, -25, -16],\n [7, 7, -13, -8, -12],\n [-20, 40, 15, 20, 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[[28, 60, -20, -54, -12],\n [28, 60, -20, -54, -12],\n [-6, -12, 3, 11, 4],\n [-8, -24, 16, 20, -8],\n [-24, -54, 21, 48, 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 5x5 matrix:\n[[-24, 24, -30, 36, 36],\n [-20, 20, -25, 30, 30],\n [16, -16, 20, -24, -24],\n [24, -24, 30, -36, -36],\n [16, -16, 20, -24, -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[[3, -18, 3, 12, 9],\n [-1, 6, -1, -4, -3],\n [1, -6, 1, 4, 3],\n [5, -30, 5, 20, 15],\n [-2, 12, -2, -8, -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 5x5 matrix:\n[[7, -10, 29, -8, -51],\n [10, -38, 62, -8, -2],\n [-11, 9, 16, 25, -10],\n [3, -35, 12, -9, -10],\n [6, -7, -4, -13, -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 5x5 matrix:\n[[-7, -5, -4, 4, 2],\n [1, -1, -6, 0, -6],\n [35, 25, 20, -20, -10],\n [12, 0, -26, -4, -32],\n [26, 22, 28, -16, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, -9, 3, -20, 10],\n [48, -9, -27, 0, 0],\n [14, -6, -9, -6, 3],\n [-42, 9, 24, 2, -1],\n [18, -9, -12, -10, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, -3, 3, -4, -6],\n [9, 9, -9, 12, 18],\n [-15, -15, 15, -20, -30],\n [-12, -12, 12, -16, -24],\n [-9, -9, 9, -12, -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 5x5 matrix:\n[[30, 36, -60, 51, -64],\n [-10, 41, 42, -16, -13],\n [43, 5, -13, -2, -31],\n [-67, 31, -21, 51, 31],\n [-10, -7, -9, 8, 6]]\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, -36, 19, 23, -25],\n [3, 2, -3, 44, -5],\n [26, -5, 30, -37, -20],\n [16, -33, 18, -24, -29],\n [31, -8, 38, 16, -29]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[43, 49, 31, 33, -9],\n [-12, -24, -18, -8, -6],\n [30, 56, 52, 10, -22],\n [13, 28, 34, 13, 7],\n [-21, -19, -23, -24, 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 5x5 matrix:\n[[-4, -3, 5, 0, 3],\n [-12, -9, 15, 0, 9],\n [-4, -3, 5, 0, 3],\n [-24, -18, 30, 0, 18],\n [-4, -3, 5, 0, 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[[1, 3, 3, -6, 4],\n [5, 15, 15, -30, 20],\n [5, 15, 15, -30, 20],\n [6, 18, 18, -36, 24],\n [6, 18, 18, -36, 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[[-19, 3, 14, 16, 1],\n [50, 54, -31, 17, 27],\n [-17, -13, 16, 10, -31],\n [-15, -37, 1, -27, -40],\n [10, 10, -27, -21, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[8, -16, -8, -12, 4],\n [0, 0, 0, 0, 0],\n [4, -8, -4, -6, 2],\n [-8, 16, 8, 12, -4],\n [-8, 16, 8, 12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[21, 17, -10, -32, -23],\n [11, -14, 17, 18, -40],\n [-31, -4, 14, 15, 25],\n [-25, 41, -3, -7, 14],\n [36, 14, 4, -58, -64]]\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 5x5 matrix:\n[[16, 3, 27, -4, 1],\n [-8, -18, 6, -32, -40],\n [-1, 7, -19, 18, 12],\n [8, 23, -17, 44, 49],\n [20, 3, 27, -4, -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[[10, -2, 10, 4, 0],\n [-30, 6, -30, -12, 0],\n [0, 0, 0, 0, 0],\n [-5, 1, -5, -2, 0],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[4, 0, 0, -6, 8],\n [-36, 36, 24, -18, 6],\n [24, -36, -24, 36, -30],\n [-8, 6, 4, 0, -3],\n [36, -36, -24, 18, -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 5x5 matrix:\n[[6, -30, -41, -20, -21],\n [6, 25, 36, 24, 23],\n [18, -20, -25, -4, -7],\n [-18, 25, 32, 8, 11],\n [-6, 20, 27, 12, 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[[9, 29, 13, -26, -3],\n [1, 8, -20, -20, -13],\n [-15, 6, 12, 12, -3],\n [-15, 28, 20, -4, -9],\n [19, 56, 58, -32, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, 9, 6, -5, -5],\n [9, -11, 11, -10, 15],\n [42, 16, -34, -74, -38],\n [8, 0, -12, 8, -6],\n [-38, 14, -2, 48, -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[[29, -12, -35, -12, -23],\n [65, 4, 5, 26, -45],\n [57, 10, 10, 32, -34],\n [-13, -18, -45, -49, -24],\n [-50, -22, 0, -30, 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 5x5 matrix:\n[[-4, 8, 16, 12, 20],\n [2, -4, -8, -6, -10],\n [-4, 8, 16, 12, 20],\n [4, -8, -16, -12, -20],\n [-3, 6, 12, 9, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-4, 20, 31, 0, 20],\n [-29, -3, -26, 7, -7],\n [18, -12, -39, 12, -42],\n [-37, -7, 6, -13, 33],\n [-11, -7, -28, 7, -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 5x5 matrix:\n[[34, -2, -36, -8, -23],\n [-24, 6, 30, -2, 30],\n [12, 3, -9, -9, 3],\n [38, -1, -39, -11, -22],\n [0, 3, 3, -5, 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[[-4, -10, -12, -14, 4],\n [11, 18, 23, 24, -4],\n [0, 19, 20, 29, -14],\n [15, 28, 35, 38, -8],\n [-12, -11, -16, -13, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[39, 42, -54, -5, -22],\n [-18, 12, 25, 15, 5],\n [17, 5, 0, 52, 26],\n [-1, 24, -2, 17, 54],\n [0, -18, -22, -60, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-43, -40, -2, -5, 19],\n [-9, 32, 11, -25, -18],\n [-5, 20, 0, -15, -25],\n [14, 12, 8, 2, 10],\n [-8, -46, -13, 22, 21]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[8, -6, 8, 4, 10],\n [20, -15, 20, 10, 25],\n [-12, 9, -12, -6, -15],\n [16, -12, 16, 8, 20],\n [4, -3, 4, 2, 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 5x5 matrix:\n[[-3, 6, 6, 5, 6],\n [-15, 30, 30, 25, 30],\n [-6, 12, 12, 10, 12],\n [9, -18, -18, -15, -18],\n [3, -6, -6, -5, -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[[-9, -8, 6, -10, 18],\n [16, 49, -4, -32, 15],\n [-19, 8, -18, 18, 2],\n [-19, -19, -12, 30, -1],\n [-26, -83, 1, 60, -12]]\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[[68, 31, -74, 19, 9],\n [-10, -19, -7, -23, 35],\n [-37, -21, 37, -19, -1],\n [72, 46, -72, 30, 22],\n [48, 13, -57, 45, -17]]?\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 5x5 matrix:\n[[-25, -2, -25, 13, -45],\n [-2, 52, 50, -38, 18],\n [-20, 24, 28, -16, -20],\n [2, 6, -14, -1, -14],\n [4, -20, -40, 22, 0]]\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[[30, 0, 18, -12, 24],\n [15, -8, 15, -22, 28],\n [25, 4, 12, -2, 12],\n [-5, 0, -3, 2, -4],\n [-25, -4, -12, 2, -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[[12, 21, -8, -16, -28],\n [-4, -3, 2, 2, 6],\n [-16, -14, 23, 11, -1],\n [32, -8, -29, 9, 12],\n [-16, -46, 10, 36, 59]]?\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, 18, -9, -3, -7],\n [54, 12, -18, -6, -10],\n [3, 24, 9, 3, 0],\n [-3, 18, 9, 3, 1],\n [23, 16, -3, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-5, -25, 13, 11, -23],\n [27, 19, -35, -7, 25],\n [-15, -3, 18, 0, -9],\n [0, 12, -24, 6, 48],\n [11, 19, -14, -10, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, -1, -9, -20, -15],\n [8, 5, 26, 5, 18],\n [-12, -2, -6, 20, 6],\n [6, -1, -9, -20, -15],\n [-12, -4, -18, 10, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-60, 19, -36, -33, 26],\n [-15, 12, 69, -18, -21],\n [3, -8, -24, 23, -27],\n [-12, 32, 18, -26, -36],\n [17, 48, -16, -43, -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[[-14, -30, -17, 29, -23],\n [-18, 6, 1, 27, -27],\n [27, 1, 15, -3, 18],\n [-46, 45, 1, 9, -35],\n [35, -39, 15, 37, -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[[-36, -18, 0, 0, -6],\n [-12, -6, 0, 0, -2],\n [-12, -6, 0, 0, -2],\n [30, 15, 0, 0, 5],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[31, 5, 19, 105, -28],\n [-10, -16, 17, 50, -8],\n [-12, -1, 7, 11, -6],\n [0, -48, 39, -21, 36],\n [-41, -26, -16, -36, 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 5x5 matrix:\n[[-3, 11, 5, -1, -10],\n [-18, 66, 30, -6, -60],\n [-26, 18, -2, -11, -1],\n [-17, 21, -35, -8, 17],\n [37, -3, 4, 16, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[12, 0, 12, -24, -30],\n [-6, 0, -6, 12, 15],\n [8, 0, 8, -16, -20],\n [10, 0, 10, -20, -25],\n [-12, 0, -12, 24, 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[[-20, 16, 0, -2, 2],\n [-22, -16, 42, 23, 19],\n [-8, -20, 33, 19, 14],\n [40, -20, -15, -5, -10],\n [-2, 4, -3, -2, -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[[9, 18, -42, 39, -36],\n [16, -3, -14, 4, 6],\n [-8, -6, 20, -16, 12],\n [-1, -12, 22, -23, 24],\n [6, -3, -2, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-23, 14, -33, 38, 9],\n [-2, 16, -12, 14, 28],\n [5, -6, 33, -44, -17],\n [57, -21, 11, 17, 37],\n [44, -16, -18, 2, 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[[0, -12, 18, -12, -18],\n [-46, -70, 23, 10, 23],\n [21, 22, -1, 2, -20],\n [-5, -33, 27, 17, -22],\n [-28, -46, 18, 6, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, -28, 1, 27, 0],\n [28, 7, 5, 14, -13],\n [8, 9, -17, -14, -23],\n [18, -26, -16, 25, -29],\n [-13, -5, -28, -21, -21]]?\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, 0, 0, 0, 0],\n [-3, -3, 9, 18, 3],\n [-4, -4, 12, 24, 4],\n [-6, -6, 18, 36, 6],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-20, 22, -26, -3, -11],\n [-44, 8, -40, -10, -6],\n [-19, 23, 11, -54, -19],\n [-34, 10, -15, -32, -10],\n [-8, -20, -5, 6, 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[[6, 4, 6, -8, -6],\n [15, 10, 15, -20, -15],\n [15, 10, 15, -20, -15],\n [3, 2, 3, -4, -3],\n [-9, -6, -9, 12, 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[[20, 14, -24, -13, -34],\n [9, 20, -27, -34, -9],\n [22, 12, -18, -6, -34],\n [24, 12, 6, 3, -10],\n [10, -2, 12, 16, -6]]\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[[-34, -38, 11, 25, 9],\n [-12, -14, -19, 47, -27],\n [-36, -24, 48, -32, 44],\n [-36, -2, 9, 0, 16],\n [-2, 8, 16, -11, -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 5x5 matrix:\n[[-20, 25, 10, 0, 20],\n [-20, 25, 10, 0, 20],\n [-4, 5, 2, 0, 4],\n [8, -10, -4, 0, -8],\n [-8, 10, 4, 0, 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[[-43, -6, -12, -8, 34],\n [-18, -11, -18, 9, 29],\n [-5, -14, -34, 4, -4],\n [-23, 5, 12, -13, 15],\n [-29, -21, -26, -9, 34]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-15, 5, 5, 30, 0],\n [-3, 1, 1, 6, 0],\n [-12, 4, 4, 24, 0],\n [15, -5, -5, -30, 0],\n [3, -1, -1, -6, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[5, -30, -15, 20, -15],\n [6, -36, -18, 24, -18],\n [-1, 6, 3, -4, 3],\n [6, -36, -18, 24, -18],\n [-6, 36, 18, -24, 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[[4, -18, -2, -10, 6],\n [-10, 1, 11, -3, -7],\n [4, -18, -2, -10, 6],\n [26, -7, -28, 5, 19],\n [-16, 6, 17, -2, -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[[10, 22, 9, -10, 2],\n [-14, -14, -27, -34, 2],\n [0, 42, 54, 60, 12],\n [34, 16, 9, -10, -10],\n [-10, -50, -54, -48, -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[[5, 5, -6, 2, 6],\n [20, 20, -24, 8, 24],\n [15, 15, -18, 6, 18],\n [0, 0, 0, 0, 0],\n [-5, -5, 6, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-13, 12, -20, -5, -39],\n [-12, 36, -24, -24, -36],\n [6, -36, 16, 26, 18],\n [-3, 54, -16, -41, -9],\n [-8, 60, -24, -44, -24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-7, 5, -24, 12, 48],\n [-18, 13, 17, -33, -24],\n [35, 0, 22, -8, -33],\n [-3, 0, -26, 18, 27],\n [-8, -15, 18, 1, -36]]\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 5x5 matrix:\n[[-10, -6, 10, 10, 8],\n [10, 6, -10, -10, -8],\n [30, 18, -30, -30, -24],\n [20, 12, -20, -20, -16],\n [5, 3, -5, -5, -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[[-19, -39, -8, 4, -22],\n [31, 42, -20, -34, 27],\n [-39, -9, 66, 48, 6],\n [-1, -1, 1, 4, 3],\n [-43, -12, 27, -26, 49]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, -25, 10, 33, -29],\n [8, -38, 0, 14, -33],\n [10, -4, -7, 18, 8],\n [13, 12, -8, 11, 1],\n [14, 14, -19, -44, 32]]\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, 53, 22, 27, 76],\n [-3, 15, -66, 27, -34],\n [-79, -31, 14, -20, 1],\n [-49, -9, 2, -19, 4],\n [-48, -39, 60, -39, 16]]\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, 0, 0, 0, 0],\n [-6, 8, -8, 8, -4],\n [3, -4, 4, -4, 2],\n [12, -16, 16, -16, 8],\n [-12, 16, -16, 16, -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 5x5 matrix:\n[[8, -10, 2, 2, 0],\n [8, -10, 2, 2, 0],\n [8, -10, 2, 2, 0],\n [-8, 10, -2, -2, 0],\n [12, -15, 3, 3, 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[[1, 16, 11, -7, -14],\n [11, 7, 29, 24, -51],\n [13, 18, 32, -32, -27],\n [29, -63, -8, 29, 18],\n [7, -12, -25, -5, 45]]\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 5x5 matrix:\n[[-32, -40, 50, 60, -4],\n [16, 8, -7, -40, -8],\n [-11, -32, 24, 25, 3],\n [9, -22, -11, 0, 18],\n [-6, -24, 0, 30, 18]]\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, 34, 36, -39, 29],\n [2, -32, 21, -19, 32],\n [-14, 56, -1, -1, -12],\n [-9, 18, -17, 23, -5],\n [3, -54, 23, -17, 47]]\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 5x5 matrix:\n[[-57, -21, -33, -30, 27],\n [41, 9, 27, 24, -25],\n [-52, -22, -42, -14, 23],\n [25, -12, 20, 47, -9],\n [-48, -26, -35, -3, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, -8, 12, -6, -4],\n [0, -36, 32, 0, 12],\n [-10, -2, 14, -15, -16],\n [14, -17, -2, 21, 29],\n [6, -6, -2, 9, 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 5x5 matrix:\n[[10, 0, 12, -2, 2],\n [5, 0, 6, -1, 1],\n [30, 0, 36, -6, 6],\n [-10, 0, -12, 2, -2],\n [-25, 0, -30, 5, -5]]\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, -22, 3, -1, -12],\n [-1, 2, 15, 16, 17],\n [5, -36, 42, 37, 19],\n [-2, 6, -6, -12, -4],\n [-1, 26, -39, -22, -19]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[20, -20, 25, 15, 0],\n [0, 0, 0, 0, 0],\n [20, -20, 25, 15, 0],\n [16, -16, 20, 12, 0],\n [4, -4, 5, 3, 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[[-38, -2, -41, 13, 15],\n [16, 26, 19, -20, 24],\n [32, 24, 40, -14, 6],\n [24, 12, 34, 4, -12],\n [24, -54, 3, -24, -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 5x5 matrix:\n[[7, -12, -6, -11, 10],\n [8, -12, -6, -13, 11],\n [4, -16, -8, -4, 8],\n [11, -28, -14, -15, 18],\n [-4, 16, 8, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[5, -24, 11, 0, -11],\n [10, 22, 8, 14, -8],\n [20, -26, 30, 14, -30],\n [-15, -13, -16, -17, 16],\n [-30, -11, -35, -31, 35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[14, 19, -28, -7, 3],\n [-17, 4, 0, -11, 12],\n [40, 33, -32, 13, -7],\n [-12, 30, 6, 6, 18],\n [21, 27, -36, -6, 3]]?\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, -7, -38, -41, -10],\n [22, 17, 34, 31, 2],\n [16, -16, 20, 32, 18],\n [8, -32, 6, 24, 23],\n [4, 38, 12, -6, -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[[3, -7, 2, -6, 6],\n [3, -3, 33, 21, 27],\n [29, 19, 47, -5, 9],\n [-19, -25, 2, 26, 30],\n [-9, -11, -1, 11, 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[[36, -1, 55, 28, 11],\n [-27, 11, -56, -18, -12],\n [32, 43, 59, 16, 15],\n [43, -30, 62, 20, 22],\n [23, -15, 42, 15, 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[[5, 18, -19, -63, 25],\n [-31, -56, 16, 80, -60],\n [-38, 0, 20, 28, -30],\n [1, -27, -20, 9, -4],\n [24, -7, -14, 7, 16]]\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[[-18, 0, 3, 9, 15],\n [0, -18, 28, 6, -4],\n [16, 6, -12, -10, -12],\n [10, -12, 17, -1, -11],\n [32, 3, -10, -17, -26]]\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, 10, -21, 14, 15],\n [-2, 45, 24, 32, -15],\n [29, -5, 10, -9, -10],\n [13, -12, -17, -24, -13],\n [20, -6, 18, -7, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-31, 9, -1, 16, 12],\n [9, 2, 12, -14, 8],\n [-15, 11, -87, 26, 29],\n [50, 2, -6, -6, -15],\n [-20, -41, 48, -43, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 0, 28, -16, -28],\n [17, 6, 17, -14, -23],\n [20, 8, 4, -8, -12],\n [-11, -6, 25, -10, -19],\n [-44, -20, 32, -4, -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 5x5 matrix:\n[[4, -4, 1, -4, 4],\n [-24, 24, -6, 24, -24],\n [-20, 20, -5, 20, -20],\n [-20, 20, -5, 20, -20],\n [-20, 20, -5, 20, -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 5x5 matrix:\n[[-37, 12, 40, -6, 35],\n [-7, 10, 21, -14, -18],\n [7, 8, 21, -35, 18],\n [20, 4, 5, -25, 1],\n [16, 26, 37, 6, -1]]\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[[-38, 19, 21, -19, -27],\n [-14, 29, 7, -15, -17],\n [40, -25, 19, -39, 5],\n [-32, -8, -16, 14, 4],\n [3, 23, -14, 5, 1]]\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, 11, -14, 7, -6],\n [14, -16, 9, 8, -14],\n [-6, 6, -4, -2, 4],\n [7, -5, 5, -1, 0],\n [-2, -2, -2, 6, -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[[-8, -5, -6, -7, -14],\n [-34, -25, 0, -17, -40],\n [22, 20, -26, -2, 6],\n [22, 20, -26, -2, 6],\n [10, 5, 16, 13, 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[[3, 3, -9, 15, -12],\n [5, 5, -15, 25, -20],\n [1, 1, -3, 5, -4],\n [-2, -2, 6, -10, 8],\n [5, 5, -15, 25, -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[[5, -5, -10, -30, -10],\n [5, -5, -10, -30, -10],\n [-3, 3, 6, 18, 6],\n [0, 0, 0, 0, 0],\n [-2, 2, 4, 12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[0, 3, -21, -3, -18],\n [-30, -23, 6, -27, -2],\n [6, 8, -25, 2, -20],\n [30, 19, 22, 31, 26],\n [-12, -7, -13, -13, -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 5x5 matrix:\n[[-15, 3, -45, 33, 72],\n [13, -22, 16, -16, -33],\n [-7, -13, 19, -31, 0],\n [-15, 40, 6, 2, 9],\n [27, 3, 0, 24, -54]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[21, 15, 25, 17, 27],\n [-16, -20, 0, 8, -52],\n [15, 13, 15, 8, 27],\n [-39, -1, -35, -51, 27],\n [16, 16, 20, 9, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-43, 12, 27, 49, 4],\n [7, -4, 36, -12, 6],\n [-17, 17, -3, 0, 0],\n [46, -8, -7, -48, -1],\n [26, -3, -18, 3, -4]]?\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, -33, -21, 54, -18],\n [0, -15, -25, 30, -20],\n [0, -3, -5, 6, -4],\n [-24, -9, 19, 6, 14],\n [4, 1, -4, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-17, -7, 18, 12, 6],\n [17, 33, 5, 26, -38],\n [31, 25, -22, -4, -26],\n [7, 9, -2, 4, -10],\n [28, 36, -8, 16, -40]]?\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, 6, 24, -6, -12],\n [0, 0, 0, 0, 0],\n [-4, 1, 4, -1, -2],\n [20, -5, -20, 5, 10],\n [-16, 4, 16, -4, -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[[0, 0, 0, 0, 0],\n [-6, 18, 0, -24, 6],\n [-5, 15, 0, -20, 5],\n [4, -12, 0, 16, -4],\n [-6, 18, 0, -24, 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[[-4, -8, 16, -4, -16],\n [0, 0, 0, 0, 0],\n [6, 12, -24, 6, 24],\n [0, 0, 0, 0, 0],\n [-4, -8, 16, -4, -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[[-18, 18, -36, 24, -12],\n [6, -6, 12, -8, 4],\n [-9, 9, -18, 12, -6],\n [-18, 18, -36, 24, -12],\n [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[[19, -22, -23, -8, -21],\n [-15, 10, 15, -20, 25],\n [9, -6, -9, 12, -15],\n [-21, 21, 24, -3, 27],\n [15, -10, -15, 20, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-24, -23, -51, 54, 30],\n [28, -21, -3, 20, -34],\n [-44, -44, -68, 84, 30],\n [4, 13, -19, 8, 23],\n [63, 34, 10, 0, -36]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[27, -30, -5, 2, -11],\n [-30, 15, 30, 21, 0],\n [10, 10, -30, -26, 10],\n [-3, -15, 25, 23, -11],\n [-12, 0, 20, 16, -4]]\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[[-42, -24, 30, -21, 15],\n [-21, -28, 15, -21, 17],\n [12, 39, -5, 31, -15],\n [27, -21, -18, -9, 15],\n [48, 27, -45, 12, -42]]\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[[-2, 5, 6, 0, 5],\n [14, -44, -54, 30, -32],\n [19, -10, -46, 28, -3],\n [15, 9, -22, -2, 4],\n [-20, -13, 28, 6, -5]]\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[[19, -3, 27, 9, 17],\n [0, -2, -25, 15, 13],\n [20, 14, -71, 67, 61],\n [31, 1, -30, 59, 51],\n [-5, 1, 46, -36, -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[[-19, -18, 14, 4, -19],\n [35, 18, -22, -23, 26],\n [-19, -18, 14, 4, -19],\n [4, 24, -8, 20, 16],\n [-9, 10, 2, 21, 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[[-7, -9, -17, 25, -27],\n [-11, -8, -18, 0, 25],\n [-31, 10, -2, 10, 1],\n [-26, -13, -28, 27, -8],\n [32, 21, 21, -32, 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[[-21, -25, 25, -48, -4],\n [-22, 39, 74, 9, 29],\n [-2, 29, 62, -3, 39],\n [40, -6, -32, -8, 2],\n [21, 28, -13, 52, 23]]?\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 5x5 matrix:\n[[19, -18, 0, 14, 6],\n [54, -29, 25, 21, -28],\n [11, -3, -7, 1, -1],\n [-43, 1, 6, -2, 16],\n [4, -41, 4, 14, -10]]\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 5x5 matrix:\n[[12, -6, -3, 12, 12],\n [-4, 2, 1, -4, -4],\n [-20, 10, 5, -20, -20],\n [-4, 2, 1, -4, -4],\n [16, -8, -4, 16, 16]]\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, 17, -43, -21, 32],\n [15, 21, -15, -9, 6],\n [28, -13, -5, -5, 1],\n [33, -54, 46, -4, 23],\n [-1, 37, -51, -8, -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[[0, 37, -19, 48, 31],\n [10, 33, -11, 42, 29],\n [-40, -21, -13, -24, -23],\n [-35, -23, -9, -27, -24],\n [14, -13, 15, -18, -9]]\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 5x5 matrix:\n[[-20, 30, -10, -5, 0],\n [24, -36, 12, 6, 0],\n [20, -30, 10, 5, 0],\n [12, -18, 6, 3, 0],\n [-8, 12, -4, -2, 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[[-54, 18, 52, 51, -2],\n [-69, -17, 24, 18, 9],\n [6, -6, -8, -8, 6],\n [-69, -16, 30, 25, 20],\n [-18, 1, 6, 4, -13]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[10, -2, -4, -12, -10],\n [5, -1, -2, -6, -5],\n [5, -1, -2, -6, -5],\n [-25, 5, 10, 30, 25],\n [-20, 4, 8, 24, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[24, 22, -24, -9, 17],\n [-8, 20, 10, -2, -10],\n [-1, 21, 11, -1, -19],\n [56, 2, -31, -3, -3],\n [15, 35, -15, -10, 10]]\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, 20, -26, -16, -45],\n [24, -48, 48, 18, 66],\n [8, -20, 22, 12, 34],\n [-12, 44, -34, -4, -32],\n [26, -8, 16, 6, 31]]\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, 25, 33, 40, -9],\n [16, 9, -29, 42, -1],\n [11, -1, 54, 20, 20],\n [18, -50, -8, -42, 38],\n [10, -2, 30, 28, -2]]\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[[13, 9, 11, -12, 0],\n [12, 6, -22, -6, -1],\n [-18, -14, 27, 51, -17],\n [7, -28, -30, -35, -16],\n [3, 33, 0, -27, 36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 16, 4, -24, -16],\n [0, 0, 0, 0, 0],\n [-4, 16, 4, -24, -16],\n [2, -8, -2, 12, 8],\n [-4, 16, 4, -24, -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 5x5 matrix:\n[[12, 6, -18, -9, 12],\n [-8, -4, 12, 6, -8],\n [8, 4, -12, -6, 8],\n [4, 2, -6, -3, 4],\n [24, 12, -36, -18, 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[[0, 6, 6, 47, -10],\n [37, 32, -31, 16, -10],\n [-65, -10, 21, -21, -16],\n [3, -36, 35, 38, 22],\n [12, 36, -32, -6, -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[[-20, 24, -20, -4, 8],\n [-15, 18, -15, -3, 6],\n [15, -18, 15, 3, -6],\n [-15, 18, -15, -3, 6],\n [15, -18, 15, 3, -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 5x5 matrix:\n[[-50, -21, 13, -54, -31],\n [-13, 3, 32, -75, -19],\n [42, 23, 3, 74, 13],\n [74, 45, 11, 57, 29],\n [14, -7, -43, 59, 29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-38, -11, -42, -35, -20],\n [-3, 19, 12, 50, 38],\n [35, -50, 90, 23, 44],\n [19, -51, 69, -15, -11],\n [8, -5, 33, 37, 40]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[24, -24, 16, 4, -12],\n [16, -60, 4, 6, -22],\n [-40, 18, -30, -5, 13],\n [10, -54, 0, 5, -19],\n [-43, -12, -37, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-6, 2, -6, 4, -1],\n [0, 0, 0, 0, 0],\n [24, -8, 24, -16, 4],\n [-6, 2, -6, 4, -1],\n [6, -2, 6, -4, 1]]\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, -4, 4, 6, -5],\n [30, -24, 24, 36, -30],\n [25, -20, 20, 30, -25],\n [-20, 16, -16, -24, 20],\n [-20, 16, -16, -24, 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[[-30, 20, -24, 30, 31],\n [4, 2, 6, 10, 8],\n [-30, 15, -27, 15, 18],\n [-40, 20, -36, 20, 24],\n [-8, 11, -3, 25, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-36, -30, 36, -6, 12],\n [42, -10, -30, -2, 10],\n [-33, -20, 31, -4, 7],\n [18, 0, -14, 0, 2],\n [18, -30, -6, -6, 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[[-2, -31, 53, -28, 2],\n [40, 15, 23, 9, -39],\n [-8, -42, 34, -48, 8],\n [44, 12, -16, 36, 16],\n [-48, 12, -24, -6, -6]]\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[[20, -44, -2, 21, -12],\n [-27, -2, 20, 5, 34],\n [20, -16, 12, 14, 16],\n [20, -16, 12, 14, 16],\n [-8, 34, -19, -23, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[19, -46, -34, -14, 87],\n [-9, -11, 64, -2, -30],\n [29, -31, 14, 42, 32],\n [49, 21, -5, -18, -20],\n [32, -20, 5, -48, 28]]\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, -26, 10, -4, -1],\n [15, 24, -31, 27, -12],\n [4, -28, 16, -48, 28],\n [-15, -13, 22, 10, -11],\n [-25, 23, 8, 44, -29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[21, -36, 24, -18, 36],\n [-31, 28, -4, -19, -6],\n [20, -16, 0, 16, 0],\n [18, -24, 12, -3, 18],\n [12, -16, 8, -2, 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[[-1, -39, -13, -13, -30],\n [0, -30, 24, -38, 32],\n [2, 11, 8, 3, 15],\n [9, 48, -6, 41, -2],\n [-14, -8, 34, -36, 60]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[22, -9, -5, -13, -12],\n [-2, -12, 9, 15, -8],\n [16, -10, 1, -31, 2],\n [31, -10, -16, -21, -19],\n [-4, 34, 36, 14, 34]]\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 5x5 matrix:\n[[6, -18, 12, -36, -11],\n [15, -12, 18, -14, 44],\n [-35, 6, -27, -24, -26],\n [16, 5, 14, 23, -15],\n [-15, 2, -13, -10, -29]]\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[[-18, -30, -36, -18, 18],\n [-3, -5, -6, -3, 3],\n [-6, -10, -12, -6, 6],\n [9, 15, 18, 9, -9],\n [-3, -5, -6, -3, 3]]\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[[-12, 0, 35, 7, -29],\n [9, 0, 26, 9, -40],\n [15, 0, -30, -5, 20],\n [27, 0, 12, 9, -42],\n [-3, 0, 17, 4, -17]]\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, 9, 9, -15, 15],\n [-8, 12, 12, -20, 20],\n [-6, 9, 9, -15, 15],\n [12, -18, -18, 30, -30],\n [2, -3, -3, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0, 0],\n [6, -36, 12, 18, 30],\n [3, -18, 6, 9, 15],\n [-3, 18, -6, -9, -15],\n [1, -6, 2, 3, 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[[2, 39, 1, 8, -4],\n [24, -18, -6, 24, -12],\n [16, 15, -3, 20, -10],\n [-5, -30, 0, -10, 5],\n [-30, -18, 6, -36, 18]]\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, 14, -20, 16, -6],\n [18, 16, 44, -10, 24],\n [0, -25, -20, -5, -15],\n [-12, 11, -12, 11, -3],\n [12, -6, 16, -10, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, -4, 4, -2, -8],\n [-3, 2, -2, 1, 4],\n [-15, 10, -10, 5, 20],\n [0, 0, 0, 0, 0],\n [6, -4, 4, -2, -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[[3, 34, -9, 47, -54],\n [-8, -19, 49, -16, 44],\n [19, 30, -11, 45, -38],\n [-20, -18, 4, -30, 16],\n [43, -11, 1, -4, 46]]?\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 5x5 matrix:\n[[-10, -24, -10, -4, -23],\n [-12, 12, 10, -8, 2],\n [-32, -17, -10, -52, 14],\n [8, -24, -22, -16, 16],\n [28, -15, -18, 12, 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 5x5 matrix:\n[[8, 2, 13, 11, 6],\n [-2, -4, -19, 13, 30],\n [5, 3, 16, -1, -12],\n [-14, -2, -16, -26, -24],\n [6, 2, 12, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-6, 18, 12, -6, 0],\n [-5, -3, 4, -5, -3],\n [6, -18, -12, 6, 0],\n [-2, -30, -8, -2, -6],\n [1, 27, 8, 1, 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[[-28, 63, -16, -19, -13],\n [-13, 9, -15, 32, 1],\n [-3, -21, -20, 57, 11],\n [4, 13, 14, -43, -7],\n [-1, -3, -13, 14, 5]]\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 5x5 matrix:\n[[15, -30, 10, -20, 15],\n [-15, 30, -10, 20, -15],\n [0, 0, 0, 0, 0],\n [15, -30, 10, -20, 15],\n [-6, 12, -4, 8, -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[[-5, 16, -3, 4, -27],\n [-4, -8, 4, 14, 7],\n [-13, -22, 0, 14, 30],\n [2, 22, -5, -10, -31],\n [33, 14, 4, -36, -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[[14, 7, 25, -5, 0],\n [-26, -1, -55, 3, -8],\n [-3, -9, 0, 5, 5],\n [15, 45, 0, -25, -25],\n [0, -21, 15, 11, 14]]\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, -5, -25, -15, -6],\n [-32, -33, 4, -8, 28],\n [28, 14, -6, -21, -25],\n [-48, -13, 26, 26, 16],\n [0, -12, 29, -12, 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 5x5 matrix:\n[[14, -18, -36, -19, 51],\n [-11, 69, -11, 8, -52],\n [28, -10, -43, 7, -18],\n [-43, 24, 58, -23, 17],\n [1, 42, -47, -25, 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 5x5 matrix:\n[[27, -65, 30, -17, 11],\n [2, -70, 20, -38, 34],\n [-17, 10, 1, 27, -2],\n [-14, 55, -23, 16, -15],\n [-4, -35, 11, -13, 18]]\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 5x5 matrix:\n[[-6, 0, 0, 0, -12],\n [-12, 0, 0, 0, -24],\n [-6, 0, 0, 0, -12],\n [-2, 0, 0, 0, -4],\n [10, 0, 0, 0, 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[[-6, -6, 3, 3, -9],\n [-4, -4, 2, 2, -6],\n [-10, -10, 5, 5, -15],\n [-8, -8, 4, 4, -12],\n [-6, -6, 3, 3, -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[[-1, 10, 5, 7, 5],\n [-6, -36, 6, 6, -6],\n [3, -14, -11, -15, -9],\n [-7, -2, 17, 22, 8],\n [8, 0, -20, -26, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 3, 6, 12, 18],\n [-8, 2, 4, 8, 12],\n [16, -4, -8, -16, -24],\n [24, -6, -12, -24, -36],\n [-4, 1, 2, 4, 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[[-6, 9, -1, 29, -22],\n [2, -8, 12, -33, 34],\n [-17, -13, 3, -6, 5],\n [-13, -22, -8, -19, 5],\n [31, 44, 46, -2, 45]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-4, 34, 21, 9, 15],\n [3, -28, -26, -14, -6],\n [-15, 4, 33, 27, -19],\n [9, 17, 40, 25, -15],\n [3, 35, 2, -7, 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[[-4, 12, 8, -12, -8],\n [-6, 18, 12, -18, -12],\n [8, -24, -16, 24, 16],\n [6, -18, -12, 18, 12],\n [12, -36, -24, 36, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, 2, 38, 31, 28],\n [22, 16, -12, 22, -36],\n [12, 0, -2, 16, -1],\n [-8, -22, 12, -1, 47],\n [-22, -8, 30, -14, 37]]\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[[4, 21, 24, 21, -14],\n [-10, 8, 46, 12, -2],\n [-4, -4, -5, -3, 1],\n [-5, -7, -20, -6, 0],\n [-5, -36, 9, -36, 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 5x5 matrix:\n[[-34, -28, 31, 38, 24],\n [15, 13, -16, -16, -10],\n [9, 8, -12, -10, -5],\n [-40, -31, 48, 54, 21],\n [-4, 3, 13, 24, -7]]\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, 27, -16, 8, 24],\n [-24, 17, 2, 7, 12],\n [5, 20, -22, 22, 19],\n [24, 8, -28, 22, 12],\n [22, 14, -1, -17, 8]]\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 5x5 matrix:\n[[33, 9, 0, -15, 6],\n [-9, -1, 2, 2, 14],\n [-27, -23, -16, 33, 22],\n [13, -41, -48, 46, 46],\n [-15, -57, -66, 30, 6]]\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[[-4, -9, -28, -30, -36],\n [12, 11, 4, 10, 12],\n [-16, -15, -7, -15, -18],\n [32, 30, 14, 30, 36],\n [8, 3, -19, -15, -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 5x5 matrix:\n[[-33, 18, -39, -15, -6],\n [18, 19, -18, 25, -18],\n [19, -23, 35, 2, -6],\n [12, -3, 0, 9, -38],\n [-43, 7, -23, -30, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[23, -28, 39, -27, -30],\n [-18, 0, 24, -34, -2],\n [14, -32, 48, -61, -34],\n [41, -19, -39, 10, -13],\n [2, 16, -29, 9, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[19, -20, 3, 43, -29],\n [3, -12, 7, -33, -5],\n [-10, -52, 6, 35, -25],\n [20, -16, 8, -55, 4],\n [26, 42, 1, -24, -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[[1, 2, -1, 7, 5],\n [13, -27, -10, -39, -36],\n [6, -19, 1, 1, -2],\n [-7, 18, 1, -15, -6],\n [-19, -30, 15, 24, 3]]?\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, 12, 2, -6, 12],\n [5, 6, 1, -3, 6],\n [5, 6, 1, -3, 6],\n [-30, -36, -6, 18, -36],\n [10, 12, 2, -6, 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[[21, -3, -9, -6, 1],\n [0, 48, 39, -30, -30],\n [-18, -34, -22, 28, 22],\n [-27, -3, 6, 12, 3],\n [6, -26, -23, 14, 16]]\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, -37, -7, -60, 90],\n [17, -15, -19, -44, 52],\n [-15, 11, 15, 32, -38],\n [-28, 29, -53, -8, -26],\n [30, -16, -19, -34, 46]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[30, 0, 6, -36, -6],\n [25, 0, 5, -30, -5],\n [0, 0, 0, 0, 0],\n [-25, 0, -5, 30, 5],\n [5, 0, 1, -6, -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[[-16, -16, -8, 24, -9],\n [-20, -34, -26, -52, -70],\n [-47, -1, 4, 26, 1],\n [-38, 13, -9, -25, -33],\n [-18, -35, 5, -34, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[10, -50, -28, -14, 4],\n [-20, 50, -25, 20, 20],\n [3, -25, 7, -9, -10],\n [32, 15, 28, 0, 3],\n [-55, -40, 15, -11, -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[[-18, 33, 42, 31, -9],\n [-22, 41, -19, -41, 29],\n [-39, 75, 0, -18, 33],\n [14, -5, -22, -51, 17],\n [9, -27, 24, 22, -27]]\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[[-17, -19, -8, -31, 14],\n [-22, -26, -28, -31, 19],\n [0, 8, 12, 1, -3],\n [25, -29, 4, -8, -1],\n [9, 32, 9, 36, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[10, -2, -4, -6, 0],\n [-20, 4, 8, 12, 0],\n [-15, 3, 6, 9, 0],\n [-15, 3, 6, 9, 0],\n [30, -6, -12, -18, 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[[-52, 4, 5, -4, 11],\n [-21, -17, -15, 23, 10],\n [18, 5, 19, -13, -27],\n [-50, -6, 7, -6, -40],\n [-10, -12, -25, 24, 34]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-39, 19, 19, 6, 35],\n [61, -31, -31, -12, -55],\n [-2, 17, 17, 33, 5],\n [11, 19, 19, 48, -5],\n [-4, -16, -16, -36, 0]]?\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[[30, -3, 14, -3, -18],\n [0, 50, 45, 5, -15],\n [54, 11, -3, 44, -15],\n [-2, -32, -2, -28, 12],\n [-10, 16, 51, -33, 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[[-58, 29, -42, 8, 8],\n [-59, -5, -53, -2, 23],\n [2, 4, 10, 2, 12],\n [-12, 42, 0, 12, -18],\n [-43, -21, -45, -7, 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[[21, 0, -35, -8, -40],\n [-12, -30, 0, -34, -6],\n [-12, 33, -14, 27, 5],\n [5, -3, -11, -6, -13],\n [2, 12, 14, 18, 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 5x5 matrix:\n[[-44, -4, 26, -56, -26],\n [8, -4, -2, 16, 14],\n [-21, -18, 12, -22, -11],\n [16, 24, -10, 12, 4],\n [9, 2, -6, 10, 3]]\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[[-2, 5, 1, 6, 6],\n [-6, 15, 3, 18, 18],\n [8, -20, -4, -24, -24],\n [-6, 15, 3, 18, 18],\n [4, -10, -2, -12, -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[[3, -18, 15, -3, -18],\n [6, -36, 30, -6, -36],\n [-5, 30, -25, 5, 30],\n [4, -24, 20, -4, -24],\n [3, -18, 15, -3, -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[[32, 6, 14, 29, -20],\n [14, 1, 11, 7, -12],\n [-6, -3, 3, -12, 0],\n [2, -5, 17, -17, -12],\n [-2, 3, -11, 10, 8]]\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, 34, 3, -8, -4],\n [-28, -34, 3, 8, 4],\n [30, 46, -16, -8, -12],\n [-33, -33, -12, 12, -6],\n [-1, 7, -20, 4, -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 5x5 matrix:\n[[16, 27, 32, -18, -6],\n [36, -21, 18, 2, -22],\n [0, -54, -26, 44, 16],\n [24, 36, 43, -28, -14],\n [-14, -18, -26, 10, 2]]\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[[25, 50, 3, -29, -1],\n [-22, -36, 1, 29, 5],\n [30, 2, -25, -50, -36],\n [13, 26, 0, -8, -4],\n [-33, -22, 21, 35, 35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -4, 4, -20, 12],\n [0, -6, 6, -30, 18],\n [0, -1, 1, -5, 3],\n [0, 1, -1, 5, -3],\n [0, -4, 4, -20, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-13, -5, -10, 5, 19],\n [30, 4, 17, -3, -36],\n [17, 7, 14, -10, -29],\n [25, 7, 17, -6, -33],\n [15, 17, 19, -10, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-36, -6, 18, -12, 12],\n [36, 6, -18, 12, -12],\n [-24, -4, 12, -8, 8],\n [-24, -4, 12, -8, 8],\n [6, 1, -3, 2, -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[[16, 3, 21, 3, -12],\n [-4, -12, -3, -12, -6],\n [12, -9, 18, -9, -18],\n [-16, -8, -20, -8, 8],\n [8, -1, 11, -1, -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[[-14, 24, 17, -9, 14],\n [16, -12, 13, -8, -27],\n [-11, -33, -56, -53, -9],\n [11, 5, 19, -9, -34],\n [29, -13, 76, 21, 17]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, -36, 16, -12, 16],\n [6, -18, 9, -3, 9],\n [3, 12, -12, 9, 0],\n [-20, -4, 6, -22, -10],\n [-4, 36, -7, 14, -19]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, -17, 16, 42, 7],\n [20, 4, -32, 19, -30],\n [0, -15, 56, 6, 41],\n [-40, -10, 0, -29, 10],\n [5, 7, 18, 4, 14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-16, 8, -16, 0, -16],\n [8, -4, 8, 0, 8],\n [24, -12, 24, 0, 24],\n [-12, 6, -12, 0, -12],\n [24, -12, 24, 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 5x5 matrix:\n[[45, -5, -20, 20, 20],\n [-18, -40, 20, -2, -11],\n [-24, -16, 16, -8, -12],\n [21, -21, -4, 12, 8],\n [15, 45, -20, 0, 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[[-3, 0, -4, -2, -5],\n [3, 0, 4, 2, 5],\n [-18, 0, -24, -12, -30],\n [-9, 0, -12, -6, -15],\n [-15, 0, -20, -10, -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[[0, 18, 36, 24, -20],\n [-18, -9, -45, -6, 5],\n [12, -15, -12, -24, 20],\n [18, -9, 9, -18, 15],\n [2, -13, -23, -18, 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[[3, -8, -11, -15, 15],\n [-1, 28, -17, -51, -5],\n [-18, 30, -24, -18, 27],\n [-1, 26, -10, -39, -11],\n [-1, 14, -2, -15, -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[[-12, 36, -18, -6, 12],\n [-6, 18, -9, -3, 6],\n [-8, 24, -12, -4, 8],\n [6, -18, 9, 3, -6],\n [-8, 24, -12, -4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, 12, 17, 0, -6],\n [23, -16, -21, -15, -12],\n [16, -12, -17, 0, 6],\n [-16, 8, 6, 48, 60],\n [11, -8, -11, -3, 0]]\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, 42, 8, 22, -46],\n [13, -66, -22, -29, 33],\n [-23, -30, -4, -17, 42],\n [-21, -12, 20, -11, 44],\n [-46, 6, 2, -2, 31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 12, 27, 18, -9],\n [8, 40, 22, 36, -10],\n [4, -4, -9, -6, 3],\n [24, 18, -19, 6, 4],\n [16, 14, -11, 6, 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[[-5, -4, -6, -4, 1],\n [-15, -12, -18, -12, 3],\n [10, 8, 12, 8, -2],\n [-10, -8, -12, -8, 2],\n [-15, -12, -18, -12, 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[[-2, 34, -37, 36, 11],\n [19, -27, -17, -8, -6],\n [5, -40, 10, -36, -13],\n [-40, 22, 37, -8, 13],\n [-28, 59, 12, 12, -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[[-54, -22, 18, -40, 27],\n [-23, 28, -2, 4, -24],\n [6, 12, 12, 9, -28],\n [-34, 36, -4, 3, -28],\n [28, -8, -8, 10, 8]]\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, -31, -7, 23, -10],\n [16, -25, -9, 15, -8],\n [-40, -7, -14, 6, -26],\n [25, 11, 28, 2, 32],\n [22, -32, -48, -4, -36]]\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[[-56, -3, 28, -34, 1],\n [24, -8, -12, 16, -4],\n [-2, -21, 1, 2, -8],\n [48, 10, -24, 28, 2],\n [-40, 9, 20, -26, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[30, -27, 41, 20, -46],\n [26, 28, 7, -27, 1],\n [-10, -21, 3, 20, -8],\n [-14, 30, -29, -37, 27],\n [12, 16, 2, 14, 22]]\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[[42, 8, 5, -19, 2],\n [-37, -14, -17, 18, -30],\n [28, -18, 6, 15, 16],\n [-41, 12, -18, -7, -8],\n [30, 30, 12, -38, 0]]?\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, -10, -10, 10, 2],\n [-18, -15, -15, 15, 3],\n [-12, -10, -10, 10, 2],\n [6, 5, 5, -5, -1],\n [-18, -15, -15, 15, 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[[24, -12, -4, 16, 16],\n [-6, 3, 1, -4, -4],\n [24, -12, -4, 16, 16],\n [36, -18, -6, 24, 24],\n [24, -12, -4, 16, 16]]\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, 0, -23, -15, 12],\n [24, -4, -41, -29, 18],\n [9, -26, -25, -31, -9],\n [-7, -14, 6, -4, -15],\n [18, 60, -6, 30, 54]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 24, 4, -12, 12],\n [-18, -36, -6, 18, -18],\n [0, 0, 0, 0, 0],\n [-9, -18, -3, 9, -9],\n [-3, -6, -1, 3, -3]]?\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],\n [-9, -6, 12, -3, -3],\n [3, 2, -4, 1, 1],\n [9, 6, -12, 3, 3],\n [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[[29, 38, 39, 45, 27],\n [-28, -35, 8, -11, -44],\n [-37, -47, -35, -34, -35],\n [-24, -29, 20, 7, -40],\n [34, 41, 2, -5, 38]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -40, -24, 0, 16],\n [3, 6, -23, 29, 27],\n [-16, 4, -14, 21, 15],\n [-18, -31, -54, 57, 22],\n [-40, -15, -20, 9, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-19, 33, -29, 10, 13],\n [26, -6, -32, -15, -6],\n [28, -12, -25, -18, -7],\n [21, -3, -24, -9, -7],\n [42, -38, 12, -21, -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[[36, -30, -24, 6, 18],\n [13, -10, -7, -7, 14],\n [1, 0, 1, -9, 8],\n [-11, 9, 7, 0, -7],\n [-6, 6, 6, -12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -18, 36, 0, -6],\n [0, 12, -24, 0, 4],\n [0, -6, 12, 0, -2],\n [0, -6, 12, 0, -2],\n [0, -12, 24, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[8, -10, 2, 4, -12],\n [-24, 30, -6, -12, 36],\n [-16, 20, -4, -8, 24],\n [8, -10, 2, 4, -12],\n [20, -25, 5, 10, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-20, 24, 60, -8, -4],\n [-15, 21, 48, -5, -2],\n [0, -36, -36, -12, -12],\n [20, 18, -18, 22, 18],\n [-10, 30, 48, 2, 4]]\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, -36, -18, -18, 18],\n [4, -24, -12, -12, 12],\n [-2, 12, 6, 6, -6],\n [-2, 12, 6, 6, -6],\n [-5, 30, 15, 15, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[8, 0, 24, -12, 4],\n [2, 8, -12, -1, -11],\n [-26, -28, -15, 32, 29],\n [-16, -12, -21, 21, 10],\n [8, 8, 6, -10, -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[[-8, -12, 0, 8, 4],\n [2, 3, 0, -2, -1],\n [6, 9, 0, -6, -3],\n [8, 12, 0, -8, -4],\n [-6, -9, 0, 6, 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[[38, -2, 9, -57, 20],\n [-28, -10, -9, 57, -30],\n [-8, -33, -4, -13, 5],\n [22, 2, 18, -24, -8],\n [6, -5, 16, -23, -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[[0, -8, -16, -8, 20],\n [0, -8, -16, -8, 20],\n [-30, -24, -30, 36, 18],\n [-30, -26, -34, 34, 23],\n [-15, -2, 5, 28, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 4, -16, -4, -16],\n [-10, -5, 20, 5, 20],\n [12, 6, -24, -6, -24],\n [-2, -1, 4, 1, 4],\n [2, 1, -4, -1, -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[[-24, 14, -10, -2, -39],\n [-25, -44, 26, -9, -16],\n [-26, 11, -7, -4, -36],\n [-30, 0, -4, -2, -50],\n [-32, 26, -14, -6, -41]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 12, -16, 24, -16],\n [1, -3, 4, -6, 4],\n [-1, 3, -4, 6, -4],\n [3, -9, 12, -18, 12],\n [-5, 15, -20, 30, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-12, 6, 3, 9, 6],\n [-4, 2, 1, 3, 2],\n [-12, 6, 3, 9, 6],\n [20, -10, -5, -15, -10],\n [8, -4, -2, -6, -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[[13, 0, 5, -22, 44],\n [0, 89, 6, -59, -50],\n [35, -29, -14, 51, 26],\n [4, -13, 6, 5, 16],\n [17, -6, -30, 26, 4]]\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[[-19, -2, -16, 22, 7],\n [-17, -18, -4, 2, -7],\n [0, 11, -7, 12, 9],\n [8, 13, -1, 4, 7],\n [34, 25, 15, -16, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-48, 9, -28, 18, -19],\n [-54, 9, -33, 21, -21],\n [12, -18, -14, 6, 10],\n [-12, 0, -10, 6, -4],\n [-18, 18, 9, -3, -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 5x5 matrix:\n[[2, -10, 2, -4, 4],\n [-5, 25, -5, 10, -10],\n [5, -25, 5, -10, 10],\n [6, -30, 6, -12, 12],\n [-4, 20, -4, 8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0, 0],\n [-12, 4, 2, 10, -6],\n [-30, 10, 5, 25, -15],\n [12, -4, -2, -10, 6],\n [-12, 4, 2, 10, -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 5x5 matrix:\n[[-10, -2, 10, -2, -10],\n [-30, -6, 30, -6, -30],\n [10, 2, -10, 2, 10],\n [-5, -1, 5, -1, -5],\n [-20, -4, 20, -4, -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[[-48, -18, 13, -23, -63],\n [-25, -43, 26, -13, -35],\n [-18, 18, -12, -26, -46],\n [49, -20, 7, 0, 33],\n [-30, -3, -17, -5, -36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[36, -42, 6, -25, -63],\n [18, -30, -30, -23, -15],\n [27, 6, 51, 16, -15],\n [12, 36, -64, 16, -22],\n [44, -36, -59, -29, -53]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 12, -2, -4, -10],\n [-24, -24, 4, 8, 20],\n [6, 6, -1, -2, -5],\n [-30, -30, 5, 10, 25],\n [-6, -6, 1, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[9, -36, 12, -18, 0],\n [0, -18, 7, -8, -5],\n [-15, -12, 8, -2, -20],\n [39, -30, 3, -22, 35],\n [18, 18, -11, 4, 25]]\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[[-9, -16, 45, -7, 1],\n [10, 16, -50, 6, 2],\n [1, 4, -5, 3, -4],\n [-5, -24, 25, -19, 27],\n [10, 20, -50, 10, -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[[-21, 20, -51, 8, -25],\n [21, -24, 30, -8, -6],\n [-8, 8, -10, 12, -10],\n [28, -30, 26, 1, -3],\n [-6, 7, -6, -22, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 10, -6, -12, 10],\n [0, 0, 0, 0, 0],\n [-6, -5, 3, 6, -5],\n [6, 5, -3, -6, 5],\n [-30, -25, 15, 30, -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[[-15, -8, -25, 4, -7],\n [-1, 20, -9, 38, -27],\n [-11, 10, -4, 3, 6],\n [11, 40, 39, 12, 13],\n [30, 4, 35, -2, -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[[14, 32, 15, 42, 18],\n [48, -12, -32, 40, -26],\n [-8, 14, 14, 40, 14],\n [4, -35, -29, -8, -26],\n [19, -1, -11, 3, -8]]?\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, -20, 13, 1, -38],\n [-42, -40, 10, -10, -10],\n [-10, -16, 6, 2, -10],\n [34, 27, -8, -6, 6],\n [6, 14, -8, -16, 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 5x5 matrix:\n[[32, -9, 2, 1, -4],\n [42, 27, -16, -4, 26],\n [-40, -78, -6, 52, -2],\n [24, -39, 7, 14, -15],\n [-36, -66, 3, 37, -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[[30, 24, 15, 45, -4],\n [-45, -3, 18, -23, 2],\n [41, -21, -44, 1, -2],\n [38, 9, -5, 46, -7],\n [-4, 39, 46, 21, 3]]\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[[-10, 0, -2, 0, -8],\n [30, 0, 6, 0, 24],\n [0, 0, 0, 0, 0],\n [-20, 0, -4, 0, -16],\n [-25, 0, -5, 0, -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 5x5 matrix:\n[[-20, -20, -20, -16, 4],\n [15, 29, 35, 12, -17],\n [-5, 37, 55, -4, -41],\n [10, -4, -10, 8, 12],\n [30, 30, 30, 24, -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 5x5 matrix:\n[[13, 5, 23, 15, -22],\n [-26, -2, -4, -32, -12],\n [-41, -5, -16, -50, -6],\n [13, 1, 2, 16, 6],\n [7, -1, -7, 9, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 6, 3, -18, 12],\n [36, 18, -1, -34, 36],\n [-30, -15, -2, 34, -30],\n [6, 3, -2, -2, 6],\n [6, 3, 3, -12, 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[[-5, 4, 11, -12, -3],\n [1, 0, 1, 0, -1],\n [30, -10, -10, 30, -10],\n [-23, 10, 17, -30, 3],\n [-35, 12, 13, -36, 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 5x5 matrix:\n[[0, 36, 30, 6, 24],\n [0, 6, 5, 1, 4],\n [0, 24, 20, 4, 16],\n [0, 6, 5, 1, 4],\n [0, -6, -5, -1, -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[[-5, -7, -45, -57, 13],\n [19, 20, 6, 4, 13],\n [14, 19, 39, 35, -16],\n [13, 21, -15, -49, -11],\n [-7, -13, -33, -25, 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[[3, -6, -16, 6, -23],\n [25, 28, 32, -15, 20],\n [-16, -16, 2, 27, 20],\n [45, 30, 18, 1, 1],\n [44, 41, 43, -21, 7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-20, 8, 4, -16, 24],\n [30, -12, -6, 24, -36],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [-30, 12, 6, -24, 36]]?\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 5x5 matrix:\n[[-30, -2, -4, -12, -4],\n [-2, -18, -40, -38, -32],\n [20, -18, -35, -15, -37],\n [31, -1, -3, 5, -1],\n [14, 4, 9, 13, 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[[-10, -20, 0, 0, 15],\n [-12, -6, 2, 3, 8],\n [-2, 14, 2, 3, -7],\n [8, -2, -2, -3, -2],\n [20, -50, -10, -15, 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[[16, 9, -8, -6, 1],\n [-6, 3, 8, -10, 57],\n [-22, 45, 9, 37, 17],\n [-49, 48, -9, 33, 31],\n [43, -34, -5, -39, -7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-7, -17, -8, 4, -9],\n [23, 15, 42, -10, 39],\n [-9, -33, -6, 6, -9],\n [-13, -39, -12, 8, -15],\n [-14, -34, -16, 8, -18]]\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[[-4, 19, -6, -3, -30],\n [20, -23, 14, 7, 6],\n [-44, 38, -28, -14, 12],\n [12, -30, 12, 6, 36],\n [-24, 24, -16, -8, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -12, 20, 0, 4],\n [-9, 9, -15, 0, -3],\n [-18, 18, -30, 0, -6],\n [15, -15, 25, 0, 5],\n [-12, 12, -20, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[39, 6, -30, -35, 4],\n [7, -10, -15, -8, 11],\n [-18, 21, 1, 2, -9],\n [20, -8, 9, -7, 13],\n [-11, -7, 34, 28, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[20, 16, 16, 28, 6],\n [-26, 11, -38, -13, -36],\n [-31, 25, -37, -28, -34],\n [13, -40, 45, -3, 47],\n [6, -12, -6, 14, -5]]?\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[[20, -30, -10, 0, -30],\n [-24, 30, 10, -4, 35],\n [-24, 30, 10, -4, 35],\n [-16, 36, 12, 8, 26],\n [8, 18, 6, 20, -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[[6, 0, 30, -24, -6],\n [3, 0, 15, -12, -3],\n [3, 0, 15, -12, -3],\n [3, 0, 15, -12, -3],\n [3, 0, 15, -12, -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[[-27, -8, 26, 19, 17],\n [33, 17, 4, 4, -37],\n [-18, 16, 35, 38, 49],\n [14, 20, 30, 22, -16],\n [50, 20, -27, -23, -43]]?\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, -14, 12, 11, 7],\n [-24, 24, -18, -19, -10],\n [0, -8, -6, 7, -6],\n [24, 0, 36, -2, 28],\n [-15, -10, -30, 10, -25]]\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, -11, -24, 29, -28],\n [2, 7, -3, -26, 9],\n [-40, -34, 36, 48, -13],\n [32, -19, -36, 15, -37],\n [22, 43, -9, 6, 22]]\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 5x5 matrix:\n[[21, 9, 15, -48, -40],\n [14, 5, 16, -13, -20],\n [20, -19, -6, 3, -14],\n [21, -6, -11, -44, -13],\n [-16, -31, -38, 39, 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[[-4, 4, -4, 8, 0],\n [10, -10, 10, -20, 0],\n [10, -10, 10, -20, 0],\n [-12, 12, -12, 24, 0],\n [-2, 2, -2, 4, 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[[-2, -21, -39, -10, -11],\n [-21, -16, -26, -39, -6],\n [-20, 19, -2, 1, 27],\n [-3, 15, 33, -2, 2],\n [-8, -13, -9, -23, -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[[9, -11, -19, 16, -4],\n [17, -1, -14, 12, 6],\n [21, 41, 34, 25, -31],\n [30, 40, 24, 22, -6],\n [15, -5, -15, 19, -15]]\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, 6, -54, -36, 18],\n [-17, 12, 6, 7, -40],\n [1, -16, 42, 19, -10],\n [7, -6, -12, -11, 20],\n [-6, 41, -27, 11, -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[[-20, 4, -10, 18, -10],\n [10, 22, -1, 33, 11],\n [-15, -11, -4, -11, -11],\n [0, 16, -4, 28, 4],\n [-40, -16, -14, -6, -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[[33, 38, -41, -12, 14],\n [-12, -48, 30, 27, -24],\n [-14, -44, 64, 13, 7],\n [45, 22, -35, 1, 9],\n [-2, 28, -12, -19, 15]]\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[[-8, -4, 2, -8, -12],\n [8, 4, -2, 8, 12],\n [12, 6, -3, 12, 18],\n [16, 8, -4, 16, 24],\n [-12, -6, 3, -12, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, -20, 12, 8, 4],\n [-3, -5, 3, 2, 1],\n [9, 15, -9, -6, -3],\n [-9, -15, 9, 6, 3],\n [15, 25, -15, -10, -5]]\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[[-48, -10, -51, -62, 0],\n [28, 8, 38, 38, -6],\n [13, 23, -7, -2, 19],\n [27, 21, 3, 17, 22],\n [7, 7, 2, 4, 5]]?\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 5x5 matrix:\n[[-9, -30, -6, 9, 45],\n [-13, -18, -4, 23, 7],\n [-20, -10, -7, 31, -19],\n [-53, -30, -35, 37, -1],\n [-26, -16, -18, 16, 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[[25, 25, 33, 20, -38],\n [-29, -32, -20, 41, 12],\n [14, 5, 13, -5, -5],\n [-24, -8, -12, 44, -11],\n [-35, -39, -35, 12, 35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[4, -13, 10, -16, 2],\n [-24, -42, 60, -24, -36],\n [-20, -5, 20, 10, -24],\n [-8, 16, -10, 22, -6],\n [4, -28, 25, -31, -1]]\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, 26, -21, -15, -36],\n [24, 34, -4, 12, -28],\n [64, -26, 50, 30, 52],\n [6, -27, 41, 51, 56],\n [12, -31, 19, -3, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[13, 37, 42, -3, 7],\n [24, -40, -32, -20, -8],\n [32, -32, -8, -46, -40],\n [-8, -16, -28, 18, 20],\n [17, -27, -16, -23, -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 5x5 matrix:\n[[12, 1, 1, -5, 4],\n [20, 6, -21, -16, 64],\n [-14, 17, 2, -21, 34],\n [-38, 12, 10, -6, -2],\n [34, -5, -6, -3, 10]]\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[[19, -21, 11, -33, -7],\n [-46, 9, -27, 28, -5],\n [-5, 15, -30, 3, 34],\n [17, -7, -3, -13, 40],\n [12, 2, -25, -28, 21]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-36, -12, 30, 24, 24],\n [-4, -2, 5, -14, 2],\n [-40, -14, 35, 10, 26],\n [11, 4, -10, 1, -7],\n [-14, -4, 10, 26, 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[[7, 0, -3, -3, -6],\n [-34, 2, 36, 3, 10],\n [-72, -17, 60, 36, 38],\n [-12, -5, 22, 3, -4],\n [50, -4, -40, -9, -26]]\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, -22, -28, 0, -29],\n [12, -6, 6, -30, -12],\n [-10, 17, 13, 19, 25],\n [-10, 21, 19, 17, 30],\n [10, 11, 29, -33, 10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -6, 18, -12, 12],\n [3, -3, 9, -6, 6],\n [0, 0, 0, 0, 0],\n [-2, 2, -6, 4, -4],\n [1, -1, 3, -2, 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 5x5 matrix:\n[[0, 4, -4, 4, 3],\n [0, -20, 20, -20, -15],\n [0, 12, -12, 12, 9],\n [0, -24, 24, -24, -18],\n [0, -12, 12, -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 5x5 matrix:\n[[0, 0, 0, 0, 0],\n [5, 25, 15, 15, 20],\n [2, 10, 6, 6, 8],\n [-4, -20, -12, -12, -16],\n [-1, -5, -3, -3, -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[[-12, -24, 4, 16, -20],\n [12, 6, -1, -3, 14],\n [-3, 30, -5, -22, 7],\n [-27, 0, 0, -3, -27],\n [9, 18, -3, -12, 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[[0, 0, 0, 0, 0],\n [-12, 24, 16, 0, -16],\n [-15, 30, 20, 0, -20],\n [-3, 6, 4, 0, -4],\n [18, -36, -24, 0, 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[[-4, 13, -10, -19, -12],\n [-12, 33, -22, -30, 18],\n [-13, 26, -19, -21, 18],\n [34, -43, 44, 52, 30],\n [25, -9, 21, 11, 24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 6, 10, 10, -10],\n [6, -3, -5, -5, 5],\n [-30, 15, 25, 25, -25],\n [0, 0, 0, 0, 0],\n [-12, 6, 10, 10, -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 5x5 matrix:\n[[3, -6, -9, 4, 0],\n [-4, -12, 2, -42, 30],\n [9, -36, -36, -21, 27],\n [0, -6, -3, -11, 9],\n [-2, 0, 4, -10, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-18, -27, 22, -36, 28],\n [-9, -5, 16, -16, 32],\n [-2, 5, 0, 0, 0],\n [18, 31, -13, 30, -26],\n [-18, -4, -6, -12, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, -1, 20, -30, -38],\n [-6, -9, 12, 6, 6],\n [-31, 18, -5, -14, 8],\n [-33, 36, -42, 21, 59],\n [18, -5, 10, -19, -36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[23, -9, -5, -6, 4],\n [-22, 11, 4, 0, 0],\n [-12, -21, 7, 24, -50],\n [-24, -11, 10, 36, -40],\n [8, 10, 2, 48, 36]]\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[[-2, 8, -16, 22, 29],\n [12, -16, 32, -28, -30],\n [6, -48, 12, -46, -27],\n [4, 8, -10, 27, 38],\n [-10, 4, -14, 0, -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[[-15, -2, 2, 8, -6],\n [39, -8, -22, -22, 6],\n [-6, -14, -16, 2, -12],\n [18, 20, 20, -8, 20],\n [-9, 1, 4, 5, -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[[30, -11, 21, 22, 23],\n [5, -10, -35, -10, -40],\n [-12, 4, 12, -2, 8],\n [81, -37, -26, 31, -19],\n [-42, 26, -24, -28, -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[[6, -12, -36, -10, 12],\n [0, 16, 32, 0, -8],\n [12, -8, -40, -20, 16],\n [3, -8, -22, -5, 7],\n [-21, -8, 26, 35, -17]]\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, -24, -33, 3, 2],\n [-30, 31, 24, -28, -2],\n [42, -26, -18, 38, -8],\n [-21, -5, -19, -19, 4],\n [63, -50, -25, 59, 6]]\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, -34, 10, -14, -34],\n [24, 39, -9, 27, 15],\n [22, 17, -11, 14, -4],\n [8, 19, 3, 19, -1],\n [-7, -2, -12, -23, 41]]\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 5x5 matrix:\n[[5, -7, 13, 11, -16],\n [-6, 16, 6, 46, -38],\n [-15, -53, 1, -23, -2],\n [-28, -16, -9, 29, -31],\n [-42, -44, -7, 4, -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[[5, 31, 5, -33, -26],\n [14, 66, 60, -4, -30],\n [14, 30, 3, 1, -47],\n [8, 28, 17, -3, -23],\n [11, 29, 22, 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[[-4, 6, -2, 3, -1],\n [-16, 24, -8, 12, -4],\n [-8, 12, -4, 6, -2],\n [0, 0, 0, 0, 0],\n [8, -12, 4, -6, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, 12, -12, 12, 3],\n [17, -18, 32, -18, -13],\n [11, 6, 8, 6, -7],\n [-13, 2, -16, 2, 9],\n [-16, -11, -10, -11, 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[[13, 13, 13, -1, 14],\n [44, -10, -21, 16, -17],\n [2, 44, 19, -6, 19],\n [47, -37, -40, 20, -26],\n [-51, 43, 56, -27, 47]]\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[[30, -15, -20, 15, 15],\n [-6, 3, 4, -3, -3],\n [6, -3, -4, 3, 3],\n [-18, 9, 12, -9, -9],\n [6, -3, -4, 3, 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[[12, 16, -20, 24, 16],\n [9, 12, -15, 18, 12],\n [-12, -16, 20, -24, -16],\n [-9, -12, 15, -18, -12],\n [12, 16, -20, 24, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, 18, 18, -7, -20],\n [3, 6, 22, -25, -44],\n [31, 8, -11, 32, -34],\n [27, -30, -26, -2, -16],\n [-9, -54, -36, -12, 60]]\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 5x5 matrix:\n[[0, 0, 0, 0, 0],\n [12, 24, -36, -6, -24],\n [-4, -8, 12, 2, 8],\n [4, 8, -12, -2, -8],\n [-12, -24, 36, 6, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, 3, -4, 18, 13],\n [-9, 36, -20, -36, -19],\n [6, -12, 8, 0, -2],\n [-7, 20, -12, -12, -5],\n [1, -8, 4, 12, 7]]\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 5x5 matrix:\n[[0, -16, -8, 22, -40],\n [-36, 0, -40, 12, 24],\n [-24, -10, -2, -45, -9],\n [-6, 8, -16, 21, 24],\n [0, 2, -14, 31, 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[[10, -5, -25, -30, 25],\n [2, -1, -5, -6, 5],\n [0, 0, 0, 0, 0],\n [12, -6, -30, -36, 30],\n [-4, 2, 10, 12, -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[[13, 12, 12, -27, -18],\n [22, -1, 16, -18, -12],\n [55, -45, 33, 14, 7],\n [12, -28, 10, 42, 18],\n [36, -1, 37, -5, -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[[10, -6, -6, -26, 22],\n [-5, -34, -39, 2, 26],\n [-15, -23, -29, 8, -7],\n [23, 12, 14, -22, -29],\n [20, 10, 12, -29, -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[[-8, -15, -2, 3, 10],\n [-4, -15, 4, 14, 20],\n [4, 0, 6, 11, 10],\n [-24, -18, -24, -36, -24],\n [20, 18, 18, 25, 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[[16, 40, 6, -30, -12],\n [2, 12, 6, -10, -2],\n [9, -2, -15, 5, -5],\n [12, 16, -6, -10, -8],\n [10, 4, -12, 0, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, -2, 8, 6, 6],\n [6, -2, 8, 6, 6],\n [-6, 2, -8, -6, -6],\n [-15, 5, -20, -15, -15],\n [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[[28, 6, 27, -32, -14],\n [26, 2, 23, -10, 8],\n [-20, -20, -5, 44, 8],\n [-10, 4, -25, -11, 15],\n [-39, -4, -31, 3, -27]]\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[[9, -37, -41, 6, 17],\n [-21, 41, 9, -7, -6],\n [-3, -65, -9, -27, -19],\n [6, -30, -34, -4, -26],\n [-29, -23, 15, -35, 4]]\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, 0, 0, 0, 0],\n [5, 0, 20, -15, -30],\n [2, 0, 8, -6, -12],\n [1, 0, 4, -3, -6],\n [-2, 0, -8, 6, 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[[-14, -24, -8, 34, 22],\n [18, -54, 15, -6, 33],\n [2, -48, 4, 18, 34],\n [18, 18, 11, -38, -19],\n [-10, 6, -7, 14, -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[[-52, 11, 16, -32, -41],\n [20, -21, 14, 41, 26],\n [-4, 7, -28, -26, -18],\n [-7, -3, -8, 12, 13],\n [38, 5, 30, 17, 27]]\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 5x5 matrix:\n[[-18, 18, 0, -36, 24],\n [9, -9, 0, 18, -12],\n [-12, 12, 0, -24, 16],\n [0, 0, 0, 0, 0],\n [-12, 12, 0, -24, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[11, -45, 37, 11, -33],\n [-10, 26, -20, -11, 17],\n [-15, 25, -9, -39, 16],\n [19, -29, 9, 9, -24],\n [15, -42, 32, -6, -32]]\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, 0, 0, 0, 0],\n [-20, 5, 5, 5, -20],\n [4, -1, -1, -1, 4],\n [4, -1, -1, -1, 4],\n [-16, 4, 4, 4, -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 5x5 matrix:\n[[-10, -16, -2, -14, 10],\n [-10, -33, 1, -26, 16],\n [0, -1, 3, -4, -10],\n [-12, -13, 3, -20, -14],\n [-10, -9, 1, -14, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[4, -2, -3, -4, -5],\n [4, -2, -3, -4, -5],\n [8, -4, -6, -8, -10],\n [-4, 2, 3, 4, 5],\n [12, -6, -9, -12, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-27, -4, 21, 11, 5],\n [-31, 9, 19, -8, -6],\n [18, -7, -9, 25, -8],\n [6, -6, -9, -10, 23],\n [-12, -14, -9, 22, 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[[44, 22, -18, 4, 12],\n [38, 7, -21, 1, 9],\n [-26, -20, 11, -4, -10],\n [-38, -26, -3, -4, -2],\n [-26, 13, -13, 5, 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[[36, 46, -50, -2, -23],\n [17, 34, -40, -16, -22],\n [-10, -6, 7, -2, 0],\n [8, 6, -8, -2, -1],\n [23, 22, -22, 8, -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[[-17, 20, -21, -6, -5],\n [4, 8, -33, -22, -24],\n [1, -4, -15, -18, -11],\n [-45, -7, 16, -8, 32],\n [-57, -1, 10, -12, 34]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[15, -1, 19, 28, 27],\n [26, 15, 33, 20, 28],\n [-7, -20, -32, -12, -56],\n [-7, 45, 56, 4, 34],\n [-39, 36, 13, -40, -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 5x5 matrix:\n[[27, 9, 3, -21, -6],\n [14, 2, 4, -13, -6],\n [16, -8, 14, -23, -18],\n [17, 35, -25, 10, 28],\n [-1, 29, -27, 24, 32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, 12, -12, -4, 20],\n [-4, 6, -6, -2, 10],\n [12, -18, 18, 6, -30],\n [10, -15, 15, 5, -25],\n [6, -9, 9, 3, -15]]\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, -3, -22, 2, -23],\n [-44, -21, -42, -10, -49],\n [40, 24, 36, 14, 44],\n [8, 3, 8, 1, 9],\n [16, 42, 0, 38, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-34, 14, -19, -4, -10],\n [22, -18, 24, -5, -26],\n [-22, -7, -8, -12, -15],\n [54, -6, 36, 12, -6],\n [-31, -19, -19, -16, 5]]\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, 0, 0, 0, 0],\n [-10, 2, -6, 8, -6],\n [15, -3, 9, -12, 9],\n [-30, 6, -18, 24, -18],\n [-30, 6, -18, 24, -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 5x5 matrix:\n[[12, 57, 0, 3, -46],\n [3, 3, -3, -2, -2],\n [7, 52, 9, 5, -42],\n [38, -16, -36, -44, 23],\n [3, 57, 9, 12, -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 5x5 matrix:\n[[-1, -24, -1, -18, -17],\n [-68, 5, 30, 30, 21],\n [15, 39, 26, 12, 44],\n [-11, -40, -21, -33, -27],\n [-46, 12, -7, 36, 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 5x5 matrix:\n[[-9, 3, -35, 20, 11],\n [-17, -14, -23, 1, -12],\n [-29, -29, -15, -16, -29],\n [30, 42, -6, 36, 50],\n [-19, -7, -17, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 16, 4, 24, -12],\n [-3, 12, 3, 18, -9],\n [3, -12, -3, -18, 9],\n [-3, 12, 3, 18, -9],\n [-2, 8, 2, 12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[15, -12, -6, -6, 6],\n [-30, 24, 12, 12, -12],\n [-17, 40, -14, -10, 2],\n [26, -1, -26, -23, 17],\n [5, -4, -2, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-18, -18, 0, -24, 6],\n [-6, -6, 0, -8, 2],\n [3, 3, 0, 4, -1],\n [-15, -15, 0, -20, 5],\n [12, 12, 0, 16, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[5, 61, -23, 10, 26],\n [-4, -35, 3, -1, -40],\n [0, -30, 30, -12, 36],\n [3, -18, 28, -4, 60],\n [-1, 0, -38, 31, -70]]?\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, -6, -3, -15, 24],\n [-37, -12, 23, 38, -46],\n [-53, -6, 4, 21, 16],\n [-26, -2, 6, 19, -9],\n [37, 10, -15, -27, 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[[-6, 8, 10, 10, 8],\n [15, -20, -25, -25, -20],\n [-15, 20, 25, 25, 20],\n [6, -8, -10, -10, -8],\n [6, -8, -10, -10, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[20, -24, 4, 16, 20],\n [15, -18, 3, 12, 15],\n [25, -30, 5, 20, 25],\n [-25, 30, -5, -20, -25],\n [-10, 12, -2, -8, -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 5x5 matrix:\n[[-6, 6, 6, -48, -6],\n [-30, -5, 30, 26, 26],\n [4, 6, -4, -44, -12],\n [-20, 0, 20, -8, 12],\n [-13, -2, 13, 10, 11]]\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[[29, -1, -8, 24, 37],\n [-4, -19, -21, 25, -16],\n [2, -3, 3, 5, -12],\n [-35, 10, 6, -40, -14],\n [41, 6, 11, 21, 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 5x5 matrix:\n[[-29, 18, -11, 29, 23],\n [-6, -8, 6, 6, 12],\n [-12, 52, -36, 12, -18],\n [-2, 20, -14, 2, -10],\n [9, 12, -9, -9, -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 5x5 matrix:\n[[-1, -8, 8, 23, -9],\n [-34, 48, 32, -10, 40],\n [-11, -4, 8, 23, -12],\n [9, 12, 8, -13, 24],\n [-33, 44, 24, -15, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-22, -22, -10, 12, 20],\n [7, -8, 10, -7, 5],\n [-22, -22, -10, 12, 20],\n [-7, -25, 5, 0, 20],\n [-2, -26, 10, -4, 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[[-10, 1, -10, -13, 8],\n [-3, -3, 6, -13, 1],\n [13, -5, -6, 37, 5],\n [9, -34, -4, 28, 39],\n [12, -4, 8, 20, -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[[-28, 6, 10, -6, 10],\n [14, -2, -1, -12, -15],\n [-14, 2, 1, 12, 15],\n [-4, -1, -6, 27, 20],\n [6, 1, 7, -33, -25]]\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[[-41, 19, -27, 54, 58],\n [-25, 1, 1, 42, 29],\n [55, -30, 23, -38, -66],\n [-35, 17, -33, 46, 45],\n [-45, 26, -27, 44, 64]]\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, 5, -19, 1, -38],\n [18, -18, 6, 6, 36],\n [-3, 4, 3, -2, -1],\n [3, -8, -19, 6, -19],\n [-18, 18, -6, -6, -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[[0, 0, 0, 0, 0],\n [3, 0, 6, 6, 7],\n [-6, -24, -4, 4, 6],\n [-15, -54, -12, 6, 10],\n [3, 0, 6, 6, 7]]?\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[[31, 8, -8, -7, 30],\n [-42, -16, 0, 2, -44],\n [-15, -20, -30, -20, -25],\n [9, 12, 18, 12, 15],\n [20, 20, 26, 17, 29]]\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 5x5 matrix:\n[[-49, 41, 7, -40, -1],\n [-21, 3, -3, -15, -7],\n [-37, 49, 5, 1, -3],\n [-11, 19, 3, -35, -9],\n [54, -58, -3, 29, 16]]\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, -12, 26, 7, -30],\n [32, -8, 8, 14, -11],\n [36, -13, -12, -22, -19],\n [-44, 23, 24, 32, 35],\n [7, 2, 2, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 37, 15, 28, -18],\n [32, 60, 49, 34, 2],\n [-28, -6, -23, -2, -30],\n [0, -36, -18, -45, -6],\n [-10, -23, -19, -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[[-10, 0, 0, -2, -2],\n [10, 0, 0, 2, 2],\n [5, 0, 0, 1, 1],\n [0, 0, 0, 0, 0],\n [10, 0, 0, 2, 2]]?\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[[1, -18, -5, 6, 2],\n [37, -5, 18, 27, -13],\n [30, 11, 18, -25, -12],\n [18, 18, 15, 6, -9],\n [39, -11, 15, -47, -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[[0, 2, -5, 5, -4],\n [0, 6, -15, 15, -12],\n [0, 12, -30, 30, -24],\n [0, -4, 10, -10, 8],\n [0, -12, 30, -30, 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[[-4, 20, 4, 14, 16],\n [-3, -12, -15, -15, -9],\n [11, 8, 31, 21, 5],\n [-5, -2, -13, -8, -1],\n [16, -26, 20, -5, -22]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, -30, 50, 6, 18],\n [-3, -12, -8, 56, 16],\n [-12, -28, 12, -32, 8],\n [0, -84, 60, 34, 10],\n [-15, 2, -38, 24, -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 5x5 matrix:\n[[-4, 8, -6, -8, 0],\n [8, -16, 12, 16, 0],\n [0, 0, 0, 0, 0],\n [4, -8, 6, 8, 0],\n [-10, 20, -15, -20, 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 5x5 matrix:\n[[-9, -14, 10, 31, -12],\n [-1, -6, -18, -9, 4],\n [-24, -58, -19, -4, 0],\n [15, 30, 0, -25, 10],\n [-10, -32, -20, -38, 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[[-20, -30, 0, 36, -17],\n [-2, -8, -22, -5, 12],\n [-14, -36, -42, -3, 10],\n [-26, -58, -18, 3, -23],\n [14, 46, 27, 9, 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[[32, 6, 70, 74, -14],\n [39, 0, 41, 36, -13],\n [50, 42, 22, 22, -40],\n [3, -36, 40, 36, 19],\n [21, 0, 9, 4, -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[[34, 4, -7, 7, -22],\n [-46, -26, 18, -38, -7],\n [-2, -2, -12, -40, -73],\n [-21, -20, 40, 16, -10],\n [-15, -24, 25, -17, -39]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-12, -14, 2, 18, -14],\n [-29, -34, -31, 49, -50],\n [23, -13, 42, 20, 13],\n [-11, -31, 32, 40, -15],\n [21, 15, 45, -24, 38]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, 16, -39, -35, 8],\n [32, -13, 7, 27, -1],\n [18, -29, -8, -8, 31],\n [-21, 44, -49, -40, -13],\n [-6, 18, -33, -11, 0]]\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, -22, 13, 23, 16],\n [19, -13, 22, 17, 19],\n [-5, -25, 10, 25, 15],\n [-38, -28, -14, 22, 0],\n [29, 10, 17, -5, 8]]\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, -41, -32, 32, -24],\n [-3, 17, 24, -24, 8],\n [30, 6, -20, 20, 8],\n [12, 4, -6, 6, 4],\n [-21, -9, 8, -8, -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 5x5 matrix:\n[[14, 12, 10, 0, -24],\n [35, 3, 19, -1, -8],\n [-43, 25, -57, -9, 29],\n [2, 48, -44, -14, 11],\n [8, 38, -34, -12, 13]]\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[[-10, -36, 1, -35, -16],\n [-15, -5, -30, 10, -35],\n [-29, 7, -23, -11, 5],\n [53, 33, 29, 60, 8],\n [-44, -2, -39, -19, -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 5x5 matrix:\n[[6, 12, -22, 42, 30],\n [-12, 6, -6, -24, -30],\n [8, -4, 4, 16, 20],\n [-6, 12, -18, 6, -6],\n [10, -8, 10, 14, 22]]\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[[-12, -31, 36, -3, 0],\n [18, -1, -16, -43, -38],\n [-3, -9, 10, -2, -1],\n [-9, 18, -6, 39, 33],\n [18, 49, -56, 7, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[48, 36, 66, -30, -30],\n [-2, 36, 16, -20, -10],\n [12, -36, -6, 18, 6],\n [34, 18, 43, -17, -19],\n [-17, -24, -29, 17, 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 5x5 matrix:\n[[-48, -58, 14, -76, 6],\n [-33, -43, 20, -59, 2],\n [-12, -10, -44, 33, 16],\n [-62, -43, -53, -38, 9],\n [25, 29, -8, 24, 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[[-6, 0, -19, 26, 15],\n [-11, 37, 36, -15, -33],\n [-16, -77, -10, 30, 36],\n [16, 0, 21, -52, -3],\n [-24, -50, -7, 32, 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 5x5 matrix:\n[[7, -4, 9, 5, -16],\n [46, 8, 18, -25, -15],\n [6, -24, -30, 0, 18],\n [48, 0, 8, -25, -9],\n [25, -16, -23, -15, 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 5x5 matrix:\n[[-21, -3, 23, -10, 12],\n [61, 31, -60, 34, -46],\n [-6, 30, 16, 4, -12],\n [-22, -10, 22, -12, 16],\n [12, -24, -21, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[19, 42, -25, 16, 4],\n [8, -9, -29, -9, -12],\n [-29, -12, 7, -1, 25],\n [23, -6, -13, -8, -28],\n [-8, 6, 34, 8, 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[[1, -5, -4, -4, -2],\n [5, -25, -20, -20, -10],\n [-2, 10, 8, 8, 4],\n [3, -15, -12, -12, -6],\n [4, -20, -16, -16, -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[[-25, -13, 22, 22, 3],\n [28, -12, -6, -38, -6],\n [-1, -2, -13, 12, 21],\n [-33, 20, 24, 31, -22],\n [12, -21, 12, -27, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[20, 15, -5, 5, 5],\n [-20, -15, 5, -5, -5],\n [16, 12, -4, 4, 4],\n [-8, -6, 2, -2, -2],\n [24, 18, -6, 6, 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[[15, 10, -7, -14, 27],\n [13, -4, 5, -34, 35],\n [-18, 20, 30, 28, -2],\n [22, 5, -37, -10, 14],\n [9, -18, 17, -34, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[28, 8, -14, 10, -20],\n [-12, -7, 5, -8, 21],\n [-36, -40, 27, -51, -8],\n [3, -1, -21, 15, -14],\n [-15, 7, 37, -17, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[19, -22, 56, -16, 51],\n [5, 0, 2, -10, 3],\n [-18, 14, -38, 22, -36],\n [-22, 6, -22, 38, -24],\n [-15, 20, -50, 10, -45]]\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 5x5 matrix:\n[[11, 22, 25, -21, 1],\n [-22, 24, -10, -10, 34],\n [9, 48, 15, -42, 45],\n [10, -7, 0, 1, -5],\n [-26, 31, 0, -13, 29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 6, -28, -26, 20],\n [0, 1, 8, 9, -8],\n [-1, -9, -34, -41, 38],\n [7, 33, -2, 17, -26],\n [-1, -6, -10, -14, 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 5x5 matrix:\n[[10, -22, 22, 14, 2],\n [23, -17, 9, -25, 29],\n [-20, -40, -20, -9, 11],\n [21, 39, 25, 15, -14],\n [6, 30, 14, 19, -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 5x5 matrix:\n[[33, -13, -8, 28, -22],\n [28, -42, -26, 36, -2],\n [19, -41, -9, 20, -4],\n [13, 11, 29, -8, -30],\n [28, -42, 16, 12, -26]]\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, 3, -56, -10, -80],\n [20, -31, 16, 40, 24],\n [-29, 40, 24, -65, 17],\n [16, 9, 28, 5, 22],\n [29, -9, -7, 37, -16]]\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, -9, -11, 15, -17],\n [10, -10, -15, -25, -5],\n [-20, 8, 10, -10, 14],\n [8, -8, -12, -20, -4],\n [-26, 11, 14, -10, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, -2, 10, 0, -2],\n [-4, -4, 20, 0, -4],\n [3, 3, -15, 0, 3],\n [-4, -4, 20, 0, -4],\n [1, 1, -5, 0, 1]]\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, 10, -4, 4, -8],\n [24, 20, -8, 8, -16],\n [6, 5, -2, 2, -4],\n [12, 10, -4, 4, -8],\n [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[[24, -6, -30, 18, 30],\n [-12, 3, 15, -9, -15],\n [-8, 2, 10, -6, -10],\n [-20, 5, 25, -15, -25],\n [12, -3, -15, 9, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[15, -11, -1, 0, 21],\n [18, -16, 7, -9, 12],\n [1, 5, -6, 11, 25],\n [3, -2, 6, -4, 3],\n [-53, 53, -8, 25, -17]]\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[[46, -6, -36, -12, -8],\n [-1, 9, -1, -5, -8],\n [34, -11, -35, 9, 11],\n [-9, -21, -19, 33, 42],\n [-9, -5, 5, 9, 10]]\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 5x5 matrix:\n[[-5, -52, 23, 40, 5],\n [29, -4, -4, -32, -7],\n [-30, 24, -11, -40, 10],\n [-15, -30, -28, -14, 35],\n [-23, -37, -11, -23, 29]]\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 5x5 matrix:\n[[-46, 11, 6, 4, 6],\n [-15, -1, 20, -11, -19],\n [7, 2, -5, -11, -1],\n [-6, 10, -17, 11, 22],\n [2, 1, -5, -14, -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[[10, -19, 50, -8, 7],\n [0, -24, 20, -8, 12],\n [0, -18, 15, -6, 9],\n [-4, -38, 18, -12, 20],\n [-12, 18, -56, 8, -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 5x5 matrix:\n[[0, 15, -25, 30, -25],\n [0, 18, -30, 36, -30],\n [0, 3, -5, 6, -5],\n [0, -9, 15, -18, 15],\n [0, -9, 15, -18, 15]]\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[[-30, -3, 18, -4, 24],\n [-15, 30, -10, -19, -11],\n [-53, -71, -1, -30, 55],\n [-23, 27, 27, 24, -13],\n [-36, 19, 55, 29, 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[[-6, 2, -1, 4, 0],\n [6, -2, 1, -4, 0],\n [-18, 6, -3, 12, 0],\n [-12, 4, -2, 8, 0],\n [30, -10, 5, -20, 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[[-2, -7, 15, -4, -41],\n [-2, -4, 7, -25, -26],\n [10, 5, -20, -25, 15],\n [28, 5, -32, 7, 39],\n [24, -9, -2, 14, 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[[-48, -12, -48, 72, 0],\n [28, 22, 38, -42, 5],\n [-40, -4, -36, 60, 2],\n [20, -4, 14, -30, -3],\n [16, 16, 24, -24, 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[[-36, 28, 60, -59, 30],\n [-10, 4, -46, 34, -34],\n [17, -6, -37, 34, -25],\n [-24, 34, 30, -33, 3],\n [-6, 28, -18, 10, -30]]?\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, 11, 6, -49, -1],\n [-42, -4, -6, 14, -34],\n [30, 2, 4, -6, 26],\n [-39, 1, -4, -9, -41],\n [-12, 7, 1, -34, -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[[3, -18, 18, 16, 0],\n [-37, -32, -22, -2, 42],\n [18, 18, 18, -12, -18],\n [14, -8, 26, 14, -12],\n [9, 16, 4, -12, -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[[11, 54, 22, -31, 36],\n [-23, -62, -31, 33, -43],\n [-61, -50, -49, 16, -40],\n [14, 28, 12, -14, 32],\n [-16, 8, -9, -9, 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[[14, -64, -31, -2, -12],\n [-16, -2, 8, 24, -32],\n [-1, -26, -4, -30, 16],\n [33, 8, -21, -4, 28],\n [20, -20, -25, 30, -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[[-15, 33, -25, 13, 18],\n [-3, 27, -5, 6, 24],\n [12, -24, 20, -10, -12],\n [3, -33, 5, -7, -30],\n [12, 6, 20, -5, 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 5x5 matrix:\n[[48, -33, -38, 2, -11],\n [20, 8, -7, -41, -9],\n [-64, 68, 82, -28, 44],\n [18, -57, -57, 53, -57],\n [14, 2, 6, -18, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[54, 10, -12, 20, -52],\n [-23, -9, -1, -12, 17],\n [32, 31, -12, 11, -35],\n [-2, -40, -16, 2, 2],\n [37, 17, -20, 46, -8]]\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, -5, -10, 7, -4],\n [12, 2, -10, -14, -32],\n [3, -4, -25, -8, -44],\n [12, 6, 10, -10, 0],\n [27, 12, 15, -24, -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 5x5 matrix:\n[[23, -24, 2, -25, -38],\n [-32, -16, 7, 16, 59],\n [40, 6, -15, -45, 3],\n [15, 17, -15, -9, 9],\n [-40, -20, 15, 25, 45]]\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, 5, -5, -9, 0],\n [32, 0, -20, -42, 20],\n [-14, -22, 6, 6, 16],\n [-14, -6, 8, 15, -2],\n [24, -8, -16, -36, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-19, -7, -21, -3, -27],\n [-9, -11, 4, 27, -32],\n [-18, 7, -32, -36, 1],\n [17, -13, 15, 21, -1],\n [1, -1, -20, -27, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-25, 30, 10, 20, 0],\n [15, -18, -6, -12, 0],\n [-25, 30, 10, 20, 0],\n [-10, 12, 4, 8, 0],\n [10, -12, -4, -8, 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, 20, -12, 24, 20],\n [0, 30, -18, 36, 30],\n [0, 20, -12, 24, 20],\n [0, -20, 12, -24, -20],\n [0, -30, 18, -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[[35, 39, 61, -39, -43],\n [-25, -33, -23, 15, 32],\n [23, 11, 5, 21, 4],\n [-16, -20, 24, -26, 7],\n [-8, 2, 18, -31, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-18, -6, -1, -22, -4],\n [-12, -4, 4, -3, 2],\n [-36, -12, -6, -54, -12],\n [24, 8, -10, 1, -6],\n [-36, -12, 6, -24, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[0, -15, -30, -10, -5],\n [0, -15, -30, -10, -5],\n [0, -9, -18, -6, -3],\n [0, 3, 6, 2, 1],\n [0, -15, -30, -10, -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[[3, -3, -18, 6, 0],\n [0, 0, 0, 0, 0],\n [-3, 3, 18, -6, 0],\n [3, -3, -18, 6, 0],\n [-1, 1, 6, -2, 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[[-16, -12, -4, -20, 24],\n [8, 6, 2, 10, -12],\n [24, 18, 6, 30, -36],\n [-4, -3, -1, -5, 6],\n [8, 6, 2, 10, -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[[20, -23, -21, 41, 34],\n [-18, 14, -5, -27, 1],\n [30, -31, 61, -3, -17],\n [-46, 19, 3, -34, 7],\n [-6, 5, -10, -18, 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, 27, -8, 38, -1],\n [13, -24, -41, 32, -31],\n [20, 7, -4, 16, -49],\n [-45, -24, -33, 6, 39],\n [-11, 23, 5, 22, -12]]\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, 16, 54, -16, 44],\n [-16, -9, 9, -52, 59],\n [-4, 21, -45, -36, -27],\n [3, -1, 33, 6, 42],\n [16, 39, 61, -12, 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 5x5 matrix:\n[[-79, 53, 36, 0, 75],\n [44, -42, 6, 24, -50],\n [17, -3, 4, 48, -5],\n [22, 45, -55, 30, 29],\n [-21, 19, -22, 31, 33]]\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 5x5 matrix:\n[[-20, 8, -12, -24, 24],\n [-5, 2, -3, -6, 6],\n [-25, 10, -15, -30, 30],\n [15, -6, 9, 18, -18],\n [25, -10, 15, 30, -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 5x5 matrix:\n[[6, -2, 2, -10, -6],\n [-3, 1, -1, 5, 3],\n [-6, 2, -2, 10, 6],\n [9, -3, 3, -15, -9],\n [-18, 6, -6, 30, 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[[-8, -8, 8, 6, -8],\n [-36, -20, 14, 16, -32],\n [16, 16, -16, -12, 16],\n [60, 12, 6, -12, 48],\n [0, -32, 44, 22, -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[[-27, -27, -17, -12, -12],\n [35, 43, 9, -34, -18],\n [40, 47, 24, -5, -9],\n [-20, -22, 4, 13, -12],\n [-30, -42, -26, -21, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-10, 5, -25, -20, 5],\n [4, -2, 10, 8, -2],\n [-10, 5, -25, -20, 5],\n [-10, 5, -25, -20, 5],\n [-4, 2, -10, -8, 2]]\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, -3, -12, 12, 0],\n [0, -2, -8, 8, 0],\n [0, -6, -24, 24, 0],\n [0, -3, -12, 12, 0],\n [0, 2, 8, -8, 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[[-12, -63, -12, 12, -9],\n [-59, -28, -3, 31, -53],\n [-11, -8, -9, 25, -17],\n [2, 29, -3, 17, -7],\n [55, -11, -3, -29, 52]]\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, -46, 40, -18, 15],\n [0, -24, 16, -8, 12],\n [-12, -18, 19, -8, 3],\n [-20, -50, 45, -20, 15],\n [24, 42, -42, 18, -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[[2, 2, 4, -3, 2],\n [4, 4, 8, -6, 4],\n [-6, -6, -12, 9, -6],\n [6, 6, 12, -9, 6],\n [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[[-54, 8, 41, -18, -38],\n [9, 0, -32, 3, -20],\n [33, -42, -30, 5, 21],\n [6, 16, 8, 6, 15],\n [48, -8, -40, 16, 30]]\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, 0, 42, 24, 3],\n [-15, -20, 8, 36, 17],\n [23, 32, -10, -56, -27],\n [-17, -8, 34, 32, 9],\n [-6, -14, -7, 18, 11]]\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, -12, 0, 12, 15],\n [-5, -20, 0, 20, 25],\n [4, 16, 0, -16, -20],\n [-2, -8, 0, 8, 10],\n [1, 4, 0, -4, -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[[0, 2, -5, 6, 6],\n [0, 4, -10, 12, 12],\n [0, 2, -5, 6, 6],\n [0, -8, 20, -24, -24],\n [0, 6, -15, 18, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[52, 1, -35, -16, -17],\n [-36, 5, 54, 33, 14],\n [-29, 44, 52, 27, 53],\n [-45, 4, 28, 12, 20],\n [39, 62, 23, 9, 49]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 8, 4, -24, -24],\n [-5, -10, -5, 30, 30],\n [-4, -8, -4, 24, 24],\n [0, 0, 0, 0, 0],\n [-6, -12, -6, 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[[-6, 6, -12, -8, 2],\n [15, -15, 30, 20, -5],\n [3, -3, 6, 4, -1],\n [-3, 3, -6, -4, 1],\n [-12, 12, -24, -16, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[16, 61, 4, 9, -5],\n [-24, 25, -20, -10, -8],\n [14, 36, 24, 14, -9],\n [38, 15, 10, 25, -5],\n [-28, -85, -20, -15, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, -14, 6, 36, -18],\n [4, 7, 3, -10, 4],\n [-18, -22, -18, 52, -30],\n [9, -4, 36, 16, -3],\n [8, 4, 24, 8, -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[[0, -5, 8, -2, -11],\n [12, -11, 16, -5, -12],\n [29, 41, -37, -38, 15],\n [-2, 10, -21, 8, 40],\n [-60, -39, 39, 27, -38]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[13, -24, -23, 2, -31],\n [7, -21, 7, 5, -7],\n [1, -1, -23, -26, -27],\n [16, -12, -64, -34, -60],\n [0, -14, -16, 0, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, 24, -20, -16, -12],\n [6, -18, 15, 12, 9],\n [2, -6, 5, 4, 3],\n [4, -12, 10, 8, 6],\n [-12, 36, -30, -24, -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[[64, -10, 12, 22, -41],\n [-15, -10, 7, -10, 23],\n [9, -16, 13, 32, 32],\n [3, -34, 27, 14, 51],\n [-38, 32, -28, 16, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[3, -6, -12, 12, -12],\n [-4, 8, 16, -16, 16],\n [-3, 6, 12, -12, 12],\n [-6, 12, 24, -24, 24],\n [4, -8, -16, 16, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[20, -24, 8, -12, 24],\n [25, -30, 10, -15, 30],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [15, -18, 6, -9, 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[[1, -48, -20, 28, 5],\n [-12, 33, 57, 13, 14],\n [16, 6, 27, -17, 15],\n [9, 57, -6, 14, -29],\n [9, 81, 20, 0, -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[[-21, 4, 0, -14, -21],\n [4, 0, -60, -9, -32],\n [-54, 42, -20, -41, -24],\n [5, 24, -92, -19, -19],\n [41, -28, 4, 32, 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[[28, -23, -43, 29, -19],\n [-6, 9, -59, 21, -23],\n [-13, 1, 57, -26, 30],\n [42, -40, 8, 10, 0],\n [-13, 24, 12, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-58, -46, -15, 7, 29],\n [1, 4, -39, 17, -2],\n [29, 24, 2, 27, -29],\n [-7, -4, -33, -2, 11],\n [35, 44, 2, -20, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 24, -16, 0, 0],\n [0, -18, -6, -12, 6],\n [0, 6, 2, 4, -2],\n [-12, -24, 28, 8, -4],\n [0, -15, -5, -10, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-23, -3, -3, 9, -12],\n [-4, 6, 26, 7, -6],\n [9, 3, -19, -23, 18],\n [12, 9, 18, -9, 9],\n [-8, 1, 18, 13, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[25, -19, 11, 25, -16],\n [18, -13, 8, 41, 1],\n [-8, 40, -2, 2, 19],\n [-27, 15, -3, 41, 49],\n [-18, -84, 23, 18, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-15, -3, 3, 18, 3],\n [-30, -6, 6, 36, 6],\n [-25, -5, 5, 30, 5],\n [-25, -5, 5, 30, 5],\n [25, 5, -5, -30, -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 5x5 matrix:\n[[3, 3, 4, -6, 6],\n [15, 15, 20, -30, 30],\n [3, 3, 4, -6, 6],\n [15, 15, 20, -30, 30],\n [18, 18, 24, -36, 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[[-5, -2, 2, -3, 0],\n [0, 0, 0, 0, 0],\n [-5, -2, 2, -3, 0],\n [10, 4, -4, 6, 0],\n [25, 10, -10, 15, 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 5x5 matrix:\n[[17, 53, 46, -49, -44],\n [28, 9, -2, -7, -9],\n [42, 0, 2, -79, -34],\n [3, 78, 58, 19, -35],\n [15, 60, 42, -6, -29]]\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[[-3, 12, 12, -9, 18],\n [-4, 16, 16, -12, 24],\n [-4, 16, 16, -12, 24],\n [-3, 12, 12, -9, 18],\n [5, -20, -20, 15, -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[[-30, -28, 20, 0, 18],\n [1, 9, -8, -11, -5],\n [-38, -34, 24, -2, 22],\n [25, 5, 0, 25, -5],\n [-30, -28, 20, 0, 18]]\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, -20, 6, -6, 6],\n [-18, 8, 40, 2, 0],\n [15, -24, 2, -8, -6],\n [-16, 21, -40, 9, 28],\n [-31, 21, -10, 9, 34]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-28, -6, -30, 24, -12],\n [-10, -30, 6, 29, 18],\n [-16, 3, -21, 9, -12],\n [28, -24, 48, -2, 36],\n [18, 36, 0, -39, -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 5x5 matrix:\n[[-8, 12, -27, -19, 38],\n [2, -1, 5, 3, -6],\n [18, 31, 10, -8, 16],\n [-10, 5, -25, -15, 30],\n [-4, -30, 18, 22, -44]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-23, -42, -17, -21, 27],\n [5, 6, -13, 39, 24],\n [3, 2, -19, 47, 36],\n [20, 60, 40, -15, -10],\n [23, 58, 33, 1, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-20, 8, 12, 4, -16],\n [-30, 12, 18, 6, -24],\n [5, -2, -3, -1, 4],\n [-10, 4, 6, 2, -8],\n [-10, 4, 6, 2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-42, 40, 44, -4, -54],\n [54, -86, -26, 4, 90],\n [18, 14, -26, 18, 4],\n [14, -37, 21, 60, 26],\n [35, -60, -10, 20, 59]]\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, 24, -18, -18, -12],\n [0, -4, 3, 3, 2],\n [0, 20, -15, -15, -10],\n [0, -24, 18, 18, 12],\n [0, 24, -18, -18, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, -15, 27, -9, 19],\n [4, 6, -18, 0, -52],\n [4, -20, 19, -18, -39],\n [-2, -29, 31, -23, -13],\n [-24, 10, -29, 8, 41]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-16, 15, -19, 6, 8],\n [21, -21, 24, -9, -9],\n [33, -27, 42, -9, -21],\n [19, -27, 16, -15, 1],\n [-20, 24, -20, 12, 4]]?\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[[-23, 19, -17, -26, 12],\n [25, -20, 20, 25, -10],\n [45, -39, 29, 60, -32],\n [7, -5, 7, 4, 0],\n [5, -1, 11, -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 5x5 matrix:\n[[34, 9, -28, 16, -12],\n [30, -30, -16, 28, 18],\n [32, 12, -67, -2, -26],\n [32, 21, -22, 15, -18],\n [11, 42, 3, -13, -31]]\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, 9, 12, 6, -3],\n [24, -12, -16, -8, 4],\n [-30, 15, 20, 10, -5],\n [-18, 9, 12, 6, -3],\n [-18, 9, 12, 6, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-24, -13, 16, 3, 1],\n [-13, -3, 4, -9, 9],\n [-36, 42, -16, -6, -20],\n [-21, 24, -12, -18, 3],\n [5, 24, -20, -18, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, 36, -30, -24, 24],\n [6, 18, -15, -12, 12],\n [8, 24, -20, -16, 16],\n [-4, -12, 10, 8, -8],\n [6, 18, -15, -12, 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[[-30, -34, 2, -50, -22],\n [-9, -12, 9, -1, 1],\n [-3, -3, -9, -2, -10],\n [18, 17, 8, 62, 22],\n [-27, -36, 21, 2, -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[[0, 3, -14, -60, 2],\n [-24, 41, -2, -30, -13],\n [-66, 35, 25, 18, -40],\n [-1, 4, 11, -10, -14],\n [11, 38, 2, -10, -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 5x5 matrix:\n[[16, -12, 40, 31, 30],\n [5, 1, 16, 8, 8],\n [21, 54, -9, -21, -6],\n [-33, -49, 0, 7, -10],\n [21, 32, 9, -2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-32, 7, 16, -4, -11],\n [-19, 29, -43, -15, 20],\n [18, -21, -27, -6, 10],\n [6, 36, -27, -6, 17],\n [-17, -5, -20, -57, -19]]\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, 36, 22, 18, 24],\n [-34, 48, 30, 26, 36],\n [-2, 24, 10, -2, -12],\n [1, 6, 2, -2, -6],\n [-18, 0, 6, 18, 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[[-9, -1, 50, 11, 28],\n [10, 3, -53, 6, -28],\n [-17, 10, -5, -4, 21],\n [-9, -2, 11, -36, 9],\n [8, -12, -8, 27, -29]]\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 5x5 matrix:\n[[6, -17, 12, 9, 0],\n [12, 1, 10, 11, -28],\n [-15, 10, -17, -16, 26],\n [-6, -18, 2, -2, 28],\n [12, -24, 20, 16, -8]]\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[[22, -18, 27, 58, -12],\n [22, 12, 16, 12, 20],\n [10, -15, 30, 49, -31],\n [2, 12, 22, 4, -16],\n [1, 6, -19, -22, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[26, -2, -7, 22, -15],\n [-32, -4, 0, -12, 12],\n [0, 12, 16, -28, 12],\n [26, -2, -7, 22, -15],\n [36, 0, -6, 24, -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 5x5 matrix:\n[[12, -6, 24, -36, -6],\n [0, 0, 0, 0, 0],\n [-4, 2, -8, 12, 2],\n [10, -5, 20, -30, -5],\n [2, -1, 4, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, 6, -3, -23, 21],\n [-5, -15, 10, 25, 5],\n [-39, -19, -22, -6, -18],\n [61, 50, 30, -4, 3],\n [-4, 19, 11, -20, 25]]\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[[-2, 6, 6, -2, -2],\n [-3, 9, 9, -3, -3],\n [2, -6, -6, 2, 2],\n [4, -12, -12, 4, 4],\n [-5, 15, 15, -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[[45, 10, -39, 0, 9],\n [-16, -4, 22, -18, 3],\n [15, -10, -17, -4, -19],\n [9, -28, -44, 17, -34],\n [15, -34, -61, 32, -49]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-10, 2, -12, -2, 0],\n [-15, -21, 26, -3, 24],\n [-10, -22, 32, -2, 24],\n [10, -2, 12, 2, 0],\n [-30, 6, -36, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-50, -22, -23, 33, 36],\n [9, 10, 35, -42, -24],\n [-25, -35, -19, 50, 36],\n [31, 47, -44, -1, -24],\n [-18, 2, 7, -14, 6]]\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 5x5 matrix:\n[[-6, -3, -23, -6, -17],\n [-12, -12, 10, 24, 6],\n [34, 3, 17, -4, -34],\n [-14, 6, -23, -16, 13],\n [40, 9, 24, -10, -26]]\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, -3, 21, -11, 14],\n [10, -9, 33, -13, 17],\n [-4, 12, 12, -20, 24],\n [6, -15, -9, 21, -25],\n [-12, 15, -27, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, -12, 30, 24, 30],\n [-3, -6, 15, 12, 15],\n [-1, -2, 5, 4, 5],\n [4, 8, -20, -16, -20],\n [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[[-4, 5, -6, 1, -2],\n [-8, 10, -12, 2, -4],\n [20, -25, 30, -5, 10],\n [0, 0, 0, 0, 0],\n [-24, 30, -36, 6, -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[[-41, -27, 29, -18, 9],\n [78, 17, -8, -11, 6],\n [-10, -15, 25, 0, 18],\n [-30, -14, 4, -30, -9],\n [20, 22, -14, 52, 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[[-50, 20, 20, -20, -44],\n [35, -13, -14, 12, 31],\n [15, -12, -6, 18, 12],\n [-45, 11, 18, -4, -41],\n [5, 11, -2, -24, 7]]\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, -65, -20, -42, 25],\n [-31, -26, -16, -25, 1],\n [14, 13, 8, 10, 2],\n [-9, -18, 12, 5, 28],\n [34, 30, 20, 26, 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[[30, -5, -30, -25, -30],\n [30, -8, 0, -28, -12],\n [15, 0, -40, -10, -30],\n [-3, 2, -12, 4, -6],\n [18, -5, 2, -17, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-14, 34, -34, 0, -10],\n [14, 46, -6, -35, -15],\n [32, 48, 0, -38, -34],\n [-15, -20, 2, 13, 19],\n [6, 43, -17, -22, -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 5x5 matrix:\n[[0, 9, 15, 10, 16],\n [-26, -3, 9, -3, -15],\n [-37, -15, 16, -8, -35],\n [23, 3, -20, 24, 12],\n [-9, 9, 36, 39, 18]]\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, -50, -20, 36, 20],\n [-11, 12, 34, -16, -2],\n [-38, 2, 56, -37, -10],\n [6, -1, -2, 23, 4],\n [19, 9, -2, -5, 28]]?\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[[-37, 5, -39, 17, 32],\n [-28, -13, -2, -16, -4],\n [8, 6, 40, -12, -17],\n [-63, 37, -31, 37, 55],\n [27, -29, 13, -23, -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[[9, 36, -32, 4, 11],\n [-8, -12, 16, -12, -16],\n [-24, -36, 32, 16, 4],\n [-6, -30, 24, 9, -7],\n [15, 3, -4, -20, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-21, -5, 10, -2, 13],\n [54, -7, -1, 17, -45],\n [3, 4, -5, -11, 8],\n [-59, 6, 3, -15, 46],\n [32, 16, -26, 4, -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[[-8, 0, -4, -16, -8],\n [-10, 0, -5, -20, -10],\n [2, 0, 1, 4, 2],\n [-10, 0, -5, -20, -10],\n [6, 0, 3, 12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 20, 15, 15, -30],\n [0, 4, 3, 3, -6],\n [0, -4, -3, -3, 6],\n [0, 24, 18, 18, -36],\n [0, 20, 15, 15, -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[[-20, 8, 15, 51, -33],\n [17, 3, 25, 45, -16],\n [-8, 24, 32, 23, -21],\n [-28, 28, 36, 53, -43],\n [-24, -8, -28, -23, 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[[-5, 30, 0, 10, -10],\n [3, -18, 0, -6, 6],\n [4, -24, 0, -8, 8],\n [-6, 36, 0, 12, -12],\n [2, -12, 0, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -18, 3, 0, 9],\n [-10, 30, -5, 0, -15],\n [10, -30, 5, 0, 15],\n [-8, 24, -4, 0, -12],\n [-10, 30, -5, 0, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[48, -18, -11, -18, -39],\n [-25, 39, 7, -5, 21],\n [-19, 13, 6, 3, 15],\n [46, -24, 20, -2, -53],\n [14, -35, -12, 2, -8]]\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, 7, -10, -21, 13],\n [6, -3, -6, 9, -9],\n [-24, -6, 24, 18, -6],\n [-24, -15, 24, 45, -27],\n [-12, 3, 12, -9, 11]]?\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[[11, -4, 18, -45, 3],\n [11, -14, 8, -10, -12],\n [0, 29, -15, -32, 26],\n [16, -8, -24, 18, -18],\n [0, -46, 42, 22, -34]]\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 5x5 matrix:\n[[-10, -38, 11, 18, 19],\n [12, 27, -7, -3, -29],\n [10, 32, -9, -12, -21],\n [6, 15, -4, -3, -14],\n [0, 6, -2, -6, 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[[9, -7, -29, 45, 29],\n [-27, -4, 31, -18, 14],\n [15, 7, -13, 6, -5],\n [-90, -42, 78, -36, 30],\n [54, 34, -34, 0, -30]]?\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[[-17, 4, 24, 6, 14],\n [18, -17, -21, -2, -15],\n [-6, -33, -24, 8, -18],\n [-26, 42, 39, 3, 42],\n [57, -10, 9, -9, 0]]\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, 0, -20, -24, 12],\n [6, 0, -5, -6, 3],\n [30, 0, -25, -30, 15],\n [24, 0, -20, -24, 12],\n [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[[-25, 20, 5, 0, -25],\n [25, -20, -5, 0, 25],\n [-15, 12, 3, 0, -15],\n [-25, 20, 5, 0, -25],\n [10, -8, -2, 0, 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[[6, -12, 2, -22, 16],\n [5, -9, 4, -16, 11],\n [9, -15, 10, -26, 17],\n [-2, -3, -17, -9, 11],\n [0, -6, -14, -14, 14]]\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[[30, -6, 36, 6, -6],\n [20, -4, 24, 4, -4],\n [10, -2, 12, 2, -2],\n [-30, 6, -36, -6, 6],\n [-15, 3, -18, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-24, -18, -12, -30, 12],\n [0, 0, 0, 0, 0],\n [-24, -18, -12, -30, 12],\n [20, 15, 10, 25, -10],\n [16, 12, 8, 20, -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[[16, 14, 18, -34, 32],\n [-20, -10, -30, 55, -55],\n [-8, 2, -18, 32, -34],\n [24, 42, 6, -16, 6],\n [-12, -15, -9, 18, -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 5x5 matrix:\n[[-44, -16, -23, -15, 8],\n [-12, 16, 14, -20, -4],\n [-26, -58, 1, -9, 35],\n [-16, -40, 1, -5, 24],\n [-28, 12, 6, -26, -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[[36, 18, 30, 42, -24],\n [-20, 30, -6, 28, 18],\n [8, 12, 36, 8, -12],\n [13, 12, 48, 7, -18],\n [13, -19, -9, -12, -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[[21, 6, 10, 3, -14],\n [-54, -20, -10, 2, 30],\n [-37, -10, 9, 4, 19],\n [-19, 2, -6, -8, 16],\n [-33, 38, -44, -56, 54]]?\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, 0, 27, 12, 9],\n [20, -7, -19, -31, 17],\n [-28, 1, 31, 17, 7],\n [8, 2, -10, 2, -10],\n [-24, -6, 30, -6, 30]]\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 5x5 matrix:\n[[20, -2, 15, -23, 2],\n [-36, 32, 8, 16, 0],\n [-8, 14, 15, -3, 14],\n [-3, -8, -5, -1, 12],\n [32, -24, -11, 3, -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[[-50, -31, 41, -18, -34],\n [14, -2, 0, 16, -4],\n [52, 36, -60, 29, 39],\n [13, 17, -50, 39, 13],\n [10, 1, -51, 53, -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[[-6, 0, 2, -12, 6],\n [-3, 16, 1, -50, 15],\n [3, 24, -1, -60, 15],\n [-36, -40, 0, -5, 9],\n [-3, -26, -5, 44, -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[[8, -24, 6, -12, -12],\n [24, -37, -3, -29, -15],\n [4, 18, -15, 0, 12],\n [-20, -15, 30, 15, -15],\n [-20, 35, 0, 25, 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 5x5 matrix:\n[[-56, 35, 35, 12, -31],\n [14, 54, 22, -48, -10],\n [-21, -27, 4, -5, -73],\n [74, -29, -31, -11, 50],\n [8, -6, -22, -29, -9]]\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 5x5 matrix:\n[[3, 39, -3, -3, 42],\n [1, -1, -5, 1, -4],\n [4, 10, -16, 2, 2],\n [-2, -19, 4, 1, -19],\n [2, -16, -14, 4, -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[[-6, -10, -3, -4, -39],\n [-12, 6, 12, 4, 16],\n [16, -18, 27, -21, 12],\n [6, -10, 27, -13, -18],\n [-12, 5, -24, 11, -15]]\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, -6, -12, -12, 15],\n [24, -12, -24, -24, 30],\n [-8, 4, 8, 8, -10],\n [12, -6, -12, -12, 15],\n [-12, 6, 12, 12, -15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-6, 2, 0, 4, -2],\n [9, -3, 0, -6, 3],\n [3, -1, 0, -2, 1],\n [9, -3, 0, -6, 3],\n [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[[-44, 48, 3, 18, 64],\n [31, -32, 11, 36, -46],\n [-8, 14, -18, -48, 22],\n [7, -7, -23, 2, -28],\n [-30, 39, 3, -12, 63]]\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[[-13, -20, 30, 45, -9],\n [25, 20, -38, -55, 7],\n [32, -23, -40, -11, 23],\n [-8, -34, 0, 42, 22],\n [22, 2, 12, -6, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-14, 36, 44, -2, -2],\n [4, 0, -10, -2, -2],\n [2, -12, -8, 2, 2],\n [2, 36, 4, -10, -10],\n [3, -6, -9, 0, 0]]?\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[[16, 6, -6, -16, -2],\n [5, -20, 20, -5, 23],\n [-5, -30, 30, 5, 31],\n [-2, -7, 7, 2, 7],\n [-18, -13, 13, 18, 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[[9, -12, 12, 9, 9],\n [12, -16, 16, 12, 12],\n [18, -24, 24, 18, 18],\n [18, -24, 24, 18, 18],\n [6, -8, 8, 6, 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[[-6, -4, 3, 1, 5],\n [18, 12, -9, -3, -15],\n [-6, -4, 3, 1, 5],\n [18, 12, -9, -3, -15],\n [-12, -8, 6, 2, 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[[5, 15, 10, 25, 20],\n [-2, -6, -4, -10, -8],\n [-3, -9, -6, -15, -12],\n [-3, -9, -6, -15, -12],\n [3, 9, 6, 15, 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[[-31, 15, 17, -32, -2],\n [-15, -4, 3, -9, 1],\n [-18, -66, -2, 40, 28],\n [-12, 41, 27, -27, -5],\n [16, 12, -1, 6, -4]]\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, -36, -15, 34, 28],\n [-5, 6, 14, 2, 3],\n [-12, -24, -8, 24, 20],\n [-10, 0, 15, 10, 10],\n [16, 36, 15, -34, -28]]\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, 0, 0, 0, 0],\n [30, -15, -25, 30, 15],\n [18, -9, -15, 18, 9],\n [-36, 18, 30, -36, -18],\n [24, -12, -20, 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[[-8, -12, -52, 4, 14],\n [-32, 34, 10, 8, 28],\n [52, -39, 29, -11, -49],\n [36, -43, -31, -21, -37],\n [-12, 17, 13, -1, 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[[36, -28, 29, 3, -29],\n [-17, 25, -14, 10, -5],\n [19, 7, 15, 25, -82],\n [23, -40, 36, -16, 27],\n [-26, 20, -22, -2, 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[[5, 10, 4, 9, -6],\n [-8, -13, -6, -13, 6],\n [-11, -16, -8, -17, 6],\n [11, 16, 8, 17, -6],\n [11, -14, 4, 3, 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[[0, 0, 0, 0, 0],\n [9, -20, 3, 33, 33],\n [5, -4, -1, 9, 13],\n [3, -12, 3, 18, 15],\n [-18, -8, 12, -3, -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[[-16, -8, 8, 4, -8],\n [36, 28, -32, -10, 28],\n [-10, 0, -2, 2, 0],\n [14, 22, -28, -5, 22],\n [-17, -16, 19, 5, -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 5x5 matrix:\n[[25, -15, -15, 15, 30],\n [20, -12, -12, 12, 24],\n [5, -3, -3, 3, 6],\n [-5, 3, 3, -3, -6],\n [15, -9, -9, 9, 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[[1, 3, -4, -6, 3],\n [-1, -3, 4, 6, -3],\n [-3, -9, 12, 18, -9],\n [-1, -3, 4, 6, -3],\n [-2, -6, 8, 12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-19, -3, -9, -6, -6],\n [-26, -7, -27, 10, -13],\n [-45, -31, -52, 44, 1],\n [-6, -2, -9, 18, -11],\n [16, 17, 11, -19, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[32, -20, -21, -20, 0],\n [40, 0, -45, -40, -20],\n [2, 25, -21, -17, -21],\n [-6, -35, 33, 27, 31],\n [-6, 45, -27, -21, -33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -28, 17, -15, 22],\n [0, 26, -7, 15, -9],\n [-18, 22, -6, -10, 16],\n [15, -9, 8, -10, 11],\n [-12, -19, 4, 5, -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 5x5 matrix:\n[[-8, 12, 4, -8, 10],\n [16, -24, -8, 16, -20],\n [-24, 36, 12, -24, 30],\n [-8, 12, 4, -8, 10],\n [-8, 12, 4, -8, 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[[6, -25, -11, -15, -9],\n [2, -25, -7, -15, -13],\n [-2, -15, -1, -9, -11],\n [2, 20, 2, 12, 14],\n [6, -10, -8, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[30, -3, 12, -9, 0],\n [-14, -13, -14, 9, 12],\n [26, -17, 2, -3, 12],\n [56, -8, 21, -16, 2],\n [-12, 6, -2, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, -28, -4, 4, -12],\n [10, 20, -2, 0, 5],\n [-8, 1, -29, 17, -21],\n [-14, -17, -17, 11, -18],\n [-2, 4, -14, 8, -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[[-12, 0, -10, 2, -10],\n [-24, 0, -20, 4, -20],\n [30, 0, 25, -5, 25],\n [-18, 0, -15, 3, -15],\n [-36, 0, -30, 6, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 12, -15, -6, 3],\n [-2, -4, 5, 2, -1],\n [-4, -8, 10, 4, -2],\n [-12, -24, 30, 12, -6],\n [6, 12, -15, -6, 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[[-56, -41, 34, 30, -11],\n [-26, -13, 1, -20, 49],\n [-24, -14, 31, 20, -4],\n [24, 25, -10, -30, 43],\n [-41, -27, -1, -15, 42]]\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, -18, 22, -12, 0],\n [0, 0, -14, 24, 18],\n [-32, -16, -10, 40, 38],\n [-10, -5, -11, 26, 22],\n [48, 24, -20, 0, -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[[8, -12, -6, -6, -8],\n [4, -6, -3, -3, -4],\n [-24, 36, 18, 18, 24],\n [20, -30, -15, -15, -20],\n [-20, 30, 15, 15, 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[[0, 0, 0, 0, 0],\n [-4, -4, 16, -20, -20],\n [6, 6, -24, 30, 30],\n [1, 1, -4, 5, 5],\n [6, 6, -24, 30, 30]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -2, -5, 5, 5],\n [30, 10, 25, -25, -25],\n [18, 6, 15, -15, -15],\n [-36, -12, -30, 30, 30],\n [-6, -2, -5, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[35, -5, -5, 6, -5],\n [-20, 0, 10, 8, 0],\n [40, 4, -30, -32, 4],\n [30, 0, -15, -12, 0],\n [-20, -8, 30, 40, -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[[53, -18, -50, 1, -56],\n [-10, -9, 10, -5, -38],\n [-36, 18, 30, 6, 54],\n [35, -3, -50, 24, -32],\n [-19, 6, 25, -9, 31]]\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, -20, 20, 0, -15],\n [-30, 20, -20, 0, 15],\n [-36, 24, -24, 0, 18],\n [30, -20, 20, 0, -15],\n [12, -8, 8, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 24, 16, 0, 20],\n [-2, -36, -20, 16, -18],\n [-1, -18, -10, 8, -9],\n [-9, -36, -27, -12, -39],\n [-2, 18, 7, -20, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-47, -18, 15, 6, 5],\n [-20, 41, 17, -4, -50],\n [20, 50, -10, 4, -48],\n [25, 62, -1, -6, -59],\n [43, 24, -21, 2, -13]]?\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[[-3, 0, -18, 18, -18],\n [-39, 30, 12, 6, -24],\n [-30, 20, -16, 28, -40],\n [-19, 15, 9, 0, -9],\n [-18, 10, -26, 32, -38]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-21, 18, 21, 18, 0],\n [-27, 14, 15, 10, 0],\n [-2, 20, 26, 28, 0],\n [33, 6, 12, 21, 0],\n [12, 8, 12, 16, 0]]\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, 7, 45, -7, 4],\n [18, -12, -27, 0, 3],\n [-12, 18, -14, -42, -48],\n [-2, -16, 14, -10, 15],\n [4, -1, 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[[31, -51, 9, 44, -7],\n [2, 47, -24, -40, -20],\n [2, 48, -31, -48, -13],\n [13, 11, -18, -60, 8],\n [-32, 14, 1, -14, 29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-10, 5, 35, -5, -50],\n [22, 7, -3, 21, -14],\n [12, 13, 15, 17, -40],\n [-33, -5, 6, -28, 14],\n [59, -13, -12, 36, -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[[-45, 25, -20, 50, 15],\n [30, -16, 15, -35, -11],\n [-18, 14, 2, 10, 0],\n [-15, 15, 10, 0, -5],\n [12, -4, 12, -20, -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[[-28, 22, 72, 30, -55],\n [32, -6, 28, -24, 40],\n [0, 17, 70, 0, -10],\n [-20, 36, -4, -24, 0],\n [-10, 12, 10, 0, -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[[0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [6, -6, -6, 4, -2],\n [12, -12, -12, 8, -4],\n [-12, 12, 12, -8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[29, 21, -4, 21, -19],\n [-6, 14, -4, -42, 30],\n [-7, 10, -3, -36, 26],\n [19, 19, -4, 3, -5],\n [33, 37, -8, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-32, 39, 5, 27, 0],\n [-3, -1, 23, 4, -21],\n [11, -33, 3, 2, 11],\n [-42, 60, -2, 10, -14],\n [-35, 51, -1, 8, -13]]?\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, 5, 4, 21, 17],\n [6, 8, 6, 30, 24],\n [-48, 23, 10, 21, 11],\n [12, 4, 4, 24, 20],\n [-24, 10, 4, 6, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[49, 32, -18, -21, -52],\n [1, 22, -4, -3, 14],\n [-13, -17, 15, 20, -15],\n [41, 23, 10, -21, -35],\n [-64, -25, -2, 48, 35]]\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[[-5, -7, -8, 2, 18],\n [24, 39, -21, -28, -4],\n [-13, -21, 10, 34, -20],\n [18, 31, -35, -16, 10],\n [7, 15, -46, -6, 36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[10, 6, -56, 6, 36],\n [0, 0, 0, 0, 0],\n [0, -2, 11, 0, -7],\n [-25, 13, -14, -15, 8],\n [-60, 24, 6, -36, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -30, 3, -3, 42],\n [-4, 12, 0, 4, -16],\n [6, -18, 0, -6, 24],\n [12, -36, 0, -12, 48],\n [12, 8, -11, -23, -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 5x5 matrix:\n[[-55, -39, -22, -16, 4],\n [-16, -21, -51, 5, 8],\n [-45, 12, 0, 8, 30],\n [-6, -48, -14, -18, -36],\n [-73, -36, -34, -12, 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[[6, -18, 24, 6, -6],\n [3, -9, 12, 3, -3],\n [-1, 3, -4, -1, 1],\n [-6, 18, -24, -6, 6],\n [3, -9, 12, 3, -3]]\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[[20, 16, 0, 4, -16],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [20, 16, 0, 4, -16],\n [-30, -24, 0, -6, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[22, -8, -12, -14, -30],\n [-33, 40, 43, 11, 12],\n [24, -10, 0, -10, -6],\n [1, 12, 11, 3, 4],\n [25, 16, 7, -21, -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 5x5 matrix:\n[[21, 42, 15, 35, -30],\n [-5, -6, 32, -7, -4],\n [25, 22, -17, 31, -32],\n [37, -12, -7, 56, 36],\n [-6, 36, 3, -3, -23]]\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, 7, -8, 5, 10],\n [-30, 15, 10, -15, 10],\n [36, -26, 8, 2, -28],\n [-30, 15, 10, -15, 10],\n [-36, 24, -3, -6, 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 5x5 matrix:\n[[-36, 33, 40, -7, 16],\n [23, -28, -33, 19, 10],\n [9, 0, 0, -4, 4],\n [-21, 42, 51, -19, 34],\n [18, -3, -5, -20, -34]]\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 5x5 matrix:\n[[33, 56, -15, -19, -30],\n [-34, -42, 13, -10, -7],\n [-69, -26, 6, -17, -9],\n [41, 4, 1, 3, -4],\n [46, 56, -13, -31, -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[[13, 12, -8, 33, 0],\n [58, 18, -2, 15, -12],\n [6, -10, 10, -11, 12],\n [-14, -40, 30, -6, 62],\n [-73, -12, -7, 3, 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 5x5 matrix:\n[[-14, 8, -4, -15, 22],\n [-16, 12, 4, -5, 8],\n [24, -24, -24, -18, 24],\n [4, 0, 8, 14, -20],\n [-19, 18, 16, 10, -13]]\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 5x5 matrix:\n[[17, -41, -27, 12, -37],\n [-26, -6, 2, 16, -30],\n [-10, 46, 51, -38, 34],\n [0, 5, -35, 31, 32],\n [-6, 33, 6, -1, 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[[24, 0, 0, 18, -12],\n [0, 0, 0, 0, 0],\n [24, 0, 0, 18, -12],\n [-8, 0, 0, -6, 4],\n [8, 0, 0, 6, -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[[-12, 3, -8, -14, 0],\n [-12, 15, 6, -39, -3],\n [-16, 8, -4, 14, -22],\n [-50, 19, -22, 5, -41],\n [16, 5, 20, -24, 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 5x5 matrix:\n[[-31, 11, -19, -31, -11],\n [-22, -15, 21, 19, -34],\n [-14, -35, 7, -17, -50],\n [-37, -3, -18, -47, -29],\n [17, -7, 8, -20, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[21, 12, -3, -7, -10],\n [-6, -8, 10, 17, -10],\n [-25, -20, 15, 15, 20],\n [15, 8, -1, 0, -15],\n [-5, -8, 11, 10, 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[[3, 6, 18, 18, 15],\n [23, -18, -30, 14, 11],\n [-17, 17, 39, 8, 3],\n [42, -11, -33, 12, 30],\n [-20, 18, 18, -30, -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 5x5 matrix:\n[[-38, -3, -10, 22, 13],\n [-17, 50, 46, -49, 11],\n [-11, -27, -31, 13, 34],\n [-29, 4, -5, 7, 5],\n [30, 10, 16, -16, -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[[10, 9, 25, 22, -9],\n [-12, 10, 10, -4, 6],\n [44, -15, 5, 38, -27],\n [0, 0, 0, 0, 0],\n [2, -6, -10, -4, 0]]\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[[-22, 27, 44, 1, -23],\n [20, -28, -16, -16, 10],\n [40, -25, -12, -13, 23],\n [48, -16, -19, 12, 31],\n [0, -7, -41, 53, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, -37, 7, -5, -29],\n [24, 48, 67, 58, 27],\n [-25, -54, -25, -29, 5],\n [38, 77, 54, 54, 19],\n [18, 6, -7, -8, 29]]?\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[[18, -3, 0, -9, 15],\n [12, -2, 0, -6, 10],\n [12, -2, 0, -6, 10],\n [36, -6, 0, -18, 30],\n [18, -3, 0, -9, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-14, 19, -26, -34, 20],\n [32, 2, 41, -2, -5],\n [-19, 2, -25, -2, 10],\n [10, 1, 13, 0, 1],\n [1, -21, 8, 30, -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 5x5 matrix:\n[[30, -6, -12, 0, 0],\n [5, -1, -2, 0, 0],\n [-30, 6, 12, 0, 0],\n [10, -2, -4, 0, 0],\n [-10, 2, 4, 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[[76, 7, 50, 5, 5],\n [-38, -21, 22, -6, -4],\n [58, 4, 42, 1, 3],\n [55, -24, 51, 37, 40],\n [-3, 0, -27, 3, 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[[-12, -16, 8, -24, -20],\n [-4, -23, -26, -22, -12],\n [4, -17, -34, -8, -3],\n [16, 6, -12, 28, 8],\n [4, 9, 18, 16, -1]]\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[[-5, -5, 0, -4, 6],\n [-5, -5, 0, -4, 6],\n [0, 0, 0, 0, 0],\n [25, 25, 0, 20, -30],\n [-5, -5, 0, -4, 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, 15, -5, -15, -5],\n [0, 0, 0, 0, 0],\n [6, -3, 1, 3, 1],\n [-24, 12, -4, -12, -4],\n [-24, 12, -4, -12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[56, 14, 29, -27, -15],\n [29, 5, 11, -22, -12],\n [37, 31, 51, 1, -23],\n [7, -13, -17, -22, 12],\n [-6, -32, -49, -53, 7]]?\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, -18, -18, -12, 24],\n [-6, 3, 3, 2, -4],\n [-30, 15, 15, 10, -20],\n [-30, 15, 15, 10, -20],\n [-36, 18, 18, 12, -24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[13, 11, -3, 16, 21],\n [-19, -2, -12, -17, 13],\n [34, 12, 9, 38, 3],\n [-14, -21, 9, -7, -54],\n [-26, -9, -14, -39, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -4, -4, 4, -12],\n [-12, -12, 6, -14, -12],\n [28, 16, 4, 28, -28],\n [-32, -29, -32, -12, 11],\n [-4, -5, -20, 8, 7]]\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 5x5 matrix:\n[[-6, -50, -14, -42, 20],\n [-5, -35, -11, -30, 14],\n [-9, 5, -13, -3, -2],\n [14, 10, 22, 18, -4],\n [6, 10, 10, 12, -4]]\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[[-52, 46, 16, -32, 34],\n [-28, 22, 33, -18, 14],\n [-8, 14, -35, -16, 24],\n [12, -11, -46, 13, -20],\n [16, -15, 31, 13, -6]]\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, -4, -10, 0, 4],\n [3, -11, -8, 0, 5],\n [14, 26, 0, 0, -6],\n [-15, -3, 12, 0, -3],\n [-35, 22, 42, 0, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0, 0],\n [8, 12, 8, 12, 12],\n [8, 12, 8, 12, 12],\n [-2, -3, -2, -3, -3],\n [2, 3, 2, 3, 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[[41, 25, -49, -23, 22],\n [16, 24, -8, 0, 8],\n [-13, -15, 17, 21, -16],\n [-2, -12, -5, -3, -2],\n [37, 19, -47, -23, 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[[-32, -23, 36, -5, 30],\n [7, 22, -1, 19, 2],\n [20, 8, -42, -2, -45],\n [37, 35, -39, 16, -30],\n [7, 28, 15, 27, 27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[14, 4, -15, 2, 25],\n [-10, -6, 6, -14, -21],\n [-6, 2, 12, 14, -7],\n [-20, -10, 15, -20, -40],\n [-8, 2, 15, 16, -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 5x5 matrix:\n[[10, 25, 5, 30, -30],\n [8, 20, 4, 24, -24],\n [12, 30, 6, 36, -36],\n [-12, -30, -6, -36, 36],\n [6, 15, 3, 18, -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[[9, -25, 40, -30, 5],\n [-7, -42, -1, 15, -35],\n [29, 47, 10, -26, 34],\n [26, -7, 13, -11, -11],\n [-33, 13, -56, 50, -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[[-5, -7, -2, -3, 2],\n [41, -5, 34, -34, 3],\n [22, -35, 18, -39, 3],\n [36, -26, 28, -42, 2],\n [18, -39, 18, -42, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[9, -15, -12, 3, -3],\n [-15, 25, 20, -5, 5],\n [18, -30, -24, 6, -6],\n [9, -15, -12, 3, -3],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-10, -15, -25, -5, -5],\n [-4, -6, -10, -2, -2],\n [6, 9, 15, 3, 3],\n [-6, -9, -15, -3, -3],\n [8, 12, 20, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, -9, 12, 6, 12],\n [-20, -15, 20, 10, 20],\n [24, 18, -24, -12, -24],\n [20, 15, -20, -10, -20],\n [4, 3, -4, -2, -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[[29, 9, 3, -35, -1],\n [-16, -8, 2, 22, -20],\n [-10, -26, 2, 46, -22],\n [-48, 4, -13, 33, 50],\n [-12, 2, -2, 6, 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[[-18, -18, -18, -36, -36],\n [-3, -3, -3, -6, -6],\n [-18, -18, -18, -36, -36],\n [9, 9, 9, 18, 18],\n [6, 6, 6, 12, 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[[-15, -37, 12, 32, 32],\n [9, 11, -24, -8, -8],\n [15, 41, -6, -36, -36],\n [-18, -6, 72, 0, 0],\n [6, 14, -6, -12, -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[[-4, -10, -10, 4, 12],\n [-4, -10, -10, 4, 12],\n [2, 5, 5, -2, -6],\n [-2, -5, -5, 2, 6],\n [-2, -5, -5, 2, 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[[19, -22, -5, -16, 15],\n [-50, 56, 16, 26, -21],\n [23, -26, -7, -14, 12],\n [24, -24, -12, 12, -18],\n [6, -8, 0, -14, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-60, 36, 30, -36, 45],\n [34, 2, 11, 21, -1],\n [-56, 16, 16, -58, 33],\n [6, -29, -24, 4, 37],\n [-12, 37, 29, 7, -18]]?\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, -60, 12, 36, -12],\n [-26, 40, 18, -31, 32],\n [8, -12, -8, 10, -12],\n [24, -36, -24, 30, -36],\n [-16, 26, 0, -17, 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, 6, 43, 8, 2],\n [-16, -5, 18, -24, -5],\n [-30, 14, 16, 32, 8],\n [-4, -20, -63, -4, -14],\n [-2, 18, -20, 32, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 18, -3, -18, 9],\n [0, -30, 5, 30, -15],\n [0, -12, 2, 12, -6],\n [0, -24, 4, 24, -12],\n [0, -36, 6, 36, -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[[16, 8, 16, -24, -20],\n [32, 7, 23, -21, -40],\n [20, 13, 23, -39, -25],\n [0, 0, 0, 0, 0],\n [24, -6, 6, 18, -30]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[18, 27, 33, 30, -24],\n [-38, -6, -36, -26, -6],\n [-50, 2, -24, -4, -22],\n [8, -13, 15, 18, 14],\n [-36, -14, -42, -34, 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[[4, 25, 22, 15, 18],\n [40, 20, -10, 12, 42],\n [44, 30, -3, 18, 51],\n [-12, -10, -1, -6, -15],\n [20, 15, 0, 9, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[40, 14, 4, 42, 3],\n [4, -30, 16, 17, 9],\n [28, 30, -8, 20, -3],\n [-6, 56, 2, 18, -37],\n [-20, -34, 16, -3, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-10, 15, 8, 29, -11],\n [-45, 45, -6, 3, 12],\n [-6, -15, -12, -57, 27],\n [54, 0, -39, -21, 6],\n [-60, -10, 48, 18, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[30, 18, -36, 36, 6],\n [-5, -3, 6, -6, -1],\n [10, 6, -12, 12, 2],\n [25, 15, -30, 30, 5],\n [15, 9, -18, 18, 3]]?\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],\n [0, -9, 18, 6, -9],\n [0, 12, -24, -8, 12],\n [0, 15, -30, -10, 15],\n [0, 9, -18, -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[[-46, -21, 19, -14, -14],\n [-13, 12, 0, 15, 39],\n [-2, 7, 41, -3, 47],\n [45, 5, -1, -4, -22],\n [-35, -23, 55, -26, -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[[2, 2, 6, 0, 0],\n [0, 0, 0, 0, 0],\n [-8, -8, -24, 0, 0],\n [-2, -2, -6, 0, 0],\n [-4, -4, -12, 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[[-11, -7, -5, 10, 15],\n [-15, 45, -5, -30, -5],\n [-6, 18, -2, -12, -2],\n [14, -2, 6, -4, -14],\n [1, 17, 1, -14, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-23, 24, -10, 35, -14],\n [0, -70, 35, 35, 65],\n [-11, -40, 23, 29, 41],\n [-25, 17, -7, 20, -10],\n [0, 24, -28, 6, -32]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[16, 48, -36, 79, -43],\n [-28, 12, -72, 53, -1],\n [-8, 46, -39, 53, -35],\n [-10, -34, -12, -35, 47],\n [20, -16, 24, -35, 25]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[20, -30, 0, 15, 15],\n [0, 0, 0, 0, 0],\n [-20, 30, 0, -15, -15],\n [-16, 24, 0, -12, -12],\n [-20, 30, 0, -15, -15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[9, -22, 7, -10, 25],\n [12, -22, 16, -31, 11],\n [12, -8, 8, -6, 34],\n [-18, 64, -22, 46, -28],\n [12, 15, 9, -5, 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[[12, 24, 18, -12, 36],\n [0, 0, 0, 0, 0],\n [-6, -12, -9, 6, -18],\n [-10, -20, -15, 10, -30],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-18, 12, -9, -12, 12],\n [-12, 8, -6, -8, 8],\n [-36, 24, -18, -24, 24],\n [-30, 20, -15, -20, 20],\n [36, -24, 18, 24, -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 5x5 matrix:\n[[32, -41, 19, -14, 13],\n [-12, -30, 30, -36, 24],\n [-20, 5, 5, -10, 5],\n [-30, 24, -6, 0, -3],\n [8, -24, 16, -16, 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[[6, 18, 18, -51, 9],\n [-26, 2, -30, -11, 17],\n [20, 0, 24, 4, -12],\n [-15, -10, -24, 26, 2],\n [-5, 0, -6, -1, 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[[-21, -58, -3, 28, 16],\n [33, 11, 22, -7, 2],\n [15, -3, -42, 15, 45],\n [15, 36, -1, -10, -12],\n [18, -27, -15, 93, -27]]\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 5x5 matrix:\n[[12, 0, 12, 6, -8],\n [12, 0, 12, 6, -8],\n [36, 0, 36, 18, -24],\n [6, 0, 6, 3, -4],\n [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[[2, -6, 1, 3, 0],\n [-2, 6, -1, -3, 0],\n [0, 0, 0, 0, 0],\n [4, -12, 2, 6, 0],\n [8, -24, 4, 12, 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 5x5 matrix:\n[[-18, -19, -10, 24, -26],\n [-2, 5, 38, -8, 22],\n [6, 15, 51, -21, 39],\n [16, 16, 4, -20, 20],\n [-8, -10, -13, 13, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-30, 5, 27, -33, 42],\n [-15, 15, -3, -3, 12],\n [-17, -3, 23, -25, 28],\n [-20, 20, -4, -4, 16],\n [18, -38, 30, -18, 0]]?\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[[-19, 19, 0, 41, 34],\n [-19, 32, 2, 25, 56],\n [20, -33, 6, -20, -30],\n [-19, 43, -8, 1, 34],\n [4, -1, 12, -2, 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[[10, 5, -30, 45, 30],\n [-4, 30, -16, 4, -36],\n [-9, 59, -22, -11, -78],\n [17, -19, -16, 34, 66],\n [18, -1, 16, -58, 30]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[39, 12, -27, 60, 27],\n [-17, 13, 5, -26, -4],\n [-25, -7, -9, -14, 0],\n [12, -3, 1, 12, 1],\n [2, -13, -23, 28, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-23, 15, -17, -11, 1],\n [14, -12, 18, 11, -3],\n [16, -12, 16, 10, -2],\n [1, -3, 7, 4, -2],\n [-10, 12, -22, -13, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-58, 46, 16, -4, 38],\n [-20, 20, 12, -20, -14],\n [-14, -1, -8, 18, 21],\n [-15, 6, -6, 30, 57],\n [44, -35, -12, 2, -31]]\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, -10, 7, -20, 17],\n [-16, 16, -10, 20, -22],\n [-51, 51, -24, -15, -36],\n [-20, 20, -11, 10, -21],\n [60, -60, 27, 30, 37]]\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, 25, 31, -2, -35],\n [-13, -26, -14, 20, 33],\n [25, 23, 62, -10, 8],\n [10, 12, 20, -24, 14],\n [-5, -16, 2, 8, 35]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1, 7, -7, -8, -5],\n [51, -29, 69, 32, -25],\n [-15, 37, -49, -30, 9],\n [15, 5, 9, -8, -23],\n [-2, 26, -30, -12, 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[[6, -9, 18, -9, -12],\n [33, -2, 44, -27, -36],\n [0, 0, 0, 0, 0],\n [10, 4, 8, -6, -8],\n [10, 23, -14, 3, 4]]?\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[[16, -16, 12, 0, 12],\n [16, -16, 12, 0, 12],\n [20, -20, 15, 0, 15],\n [12, -12, 9, 0, 9],\n [-8, 8, -6, 0, -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[[-50, -17, 29, -24, 12],\n [32, -16, -2, -1, -21],\n [30, -8, -5, -8, -19],\n [53, -34, -1, -31, -53],\n [5, -29, 45, -64, 13]]\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[[4, -2, 58, 28, -36],\n [16, 8, 14, 11, -6],\n [62, 10, -24, -7, 54],\n [-30, -18, -6, -12, 0],\n [42, 13, -33, -10, 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[[-17, -6, -18, 30, 14],\n [1, -18, -30, 18, 2],\n [-3, -24, -42, 30, 6],\n [-22, -7, -22, 38, 18],\n [12, -21, -30, 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[[-35, -41, 40, 38, -8],\n [40, 53, -42, -43, -3],\n [-30, -8, -4, 6, 2],\n [49, 24, -6, -19, -3],\n [28, 2, 10, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, -60, 4, -28, 26],\n [-29, 33, -30, 13, 11],\n [-15, 41, 4, 13, -32],\n [42, -9, 12, -28, -2],\n [-3, -7, 8, 17, -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 5x5 matrix:\n[[-8, -20, 12, 24, 12],\n [2, 5, -3, -6, 8],\n [-10, -25, 15, 30, 36],\n [8, 20, -12, -24, -12],\n [2, 5, -3, -6, -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[[7, 46, 26, 46, 45],\n [-34, -28, -20, -22, 22],\n [-13, 22, -1, 16, 47],\n [-24, -34, 17, -2, 7],\n [-6, -24, -11, -28, -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[[-3, 15, -13, -9, 1],\n [3, -9, 10, -6, -16],\n [-1, 2, -2, 0, 3],\n [-8, 7, -4, -18, 3],\n [8, 5, -2, -12, -33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, 3, -21, 42, -33],\n [-16, -16, -48, 26, 82],\n [6, -22, 2, -9, -3],\n [0, 34, 28, -10, -34],\n [1, -44, -72, 50, 36]]\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, -26, -22, 0, -27],\n [1, 26, 10, 21, -15],\n [0, 4, -8, 13, -8],\n [2, 24, 12, 15, -6],\n [-9, -26, -6, -13, -31]]?\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, 25, -5, 20, -5],\n [-4, 5, -1, 4, -1],\n [-8, 10, -2, 8, -2],\n [-16, 20, -4, 16, -4],\n [-8, 10, -2, 8, -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 5x5 matrix:\n[[5, 26, -18, -39, 33],\n [-41, 14, 6, 23, -9],\n [21, 52, -20, 23, 44],\n [18, -61, 9, 13, -24],\n [-19, 35, -21, -12, 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[[-27, 42, -47, -52, 26],\n [-12, 9, -20, -17, 33],\n [-6, 60, -23, -19, 74],\n [13, -4, 59, 50, 18],\n [19, 23, 5, 17, 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[[16, -12, -2, 5, -7],\n [10, 8, 10, -4, -4],\n [-11, -10, 7, -10, 8],\n [-36, -14, 2, -14, 20],\n [33, -47, -36, 33, -18]]\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, -48, -58, 50, 1],\n [-25, 14, 39, -55, 2],\n [35, -32, -37, 79, 31],\n [15, -4, 10, 3, -19],\n [-43, 38, 36, -89, -35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[36, -6, -30, -24, -12],\n [-6, 1, 5, 4, 2],\n [-12, 2, 10, 8, 4],\n [24, -4, -20, -16, -8],\n [36, -6, -30, -24, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-16, 12, 9, 35, -27],\n [-24, 0, -1, 41, -33],\n [38, 47, 26, -8, 7],\n [-32, -12, 11, 3, 3],\n [6, 3, -12, 21, -21]]?\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[[12, -24, 24, 4, 26],\n [1, -7, 13, 1, 2],\n [15, 5, -40, -12, 16],\n [-16, 8, 14, 11, -16],\n [-36, 34, 5, 18, -36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 5, 44, 8, -15],\n [-24, 1, 28, -6, -6],\n [-13, -14, -12, -3, 9],\n [3, 44, 56, 43, -90],\n [-17, 14, 32, 21, -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[[7, 20, -21, 2, -7],\n [16, -4, -10, -1, -2],\n [35, -9, -10, 19, 0],\n [-32, -4, 20, -16, 4],\n [4, 16, -12, 8, -4]]?\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 5x5 matrix:\n[[-9, -15, 15, -15, -3],\n [-18, -30, 30, -30, -6],\n [-15, -25, 25, -25, -5],\n [18, 30, -30, 30, 6],\n [9, 15, -15, 15, 3]]\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[[2, -10, -12, 2, 12],\n [3, -15, -18, 3, 18],\n [4, -20, -24, 4, 24],\n [3, -15, -18, 3, 18],\n [2, -10, -12, 2, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[7, -7, -15, -4, -2],\n [-5, 1, 25, 4, 10],\n [-22, 24, 40, 12, 2],\n [9, -20, 20, -2, 21],\n [21, -35, 5, -8, 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 5x5 matrix:\n[[-11, -15, 57, -30, -34],\n [13, -25, -75, 31, -3],\n [-6, 27, 15, 6, -48],\n [-5, 13, 21, -12, -2],\n [7, 22, -36, 21, 31]]\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, -46, 19, -34, -2],\n [33, 43, 11, 54, 39],\n [6, -9, -9, -2, 4],\n [-7, 13, 14, 4, -4],\n [27, -26, 35, -2, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 3, -9, -18, -18],\n [6, -3, 9, 18, 18],\n [8, -4, 12, 24, 24],\n [12, -6, 18, 36, 36],\n [2, -1, 3, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-7, 10, -36, 20, 2],\n [4, -6, -6, 3, 6],\n [40, -47, -66, 26, 35],\n [43, -37, -18, -8, -3],\n [19, -20, -48, 20, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[28, -14, 5, -24, -3],\n [-40, 20, -10, 35, 5],\n [-36, 18, -11, 32, 5],\n [-20, 10, -11, 19, 4],\n [-12, 6, 3, 9, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[27, 44, -28, -10, 10],\n [45, 22, 16, -40, -24],\n [-36, -62, 36, 21, -10],\n [-9, 9, -4, -9, -8],\n [-43, 10, -30, 21, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[28, -35, -27, 30, -35],\n [-17, 10, 9, -24, 10],\n [40, -5, -9, 66, -5],\n [18, 10, 4, 36, 10],\n [-38, 10, 12, -60, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[5, -10, 25, -15, 15],\n [4, -8, 20, -12, 12],\n [6, -12, 30, -18, 18],\n [-1, 2, -5, 3, -3],\n [4, -8, 20, -12, 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[[-16, 36, -16, 28, -40],\n [9, -3, 4, 11, -23],\n [38, -3, -18, 24, -21],\n [39, -6, -22, 15, 0],\n [2, -24, 16, -24, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-13, 0, 28, -29, -35],\n [13, -19, -1, 2, -20],\n [26, -12, 7, 18, 34],\n [13, -21, -19, 10, -25],\n [-18, 0, 0, -22, -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 5x5 matrix:\n[[4, 8, -2, 2, -8],\n [6, 12, -3, 3, -12],\n [0, 0, 0, 0, 0],\n [2, 4, -1, 1, -4],\n [2, 4, -1, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-37, 12, 1, 8, -9],\n [-36, 6, 18, -30, 18],\n [18, 15, 23, -4, 29],\n [-29, -19, 0, -44, 4],\n [8, -21, 9, -50, 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[[-40, 22, 5, 42, 28],\n [13, 43, -17, 10, 35],\n [-25, -6, 9, -3, 12],\n [-15, -28, 25, 10, -7],\n [-52, -16, 4, 18, -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[[45, -57, 38, -24, 5],\n [-41, 30, -37, 5, -12],\n [39, -3, 50, -12, 59],\n [0, -9, -1, -25, 15],\n [26, 20, 34, -22, 76]]?\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 5x5 matrix:\n[[0, 49, 12, 62, 44],\n [35, -25, -15, 16, 14],\n [-15, 30, -13, 26, 56],\n [-5, 94, 3, 44, 43],\n [-15, -18, -9, -18, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, 4, 6, 0, 4],\n [3, -4, -6, 0, -4],\n [6, -8, -12, 0, -8],\n [18, -24, -36, 0, -24],\n [-15, 20, 30, 0, 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 5x5 matrix:\n[[27, -23, 25, -8, 36],\n [-14, 14, -12, 4, -20],\n [47, 17, 32, -18, -12],\n [17, -1, -4, -6, -12],\n [-22, -2, -18, 8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, -6, -36, 36, -24],\n [4, 2, 12, -12, 8],\n [-4, -2, -12, 12, -8],\n [-8, -4, -24, 24, -16],\n [6, 3, 18, -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 5x5 matrix:\n[[-6, -12, -4, 4, 2],\n [-9, -18, -6, 6, 3],\n [12, 24, 8, -8, -4],\n [-9, -18, -6, 6, 3],\n [6, 12, 4, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[16, -4, -12, 12, 8],\n [16, -4, -12, 12, 8],\n [-20, 5, 15, -15, -10],\n [-20, 5, 15, -15, -10],\n [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[[4, 41, -10, 21, 27],\n [-59, -1, -5, 4, -9],\n [85, 18, 4, 2, 18],\n [1, 33, -20, -9, -1],\n [-30, -1, -4, -11, -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[[32, 6, -6, 12, 22],\n [-6, 2, 20, -20, 14],\n [-17, -3, 27, -29, 9],\n [-28, 16, 4, -8, -8],\n [-11, 23, -28, 26, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, -15, 6, -45, 1],\n [-1, 1, -4, 15, -3],\n [-3, 14, 18, -5, 2],\n [-5, -7, 16, -48, 5],\n [11, -1, -4, 35, -5]]\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, -4, -8, -4, 4],\n [-24, -8, -16, -8, 8],\n [36, 12, 24, 12, -12],\n [12, 4, 8, 4, -4],\n [-36, -12, -24, -12, 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[[-17, 17, 51, -36, 5],\n [-13, 13, 39, -24, 5],\n [-18, 36, -24, -6, -8],\n [6, 6, -70, 24, -14],\n [22, -40, 12, 12, 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 5x5 matrix:\n[[26, -21, 16, 14, 65],\n [21, 43, -37, 30, 2],\n [5, -40, 19, 10, 23],\n [-26, -34, 22, -16, -24],\n [-4, -42, 36, -44, -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[[-24, 6, -24, -36, -18],\n [16, -4, 16, 24, 12],\n [8, -2, 8, 12, 6],\n [-4, 1, -4, -6, -3],\n [-12, 3, -12, -18, -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[[4, -10, 10, -10, 10],\n [10, -25, 25, -25, 25],\n [-12, 30, -30, 30, -30],\n [8, -20, 20, -20, 20],\n [-8, 20, -20, 20, -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 5x5 matrix:\n[[-69, -27, -24, 30, 0],\n [28, -24, -2, -45, 24],\n [4, 6, -38, 25, 18],\n [-18, -42, -26, 13, 40],\n [11, 42, -4, -8, -33]]\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 5x5 matrix:\n[[15, 0, -6, -6, -12],\n [-25, 0, 10, 10, 20],\n [5, 0, -2, -2, -4],\n [5, 0, -2, -2, -4],\n [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[[15, -26, 8, -18, 13],\n [-10, 14, 16, -7, 9],\n [24, -10, -24, 10, -24],\n [-1, 20, 32, -29, 8],\n [40, 18, 65, -58, 24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, 31, -25, 14, -34],\n [-25, -12, 1, 17, 13],\n [12, -43, 22, -23, 19],\n [16, 17, -31, -43, -21],\n [-10, 24, -12, 36, -46]]?\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, 24, -12, -36, 24],\n [0, 24, -12, -36, 24],\n [0, 4, -2, -6, 4],\n [0, 24, -12, -36, 24],\n [0, 16, -8, -24, 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[[-30, -23, -29, -45, -16],\n [-43, -8, 39, 3, -54],\n [-54, 2, 10, 13, -43],\n [18, 13, -7, 8, 22],\n [-14, 15, 9, 49, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-32, 17, 35, -41, 37],\n [-44, -4, 28, -8, 13],\n [12, -61, 8, -26, -28],\n [-10, -59, 15, 7, -29],\n [-1, 44, 3, 19, 27]]\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 5x5 matrix:\n[[-34, 46, -38, 50, -7],\n [-41, -13, -57, 34, -51],\n [14, 27, 4, 7, -10],\n [66, 30, 18, -24, 30],\n [-32, -1, -94, 45, -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[[0, 0, 0, 0, 0],\n [9, 18, 9, -9, 9],\n [6, 12, 6, -6, 6],\n [-12, -24, -12, 12, -12],\n [12, 24, 12, -12, 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[[-17, -36, -24, 35, 32],\n [33, -32, -42, 0, 36],\n [37, -23, -15, -1, 20],\n [-13, -47, -51, 34, 49],\n [-13, 20, 36, 1, -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[[-10, -2, 8, 12, 2],\n [-20, -4, 16, 24, 4],\n [33, 9, 0, -48, 27],\n [7, 3, 12, -14, 21],\n [13, 3, -6, -17, 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, 10, 23, -12, 5],\n [-60, 9, 39, -20, 3],\n [10, 0, 17, 0, 2],\n [43, -8, -18, 12, -3],\n [-17, 1, 21, -8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-23, 4, 24, 8, 41],\n [2, -4, -7, -1, -4],\n [-20, -9, -7, -2, 12],\n [13, -19, -25, 2, -3],\n [0, 0, 7, 5, 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[[-36, -12, -24, -24, -30],\n [-24, -8, -16, -16, -20],\n [-6, -2, -4, -4, -5],\n [18, 6, 12, 12, 15],\n [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[[3, -9, -6, 9, -9],\n [4, -12, -8, 12, -12],\n [5, -15, -10, 15, -15],\n [0, 0, 0, 0, 0],\n [4, -12, -8, 12, -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[[-6, -6, -6, -6, 0],\n [8, 8, 8, 8, 0],\n [10, 10, 10, 10, 0],\n [-6, -6, -6, -6, 0],\n [8, 8, 8, 8, 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[[-2, 4, -8, 22, 32],\n [28, -22, 40, -8, -2],\n [-25, -22, -11, 1, 17],\n [-32, -39, -7, -4, 20],\n [19, 33, -4, 17, 5]]\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[[-32, 16, 32, 59, 12],\n [61, 14, 22, -33, -25],\n [-71, -3, -6, 57, 28],\n [-23, -4, -11, 5, 2],\n [-6, -14, -12, -14, -8]]?\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 5x5 matrix:\n[[4, -11, -12, -22, -30],\n [-26, 43, -11, -57, 5],\n [-4, 2, -24, -12, -12],\n [-40, 50, -8, -16, 20],\n [-49, 56, 21, -1, 27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, 16, -12, 8, 14],\n [-12, 24, -18, 12, 21],\n [-17, -11, 24, 17, 5],\n [-5, -15, 20, 5, -5],\n [-34, 18, 4, 34, 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[[54, 29, 2, 9, -17],\n [-21, -27, -18, -1, -13],\n [34, 6, 10, 36, 1],\n [-16, 1, -18, -39, -17],\n [-41, 0, 14, -30, 30]]\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, -11, 9, 32, 11],\n [25, 2, -7, 6, -31],\n [5, 38, 3, -26, -16],\n [4, 11, -10, -42, -4],\n [-14, 35, 8, -30, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-9, 9, 0, 18, 0],\n [-9, 9, 0, 18, 0],\n [3, -3, 0, -6, 0],\n [15, -15, 0, -30, 0],\n [-6, 6, 0, 12, 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[[-20, -20, -8, 20, 4],\n [10, -25, -34, -20, 27],\n [12, -9, -18, -18, 15],\n [-20, -20, -8, 20, 4],\n [9, 37, 34, -1, -25]]\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, 6, 24],\n [-12, -20, 12, -4, -16],\n [0, 0, 0, 0, 0],\n [18, 30, -18, 6, 24],\n [18, 30, -18, 6, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 19, 4, -24, -32],\n [-7, -20, 8, -23, 26],\n [4, -4, 7, -22, 4],\n [46, -4, 19, -20, 24],\n [62, 16, 20, -26, -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[[55, -44, -26, 19, 6],\n [-40, 32, 23, -22, -18],\n [-10, 8, 14, -22, -32],\n [30, -24, -21, 24, 26],\n [30, -24, -21, 24, 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 5x5 matrix:\n[[2, -4, -6, 11, -23],\n [22, -16, 18, -19, -1],\n [8, -9, -3, 9, -29],\n [-26, 18, -24, 27, -7],\n [-18, 14, -12, 11, 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[[17, -31, 20, -3, -14],\n [1, 15, -21, 9, 16],\n [10, -4, -7, 6, 6],\n [-30, 12, 21, -18, -18],\n [18, -16, -1, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[36, 5, 38, 0, -10],\n [24, -15, 22, 20, -30],\n [24, 30, 28, -7, 18],\n [-27, -4, -30, 15, 1],\n [-42, 4, -44, 4, 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[[-38, -31, -53, -4, 46],\n [-14, -11, -17, 0, 14],\n [0, 9, 4, -16, -18],\n [18, 18, -5, -34, 0],\n [-20, -6, -6, -4, -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[[19, -54, 16, 20, -20],\n [11, 26, -32, -4, 4],\n [16, -72, 34, 23, -26],\n [31, -30, 4, 2, -44],\n [-2, -12, 28, -10, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[20, -20, 4, -16, -8],\n [-30, -2, 14, 8, 28],\n [0, -8, 5, -4, 4],\n [-10, 42, -22, 24, -12],\n [30, -14, -4, -16, -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[[-38, 17, 43, 34, -4],\n [-26, -10, -12, -21, 6],\n [-14, 30, -52, -17, -54],\n [30, 18, -3, 15, -17],\n [62, -2, -44, -23, -6]]\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, -12, 4, 4, -6],\n [-12, -12, 4, 4, -6],\n [-36, -36, 12, 12, -18],\n [0, 0, 0, 0, 0],\n [-6, -6, 2, 2, -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[[-4, -36, -16, 28, 28],\n [-24, 12, 22, 50, 6],\n [-28, 41, -16, -31, -54],\n [19, -11, 52, 36, 42],\n [36, -4, -18, 6, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, -7, 20, 5, 12],\n [-5, 2, 6, 6, 24],\n [-5, -19, 46, -31, 36],\n [-12, -9, 25, -22, 30],\n [-22, 28, -52, 28, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[10, 4, 0, -8, 8],\n [13, 10, 0, -4, 12],\n [32, 20, 0, -16, 28],\n [5, 2, 0, -4, 4],\n [15, 18, 0, 4, 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[[-10, 15, -30, 0, 0],\n [-12, 18, -36, 0, 0],\n [6, -9, 18, 0, 0],\n [6, -9, 18, 0, 0],\n [-4, 6, -12, 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 5x5 matrix:\n[[20, -24, 3, -20, -67],\n [-32, -5, -11, -13, 7],\n [40, 39, 66, -76, 19],\n [5, 7, 14, 5, 37],\n [-6, -9, 0, -6, -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 5x5 matrix:\n[[-24, -15, 28, -8, 24],\n [15, 35, -29, 29, -41],\n [24, 38, -39, 22, -38],\n [11, 49, -39, 28, -32],\n [23, -61, 38, -49, 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[[56, 38, 1, 6, -29],\n [-30, -28, -38, -10, 2],\n [23, 14, -18, -11, -24],\n [14, 1, -16, 23, 0],\n [-5, -12, -29, 7, -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[[-5, -17, -24, -2, -12],\n [0, -13, -10, 3, -9],\n [7, -11, -30, -26, -27],\n [35, 36, 34, -37, -11],\n [-9, 20, 8, -3, 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[[24, -4, -16, -24, 16],\n [36, -6, -24, -36, 24],\n [-36, 6, 24, 36, -24],\n [12, -2, -8, -12, 8],\n [-30, 5, 20, 30, -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[[8, -5, 4, -9, -1],\n [2, 25, 15, 24, 40],\n [-18, -30, -31, -21, -61],\n [-48, 30, -24, 54, 6],\n [-16, 10, -8, 18, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[10, -9, 6, -8, 19],\n [-28, -14, -54, -4, 13],\n [-10, 19, -32, 8, -21],\n [-43, -22, 7, -3, 28],\n [3, 14, -52, 1, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[10, 32, -42, 16, 6],\n [-27, -37, 47, -14, 14],\n [-11, 22, -26, -40, 19],\n [28, 22, -26, -4, -26],\n [0, -13, 17, -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[[51, -23, 5, -18, -22],\n [24, 6, -29, 42, -57],\n [-39, 12, 4, 42, 9],\n [-6, 5, -4, -6, 4],\n [-3, -7, 17, -54, 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 5x5 matrix:\n[[0, 20, -11, 12, 14],\n [-22, 12, -11, -28, 26],\n [0, 20, -11, 12, 14],\n [-25, 20, -16, -28, 34],\n [-21, 16, -13, -24, 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[[29, -16, -21, -27, 28],\n [-34, 14, 24, 30, -26],\n [-30, -12, 18, 18, 12],\n [-34, 14, 24, 30, -26],\n [29, -16, -21, -27, 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[[19, 3, 23, -14, 2],\n [21, 14, 30, 12, -10],\n [10, -1, 11, -14, 4],\n [-18, -1, -21, 18, -4],\n [-14, -14, -22, -20, 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[[-2, -10, -4, -4, 4],\n [6, 30, 12, 12, -12],\n [-6, -30, -12, -12, 12],\n [6, 30, 12, 12, -12],\n [-6, -30, -12, -12, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[7, 6, -40, 15, -2],\n [35, -10, 20, 3, -6],\n [13, -6, 20, -3, -2],\n [42, -4, -20, 18, -8],\n [21, -12, 45, -9, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, -26, 0, 40, -10],\n [-4, -14, 8, 32, -6],\n [-16, -28, -10, 30, -10],\n [18, 25, 21, -11, 8],\n [-20, -26, -26, 6, -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[[26, -50, 8, 19, 26],\n [-41, -5, -23, 56, -37],\n [14, -18, 30, 6, 18],\n [-4, 28, -10, -26, -7],\n [-24, 20, -12, 9, -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 5x5 matrix:\n[[0, 53, -25, 17, 29],\n [34, -12, 12, 7, -17],\n [23, -43, 23, 25, 4],\n [9, 69, -30, -45, -48],\n [-27, -19, 11, 5, 38]]\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[[8, 32, -32, -12, 12],\n [-1, -4, 13, 15, -24],\n [-10, -40, 40, 15, -15],\n [2, 8, -12, -9, 13],\n [1, 4, -9, -9, 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 5x5 matrix:\n[[-21, 4, -18, -37, -12],\n [25, -21, 17, -15, 1],\n [-32, 26, -22, 16, -2],\n [8, -12, 4, -24, -4],\n [22, -11, 17, 14, 7]]\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 5x5 matrix:\n[[-4, 6, -12, -6, 8],\n [10, -15, 30, 15, -20],\n [-8, 12, -24, -12, 16],\n [-12, 18, -36, -18, 24],\n [4, -6, 12, 6, -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 5x5 matrix:\n[[21, -33, -9, 0, -3],\n [4, 23, 13, 19, -20],\n [10, 12, 15, 23, -22],\n [7, 4, 39, 42, -25],\n [27, -18, 3, 18, -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[[-3, -2, -40, 5, 8],\n [15, -21, 30, -19, -29],\n [-40, 13, -10, -63, -35],\n [25, -24, 28, 48, 12],\n [28, -3, 46, 3, -3]]?\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, -30, -31, -29, -50],\n [-3, 9, 9, 3, 15],\n [-4, 2, -7, -18, 1],\n [10, -19, -31, -28, -27],\n [-7, 4, 45, 59, 15]]\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[[-9, -12, 0, -9, 15],\n [-12, -16, 0, -12, 20],\n [9, 12, 0, 9, -15],\n [-3, -4, 0, -3, 5],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-48, 65, -16, 16, -24],\n [38, -38, 46, -22, 14],\n [24, -20, -26, -5, -26],\n [-6, 23, 26, 2, 58],\n [-24, 12, 30, -1, -18]]\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, -24, 15, 32, -17],\n [36, -33, 4, 33, 6],\n [-12, -12, -8, 0, -8],\n [-34, -23, 9, -17, 19],\n [4, -10, -42, 18, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[34, 44, -42, 26, 12],\n [-38, -37, 30, -17, 13],\n [7, 5, 25, 6, -19],\n [-11, -22, -17, -23, -2],\n [-18, -15, -10, -9, 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[[0, 0, -20, -24, 4],\n [0, 0, -10, -12, 2],\n [0, 0, -25, -30, 5],\n [0, 0, -30, -36, 6],\n [0, 0, -20, -24, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[46, 30, 5, 0, 26],\n [34, 48, 23, -18, 20],\n [2, -60, -42, 35, 7],\n [-22, 18, 22, -23, -11],\n [-18, 6, 20, -31, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-35, 15, 21, 25, -9],\n [-3, 38, 56, 8, 30],\n [-18, 42, 82, 6, 44],\n [37, -36, -36, -8, -26],\n [-59, 14, 12, 36, -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[[11, -9, -21, -21, 0],\n [-43, 30, 7, 48, 6],\n [1, -9, 9, 39, 0],\n [24, -5, 3, -69, -5],\n [6, -4, 1, -6, -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 5x5 matrix:\n[[-11, -40, -19, -15, -7],\n [-12, -46, -22, -18, -6],\n [-3, -18, -9, -9, 3],\n [-7, -3, 0, 6, -20],\n [8, 35, 17, 15, 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[[6, -30, -22, -20, -18],\n [2, -10, 2, -8, -2],\n [3, -15, 10, -13, 0],\n [0, 0, -28, 4, -12],\n [-7, 35, 28, 23, 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[[-20, 22, 8, 6, -8],\n [19, -16, -2, 9, -19],\n [20, -15, 0, 15, -30],\n [-21, 14, -2, -21, 41],\n [1, 1, 2, 6, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[7, 55, 11, -19, -31],\n [-4, -36, 16, 7, 29],\n [8, 16, -64, 15, 39],\n [-36, -33, 12, 66, 5],\n [-12, 15, -36, 51, 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[[11, -20, -12, -8, -48],\n [-16, -4, 8, -16, -38],\n [2, -31, 33, 11, 60],\n [66, -29, 7, 47, 48],\n [-43, 22, -10, -30, -24]]\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[[1, -22, 2, -22, -17],\n [-33, 6, 34, 6, 21],\n [-22, -20, 26, -20, -4],\n [33, -6, -34, -6, -21],\n [-12, -24, 16, -24, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[10, -15, -16, 16, -8],\n [25, 25, -35, -15, -5],\n [-3, -18, 3, 15, -3],\n [-22, -7, 32, 0, 8],\n [14, 9, -20, -4, -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[[0, -25, 0, -30, -15],\n [0, 10, 0, 12, 6],\n [0, -10, 0, -12, -6],\n [0, 10, 0, 12, 6],\n [0, 5, 0, 6, 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[[-25, 30, 20, -5, -5],\n [-22, -12, 26, 4, 28],\n [-37, 6, 38, 1, 25],\n [-30, 36, 24, -6, -6],\n [-14, 36, 7, -7, -19]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0, 0],\n [-6, 8, -2, 10, 10],\n [-6, 8, -2, 10, 10],\n [0, 0, 0, 0, 0],\n [3, -4, 1, -5, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-5, 8, -4, 14, 7],\n [1, -16, 32, 2, 37],\n [0, 6, -13, -2, -16],\n [-14, 32, -32, 36, -6],\n [-16, 34, -31, 42, 0]]\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[[6, -2, -27, 23, -11],\n [12, 6, 16, -14, -2],\n [36, 8, -22, 18, -26],\n [24, 10, 18, -16, -8],\n [0, 6, 42, -36, 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[[30, -30, 36, 12, -12],\n [-30, 30, -36, -12, 12],\n [-30, 30, -36, -12, 12],\n [0, 0, 0, 0, 0],\n [10, -10, 12, 4, -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[[30, 20, 15, 0, 25],\n [6, 4, 3, 0, 5],\n [-18, -12, -9, 0, -15],\n [12, 8, 6, 0, 10],\n [36, 24, 18, 0, 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, -17, 26, -53, 7],\n [25, -7, -2, -2, 4],\n [-1, -5, 12, 34, -6],\n [-9, 11, -15, 16, -5],\n [25, -24, 18, -21, -13]]\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[[-50, -5, -2, -49, -11],\n [-22, 12, -40, -14, 23],\n [-48, -8, -3, -35, -13],\n [10, -16, 19, 41, -20],\n [-20, 0, -50, 18, 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[[-18, -48, 21, 1, 16],\n [-13, 42, -1, 13, 16],\n [8, -64, 0, -14, -8],\n [38, -14, -34, -40, 24],\n [1, 20, 12, 8, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[45, 7, 16, -15, 14],\n [11, -3, -3, -4, 16],\n [51, 13, 0, 31, -22],\n [-20, 7, -13, -6, -8],\n [63, 2, 1, 49, -14]]?\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, 3, -7, -8, 20],\n [4, 39, -31, -35, 17],\n [-12, 14, -6, -20, -41],\n [12, -30, 5, 1, 46],\n [-14, 18, 8, 10, -42]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-9, 21, 11, 10, 5],\n [-5, 1, 7, 10, 9],\n [-9, -27, 15, 30, 33],\n [-9, 9, 12, 15, 12],\n [0, 12, -1, -5, -7]]\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, 46, 24, 42, 35],\n [-3, -24, 3, -19, -19],\n [-6, 20, -6, 14, 42],\n [8, 27, 7, 23, 28],\n [-6, -18, -12, -16, -34]]\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[[-7, -29, 5, 9, -18],\n [-4, 15, -19, -24, 31],\n [-6, -10, -6, -6, 4],\n [-9, -41, 9, 15, -28],\n [3, -8, 12, 15, -19]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[11, 0, 12, 26, -6],\n [-6, -36, -36, -24, 0],\n [6, -8, 0, 12, -4],\n [-3, 37, 27, 3, 5],\n [3, 51, 45, 21, 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[[6, 0, 9, 12, 18],\n [12, 0, 18, 24, 36],\n [2, 0, 3, 4, 6],\n [-6, 0, -9, -12, -18],\n [-12, 0, -18, -24, -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[[-9, -15, 9, 3, 6],\n [12, 20, -12, -4, -8],\n [9, 15, -9, -3, -6],\n [12, 20, -12, -4, -8],\n [-3, -5, 3, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, -4, -8, -10, 6],\n [-1, -2, -4, -5, 3],\n [-6, -12, -24, -30, 18],\n [5, 10, 20, 25, -15],\n [-5, -10, -20, -25, 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[[0, -3, -12, -12, 15],\n [30, 18, 60, 6, -66],\n [-15, -2, -2, 25, -2],\n [-10, 0, 4, 22, -8],\n [-10, -3, -8, 10, 7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, 19, -71, -46, 26],\n [-25, -12, -7, 0, -12],\n [58, -34, -7, 40, -27],\n [-46, 32, 43, 3, -53],\n [49, 10, -31, 3, -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[[2, -4, -12, 10, 4],\n [6, -12, -36, 30, 12],\n [-1, 2, 6, -5, -2],\n [4, -8, -24, 20, 8],\n [1, -2, -6, 5, 2]]?\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[[-44, 12, -6, -34, -31],\n [-26, 6, -22, -6, -30],\n [20, -10, -20, 20, 25],\n [-35, 12, 38, -60, 3],\n [42, -10, 22, 22, 36]]\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[[32, 35, -6, 15, 3],\n [11, 0, 17, -20, 9],\n [22, -10, 9, -30, 35],\n [-26, -17, 30, -21, -21],\n [39, 11, 2, -17, 35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[16, 16, 20, 8, 16],\n [0, 0, 0, 0, 0],\n [24, 24, 30, 12, 24],\n [0, 0, 0, 0, 0],\n [-4, -4, -5, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-23, 28, 29, 22, -22],\n [-14, 18, 29, 22, -3],\n [-24, 45, 50, 31, -19],\n [14, 4, 7, -4, 17],\n [2, -23, -24, -9, 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[[21, 70, 27, 15, 66],\n [30, 8, -42, 10, -18],\n [-54, -30, 42, 12, -6],\n [-21, -4, 1, -12, 16],\n [-21, 11, 15, 41, 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 5x5 matrix:\n[[0, -3, 2, 6, 3],\n [0, -15, 10, 30, 15],\n [0, -3, 2, 6, 3],\n [0, -12, 8, 24, 12],\n [0, 3, -2, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-10, -3, 75, 56, -13],\n [5, 13, -60, -52, 8],\n [-45, 20, -59, -28, 45],\n [0, 7, 54, -1, -28],\n [-41, 39, -11, -15, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-22, 41, -9, -70, 0],\n [34, -24, 11, 34, 4],\n [-31, 63, -39, -71, -7],\n [-5, 17, 2, -4, 6],\n [3, -25, 31, 20, 8]]\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 5x5 matrix:\n[[1, -6, -34, 20, 4],\n [-20, 3, -17, 8, 2],\n [1, 1, 3, 32, 12],\n [11, 19, 56, 41, 18],\n [36, -5, 12, 29, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 11, 21, -2, 7],\n [24, -17, 13, 14, -29],\n [3, -1, 14, 4, -7],\n [-3, 1, -14, -4, 7],\n [-21, 19, 34, -4, 13]]\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 5x5 matrix:\n[[15, 12, -18, -3, 12],\n [10, 8, -12, -2, 8],\n [25, 20, -30, -5, 20],\n [-25, -20, 30, 5, -20],\n [25, 20, -30, -5, 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[[-5, 10, -15, -15, 0],\n [-4, 8, -12, -12, 0],\n [5, -10, 15, 15, 0],\n [-6, 12, -18, -18, 0],\n [-2, 4, -6, -6, 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[[5, -36, 31, -9, -26],\n [-15, 24, -23, -1, 22],\n [30, -30, 31, 8, -32],\n [-5, 18, -16, 3, 14],\n [30, 12, -4, 22, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-42, 42, 0, 44, -38],\n [-8, 9, 11, 7, -20],\n [-43, 48, 12, 30, -69],\n [-27, 30, -37, 9, -5],\n [-5, 3, 31, 17, -19]]\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 5x5 matrix:\n[[5, 1, 29, -1, 5],\n [8, 18, 24, 6, -14],\n [4, 8, -15, 7, -11],\n [-20, 22, -59, -51, 39],\n [-5, -46, 12, 51, -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 5x5 matrix:\n[[-3, 4, -5, 5, -4],\n [6, -8, 10, -10, 8],\n [-3, 4, -5, 5, -4],\n [12, -16, 20, -20, 16],\n [6, -8, 10, -10, 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[[25, -25, -5, 20, -25],\n [-15, 15, 3, -12, 15],\n [-25, 25, 5, -20, 25],\n [-25, 25, 5, -20, 25],\n [10, -10, -2, 8, -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[[-5, -7, 0, 8, 0],\n [13, -14, -21, 3, -35],\n [-13, -9, 6, 14, 10],\n [-9, -8, 3, 11, 5],\n [-19, 1, 18, 10, 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[[0, 0, 0, 0, 0],\n [-3, -12, 3, -18, -3],\n [1, 4, -1, 6, 1],\n [2, 8, -2, 12, 2],\n [-6, -24, 6, -36, -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 5x5 matrix:\n[[-16, 12, -16, -16, -16],\n [4, -1, 10, 9, 6],\n [-20, 35, 40, 30, 0],\n [-24, 40, 42, 31, -2],\n [20, -21, 2, 5, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, 25, 35, -25, -15],\n [-4, -3, -4, -15, -20],\n [-8, 7, 10, -40, -44],\n [-9, -21, -33, -5, -15],\n [-12, -12, -24, -10, -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 5x5 matrix:\n[[37, 0, -32, 0, 9],\n [4, 0, -5, 0, 2],\n [33, 0, -30, 0, 9],\n [21, 0, -18, 0, 5],\n [32, 0, -28, 0, 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[[27, -20, 23, 21, -1],\n [-15, -24, 17, -11, -45],\n [-30, -13, -14, 35, 12],\n [-20, 56, -44, -42, 30],\n [-8, 16, -6, -46, -8]]\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, 13, 6, -16, 4],\n [16, -12, -12, 24, -4],\n [17, -5, -12, 20, -2],\n [-10, 23, 9, -26, 7],\n [-40, -1, 27, -38, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, -29, -4, 16, -23],\n [16, 4, 4, -16, 8],\n [12, 26, 6, -24, 24],\n [18, -30, 0, 0, -18],\n [-15, -21, -6, 24, -21]]\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, -18, 18, -6, -18],\n [0, 12, -12, 4, 12],\n [0, -24, 24, -8, -24],\n [0, -24, 24, -8, -24],\n [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[[-23, 20, -15, 42, 24],\n [18, -30, 0, -72, 6],\n [-17, -1, -24, -12, 45],\n [18, -8, 18, -12, -32],\n [-21, 13, -18, 24, 31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, -7, -23, 18, 0],\n [-12, 12, 36, -4, -8],\n [0, 1, 1, 8, -2],\n [-2, -35, -31, -62, -34],\n [6, 1, -11, -8, 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[[-15, 23, 28, -15, 20],\n [0, -8, -16, 24, -20],\n [30, -36, -36, 0, -15],\n [-25, 27, 24, 9, 5],\n [-5, 17, 28, -33, 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[[8, -7, -4, -15, -26],\n [27, 7, 19, -15, 1],\n [7, -10, -13, -18, -39],\n [-29, -36, 23, -12, -15],\n [26, 41, -10, 21, 40]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[27, -24, -9, -10, 3],\n [64, -26, -28, -51, -8],\n [-4, 14, 32, 19, 50],\n [38, -4, 6, -20, 32],\n [-32, 22, 36, 37, 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[[-15, -6, 0, -6, 12],\n [-9, 8, -6, 0, 10],\n [16, -11, 9, 1, -17],\n [-29, 0, -6, -8, 26],\n [12, 28, -12, 12, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-58, 5, 67, -19, 14],\n [-54, 8, 34, 16, 12],\n [-12, 44, -59, 43, -6],\n [12, 18, -1, -31, -2],\n [27, -2, -51, 24, -18]]\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[[-35, 23, -29, 26, 17],\n [-36, 36, 4, 24, -4],\n [-33, 21, -7, 22, 11],\n [62, -44, -2, -40, -12],\n [-7, -11, 7, 2, 15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-10, -6, 12, 22, 2],\n [-25, -28, 4, 16, -34],\n [15, 14, -8, -18, 12],\n [-25, -26, 8, 22, -28],\n [5, 4, -4, -8, 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[[-40, 38, -8, -2, 23],\n [48, 35, 9, 22, 39],\n [-8, -33, -15, -6, -27],\n [58, -37, 46, 10, -20],\n [42, -11, -28, -28, -7]]?\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, 8, 24, -24, -21],\n [-50, -39, -10, 7, -27],\n [-68, 3, -16, -5, -54],\n [47, 52, 23, -35, -9],\n [10, -65, -12, 39, 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[[18, -24, 18, -6, 0],\n [9, -12, 9, -3, 0],\n [-9, 12, -9, 3, 0],\n [12, -16, 12, -4, 0],\n [-15, 20, -15, 5, 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[[-5, 27, -33, 1, -11],\n [37, 20, -17, -3, 14],\n [13, 18, -21, -15, 12],\n [22, -14, -4, 36, -20],\n [38, -2, 8, 8, 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[[-4, -62, 32, 14, 66],\n [-31, 52, 2, -34, 20],\n [18, 12, 11, -2, 20],\n [31, 6, -23, 31, -8],\n [50, -54, -21, 67, 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[[-20, -1, 13, -62, 16],\n [56, -28, 60, 36, -76],\n [22, -15, -17, 56, -14],\n [42, 0, 12, 84, -48],\n [-12, 19, 25, -38, 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[[16, -4, 17, 28, 2],\n [19, 19, 33, 53, -33],\n [-21, -12, -7, -45, 15],\n [30, 9, -25, 0, -60],\n [-21, 11, 32, 7, 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[[-68, 12, -16, 46, -22],\n [6, -17, 11, 32, 56],\n [-20, -14, 16, -60, -70],\n [50, 1, -13, -50, 6],\n [-22, -14, 20, 28, 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[[9, 44, -12, -3, -8],\n [-27, 39, -86, -43, 11],\n [-40, -10, -23, -14, 22],\n [-9, 7, -27, -15, -5],\n [-4, -47, 17, 6, 9]]\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 5x5 matrix:\n[[13, -16, 3, 27, -5],\n [9, 15, -32, 3, -5],\n [-27, 21, 24, -45, 9],\n [2, -21, -34, 0, 9],\n [-12, 34, 43, -18, -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[[-33, 46, 48, -17, 21],\n [10, -40, -25, 0, 54],\n [-42, -9, 26, -19, 73],\n [29, -27, -10, -36, -30],\n [-32, 55, 34, 19, -3]]\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[[8, 0, -44, 28, 4],\n [-10, 0, 55, -35, -5],\n [8, 0, -20, 16, -12],\n [8, 0, -20, 16, -12],\n [0, 0, -18, 9, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 0, -8, 12, -4],\n [-18, 0, 12, -18, 6],\n [12, 0, -8, 12, -4],\n [6, 0, -4, 6, -2],\n [15, 0, -10, 15, -5]]\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[[-16, -12, -4, 24, -8],\n [4, 3, 1, -6, 2],\n [12, 9, 3, -18, 6],\n [-12, -9, -3, 18, -6],\n [-12, -9, -3, 18, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-30, -3, -5, -21, 24],\n [44, -2, 13, 19, -33],\n [-41, -13, -2, -43, 45],\n [50, -5, 18, 16, -39],\n [34, -1, 12, 14, -33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 6, 0, 12, 0],\n [8, -8, 0, -16, 0],\n [-10, 10, 0, 20, 0],\n [10, -10, 0, -20, 0],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[46, -81, 31, 1, -31],\n [-47, 48, 16, 16, -25],\n [4, -18, 28, -48, -18],\n [-5, -30, -59, -39, 46],\n [28, 10, 24, -12, 0]]\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 5x5 matrix:\n[[-6, 2, -8, 6, 6],\n [6, -2, 8, -6, -6],\n [9, -3, 12, -9, -9],\n [-9, 3, -12, 9, 9],\n [3, -1, 4, -3, -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[[-36, 0, 11, -6, -7],\n [24, 0, -6, 12, 30],\n [-8, 0, 4, 8, 28],\n [-10, 0, 4, 4, 16],\n [-26, 0, 7, -10, -23]]\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[[-34, 33, -31, 19, -2],\n [-8, 11, -39, -2, 9],\n [26, -16, -2, -33, 5],\n [-34, 29, -35, 27, 2],\n [0, 4, 4, -8, -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[[-30, 6, -38, -32, 76],\n [-15, 4, -2, 67, -6],\n [-27, 11, -14, -14, 22],\n [-21, 3, -29, -14, 58],\n [30, -16, -9, -60, 36]]\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, -16, -13, 1, 9],\n [4, -51, 11, 5, -3],\n [-53, 33, -6, 12, -27],\n [13, 0, 39, -21, 18],\n [16, -41, -21, 13, -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[[-18, -12, 9, 3, -9],\n [36, 24, -18, -6, 18],\n [-6, -4, 3, 1, -3],\n [24, 16, -12, -4, 12],\n [24, 16, -12, -4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, -20, 16, -20, 12],\n [-12, -20, 16, -20, 12],\n [18, 30, -24, 30, -18],\n [-12, -20, 16, -20, 12],\n [-6, -10, 8, -10, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[29, -12, -21, -5, 5],\n [-80, 36, 63, 13, -1],\n [-4, 18, 9, 23, 19],\n [6, 24, -18, -9, -22],\n [25, -39, -12, -17, 9]]?\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 5x5 matrix:\n[[-48, -11, 4, 34, 21],\n [26, -4, -12, -42, -10],\n [-10, 54, -52, -22, 50],\n [29, 1, 44, 37, 29],\n [19, -14, 22, 3, -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[[-22, 2, 16, 18, -8],\n [7, -7, -27, -31, 8],\n [-1, -25, -39, -40, 11],\n [1, 9, 1, -2, -1],\n [12, -14, -42, -47, 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[[3, -15, 6, 9, -9],\n [-3, 15, -6, -9, 9],\n [2, -10, 4, 6, -6],\n [6, -30, 12, 18, -18],\n [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[[-9, 25, 2, 44, -13],\n [-1, 18, 20, -24, 14],\n [-11, -16, -19, 3, 32],\n [-3, 6, -20, 40, -38],\n [19, 6, -5, 17, -86]]\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[[-2, 1, 0, -2, 6],\n [-5, -2, 0, -8, 29],\n [-17, 31, 0, -2, -19],\n [-7, 26, 0, 8, -49],\n [21, -33, 0, 6, 7]]?\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, -36, 18, 15, -21],\n [5, 18, -19, 1, 23],\n [12, 12, 22, -12, -28],\n [12, 18, 9, -12, -12],\n [11, 24, -8, -3, 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 5x5 matrix:\n[[24, 0, 19, 14, 4],\n [-25, 5, -31, -26, 13],\n [12, -84, 6, -3, -80],\n [-37, 65, 31, -25, 29],\n [-5, -29, 44, -8, -57]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-18, -21, 3, 4, 46],\n [2, 14, 59, -13, 0],\n [1, -11, 16, -10, 16],\n [-3, 33, 14, 12, -20],\n [10, -32, 31, -31, -26]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-9, 9, 12, -15, 0],\n [-2, 38, 40, 30, -18],\n [2, 30, 24, 30, -16],\n [11, -3, -8, 25, -4],\n [-17, 13, 23, -30, 2]]\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 5x5 matrix:\n[[-35, -2, -37, -1, -40],\n [55, -19, 36, 6, 54],\n [-15, 7, -8, -2, -14],\n [-25, 15, -10, -4, -22],\n [10, -23, -13, 5, 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[[-4, -4, 2, -4, 1],\n [-20, -18, 2, -20, 2],\n [-32, -28, 0, -32, 2],\n [16, 6, 32, 16, 11],\n [4, 0, 14, 4, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-32, -37, 21, -31, 10],\n [-20, -48, 38, -1, 26],\n [-43, 4, -23, 6, 16],\n [0, 47, -49, -25, -26],\n [40, 11, 2, -17, -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[[-23, -9, -25, -14, 4],\n [-31, 14, 31, 22, -12],\n [-10, 3, -6, 0, 0],\n [14, -7, 18, 2, -2],\n [64, -1, -24, -13, 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 5x5 matrix:\n[[-33, 15, -1, 2, -5],\n [4, -16, 1, -6, 34],\n [-30, 20, -10, -5, -20],\n [7, -5, -6, -8, 5],\n [23, 1, 9, 13, -23]]\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, -12, -12, -24, 30],\n [-4, -24, -28, -8, 2],\n [14, -30, -34, -20, 17],\n [48, 3, 6, -24, 36],\n [-44, 2, 0, 24, -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 5x5 matrix:\n[[-37, -1, 4, -6, 30],\n [-25, -3, 14, -6, -1],\n [-5, -14, 38, -49, -48],\n [42, 5, -16, 19, -17],\n [-9, -1, -10, -20, 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[[26, 32, 25, -7, -31],\n [-4, -22, -5, -20, 38],\n [-35, -15, 23, -50, 14],\n [28, -1, 5, -2, 13],\n [15, 1, 0, 39, -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[[24, -37, -41, -1, -12],\n [-6, 22, 38, 4, -6],\n [-1, 3, 19, 4, -18],\n [10, 4, 44, 10, -42],\n [-7, -17, -25, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 18, 4, 3, -27],\n [-38, 28, 13, 20, -33],\n [7, 2, 1, -4, 21],\n [33, -6, -32, -46, 21],\n [39, 12, -11, -33, -27]]\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 5x5 matrix:\n[[20, 24, 12, 24, -24],\n [25, 30, 15, 30, -30],\n [15, 18, 9, 18, -18],\n [-15, -18, -9, -18, 18],\n [15, 18, 9, 18, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0, 0],\n [0, 15, 12, -12, -3],\n [0, 25, 20, -20, -5],\n [0, -10, -8, 8, 2],\n [0, 5, 4, -4, -1]]\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[[1, 12, 0, 27, 1],\n [9, -36, 12, 60, 36],\n [-5, 60, -16, -26, -38],\n [8, -72, 20, 46, 50],\n [-14, -12, 6, -42, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, -10, 50, 4, 36],\n [-16, 62, -55, 50, 0],\n [-47, 6, -20, 29, 2],\n [25, 28, -19, -25, -34],\n [-17, -47, 23, -29, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[18, -30, -24, 30, 24],\n [0, 0, 0, 0, 0],\n [6, -10, -8, 10, 8],\n [18, -30, -24, 30, 24],\n [3, -5, -4, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[5, 6, 6, -1, 1],\n [-5, -6, -6, 1, -1],\n [-5, -6, -6, 1, -1],\n [30, 36, 36, -6, 6],\n [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[[4, 16, -8, -2, 34],\n [-18, -8, -12, -3, 3],\n [1, -4, 4, 1, -11],\n [29, 12, 20, 5, -7],\n [-6, 8, -12, -3, 27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-31, 3, 11, 28, 26],\n [5, 9, 5, -2, 16],\n [-62, -13, 0, 52, 34],\n [5, 56, -4, -7, 12],\n [-9, 25, -8, 7, 29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-10, -16, -1, -19, 6],\n [8, 0, -12, -20, 8],\n [22, 10, -20, -15, 8],\n [-26, 12, 21, -27, 2],\n [2, 42, 18, 23, -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[[6, 9, 9, 6, 6],\n [-10, -15, -15, -10, -10],\n [-12, -18, -18, -12, -12],\n [-8, -12, -12, -8, -8],\n [-10, -15, -15, -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[[-24, -12, -24, -4, 12],\n [-6, -3, -6, -1, 3],\n [6, 3, 6, 1, -3],\n [-36, -18, -36, -6, 18],\n [18, 9, 18, 3, -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[[-30, 10, -30, -25, -25],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [-30, 10, -30, -25, -25],\n [18, -6, 18, 15, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-10, -2, -10, -4, 10],\n [-30, -6, -30, -12, 30],\n [5, 1, 5, 2, -5],\n [5, 1, 5, 2, -5],\n [-15, -3, -15, -6, 15]]\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[[12, 18, 15, 6, -12],\n [20, 30, 25, 10, -20],\n [-12, -18, -15, -6, 12],\n [-24, -36, -30, -12, 24],\n [20, 30, 25, 10, -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 5x5 matrix:\n[[17, -17, 24, 11, -5],\n [-12, 7, 32, -19, -12],\n [-6, 16, 10, 36, -29],\n [23, -32, -24, -2, 23],\n [-17, 39, 44, 23, -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[[12, 9, -12, 3, 18],\n [46, 18, -54, 24, -12],\n [2, 7, -1, -2, 20],\n [8, -5, -8, 5, -10],\n [0, -11, -5, 8, -52]]?\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[[-4, 32, 16, 38, 22],\n [11, 38, 10, 35, 34],\n [-36, -48, 0, -30, -54],\n [12, -12, -12, -21, -3],\n [31, 18, -10, 0, 29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -9, -3, 18, -9],\n [24, 3, -15, -54, 23],\n [-6, 3, 5, 6, -2],\n [-12, 24, 16, -24, 14],\n [36, -36, -36, 0, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[29, -3, -21, 25, -39],\n [59, -35, -60, 0, 19],\n [-29, 9, -9, -11, 29],\n [-74, 45, 24, 2, -12],\n [18, -27, -3, -27, 54]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 26, 6, 36, -26],\n [-12, -12, 12, 8, -4],\n [12, 20, -12, 0, -2],\n [3, 19, -3, 14, -11],\n [6, -26, -6, -36, 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[[-14, -10, 22, 1, 33],\n [-35, -22, 6, 13, 59],\n [-16, -10, 0, 13, 21],\n [-22, -6, 24, 47, 27],\n [11, -8, 8, -38, -8]]\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 5x5 matrix:\n[[-7, -19, 30, 14, 26],\n [3, 17, -30, -13, -22],\n [-4, 7, -27, 4, 10],\n [-18, -8, -6, 8, 24],\n [-7, 6, -21, -3, 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[[15, -25, -20, 30, -5],\n [-12, 20, 16, -24, 4],\n [3, -5, -4, 6, -1],\n [-18, 30, 24, -36, 6],\n [9, -15, -12, 18, -3]]\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[[10, -25, -5, 20, -10],\n [-12, 30, 6, -24, 12],\n [6, -15, -3, 12, -6],\n [10, -25, -5, 20, -10],\n [12, -30, -6, 24, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-24, -4, 4, 16, 24],\n [36, 6, -6, -24, -36],\n [0, 0, 0, 0, 0],\n [12, 2, -2, -8, -12],\n [-24, -4, 4, 16, 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[[-18, 12, -6, 36, -6],\n [0, 0, 0, 0, 0],\n [18, -12, 6, -36, 6],\n [-12, 8, -4, 24, -4],\n [6, -4, 2, -12, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-22, -23, 16, 3, 16],\n [-12, -19, 10, 7, 9],\n [4, 9, -2, -14, -9],\n [4, -8, 0, 7, -4],\n [6, 28, -10, -12, -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[[-13, 6, -7, -17, -13],\n [3, 20, 29, 24, 5],\n [-36, -18, -13, -4, -34],\n [13, -43, -13, 43, -13],\n [-42, -11, 11, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -21, -35, -14, -17],\n [-16, -2, -5, 13, -8],\n [-23, -18, -59, 19, -35],\n [3, -21, -12, -34, 18],\n [34, 19, 6, 0, -3]]\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[[-3, 10, 1, 7, -6],\n [-1, -18, 3, -3, 30],\n [-6, 36, 0, 18, -36],\n [3, 14, -4, -1, -30],\n [-7, 10, 4, 13, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[55, -1, -41, -36, -34],\n [-30, 12, 2, 26, 16],\n [-12, 57, -52, 49, 14],\n [21, 15, -38, -4, -14],\n [-76, 31, -1, 65, 38]]\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 5x5 matrix:\n[[10, 41, 23, 8, -11],\n [27, -1, -1, -34, -36],\n [24, 4, 26, -18, -32],\n [-24, -4, -26, 18, 32],\n [20, 46, 23, -3, -24]]\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[[-22, -26, -40, 39, 40],\n [-10, 30, -14, 24, 14],\n [-20, 0, -34, 39, 34],\n [-14, -22, -26, 24, 26],\n [10, -10, 16, -21, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-47, 33, -54, -24, -36],\n [-28, 13, -43, -2, -27],\n [-26, 19, -19, -10, -15],\n [-44, 25, -61, -12, -39],\n [-45, 27, -54, -12, -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 5x5 matrix:\n[[34, -5, -21, -25, -49],\n [4, -20, 5, -12, -31],\n [12, -30, 25, -22, 25],\n [-6, 0, 2, 4, 0],\n [38, 20, -40, -16, -46]]\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[[8, -2, -1, 11, -25],\n [-27, 6, -33, 27, -13],\n [29, -17, 2, 2, 54],\n [6, 12, 29, -38, 7],\n [15, -18, -18, 24, 38]]\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, 0, 6, -3, 18],\n [44, 0, -27, -24, -41],\n [-4, 0, 4, 13, -4],\n [12, 0, -8, -11, -8],\n [-12, 0, 4, -17, 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 5x5 matrix:\n[[-34, 24, -2, -12, 24],\n [-18, 24, 11, 9, 9],\n [-42, 30, -21, -47, 45],\n [42, -36, 17, 43, -45],\n [40, 6, -2, -10, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 6, 12, 9, -18],\n [0, -10, -20, -15, 30],\n [0, 8, 16, 12, -24],\n [0, 0, 0, 0, 0],\n [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[[0, 5, 0, -5, 5],\n [0, 4, 0, -4, 4],\n [0, 5, 0, -5, 5],\n [0, 1, 0, -1, 1],\n [0, -5, 0, 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[[12, 30, -2, 14, -9],\n [6, -30, 6, -22, 18],\n [-15, 32, -6, 27, -17],\n [-9, 42, -24, 33, -69],\n [24, -12, 4, -18, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[19, 11, 3, -17, 3],\n [16, -12, 4, -16, 8],\n [-5, 6, -8, 23, -31],\n [-12, -18, 6, -24, 48],\n [30, 19, -5, -8, -28]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 21, 9, 2, 32],\n [54, 29, -15, 18, 0],\n [24, -6, -18, 8, -34],\n [-24, -19, 3, -8, -11],\n [-36, -31, 3, -12, -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 5x5 matrix:\n[[-2, 6, -9, -5, -21],\n [-20, -10, -40, 15, 0],\n [14, 22, 16, -18, -9],\n [-2, -16, 9, 4, -19],\n [12, 16, 17, -19, -34]]\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, 3, 3, -50, -31],\n [25, -26, -5, -11, 24],\n [4, -29, 41, -4, -19],\n [-25, 16, 16, 2, -31],\n [0, -13, 22, -1, -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[[15, -18, -12, 0, 18],\n [-20, 24, 16, 0, -24],\n [-30, 36, 24, 0, -36],\n [-25, 30, 20, 0, -30],\n [-15, 18, 12, 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[[-15, 0, 20, -30, 15],\n [18, 0, -24, 36, -18],\n [-6, 0, 8, -12, 6],\n [-12, 0, 16, -24, 12],\n [-6, 0, 8, -12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-24, 10, 16, 12, -4],\n [-12, 12, 10, 12, -4],\n [-24, 31, 22, 30, -10],\n [24, -3, -14, -6, 2],\n [-48, 13, 30, 18, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[10, -20, 26, 12, 0],\n [-38, 22, -27, -7, 18],\n [18, -29, -21, 10, -20],\n [-18, 6, -10, -2, 8],\n [37, 20, -8, -40, -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[[-14, 30, -42, -35, 25],\n [0, -25, 8, 5, -18],\n [-12, -25, 20, 5, -30],\n [-1, -5, 1, 0, -4],\n [-22, 20, -10, -20, 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[[36, -8, 6, -32, -4],\n [-24, 4, -12, 34, 8],\n [-14, 8, 27, -34, -18],\n [-28, 6, -6, 27, 4],\n [-4, 4, 18, -26, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 15, 12, 30, -14],\n [-10, 16, -3, 1, -1],\n [-48, 31, -21, -23, 1],\n [18, 8, 15, 29, -7],\n [37, -61, 22, 24, -15]]\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[[-18, -11, -2, -25, -12],\n [-12, -17, 13, -6, -16],\n [23, 30, -36, -53, 10],\n [-17, -9, -6, -14, -6],\n [-36, 2, -7, 9, 16]]\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, -17, -32, 31, -42],\n [6, 9, -30, 12, 0],\n [3, 6, -30, 7, 1],\n [28, 17, -22, 44, -18],\n [50, -14, -20, 64, -66]]\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[[-9, 3, -4, 18, -9],\n [5, 3, -14, 5, 19],\n [26, 36, 38, -25, 8],\n [11, -9, 16, -18, -9],\n [-5, 21, 4, 42, -19]]?\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[[-61, -8, 23, -2, -19],\n [-36, -10, 0, 16, -12],\n [39, 7, 18, -21, 3],\n [-55, -27, 17, 20, -29],\n [41, -27, 8, -38, 10]]\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 5x5 matrix:\n[[-8, 2, -30, 24, 24],\n [-3, 0, -18, 13, 2],\n [-11, 13, 51, -12, -26],\n [2, 3, 39, -21, -32],\n [5, -7, -33, 9, 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[[4, 12, -10, -8, -6],\n [10, -3, -22, 1, -18],\n [-10, -42, 3, 12, -11],\n [-12, -8, 39, 14, 33],\n [1, 17, 2, -7, 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 5x5 matrix:\n[[-3, 9, 11, -1, 2],\n [-21, 31, -15, -3, -38],\n [-21, 9, -46, -4, -46],\n [-13, -19, -8, -10, 10],\n [20, -44, -56, 8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 6, -6, 18, -18],\n [20, -10, 10, -30, 30],\n [-16, 8, -8, 24, -24],\n [20, -10, 10, -30, 30],\n [-16, 8, -8, 24, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-10, 0, 20, -25, -15],\n [-16, -8, -28, 30, 22],\n [-14, -8, -32, 35, 25],\n [18, 12, 54, -60, -42],\n [-12, 0, 24, -30, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-20, -8, -8, -20, -8],\n [25, 10, 10, 25, 10],\n [-20, -8, -8, -20, -8],\n [-25, -10, -10, -25, -10],\n [-20, -8, -8, -20, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[17, 18, 11, 3, -30],\n [2, 26, -10, 1, -8],\n [11, -20, 5, -16, -16],\n [-1, -8, -25, -28, -1],\n [-7, 34, -1, 23, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[19, 18, 56, -3, 15],\n [-10, -60, -74, -22, -16],\n [11, -48, 14, -13, 13],\n [11, -9, -20, -8, 9],\n [17, 39, 24, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-14, 25, -5, -25, 27],\n [-2, -25, 7, 17, -5],\n [2, -35, 6, 21, -14],\n [-10, 7, -16, -35, 14],\n [10, 37, -17, -31, -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[[-28, 14, 3, 6, 28],\n [-28, 32, -12, -12, 20],\n [1, -40, 3, 35, 26],\n [5, -26, 7, 21, 10],\n [-10, 46, -40, -46, -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[[36, -6, 10, 0, -5],\n [14, 20, 14, -45, -10],\n [10, 19, -26, 27, -29],\n [52, -1, 16, -12, -11],\n [-26, 24, -22, 3, -16]]?\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, 3, 2, 2, -6],\n [0, 12, 8, 8, -24],\n [0, -15, -10, -10, 30],\n [0, 12, 8, 8, -24],\n [0, -18, -12, -12, 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[[5, -10, -28, 24, -23],\n [30, 0, -36, -12, -36],\n [15, 10, 4, -32, -1],\n [-5, 0, 6, 2, 6],\n [-14, -4, 8, 16, 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[[-14, -5, -3, -35, -11],\n [-44, 10, 14, -5, 39],\n [-7, 5, -9, 40, 7],\n [-20, 10, 14, 15, 35],\n [16, 1, -17, 51, -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[[-3, -8, 25, 24, 12],\n [-12, 3, 0, -28, 17],\n [15, -9, 15, 12, -27],\n [-39, -6, 45, -36, 69],\n [15, -2, -5, 20, -25]]\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[[-17, -18, 14, -8, -14],\n [-8, -12, -4, -22, 4],\n [22, 24, -16, 14, 16],\n [2, 0, -8, -10, 8],\n [-13, -18, -2, -28, 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, 16, -8, 4, 24],\n [-6, -24, 12, -6, -36],\n [1, 4, -2, 1, 6],\n [0, 0, 0, 0, 0],\n [-6, -24, 12, -6, -36]]\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 5x5 matrix:\n[[3, 0, -5, 0, -2],\n [18, 0, -30, 0, -12],\n [15, 0, -25, 0, -10],\n [-18, 0, 30, 0, 12],\n [15, 0, -25, 0, -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 5x5 matrix:\n[[-18, -43, -11, -35, -16],\n [48, 73, -8, 24, -6],\n [-13, -8, -28, -25, 18],\n [16, 31, 0, 16, 6],\n [-25, -50, 11, -16, -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[[12, 3, -4, -8, -36],\n [-18, -10, -16, 34, 10],\n [33, 28, 47, -45, 31],\n [-48, -38, -49, 32, -12],\n [9, 5, 5, -9, -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 5x5 matrix:\n[[-9, -3, -18, 34, -17],\n [-60, 27, -41, -13, -25],\n [35, -17, 37, -22, 26],\n [50, -13, 12, -5, 5],\n [12, 17, -38, 27, -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[[0, 20, 25, 15, 0],\n [0, -24, -30, -18, 0],\n [0, -4, -5, -3, 0],\n [0, -20, -25, -15, 0],\n [0, 12, 15, 9, 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[[12, -72, 30, 54, 54],\n [-20, 24, -24, -20, -12],\n [30, -36, 36, 30, 18],\n [-14, -12, -9, 7, 15],\n [2, 36, -8, -26, -30]]\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 5x5 matrix:\n[[8, -11, 3, 17, 23],\n [-3, 4, -1, -6, -9],\n [2, -4, 2, 8, 2],\n [6, -8, 2, 12, 18],\n [7, -11, 4, 19, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-33, 50, -45, 27, 13],\n [-13, -15, -10, -16, -5],\n [24, -94, 70, -24, -28],\n [-6, -8, 3, -9, 11],\n [-24, -36, 38, 21, 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[[0, -18, -12, 0, 6],\n [0, 15, 10, 0, -5],\n [0, -12, -8, 0, 4],\n [0, -9, -6, 0, 3],\n [0, 12, 8, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 18, -24, 30, -12],\n [-5, 15, -20, 25, -10],\n [5, -15, 20, -25, 10],\n [-2, 6, -8, 10, -4],\n [4, -12, 16, -20, 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[[-16, -4, -20, 32, 12],\n [34, -14, -25, 4, -3],\n [-6, 6, 15, -12, -3],\n [24, -9, -15, 0, -3],\n [-24, 4, 0, 16, 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[[-8, 32, 9, 27, 56],\n [-6, 25, -3, 34, 56],\n [-16, 28, -7, 29, 31],\n [-4, -14, -7, -19, -50],\n [20, -42, -25, -5, -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[[0, 0, 25, 30, -15],\n [0, 0, -10, -12, 6],\n [0, 0, -20, -24, 12],\n [0, 0, -25, -30, 15],\n [0, 0, -20, -24, 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[[-30, 18, 18, -24, 12],\n [0, 0, 0, 0, 0],\n [15, -9, -9, 12, -6],\n [30, -18, -18, 24, -12],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[30, 10, -5, -15, -30],\n [-6, -2, 1, 3, 6],\n [6, 2, -1, -3, -6],\n [-6, -2, 1, 3, 6],\n [-36, -12, 6, 18, 36]]\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 5x5 matrix:\n[[16, 4, 12, 10, 11],\n [28, 32, 38, 16, 13],\n [-40, -17, 16, -37, -19],\n [14, 3, -3, 12, 8],\n [10, 18, 3, 9, 1]]\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[[17, 12, -14, -14, -28],\n [18, 54, -24, -24, 30],\n [23, 48, -26, -26, 8],\n [-14, -48, 20, 20, -32],\n [10, -12, -4, -4, -44]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 4, -10, -14, 16],\n [-30, 47, -20, 23, -27],\n [72, -13, -54, -21, 51],\n [18, -5, -16, -17, 25],\n [18, -19, 4, -7, 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[[-3, -9, 12, 18, 18],\n [3, 9, -12, -18, -18],\n [0, 0, 0, 0, 0],\n [-6, -18, 24, 36, 36],\n [-1, -3, 4, 6, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, 44, 12, 2, -31],\n [-28, -4, -12, -22, 41],\n [27, -4, 10, 22, -36],\n [12, -4, 4, 10, -15],\n [3, 44, 10, -2, -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[[-2, -1, -2, 12, -4],\n [60, 33, 40, -25, 14],\n [10, -13, -4, 7, -14],\n [-46, -35, -36, 21, -18],\n [54, 15, 28, -21, 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[[18, 7, 25, 22, 17],\n [6, -3, -15, -2, -19],\n [72, 48, 60, 78, 18],\n [54, 13, 23, 46, -5],\n [54, 33, 51, 60, 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[[3, -24, -60, -48, 0],\n [-4, 12, 6, 4, 0],\n [-39, -48, -27, -6, 0],\n [23, -24, 27, 22, 0],\n [28, 36, 24, 8, 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[[-28, -24, 22, 18, -1],\n [-33, -33, 12, 29, -7],\n [-25, -12, 16, 11, -8],\n [48, 45, -12, -42, 15],\n [17, 14, 12, -19, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 6, 24, -10, -20],\n [-24, 18, 27, 30, 0],\n [5, -9, -24, -1, 14],\n [-4, -6, -27, 14, 24],\n [-8, 6, 9, 10, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-18, 24, -32, -2, 18],\n [-18, -21, -38, 10, 27],\n [21, -5, 34, -21, -1],\n [24, -18, 36, -24, 6],\n [10, -18, 20, 10, -20]]\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 5x5 matrix:\n[[-12, -12, 0, -6, -24],\n [10, 10, 0, 5, 20],\n [4, 4, 0, 2, 8],\n [-6, -6, 0, -3, -12],\n [-10, -10, 0, -5, -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[[0, -2, 6, 0, -5],\n [0, -19, 48, 15, -37],\n [0, 3, 6, -25, -10],\n [0, -11, 30, 5, -24],\n [0, -4, 0, 20, 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[[-12, 24, 0, -20, -16],\n [6, -12, 0, 10, 8],\n [0, 0, 0, 0, 0],\n [-6, 12, 0, -10, -8],\n [6, -12, 0, 10, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[10, -12, -3, -5, 22],\n [6, -8, -4, -4, 8],\n [-19, 32, 31, 21, 18],\n [18, -32, -34, -22, -28],\n [-16, 28, 29, 19, 22]]\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, -24, 0, 18, 36],\n [1, -56, 36, 15, 66],\n [5, -30, 30, 0, 30],\n [6, 4, 12, -12, -12],\n [-5, 0, -12, 9, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, -31, 23, 4, -5],\n [-3, 36, -2, 5, 21],\n [-3, 23, -1, 1, 16],\n [6, -6, 42, 48, -12],\n [-5, -7, 9, -6, 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 5x5 matrix:\n[[-40, -22, -12, 9, 10],\n [-20, -18, -8, 21, 30],\n [-4, -12, -4, 24, 36],\n [-10, -2, -2, -6, -10],\n [-12, 6, 0, -27, -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[[9, -15, 9, -15, 18],\n [-3, 5, -3, 5, -6],\n [9, -15, 9, -15, 18],\n [6, -10, 6, -10, 12],\n [6, -10, 6, -10, 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[[11, 14, 22, -22, 32],\n [-7, -6, -6, 10, -12],\n [-26, -12, 6, 23, -15],\n [2, -4, -14, 5, -13],\n [-4, -8, -16, 12, -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[[15, 20, -5, 30, 10],\n [-18, -24, 6, -36, -12],\n [3, 4, -1, 6, 2],\n [-3, -4, 1, -6, -2],\n [9, 12, -3, 18, 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 5x5 matrix:\n[[-5, 20, -12, -24, -25],\n [24, -12, 22, 25, 11],\n [-27, 3, -24, -15, -8],\n [-22, 25, -24, -39, -23],\n [16, -1, 24, 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[[10, -20, 25, 0, 30],\n [-2, 4, -5, 0, -6],\n [8, -16, 20, 0, 24],\n [10, -20, 25, 0, 30],\n [-2, 4, -5, 0, -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[[0, 30, -32, 44, -27],\n [22, -13, 46, -53, 23],\n [75, 56, 35, -13, 2],\n [42, 13, 50, -49, 8],\n [26, -3, -28, 35, 43]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-27, -9, -22, -6, -21],\n [-16, -6, 32, -8, -28],\n [0, 12, 27, -11, -21],\n [15, 33, 6, 18, -27],\n [-34, -6, -29, -11, -31]]\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[[53, 54, -15, 16, 57],\n [-31, -42, -10, -12, -51],\n [44, 46, -16, 24, 34],\n [-14, -17, -11, 5, -42],\n [17, 53, 41, 69, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, -6, -9, 18, 12],\n [6, -6, -9, 18, 12],\n [10, -10, -15, 30, 20],\n [2, -2, -3, 6, 4],\n [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[[-33, 33, -43, 7, -10],\n [-7, 12, -24, 9, 10],\n [-22, 8, 0, 34, 20],\n [-56, 34, -2, 5, -42],\n [27, -9, -36, 28, 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[[12, 16, 12, 4, 24],\n [15, 20, 15, 5, 30],\n [18, 24, 18, 6, 36],\n [12, 16, 12, 4, 24],\n [15, 20, 15, 5, 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 5x5 matrix:\n[[4, 32, -42, -3, -8],\n [-12, 0, -6, 27, -24],\n [0, -16, 22, -3, 8],\n [3, -12, 18, -9, 12],\n [-2, -8, 10, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[20, 5, -21, 18, 1],\n [-31, 6, 30, -17, 5],\n [-9, 24, -22, -17, 23],\n [35, -15, -7, 41, -20],\n [28, -13, -26, 9, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-28, 66, -32, -16, -48],\n [56, -43, 4, 36, 54],\n [-9, 28, -17, 8, -25],\n [-14, 42, -24, 4, -34],\n [54, 24, -40, 36, 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[[-5, 29, -3, 4, 6],\n [-20, 26, 18, -14, 9],\n [-15, -15, 25, -22, 1],\n [25, -13, -29, 24, -8],\n [0, 30, -10, 10, 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[[0, 0, 0, 0, 0],\n [4, -12, -8, -16, 20],\n [4, -12, -8, -16, 20],\n [-4, 12, 8, 16, -20],\n [-1, 3, 2, 4, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-17, 35, -29, 0, 12],\n [4, 4, 2, -24, -2],\n [16, -16, -9, 26, 11],\n [9, -23, 12, 19, -3],\n [2, 2, -13, 16, 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[[25, -1, -28, 1, -10],\n [-15, 49, 16, 37, -10],\n [-1, 20, 26, -5, 6],\n [9, -14, -20, -2, -4],\n [-11, 21, -12, 35, -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[[25, -2, -19, -27, -9],\n [-6, 25, 12, 15, 44],\n [-2, 25, 12, 8, 12],\n [-20, 5, 20, 7, -22],\n [-53, 44, 64, -14, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 4, 2, 4, -2],\n [0, 0, 0, 0, 0],\n [0, -4, -2, -4, 2],\n [0, 12, 6, 12, -6],\n [0, -8, -4, -8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-29, 12, 7, -36, -7],\n [42, 2, 1, 18, -9],\n [-29, -1, 35, -6, -40],\n [-35, 23, 11, -7, -14],\n [-29, -47, 6, -6, 9]]?\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 5x5 matrix:\n[[-39, 13, 9, 9, -34],\n [30, -2, -10, -6, 24],\n [-24, 9, 37, 42, -25],\n [14, -12, -24, -31, 17],\n [-29, 7, 3, 1, -24]]\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[[-34, 8, 1, -18, 36],\n [-47, 36, 0, -42, 40],\n [-7, -22, -23, -6, 45],\n [16, 0, 18, 20, -40],\n [-28, 18, 9, -16, 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[[-22, 17, 24, 37, 20],\n [19, -46, -39, -20, -28],\n [-29, 28, 21, 14, 18],\n [10, -34, -28, -16, -18],\n [-1, -40, -20, 27, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, 8, -16, 12, 26],\n [37, -10, 20, -42, 8],\n [12, -4, 8, -14, -1],\n [15, -6, 12, -18, -6],\n [-3, -2, 4, 2, -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[[3, 29, 36, 10, -52],\n [25, 2, 24, -45, 18],\n [-25, -5, -30, 40, -2],\n [9, -28, -12, -15, 10],\n [-15, 4, -12, 25, -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[[8, -21, 14, 18, 17],\n [9, -1, -4, 13, 2],\n [-11, 11, 0, -35, -18],\n [-21, 21, -10, -23, -12],\n [16, -21, 20, -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[[-30, 0, 10, 25, -25],\n [6, 0, -2, -5, 5],\n [36, 0, -12, -30, 30],\n [0, 0, 0, 0, 0],\n [-36, 0, 12, 30, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[40, -47, 14, -9, -35],\n [-25, 23, 3, -3, 20],\n [-10, 12, -17, 17, 15],\n [-35, 44, -6, -1, 26],\n [-10, 43, -19, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [-10, 2, -4, 12, 12],\n [20, -4, 8, -24, -24],\n [-15, 3, -6, 18, 18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-30, 36, -36, 12, 12],\n [-20, 24, -24, 8, 8],\n [0, 0, 0, 0, 0],\n [-15, 18, -18, 6, 6],\n [15, -18, 18, -6, -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 5x5 matrix:\n[[42, 15, -20, 32, -25],\n [-7, 14, 18, -20, 17],\n [2, 3, -10, 6, 28],\n [15, -30, 36, 54, -6],\n [-38, -14, 18, -34, 1]]\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, 9, 26, 25, 28],\n [8, -13, -22, -20, -31],\n [5, -7, -14, -13, -18],\n [-7, -10, 24, 27, 1],\n [-2, -8, 8, 10, -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[[-7, 23, -21, -5, 22],\n [-10, 42, -30, 2, 36],\n [6, -22, 18, 2, -20],\n [-4, 18, -12, 2, 15],\n [7, -23, 21, 5, -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[[-31, -1, 3, 14, -71],\n [-38, 20, 33, 45, -16],\n [-37, -28, 36, 80, 37],\n [-8, 0, -15, -13, -14],\n [4, -27, -38, -27, 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[[11, 20, 18, -12, -28],\n [2, -16, -36, 24, 26],\n [-6, -12, -12, 8, 17],\n [-6, 12, 36, -24, -21],\n [-3, 12, 30, -20, -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[[13, -20, 33, -13, -7],\n [-11, 19, -24, 8, 5],\n [-15, 21, -42, 18, 9],\n [16, -26, 38, -14, -8],\n [-16, 35, -21, 1, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[33, 39, 9, -8, -8],\n [-31, -33, -3, 6, 16],\n [28, 36, 12, -8, 0],\n [-5, -15, -15, 5, -20],\n [-9, -3, 9, -1, 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[[-4, 0, -56, 6, -17],\n [-21, -21, 8, 24, 1],\n [-32, 14, 36, 30, 12],\n [-20, 16, -32, 0, -14],\n [14, -62, 10, 34, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[40, 6, -24, 30, -34],\n [-20, -3, 12, -15, 17],\n [10, 11, 1, 15, -9],\n [-32, -1, 22, -21, 27],\n [-4, 7, 8, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-40, 7, 1, 19, 31],\n [-38, 8, 5, -13, -7],\n [24, -3, 3, -39, -51],\n [-48, 10, 6, -14, -6],\n [26, -5, -2, -2, -8]]?\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[[-2, -10, 2, 6, -10],\n [-5, -25, 5, 15, -25],\n [5, 25, -5, -15, 25],\n [4, 20, -4, -12, 20],\n [-3, -15, 3, 9, -15]]\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[[2, -12, 0, -8, 2],\n [-5, 16, 37, 1, 29],\n [43, 33, 21, -22, -26],\n [-5, -17, -13, 2, 4],\n [60, 40, 34, -35, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -1, -5, -4, -5],\n [-12, 13, -31, 12, -27],\n [-8, 22, -34, 28, -28],\n [20, 13, 17, 32, 19],\n [-16, 12, -36, 8, -32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[7, 11, -14, -1, 11],\n [-8, -32, 33, -28, 2],\n [12, 12, -18, -12, 24],\n [9, -3, -3, -27, 27],\n [2, -14, 11, -26, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[65, -64, 31, -12, 29],\n [-24, 48, -6, 9, 18],\n [6, 0, -16, 19, 0],\n [6, -18, 12, -12, 51],\n [31, -30, -5, 14, 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[[19, 12, -6, 3, -1],\n [-54, 36, 19, -11, 28],\n [-29, 48, 27, 45, 22],\n [-16, 12, -2, 62, 4],\n [37, -6, 30, 27, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[30, 36, 12, -18, 0],\n [0, 0, 0, 0, 0],\n [-25, -30, -10, 15, 0],\n [10, 12, 4, -6, 0],\n [-5, -6, -2, 3, 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[[-24, -28, 16, -8, 14],\n [27, 21, 10, 23, -21],\n [-24, -10, -32, -32, 23],\n [0, 18, -48, -24, 9],\n [-6, -22, 44, 18, -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[[-7, 18, -40, 33, -20],\n [15, -7, 30, -31, 3],\n [35, -31, -14, -12, 22],\n [25, -3, -50, 1, -3],\n [31, 6, -20, 11, -26]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-6, -12, -9, -9, -6],\n [-4, 2, -13, -50, -3],\n [-52, -68, -8, -12, -62],\n [-14, -34, 0, 45, -17],\n [-18, -14, 8, -5, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[10, 8, 6, 8, -10],\n [-30, -24, -18, -24, 30],\n [30, 24, 18, 24, -30],\n [-15, -12, -9, -12, 15],\n [20, 16, 12, 16, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[24, 36, -18, -44, -14],\n [-34, -8, -1, 13, -10],\n [-46, -22, 3, 49, -10],\n [-16, 8, -12, 24, -20],\n [16, 38, -26, -6, -28]]\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, -2, 0, 6, -2],\n [0, 0, 0, 0, 0],\n [-30, -6, 0, 18, -6],\n [15, 3, 0, -9, 3],\n [-5, -1, 0, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-13, -8, -11, -8, -15],\n [-20, -28, 24, 44, 7],\n [12, 20, -10, -22, 2],\n [15, 30, -2, -16, 16],\n [79, 14, 30, 10, 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[[-20, 5, -27, -33, -2],\n [20, 35, -48, 54, -9],\n [8, 34, -29, 45, -13],\n [-46, 16, 23, 0, 4],\n [18, 29, -29, 54, -7]]\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 5x5 matrix:\n[[-30, -12, 36, 12, -12],\n [-15, -6, 18, 6, -6],\n [10, 4, -12, -4, 4],\n [-20, -8, 24, 8, -8],\n [-5, -2, 6, 2, -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 5x5 matrix:\n[[-8, -12, -12, 6, -12],\n [-8, -12, -12, 6, -12],\n [12, 18, 18, -9, 18],\n [-4, -6, -6, 3, -6],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[9, -12, -12, -3, -6],\n [3, -4, -4, -1, -2],\n [9, -12, -12, -3, -6],\n [-3, 4, 4, 1, 2],\n [9, -12, -12, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, 20, 14, 24, -30],\n [-12, -18, 0, -24, 36],\n [-33, -1, -6, -7, 7],\n [19, -13, -14, -11, 11],\n [-28, 41, 28, 42, -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 5x5 matrix:\n[[22, 4, -10, 16, 10],\n [2, 16, 18, -40, 6],\n [15, 40, 19, 41, 35],\n [24, 0, -12, 1, 6],\n [19, 48, 31, -9, 35]]\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, 10, -6, 2, -2],\n [5, -1, 9, -1, 5],\n [7, 35, -42, 9, -19],\n [7, 21, -21, 5, -9],\n [4, 30, -39, 8, -18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-44, 25, -25, -24, 5],\n [8, 32, 19, -19, 6],\n [0, -30, -1, 15, -4],\n [-16, 26, -9, -17, 4],\n [4, -44, 1, 23, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[53, -31, 8, -20, -7],\n [27, -15, 0, -12, -3],\n [-24, 18, -24, 0, 6],\n [26, 3, 26, 0, 11],\n [3, 14, 12, 4, 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[[37, 49, -8, 16, 2],\n [-36, -52, 20, -14, -5],\n [-8, -4, 28, -10, -44],\n [20, 34, 3, 5, 8],\n [-32, -42, -3, -13, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[16, -22, -24, 27, -15],\n [-6, 15, 24, -27, 24],\n [-5, -3, -45, 10, -34],\n [-17, 13, 11, -1, -9],\n [-4, -7, 10, 31, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, 1, -32, -35, 42],\n [-17, -29, 14, 10, -31],\n [6, 4, -20, -5, 24],\n [-26, -54, -38, -15, 17],\n [10, 6, -24, 0, 28]]\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, -50, -12, -14, -44],\n [23, 9, 65, -47, 33],\n [-4, -26, -49, 20, -25],\n [9, -37, -54, 18, -39],\n [-28, -33, -22, 5, -32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-11, -4, 0, 1, 7],\n [-3, -8, -10, 39, 25],\n [-19, -39, -26, -18, -19],\n [-39, -69, -39, 7, 10],\n [-17, -49, -36, 13, -1]]?\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[[33, 0, -10, -2, -22],\n [33, 33, 21, 24, 0],\n [36, -15, -25, -14, -34],\n [-23, -17, -9, -12, 4],\n [-29, -20, -10, -14, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-36, 44, 2, -10, -17],\n [-45, 35, 13, -31, -3],\n [-27, 33, 3, -3, -18],\n [12, -16, -4, -10, 21],\n [-6, 6, 0, -6, 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[[-13, 5, 24, 23, -3],\n [16, -6, -30, -27, 4],\n [14, -6, -24, -30, 2],\n [-21, 3, 54, -6, -15],\n [-10, 2, 24, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[7, -52, 30, -28, -28],\n [13, -22, -15, 17, -16],\n [26, -16, -18, -34, 26],\n [5, -12, -6, 12, -12],\n [34, -14, -33, -31, 34]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[15, -15, 12, 18, 0],\n [-25, 25, -20, -30, 0],\n [-10, 10, -8, -12, 0],\n [0, 0, 0, 0, 0],\n [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[[0, -6, 51, 15, -27],\n [-24, 18, 23, 3, -1],\n [-15, -21, 9, -15, -6],\n [12, 22, -17, 11, 11],\n [-35, 35, -5, -5, 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[[-4, 14, 26, 0, 36],\n [4, -18, 12, -16, 2],\n [-28, -4, -25, -16, 45],\n [20, 30, 48, 24, -2],\n [-2, -1, 5, -4, 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[[-11, -26, -4, 29, -6],\n [-9, -6, 4, 21, -4],\n [-10, -4, 34, 19, -21],\n [-19, 54, -30, 42, 37],\n [26, -36, 28, -60, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 29, -11, 32, 22],\n [-48, 16, -52, 40, 32],\n [-46, 4, -38, 22, 24],\n [13, -16, 21, -25, -16],\n [30, -12, 3, -12, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[28, -52, -18, 16, -18],\n [-1, -57, -3, 2, 25],\n [64, -13, 51, -10, 9],\n [3, 9, -12, 14, 6],\n [21, -21, 8, 4, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-14, -25, -24, 16, 21],\n [-12, -10, -16, 8, 10],\n [-6, 15, 0, -6, -9],\n [4, -40, -12, 19, 27],\n [-6, -5, -8, 4, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-18, -9, -6, 18, -9],\n [-46, -20, -4, 36, -12],\n [-30, -6, 24, 0, 18],\n [24, 12, 8, -24, 12],\n [3, -3, -16, 12, -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[[-2, 2, 3, -11, -4],\n [12, 22, 27, 1, 14],\n [9, 12, -13, 23, 5],\n [-5, -22, 16, 2, 9],\n [7, 20, -3, 1, -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[[0, -12, 0, 6, 0],\n [0, -30, 0, 15, 0],\n [0, -6, 0, 3, 0],\n [0, -12, 0, 6, 0],\n [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[[-33, 10, 3, 83, 0],\n [-36, -6, 4, 70, -24],\n [-4, -23, -11, -8, -22],\n [21, 22, 0, 10, -22],\n [-4, -10, -33, 21, 30]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[44, 20, 2, -6, -18],\n [12, -15, 11, -2, -8],\n [26, 65, -21, -16, -7],\n [26, 63, -21, -14, -3],\n [-30, -24, 5, 1, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[18, 6, 0, -33, 3],\n [24, 6, 15, -48, 3],\n [28, 8, 10, -54, 4],\n [6, 0, 15, -15, 0],\n [14, 12, -55, -11, 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 5x5 matrix:\n[[0, 0, 0, 0, 0],\n [18, -15, -12, 0, 18],\n [30, -25, -20, 0, 30],\n [-12, 10, 8, 0, -12],\n [-24, 20, 16, 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[[4, -1, -5, -4, 4],\n [16, -4, -20, -16, 16],\n [-12, 3, 15, 12, -12],\n [-20, 5, 25, 20, -20],\n [-8, 2, 10, 8, -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 5x5 matrix:\n[[18, -12, 18, 0, -9],\n [-30, 20, -30, 0, 15],\n [-30, 20, -30, 0, 15],\n [24, -16, 24, 0, -12],\n [-24, 16, -24, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-40, 30, 6, -18, -2],\n [-30, 5, 16, -8, 23],\n [10, 4, -15, 2, -26],\n [-40, 16, 12, -13, 12],\n [6, 16, -13, -4, -26]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, 10, 12, 2, 2],\n [12, 20, 24, 4, 4],\n [3, 5, 6, 1, 1],\n [15, 25, 30, 5, 5],\n [-18, -30, -36, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[15, -23, 38, 35, -12],\n [-16, -14, 17, -40, 27],\n [7, -23, 27, 3, 4],\n [19, -15, 3, 3, 3],\n [-14, -2, 19, 46, -49]]?\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[[-62, 71, -18, 4, -8],\n [-5, 13, -10, -27, 54],\n [-35, 23, 29, 37, -13],\n [9, -12, -3, 18, -75],\n [-6, -9, 40, 24, 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[[0, 0, 0, 0, 0],\n [16, 4, -24, -4, 16],\n [12, 3, -18, -3, 12],\n [-8, -2, 12, 2, -8],\n [-16, -4, 24, 4, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-40, 1, -35, -21, -9],\n [-17, 1, -35, -13, 5],\n [-5, 26, 28, 38, -38],\n [40, -15, 8, 3, 38],\n [-22, -13, 4, -43, -19]]\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 5x5 matrix:\n[[-4, 4, -6, 6, -5],\n [44, 16, 12, -66, 43],\n [28, 22, -3, -42, 25],\n [24, -4, 18, -36, 26],\n [0, 30, -27, 0, -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 5x5 matrix:\n[[0, -32, -5, 5, -20],\n [28, -8, 25, 31, -40],\n [-17, 6, -15, -19, 25],\n [-34, 12, -30, -38, 50],\n [-11, -30, -15, -7, -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[[-12, -3, 0, 0, -15],\n [-8, -2, 0, 0, -10],\n [8, 2, 0, 0, 10],\n [4, 1, 0, 0, 5],\n [12, 3, 0, 0, 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, -31, -8, 28, -15],\n [20, 28, 8, -24, 16],\n [4, 12, 0, -16, -4],\n [13, 7, 8, 4, 23],\n [13, 7, 8, 4, 23]]?\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, -20, -8, -20],\n [-5, 30, -25, -10, -25],\n [3, -18, 15, 6, 15],\n [-1, 6, -5, -2, -5],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-4, -7, 1, 7, 16],\n [-12, -17, 4, 18, 37],\n [0, -16, -4, 12, 44],\n [20, -9, -16, -2, 41],\n [32, 0, -22, -14, 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 5x5 matrix:\n[[-45, -6, 3, -6, 7],\n [-25, -50, 25, -20, 0],\n [20, -8, 19, -2, -4],\n [30, -24, -23, -4, -7],\n [-28, 52, 12, 14, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-47, 2, -31, -58, 61],\n [-3, 18, -5, 0, -7],\n [0, 0, 0, 0, 0],\n [36, -5, 27, 49, -58],\n [49, 18, 16, 39, -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[[17, 6, 0, -20, 13],\n [21, 0, 6, -36, 21],\n [-6, -12, 8, -8, 2],\n [32, 16, -8, -34, 20],\n [-19, -16, -26, -20, -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[[-21, 12, 30, -21, -3],\n [-8, 8, 8, 16, 4],\n [-7, 6, 8, 7, 2],\n [-7, 4, 10, -7, -1],\n [9, -8, -10, -11, -3]]\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 5x5 matrix:\n[[14, -12, 12, -14, -8],\n [-37, 44, -38, 53, -38],\n [-1, -10, -16, -9, 28],\n [-33, 34, -44, 43, -24],\n [-23, 24, -34, 31, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[20, -24, 4, -28, 4],\n [6, 36, 6, 18, -18],\n [37, 6, 13, -21, -15],\n [-14, 24, -2, 24, -6],\n [8, -24, 0, -20, 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[[-2, 0, 4, 6, 3],\n [-26, 10, -33, -2, -1],\n [0, 4, -34, -32, -16],\n [-44, 12, -14, 36, 18],\n [12, -6, 27, 12, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, -10, -6, -6, 16],\n [14, -10, -42, -42, -18],\n [10, -14, -30, -30, 2],\n [-8, 22, 24, 24, -25],\n [-6, 12, 18, 18, -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[[25, 10, -5, -5, 0],\n [-5, -2, 1, 1, 0],\n [20, 8, -4, -4, 0],\n [-30, -12, 6, 6, 0],\n [-15, -6, 3, 3, 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[[-42, -21, -21, -27, 48],\n [4, 5, -3, -1, -6],\n [-19, -8, -12, -14, 21],\n [-25, -5, -25, -25, 25],\n [9, 6, 2, 4, -11]]?\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, -2, 1, 3, -5],\n [18, -12, 6, 18, -30],\n [12, -8, 4, 12, -20],\n [0, 0, 0, 0, 0],\n [-3, 2, -1, -3, 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[[-6, 22, -28, 9, -11],\n [10, 26, -13, -33, 15],\n [-29, -39, 30, 14, -5],\n [-19, -9, -2, 20, -13],\n [15, -27, 14, 47, -18]]\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[[-11, -14, 0, -30, 53],\n [-32, 4, -33, 3, 38],\n [3, 33, -27, 51, -27],\n [32, -2, 32, 0, -34],\n [45, 3, 37, -1, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-25, 33, -30, -24, -10],\n [-28, -30, 44, 21, 20],\n [41, 9, -42, 6, -26],\n [-17, 30, -50, -48, -26],\n [-24, 33, 8, -12, 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 5x5 matrix:\n[[-18, -7, 0, 15, 12],\n [4, 61, 45, 30, 1],\n [14, 5, -18, -21, 8],\n [-14, -9, 31, 27, -24],\n [0, -11, -8, -6, -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[[18, -28, 30, -4, -24],\n [21, 22, -31, 12, 10],\n [0, -4, -16, 8, 16],\n [3, -50, 27, 0, -6],\n [9, 49, -38, 7, 11]]?\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 5x5 matrix:\n[[-8, -8, 8, 0, 4],\n [-35, -10, 20, -5, -25],\n [-26, -6, 14, -4, -21],\n [-42, -12, 24, -6, -30],\n [20, 10, -14, 2, 7]]\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, 10, -4, 12, -8],\n [25, 25, -10, 30, -20],\n [-5, -5, 2, -6, 4],\n [-15, -15, 6, -18, 12],\n [30, 30, -12, 36, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, -20, 12, -24, -4],\n [-6, -30, 18, -36, -6],\n [-4, -20, 12, -24, -4],\n [-4, -20, 12, -24, -4],\n [2, 10, -6, 12, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-27, 23, 21, 11, 39],\n [-16, 19, 6, -1, 7],\n [-19, 16, 15, 8, 28],\n [-14, 11, 12, 7, 23],\n [-43, 37, 33, 17, 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[[22, 10, -33, 11, 11],\n [-6, 7, 1, 4, -19],\n [31, 24, -7, -1, -22],\n [32, 31, -19, 8, 19],\n [24, 7, -5, -6, -49]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[11, -20, -16, 6, 24],\n [15, 53, -20, 37, -7],\n [4, 3, -4, 1, -1],\n [-10, -33, 4, 5, 31],\n [20, 26, -24, 22, 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[[-6, 12, -4, -10, 6],\n [-6, 12, -4, -10, 6],\n [15, -30, 10, 25, -15],\n [0, 0, 0, 0, 0],\n [6, -12, 4, 10, -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[[-21, 3, -21, 28, -27],\n [-51, -28, -13, -46, -33],\n [-14, -24, 38, 10, 21],\n [-69, -42, 9, -6, -27],\n [25, 12, -1, -12, 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[[-5, -1, -2, 6, -4],\n [20, 4, 8, -24, 16],\n [5, 1, 2, -6, 4],\n [25, 5, 10, -30, 20],\n [-25, -5, -10, 30, -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[[-75, -39, 11, 45, 14],\n [-35, -28, 26, 29, 24],\n [6, 39, -1, -18, -46],\n [9, -23, 31, 12, 41],\n [-3, -8, -22, 0, 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[[-22, -33, -1, -24, -65],\n [-21, -10, -15, 14, -42],\n [-29, -18, 17, -3, -11],\n [-5, 18, -23, 9, -37],\n [-26, -30, 32, 6, 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 5x5 matrix:\n[[2, -6, 2, -10, 2],\n [-5, 15, -5, 25, -5],\n [-1, 3, -1, 5, -1],\n [-1, 3, -1, 5, -1],\n [4, -12, 4, -20, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[15, 6, 2, 28, 29],\n [-86, 29, 24, -59, -45],\n [-34, 56, 44, -60, 9],\n [104, -20, -14, 54, 54],\n [-9, -7, -10, -5, -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 5x5 matrix:\n[[1, -22, -10, 10, 7],\n [16, 20, -10, -31, -41],\n [-18, 36, 52, 22, 38],\n [16, -40, -36, -2, -18],\n [-31, -2, -20, -13, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[24, 18, -12, -57, -10],\n [-8, 26, -4, 3, 38],\n [16, 8, -16, -45, -14],\n [0, -20, -20, -15, -30],\n [-24, -74, -20, 39, -66]]\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, -8, -20, -17, 15],\n [-42, 38, 54, 47, -15],\n [-27, 16, 21, 19, -5],\n [-3, 18, -9, -3, 35],\n [-48, 17, 25, 23, -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[[0, -37, 19, -24, 10],\n [-19, 3, -19, -15, -8],\n [22, 16, 12, 30, 4],\n [-5, -7, -1, -9, 0],\n [33, 24, 18, 45, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-18, 25, -57, 18, -6],\n [-2, -54, 54, 20, 39],\n [-2, -38, -22, 10, 8],\n [19, 34, -25, -23, -31],\n [1, 50, -68, -27, -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[[41, -27, -86, -55, -55],\n [31, -13, -36, -18, -22],\n [19, 7, 38, 41, 29],\n [-3, 9, 28, 9, 11],\n [-30, -6, -24, 0, 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[[8, 32, 32, 16, 34],\n [-13, 32, 4, 3, 29],\n [2, -46, -28, 25, -8],\n [7, -20, -4, -19, -34],\n [-31, 20, -28, -13, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -10, -5, -15, -40],\n [-3, -11, -7, -15, -36],\n [18, 18, 18, 18, 24],\n [12, 10, 11, 9, 8],\n [-21, -13, -17, -9, 4]]\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, -12, 18, 0, -18],\n [0, 20, -30, 0, 30],\n [0, -20, 30, 0, -30],\n [0, 16, -24, 0, 24],\n [0, -4, 6, 0, -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[[0, 0, 0, 0, 0],\n [0, -18, 18, -6, -24],\n [0, 15, -15, 5, 20],\n [0, 0, 0, 0, 0],\n [0, 3, -3, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[26, -34, -10, 27, -40],\n [-104, 19, 7, -75, 61],\n [52, -4, 6, 43, -32],\n [32, 5, -20, 25, -14],\n [-2, 15, -20, 3, 6]]?\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[[15, -13, -3, 17, 12],\n [53, -45, 6, 1, -12],\n [3, 0, 39, 9, -63],\n [27, -19, 25, -3, -58],\n [-29, 23, -1, 9, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[14, -4, 6, 14, 14],\n [-8, -3, 2, -23, -23],\n [-43, -1, -23, 4, 50],\n [48, -10, 47, 3, -24],\n [-23, 22, -24, 22, 23]]\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, 3, -38, -32, -2],\n [-50, -92, 36, 38, -42],\n [-15, -7, -38, -19, -5],\n [-50, -85, 38, 48, -28],\n [5, 10, -52, -37, 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[[-3, -18, -3, -15, 0],\n [5, 30, 5, 25, 0],\n [-2, -12, -2, -10, 0],\n [3, 18, 3, 15, 0],\n [4, 24, 4, 20, 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[[13, 48, 4, 5, -14],\n [-8, 32, 17, 34, -15],\n [-19, 31, 10, 38, -21],\n [-6, 35, 13, 29, -16],\n [-45, -15, -36, 6, -21]]?\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, 0, 18, -10, 63],\n [-12, 30, -23, 50, 18],\n [-8, 1, -29, 33, 15],\n [-28, 20, -21, 26, -19],\n [24, -2, -1, -2, 29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-5, -25, 0, -5, -30],\n [-4, -20, 0, -4, -24],\n [-3, -15, 0, -3, -18],\n [-6, -30, 0, -6, -36],\n [-5, -25, 0, -5, -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 5x5 matrix:\n[[9, -2, -3, -4, 12],\n [43, 12, -40, 13, 15],\n [51, -33, -50, 0, -35],\n [-21, 45, 14, 18, 29],\n [-15, 35, 11, 13, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-10, -15, -20, 15, -8],\n [-10, -18, -13, -4, 20],\n [-30, -6, 2, -14, 20],\n [-55, -42, -41, 12, 14],\n [20, 15, 6, 13, -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 5x5 matrix:\n[[-21, -7, -15, -6, -10],\n [8, -13, -11, -15, 21],\n [-20, -14, -26, 50, -54],\n [0, -14, -16, 2, 1],\n [-14, -28, -40, 54, -50]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[6, -9, 5, 9, -16],\n [-18, -7, -15, 6, -46],\n [6, -14, 14, 21, -24],\n [9, -12, 49, 45, 7],\n [-6, -2, 8, 12, -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 5x5 matrix:\n[[27, -26, 16, 8, 0],\n [-11, 43, 5, -38, 25],\n [-2, 9, 43, 2, -1],\n [-13, 44, 4, -34, 26],\n [30, -21, -28, -1, 19]]\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, -8, 6, -8, 8],\n [-27, -31, 28, -21, 23],\n [-72, -36, 0, -42, 24],\n [0, 5, -13, -6, 1],\n [21, 33, -36, 19, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, 41, 45, 53, -22],\n [20, 17, 21, -1, -7],\n [45, 44, 50, 9, -7],\n [-25, -18, -30, -26, -17],\n [-15, 20, 16, 38, -9]]\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 5x5 matrix:\n[[8, -3, -2, -22, -15],\n [-20, 25, 0, 22, 11],\n [-42, 32, -11, 9, 12],\n [-10, -20, -3, 17, 24],\n [-6, -19, -5, 0, 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, -12, 4, 0, -20],\n [4, 12, -4, 0, 20],\n [-2, -6, 2, 0, -10],\n [1, 3, -1, 0, 5],\n [-4, -12, 4, 0, -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[[-19, -23, 20, -25, -19],\n [13, 13, -12, 19, 9],\n [-2, 14, -8, -14, 22],\n [-2, 1, 0, -5, 3],\n [2, -14, 8, 14, -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[[-3, -5, -1, -3, -4],\n [15, 25, 5, 15, 20],\n [-6, -10, -2, -6, -8],\n [-15, -25, -5, -15, -20],\n [-15, -25, -5, -15, -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[[6, 8, -8, 4, -12],\n [-3, -4, 4, -2, 6],\n [9, 12, -12, 6, -18],\n [-18, -24, 24, -12, 36],\n [3, 4, -4, 2, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-23, -7, 15, -16, -13],\n [7, 17, 8, -23, -8],\n [-35, -9, -10, -3, -26],\n [-3, 9, -27, 6, -15],\n [-14, -15, 30, -11, 5]]?\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 5x5 matrix:\n[[0, 10, 22, 4, -6],\n [-7, -6, 19, -1, -2],\n [-14, -12, 38, -2, -4],\n [5, 20, 21, 7, -8],\n [-5, 0, 23, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[14, -22, -46, 46, -26],\n [-18, -27, 5, 12, 43],\n [-1, 27, 17, -32, -25],\n [17, 38, 0, -2, -32],\n [8, -9, 11, -32, 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 5x5 matrix:\n[[-28, -27, -17, -29, 13],\n [-30, 25, -43, 29, -14],\n [20, 14, 11, 20, -7],\n [40, -34, 18, 18, 14],\n [18, 46, 23, 14, -20]]\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 5x5 matrix:\n[[-4, -3, 13, 16, 17],\n [2, 6, -12, -12, -14],\n [6, -27, 19, 4, 13],\n [-4, 24, -20, -8, -16],\n [-7, 6, 9, 18, 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 5x5 matrix:\n[[-12, -9, -9, -3, 9],\n [-12, -9, -9, -3, 9],\n [4, 3, 3, 1, -3],\n [16, 12, 12, 4, -12],\n [-24, -18, -18, -6, 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[[-12, -12, 30, -6, 6],\n [8, 8, -20, 4, -4],\n [0, 0, 0, 0, 0],\n [6, 6, -15, 3, -3],\n [-6, -6, 15, -3, 3]]\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[[-7, -15, -34, -2, 25],\n [9, 22, 22, -11, -24],\n [-9, -21, -30, 6, 27],\n [1, 5, -18, -14, 5],\n [9, 21, 30, -6, -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[[3, 5, -1, 5, -15],\n [-24, 30, 15, 30, -6],\n [-10, 0, 5, 0, 20],\n [18, -20, -11, -20, 0],\n [24, -20, -14, -20, -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 5x5 matrix:\n[[-52, 42, 2, -6, -54],\n [30, -24, -3, 0, 33],\n [2, -1, -5, -9, 7],\n [-4, 5, -14, -27, 10],\n [40, -32, -4, 0, 44]]\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[[23, -35, 28, -28, 18],\n [2, 7, 1, -21, 62],\n [47, 1, 28, -36, -10],\n [4, 13, -16, 8, -53],\n [3, 9, -2, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, 24, 5, 20, -37],\n [-10, -4, 4, 16, -18],\n [-10, -8, 3, 12, -11],\n [-6, -8, 1, 4, -1],\n [-12, -8, 4, 16, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[20, -25, -20, -30, -10],\n [-8, 10, 8, 12, 4],\n [-8, 10, 8, 12, 4],\n [12, -15, -12, -18, -6],\n [24, -30, -24, -36, -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[[33, -9, 24, -36, 30],\n [-31, 15, -32, 20, -2],\n [-10, -3, 1, 23, -32],\n [-18, 9, -19, 11, 0],\n [10, -6, 12, -4, -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[[24, -30, -40, 41, 23],\n [-6, -13, -39, 29, 13],\n [13, -12, 3, -22, -8],\n [17, 33, -22, 24, 40],\n [-16, 47, 36, -28, -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 5x5 matrix:\n[[6, -6, -15, 15, -18],\n [-10, 10, 25, -25, 30],\n [6, -6, -15, 15, -18],\n [6, -6, -15, 15, -18],\n [4, -4, -10, 10, -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[[5, -24, 12, -19, 30],\n [36, -25, 22, 28, -42],\n [3, 12, -6, 33, -54],\n [-27, -4, -14, 19, -42],\n [-14, -55, 10, 2, -18]]\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 5x5 matrix:\n[[-2, -36, -4, 0, 22],\n [-25, 0, 22, -16, -16],\n [54, 12, -68, 8, 24],\n [30, 18, -36, 4, 6],\n [18, -27, -12, 22, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-31, -35, -28, 38, 47],\n [38, 26, -6, 22, -12],\n [-15, -14, -8, 8, 16],\n [18, 1, 23, 1, -18],\n [0, -20, 25, 5, -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[[1, -8, -20, 30, -57],\n [-3, -15, 4, 15, 17],\n [-11, -30, -12, 44, -11],\n [-8, 5, -16, 1, -28],\n [-38, -22, -24, 22, 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[[-7, 18, 33, -24, 8],\n [21, 15, -81, 57, -9],\n [20, -23, -56, 41, 3],\n [-4, 74, 37, -42, -21],\n [6, 64, 13, -30, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0, 0],\n [6, -30, -24, 6, -24],\n [-1, 5, 4, -1, 4],\n [-5, 25, 20, -5, 20],\n [5, -25, -20, 5, -20]]\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[[-60, 36, 7, -39, 23],\n [-38, 14, -71, -37, 25],\n [12, 22, 9, 5, -41],\n [13, 48, 55, 22, 20],\n [-16, -39, -25, -16, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 27, 13, -8, -6],\n [32, -21, -7, -10, -12],\n [2, 13, -5, 8, -10],\n [36, -40, -26, 6, -14],\n [-12, -6, -15, 21, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 6, -27, -12, -3],\n [-21, 2, 21, 26, 29],\n [5, 0, -6, -6, -6],\n [-4, -12, 30, 0, -18],\n [14, -8, 0, -20, -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[[30, 0, 6, -18, 36],\n [30, 0, 6, -18, 36],\n [-30, 0, -6, 18, -36],\n [-10, 0, -2, 6, -12],\n [5, 0, 1, -3, 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[[-24, 0, -6, -34, 26],\n [60, 51, 14, 19, -38],\n [-12, -8, 27, -14, -10],\n [52, 56, 19, 68, -36],\n [-35, -5, -44, 15, 54]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-20, -20, 15, 20, -5],\n [6, 21, -9, -36, -9],\n [-32, -12, 18, -8, -22],\n [4, -6, 0, 16, 8],\n [-18, 7, 6, -32, -22]]\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[[-28, -73, 0, 14, -38],\n [-10, 9, 30, -21, 20],\n [27, 16, -68, 8, -27],\n [-18, 9, 44, -37, 28],\n [-1, -45, 14, 30, 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[[-1, 0, -3, -12, -4],\n [4, 16, 24, -4, -16],\n [-3, -8, -33, -28, -8],\n [-6, -12, 6, 0, 22],\n [8, 28, 30, -10, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-32, -14, -6, -16, 11],\n [-9, -6, -47, -26, -13],\n [-4, 2, -34, -40, -32],\n [-27, -12, 17, 2, 22],\n [17, 14, 23, -6, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-16, 0, 12, -20, 4],\n [0, 8, -14, 6, -6],\n [2, 18, -33, 16, -14],\n [-4, 0, 3, -5, 1],\n [10, 6, -18, 17, -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[[32, -6, -34, -4, 10],\n [9, 21, -2, -19, -2],\n [33, 0, -33, -9, 9],\n [-19, 18, 25, -9, -9],\n [21, -39, -34, 25, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[30, -29, -31, 19, 18],\n [-12, 11, 13, -4, -6],\n [6, -8, -4, 17, 8],\n [-24, 22, 26, -8, -12],\n [36, -40, -32, 54, 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 5x5 matrix:\n[[-4, -9, -15, 16, 56],\n [-2, 10, 4, -6, -42],\n [-6, -17, -5, 3, -30],\n [-13, -4, 7, 2, -17],\n [-11, -15, -6, 14, 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[[22, -2, -2, 36, 42],\n [0, -27, 3, -27, 15],\n [15, -30, 48, 19, 33],\n [-11, -8, -10, -33, -13],\n [-8, -23, 63, -7, -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[[-24, -12, 24, 20, 20],\n [18, 9, -18, -15, -15],\n [-30, -15, 30, 25, 25],\n [36, 18, -36, -30, -30],\n [24, 12, -24, -20, -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[[-13, -7, -14, 6, -28],\n [-8, -12, 16, -4, 32],\n [-11, -9, -2, 2, -4],\n [-45, -40, 2, 5, 4],\n [38, 32, 4, -6, 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[[-8, -12, -20, -24, 20],\n [-6, -9, -15, -18, 15],\n [-2, -3, -5, -6, 5],\n [10, 15, 25, 30, -25],\n [-12, -18, -30, -36, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, -4, 16, 0, -8],\n [0, 0, 0, 0, 0],\n [-3, -3, 12, 0, -6],\n [4, 4, -16, 0, 8],\n [6, 6, -24, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[38, -37, -21, -10, 34],\n [-18, -31, 13, -19, 3],\n [42, 15, 7, -4, 28],\n [18, -40, 14, -21, 29],\n [-19, 7, -10, -4, -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[[-15, -5, -25, -25, -5],\n [-6, -6, -9, -8, -4],\n [0, -20, 5, 10, -10],\n [27, 21, 42, 39, 15],\n [-24, -16, -38, -36, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-11, 17, 37, 5, -25],\n [15, -59, -6, 30, 37],\n [-22, -20, -2, 32, -26],\n [2, -57, -6, 39, 18],\n [22, -13, -25, -14, 38]]\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, 15, -6, 36, 6],\n [-24, 16, -4, 12, 8],\n [-42, 26, -2, -30, 16],\n [55, -35, 5, 15, -20],\n [-30, 20, -5, 15, 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 5x5 matrix:\n[[1, 1, 43, 2, -35],\n [-21, -3, -33, 0, 27],\n [-31, -1, -61, -5, 47],\n [5, -7, -9, 8, 13],\n [34, 4, 12, -2, -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[[13, 43, 22, 17, -22],\n [-18, -2, 28, -16, 14],\n [-69, -22, 56, -49, 26],\n [31, 45, 5, 33, -51],\n [5, -14, -10, 1, -8]]\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[[-31, -11, -4, 1, 30],\n [-19, 0, -6, -4, 12],\n [-25, -15, 0, 5, 30],\n [-27, -1, -8, -5, 18],\n [-43, -3, -12, -7, 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[[-9, 17, -37, -34, 58],\n [-6, -12, 39, 3, -21],\n [-45, -34, 11, -16, -11],\n [-15, -1, 5, -22, 22],\n [-3, 12, -48, -15, 36]]\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[[17, 22, -13, 6, -6],\n [-13, -18, -8, 21, -13],\n [24, 6, 41, 16, -31],\n [37, 32, 18, -30, -1],\n [-2, -4, 22, 4, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[32, 11, -6, 1, -26],\n [0, -15, -2, -13, 2],\n [12, -9, -4, -11, -8],\n [-30, -30, 3, -18, 27],\n [20, 35, 0, 25, -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[[-22, 20, 20, 5, -27],\n [0, -4, -26, -23, 23],\n [-23, 16, -11, -23, 0],\n [-25, 16, -21, -33, 8],\n [-6, 0, -30, -30, 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 5x5 matrix:\n[[2, -6, 47, -17, -62],\n [-3, -17, -4, 22, -2],\n [7, -18, 29, 3, -48],\n [-74, -14, 38, 10, -68],\n [6, -1, 44, -20, -50]]\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, 0, 0, 0, 0],\n [6, 6, 4, 2, -8],\n [-3, -3, -2, -1, 4],\n [-12, -12, -8, -4, 16],\n [-9, -9, -6, -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[[0, 3, 7, -4, -3],\n [-8, -34, -35, 27, 35],\n [1, 8, 12, -5, -7],\n [2, 13, 18, -9, -12],\n [0, -3, -9, 10, 5]]\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 5x5 matrix:\n[[-20, 30, -20, -30, -5],\n [16, -24, 16, 24, 4],\n [4, -6, 4, 6, 1],\n [8, -12, 8, 12, 2],\n [-8, 12, -8, -12, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-21, 15, 30, -42, 3],\n [2, -4, -14, 20, 0],\n [30, -6, 24, -36, -6],\n [-12, 6, 6, -8, 2],\n [-4, -1, -11, 16, 1]]\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[[5, 21, -32, 34, -59],\n [6, -25, -9, -15, 3],\n [7, -31, 7, -38, 69],\n [-31, 32, -15, 21, -12],\n [5, 51, -21, 60, -89]]?\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[[18, 6, -15, 9, 6],\n [36, 12, -30, 18, 12],\n [-6, -2, 5, -3, -2],\n [18, 6, -15, 9, 6],\n [-24, -8, 20, -12, -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[[-17, -29, -3, 6, -1],\n [-25, -24, -4, 0, -8],\n [-12, -25, -3, 6, 1],\n [-48, -2, -38, -36, -26],\n [6, 21, -21, -18, 0]]?\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[[2, -5, 3, 2, 4],\n [-20, -14, -22, -4, 16],\n [6, -15, 9, 6, 12],\n [4, 6, 4, 0, -6],\n [22, 1, 26, 8, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-58, -11, 35, 41, 6],\n [11, -6, -42, 16, 23],\n [47, 0, -50, -23, 9],\n [-7, 22, 22, 14, -7],\n [28, -2, -34, -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[[4, -23, 32, -52, 41],\n [17, -19, -27, -19, 15],\n [-23, 16, 52, -18, 31],\n [-7, -48, 14, -14, -5],\n [12, -3, -18, 4, -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[[-18, 18, 9, 12, -9],\n [6, -6, -3, -4, 3],\n [6, -6, -3, -4, 3],\n [6, -6, -3, -4, 3],\n [-12, 12, 6, 8, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 18, -15, -15, -6],\n [0, 24, -20, -20, -8],\n [0, -30, 25, 25, 10],\n [0, -12, 10, 10, 4],\n [0, 36, -30, -30, -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[[-26, -11, 39, 4, -5],\n [24, 12, -36, 0, 12],\n [8, 11, -12, 14, 32],\n [-14, -5, 21, 4, 1],\n [6, -6, -9, -18, -33]]\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[[-16, -10, 0, -12, -4],\n [7, -5, 25, -6, 28],\n [21, 30, -45, 36, -42],\n [-38, -20, -10, -24, -20],\n [18, 15, -10, 18, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1, -31, -26, 11, 17],\n [14, -14, -6, 16, -6],\n [1, -5, 2, 19, 11],\n [-2, 14, -14, 61, 20],\n [18, -14, -8, -51, -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 5x5 matrix:\n[[41, -3, -12, 14, -3],\n [12, 4, 0, 8, -4],\n [-4, -3, -18, -25, 1],\n [-3, -1, 24, 28, 3],\n [-20, -5, 18, 9, 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[[-5, -30, -10, -20, -20],\n [1, 6, 2, 4, 4],\n [0, 0, 0, 0, 0],\n [6, 36, 12, 24, 24],\n [-1, -6, -2, -4, -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[[3, -15, 9, 3, -12],\n [2, -10, 6, 2, -8],\n [0, 0, 0, 0, 0],\n [6, -30, 18, 6, -24],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-3, 12, -12, 2, -22],\n [-30, 0, -27, -32, -10],\n [-68, 40, -57, -20, -34],\n [-43, 44, -45, 1, -45],\n [-56, 16, -45, -35, -17]]\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, -24, -12, -8, 40],\n [-10, -12, -6, -4, 20],\n [-34, -24, -18, 0, 36],\n [-23, 6, -9, 18, -18],\n [31, 12, 15, -8, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -6, 2, -12, -10],\n [4, -6, 2, -12, -10],\n [8, -12, 4, -24, -20],\n [-2, 3, -1, 6, 5],\n [8, -12, 4, -24, -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 5x5 matrix:\n[[5, 30, 10, -10, 30],\n [5, 30, 10, -10, 30],\n [-6, -36, -12, 12, -36],\n [-3, -18, -6, 6, -18],\n [-2, -12, -4, 4, -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[[-14, -50, 4, 46, 18],\n [-12, 19, 33, -22, 45],\n [-6, 43, 0, -34, 6],\n [-22, 32, 29, -28, 51],\n [-2, -18, -32, 26, -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 5x5 matrix:\n[[60, 1, 41, 28, -6],\n [-41, -26, -12, -15, 1],\n [-35, -21, -11, -13, 1],\n [20, -16, 24, 12, -4],\n [24, 20, 4, 8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, -30, 5, 18, 10],\n [-26, -3, -49, 32, -32],\n [34, -33, 25, 7, 30],\n [-5, -27, -8, 21, -14],\n [21, -11, -2, 6, 4]]\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, 8, -4, 6, -12],\n [-5, 4, -2, 3, -6],\n [-25, 20, -10, 15, -30],\n [-30, 24, -12, 18, -36],\n [20, -16, 8, -12, 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[[36, 10, -45, -5, -24],\n [36, 8, 8, -8, -28],\n [58, 21, -13, -3, -38],\n [-72, -25, 15, 5, 48],\n [-56, -4, 22, 22, 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 5x5 matrix:\n[[-20, 18, -24, 52, -26],\n [15, -9, -3, -6, -12],\n [4, -3, 2, -6, 1],\n [-20, 15, -10, 30, -5],\n [11, -12, 23, -44, 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[[-4, -3, 5, -38, 18],\n [8, 3, 20, 21, -26],\n [0, 6, -15, 35, -10],\n [-2, -33, -20, -34, 39],\n [8, -24, 29, -39, 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[[-20, -2, -48, -2, 68],\n [5, 18, -24, -11, 38],\n [25, 20, 18, 27, 20],\n [-35, -41, -6, 16, -6],\n [25, 22, 21, -17, -33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, -3, -3, 0, 1],\n [-6, 18, 18, 0, -6],\n [3, -9, -9, 0, 3],\n [-2, 6, 6, 0, -2],\n [6, -18, -18, 0, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0, 0],\n [0, 6, -6, -6, -12],\n [0, 0, 0, 0, 0],\n [0, -18, 18, 18, 36],\n [0, 18, -18, -18, -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[[-12, 10, 6, -10, 2],\n [18, -15, -9, 15, -3],\n [18, -15, -9, 15, -3],\n [-30, 25, 15, -25, 5],\n [-24, 20, 12, -20, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-31, -44, -6, 17, -5],\n [-14, -28, 25, -26, 14],\n [-49, -76, 1, 31, -7],\n [6, 9, 45, -9, 3],\n [21, 64, -26, 17, -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[[21, 6, -54, 0, -33],\n [22, -13, -18, 18, -32],\n [0, 15, -30, -14, -2],\n [1, -19, 36, 18, 1],\n [-20, 20, 0, -24, 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[[-20, -8, 20, -4, 4],\n [0, 0, 0, 0, 0],\n [25, 10, -25, 5, -5],\n [25, 10, -25, 5, -5],\n [-30, -12, 30, -6, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-10, -10, 4, 12, 4],\n [20, 20, -8, -24, -8],\n [5, 5, -2, -6, -2],\n [20, 20, -8, -24, -8],\n [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[[38, 1, 1, 36, -49],\n [13, -9, -35, 25, -43],\n [14, -1, 17, 8, -17],\n [5, -5, -11, 9, -19],\n [6, -5, -5, 8, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[42, 63, -11, -2, 10],\n [-4, 6, -6, -52, 26],\n [22, 1, -15, 23, -42],\n [38, 37, -9, 42, -24],\n [12, 36, 10, -2, -20]]\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, -13, -39, 24, 41],\n [21, 0, 16, -16, -29],\n [-16, -27, -17, -46, 9],\n [-12, 4, 0, 24, 7],\n [-25, -15, 15, -14, 3]]\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[[3, 2, -2, -1, 19],\n [2, 34, -36, 11, -6],\n [-31, -24, 50, 8, -41],\n [28, -6, 20, 35, 26],\n [18, 6, -16, 1, 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[[56, 10, 42, 94, -30],\n [-14, 33, -18, -9, 8],\n [-15, -34, -36, -58, 46],\n [-7, -32, 7, -23, 1],\n [-7, -10, 16, -4, -18]]\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[[14, 2, 3, 10, -2],\n [-7, 1, -9, -16, -8],\n [-44, -4, -18, -44, -4],\n [-5, -1, 0, -2, 2],\n [-1, 3, -12, -18, -14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, 27, 24, 15, 9],\n [-4, -20, -8, -8, -24],\n [11, -21, -26, -14, 6],\n [13, 8, -10, -1, 33],\n [19, 0, -22, -7, 39]]\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[[2, -2, 10, 10, -6],\n [-3, 3, -15, -15, 9],\n [1, -1, 5, 5, -3],\n [4, -4, 20, 20, -12],\n [5, -5, 25, 25, -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[[38, -50, 18, 22, -20],\n [22, -10, -14, 20, 56],\n [42, -16, -1, -1, -16],\n [-23, 21, -8, -2, 34],\n [24, -40, 23, 6, -66]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[35, 14, -3, -34, 13],\n [-7, -7, 3, -1, 1],\n [38, 20, -6, -28, 10],\n [-16, -4, 0, 20, -8],\n [20, 12, -4, -12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[26, 33, 30, 22, -7],\n [-10, 3, -5, -15, 4],\n [-18, -45, -30, -6, 3],\n [36, 18, 30, 42, -12],\n [-18, 3, -10, -26, 7]]\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[[27, -59, -51, 18, -42],\n [-13, -23, -35, 2, -14],\n [-32, 45, 25, -49, 48],\n [-31, -2, -21, 0, -1],\n [-2, 18, 13, -37, 27]]?\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, 22, -18, 6, -56],\n [-25, -3, 11, -19, -39],\n [19, 3, 7, -11, 3],\n [-34, -7, -14, 24, 5],\n [30, 19, -18, 12, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-18, -6, 6, 24, 18],\n [-15, -5, 5, 20, 15],\n [0, 0, 0, 0, 0],\n [-6, -2, 2, 8, 6],\n [9, 3, -3, -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 5x5 matrix:\n[[1, 12, -7, 15, 39],\n [-15, -26, -9, 11, -27],\n [9, 9, 16, -27, -18],\n [14, 4, 5, -10, -15],\n [-1, -22, -4, 1, -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[[-3, 40, -49, 12, 19],\n [-7, -27, 42, -11, -23],\n [-46, 21, -19, 17, -8],\n [-3, -38, 40, -5, -14],\n [35, -22, 15, -10, 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 5x5 matrix:\n[[-8, 60, 8, -6, 20],\n [14, -45, -14, 3, -5],\n [4, 26, -4, -4, 18],\n [-12, 50, 12, -4, 10],\n [18, -3, -18, -3, 21]]\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, 12, 2, -8, -4],\n [8, -21, -7, 7, 14],\n [14, 38, 4, -30, -8],\n [9, 31, 4, -23, -8],\n [25, 35, 0, -35, 0]]\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, 2, -22, -18, -15],\n [40, 36, -24, -42, 7],\n [-6, 32, 30, -22, 10],\n [-43, -82, -10, 96, 8],\n [12, -36, -40, 22, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, -3, 3, -18, 0],\n [15, 15, 25, 0, 0],\n [16, 22, 42, -12, 0],\n [15, 24, 48, -18, 0],\n [20, 14, 18, 12, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[2, 10, 8, -6, 4],\n [-6, -42, -40, 14, -4],\n [-2, -4, 0, 8, -8],\n [-5, -34, -32, 12, -4],\n [-6, -24, -16, 20, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[17, 15, -5, 16, 8],\n [21, -17, -30, 36, 8],\n [-8, 4, 17, -20, -8],\n [4, 18, -4, 10, 11],\n [-20, 24, 32, -36, -6]]\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, -30, -7, 34, 0],\n [47, -32, 7, -10, 60],\n [18, -36, 3, 42, -18],\n [56, -43, 23, 8, 23],\n [-68, 76, 4, -76, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-10, -20, 37, -24, -35],\n [18, -28, 19, -24, -5],\n [3, -5, 8, -3, -13],\n [-13, 34, -38, 30, 34],\n [17, -8, 4, 0, -14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-25, 14, -8, 34, -24],\n [-27, -58, -17, 6, 50],\n [-57, 3, 1, 40, -36],\n [-28, -18, -52, 48, -4],\n [1, 11, -6, 28, 18]]?\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, -24, 36, -6, -6],\n [4, -16, 24, -4, -4],\n [-5, 20, -30, 5, 5],\n [2, -8, 12, -2, -2],\n [-4, 16, -24, 4, 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[[-26, -15, 5, 5, -20],\n [-2, -15, -34, -16, 1],\n [10, -29, -12, 2, 21],\n [52, -22, 31, 29, 65],\n [42, -17, 45, 35, 54]]\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, 0, 0, 0, 0],\n [18, 9, 15, 6, -18],\n [-12, -6, -10, -4, 12],\n [-36, -18, -30, -12, 36],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[31, 12, -4, -36, 15],\n [-20, 10, -40, -30, -15],\n [32, 4, 16, -12, 18],\n [-19, 12, -44, -36, -15],\n [15, -10, 36, 30, 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[[-4, -1, -2, 54, 28],\n [25, -12, 23, 26, 48],\n [-3, 40, 10, -47, -31],\n [41, -10, 23, 26, 30],\n [-14, 34, -4, -18, -31]]?\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, 4, 10, -2, 6],\n [0, -2, -5, 1, -3],\n [0, -2, -5, 1, -3],\n [0, 4, 10, -2, 6],\n [0, -2, -5, 1, -3]]?\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[[-12, 43, -15, -14, 1],\n [-9, 34, -45, -26, 30],\n [5, 23, 36, 12, -29],\n [17, 49, -57, -28, -15],\n [50, -22, -12, 0, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[18, -9, -15, -9, -15],\n [-12, 6, 10, 6, 10],\n [-54, 36, 30, 6, 54],\n [-42, 30, 20, 0, 44],\n [-42, 27, 25, 7, 41]]\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, 7, 12, -24, -5],\n [11, 25, 20, -33, -32],\n [-12, -28, -20, 30, 34],\n [0, 25, 20, -30, -25],\n [44, 32, 8, 0, -48]]\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, 5, 30, 15, 0],\n [3, 1, 6, 3, 0],\n [-3, -1, -6, -3, 0],\n [9, 3, 18, 9, 0],\n [6, 2, 12, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-36, -6, 18, 24, -36],\n [7, 2, -6, 42, -3],\n [-3, -1, 3, -26, 3],\n [21, 3, -9, -42, 27],\n [8, 2, -6, 32, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, -3, -5, 5],\n [0, 0, -18, -30, 30],\n [0, 0, -9, -15, 15],\n [0, 0, 0, 0, 0],\n [0, 0, -15, -25, 25]]?\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, -2, -19, -24, -8],\n [-19, 4, 17, 21, 7],\n [16, -10, -18, -21, -7],\n [-7, 10, 11, 12, 4],\n [-12, -24, -4, 0, 0]]?\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, 16, -17, -6, 3],\n [-13, 1, -11, -17, 10],\n [15, -35, -5, -21, 16],\n [-45, 45, -45, -9, 4],\n [10, -10, -34, 2, 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[[31, -15, -21, 9, 26],\n [0, 45, 33, -53, 23],\n [-1, -19, -37, 12, 8],\n [16, 22, 10, -13, 20],\n [-1, 35, -55, -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[[-61, -41, -52, -21, -10],\n [0, 6, 8, 20, -24],\n [-36, 12, 24, 42, -36],\n [16, 11, -12, 14, -50],\n [9, -8, -12, -12, 6]]?\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 5x5 matrix:\n[[28, 26, 20, -12, 40],\n [-10, 25, -20, 30, 20],\n [-12, 30, -24, 36, 24],\n [-36, -6, -36, 36, -24],\n [-28, -26, -20, 12, -40]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-52, 26, 10, 26, -26],\n [-22, -25, 7, 47, 7],\n [6, -27, 3, 15, 18],\n [24, 2, -8, -20, 2],\n [-6, 43, -5, -29, -27]]\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[[3, -4, -1, -2, 3],\n [12, -16, -4, -8, 12],\n [-12, 16, 4, 8, -12],\n [-9, 12, 3, 6, -9],\n [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[[-6, -9, 1, 8, 18],\n [-6, -29, 25, -3, 25],\n [6, 18, 20, -33, -17],\n [30, 0, -6, -1, 7],\n [28, -8, 4, -7, -3]]\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, -1, 7, -16, -44],\n [26, -3, -9, 8, -18],\n [-18, 9, -3, 15, 15],\n [12, 14, 12, -5, -15],\n [7, 16, -12, 33, -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[[-1, 9, -11, -7, 17],\n [-8, 14, 50, -24, -21],\n [1, 4, 24, -12, -8],\n [-4, 7, -1, -5, 5],\n [-7, 12, 56, -24, -26]]\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[[22, 64, -6, 8, 22],\n [-25, -25, 60, -38, -8],\n [-7, 40, 52, -18, 3],\n [28, 22, 12, -19, 2],\n [-14, -15, 28, -17, -5]]\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[[18, 66, 0, 18, -12],\n [-9, -8, 20, 21, -19],\n [-18, -11, 44, 48, -43],\n [12, 14, -24, -24, 22],\n [-6, -32, -8, -18, 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 5x5 matrix:\n[[-25, -5, 8, -16, 1],\n [15, 5, -28, 24, -55],\n [42, 13, 16, 17, 52],\n [48, 15, 13, 28, 58],\n [-15, 4, 3, 8, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-39, 12, 15, -6, 33],\n [-44, -73, 32, -30, 16],\n [-12, -42, 14, 24, -14],\n [-13, -48, 34, -22, -9],\n [-61, -22, -33, -2, 65]]?\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[[30, -6, 12, -24, -6],\n [25, -5, 10, -20, -5],\n [-20, 4, -8, 16, 4],\n [25, -5, 10, -20, -5],\n [10, -2, 4, -8, -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[[21, -21, -18, 9, 0],\n [-16, 17, 12, -12, 4],\n [0, -7, 12, 36, -28],\n [-18, 13, 24, 18, -20],\n [15, -12, -18, -9, 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[[-11, 18, -8, 13, 22],\n [40, -14, 55, 25, 9],\n [10, -2, 28, -36, -22],\n [8, 2, 5, -28, -45],\n [5, -18, 7, -9, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[16, -30, 8, 28, 12],\n [-29, -24, -5, -8, 2],\n [15, -24, 7, 24, 10],\n [-2, 12, -2, -8, -4],\n [-5, -3, -1, -2, 0]]\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, -16, 12, -16, -16],\n [-30, 20, -15, 20, 20],\n [-18, 12, -9, 12, 12],\n [6, -4, 3, -4, -4],\n [-24, 16, -12, 16, 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 5x5 matrix:\n[[4, 4, -12, -10, 2],\n [-18, -24, -6, -21, 15],\n [-16, -22, -12, -26, 16],\n [-8, -9, 14, 9, 0],\n [-20, -24, 20, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 16, -42, 38, 13],\n [-3, -15, 67, -38, -10],\n [1, 28, 41, -38, -41],\n [16, 3, 16, 2, 2],\n [-24, -49, -12, 14, 40]]\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, -14, 13, -2, 13],\n [-2, 7, -34, -19, 1],\n [20, 5, 15, 15, -10],\n [-22, -7, -10, -13, 11],\n [10, -2, 27, 18, -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[[9, 3, -19, -40, 4],\n [-6, -10, 16, 31, 14],\n [-17, -17, 29, 59, -4],\n [-23, -45, 25, 46, 0],\n [-10, -48, 0, -9, 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[[31, 8, -63, 7, 44],\n [57, 6, -51, 29, 23],\n [51, -12, -33, 37, 11],\n [-47, 23, 9, -14, 17],\n [19, 16, -24, -7, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[28, -7, -9, -9, -4],\n [-25, 25, 4, 13, -7],\n [-26, 11, 8, 24, 5],\n [-10, -8, -4, 12, 10],\n [-41, 5, 6, 29, 13]]\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, 30, -6, -3, 32],\n [-28, 27, 36, -5, 15],\n [-24, 9, 36, -3, -3],\n [39, -27, -54, 6, -9],\n [30, -36, -36, 6, -24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-19, -11, -24, -1, 46],\n [5, 5, -21, -10, 44],\n [31, 24, 22, -43, -30],\n [8, 8, -37, 15, 46],\n [3, 5, 0, -6, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 16, 3, -10, 1],\n [13, 11, 29, -3, 19],\n [25, -45, 3, 21, 29],\n [-4, 60, 29, -31, 5],\n [-32, 16, -47, -15, -39]]\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, -5, -25, 25, 43],\n [-4, -15, -19, 5, 17],\n [-3, 5, -11, 20, 29],\n [1, 10, 6, 5, 2],\n [-3, 0, -12, 15, 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 5x5 matrix:\n[[15, 15, 20, 30, 10],\n [12, 12, 16, 24, 8],\n [-12, -12, -16, -24, -8],\n [15, 15, 20, 30, 10],\n [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[[-10, 5, -25, 25, -10],\n [12, -6, 30, -30, 12],\n [-10, 5, -25, 25, -10],\n [8, -4, 20, -20, 8],\n [12, -6, 30, -30, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -4, 9, 4, 29],\n [-8, 12, -7, -12, -11],\n [-34, 44, -14, -44, 4],\n [-13, 18, -8, -18, -7],\n [-19, 26, -11, -26, -8]]\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, 12, -12, -8, 8],\n [6, 3, -3, -2, 2],\n [30, 15, -15, -10, 10],\n [6, 3, -3, -2, 2],\n [24, 12, -12, -8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-5, 5, 5, 0, 20],\n [6, -6, -6, 0, -24],\n [-5, 5, 5, 0, 20],\n [2, -2, -2, 0, -8],\n [2, -2, -2, 0, -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 5x5 matrix:\n[[-25, 25, 0, -30, 25],\n [0, 0, 0, 0, 0],\n [5, -5, 0, 6, -5],\n [0, 0, 0, 0, 0],\n [20, -20, 0, 24, -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[[-31, -51, 31, -18, 14],\n [7, 35, -29, 13, 17],\n [0, 35, -35, 10, 40],\n [-4, 30, -32, 9, 41],\n [-2, 22, -24, 5, 33]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-13, -18, 17, 11, 9],\n [-1, -18, 11, 5, -9],\n [-6, -24, 17, 9, -5],\n [16, 36, -29, -17, -3],\n [18, 12, -16, -12, -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[[14, -34, 20, 10, 12],\n [-34, 14, -20, 50, -12],\n [4, -8, 5, 1, 3],\n [2, 2, 0, -6, 0],\n [18, 6, 5, -41, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -27, -17, 16, -7],\n [0, 5, 11, -22, -1],\n [-22, 21, 11, 11, -2],\n [24, 8, -10, 6, 18],\n [10, 20, 0, 5, 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[[-30, 12, 0, 1, 2],\n [18, 12, 24, 31, -22],\n [12, 0, 24, 16, -22],\n [0, 16, 32, 32, -28],\n [8, -16, -28, -27, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-21, 4, -6, 42, -14],\n [17, 19, -6, -26, -11],\n [27, 29, -16, -39, -18],\n [-32, -28, 12, 50, 14],\n [34, 34, -6, -55, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[18, -5, -14, 5, -6],\n [12, 14, -28, 34, -6],\n [-19, -22, 50, -17, -34],\n [50, 9, -66, 39, -1],\n [34, 4, -44, 14, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, -4, 12, 4, 20],\n [0, 0, 0, 0, 0],\n [-9, 3, -9, -3, -15],\n [9, -3, 9, 3, 15],\n [-9, 3, -9, -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[[-20, 20, -25, -15, -30],\n [12, -12, 15, 9, 18],\n [4, -4, 5, 3, 6],\n [8, -8, 10, 6, 12],\n [4, -4, 5, 3, 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[[12, -6, 20, 18, 34],\n [-24, -8, -25, -6, -38],\n [12, 26, -4, -30, -14],\n [30, 49, 2, -51, -11],\n [0, 4, -3, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-20, -34, -36, 20, 36],\n [-30, -17, 8, 12, 34],\n [-60, -54, -12, 18, 60],\n [24, -7, -53, 19, 6],\n [-30, -36, -21, 11, 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[[42, -6, -48, -40, 64],\n [12, 57, 54, 86, -26],\n [-96, -21, -24, 10, 20],\n [42, 33, -12, 50, 5],\n [2, -45, -32, -66, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[30, -20, 0, 0, -30],\n [-18, 12, 0, 0, 18],\n [36, -24, 0, 0, -36],\n [-24, 16, 0, 0, 24],\n [-30, 20, 0, 0, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 15, 50, -14, 43],\n [-14, 38, 8, -22, -10],\n [15, -2, 36, 12, 20],\n [10, -20, -4, 2, 6],\n [23, -8, 32, -10, 21]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-8, -21, -65, 25, 12],\n [-4, 6, -38, 22, -3],\n [-58, -6, -33, -5, 48],\n [32, 6, 30, 2, -18],\n [-44, -63, -13, -47, 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, 12, -3, -12, 6],\n [-3, -12, 3, 12, -6],\n [3, 12, -3, -12, 6],\n [5, 20, -5, -20, 10],\n [3, 12, -3, -12, 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 5x5 matrix:\n[[19, -43, -21, 16, 28],\n [17, 40, -5, 13, 3],\n [24, -25, -24, 22, 28],\n [-38, -1, -46, -21, 14],\n [3, 34, -29, 10, 12]]\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, 5, -13, -11, -32],\n [-11, 2, -3, 0, -4],\n [14, 2, -8, -10, -24],\n [33, -6, 9, 0, 12],\n [17, -4, 7, 2, 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[[-25, 10, -20, 25, -15],\n [-25, 10, -20, 25, -15],\n [5, -2, 4, -5, 3],\n [-5, 2, -4, 5, -3],\n [-5, 2, -4, 5, -3]]?\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[[15, 30, 30, -30, -20],\n [9, -9, 0, -6, 26],\n [4, 17, 14, -12, -18],\n [-3, 21, 12, -6, -34],\n [-13, 19, 4, 6, -46]]\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 5x5 matrix:\n[[-20, -20, 8, -16, 8],\n [25, 25, -10, 20, -10],\n [5, 6, 4, 10, -6],\n [0, 4, 24, 24, -16],\n [-5, 1, 38, 32, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-15, -31, 18, 37, -30],\n [-6, 22, 30, 0, 10],\n [-2, -20, -3, 15, -15],\n [34, 18, 12, -6, 20],\n [8, -4, -6, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-32, -56, 22, 14, -18],\n [41, 29, -42, -1, 19],\n [-31, -16, 16, 14, -19],\n [-12, 42, 4, 2, -8],\n [-26, -23, 54, -23, -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[[26, 2, 14, -24, -16],\n [33, 9, 27, 0, 0],\n [-54, -16, -46, -6, -4],\n [-20, -1, -10, 21, 14],\n [18, 10, 22, 24, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-21, -7, 16, -15, 1],\n [-42, 34, -35, -14, 9],\n [-41, -7, -27, -7, 12],\n [6, -15, 26, -11, 13],\n [2, -28, 19, -8, 19]]\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, 9, -3, 15, 9],\n [-20, -12, 4, -20, -12],\n [-10, -6, 2, -10, -6],\n [-30, -18, 6, -30, -18],\n [10, 6, -2, 10, 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 5x5 matrix:\n[[0, 0, 0, 0, 0],\n [30, -18, 6, 18, 24],\n [-15, 9, -3, -9, -12],\n [-15, 9, -3, -9, -12],\n [20, -12, 4, 12, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-28, 0, -36, -8, 32],\n [-22, -36, -18, -32, 2],\n [-5, -12, -3, -10, -2],\n [-38, -24, -42, -28, 28],\n [-34, -48, -30, -44, 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[[33, 20, 8, -13, 5],\n [27, -6, -4, -2, 12],\n [-15, -35, -17, 12, 6],\n [24, -9, -19, 12, 20],\n [27, 10, 4, -31, -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[[3, -6, -11, -11, -33],\n [6, 31, 12, 27, 78],\n [15, -3, 20, -3, 52],\n [-11, 3, 56, 3, 18],\n [36, -12, -30, -30, -18]]?\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[[-8, -20, -8, 22, 4],\n [-76, 10, 4, -6, -12],\n [63, -20, 3, 10, 6],\n [41, -20, 5, 10, 2],\n [36, -30, -12, 30, 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[[15, 12, 46, 24, -10],\n [-46, -24, 6, 19, -40],\n [-12, 11, 34, 13, -9],\n [-42, -12, 30, -6, -10],\n [35, 18, 9, -32, 47]]\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, 24, -14, -35, 7],\n [3, 1, -1, -24, -2],\n [-9, 12, -42, 12, -9],\n [37, -7, -31, -46, -2],\n [4, 18, 4, -28, 8]]\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, -10, 26, -10, 16],\n [8, -38, -24, 42, 52],\n [-30, 12, 2, -32, -10],\n [-7, 24, 38, -20, -33],\n [-37, -31, 54, 43, 54]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, -10, -6, -8, 12],\n [-4, -5, -3, -4, 6],\n [-20, -25, -15, -20, 30],\n [-12, -15, -9, -12, 18],\n [-8, -10, -6, -8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 2, -9, -11, 0],\n [-13, 2, -21, -28, 3],\n [7, -14, 3, -8, 15],\n [3, -8, 0, -7, 9],\n [31, -22, 39, 36, 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[[-8, 28, 12, -26, -36],\n [12, -32, -18, 34, 34],\n [-10, 20, 15, -25, -15],\n [8, -20, -12, 22, 20],\n [-12, 30, 18, -33, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-17, 45, -19, 29, 12],\n [19, 7, 23, 1, -30],\n [37, 47, 29, 18, -36],\n [14, -9, 13, -6, -12],\n [15, 19, 1, 21, 1]]\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[[31, -7, 15, -13, -11],\n [16, -18, 10, -18, -14],\n [-17, -33, -29, 17, 45],\n [33, 29, 32, -17, -40],\n [-27, -13, -16, 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[[0, 0, -6, 36, -36],\n [0, 0, 3, -18, 18],\n [0, 0, 1, -6, 6],\n [0, 0, 6, -36, 36],\n [0, 0, 2, -12, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[17, 1, -18, -12, 14],\n [24, 12, -16, -3, 18],\n [3, -29, -22, 0, -14],\n [-8, -24, -8, 0, -16],\n [3, -5, -12, -33, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 0, -6, -5, 6],\n [-24, -18, 48, 10, -30],\n [28, 24, -60, -10, 36],\n [-18, 36, -30, 35, -6],\n [18, 0, -18, -15, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0, 0],\n [0, 18, -12, 3, 9],\n [-8, 42, -4, 25, 11],\n [6, -33, 4, -19, -9],\n [4, -18, 0, -12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[15, 15, 18, -12, -18],\n [10, 10, 12, -8, -12],\n [20, 20, 24, -16, -24],\n [0, 0, 0, 0, 0],\n [30, 30, 36, -24, -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[[-12, -18, -9, 12, 0],\n [0, 0, 0, 0, 0],\n [-24, -36, -18, 24, 0],\n [24, 36, 18, -24, 0],\n [4, 6, 3, -4, 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[[-13, 10, 6, -37, -39],\n [-23, -6, -6, -29, -33],\n [-5, -4, 13, 3, -21],\n [-26, -8, -43, -1, 18],\n [-13, 25, -26, 9, 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[[30, -30, 15, -5, 25],\n [-6, -6, 15, -24, -12],\n [-46, 28, -1, -29, -52],\n [8, -16, -14, -13, -17],\n [-44, 48, 12, 9, -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 5x5 matrix:\n[[25, 22, 18, 16, -13],\n [-27, -18, -72, -45, -3],\n [3, -29, -25, -27, 15],\n [36, -4, 59, 28, 8],\n [44, 33, 60, 39, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-19, 57, 22, -17, -19],\n [4, 20, 37, -31, 3],\n [0, -64, -25, 21, 14],\n [-10, -38, -37, 33, 5],\n [9, 42, 28, -26, -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[[-10, -19, -17, -16, 42],\n [-1, 26, -6, -13, -25],\n [15, -27, -13, -27, -5],\n [18, 15, 31, 17, -22],\n [-1, 14, -26, -29, -41]]\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, 25, -30, -30, -5],\n [16, 20, -24, -24, -4],\n [8, 10, -12, -12, -2],\n [-24, -30, 36, 36, 6],\n [12, 15, -18, -18, -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[[-6, 15, 3, -3, -3],\n [-8, 20, 4, -4, -4],\n [-8, 20, 4, -4, -4],\n [-4, 10, 2, -2, -2],\n [6, -15, -3, 3, 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, 48, 43, 4, 29],\n [-4, -26, -48, 1, -24],\n [-20, -21, 7, -8, -8],\n [-12, 13, 18, -2, 13],\n [0, -41, -46, 5, -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[[8, -12, -4, 8, 24],\n [10, -15, -5, 10, 30],\n [-2, 3, 1, -2, -6],\n [6, -9, -3, 6, 18],\n [-10, 15, 5, -10, -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 5x5 matrix:\n[[-10, -12, -34, 36, 28],\n [32, 12, -4, 15, -8],\n [0, -14, -20, 50, 27],\n [0, 2, 32, -5, -3],\n [27, -26, -6, 5, -47]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, 5, 16, -15, 10],\n [2, 6, 8, -2, 8],\n [9, 23, 12, 19, 24],\n [-4, -11, -10, -3, -13],\n [-2, -1, 22, -33, 7]]\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 5x5 matrix:\n[[1, 3, 1, 12, -9],\n [15, 6, -1, 26, 20],\n [0, -31, -52, -15, 21],\n [0, 41, 60, -1, -39],\n [-13, -19, -18, -21, -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[[-5, 4, -4, 5, 9],\n [6, 4, 8, -6, -10],\n [-26, 12, 48, 26, 10],\n [-27, 26, -20, 27, 49],\n [6, -18, -16, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-16, -36, 18, 28, 28],\n [-8, -22, 7, 26, 26],\n [-2, 3, 6, -19, -19],\n [6, 5, -11, 15, 15],\n [8, 20, -8, -20, -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[[-6, -3, -18, -3, -15],\n [-4, -2, -12, -2, -10],\n [6, 3, 18, 3, 15],\n [-10, -5, -30, -5, -25],\n [-6, -3, -18, -3, -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[[15, -20, 24, 20, 9],\n [-27, 4, -24, -36, 3],\n [-9, -32, 12, -12, 21],\n [12, -24, 24, 16, 12],\n [0, 30, -18, 0, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, -33, -18, -34, -15],\n [14, 4, 14, 10, -4],\n [13, -21, 0, -11, -21],\n [-13, -10, -16, -15, 0],\n [26, -27, 18, -28, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 6, -22, 2, 4],\n [0, 12, -44, 4, 8],\n [-35, -32, 24, 1, -12],\n [30, 15, 25, -5, 2],\n [0, -18, 66, -6, -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 5x5 matrix:\n[[-8, -8, -20, 0, -24],\n [-8, -8, -20, 0, -24],\n [2, 2, 5, 0, 6],\n [8, 8, 20, 0, 24],\n [2, 2, 5, 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 5x5 matrix:\n[[-6, -15, 18, -15, 6],\n [6, 15, -18, 15, -6],\n [-4, -10, 12, -10, 4],\n [-12, -30, 36, -30, 12],\n [-2, -5, 6, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, -30, 12, -30, -36],\n [2, -5, 2, -5, -6],\n [10, -25, 10, -25, -30],\n [-12, 30, -12, 30, 36],\n [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[[29, -25, -44, 6, -28],\n [-11, -14, -34, 21, -57],\n [34, -10, -18, 29, 5],\n [30, -47, 2, -22, 32],\n [-19, 35, 9, 27, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-24, 24, 8, -12, 8],\n [-36, 36, 12, -18, 12],\n [-6, 6, 2, -3, 2],\n [18, -18, -6, 9, -6],\n [-30, 30, 10, -15, 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[[36, 0, -22, 27, -49],\n [-25, 0, -3, -17, 63],\n [-46, 0, -8, 11, 39],\n [2, 0, -49, 56, -23],\n [-61, 0, -27, 55, 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[[-10, -4, 4, -2, -12],\n [10, 4, -4, 2, 12],\n [-10, -4, 4, -2, -12],\n [-15, -6, 6, -3, -18],\n [-25, -10, 10, -5, -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 5x5 matrix:\n[[-33, -21, 24, -30, 60],\n [-7, -2, 20, -12, -13],\n [-10, -11, 12, 26, 5],\n [13, 31, -29, -51, -2],\n [-9, 9, -22, 43, 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 5x5 matrix:\n[[24, -10, -20, -6, -31],\n [-100, -48, -11, -10, -4],\n [16, -26, 6, 33, 26],\n [-76, -52, -28, -1, 1],\n [32, 0, -5, 47, 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[[52, 20, 31, 2, 2],\n [-62, 8, -8, -8, -36],\n [-5, 8, 28, 19, -6],\n [-17, 41, -5, -49, -55],\n [-43, -17, -18, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-22, 0, -21, -27, 20],\n [-4, 24, -30, -10, 24],\n [-28, -12, -18, -10, 24],\n [-24, 12, -40, -12, 40],\n [-22, 9, -35, -8, 36]]\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, -1, -1, 6],\n [0, -4, -1, -1, 6],\n [0, 4, 1, 1, -6],\n [0, 0, 0, 0, 0],\n [0, -16, -4, -4, 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[[-28, -42, -20, -30, 8],\n [20, -21, -21, 15, 19],\n [18, -25, 6, 5, 60],\n [20, 38, 29, 20, 3],\n [42, 45, 9, 45, -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[[-73, -13, 25, -25, 30],\n [6, 65, -27, 11, 28],\n [9, 4, -40, 5, -10],\n [27, 52, -2, 17, 8],\n [7, 29, -31, 13, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 3, -15, -9, 3],\n [16, 4, -20, -12, 4],\n [-8, -2, 10, 6, -2],\n [-12, -3, 15, 9, -3],\n [-20, -5, 25, 15, -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[[8, -3, -58, -38, 6],\n [-16, 1, 14, 2, 6],\n [-14, 0, 36, 46, -15],\n [-58, -4, -12, 22, -3],\n [12, 2, 36, 26, -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[[27, 22, -22, 11, 26],\n [-14, -21, 29, -4, -5],\n [-13, -27, 46, -6, -27],\n [-9, 0, 33, -47, -4],\n [31, 40, -60, 16, 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 5x5 matrix:\n[[-4, 10, -10, -2, 8],\n [42, -51, -3, 39, -18],\n [18, -27, 9, 15, -14],\n [-10, 16, -7, -8, 9],\n [-34, 49, -13, -29, 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[[-31, -36, 43, 44, -47],\n [-11, -10, 4, 15, -27],\n [1, -12, -5, 7, -24],\n [15, 18, -34, -20, 2],\n [-28, -32, 36, 39, -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[[31, -20, -8, -17, -14],\n [-42, 30, 6, 24, 24],\n [-23, 10, 14, 11, 2],\n [-14, -5, 27, 3, -18],\n [-10, 5, 5, 5, 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[[2, 54, -11, 12, 25],\n [10, -8, 17, -14, -19],\n [59, -33, -13, -54, -58],\n [-21, 5, -5, 20, 22],\n [6, -78, 12, -24, -42]]\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, 6, 3, -5, 5],\n [12, 36, 18, -30, 30],\n [10, 30, 15, -25, 25],\n [6, 18, 9, -15, 15],\n [-2, -6, -3, 5, -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 5x5 matrix:\n[[6, -2, 4, 3, 2],\n [6, -2, 4, 3, 2],\n [0, 0, 0, 0, 0],\n [-12, 4, -8, -6, -4],\n [36, -12, 24, 18, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, -2, -10, 4],\n [0, 0, -5, -25, 10],\n [0, 0, 3, 15, -6],\n [0, 0, -5, -25, 10],\n [0, 0, 5, 25, -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[[21, -23, 33, -8, -7],\n [-30, 30, 34, -6, -6],\n [21, -8, -45, 10, -10],\n [42, 4, -65, -11, -22],\n [45, 25, -91, -20, -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[[-5, -16, 6, 23, -13],\n [27, 20, -28, -15, 17],\n [8, 10, -13, -25, 18],\n [15, 18, -11, -4, 4],\n [20, -2, -31, -19, 24]]\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, -1, 28, -14, 9],\n [-15, 22, -68, 11, 25],\n [-10, -22, 22, -14, -46],\n [15, 23, -31, -2, 47],\n [3, -2, 0, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 37, -21, -11, -25],\n [-8, 2, 6, -10, -2],\n [-24, -12, 30, -27, 6],\n [-8, -22, 22, -6, 14],\n [12, 27, -29, 10, -17]]\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 5x5 matrix:\n[[-14, 27, -4, -12, -9],\n [11, -29, 20, -30, 31],\n [-18, 11, 4, -8, -13],\n [10, -11, -2, 11, 4],\n [-1, 18, -22, 41, -27]]\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, -20, 30, 0, -10],\n [-18, 24, -36, 0, 12],\n [-6, 8, -12, 0, 4],\n [15, -20, 30, 0, -10],\n [-18, 24, -36, 0, 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[[-12, 6, -42, -24, 15],\n [-4, 2, -44, -17, 8],\n [36, -18, -4, 33, -32],\n [24, -12, -16, 18, -20],\n [-16, 8, -36, -26, 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[[-17, -4, 3, -13, 2],\n [10, -25, -9, 29, 20],\n [18, -9, -2, 11, 10],\n [5, -5, 2, -4, 6],\n [12, -26, -12, 38, 20]]\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 5x5 matrix:\n[[15, 9, 0, -9, 18],\n [25, 15, 0, -15, 30],\n [15, 9, 0, -9, 18],\n [-25, -15, 0, 15, -30],\n [15, 9, 0, -9, 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[[0, 18, 30, 30, 24],\n [0, -12, -20, -20, -16],\n [0, 6, 10, 10, 8],\n [0, 18, 30, 30, 24],\n [0, 3, 5, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[7, 14, 5, 18, -27],\n [7, -6, 0, -22, 13],\n [-3, 19, 10, -8, -18],\n [-2, 28, 13, 4, -34],\n [1, -8, -5, 10, 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[[0, -6, 20, -28, -12],\n [-7, 3, -20, 27, 27],\n [-29, -33, 30, -23, -33],\n [21, 15, 0, -9, -5],\n [15, 27, -30, 21, 63]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[24, 9, -10, 0, 20],\n [-8, 13, 10, -11, 2],\n [22, -32, -10, 12, -4],\n [14, 47, 20, -37, 34],\n [13, 7, -5, -1, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[17, -4, 10, -19, 13],\n [-8, -2, 5, 7, 1],\n [-22, 2, -5, 23, -11],\n [14, 2, -5, -13, 1],\n [-14, -2, 5, 13, -1]]\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 5x5 matrix:\n[[5, 26, -15, -28, -25],\n [8, -16, -6, 2, -4],\n [-23, 2, 31, 30, 39],\n [4, 8, -8, -12, -12],\n [-20, 56, 10, -18, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[35, 17, -6, 10, 20],\n [3, -13, -17, 12, 5],\n [-27, -8, 38, -6, -17],\n [-30, -2, 27, 24, -8],\n [-22, -24, 6, -20, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[14, 30, -7, -28, -66],\n [-6, -3, -9, 15, 18],\n [24, 56, -12, 7, -31],\n [-16, -35, 14, -19, 20],\n [-20, 2, -66, 48, -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[[3, -9, 5, 5, -21],\n [-15, -1, 10, -5, 22],\n [-17, 31, -25, -3, 33],\n [11, 7, -15, 5, -17],\n [5, 25, -25, -5, 25]]?\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[[13, 21, 25, -23, 25],\n [-6, 28, -5, -24, 10],\n [-14, -7, -19, 10, -21],\n [-3, 25, -14, -21, 19],\n [14, -14, 31, 8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 10, 12, -2, -2],\n [6, -10, -12, 2, 2],\n [-15, 25, 30, -5, -5],\n [18, -30, -36, 6, 6],\n [15, -25, -30, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-49, -15, -13, 2, 8],\n [41, 11, 5, -7, -10],\n [0, -40, 45, -50, -11],\n [-12, -4, 24, 12, 12],\n [-17, -27, 10, -31, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, -2, -2, -19, 18],\n [9, -33, 30, -9, 24],\n [-3, -13, 14, 7, 0],\n [-3, 17, -16, 2, -10],\n [27, -21, 12, -40, 46]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-31, 11, -8, 3, 13],\n [10, -4, -2, 16, -50],\n [11, -12, 9, 16, -21],\n [22, -6, -28, -5, 12],\n [32, -22, -1, 19, -23]]\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 5x5 matrix:\n[[2, 1, -1, -3, 0],\n [4, 2, -2, -6, 0],\n [-6, -3, 3, 9, 0],\n [-4, -2, 2, 6, 0],\n [4, 2, -2, -6, 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 5x5 matrix:\n[[-33, 62, 2, -31, -4],\n [-13, -66, -28, -1, 36],\n [31, -46, -16, 27, -4],\n [78, 15, -12, 55, -64],\n [35, 17, -1, 31, -28]]\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 5x5 matrix:\n[[-1, 0, -12, 22, -3],\n [-8, -8, 10, -40, -30],\n [23, 25, 11, -8, 58],\n [25, 31, -42, 27, 12],\n [11, 32, -11, 30, 46]]\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[[-17, 3, 43, 11, -11],\n [9, -11, 34, 38, -33],\n [-26, 4, -17, -25, 10],\n [-17, 1, 3, -21, 28],\n [5, -13, 8, -8, 41]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, 20, -16, 8, -12],\n [3, -5, 4, -2, 3],\n [-18, 30, -24, 12, -18],\n [-3, 5, -4, 2, -3],\n [-6, 10, -8, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[38, 2, 18, 3, -29],\n [19, -21, 19, -53, -39],\n [-2, 0, 2, 12, -16],\n [-3, 11, -3, 37, 5],\n [6, 6, 6, 33, -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[[32, 3, -12, 30, 0],\n [42, 18, 0, 36, 18],\n [18, 22, 16, 12, 26],\n [-11, 6, 12, -12, 9],\n [10, -10, -16, 12, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-40, -6, -17, -37, 51],\n [45, 5, 21, 47, -59],\n [-33, -19, -26, -32, 46],\n [-32, 28, 9, -35, 35],\n [36, -47, -25, 35, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, -3, 4, -3, 4],\n [-30, 15, -20, 15, -20],\n [18, -9, 12, -9, 12],\n [18, -9, 12, -9, 12],\n [-30, 15, -20, 15, -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 5x5 matrix:\n[[-19, -29, 43, -34, 42],\n [29, 28, -33, 51, -33],\n [20, -3, 44, 3, 19],\n [17, -1, 31, 8, 16],\n [6, -5, -7, 38, 5]]\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, 14, -11, -14, 17],\n [15, 18, -33, -30, -21],\n [25, 22, -43, -62, -14],\n [4, 8, -8, -20, 14],\n [9, -10, -1, -12, -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[[-19, -21, 34, -8, 16],\n [32, 12, -35, 1, -11],\n [5, 12, 10, 25, 4],\n [8, 18, -35, -1, -19],\n [56, -18, 7, 5, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[55, -9, -44, -11, 16],\n [-27, 12, -4, 2, -23],\n [-38, -23, 15, 4, -9],\n [-21, -9, 33, 6, 6],\n [62, 2, -78, -16, 0]]\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, 24, -29, -49, 16],\n [36, 10, -19, 17, -28],\n [18, -28, 37, 41, -8],\n [-36, -4, 13, -33, 22],\n [-48, 20, -22, -54, 32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, 3, 23, 6, -8],\n [12, 3, 23, 6, -8],\n [-26, -24, -34, -23, -6],\n [-9, -12, -8, -11, -9],\n [-24, -27, -33, -11, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, 0, 4, -14, -16],\n [-30, 0, -12, -14, 20],\n [-3, 0, 2, -19, -14],\n [12, 0, 10, -23, -34],\n [-18, 0, -10, 7, 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[[0, 16, -20, 16, -24],\n [0, -4, 5, -4, 6],\n [0, -16, 20, -16, 24],\n [0, 4, -5, 4, -6],\n [0, -24, 30, -24, 36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-47, 73, -22, -55, -92],\n [-6, -29, 12, 12, 36],\n [-21, 1, -3, -18, 20],\n [6, -12, 9, -17, 22],\n [-1, -14, 7, 6, 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[[0, 32, -13, 69, 51],\n [10, -8, -8, -11, 6],\n [14, -16, -22, -25, 12],\n [22, -16, 3, -22, -3],\n [-27, 14, 30, 13, -33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[22, 20, -10, -22, -56],\n [13, -20, -35, -21, 7],\n [-14, 14, 29, 29, 7],\n [-6, 14, 19, 15, -8],\n [30, -6, -21, -33, 18]]\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[[-19, 26, -7, -24, 18],\n [34, -56, -18, 44, -8],\n [15, -12, 33, 18, -36],\n [-18, 27, 1, -23, 11],\n [-30, 51, 21, -39, 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[[-14, 1, 8, 16, -24],\n [-11, -14, 26, -17, -9],\n [-7, 5, -2, 17, -15],\n [-7, -13, 22, -19, -3],\n [-16, -4, 16, 8, -24]]\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[[37, -4, 11, 16, -58],\n [104, -42, -11, -10, 26],\n [63, -7, -23, 10, 7],\n [-46, 32, 4, 20, -36],\n [7, -9, -9, -12, 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[[8, 12, -4, -8, -4],\n [0, 0, 0, 0, 0],\n [12, 18, -6, -12, -6],\n [12, 18, -6, -12, -6],\n [-10, -15, 5, 10, 5]]?\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[[-10, 12, 6, 4, 12],\n [-5, 6, 3, 2, 6],\n [-30, 36, 18, 12, 36],\n [20, -24, -12, -8, -24],\n [20, -24, -12, -8, -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[[11, 1, -13, 28, -10],\n [6, 1, -9, 17, -5],\n [0, 10, -42, 38, 10],\n [6, -14, 54, -40, -20],\n [20, -5, 5, 25, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, 2, -1, -6, -3],\n [-6, 7, -6, -10, -5],\n [-22, 27, -26, -26, -13],\n [-24, 27, -21, -48, -24],\n [-22, 27, -26, -26, -13]]?\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 5x5 matrix:\n[[12, -16, -4, -8, -16],\n [6, -8, -2, -4, -8],\n [18, -24, -6, -12, -24],\n [-12, 16, 4, 8, 16],\n [15, -20, -5, -10, -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 5x5 matrix:\n[[2, -6, -18, -2, 2],\n [2, -6, -18, -2, 2],\n [-24, 17, 21, 9, -4],\n [14, 2, 30, -2, -2],\n [33, -22, -24, -12, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, 6, -6, -3, -3],\n [5, 10, -10, -5, -5],\n [-6, -12, 12, 6, 6],\n [5, 10, -10, -5, -5],\n [-2, -4, 4, 2, 2]]\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[[-25, 15, -10, -10, -10],\n [-30, 18, -12, -12, -12],\n [-10, 6, -4, -4, -4],\n [5, -3, 2, 2, 2],\n [-5, 3, -2, -2, -2]]\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[[-20, -1, 58, -14, 6],\n [-24, -24, 43, -70, -46],\n [-5, 5, 68, -28, 3],\n [20, -6, -23, -34, -74],\n [-26, -30, -38, -24, -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[[24, 16, 24, -16, -4],\n [24, 16, 24, -16, -4],\n [-12, -8, -12, 8, 2],\n [-24, -16, -24, 16, 4],\n [6, 4, 6, -4, -1]]?\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[[9, -15, 12, 6, 4],\n [-25, -35, 31, 37, 26],\n [8, 10, -8, -25, -24],\n [-7, -4, 0, -28, -24],\n [27, 27, -33, -24, 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[[20, 5, -20, 15, -30],\n [-24, -6, 24, -18, 36],\n [-12, -3, 12, -9, 18],\n [0, 0, 0, 0, 0],\n [-24, -6, 24, -18, 36]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-13, -24, -6, -30, -26],\n [-45, -32, 11, -5, -30],\n [-18, 56, 12, -66, -64],\n [34, 67, 22, -28, 4],\n [-22, -1, 3, -11, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[3, 4, 0, -5, 2],\n [-6, -8, 0, 10, -4],\n [-3, -4, 0, 5, -2],\n [-12, -16, 0, 20, -8],\n [12, 16, 0, -20, 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 5x5 matrix:\n[[-15, 29, 16, -7, -27],\n [39, -36, 12, -15, -4],\n [-5, 13, 28, -29, -35],\n [6, -4, -14, 20, 16],\n [-7, -11, -18, 7, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[35, -2, -9, -45, -52],\n [-37, 15, 30, 26, 65],\n [14, 10, -1, 28, 28],\n [48, 20, 12, -49, -22],\n [-43, 16, 28, 29, 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[[-31, 12, -7, -46, -56],\n [16, -10, 4, 26, 12],\n [-37, 10, 4, -26, -2],\n [-14, -18, 15, 28, -18],\n [-2, 1, 5, 9, 36]]\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, 23, 26, -2, 29],\n [-15, 4, -9, 8, -6],\n [-35, 48, 17, 46, 28],\n [-26, -22, -28, 26, -32],\n [14, 34, 38, 4, 42]]\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[[-1, -5, -5, 3, 3],\n [5, 25, 25, -15, -15],\n [-2, -10, -10, 6, 6],\n [1, 5, 5, -3, -3],\n [-2, -10, -10, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[25, 15, -25, -25, 30],\n [-3, -9, 3, -29, -18],\n [18, 0, -18, -66, 0],\n [7, -3, -7, -39, -6],\n [-1, 3, 1, 17, 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[[11, -28, 3, 12, -25],\n [28, -20, -36, 39, -65],\n [-29, -14, 17, -7, -14],\n [14, 12, 18, -19, 59],\n [-2, -40, 16, 2, -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 5x5 matrix:\n[[-9, -19, 14, 25, 11],\n [-38, -11, 34, -17, -30],\n [9, -3, -12, 33, 36],\n [19, 10, -26, 24, 38],\n [-2, -17, 10, 21, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[7, -10, 7, -28, -19],\n [-19, -5, -4, -14, -2],\n [-7, -5, -28, 34, 10],\n [-21, -10, -28, 16, 5],\n [26, -25, -3, -30, -37]]\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[[-8, -12, 0, 24, -16],\n [2, 3, 0, -6, 4],\n [-10, -15, 0, 30, -20],\n [0, 0, 0, 0, 0],\n [2, 3, 0, -6, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-14, 7, 3, 11, -2],\n [-8, 31, 3, 14, -23],\n [18, 30, -2, -3, -29],\n [34, 10, -6, -19, -17],\n [36, -24, -8, -30, 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[[-22, 22, 0, 40, 73],\n [-9, 11, -22, 12, 27],\n [19, 35, -30, 72, 24],\n [-8, -10, 48, 2, -7],\n [17, -21, 9, -29, -75]]\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, 5, -30, 20, 10],\n [31, 19, -34, 21, 28],\n [1, -2, -4, 3, -2],\n [-11, -14, 4, -1, -18],\n [21, 12, -24, 15, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 26, 20, -34, 40],\n [-20, -11, 30, -1, 0],\n [-6, 11, 20, -19, 22],\n [-4, 3, 10, -7, 8],\n [-12, -17, 10, 13, -16]]\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[[7, 15, 6, 9, -14],\n [50, 5, 15, 16, -9],\n [-26, -40, -18, -26, 38],\n [-55, 0, -15, -15, 5],\n [13, 20, 9, 13, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-15, 33, 15, -15, 3],\n [-18, 18, 0, -6, 0],\n [9, -45, -30, 23, -6],\n [-17, 5, -10, 1, -2],\n [-9, -9, -15, 7, -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[[32, 12, -22, 29, 5],\n [0, -16, 10, -19, 11],\n [-42, 3, -1, -32, -39],\n [-10, -43, 35, -30, 42],\n [-26, -27, -19, -68, -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[[6, -25, 25, -5, 4],\n [15, 27, -15, 3, 54],\n [-82, -39, 40, 15, 32],\n [33, 25, -25, -12, -48],\n [-38, -61, 30, 30, 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[[-12, -10, 0, 10, 0],\n [12, 10, 0, -10, 0],\n [30, 25, 0, -25, 0],\n [12, 10, 0, -10, 0],\n [-12, -10, 0, 10, 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[[4, 6, 10, -6, 0],\n [18, -19, 19, -13, 4],\n [-16, -1, -27, 17, -2],\n [16, 1, 27, -17, 2],\n [16, 1, 27, -17, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[14, 12, -12, -52, -10],\n [-32, -18, 40, 12, -40],\n [-16, -12, 16, 40, 0],\n [26, 12, -36, 20, 50],\n [-15, -9, 18, 12, -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[[-5, -2, 22, 43, -10],\n [-31, 32, 38, 17, -65],\n [24, 12, -27, 5, 10],\n [28, -38, 25, 17, 19],\n [-40, 20, -22, -38, -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[[0, 28, -26, -30, 21],\n [-21, -14, -20, -15, -21],\n [-23, -26, -12, -5, -31],\n [-11, -10, -8, -5, -13],\n [20, 8, 24, 20, 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[[2, 31, -4, -54, 21],\n [24, -27, -10, -2, 5],\n [12, -24, -4, 16, -4],\n [20, -26, -8, 4, 2],\n [-9, -24, 7, 56, -23]]?\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, -1, 3, 4, -2],\n [12, 3, -9, -12, 6],\n [-4, -1, 3, 4, -2],\n [-20, -5, 15, 20, -10],\n [4, 1, -3, -4, 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 5x5 matrix:\n[[-44, 29, 27, 56, 72],\n [16, 6, -19, -24, 14],\n [-12, -30, 24, 6, 42],\n [32, 26, -43, -40, -10],\n [24, -5, -19, -26, -58]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[18, -12, 12, 12, 12],\n [-15, -2, -22, 2, 8],\n [12, 2, 18, -2, -7],\n [-9, 12, 0, -12, -15],\n [6, 6, 14, -6, -11]]\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[[48, 59, 26, -35, 56],\n [67, 37, 59, -29, 57],\n [10, 3, -26, 25, -3],\n [23, 16, 27, -22, 42],\n [-25, 6, -13, -8, -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[[-18, 24, -30, 0, -36],\n [-9, 12, -15, 0, -18],\n [0, 0, 0, 0, 0],\n [15, -20, 25, 0, 30],\n [3, -4, 5, 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 5x5 matrix:\n[[4, -36, 12, -28, 4],\n [-12, 9, -18, 6, 6],\n [4, -18, 6, -12, 8],\n [5, -36, 12, -27, 7],\n [24, 45, 30, 34, -38]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-30, 36, -18, -18, -18],\n [10, -12, 6, 6, 6],\n [-30, 36, -18, -18, -18],\n [-10, 12, -6, -6, -6],\n [15, -18, 9, 9, 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[[-21, 13, 7, -54, -40],\n [3, -9, -1, 4, 6],\n [6, -23, -2, -24, -19],\n [12, -14, -4, 0, -6],\n [33, -3, -11, -8, -46]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, -3, 36, -23, -12],\n [18, -12, 54, -17, -3],\n [-10, 3, -30, 18, 9],\n [-6, 15, -18, -20, -21],\n [-22, 18, -66, 13, -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[[-12, 12, 12, 6, -8],\n [-18, 18, 18, 9, -12],\n [18, -18, -18, -9, 12],\n [-12, 12, 12, 6, -8],\n [-36, 36, 36, 18, -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[[24, -15, -35, -27, 2],\n [-36, 20, 50, 31, -7],\n [12, -50, -38, -16, 30],\n [39, -15, -51, -39, 1],\n [-21, -40, 6, 28, 39]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[0, 0, 0, 0, 0],\n [4, -3, -5, 0, 6],\n [-16, 12, 20, 0, -24],\n [-4, 3, 5, 0, -6],\n [-24, 18, 30, 0, -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[[3, -22, 51, 33, -3],\n [16, -10, -15, -3, 6],\n [-20, -26, -18, -20, 26],\n [-31, -6, 30, 6, 3],\n [-13, -26, -48, -36, 33]]\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 5x5 matrix:\n[[2, -6, -1, -6, 6],\n [-12, 36, 6, 36, -36],\n [-2, 6, 1, 6, -6],\n [6, -18, -3, -18, 18],\n [10, -30, -5, -30, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 23, -7, -20, 2],\n [-32, -5, 25, 2, -38],\n [-4, 16, -4, -14, 0],\n [20, 25, -25, -20, 30],\n [-8, -17, 13, 14, -14]]\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, 3, -10, 2, -2],\n [3, 11, -38, -2, 6],\n [3, 11, -38, -2, 6],\n [18, 0, 3, 21, -30],\n [6, 0, 1, 7, -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[[-24, -17, 25, -20, -28],\n [-33, -4, -16, -43, -23],\n [33, 4, 16, 43, 23],\n [-21, -8, 4, -23, -19],\n [-42, -11, -5, -50, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[15, -25, 10, -5, 10],\n [15, -25, 10, -5, 10],\n [12, -20, 8, -4, 8],\n [6, -10, 4, -2, 4],\n [-12, 20, -8, 4, -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 5x5 matrix:\n[[38, -30, -50, -13, -51],\n [52, -48, -57, -25, -58],\n [-34, 66, 16, 37, 25],\n [-52, 72, 36, 42, 41],\n [-10, 42, -13, 26, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[30, 15, -15, 20, -10],\n [24, 12, -12, 16, -8],\n [6, 3, -3, 4, -2],\n [12, 6, -6, 8, -4],\n [-12, -6, 6, -8, 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[[17, -17, 5, -9, 17],\n [-9, 29, 14, -28, 24],\n [48, -26, 46, 3, -50],\n [16, 46, -3, -32, 19],\n [-15, -1, -28, 18, -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[[-8, -8, -12, 0, -10],\n [12, 12, 18, 0, 15],\n [-16, -16, -24, 0, -20],\n [0, 0, 0, 0, 0],\n [-12, -12, -18, 0, -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[[60, -68, -17, -24, 35],\n [36, -22, -8, 8, 28],\n [-39, 44, -1, -19, 27],\n [-51, 52, 8, -3, -8],\n [42, -38, -11, -6, 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 5x5 matrix:\n[[-12, 8, -2, -4, 6],\n [12, -8, 2, 4, -6],\n [12, -8, 2, 4, -6],\n [-18, 12, -3, -6, 9],\n [24, -16, 4, 8, -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[[20, 30, -22, 10, -9],\n [41, 2, 22, -24, 0],\n [13, 44, 0, -14, -15],\n [50, 40, -6, -10, -12],\n [36, 12, 30, -34, -4]]\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 5x5 matrix:\n[[-20, 20, 4, 4, -16],\n [15, -15, -3, -3, 12],\n [5, -5, -1, -1, 4],\n [-20, 20, 4, 4, -16],\n [-10, 10, 2, 2, -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[[26, -4, 6, 8, -4],\n [-8, -11, 0, -20, -2],\n [20, -42, -6, -12, 46],\n [-18, -1, -28, -16, 5],\n [23, 16, -5, 8, -33]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-28, -8, 38, 25, -2],\n [30, 9, 10, 6, -28],\n [29, 13, 24, 7, -42],\n [-16, -11, -8, 7, 26],\n [-21, -21, -48, -3, 66]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[0, -6, 3, 2, -7],\n [-20, 15, 0, 0, 20],\n [-15, -9, 9, 18, -12],\n [20, -9, -3, -2, -13],\n [57, 6, -21, -50, 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[[-57, 18, 45, -21, 18],\n [20, 15, -3, -23, -12],\n [-2, -17, -9, -33, 33],\n [-12, -22, -6, -14, 33],\n [19, -16, -21, 33, -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 5x5 matrix:\n[[-20, 5, -10, -10, 0],\n [-6, -2, -6, -10, 12],\n [15, -9, 3, -3, 18],\n [11, -15, -5, -19, 42],\n [22, -9, 8, 4, 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[[43, 40, -29, -31, 8],\n [14, 10, -24, 4, 19],\n [17, -21, 11, 33, 12],\n [8, 23, 42, 6, -8],\n [-57, -27, -27, 15, 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[[-51, -32, -7, -48, 27],\n [-8, -90, -10, -43, 27],\n [54, -23, 2, 18, -17],\n [-22, -84, -14, -56, 18],\n [5, 20, 5, -14, -15]]\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[[-18, -35, 2, 47, 40],\n [16, 50, -4, -39, -45],\n [16, -24, -85, 28, 65],\n [-4, -6, 8, 6, 20],\n [12, 30, 18, -46, -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 5x5 matrix:\n[[9, 6, 6, -12, 18],\n [18, 12, 12, -24, 36],\n [3, 2, 2, -4, 6],\n [0, 0, 0, 0, 0],\n [-18, -12, -12, 24, -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[[9, -6, 10, -47, -5],\n [-8, -14, -20, 29, 5],\n [12, 9, -43, -1, 2],\n [-15, 15, 70, -36, -22],\n [11, 5, -17, -29, -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 5x5 matrix:\n[[23, -20, 38, 54, -7],\n [2, -16, 14, -6, -22],\n [-9, 12, -18, -18, 9],\n [1, 4, -2, 6, 7],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-10, 8, -22, -16, 3],\n [18, 12, 42, 12, 9],\n [4, -34, 6, 26, -18],\n [-10, 8, -22, -16, 3],\n [12, 30, 30, -6, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0, 0],\n [-3, 9, 12, -9, -15],\n [4, -12, -16, 12, 20],\n [0, 0, 0, 0, 0],\n [-2, 6, 8, -6, -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[[-21, 25, -28, -14, -13],\n [19, -18, -3, 11, -9],\n [17, 16, -19, 23, -27],\n [-13, 17, -47, -12, -29],\n [25, 18, 0, 35, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 3, 0, -3, 6],\n [9, -6, 3, 9, 12],\n [12, -16, 4, 20, 0],\n [-12, 11, -4, -15, -10],\n [0, -5, 0, 5, -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[[-19, 24, -11, 14, -12],\n [-13, 1, -3, -20, 34],\n [17, 6, 2, 40, -66],\n [10, -16, 7, -14, 14],\n [5, -1, 2, 6, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -5, 3, 3, 0],\n [-12, 15, -9, -9, 0],\n [-24, 30, -18, -18, 0],\n [-4, 5, -3, -3, 0],\n [24, -30, 18, 18, 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[[-21, 9, -5, -3, -6],\n [16, 3, 15, 5, -5],\n [-23, -2, -24, -4, 9],\n [0, -30, 21, -36, -15],\n [43, -2, 58, -4, -27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-25, 16, 25, -14, -19],\n [-2, -4, -6, 0, -6],\n [-39, 15, 15, -14, -40],\n [-23, 11, -17, 10, -28],\n [-11, -4, -21, 6, -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[[6, -6, 12, 0, -30],\n [-3, 3, -6, 0, 15],\n [4, -4, 8, 0, -20],\n [-1, 1, -2, 0, 5],\n [-2, 2, -4, 0, 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, -17, 40, -41, 28],\n [6, 12, 12, -30, 6],\n [-23, 17, -40, 41, -28],\n [-21, -9, -6, 21, -6],\n [-7, -9, 4, 5, 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[[-17, -45, 9, 17, -43],\n [33, 13, 14, 34, -34],\n [-19, -41, 13, 35, 4],\n [-6, -39, 27, 30, 3],\n [30, 51, -10, -21, 0]]\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 5x5 matrix:\n[[-18, 36, -12, -36, 0],\n [3, -6, 2, 6, 0],\n [12, -24, 8, 24, 0],\n [-12, 24, -8, -24, 0],\n [-18, 36, -12, -36, 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 5x5 matrix:\n[[2, -28, 5, -8, 2],\n [8, 31, 20, -6, -18],\n [14, -9, 35, -22, -20],\n [12, 30, 30, -12, -24],\n [-20, 5, -50, 30, 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[[-14, -12, -18, -6, -34],\n [40, -47, 29, 33, 2],\n [-56, 56, -53, -45, 12],\n [-22, 15, -37, -17, 36],\n [22, -60, 0, 24, -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 5x5 matrix:\n[[-3, -6, 8, -12, 18],\n [2, -8, 6, -24, 32],\n [22, -4, -10, -60, 64],\n [-5, -8, 9, 0, 8],\n [12, 2, -8, -30, 28]]\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, -36, 30, -30, -18],\n [-4, -24, 20, -20, -12],\n [-1, -6, 5, -5, -3],\n [6, 36, -30, 30, 18],\n [2, 12, -10, 10, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[28, -40, -25, 2, -22],\n [23, -31, -13, 9, -23],\n [-46, 28, -11, -26, -2],\n [11, 9, 17, -19, -19],\n [-32, 48, 9, -50, 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 5x5 matrix:\n[[-12, 3, -15, -18, 0],\n [24, -6, 30, 36, 0],\n [-16, 4, -20, -24, 0],\n [4, -1, 5, 6, 0],\n [-20, 5, -25, -30, 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[[-15, -52, -6, 1, -11],\n [25, -22, -31, 20, -8],\n [-20, -16, -36, -40, -20],\n [0, -54, -51, -7, -23],\n [4, -28, 38, 20, -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[[0, 16, 8, -24, -16],\n [0, -20, -10, 30, 20],\n [0, 20, 10, -30, -20],\n [0, 4, 2, -6, -4],\n [0, -20, -10, 30, 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[[3, -2, -6, 3, -4],\n [-2, 18, -61, 3, -34],\n [6, 6, -51, 9, -30],\n [33, -42, 12, 27, 0],\n [32, -38, 1, 27, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-39, -7, -3, 29, 22],\n [30, -3, 9, -32, -17],\n [-24, -22, 2, -1, -3],\n [-36, -31, 13, -1, 14],\n [48, 40, -24, 1, -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[[-43, 16, 27, -19, 16],\n [20, -18, -11, -4, -7],\n [7, -20, 0, -18, -5],\n [-35, 65, 20, 24, 33],\n [15, -8, -1, -12, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, -13, 12, 10, 18],\n [5, -45, 40, 35, 60],\n [19, 25, -24, -19, -36],\n [18, 34, -32, -26, -48],\n [-19, -25, 24, 19, 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[[-7, 15, -47, -51, -48],\n [-70, 24, 10, 14, -34],\n [-24, 6, 56, 44, 18],\n [3, 7, 31, 7, 42],\n [44, 0, 22, -14, 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[[0, 2, 1, 3, 1],\n [0, 10, 5, 15, 5],\n [0, 10, 5, 15, 5],\n [0, -10, -5, -15, -5],\n [0, 2, 1, 3, 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[[-1, -1, 5, -1, -2],\n [-4, -4, 20, -4, -8],\n [6, 6, -30, 6, 12],\n [-6, -6, 30, -6, -12],\n [-2, -2, 10, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, -2, -4, -6, 10],\n [1, -1, -2, -3, 5],\n [4, -4, -8, -12, 20],\n [-6, 6, 12, 18, -30],\n [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[[-39, -9, 16, -31, -28],\n [-27, -47, 21, 9, -60],\n [-44, -61, -46, -14, 45],\n [-2, -31, 12, 21, -43],\n [55, 66, 3, -3, -43]]\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, 0, -11, 3, -34],\n [-22, 5, 9, -23, 43],\n [24, -2, -3, 23, -46],\n [39, -34, -47, -20, -3],\n [0, -8, 6, 38, -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[[32, -12, 17, 44, 5],\n [-4, 29, -15, -24, 3],\n [4, 18, 20, 24, -40],\n [10, 20, -3, 21, -9],\n [18, -12, -25, 3, 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[[5, 47, 4, 43, -35],\n [51, -16, 3, -18, -16],\n [16, -17, 8, -40, 16],\n [-9, 5, 42, -39, 44],\n [-19, -8, 8, -11, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[15, -6, 15, -18, 18],\n [35, -4, 17, -36, 24],\n [40, 14, -14, -30, -6],\n [10, -19, 37, -21, 39],\n [-55, -3, -10, 51, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-15, -12, 15, -24, 14],\n [10, 34, -4, 4, -26],\n [-13, -6, 39, -28, 18],\n [0, -24, -33, 21, 3],\n [13, 14, 21, -16, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, -30, 6, -1, 3],\n [-2, -6, 12, -2, -12],\n [-5, -48, 30, -5, -19],\n [5, 66, -30, 5, 13],\n [2, 30, -12, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[2, -44, -44, -34, -35],\n [-6, 33, 21, 51, 45],\n [-24, -8, 18, 0, 10],\n [-12, -20, 2, -50, -40],\n [-16, 8, 2, 14, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[29, -23, -54, -49, -17],\n [-35, 0, 31, 48, 17],\n [-17, -45, -25, -4, 17],\n [-24, -2, -16, 29, -8],\n [-34, -20, 7, 33, 18]]?\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[[-46, -16, -10, -14, -46],\n [32, 2, 8, 4, 26],\n [-15, 58, -30, 49, 32],\n [-10, 43, 32, 18, 8],\n [24, -54, -21, -30, -6]]?\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[[-18, -6, 12, -70, -5],\n [1, -30, 7, -47, 30],\n [18, -30, 19, 22, 12],\n [-3, -18, 21, -24, -45],\n [1, 16, -3, 32, -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[[18, -27, 3, -18, -3],\n [12, 42, -12, 36, 60],\n [34, -49, 9, -33, -9],\n [-32, 26, -23, 18, 15],\n [-18, -9, -44, -3, 36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, -2, -4, 8, 10],\n [0, 0, 0, 0, 0],\n [-9, -3, -6, 12, 15],\n [-15, -5, -10, 20, 25],\n [12, 4, 8, -16, -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 5x5 matrix:\n[[3, -4, 2, 6, 5],\n [9, -12, 6, 18, 15],\n [-9, 12, -6, -18, -15],\n [-3, 4, -2, -6, -5],\n [-3, 4, -2, -6, -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 5x5 matrix:\n[[13, -12, 15, 49, -28],\n [11, -12, -11, -6, -9],\n [-39, -63, 39, 34, 11],\n [-23, -67, 11, 8, -7],\n [-15, -5, -16, -35, -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[[-43, 49, 23, -6, 6],\n [-12, -9, 2, 21, 11],\n [36, -30, -2, 14, 20],\n [19, -26, 11, 15, 21],\n [54, -30, 0, 48, 66]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 8, -34, 20, 10],\n [-36, 2, 32, -28, 2],\n [18, -14, 19, -2, -17],\n [24, -6, 21, -3, -26],\n [52, -2, -42, 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[[48, 55, -51, 2, 37],\n [-81, -69, 56, 34, -36],\n [0, 30, -42, 57, 28],\n [43, 38, -44, -2, 23],\n [-20, -21, 49, -33, -17]]\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, -10, 2, -13, -4],\n [18, 18, -42, 1, 36],\n [9, -18, 6, -22, -9],\n [3, 28, -32, 21, 31],\n [-18, -6, 30, 9, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, -2, 28, -20, 66],\n [1, 10, -2, 11, -21],\n [2, -15, -18, 1, -14],\n [1, 33, 24, 29, 4],\n [5, -2, -26, 25, -51]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-18, 19, -26, -2, 14],\n [26, 32, 47, 29, -23],\n [-18, 35, 2, 2, 17],\n [12, -32, -32, -2, -49],\n [-22, 30, 51, -9, 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 5x5 matrix:\n[[39, 23, 1, -15, -39],\n [2, 25, -2, -11, -16],\n [13, -16, -27, -41, -38],\n [-3, -42, -37, 1, -3],\n [-41, -62, -41, -5, 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 5x5 matrix:\n[[0, 11, 16, 25, -30],\n [-16, -6, -37, -39, 25],\n [11, 20, 36, -61, 30],\n [1, 25, 30, -22, -10],\n [-17, -2, -33, -32, 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[[1, -9, -26, 12, -16],\n [9, 17, 60, -32, 38],\n [-8, 9, 19, -6, 11],\n [-13, -16, -61, 34, -39],\n [8, 5, 23, -14, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[28, 40, 0, 6, -40],\n [-1, 17, 39, -25, -18],\n [-18, -33, -12, 0, 36],\n [27, 28, 11, -38, -2],\n [12, -4, -20, -12, 24]]\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, -8, 7, 19, -7],\n [-56, 48, -27, -17, 48],\n [-69, 60, -39, 5, 45],\n [50, -45, 21, 22, -54],\n [-24, 21, -15, 8, 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[[38, -44, 8, -59, -24],\n [-12, 23, 19, 12, 8],\n [-40, 33, 4, 21, 29],\n [35, -12, 16, -10, -28],\n [2, 22, 4, 15, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[20, -6, -8, 36, -4],\n [16, -18, -6, 28, 2],\n [8, -28, 0, 18, 10],\n [12, -32, -2, 24, 10],\n [8, 22, -18, -14, -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[[42, -10, -2, 13, -23],\n [2, -28, 23, -18, 17],\n [43, 9, 17, 58, -55],\n [11, 55, -21, 9, -20],\n [50, 46, 15, 12, -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[[-13, 8, -6, 24, 6],\n [-37, -4, 3, 25, 2],\n [-13, -22, 3, -25, 4],\n [55, 22, 18, -10, -32],\n [21, 18, 8, 12, -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 5x5 matrix:\n[[9, 5, 6, -2, -5],\n [1, -6, 11, -23, -9],\n [-7, 16, 13, -21, 47],\n [-20, -12, -25, 25, 6],\n [17, 30, 19, -16, 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[[28, -14, 18, 8, 8],\n [22, 26, 30, -36, -36],\n [0, -28, -12, 32, 32],\n [-36, -12, -36, 24, 24],\n [0, -14, -6, 16, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 4, 6, 12, 8],\n [-1, 2, 3, 6, 4],\n [-1, 2, 3, 6, 4],\n [-2, 4, 6, 12, 8],\n [6, -12, -18, -36, -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[[-5, 11, -46, -9, -5],\n [-16, -6, 23, 12, -3],\n [-26, 5, -37, -12, -23],\n [-26, -23, -35, -12, -35],\n [19, 9, -31, 31, 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[[-15, -40, -25, 55, -20],\n [-12, -31, -25, 37, -2],\n [4, 8, 20, 4, -32],\n [-4, -9, -15, 3, 18],\n [11, 28, 25, -31, -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[[38, -6, 15, -8, 7],\n [68, -20, 39, -29, -29],\n [42, -35, 30, -30, -35],\n [-10, -10, -6, 1, 2],\n [-32, 12, 6, -10, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-1, -11, 24, 18, 6],\n [8, 16, -14, 21, 41],\n [-10, 34, -16, 2, 22],\n [43, -13, -23, -16, -32],\n [31, -19, -29, -17, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-14, -18, 34, -20, -6],\n [-43, -36, 6, -5, -37],\n [-5, 15, 25, -8, 75],\n [-69, -48, 7, -4, -31],\n [34, 23, 0, 0, 16]]?\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, 35, -10, -18, 6],\n [-15, 24, 1, 3, 9],\n [23, 64, -19, 4, 72],\n [-24, -21, 10, -5, -39],\n [-4, -44, 16, 14, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0, 0],\n [0, -4, -12, -16, -20],\n [0, -6, -18, -24, -30],\n [0, -3, -9, -12, -15],\n [0, -1, -3, -4, -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 5x5 matrix:\n[[-20, 11, -18, 7, -12],\n [9, 7, -3, 19, -24],\n [5, -22, 23, -30, 42],\n [-13, 17, -21, 21, -30],\n [17, -16, 23, 0, 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 5x5 matrix:\n[[63, -38, 34, -32, 13],\n [-26, -34, -13, -11, 4],\n [30, -30, -14, -22, 24],\n [72, -62, 43, -49, 14],\n [25, 1, -7, -9, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[11, 29, -6, -18, -35],\n [-32, -24, 24, 48, 36],\n [-16, -29, 36, 8, 15],\n [-11, 4, 6, 18, 2],\n [-9, -35, 18, 6, 29]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[7, -30, -37, -2, 12],\n [-15, 10, 25, 10, -20],\n [-13, 15, 28, 8, -18],\n [1, 31, 30, -4, -2],\n [6, -23, -29, -2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, -18, 24, 0, 24],\n [6, -18, 24, 0, 24],\n [3, -9, 12, 0, 12],\n [1, -3, 4, 0, 4],\n [1, -3, 4, 0, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-2, 28, -30, -1, -3],\n [-16, -34, 36, 13, -9],\n [25, -7, -1, -6, -10],\n [5, 11, -5, -11, 23],\n [44, 10, -26, -12, -20]]\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 5x5 matrix:\n[[0, 0, 0, 0, 0],\n [-26, 7, -16, -19, 7],\n [6, -12, 6, -66, -12],\n [-5, 1, -3, -6, 1],\n [5, -1, 3, 6, -1]]\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 5x5 matrix:\n[[36, 50, 12, -30, -22],\n [0, -20, -12, 12, 4],\n [-6, 25, 18, -15, -3],\n [12, -20, -18, 12, 0],\n [-12, 5, 9, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-11, -17, 38, -9, 9],\n [-40, 18, -24, 10, -74],\n [-13, 1, 44, 14, 14],\n [17, 12, -18, 10, 14],\n [43, -15, 12, -10, 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[[-50, -23, 51, -26, 44],\n [-11, -8, 15, 1, 8],\n [-8, -2, 6, -8, 8],\n [-18, -15, 27, 6, 12],\n [-12, -3, 9, -12, 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 5x5 matrix:\n[[14, 4, 12, 4, 28],\n [4, -5, -56, -18, -5],\n [25, -8, -24, -9, 7],\n [-16, 12, 46, 13, -9],\n [-15, 3, 64, 20, -18]]\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[[43, -33, -30, -21, 8],\n [-56, 21, 18, 17, -20],\n [13, 27, 27, -31, 22],\n [-5, -49, -46, -53, -23],\n [-6, -36, -33, -30, -21]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-12, -8, -8, 2, 12],\n [-12, -8, -8, 2, 12],\n [-12, -8, -8, 2, 12],\n [30, 20, 20, -5, -30],\n [6, 4, 4, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -12, 4, -12, -6],\n [-10, -30, 10, -30, -15],\n [12, 36, -12, 36, 18],\n [2, 6, -2, 6, 3],\n [4, 12, -4, 12, 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[[21, 28, -3, 1, 39],\n [-32, 7, 11, -46, -24],\n [15, 23, -11, 30, 31],\n [-33, 33, 3, -42, -3],\n [-32, -19, -6, -27, -32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 20, 8, 0, 0],\n [-12, -6, 30, 36, 24],\n [12, -20, -8, 0, 0],\n [-14, 19, 13, 6, 4],\n [11, -1, -22, -24, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[20, -1, 19, 57, -28],\n [24, -18, 27, 72, -30],\n [-18, -11, -1, 36, -24],\n [6, 36, -9, -27, 6],\n [-30, -44, -4, 9, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, 19, 1, -18, -2],\n [21, 28, -2, -8, -7],\n [0, -7, -1, 10, 0],\n [6, 5, -1, 2, -2],\n [6, -16, -4, 32, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[11, -18, -2, -5, -20],\n [-17, 30, 38, -25, 20],\n [2, -2, 20, -20, -10],\n [10, -16, 4, -10, -20],\n [20, -34, -24, 10, -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[[-15, -34, 14, -12, -2],\n [33, -14, 12, -12, -31],\n [14, 60, -24, 18, -9],\n [-3, 6, -8, 24, 93],\n [38, 54, -47, 21, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 31, -37, 35, 41],\n [-6, 22, -24, 32, 50],\n [14, 32, -58, -2, -8],\n [-10, -14, 32, 8, -10],\n [-2, 17, -14, 16, -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[[-15, -5, 13, 8, 41],\n [-4, -10, -13, 3, -9],\n [12, 10, 1, -7, -19],\n [16, 20, 14, -10, -10],\n [-13, -5, 10, 7, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -17, 1, 5, 14],\n [-8, 10, -10, -10, -4],\n [20, -8, 24, 20, -4],\n [-2, -6, -2, 0, 6],\n [2, 40, 0, -10, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, -24, 12, 12, -42],\n [6, 18, -3, 0, 27],\n [2, -6, -7, -12, -3],\n [-4, 6, 11, 18, 0],\n [-2, 36, 22, 42, 33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[35, 10, -15, 4, -12],\n [28, 17, -1, 6, -10],\n [58, 18, -11, -4, 15],\n [33, 9, -26, 14, -44],\n [32, 18, -9, 12, -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 5x5 matrix:\n[[3, 33, 16, 39, 54],\n [17, 22, -2, 37, 40],\n [-22, -4, -16, 8, 15],\n [9, 36, 40, 24, 39],\n [-14, -39, -26, 22, 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 5x5 matrix:\n[[45, 47, -48, 24, -1],\n [54, 64, -60, 12, 10],\n [-25, -65, 57, 24, -22],\n [-13, -32, 30, 6, -7],\n [18, 23, -36, 42, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-4, 24, -7, -22, 28],\n [-16, -12, 17, -16, -14],\n [-11, -19, 10, -4, -24],\n [-35, 31, 34, -77, -6],\n [18, -20, 21, 39, -38]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 0, -12, 15, 6],\n [-20, 0, 20, -25, -10],\n [-4, 0, 4, -5, -2],\n [-4, 0, 4, -5, -2],\n [-20, 0, 20, -25, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-72, -43, 2, 49, 0],\n [-50, -31, -33, -8, -56],\n [-15, -28, 19, 23, 9],\n [-22, -25, -9, 8, -22],\n [15, 2, 25, 17, 33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[21, -5, -30, -11, 4],\n [18, -3, 45, -10, 20],\n [-47, 18, 55, 15, 20],\n [6, 14, 18, -11, -14],\n [56, -50, 40, -6, 64]]\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, -23, -55, -44, -36],\n [13, -6, -27, -27, -19],\n [18, -6, -9, -27, 15],\n [19, 37, 29, 16, -4],\n [-8, 16, 30, 30, 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[[9, 50, -46, -13, 17],\n [29, -21, -1, 14, -38],\n [-28, -19, 33, -12, 36],\n [16, 16, -36, -45, 49],\n [16, -29, 3, -42, 50]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, -12, 12, -24, 12],\n [-6, 9, -9, 18, -9],\n [6, -9, 9, -18, 9],\n [-8, 12, -12, 24, -12],\n [10, -15, 15, -30, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[20, 4, -47, -52, 28],\n [-16, 28, -14, 11, 10],\n [32, 3, -8, 4, -12],\n [-17, -13, -22, 7, -25],\n [15, 4, 7, 29, -25]]\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[[2, 14, -8, -3, 13],\n [6, -6, 24, -17, 7],\n [-8, 4, -28, 22, -12],\n [0, -18, 18, -3, -12],\n [12, -24, 60, -36, 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[[-19, -27, 9, -6, 33],\n [-2, 3, 16, -1, -2],\n [-9, -3, 4, 4, 22],\n [8, -64, -2, 0, 34],\n [18, -34, -1, 3, 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 5x5 matrix:\n[[52, -3, 19, -7, 6],\n [-6, -2, 6, 16, 0],\n [-2, 15, -13, 3, -18],\n [0, 8, -12, 34, 1],\n [-22, -32, 4, 4, 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[[4, -18, -17, 0, 6],\n [18, -26, -9, 10, 22],\n [26, -18, 11, 18, 30],\n [32, -34, -1, 20, 38],\n [36, -30, 9, 24, 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[[-15, -3, 15, -3, 12],\n [34, 14, 14, 14, -26],\n [18, 6, -2, 6, -14],\n [-12, -6, -12, -6, 9],\n [9, 9, 39, 9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[35, -37, 9, -9, 8],\n [-9, -2, -3, 5, -12],\n [31, 3, 36, -29, 23],\n [13, -1, 30, -19, -1],\n [-62, 37, -45, 36, -23]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, -9, -15, -32, 1],\n [-36, 38, -32, -5, 3],\n [4, 3, 8, 0, 3],\n [-16, 10, -24, 18, -8],\n [28, -31, 24, 4, -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[[-9, -11, 7, -12, -11],\n [9, 1, 15, -13, -24],\n [0, -11, 20, -10, -18],\n [1, -3, 1, 15, 13],\n [15, 10, 7, -4, -15]]\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[[-17, 8, -23, -12, 21],\n [-24, -10, -60, 22, 46],\n [-21, -1, -39, -16, 43],\n [-1, 3, 5, -24, 7],\n [-30, 29, -30, 4, 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[[0, 5, 5, 4, 2],\n [0, 15, 15, 12, 6],\n [0, -5, -5, -4, -2],\n [0, -10, -10, -8, -4],\n [0, 15, 15, 12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, -9, -18, 6, 24],\n [-31, 3, -36, -9, 6],\n [4, 3, 6, -2, -8],\n [-11, 3, -12, -5, -2],\n [3, 6, 6, -5, -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[[15, 12, -12, 12, -18],\n [15, 12, -12, 12, -18],\n [15, 12, -12, 12, -18],\n [5, 4, -4, 4, -6],\n [-15, -12, 12, -12, 18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-45, -61, -25, 9, -1],\n [16, 53, 37, -2, 14],\n [-25, -46, -50, 6, 3],\n [11, -19, -7, 0, -7],\n [43, 22, -2, -7, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-36, -41, 2, -4, -13],\n [12, 12, 6, -2, -4],\n [-36, -30, -42, 18, 42],\n [-36, -31, -38, 16, 37],\n [-36, -36, -18, 6, 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[[6, 6, -12, 2, 6],\n [3, 3, -6, 1, 3],\n [3, 3, -6, 1, 3],\n [-12, -12, 24, -4, -12],\n [15, 15, -30, 5, 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[[-31, 16, -39, 29, 29],\n [30, -12, 38, -30, -26],\n [-13, -20, 3, 11, -13],\n [-4, -11, -6, 11, -4],\n [17, -8, 9, -7, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[55, 3, -22, 42, 53],\n [1, -21, -52, -11, 23],\n [25, -17, -34, 20, 33],\n [30, 34, -18, 11, 52],\n [-71, -35, 2, -58, -73]]\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, -20, -38, 5, -51],\n [46, -42, -4, 12, -14],\n [-55, 14, -8, -7, -47],\n [-43, 18, -62, 10, -34],\n [-66, 28, 12, -19, -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[[0, 12, 2, 12, -10],\n [0, -36, -6, -36, 30],\n [0, 6, 1, 6, -5],\n [0, -18, -3, -18, 15],\n [0, 36, 6, 36, -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 5x5 matrix:\n[[0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [-12, 0, -36, 6, 6],\n [-6, 0, -18, 3, 3],\n [-6, 0, -18, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[20, -20, 20, -16, -4],\n [15, -15, 15, -12, -3],\n [-10, 10, -10, 8, 2],\n [-25, 25, -25, 20, 5],\n [20, -20, 20, -16, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, -25, -25, -10, 5],\n [36, -68, -20, -16, -8],\n [-4, 3, -5, 6, 3],\n [-20, 42, 10, 20, 6],\n [8, -18, -10, 1, 0]]?\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, -12, -12, -12, 12],\n [18, -12, -12, -12, 12],\n [3, -2, -2, -2, 2],\n [6, -4, -4, -4, 4],\n [-12, 8, 8, 8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 19, -5, -22, -1],\n [-14, 56, -3, -42, 37],\n [22, 27, 7, -10, 63],\n [21, 0, -1, -7, 10],\n [51, -30, 3, 15, 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[[-5, -20, -40, -25, 10],\n [-14, -14, 8, 8, 16],\n [16, 22, 8, 2, -20],\n [-28, -35, -4, 3, 34],\n [-3, -12, -24, -15, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[20, -20, 20, 24, -12],\n [15, -15, 15, 18, -9],\n [-5, 5, -5, -6, 3],\n [-10, 10, -10, -12, 6],\n [-10, 10, -10, -12, 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[[21, 0, -1, 15, -5],\n [-27, -31, 19, -6, 2],\n [27, 31, -19, 6, -2],\n [15, 25, -15, 0, 0],\n [-3, 9, -5, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-7, -35, 3, 0, 40],\n [-22, -33, -40, 15, 10],\n [-62, 10, 4, -12, 6],\n [-23, 43, 43, -12, 12],\n [-50, -30, -44, 12, 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[[-43, -18, 7, -23, 13],\n [7, -1, 4, 11, 13],\n [-6, -14, 16, 18, 46],\n [-26, -13, 7, -10, 16],\n [-19, -1, -6, -23, -21]]\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, 40, -10, 54, -14],\n [-25, 65, 8, 53, -25],\n [-68, -20, -24, 30, 10],\n [57, 13, -18, -7, -14],\n [22, 78, 24, 41, -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[[4, 8, -4, 0, 16],\n [10, -7, 14, 15, -11],\n [-8, -7, 0, -5, -15],\n [-31, 1, -25, -35, -5],\n [-6, 6, -10, -10, 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[[-2, -28, -4, -28, -38],\n [-58, 24, -62, 12, -7],\n [6, -42, -8, -14, -49],\n [-8, -38, -16, -34, -57],\n [9, 37, 35, 9, 61]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[25, 25, 30, 10, -25],\n [19, -13, 14, 2, 25],\n [-20, -20, -24, -8, 20],\n [16, -32, 6, -2, 50],\n [30, 30, 36, 12, -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[[35, -48, -21, -53, -33],\n [21, 22, -2, -33, -57],\n [29, 13, 2, -25, -21],\n [-14, 34, 28, 38, 30],\n [-1, -30, -18, 5, 45]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 18, -72, -12, 48],\n [6, -18, 72, 12, -48],\n [6, -27, 18, -15, -12],\n [-4, 12, -48, -8, 32],\n [6, -30, 0, -24, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, -1, 5, 3, 4],\n [8, -13, 35, 6, 25],\n [18, -10, 10, -14, 4],\n [21, -7, -5, -23, -8],\n [-14, 14, -30, 2, -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[[20, 30, 0, -15, 10],\n [4, 6, 0, -3, 2],\n [12, 18, 0, -9, 6],\n [12, 18, 0, -9, 6],\n [4, 6, 0, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1, 1, 13, -7, -18],\n [-33, -19, 9, -11, -39],\n [-40, -7, 7, -17, -45],\n [44, 12, 24, 0, 3],\n [-8, -13, 1, 1, -6]]\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[[-39, -3, -54, -30, 39],\n [-39, -32, -70, -12, -12],\n [45, 50, 60, 0, -10],\n [-1, 24, 6, 8, 56],\n [0, -3, 34, -30, 19]]?\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 5x5 matrix:\n[[6, -6, -30, 0, 12],\n [-3, 3, 15, 0, -6],\n [6, -6, -30, 0, 12],\n [1, -1, -5, 0, 2],\n [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[[34, -23, 4, 47, -13],\n [28, -16, -4, 48, -12],\n [-36, 42, -48, 6, 6],\n [-26, 17, -13, -42, 18],\n [-56, 42, 6, -56, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[30, -35, 0, 52, -42],\n [-5, 0, -28, 40, 9],\n [-17, 18, -14, -22, 46],\n [11, -22, -30, 52, 3],\n [8, -32, 0, -4, -34]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[5, -42, -37, -45, -8],\n [-29, 6, 7, -61, -32],\n [-13, 34, -9, -37, 4],\n [13, -7, -27, -5, 17],\n [-7, -21, 11, -7, -21]]?\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, -5, 5, 0, 10],\n [25, 0, 0, 2, 8],\n [-17, 7, -7, 2, -6],\n [-10, 35, -35, 16, -6],\n [-5, 30, -30, 14, -4]]\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, -64, 15, 61, -70],\n [12, -12, 12, -8, 19],\n [13, -18, 10, -6, 20],\n [-9, -34, -17, 25, -14],\n [0, 50, -5, -31, 23]]\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[[8, -8, -12, -2, 10],\n [16, -1, 11, 11, -10],\n [4, -13, -27, -10, 23],\n [36, -18, -12, 9, 9],\n [-40, 25, 25, -5, -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[[41, -7, 3, 12, 36],\n [6, 4, 18, 15, 12],\n [-34, 65, -48, 21, -66],\n [-9, -3, 0, 1, 0],\n [32, -17, 38, 15, 46]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-5, 4, 17, 25, -16],\n [-19, 12, 35, 11, 4],\n [11, -4, -10, 18, -19],\n [21, 38, 19, 35, 11],\n [27, 12, -19, 5, 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[[16, 10, -10, 60, 51],\n [-1, 8, 34, -32, -65],\n [-7, 7, 35, 4, -38],\n [0, 5, 30, -21, -49],\n [20, 18, -25, 49, 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[[-30, 6, -6, -6, 6],\n [25, -5, 5, 5, -5],\n [-10, 2, -2, -2, 2],\n [0, 0, 0, 0, 0],\n [20, -4, 4, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 38, 39, -41, -23],\n [-21, -10, -8, 45, 31],\n [-24, -12, -39, 15, 39],\n [49, -13, -15, -15, -8],\n [30, -9, -6, -21, -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[[-28, 2, -6, -8, -6],\n [-19, 42, -32, 6, 14],\n [-11, 11, -11, -2, -1],\n [-32, 41, -52, -18, -26],\n [2, -10, -2, -12, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[10, -6, 26, 20, -40],\n [-12, 3, -48, 18, 6],\n [-11, 5, -35, -6, 28],\n [8, -1, 36, -22, 6],\n [2, 1, 14, -18, 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[[7, 7, 4, 5, 34],\n [16, -47, 10, 38, -20],\n [-47, -13, 41, 13, 22],\n [-34, -48, 44, 38, -4],\n [15, 1, -11, -1, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, -30, -24, 30, -24],\n [-10, -25, -20, 25, -20],\n [-2, -5, -4, 5, -4],\n [-12, -30, -24, 30, -24],\n [4, 10, 8, -10, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 20, -28, -2, 22],\n [-3, -23, 49, 26, -22],\n [-7, -35, 29, 10, -6],\n [-7, -7, -19, -11, 17],\n [17, -19, -11, -28, -4]]\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 5x5 matrix:\n[[6, 50, -72, 6, 1],\n [3, 22, -18, 9, -16],\n [18, -18, 30, 6, 28],\n [-40, 22, -48, -1, -48],\n [-8, 26, -42, -9, -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[[24, 18, 15, -6, 15],\n [-36, -28, -15, 4, -17],\n [-22, -21, 20, -17, 11],\n [46, 35, 25, -9, 26],\n [-14, -11, -5, 1, -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[[14, 14, -16, -12, 16],\n [8, -7, 0, 6, -25],\n [-30, -21, -13, -20, 28],\n [-44, -35, 3, -8, 12],\n [16, 16, 10, 12, -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[[5, -1, 12, -3, -13],\n [-44, -32, -48, 18, 40],\n [32, 30, 40, -19, -15],\n [-15, -13, -4, 1, 11],\n [-17, -29, -20, 16, -18]]\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 5x5 matrix:\n[[-10, -25, 20, -5, 10],\n [6, 25, -26, 12, -11],\n [-34, -45, 12, 19, 14],\n [28, 40, -14, -13, -13],\n [22, 5, 26, -34, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -4, -16, 0, 4],\n [0, 2, 8, 0, -2],\n [0, -4, -16, 0, 4],\n [0, -2, -8, 0, 2],\n [0, 5, 20, 0, -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[[-30, 10, 25, 25, 20],\n [21, -14, 7, -8, -19],\n [-38, 22, -1, 19, 32],\n [-25, 20, -20, 5, 25],\n [49, -28, 0, -25, -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[[-4, 34, 4, 24, 34],\n [-28, 25, -30, 0, 25],\n [0, 46, -68, 32, 50],\n [14, 50, -76, 9, 45],\n [-22, -38, 36, -29, -38]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, -2, -17, -18, -28],\n [61, 5, -15, 3, 71],\n [-36, -49, 34, 12, -39],\n [32, 12, -33, -17, 5],\n [-14, -26, 3, -31, -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[[31, -47, 18, -10, 4],\n [13, -17, 12, -5, 5],\n [17, -31, 3, -4, -5],\n [-2, 2, -52, 3, 21],\n [39, -55, 34, -14, 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[[-44, 56, -24, -16, -18],\n [10, 35, -55, -30, -50],\n [-44, 56, -24, -16, -18],\n [-29, 46, -26, -15, -21],\n [46, -14, 6, 40, 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[[-2, 6, 4, 10, -10],\n [6, -18, -12, -30, 30],\n [-4, 12, 8, 20, -20],\n [-4, 12, 8, 20, -20],\n [-5, 15, 10, 25, -25]]?\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 5x5 matrix:\n[[49, -34, 48, 60, 36],\n [1, -7, 32, -6, 53],\n [64, -40, 38, 84, 5],\n [-58, 42, -50, -72, -29],\n [7, 2, -4, 12, -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[[50, -3, 15, -18, 33],\n [1, 18, -4, -33, 0],\n [-59, -14, 18, -3, -30],\n [56, 0, 20, -9, 45],\n [-32, -54, 16, -9, -45]]\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, 15, -22, -8, 18],\n [17, 25, -6, -44, -16],\n [3, -25, 46, 4, -44],\n [8, 10, 0, -20, -10],\n [15, 25, -10, -40, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 2, 0, -15, -19],\n [-8, 10, 16, -3, 9],\n [10, -14, -22, 6, -10],\n [-6, -6, -6, 18, 18],\n [-14, 22, 34, -12, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[23, 11, 4, -21, -11],\n [-21, -11, 4, 23, 11],\n [11, 5, 4, -9, -5],\n [3, -1, 20, 7, 1],\n [14, 2, 40, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[18, -12, -9, 9, -6],\n [-18, 12, 9, -9, 6],\n [-36, 24, 18, -18, 12],\n [30, -20, -15, 15, -10],\n [-30, 20, 15, -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[[-32, -8, -1, -21, -30],\n [-23, -39, 38, -21, 6],\n [-2, 8, -5, -1, 1],\n [14, -8, 2, 10, -1],\n [-19, 15, -11, -12, -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 5x5 matrix:\n[[13, 49, 12, -44, 28],\n [0, -25, -15, 15, 0],\n [-15, -25, 3, 18, -6],\n [37, 16, -33, -5, -8],\n [12, 46, 12, -38, 20]]\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 5x5 matrix:\n[[3, 18, -6, 15, 6],\n [-2, -12, 4, -10, -4],\n [-6, -36, 12, -30, -12],\n [-2, -12, 4, -10, -4],\n [-6, -36, 12, -30, -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 5x5 matrix:\n[[-9, -3, 15, 15, 12],\n [2, -2, 14, 50, 36],\n [17, 3, -11, 25, 16],\n [43, 11, -50, -5, -9],\n [-15, -1, -1, -55, -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[[-16, -6, -14, 22, -8],\n [-9, -39, 23, -9, 5],\n [-18, -48, 20, 0, 2],\n [-6, 9, -15, 15, -6],\n [4, 24, -16, 8, -4]]?\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[[36, 13, -1, -14, -16],\n [39, 27, -25, -9, 10],\n [46, 40, -32, -18, 2],\n [-34, 32, -36, -6, 12],\n [-42, -20, 28, -2, -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 5x5 matrix:\n[[9, 26, -27, 26, -1],\n [18, 8, 6, 14, -4],\n [48, 20, 8, 43, -11],\n [21, 58, -7, 22, -1],\n [42, 20, -14, 52, -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[[0, -3, -4, 4, 2],\n [0, 3, 4, -4, -2],\n [0, -18, -24, 24, 12],\n [0, 0, 0, 0, 0],\n [0, -6, -8, 8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[8, -15, -22, 10, -11],\n [-9, 20, 28, -15, 14],\n [-1, 30, 32, -35, 16],\n [4, 5, 2, -10, 1],\n [-20, 0, 16, 20, 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[[40, -1, 20, 7, 56],\n [40, -5, 25, -5, 50],\n [16, 38, 43, -50, 22],\n [28, 9, 33, -29, 32],\n [-36, 29, -22, 15, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[37, -16, -4, 46, 47],\n [-26, -1, 6, 16, 10],\n [-28, 39, 34, 18, 12],\n [-4, 27, 22, 36, 22],\n [-2, 26, 16, -14, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, -12, 8, -6, -2],\n [5, -30, 20, -15, -5],\n [-5, 30, -20, 15, 5],\n [6, -36, 24, -18, -6],\n [-2, 12, -8, 6, 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 5x5 matrix:\n[[-2, -15, 27, -9, 11],\n [-38, 12, -30, 28, 42],\n [-14, 7, -9, -43, 5],\n [-15, -8, 12, -2, 23],\n [-16, 30, -54, -6, -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[[-22, 14, 14, -10, -14],\n [-42, 65, 13, -6, 30],\n [8, 11, -29, 24, 32],\n [5, -17, 0, -1, -17],\n [11, 21, -20, 17, 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[[12, -9, 9, 0, -27],\n [4, 9, -9, -16, -21],\n [-8, 3, -3, 4, 21],\n [2, 6, -6, -10, -12],\n [10, -9, 9, 2, -21]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-11, -12, 1, -12, 12],\n [-41, -20, 27, -12, 36],\n [3, 20, 31, 24, -24],\n [29, -2, -33, -13, -21],\n [-46, -40, 6, -36, 54]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[5, 21, 5, 47, 6],\n [-37, 32, 9, -29, 39],\n [2, -37, 12, -31, -11],\n [-16, 5, -6, -19, 19],\n [-19, 3, 29, 20, 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[[-10, 0, -32, 26, 26],\n [-15, -55, -24, -77, 9],\n [12, 0, -23, 0, 13],\n [-42, 30, 29, 16, 27],\n [4, 5, -28, 6, 26]]?\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, -12, 4, 22, -4],\n [-37, -9, 12, -19, -16],\n [-29, -25, 21, -2, -13],\n [-11, -19, 23, -26, 1],\n [11, 2, 3, -16, 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 5x5 matrix:\n[[1, -63, 2, -12, -29],\n [-11, -39, -19, -21, 7],\n [10, 18, 28, -28, 28],\n [1, 17, -6, 36, -25],\n [21, -23, 42, -2, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-33, -17, -2, 11, -10],\n [11, 10, -4, -11, 13],\n [-26, 0, -16, -14, 22],\n [-21, -12, 0, 9, -9],\n [35, 20, 0, -15, 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[[18, 12, -6, 30, 36],\n [-18, -12, 6, -30, -36],\n [12, 8, -4, 20, 24],\n [-12, -8, 4, -20, -24],\n [12, 8, -4, 20, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-48, 28, 2, 46, 0],\n [-20, 0, -20, 15, 10],\n [13, -16, -58, -19, 4],\n [39, -14, -19, -37, -10],\n [-19, -44, -8, 6, 54]]\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, 3, 3, -2, -4],\n [3, -9, -9, 6, 12],\n [18, -10, -30, 28, 24],\n [-6, 7, 12, -10, -12],\n [4, -1, -6, 6, 4]]\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[[34, -44, 0, 7, -34],\n [-4, 24, -6, 26, 2],\n [14, 25, -7, 55, -48],\n [9, -14, -13, -43, 30],\n [-26, 27, -1, 0, 44]]\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, -30, 4, -24, 42],\n [12, 18, 16, 24, -30],\n [-9, -8, 21, 4, 6],\n [15, 20, 5, 20, -30],\n [30, 34, -26, 16, -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[[-21, 12, -25, 16, -26],\n [-4, -4, 12, -20, -6],\n [-24, 18, -40, 34, -29],\n [15, 0, -5, 20, 20],\n [1, -8, 21, -28, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[87, 36, 24, 3, 36],\n [-84, -75, -25, 8, -3],\n [14, 6, -5, -3, 2],\n [-66, 2, 4, -2, -42],\n [-1, 20, -8, -9, -20]]?\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[[28, -18, 10, 30, -24],\n [3, 17, 14, 4, -8],\n [24, 66, 54, 24, -36],\n [10, 0, -26, -6, 16],\n [-36, -39, -57, -42, 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[[20, 26, 26, -5, 30],\n [6, 5, 15, 14, 5],\n [18, 22, 22, -3, 25],\n [26, 31, -3, -46, 35],\n [-30, -39, -21, 30, -45]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[48, 9, 6, -12, 12],\n [-26, -3, -6, 9, -8],\n [20, 30, -36, 30, -16],\n [10, 15, -18, 15, -8],\n [14, 27, -34, 29, -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 5x5 matrix:\n[[-16, 8, 4, 24, -12],\n [-4, 12, 26, 12, 18],\n [-9, 12, 21, 18, 9],\n [-15, 20, 35, 30, 15],\n [11, -18, -34, -24, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-22, -7, 41, -20, 1],\n [-7, 2, 20, 6, -38],\n [26, -3, -13, 10, -9],\n [-27, 3, 9, -2, -2],\n [7, 0, 19, -13, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, 3, 0, -15, -9],\n [-20, 5, 0, -25, -15],\n [-12, 3, 0, -15, -9],\n [-24, 6, 0, -30, -18],\n [-24, 6, 0, -30, -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[[0, 0, 0, 0, 0],\n [0, 12, 24, -30, 0],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [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[[-18, -15, 0, -9, -18],\n [-32, -9, 2, -9, -16],\n [32, -7, -6, 9, 4],\n [7, 45, 11, 0, 35],\n [46, -24, -18, 30, 2]]\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 5x5 matrix:\n[[-8, 16, -8, 8, 8],\n [-12, 10, -14, 3, 6],\n [-34, -16, -46, -20, -2],\n [-4, 36, 0, 22, 16],\n [36, 12, 48, 18, 0]]\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, 16, 20, 10, 0],\n [-10, 11, -19, -21, -3],\n [-24, -75, -15, 20, 8],\n [-22, 14, -8, -7, -33],\n [24, -9, -3, -7, 44]]\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[[-16, -16, 32, -30, -10],\n [28, -12, -16, -10, -10],\n [-8, -8, 16, -15, -5],\n [12, 4, -16, 10, 2],\n [-6, -18, 24, -30, -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[[20, 12, 4, -12, 12],\n [-41, -12, -8, 15, -5],\n [-40, 21, 10, 51, -42],\n [34, -9, -1, -24, 12],\n [3, -33, -12, -18, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[10, 16, -12, 2, -19],\n [13, 3, -16, 49, 34],\n [79, -22, -30, 8, -17],\n [68, -12, -32, 20, -4],\n [15, -38, 22, -12, -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[[10, -10, 10, -4, -6],\n [-20, 20, -20, 8, 12],\n [0, 0, 0, 0, 0],\n [5, -5, 5, -2, -3],\n [-10, 10, -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[[-27, 5, -51, -33, -47],\n [-49, -21, 5, -19, 13],\n [-9, -31, -60, -69, -2],\n [16, 24, -12, 14, -32],\n [50, 26, -10, 20, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-49, -50, -5, 11, -5],\n [-6, -16, -6, -22, 38],\n [42, 46, 6, -2, -8],\n [36, 41, 6, 2, -13],\n [-18, -15, 0, 12, -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[[-12, -3, 2, 0, 3],\n [1, -19, 8, -14, 19],\n [-1, 19, -8, 14, -19],\n [0, -33, 14, -24, 33],\n [-15, -45, 20, -30, 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[[0, -3, 21, -6, -27],\n [-17, 13, 21, -22, 2],\n [-19, -23, -5, 18, 13],\n [-4, -22, -6, 20, -2],\n [-22, -10, -18, 12, 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 5x5 matrix:\n[[-18, -20, 45, 51, -28],\n [17, 10, 57, 5, -32],\n [30, -54, -55, 33, 2],\n [-12, -29, 2, 15, 43],\n [-7, 12, 41, 12, -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[[22, -8, -32, 14, 14],\n [19, 41, 11, 43, 60],\n [-22, -23, 7, -34, -45],\n [17, -9, -27, 9, 8],\n [-10, 29, 35, 10, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[20, 30, 20, -20, -10],\n [-12, -18, -12, 12, 6],\n [-8, -12, -8, 8, 4],\n [12, 18, 12, -12, -6],\n [-12, -18, -12, 12, 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[[-35, 8, 4, 25, 19],\n [-8, 7, 5, -15, -28],\n [23, -15, 2, 9, 44],\n [-58, 25, -20, 34, -29],\n [-15, 10, -29, 24, -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[[-22, 12, -5, -5, 5],\n [23, -16, 3, 32, -2],\n [15, -20, 2, 36, -11],\n [-4, 0, -2, 13, 2],\n [-9, 36, -4, -34, 39]]\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, -35, 24, -6, 29],\n [-20, 36, -34, 6, 26],\n [6, -26, 20, 60, -20],\n [0, 52, -36, -16, -30],\n [0, -40, 27, 67, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-12, 24, 4, 0, 20],\n [0, 0, 0, 0, 0],\n [-6, 12, 2, 0, 10],\n [3, -6, -1, 0, -5],\n [-6, 12, 2, 0, 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 5x5 matrix:\n[[-1, -15, -8, -30, 3],\n [-15, -15, 27, -9, 3],\n [15, 15, -27, 9, -3],\n [-1, 15, 13, 33, -3],\n [-4, 10, 17, 27, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-10, -20, -20, -15, -15],\n [-4, -8, -8, -6, -6],\n [-2, -4, -4, -3, -3],\n [8, 16, 16, 12, 12],\n [-10, -20, -20, -15, -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[[-8, -16, 6, 26, 23],\n [4, 8, -16, 0, 8],\n [-10, -20, 8, 32, 28],\n [6, 12, 6, -30, -33],\n [-6, -12, 4, 20, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[44, 36, 8, 30, -32],\n [52, 6, 38, 6, -10],\n [-48, 20, -17, -44, -15],\n [-6, -26, 10, -1, 18],\n [-5, -55, -8, 37, 46]]?\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, -8, -9, -16, 6],\n [-8, -9, 20, 29, -12],\n [3, -35, 11, -31, 10],\n [1, -29, 13, 1, -2],\n [33, -12, -51, 18, -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[[-28, 0, 16, -36, 4],\n [-36, -19, 7, -30, 16],\n [20, 16, 0, 12, -12],\n [4, -8, -8, 12, 4],\n [20, 16, 0, 12, -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 5x5 matrix:\n[[39, -15, -22, 4, -23],\n [24, 0, -4, 4, -20],\n [-24, 30, 35, 1, 1],\n [26, -20, -25, 1, -9],\n [15, -15, -18, 0, -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[[-15, 30, -30, -25, 5],\n [-3, -18, 24, 13, -23],\n [9, -10, 8, 9, 5],\n [-12, 12, -9, -11, -8],\n [-18, 40, -41, -33, 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[[6, 14, -52, 14, 8],\n [-5, -7, 34, -7, 5],\n [-1, 1, 2, 1, 7],\n [3, 11, -34, 11, 14],\n [5, 3, -26, 3, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-20, -38, 17, 0, 48],\n [-7, -75, 20, -20, 44],\n [8, -4, 21, 45, -2],\n [-18, -18, -10, -42, 28],\n [-10, -56, 0, -49, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[28, -54, -12, 32, 38],\n [20, -30, 0, 20, 30],\n [12, -6, 12, 8, 22],\n [-14, 12, -9, -11, -24],\n [-4, 24, 18, -10, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-20, 25, -5, -15, 0],\n [12, -15, 3, 9, 0],\n [-16, -10, 21, -42, 0],\n [-8, 40, -27, 24, 0],\n [0, -24, 20, -24, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, 12, 0, -18, -15],\n [0, 0, 0, 0, 0],\n [4, 4, 0, -6, -5],\n [-8, -8, 0, 12, 10],\n [4, 4, 0, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[24, 40, 71, 4, -26],\n [-36, -1, -41, 1, 16],\n [12, -1, -37, -18, 10],\n [-59, -88, -44, 43, 16],\n [-19, -19, -22, 28, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-14, 22, -6, 35, -8],\n [42, -12, 30, -21, -30],\n [-12, -12, -12, -18, 24],\n [28, -8, 20, -14, -20],\n [18, 9, 16, 13, -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[[29, 46, -76, 14, 50],\n [-49, 19, 30, 33, -24],\n [10, -44, 14, -18, 32],\n [-29, -16, 32, -4, 2],\n [21, -3, -13, 14, 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[[-6, 6, 0, -5, -5],\n [6, -6, 0, 5, 5],\n [18, -18, 0, 15, 15],\n [-18, 18, 0, -15, -15],\n [6, -6, 0, 5, 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 5x5 matrix:\n[[8, -27, 20, 13, -23],\n [-4, -44, 43, 40, -33],\n [8, -23, 7, 1, -12],\n [27, -15, -20, -34, -4],\n [-12, 16, 5, 12, 5]]\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 5x5 matrix:\n[[5, -20, 15, 0, -25],\n [2, -8, 6, 0, -10],\n [2, -8, 6, 0, -10],\n [4, -16, 12, 0, -20],\n [2, -8, 6, 0, -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 5x5 matrix:\n[[-15, 12, 76, 20, -3],\n [4, 48, 50, 0, -41],\n [-12, -1, -7, -15, -35],\n [16, -2, 7, 26, 42],\n [-28, 2, 44, -18, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-13, 41, -8, -41, 12],\n [-17, 9, 2, 33, 12],\n [-15, -25, 23, 49, 18],\n [-9, 25, 3, -43, 15],\n [-20, -76, 31, 56, -1]]\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[[9, -8, 68, -37, 6],\n [1, 12, 28, -27, 1],\n [11, -13, 63, -35, 10],\n [-24, 50, 10, 4, -42],\n [1, 2, -22, 1, 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[[-34, -5, 23, -33, -19],\n [14, -29, 8, 0, 2],\n [-34, -21, 32, -40, -22],\n [24, 28, -30, 34, 18],\n [-22, -7, 17, -23, -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[[-10, -8, 12, -12, 8],\n [10, -3, 2, -12, 18],\n [-29, -21, 32, -30, 18],\n [24, 17, -26, 24, -14],\n [-9, 6, -6, 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[[-8, 9, -27, -17, -5],\n [7, 3, 5, 17, 15],\n [11, 9, 21, 35, 11],\n [-4, -54, 15, -46, -1],\n [-3, 0, -18, -12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-20, 26, 6, -16, -4],\n [20, 10, 30, -20, -5],\n [36, -6, 30, -12, -3],\n [48, -12, 36, -12, -3],\n [28, -10, 18, -4, -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[[16, 12, -4, -44, -16],\n [20, 78, 17, 0, -51],\n [16, 60, 8, -14, -42],\n [24, 60, 12, -21, -43],\n [-8, -24, -14, -18, 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[[-24, 36, 12, -36, -24],\n [-20, 30, 10, -30, -20],\n [-20, 30, 10, -30, -20],\n [-24, 36, 12, -36, -24],\n [-24, 36, 12, -36, -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 5x5 matrix:\n[[0, -29, 27, -7, -35],\n [39, -6, 24, 33, -24],\n [22, 27, 31, 31, 1],\n [-41, -13, 5, -38, -4],\n [33, 22, 0, 35, 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[[0, 26, 15, 11, 22],\n [3, -9, -25, -38, -40],\n [2, -59, -28, -10, -34],\n [25, -52, -32, 13, 4],\n [25, -31, -29, 4, 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[[-10, 17, -41, 28, 7],\n [6, 34, 10, -2, -19],\n [-10, -16, 38, -54, -16],\n [1, 0, 1, 15, 0],\n [-12, 12, -26, -28, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[47, -36, 41, -4, -28],\n [4, -4, -5, -1, -21],\n [23, -22, 19, -4, -12],\n [-30, -6, -35, -11, 25],\n [-7, -24, -10, -13, 23]]\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[[-8, -37, 12, 13, -3],\n [-36, 30, 36, 2, -30],\n [6, -36, -24, -16, 6],\n [-24, -51, 18, 7, -15],\n [-5, 8, 24, 22, -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[[18, 6, -22, 16, 2],\n [-34, -8, 36, -28, 14],\n [30, 6, -30, 24, -18],\n [-13, 1, 7, -8, 27],\n [5, -2, 0, 2, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1, -25, 28, 29, -4],\n [-48, 57, -24, -45, -20],\n [-7, 40, -13, -47, -26],\n [-8, -8, -16, 16, 24],\n [-13, -13, 28, 17, -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[[5, 6, -3, 3, 3],\n [25, 30, -15, 15, 15],\n [-15, -18, 9, -9, -9],\n [-5, -6, 3, -3, -3],\n [-15, -18, 9, -9, -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[[15, -18, 15, -6, -15],\n [15, -18, 15, -6, -15],\n [30, -36, 30, -12, -30],\n [-15, 18, -15, 6, 15],\n [-5, 6, -5, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, 3, 6, 59, -11],\n [0, -12, 20, -14, -16],\n [51, -18, 36, -45, 4],\n [24, -6, 8, -40, 10],\n [39, -9, 30, 18, -1]]\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[[-16, 1, 25, 32, 26],\n [-1, 11, 0, 27, 11],\n [-14, -14, 24, -6, 10],\n [15, 10, -25, -5, -15],\n [-3, 12, 3, 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 5x5 matrix:\n[[8, -2, 25, -21, 32],\n [-8, -4, -10, -6, 16],\n [3, -3, 15, -18, 30],\n [-7, -5, -5, -12, 26],\n [8, -4, 30, -30, 48]]\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, 0, -15, -12],\n [12, 15, 0, -15, -12],\n [16, 20, 0, -20, -16],\n [-12, -15, 0, 15, 12],\n [16, 20, 0, -20, -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[[-8, 18, 9, 0, -8],\n [-29, -20, 25, 2, -27],\n [11, 20, -43, 4, 5],\n [4, -30, -73, -25, -6],\n [-23, 26, -22, 4, -29]]\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 5x5 matrix:\n[[-11, 10, -22, -8, -18],\n [29, 15, 32, 27, 38],\n [5, -30, 26, 0, 14],\n [11, 25, 0, 13, 10],\n [8, 50, -20, 14, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[32, -41, 1, -13, 22],\n [28, -10, 9, 5, -14],\n [-10, -37, -3, -25, -55],\n [-12, 21, 67, -42, 39],\n [-46, 5, -25, -7, -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[[-4, -20, -4, 12, 8],\n [-4, -20, -4, 12, 8],\n [-1, -5, -1, 3, 2],\n [-5, -25, -5, 15, 10],\n [-4, -20, -4, 12, 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[[-3, 1, -6, 0, 6],\n [15, -5, 30, 0, -30],\n [21, 39, 0, -36, 42],\n [36, 34, 30, -36, 12],\n [-23, -23, -18, 24, -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[[-25, 54, -5, 18, 5],\n [-16, -5, 15, 0, -4],\n [44, -41, -15, -16, 1],\n [-28, 16, 0, 8, -2],\n [7, 7, -20, 2, 3]]\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[[62, 36, -22, 6, 18],\n [46, 74, -12, -31, -18],\n [36, 6, -30, 28, 10],\n [-80, -76, 1, 33, -7],\n [8, 34, 2, -23, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[30, 5, 38, 13, -39],\n [35, 6, -4, 16, -25],\n [-74, -18, -20, -22, 52],\n [4, 48, -8, -24, -12],\n [-1, 15, -28, 5, -14]]\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 5x5 matrix:\n[[36, 24, -30, 30, 12],\n [-12, -8, 10, -10, -4],\n [-18, -12, 15, -15, -6],\n [30, 20, -25, 25, 10],\n [-30, -20, 25, -25, -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[[2, -42, 4, 16, 11],\n [-1, -30, -2, 16, 8],\n [-15, 50, 50, 0, -10],\n [-9, 42, 36, -6, -9],\n [-8, -18, -58, 26, 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[[30, -6, 12, -24, 12],\n [25, -5, 10, -20, 10],\n [5, -1, 2, -4, 2],\n [30, -6, 12, -24, 12],\n [-10, 2, -4, 8, -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[[-5, 2, 6, 5, -4],\n [14, -8, -27, -5, 34],\n [11, -6, -20, -5, 24],\n [-34, 12, 34, 40, -12],\n [-19, 10, 33, 10, -38]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[24, 15, -24, 34, -12],\n [-3, -24, -18, -10, 36],\n [14, -6, -28, 16, 16],\n [2, 9, 21, -12, 17],\n [-8, -6, 13, -18, 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[[30, -18, -18, -30, -30],\n [30, -18, -18, -30, -30],\n [10, -6, -6, -10, -10],\n [-20, 12, 12, 20, 20],\n [30, -18, -18, -30, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[30, -8, 43, -11, 19],\n [-36, -14, -32, -10, 5],\n [4, -38, -20, 22, 25],\n [-16, -45, -28, 10, 21],\n [-56, 2, -60, 1, -25]]\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[[20, -12, 12, 16, -12],\n [-20, 12, -12, -16, 12],\n [-30, 18, -18, -24, 18],\n [15, -9, 9, 12, -9],\n [25, -15, 15, 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[[5, -11, -13, 10, -4],\n [-6, 2, -22, -2, 10],\n [4, -13, -24, 7, 3],\n [10, -23, -30, 27, -13],\n [-18, 16, -32, -19, 29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[25, -15, 25, 10, 15],\n [-15, 9, -15, -6, -9],\n [25, -15, 25, 10, 15],\n [-10, 6, -10, -4, -6],\n [-30, 18, -30, -12, -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[[24, -16, -20, 4, -8],\n [0, 0, 0, 0, 0],\n [-30, 20, 25, -5, 10],\n [30, -20, -25, 5, -10],\n [-18, 12, 15, -3, 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[[-10, 11, 39, -29, 50],\n [45, 12, 4, 20, 60],\n [-2, 13, -23, -11, -34],\n [4, 34, 7, -26, 30],\n [8, -4, -26, 12, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 4, -2, -4, 4],\n [30, -20, 10, 20, -20],\n [-30, 20, -10, -20, 20],\n [-12, 8, -4, -8, 8],\n [-24, 16, -8, -16, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0, 0],\n [-1, 1, 3, -2, 3],\n [-2, 2, 6, -4, 6],\n [3, -3, -9, 6, -9],\n [3, -3, -9, 6, -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[[-18, -4, 0, -16, -54],\n [-25, -9, 29, -3, 21],\n [7, 39, -54, -19, -35],\n [29, 15, -28, 9, 15],\n [-51, 34, -3, -32, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[16, 29, 53, 27, -5],\n [38, 14, 28, -50, 10],\n [-11, 1, -7, -34, 21],\n [20, 16, 27, -35, 14],\n [12, 2, -5, -11, -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[[22, -41, 5, 39, 26],\n [18, -38, 20, 31, 32],\n [38, -28, 18, 47, -42],\n [-2, 27, -23, -6, -17],\n [-20, 76, -8, -40, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-30, 0, 24, 18, 0],\n [-30, 0, 24, 18, 0],\n [30, 0, -24, -18, 0],\n [-30, 0, 24, 18, 0],\n [-5, 0, 4, 3, 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[[-14, 36, -32, -42, -80],\n [14, 9, 49, 44, 19],\n [12, -11, -17, -14, -5],\n [27, -16, 1, 13, 10],\n [15, 0, 60, 42, 42]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 20, -12, -2, -8],\n [6, 20, -12, -2, -8],\n [-3, -10, 6, 1, 4],\n [-3, -22, 16, 11, 10],\n [18, 30, -11, 19, -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[[25, 33, 19, 9, 0],\n [32, 38, 36, 4, -34],\n [-42, -54, -44, -9, 30],\n [23, 6, 22, -7, -53],\n [-11, 2, 10, 16, -13]]\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, 10, 21, 4, 13],\n [-33, -18, -16, -2, -23],\n [3, -35, -12, -16, 6],\n [9, -14, -8, -14, 23],\n [7, -47, -10, -16, -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[[-14, 16, 12, 20, 22],\n [-11, 16, 7, 23, 22],\n [1, -28, 1, -27, -32],\n [17, -33, -35, 2, -34],\n [23, -17, -22, -21, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[25, -5, -25, 5, -20],\n [-15, 3, 15, -3, 12],\n [-5, 1, 5, -1, 4],\n [20, -4, -20, 4, -16],\n [5, -1, -5, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-13, 11, -4, 2, 6],\n [1, 11, 1, -25, 25],\n [1, 25, 4, -2, -14],\n [6, -48, -3, 33, -21],\n [27, -63, 3, 9, -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[[-30, -6, -24, 36, -36],\n [15, 3, 12, -18, 18],\n [0, 0, 0, 0, 0],\n [-20, -4, -16, 24, -24],\n [25, 5, 20, -30, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, 5, 10, 11, -12],\n [18, -32, -31, -50, 16],\n [7, 2, -26, 2, -2],\n [12, 2, -8, 6, -12],\n [35, -5, -16, 1, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[14, 21, -18, 18, 4],\n [37, 3, 1, 4, -18],\n [16, -39, 30, -6, -22],\n [-20, -30, 9, 30, 11],\n [-22, 30, -24, 4, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[38, 37, 29, -49, -7],\n [0, -23, -32, 26, 62],\n [10, 73, 20, -56, -9],\n [21, 5, 38, -34, -39],\n [-9, -70, -37, 61, 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[[-1, -26, 35, 42, 31],\n [6, 4, -28, -36, -26],\n [9, 51, -39, -45, -36],\n [-22, -32, 20, 24, 22],\n [9, 8, 28, 36, 23]]\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[[-4, 31, 13, 0, 27],\n [60, 12, -16, 38, 6],\n [-29, -25, -7, -24, 12],\n [-2, -16, -4, 4, 4],\n [-11, -23, -21, -28, 6]]\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 5x5 matrix:\n[[18, -34, 38, 14, 10],\n [1, 37, 27, -9, 11],\n [42, -11, -3, -19, -10],\n [-18, 46, -36, -22, -17],\n [-16, 11, 1, 11, 19]]\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, 2, -3, -12, 8],\n [0, -12, -6, 16, 8],\n [-6, 18, 12, -17, -19],\n [-12, -12, 0, 30, -6],\n [-2, 22, 12, -27, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -3, 5, 2, -3],\n [-16, 12, -20, -8, 12],\n [12, -9, 15, 6, -9],\n [24, -18, 30, 12, -18],\n [-16, 12, -20, -8, 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[[-6, 21, 5, -18, -26],\n [-14, -11, -5, 11, 4],\n [-18, 13, 3, -7, -26],\n [48, 2, -8, -29, 40],\n [-8, -7, 3, 16, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-15, 10, -15, -10, -30],\n [15, -10, 15, 10, 30],\n [-12, 8, -12, -8, -24],\n [3, -2, 3, 2, 6],\n [-9, 6, -9, -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 5x5 matrix:\n[[2, -68, 6, 6, 54],\n [-15, 0, 29, -25, 29],\n [70, 1, 0, -39, -37],\n [-1, 27, 45, -54, 38],\n [-17, -30, 27, -13, 73]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-34, -4, -56, 1, -38],\n [-9, -19, -6, 17, -2],\n [7, -18, 5, 27, 4],\n [25, 5, 44, -5, 30],\n [-42, -32, -60, 29, -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[[5, 14, 58, 32, -43],\n [24, 24, 46, 20, 34],\n [44, 9, 5, 6, 26],\n [-25, -9, -3, 1, -29],\n [28, 15, 65, 50, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[16, -18, -10, 20, 24],\n [-8, 1, 33, -51, -18],\n [-15, 3, 15, -24, 3],\n [55, -25, 55, 1, 9],\n [-18, 26, 14, -11, -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[[-14, -13, 16, 1, 41],\n [-29, -7, -12, -23, -16],\n [-14, -41, 8, -39, 5],\n [-8, -5, 6, 0, 17],\n [-35, -48, 2, -55, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-24, -12, 12, 23, -32],\n [-30, 12, 27, 35, -14],\n [6, -78, -24, -6, -6],\n [26, 2, -15, -41, 19],\n [-32, 62, 38, 16, -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[[-6, 9, 0, 6, -12],\n [4, 11, -10, -4, -12],\n [30, 23, -40, -30, -20],\n [5, -16, 5, -5, 20],\n [0, -17, 10, 0, 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[[-20, -31, -15, -15, -23],\n [-8, -36, -4, 0, -4],\n [6, 2, 37, -30, -1],\n [-24, -29, -10, -30, -32],\n [14, 19, 3, 20, 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 5x5 matrix:\n[[-29, -24, -10, 43, -14],\n [-20, 6, 47, 1, -32],\n [-2, -5, -32, 14, 5],\n [-15, -74, 4, 55, 36],\n [17, 12, -32, -13, 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 5x5 matrix:\n[[4, 8, 8, 10, 2],\n [6, 12, 12, 15, 3],\n [-8, -16, -16, -20, -4],\n [-2, -4, -4, -5, -1],\n [10, 20, 20, 25, 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[[40, -24, 27, -14, -22],\n [-8, -4, -24, 22, -8],\n [-19, 24, 12, -10, 27],\n [23, -14, 12, 11, -15],\n [-8, -8, -33, 34, -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[[3, -1, -5, -8, 3],\n [-14, 0, 12, 24, -12],\n [36, 16, 8, -16, 24],\n [0, 7, 17, 20, -3],\n [-3, 1, 5, 8, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[18, -7, -8, -14, 4],\n [-32, 8, 10, -6, -32],\n [-4, -19, -16, 2, 38],\n [22, 14, 10, 6, -14],\n [-20, 6, 7, -13, -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[[24, 8, -4, -8, -16],\n [-6, -2, 1, 2, 4],\n [-36, -12, 6, 12, 24],\n [-18, -6, 3, 6, 12],\n [-30, -10, 5, 10, 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[[0, 0, 0, 0, 0],\n [5, 15, 25, 15, -30],\n [-2, -6, -10, -6, 12],\n [2, 6, 10, 6, -12],\n [6, 18, 30, 18, -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[[12, 16, 16, -12, -16],\n [-15, -20, -20, 15, 20],\n [0, 0, 0, 0, 0],\n [-9, -12, -12, 9, 12],\n [-6, -8, -8, 6, 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[[-10, -43, 17, 15, 9],\n [-25, 69, -7, 38, -21],\n [16, -71, 21, -27, 25],\n [25, -15, -28, -14, -18],\n [-20, -19, 20, 2, 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[[29, -6, 14, -34, 30],\n [-4, 0, 8, -16, -24],\n [2, -1, 8, -17, -12],\n [2, 0, -4, 8, 12],\n [-3, 0, 6, -12, -18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[10, 6, 30, 26, -1],\n [-40, 23, 3, -23, 31],\n [-16, 8, 20, -14, 5],\n [-5, -13, 33, 24, 9],\n [-35, 7, -11, -32, 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[[22, 20, 7, 11, 7],\n [4, -19, 1, 17, 10],\n [6, -30, -34, 15, -15],\n [-11, 9, 0, 2, -16],\n [3, -12, -6, -20, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, -12, 14, -41, -36],\n [-6, 1, -6, 27, 21],\n [5, -23, 6, -14, -70],\n [-7, -14, -8, 39, -19],\n [-6, 22, -20, 32, 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[[-5, 33, -33, -20, 18],\n [29, -21, 18, -16, -36],\n [10, 27, -37, -20, 2],\n [13, 14, -25, -12, -6],\n [-32, -18, 37, 28, 22]]?\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 5x5 matrix:\n[[0, -4, -5, 2, -4],\n [0, -12, -15, 6, -12],\n [0, -8, -10, 4, -8],\n [0, 8, 10, -4, 8],\n [0, -8, -10, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[14, 11, 31, -41, -15],\n [36, 26, -24, 9, -30],\n [10, 0, 17, -3, 5],\n [2, -20, -2, -40, -25],\n [4, 56, 2, -28, -30]]\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[[-22, 53, -16, -42, -15],\n [5, -13, 10, -7, 26],\n [38, -51, 52, 56, 11],\n [-1, -51, 8, 12, 27],\n [33, -48, 54, 69, -15]]\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, -17, 5, -14, -2],\n [15, -6, 10, -16, -30],\n [-6, 27, -38, 24, 14],\n [36, -29, 0, -18, 10],\n [0, -9, 22, -14, 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[[-12, -6, 7, 12, 13],\n [-28, -4, -16, -16, 32],\n [-40, 14, 35, 20, 41],\n [21, 39, 2, -33, -25],\n [-12, -6, 7, 12, 13]]\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, 2, 10, -14, -56],\n [4, -2, -6, 4, 22],\n [14, -7, -19, 9, 60],\n [-16, 8, 10, 19, 31],\n [26, -13, -25, -9, 24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-19, -18, -60, 33, 39],\n [0, -20, -42, 34, 20],\n [17, 40, 25, -4, 22],\n [12, 2, -35, 67, 59],\n [-18, 19, 13, 22, 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[[-14, 12, 0, -48, 34],\n [14, -10, -4, -10, 4],\n [-9, 18, -8, -8, -9],\n [20, -14, 19, -14, 12],\n [-4, 6, 45, -15, 20]]?\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, 6, 4, -8, 12],\n [6, -18, -12, 24, -36],\n [-4, 12, 8, -16, 24],\n [-1, 3, 2, -4, 6],\n [2, -6, -4, 8, -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[[-26, -1, -13, 20, -4],\n [66, -35, 59, -54, -18],\n [-10, -17, 25, -38, -19],\n [50, 19, -23, 22, 35],\n [-42, 17, -35, 12, 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[[-25, 5, -5, 5, 0],\n [-20, 4, -4, 4, 0],\n [-25, 5, -5, 5, 0],\n [-30, 6, -6, 6, 0],\n [-20, 4, -4, 4, 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[[-4, 10, 10, 6, 4],\n [-12, 30, 30, 18, 12],\n [2, -5, -5, -3, -2],\n [-8, 20, 20, 12, 8],\n [-12, 30, 30, 18, 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[[-39, 54, 10, 34, 22],\n [66, -32, 23, -48, -61],\n [32, -38, -2, -30, -23],\n [63, -48, 5, -44, -48],\n [48, -52, 9, -44, -35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-20, -11, -16, 45, 36],\n [53, 6, -16, -15, -57],\n [22, 18, -5, -2, 5],\n [-10, 6, 43, -64, -5],\n [10, -32, -11, 14, -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[[-12, 40, -22, -26, 42],\n [-6, -35, 11, 26, -33],\n [-12, 14, 2, -2, 14],\n [42, -1, -9, -20, -5],\n [-48, -50, -16, 40, -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 5x5 matrix:\n[[-3, 23, -34, 29, 22],\n [-15, -15, 24, -3, -6],\n [26, 26, -14, 34, 14],\n [41, 41, -38, 37, 20],\n [36, 24, -22, 12, 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 5x5 matrix:\n[[-5, 5, -20, -45, -35],\n [-7, -3, -14, -39, -23],\n [-6, -9, -3, -18, -3],\n [14, 36, -14, 6, -32],\n [-7, -18, 7, -3, 16]]\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[[-6, 0, -9, -12, -6],\n [-4, 0, -6, -8, -4],\n [-10, 0, -15, -20, -10],\n [-8, 0, -12, -16, -8],\n [6, 0, 9, 12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, -5, 15, -8, 22],\n [-5, 2, -34, 20, -41],\n [26, -16, -8, 8, 6],\n [-13, 7, -29, 16, -40],\n [-1, 0, -20, 12, -23]]\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, 18, -9, -18, 9],\n [18, -18, 9, 18, -9],\n [-12, 12, -6, -12, 6],\n [36, -36, 18, 36, -18],\n [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[[-6, 33, -51, -24, 30],\n [-4, -3, -9, 4, 20],\n [0, 10, -10, -8, 0],\n [6, -23, 41, 16, -30],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-3, 24, -24, 3, 15],\n [0, -15, 18, 9, -3],\n [1, 7, -10, -10, -2],\n [0, 25, -30, -15, 5],\n [-5, 25, -22, 14, 22]]\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 5x5 matrix:\n[[-28, -28, -40, -16, -18],\n [2, 24, 6, 42, 17],\n [-2, 4, -2, 6, -3],\n [-6, -58, -16, -76, -5],\n [-2, 11, -1, 21, 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[[-25, -11, 22, -11, -4],\n [13, 1, -26, 3, 3],\n [16, -11, 1, -36, 36],\n [-8, -8, -20, 0, -6],\n [-6, 9, -15, 30, -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[[-17, -4, 16, -12, -8],\n [26, 16, 6, 6, 18],\n [-13, -20, -40, 12, -16],\n [22, 20, 25, -3, 19],\n [-5, -16, -41, 15, -11]]?\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, 13, -29, -17, 6],\n [44, -44, -21, -19, -17],\n [-13, 19, 1, 13, 3],\n [-22, 24, 4, 8, 18],\n [41, -38, -24, 20, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[8, -22, -18, -24, -4],\n [24, 6, -18, 36, -48],\n [12, 15, -3, 36, -30],\n [16, -36, -32, -36, -12],\n [0, -8, -4, -12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[19, -11, -11, -11, 9],\n [10, -10, -6, -10, 10],\n [-16, 24, 10, 24, -26],\n [6, 26, -2, 26, -34],\n [12, 12, -6, 12, -18]]\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[[5, -2, -6, 4, -3],\n [-25, 10, 30, -20, 15],\n [-20, 8, 24, -16, 12],\n [-25, 10, 30, -20, 15],\n [10, -4, -12, 8, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 10, -6, -2, 8],\n [-6, 5, -3, -1, 4],\n [12, -10, 6, 2, -8],\n [30, -25, 15, 5, -20],\n [-6, 5, -3, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[15, -9, 0, 3, -3],\n [-35, 3, 12, -7, 13],\n [5, -48, 30, 1, 14],\n [15, 0, -6, 3, -6],\n [5, 33, -24, 1, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[9, -9, 7, -22, -29],\n [24, -40, 31, 11, -21],\n [29, 3, -7, 0, -35],\n [-7, -5, 6, -25, -12],\n [-35, 3, 3, -14, 31]]\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[[-51, 0, 36, -12, -35],\n [5, 17, -11, -56, 36],\n [19, -16, -14, 30, 4],\n [14, -33, -24, -18, 44],\n [16, -38, -4, 14, 17]]\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[[-22, -16, 12, 7, -6],\n [-36, 0, 8, -6, -4],\n [-32, -2, 8, -4, -4],\n [54, 18, -20, -3, 10],\n [-8, -32, 16, 20, -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[[-8, -2, -16, 0, 15],\n [30, 0, 20, 30, -25],\n [12, 6, 40, -12, -35],\n [-9, -3, -22, 3, 20],\n [12, -6, -24, 36, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, -8, -8, -12],\n [0, 0, 12, 12, 18],\n [0, 0, -10, -10, -15],\n [0, 0, -4, -4, -6],\n [0, 0, 8, 8, 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[[8, -3, 31, -2, 22],\n [-16, -8, -45, 13, -30],\n [-6, 12, 51, 3, 10],\n [-6, 21, -16, 11, -10],\n [-27, 41, 26, 22, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, -4, -4, -5, 4],\n [-8, 16, 16, 20, -16],\n [-4, 8, 8, 10, -8],\n [4, -8, -8, -10, 8],\n [-2, 4, 4, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[21, -25, -10, 27, 1],\n [-19, -3, -53, 8, -2],\n [-14, 42, -15, -23, 3],\n [-3, -19, 8, 2, -1],\n [-6, -53, 38, 17, -14]]\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 5x5 matrix:\n[[16, 3, 42, -5, -23],\n [11, 0, 15, 17, 26],\n [12, -2, 50, -2, -32],\n [8, 0, 30, -4, -22],\n [10, 9, -6, -5, 13]]\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, -2, -16, 33, -5],\n [4, 8, -6, 17, 3],\n [26, 18, -16, 35, 17],\n [-6, 50, -2, 46, 10],\n [34, 23, -17, 35, 19]]\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 5x5 matrix:\n[[8, 24, -6, -21, 7],\n [-2, -6, 24, 3, 5],\n [12, 36, 26, -35, 21],\n [-18, -54, -14, 50, -24],\n [-10, -30, 0, 27, -11]]\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, -10, 6, -20, 22],\n [15, 36, -15, 27, -24],\n [-14, -1, 0, 7, -9],\n [54, 18, 2, -12, 18],\n [-52, -27, 10, 3, -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[[-2, 8, -10, 4, 18],\n [18, 20, -20, -7, 17],\n [4, 12, 22, 13, -9],\n [-5, -11, -9, -7, 1],\n [-4, 7, 34, 20, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-45, 29, 5, -26, 9],\n [-4, -32, 40, 0, -56],\n [-32, -13, 5, 18, -25],\n [-7, -1, -25, 26, 13],\n [13, 30, -40, 0, 57]]?\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, 17, 25, -43, 38],\n [15, -14, 8, -8, -9],\n [0, -16, -4, -2, -28],\n [-31, 20, -21, -3, -3],\n [-4, -11, 2, -2, -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[[52, 36, 44, 12, -16],\n [-52, -20, -24, 8, 24],\n [60, 20, 19, -23, -32],\n [8, 6, 13, 14, 1],\n [-14, 30, 20, 10, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, -12, -2, 12, -10],\n [0, 0, 0, 0, 0],\n [-36, -36, -6, 36, -30],\n [36, 36, 6, -36, 30],\n [-18, -18, -3, 18, -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[[0, 0, 0, 0, 0],\n [24, -6, 12, 30, -24],\n [-8, 2, -4, -10, 8],\n [-4, 1, -2, -5, 4],\n [-24, 6, -12, -30, 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[[3, -4, 38, 28, 10],\n [13, 37, 16, -13, 16],\n [-10, 8, 50, 22, 32],\n [-16, 10, 24, 2, 28],\n [-16, -10, 32, 22, 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[[-12, -22, 4, 4, -4],\n [12, 32, 2, -2, 16],\n [30, 20, -31, -17, -32],\n [-24, 6, 38, 18, 52],\n [-12, 3, 19, 9, 26]]\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[[22, -4, -48, 18, -18],\n [-16, 1, 30, -12, 3],\n [-4, 2, 12, -4, 10],\n [10, 2, -12, 6, 12],\n [7, 0, -12, 5, 1]]?\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[[-30, 47, 46, 5, -39],\n [31, -25, -2, 9, 14],\n [43, -27, 10, 31, 16],\n [-19, -5, -42, 9, 24],\n [-24, 18, -8, 39, 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[[12, 3, -18, -12, -9],\n [-12, -3, 18, 12, 9],\n [16, 4, -24, -16, -12],\n [16, 4, -24, -16, -12],\n [-20, -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[[-2, 5, -1, 1, -2],\n [-16, 4, 20, 4, 0],\n [28, 11, -49, -5, -8],\n [4, -10, 2, -2, 4],\n [2, -5, 1, -1, 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[[13, -34, 38, 44, -7],\n [-5, -1, -22, -21, -22],\n [6, -24, -9, -5, -27],\n [2, -22, 32, 38, -16],\n [36, -45, 6, 7, 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[[0, 20, 38, 8, -6],\n [0, -2, -8, 2, 2],\n [0, -18, -36, -6, 6],\n [0, -14, -26, -6, 4],\n [0, 12, 24, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[48, -42, -6, 30, -15],\n [8, -10, 14, -22, 11],\n [36, -30, -12, 36, -18],\n [10, -11, 10, -14, 7],\n [-44, 40, -2, -14, 7]]\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, 12, 6, 2, 10],\n [-51, -7, -56, -2, -17],\n [17, -6, -9, 13, 11],\n [-4, 20, 57, -58, -38],\n [30, -12, 37, -14, -17]]\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 5x5 matrix:\n[[0, 3, 6, -3, 1],\n [30, -44, -4, -38, 16],\n [-60, 34, 8, 46, 6],\n [0, 9, 18, -9, 3],\n [25, -12, -38, 9, -22]]\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, -15, 6, 18, 33],\n [32, -5, 16, -29, -24],\n [22, -5, 12, -19, -14],\n [8, 5, 0, -11, -16],\n [31, -15, 22, -22, -7]]\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 5x5 matrix:\n[[0, -12, 0, 20, -20],\n [0, 2, -20, -10, 20],\n [0, -10, -26, 8, 5],\n [0, -2, 2, 4, -5],\n [0, 0, -24, -8, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-38, 20, 33, -21, 38],\n [-8, -24, -22, -18, 12],\n [3, 28, 17, 3, 10],\n [1, 44, 29, 3, 18],\n [0, 20, 5, -9, 22]]\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 5x5 matrix:\n[[9, 6, -15, -9, 15],\n [9, -30, 21, 39, -21],\n [-12, -2, 14, 4, -14],\n [30, -16, -14, 18, 14],\n [-21, 16, 5, -19, -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[[-44, -26, -48, -12, 24],\n [5, 0, 10, -2, -8],\n [-24, -12, -5, 0, -4],\n [32, 7, 22, -10, -12],\n [-43, -25, -52, -12, 28]]\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, -26, 4, -18, -11],\n [50, -18, 20, -44, 40],\n [20, 49, -40, -8, 5],\n [-35, -23, 20, 26, -12],\n [5, -31, 44, 4, 33]]\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 5x5 matrix:\n[[-20, 20, 20, -5, 30],\n [-20, -40, -28, 7, -24],\n [-8, -52, -40, 10, -42],\n [-8, 8, 8, -2, 12],\n [4, 6, 4, -1, 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[[13, 3, 18, 12, -3],\n [-9, -4, -29, -11, 14],\n [-19, 1, 20, -10, -29],\n [0, 0, 0, 0, 0],\n [51, 6, 21, 39, 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[[0, 0, 0, 0, 0],\n [10, 12, -10, 8, 0],\n [20, 24, -20, 16, 0],\n [-10, -12, 10, -8, 0],\n [30, 36, -30, 24, 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[[4, 16, 16, -4, 8],\n [-5, -20, -20, 5, -10],\n [-3, -12, -12, 3, -6],\n [3, 12, 12, -3, 6],\n [-5, -20, -20, 5, -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[[10, 36, -32, -32, -48],\n [9, 29, -27, -26, -38],\n [-1, -24, 14, 20, 36],\n [16, -7, -17, 2, 22],\n [27, 2, -36, -8, 16]]?\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[[16, -21, 8, -7, 43],\n [-27, 28, -44, -24, -3],\n [3, -44, 32, 20, -13],\n [4, -4, 27, 22, -13],\n [43, -14, 6, -11, 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[[15, -9, 6, 39, 6],\n [21, 1, 18, 41, -6],\n [-12, -20, -24, -4, 24],\n [-3, 12, 6, -18, -12],\n [-4, -35, -28, 27, 38]]?\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, 9, 0, 6, 6],\n [-5, -15, 0, -10, -10],\n [4, 12, 0, 8, 8],\n [5, 15, 0, 10, 10],\n [-3, -9, 0, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-56, -18, 33, 15, -6],\n [30, -10, 12, 26, 10],\n [-58, -2, 34, 16, -2],\n [-52, -9, -12, -23, -28],\n [-65, -7, -9, -38, -22]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -1, 0, 6, 4],\n [-12, 3, 0, -18, -12],\n [-12, 3, 0, -18, -12],\n [-20, 5, 0, -30, -20],\n [4, -1, 0, 6, 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[[-16, -9, 36, -6, -16],\n [40, -9, -60, -6, 28],\n [-2, -2, 0, 4, -13],\n [6, -15, 3, -9, -3],\n [2, 16, -25, 17, -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[[-7, 3, 1, 2, 5],\n [36, 6, -48, -30, 12],\n [-1, -31, -25, 26, 11],\n [3, -2, -13, -7, 15],\n [34, 25, -7, -71, 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[[-34, -16, -46, -34, -30],\n [-7, -33, -21, -5, -14],\n [-36, -13, -16, 42, -33],\n [27, 11, 41, 40, 23],\n [-9, -36, -15, 17, -17]]?\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[[26, 2, 6, -7, 27],\n [29, -12, -36, -32, 23],\n [10, 10, 30, 13, 15],\n [16, -8, -24, -20, 12],\n [-11, 8, 24, 18, -7]]\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, -37, 44, -48, -30],\n [-42, -30, 34, -40, -20],\n [-42, -53, 54, -56, 34],\n [-27, -7, 10, -17, -36],\n [12, 27, -24, 24, -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[[-45, 3, -6, -18, -3],\n [15, -35, 26, -8, -25],\n [-34, -8, 24, 4, -2],\n [-18, 12, -60, -54, -12],\n [-19, 19, 34, 50, 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[[17, -19, -35, 2, 12],\n [41, 19, 16, -6, -11],\n [-68, -47, -43, 22, -12],\n [-14, -10, -13, 0, 17],\n [-11, -3, -10, -10, 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[[4, -5, -7, 49, 24],\n [-38, -11, 18, 18, 12],\n [-14, 10, 41, 41, -18],\n [30, 26, 24, -44, -18],\n [43, 17, -3, 23, -6]]?\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, 18, 12, -39, 0],\n [-24, -24, 36, -51, -12],\n [-19, 14, 13, 10, 19],\n [-14, -17, 15, -13, -6],\n [17, -31, -64, 8, -33]]?\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 5x5 matrix:\n[[23, 29, 0, -13, 1],\n [24, 32, -4, -16, -4],\n [31, 43, -9, -23, -10],\n [-21, -33, 15, 21, 18],\n [-5, -5, -3, 1, -4]]\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, -9, -15, 0, -6],\n [-18, -9, -15, 0, -6],\n [6, 3, 5, 0, 2],\n [-12, -6, -10, 0, -4],\n [18, 9, 15, 0, 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[[-8, -8, -27, -13, 10],\n [-14, -25, 8, 4, -9],\n [-60, -62, 7, -19, 1],\n [3, 21, 40, -1, -8],\n [-8, 11, -5, -17, 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[[-11, 47, -46, 62, -32],\n [-3, 16, -8, 32, -19],\n [-5, 15, -15, 31, 12],\n [8, -35, 35, -43, 27],\n [-3, 6, -18, -6, 15]]\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, 0, 0, 0, 0],\n [10, 25, -10, -30, 20],\n [-8, -20, 8, 24, -16],\n [12, 30, -12, -36, 24],\n [-6, -15, 6, 18, -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[[-30, 20, -45, -20, 25],\n [0, -20, 15, 30, -5],\n [-21, 34, -33, -6, 7],\n [-2, -18, 7, 15, 2],\n [21, 12, 39, 51, -42]]\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 5x5 matrix:\n[[-2, 6, 48, -4, 14],\n [14, 12, -30, -14, 16],\n [8, 10, 6, -6, 14],\n [-21, -26, 3, 30, -42],\n [7, 13, 18, -18, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-23, -5, 14, -12, -17],\n [-34, -26, 19, -8, -27],\n [-46, -22, 41, -8, -25],\n [29, 25, -15, 6, 24],\n [-30, -12, 45, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[22, 24, 3, 17, -5],\n [21, 27, 3, 18, -8],\n [18, -46, -10, -16, -10],\n [1, 43, 16, 21, 48],\n [1, 3, 3, 2, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-18, -15, -12, -3, 9],\n [36, 30, 24, 6, -18],\n [24, 20, 16, 4, -12],\n [6, 5, 4, 1, -3],\n [24, 20, 16, 4, -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[[-20, -8, 20, 8, 16],\n [-36, -9, 35, 18, 22],\n [15, 6, -15, -6, -12],\n [7, 19, -10, 8, -26],\n [18, 18, -20, 0, -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[[8, -3, 5, 6, -3],\n [-12, -5, 45, 14, 1],\n [0, 4, -12, 8, 4],\n [-34, 12, -7, -6, 15],\n [18, -7, -8, -22, -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[[2, 10, -2, -28, -7],\n [-47, 36, 8, 27, 45],\n [4, 6, -25, 84, -6],\n [-11, 14, 12, -71, 14],\n [24, -58, 23, -8, -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[[24, -16, 0, -20, 0],\n [12, -8, 0, -10, 0],\n [-24, 16, 0, 20, 0],\n [0, 0, 0, 0, 0],\n [24, -16, 0, -20, 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[[-1, 2, 9, -6, 10],\n [-11, 7, 59, -61, 45],\n [4, -5, -28, 23, -27],\n [3, -5, 31, -29, 25],\n [12, -7, -35, 43, -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[[0, -63, -26, -18, -32],\n [27, -36, -15, 0, -24],\n [27, -27, 3, 24, -18],\n [36, -21, -26, -18, -20],\n [-12, -20, -12, -16, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[7, 3, 13, 6, -10],\n [-1, -3, 29, 30, -32],\n [14, 10, -22, -36, 32],\n [2, 2, -10, -12, 12],\n [5, 5, -25, -30, 30]]\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 5x5 matrix:\n[[-11, -9, 19, 31, -5],\n [24, -32, -21, 20, 3],\n [11, 15, 19, -35, -53],\n [9, 5, -8, -5, 39],\n [-8, -6, -12, -28, -100]]\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, -10, 12, -8, 12],\n [-15, -15, 18, -12, 18],\n [5, 5, -6, 4, -6],\n [-20, -20, 24, -16, 24],\n [-15, -15, 18, -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[[22, 13, 53, -14, 20],\n [12, -4, 18, 6, 18],\n [6, 35, -3, 30, 20],\n [-38, 38, -49, 31, -11],\n [-62, 39, -5, -7, -19]]\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[[-37, 29, 1, -18, 18],\n [-37, 24, 30, 13, -6],\n [-7, -6, 35, 17, 19],\n [-50, 12, 56, 19, 17],\n [15, -17, -58, -42, 5]]\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, -24, 20, 2, -8],\n [-10, 6, -3, 14, -6],\n [12, -24, 20, -28, 8],\n [27, 42, -44, 11, 7],\n [-39, -18, 15, -11, 3]]\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[[-12, 9, -12, 15, -9],\n [12, -9, 12, -15, 9],\n [24, -18, 24, -30, 18],\n [12, -9, 12, -15, 9],\n [-8, 6, -8, 10, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-30, -24, 48, 24, 30],\n [-10, 0, -4, 0, 10],\n [0, -10, 25, 10, 0],\n [-20, -18, 37, 18, 20],\n [5, 2, -3, -2, -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[[9, 51, 47, -32, 47],\n [51, 23, 43, 18, 3],\n [-3, 38, 38, -25, 28],\n [-11, -26, -16, 25, -46],\n [14, 6, 35, -5, 15]]?\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, -30, -15, 27, 18],\n [-20, 15, 11, 38, -8],\n [6, -2, 9, 49, 14],\n [13, 26, 14, -53, 2],\n [25, -21, -16, -34, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[7, -1, -10, -23, -32],\n [22, 24, 10, 32, 8],\n [-8, 18, -59, 17, -1],\n [5, 25, -32, 33, 10],\n [12, 33, -42, 34, -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 5x5 matrix:\n[[-47, -6, 4, -8, 12],\n [46, 11, 24, -26, -5],\n [-38, 44, 20, 56, 12],\n [-24, 32, 60, -8, 40],\n [-24, 26, 30, 16, 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[[-4, 1, 2, 7, 1],\n [-27, -37, 16, 31, -2],\n [-23, -22, 20, 38, 9],\n [5, 29, 30, -3, 32],\n [13, 33, -4, -9, 8]]?\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 5x5 matrix:\n[[45, 13, -4, 22, 6],\n [-38, -13, 26, -16, -15],\n [-13, -14, 24, 10, -7],\n [-37, -2, -15, -32, -1],\n [-31, 3, 25, -36, -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[[23, 12, 40, 14, -36],\n [-19, -6, -26, -10, 18],\n [6, -6, -6, 0, 18],\n [21, 4, 24, 10, -12],\n [-24, -11, -39, -14, 33]]\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[[-25, -25, 35, 17, 8],\n [-17, 55, 2, -14, -13],\n [33, 15, -35, 15, -14],\n [0, 30, -6, 6, -12],\n [-26, -40, 37, 3, 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[[5, 2, -6, -1, 6],\n [-30, -12, 36, 6, -36],\n [-30, -12, 36, 6, -36],\n [-5, -2, 6, 1, -6],\n [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[[-13, 0, 23, 6, -23],\n [5, 30, 20, 30, -20],\n [31, 30, -26, 18, 26],\n [2, 12, 8, 12, -8],\n [-5, -30, -20, -30, 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[[10, 10, -15, -20, 25],\n [10, 10, -15, -20, 25],\n [-6, -6, 9, 12, -15],\n [0, 0, 0, 0, 0],\n [-6, -6, 9, 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[[-20, -24, -4, -8, 8],\n [-20, 57, -30, 32, -21],\n [-7, -38, 9, -18, 14],\n [-1, 37, -21, 24, -19],\n [45, 26, 9, 10, -14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[27, -9, -25, 13, 0],\n [-27, 9, 33, -15, 18],\n [0, 0, 12, -3, 27],\n [-33, 11, 35, -17, 10],\n [12, -4, -4, 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 5x5 matrix:\n[[-2, 8, 10, 0, -4],\n [2, -8, -10, 0, 4],\n [4, -16, -20, 0, 8],\n [6, -24, -30, 0, 12],\n [4, -16, -20, 0, 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[[-46, 2, 8, 10, 24],\n [-14, -1, 20, 53, 30],\n [36, -11, -44, -33, 6],\n [1, -15, 8, 41, 4],\n [27, 1, -36, -35, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-21, 20, 8, -24, -8],\n [1, 9, 19, -2, 45],\n [30, -16, -8, 24, -8],\n [-31, 18, 2, -28, -18],\n [-60, -12, -16, -18, 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[[18, 22, 10, -12, -26],\n [7, 28, -2, -5, 1],\n [-37, -53, 13, 30, -3],\n [-7, 17, 11, 8, -13],\n [1, 9, 3, 0, -5]]?\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, -65, 38, -27, 5],\n [24, 23, -1, -6, -26],\n [28, -11, 7, -25, 13],\n [-2, -37, 19, -9, 33],\n [-21, 6, -15, 39, 31]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 8, -42, -16, -45],\n [2, 30, -41, -5, -24],\n [-32, -5, 43, -25, 47],\n [40, -64, 38, 26, -17],\n [18, -18, -21, -21, -52]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[10, 18, 4, -22, -52],\n [11, -15, 6, 3, 44],\n [3, 1, 6, -25, 13],\n [2, -4, -4, 26, -6],\n [6, -12, -12, 78, -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[[52, -49, -10, -6, -35],\n [-6, 19, -11, -11, -1],\n [4, 24, -23, 10, -21],\n [40, -36, -12, 22, -36],\n [-38, -6, 21, -7, 44]]?\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, -30, -36, -6, -30],\n [4, -5, -6, -1, -5],\n [20, -25, -30, -5, -25],\n [-8, 10, 12, 2, 10],\n [12, -15, -18, -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[[-18, 6, 10, -12, -31],\n [6, -2, -4, 4, 7],\n [-36, 12, 26, -24, -32],\n [24, -8, -24, 16, -12],\n [-12, 4, 14, -8, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[30, 56, 12, -2, 36],\n [-15, -33, -9, 9, -18],\n [-70, -18, 30, -22, 60],\n [-30, -11, 11, -6, 24],\n [35, 11, -17, 59, 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[[-25, 20, 4, -2, -14],\n [-35, 0, 12, 0, -14],\n [-17, 37, 29, 26, -25],\n [27, -47, 5, 8, 19],\n [70, -65, -15, 1, 43]]?\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 5x5 matrix:\n[[30, -45, -10, 30, -45],\n [20, 15, -30, -20, -5],\n [6, -9, -2, 6, -9],\n [34, -42, -16, 26, -46],\n [-30, 18, 24, -6, 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[[-8, -3, 22, -38, -25],\n [-5, 26, 30, 10, 19],\n [-11, -8, -16, 11, 18],\n [-8, -3, 22, -38, -25],\n [8, 2, -2, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 3, -9, -9, 0],\n [6, -3, 9, 9, 0],\n [8, -4, 12, 12, 0],\n [-8, 4, -12, -12, 0],\n [-4, 2, -6, -6, 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 5x5 matrix:\n[[-8, 7, -26, -1, 7],\n [27, 40, 7, -18, 19],\n [60, 21, 16, 7, -11],\n [-27, -16, -20, -12, -7],\n [-33, 9, -19, -19, 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[[8, 4, -8, 4, -10],\n [-8, -30, 0, -6, 23],\n [13, -26, -23, 4, 0],\n [-3, -8, 1, -2, 7],\n [24, 12, -24, 12, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[60, -36, -34, 10, 26],\n [-21, 6, 22, -31, 1],\n [-24, 36, -14, 50, -26],\n [-23, 20, 9, -14, -2],\n [32, -8, -28, 4, 20]]\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 5x5 matrix:\n[[-30, -10, 30, 0, 25],\n [-18, -6, 18, 0, 15],\n [0, 0, 0, 0, 0],\n [-24, -8, 24, 0, 20],\n [-36, -12, 36, 0, 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[[-22, -17, 5, 18, -4],\n [-10, -16, 0, 18, 6],\n [-22, -24, 3, 24, 4],\n [1, -12, -4, 3, 26],\n [-3, 34, 11, -51, 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[[-6, 3, 15, 18, 6],\n [-8, 4, 20, 24, 8],\n [12, -6, -30, -36, -12],\n [-2, 1, 5, 6, 2],\n [-4, 2, 10, 12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[20, 0, -10, 0, 5],\n [4, 0, -2, 0, 1],\n [8, 0, -4, 0, 2],\n [8, 0, -4, 0, 2],\n [-20, 0, 10, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -12, 16, 24, -4],\n [0, -15, 20, 30, -5],\n [0, 9, -12, -18, 3],\n [0, -12, 16, 24, -4],\n [0, -3, 4, 6, -1]]\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[[-16, 17, -32, 17, 21],\n [45, -21, 30, -35, 38],\n [50, -25, 48, -47, 29],\n [41, -31, 28, -2, -2],\n [-45, 24, -52, 26, -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[[-8, -8, -16, -24, 0],\n [2, 2, 4, 6, 0],\n [12, 12, 24, 36, 0],\n [10, 10, 20, 30, 0],\n [-12, -12, -24, -36, 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[[-17, 37, 0, -38, 10],\n [-10, 39, -3, -26, 11],\n [-6, -8, 2, -4, -2],\n [4, 10, 10, -3, -1],\n [-19, 32, 9, -26, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-20, 24, 8, -20, -20],\n [-30, 36, 12, -30, -30],\n [-30, 36, 12, -30, -30],\n [20, -24, -8, 20, 20],\n [30, -36, -12, 30, 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[[19, -24, -2, 9, -10],\n [15, -25, 4, 15, -7],\n [-29, 40, 12, 12, -8],\n [-7, 16, 4, 12, -16],\n [1, -23, 6, -6, 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 5x5 matrix:\n[[25, -31, -25, 5, -9],\n [-21, 7, 19, -5, -9],\n [-17, -13, 13, -15, -21],\n [-38, -18, 32, 10, -48],\n [27, 13, -23, -14, 36]]\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, -6, -6, 15, 0],\n [-6, 6, 6, -15, 0],\n [2, -2, -2, 5, 0],\n [-6, 6, 6, -15, 0],\n [-8, 8, 8, -20, 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 5x5 matrix:\n[[26, -10, 20, 42, -24],\n [-34, 23, -4, -36, 6],\n [-23, 26, 21, -8, -27],\n [-4, 9, 13, 13, -9],\n [-26, 10, -20, -42, 24]]\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[[-25, -25, 22, -10, 5],\n [-7, 0, -8, -9, 35],\n [12, 12, -50, -36, -50],\n [-1, 3, 14, 18, 45],\n [2, 3, -53, -51, -55]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-9, -15, 9, -12, -15],\n [-3, -5, 3, -4, -5],\n [-15, -25, 15, -20, -25],\n [9, 15, -9, 12, 15],\n [12, 20, -12, 16, 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[[-18, 6, 6, -18, 18],\n [-43, -2, -28, 3, 66],\n [5, 4, 14, -15, -12],\n [24, 2, 14, 12, -42],\n [13, -5, -1, -6, -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[[-3, -8, -23, 18, -12],\n [-20, -8, 4, -32, -8],\n [31, 6, 33, 16, 34],\n [33, -56, 33, 34, 48],\n [-18, -28, -14, -8, -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[[24, 39, 6, 11, -46],\n [34, 15, -13, 17, 42],\n [44, 0, -39, -2, 11],\n [22, 12, -14, 16, 31],\n [38, 11, -29, -3, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -34, -22, 18, -5],\n [8, 10, 27, 11, -44],\n [0, 6, 21, -11, -4],\n [-8, -10, -36, 2, 30],\n [-20, 32, -54, 12, 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[[30, -25, 30, 0, 30],\n [6, -5, 6, 0, 6],\n [6, -5, 6, 0, 6],\n [-36, 30, -36, 0, -36],\n [-30, 25, -30, 0, -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[[-31, 21, 15, 13, -19],\n [26, -14, -11, -7, 16],\n [-36, -4, -4, -13, -11],\n [-31, 5, 7, -4, -18],\n [-22, -14, -30, -14, 22]]\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 5x5 matrix:\n[[-18, -18, 6, -30, 6],\n [-12, -12, 4, -20, 4],\n [0, 0, 0, 0, 0],\n [-9, -9, 3, -15, 3],\n [9, 9, -3, 15, -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[[-24, 16, -6, -18, -15],\n [0, -33, -24, 12, 6],\n [-4, -32, -20, 24, -4],\n [-31, -16, -31, -2, -17],\n [-45, -1, -31, -16, -26]]?\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 5x5 matrix:\n[[14, -13, 1, 4, 1],\n [2, -7, -5, -4, -13],\n [34, -38, -4, 4, -14],\n [10, -8, 2, 4, 4],\n [1, 1, 2, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[61, 9, 56, -23, -35],\n [-32, -13, -19, -6, 49],\n [-39, -18, -15, -21, 60],\n [39, 1, 49, -37, -15],\n [47, 12, 37, -7, -46]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-18, -18, -6, 9, -3],\n [-8, -8, -24, 20, 20],\n [6, 6, -30, 21, 33],\n [12, 12, 12, -12, -6],\n [12, 12, -4, 0, 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 5x5 matrix:\n[[45, 18, -29, -34, -4],\n [0, 36, 7, 2, 32],\n [-12, 12, 11, 10, 16],\n [-15, -30, 5, 10, -20],\n [-33, -30, 18, 24, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-31, -22, 1, 28, 2],\n [-10, -7, -5, 13, -34],\n [-27, -21, -8, 29, -25],\n [4, 9, 13, -7, -14],\n [-13, -25, -34, 21, 31]]\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[[-7, -18, -11, 5, 15],\n [2, -32, -24, -10, 10],\n [16, -16, -20, -28, 30],\n [10, 48, 32, -2, -30],\n [0, -60, -42, -12, 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[[30, -10, -26, -40, -8],\n [9, -3, -21, -12, 2],\n [-6, 2, -8, 8, 6],\n [12, -4, 4, -16, -8],\n [9, -3, -9, -12, -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[[29, 11, -16, -34, 5],\n [2, 37, 2, -11, -4],\n [-3, 39, -6, -20, -27],\n [12, -53, -1, 12, 35],\n [28, 12, -19, -37, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-23, -32, -20, 28, 15],\n [-34, -8, -32, -12, 8],\n [-4, -4, -5, 14, 18],\n [-39, -12, -32, -2, 32],\n [-2, -12, -4, 10, -9]]\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, 22, -4, 4, 34],\n [0, 0, 0, 0, 0],\n [10, -15, -10, 5, -30],\n [8, 2, -36, 22, -16],\n [8, -19, 6, -5, -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[[-4, -6, -5, 6, -5],\n [20, 30, 25, -30, 25],\n [4, 6, 5, -6, 5],\n [-24, -36, -30, 36, -30],\n [-24, -36, -30, 36, -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[[6, 36, -18, 30, 18],\n [2, 12, -6, 10, 6],\n [-5, -30, 15, -25, -15],\n [5, 30, -15, 25, 15],\n [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[[-21, 24, 12, -5, -11],\n [-30, 36, 16, -6, -14],\n [27, -36, -12, 3, 9],\n [-6, 24, -8, 10, 14],\n [6, -6, -4, 2, 4]]\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, -2, -14, -42, 56],\n [-9, 43, 30, -57, 56],\n [48, -14, 1, 5, -36],\n [-32, -14, -12, 32, 4],\n [-26, 15, -2, -48, 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[[-9, 9, 12, 9, 19],\n [-18, -9, -6, -9, 4],\n [18, 9, 6, 9, -4],\n [-8, 20, 24, 20, 32],\n [-18, -9, -6, -9, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[3, 9, 2, -19, -8],\n [32, -4, 38, -36, -27],\n [24, -12, 30, -12, -15],\n [-36, 0, -42, 48, 33],\n [22, 10, 24, -46, -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 5x5 matrix:\n[[-15, 10, -55, -44, -34],\n [-46, -10, -29, -27, -14],\n [-8, -4, 22, 22, -22],\n [23, 28, 2, -13, 30],\n [-5, 32, -2, -17, -8]]\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, 15, -52, -34, 47],\n [-29, -12, 22, 40, 2],\n [-14, -12, -14, -20, 46],\n [-29, -2, 8, 36, 4],\n [-26, 32, 6, 44, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[28, 26, -12, 14, 2],\n [24, 17, -19, 3, 16],\n [-39, -33, 18, -6, -3],\n [-27, -20, 22, -9, -20],\n [23, 16, -21, 7, 21]]\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[[8, -16, -4, 0, -4],\n [2, -4, -1, 0, -1],\n [8, -16, -4, 0, -4],\n [2, -4, -1, 0, -1],\n [4, -8, -2, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[17, -10, -22, -9, 36],\n [-3, -2, 2, 11, -12],\n [2, -4, -4, 6, 0],\n [6, -4, -8, -2, 12],\n [4, -2, -5, -3, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-30, -15, 30, 30, 20],\n [18, 9, -18, -18, -12],\n [18, 9, -18, -18, -12],\n [-18, -9, 18, 18, 12],\n [-12, -6, 12, 12, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-22, 42, -32, 5, 5],\n [15, 14, -3, 16, -5],\n [7, 18, 27, -25, -30],\n [-1, 18, -1, -3, -8],\n [7, -40, -15, 30, 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, 2, 16, 22, -20],\n [17, 22, 0, -6, -9],\n [30, -54, 12, 66, 54],\n [-14, 5, 18, -3, -60],\n [12, -57, 12, 57, 42]]\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, 9, 22, 30, -22],\n [9, 18, 14, 15, -23],\n [21, 36, 18, 15, -39],\n [-24, -27, 14, 30, 10],\n [-25, -30, 10, 25, 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[[0, 0, 0, 0, 0],\n [-18, 30, 30, 30, -18],\n [15, -25, -25, -25, 15],\n [6, -10, -10, -10, 6],\n [-9, 15, 15, 15, -9]]\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[[-25, -30, 30, -25, -20],\n [30, 36, -36, 30, 24],\n [20, 24, -24, 20, 16],\n [0, 0, 0, 0, 0],\n [15, 18, -18, 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[[-10, 0, -20, -15, 10],\n [12, 0, 24, 18, -12],\n [8, 0, 16, 12, -8],\n [-10, 0, -20, -15, 10],\n [-6, 0, -12, -9, 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[[15, -5, -5, -15, -4],\n [-20, -40, -15, -15, -2],\n [19, 3, -32, -26, -6],\n [-6, 12, 42, 30, 6],\n [-21, -19, 26, 16, 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[[24, 24, 12, 12, 36],\n [12, 12, 6, 6, 18],\n [4, 4, 2, 2, 6],\n [-4, -4, -2, -2, -6],\n [-4, -4, -2, -2, -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 5x5 matrix:\n[[0, -10, -5, 6, 0],\n [-20, -40, -20, 6, -10],\n [0, -40, -20, 24, 0],\n [16, 4, 2, 12, 8],\n [-4, -36, -18, 18, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[20, -30, -10, -30, 20],\n [9, -15, 18, -12, 0],\n [2, -4, 14, -2, -4],\n [2, 0, -46, -6, 20],\n [9, -13, -12, -14, 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[[25, 6, -16, 18, 33],\n [-6, -14, 16, -4, -5],\n [-30, -18, 33, -39, -39],\n [10, 20, -18, -22, 6],\n [28, 24, -33, 11, 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[[-6, 30, -24, -6, -18],\n [2, -10, 8, 2, 6],\n [-4, 20, -16, -4, -12],\n [-6, 30, -24, -6, -18],\n [3, -15, 12, 3, 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 5x5 matrix:\n[[-15, -32, -19, 3, 26],\n [-36, -22, 17, -75, 1],\n [-31, -42, -24, -30, 37],\n [-16, -34, -24, 3, 32],\n [-25, -66, -21, 24, 46]]\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[[17, -34, 0, -7, -14],\n [48, 30, 69, -12, -87],\n [-9, 20, -15, 8, -11],\n [46, 2, 19, -34, -13],\n [-28, -56, -20, 24, 12]]\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, -25, -4, -22, 26],\n [-20, 19, -2, 10, 6],\n [45, -42, 3, -24, -6],\n [-15, 16, -5, 4, 22],\n [-20, 22, -8, 4, 36]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-22, 14, -29, -22, -4],\n [8, -19, 43, 42, 20],\n [-32, 22, -46, -36, -8],\n [38, -16, 31, 18, -4],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[40, -10, 16, -30, -26],\n [18, -24, 6, -24, -39],\n [-8, 20, 8, 12, 24],\n [28, -15, -12, -17, -15],\n [-22, 19, 16, 15, 18]]?\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, -3, 10, 9],\n [-20, 25, -5, -55, 25],\n [-47, 39, -12, -23, 12],\n [42, -30, 0, 42, -18],\n [7, 29, -27, -56, 27]]\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[[-27, -54, 43, -9, 41],\n [-1, -7, 2, -7, -1],\n [-47, -32, 23, -14, 9],\n [38, -7, 15, 21, 38],\n [-1, 14, -13, -2, -17]]\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, 6, 36, 12, 0],\n [20, 4, 24, 8, 0],\n [5, 1, 6, 2, 0],\n [30, 6, 36, 12, 0],\n [5, 1, 6, 2, 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[[3, 13, 0, 0, -7],\n [3, 5, -24, 0, -47],\n [2, -10, 20, 0, 26],\n [-18, 22, -4, 0, 46],\n [-24, 28, -22, 0, 34]]\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[[-25, -4, 33, -27, -13],\n [-9, -15, -3, -9, -9],\n [3, -58, 13, 21, -9],\n [-22, -26, 34, -20, -7],\n [-18, -1, 22, -28, 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 5x5 matrix:\n[[40, -35, 0, -57, 13],\n [-4, -31, 40, -9, 41],\n [-17, 36, -25, 37, -31],\n [25, -38, 15, -15, 31],\n [15, 5, -25, 16, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-46, 1, 23, 9, -7],\n [32, -16, 12, 29, -5],\n [34, -10, -8, -11, 3],\n [-17, -53, 61, 33, -49],\n [86, 24, -57, -5, 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[[6, 2, 2, 5, 3],\n [-18, -6, -6, -15, -9],\n [30, 10, 10, 25, 15],\n [18, 6, 6, 15, 9],\n [18, 6, 6, 15, 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[[29, 17, -18, 41, -12],\n [-18, -19, 1, -33, -20],\n [37, -14, -7, 24, 4],\n [-20, 1, 18, -19, 5],\n [-27, -12, -5, -34, -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 5x5 matrix:\n[[-4, 0, -16, 0, 8],\n [4, 0, 16, 0, -8],\n [0, 0, 0, 0, 0],\n [5, 0, 20, 0, -10],\n [2, 0, 8, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-40, -9, -22, 26, -26],\n [-24, -12, -8, 16, -16],\n [-14, -18, 4, 10, -10],\n [-6, 30, -28, 2, -2],\n [-40, -9, -22, 26, -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[[-3, -6, 0, -9, 15],\n [1, 2, 0, 3, -5],\n [0, 0, 0, 0, 0],\n [-5, -10, 0, -15, 25],\n [-6, -12, 0, -18, 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[[-13, -3, 15, -3, 1],\n [-40, 6, 3, -5, -13],\n [30, -18, 36, 0, 24],\n [4, -6, 15, -1, 7],\n [-12, 18, -45, 3, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[15, -24, -16, -3, 17],\n [4, -4, -1, 0, 4],\n [-14, -1, 7, 2, 8],\n [-14, -22, -25, -6, 10],\n [16, 29, 6, 0, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[26, 12, -16, -13, 6],\n [54, 21, 9, -54, 17],\n [18, -5, -41, -15, 17],\n [-28, -34, -8, 26, -6],\n [42, 66, 45, -15, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[38, 3, -25, -30, -42],\n [-8, -15, -5, 8, -24],\n [23, 2, -13, -36, -37],\n [-37, 4, 38, 16, 58],\n [8, -17, 8, 30, 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[[0, 0, 0, 0, 0],\n [8, 0, 0, -24, -24],\n [-10, 0, 0, 30, 30],\n [6, 0, 0, -18, -18],\n [-4, 0, 0, 12, 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 5x5 matrix:\n[[-18, -34, 9, -4, 20],\n [-27, -40, -45, -1, -10],\n [-5, -14, -32, 13, -22],\n [36, 22, -24, 43, -16],\n [-22, -7, 2, -23, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[19, -11, 6, 11, -18],\n [-39, 18, -9, -18, 42],\n [28, -33, 21, 33, -8],\n [18, -44, 30, 44, 20],\n [-21, 32, -21, -32, -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[[9, 20, 0, 8, 2],\n [25, -18, 20, -4, 32],\n [-9, -63, 15, -27, 15],\n [27, 9, 11, 9, 23],\n [51, -15, 21, 15, 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[[-18, -3, -15, 9, 18],\n [-12, -2, -10, 6, 12],\n [-36, -6, -30, 18, 36],\n [-6, -1, -5, 3, 6],\n [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[[5, 21, -9, -6, -10],\n [32, -19, -13, -27, 5],\n [-21, -3, -19, 9, 10],\n [-15, -15, 11, 29, 42],\n [-39, -4, 2, 23, -1]]?\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, 11, -7, -2, 33],\n [-14, -1, 35, 10, -3],\n [31, 2, -36, -12, 10],\n [54, -8, 6, -6, -6],\n [-18, 20, -14, 2, 46]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-57, -81, 7, -17, -70],\n [-22, -33, 5, -17, -39],\n [20, 33, 1, -9, 0],\n [11, 35, 38, 3, 77],\n [-5, 4, -13, 10, -27]]?\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, -18, 6, -30, 18],\n [4, -12, 4, -20, 12],\n [-2, 6, -2, 10, -6],\n [2, -6, 2, -10, 6],\n [4, -12, 4, -20, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, -9, 15, 12, 18],\n [10, 15, -25, -20, -30],\n [8, 12, -20, -16, -24],\n [6, 9, -15, -12, -18],\n [12, 18, -30, -24, -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[[10, 8, 32, 11, -23],\n [8, 2, 4, 5, 5],\n [-46, -39, -32, 21, 14],\n [8, 0, -44, -19, 47],\n [-2, 5, -16, -21, 4]]\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 5x5 matrix:\n[[-42, -35, -51, -19, -9],\n [-28, -28, -39, -10, -4],\n [30, 5, 15, 25, 15],\n [-2, -19, -21, 9, 7],\n [26, 23, 33, 11, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, -58, -6, 54, -18],\n [-35, 2, -46, -4, -30],\n [-31, 13, -39, -6, -32],\n [8, -50, 10, 34, 10],\n [15, 9, 13, -26, 32]]\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 5x5 matrix:\n[[4, 46, -6, 13, -4],\n [-6, 18, -54, 7, 26],\n [57, -23, 7, -19, -5],\n [13, 26, 8, 19, -10],\n [35, 11, -67, -13, 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[[2, -4, -23, -4, -2],\n [-10, 8, 1, 20, -32],\n [-24, -24, -21, -6, -12],\n [24, 52, -14, 48, -58],\n [22, 8, 26, -14, 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[[-8, -16, 13, -31, -1],\n [-86, -72, 3, -35, -95],\n [8, 38, -41, 35, 15],\n [14, -30, -38, -32, -4],\n [6, 10, -3, 36, -7]]\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 5x5 matrix:\n[[-51, 33, 16, 24, 0],\n [12, -5, -10, 9, -1],\n [-1, -18, 29, 9, -39],\n [19, 8, -34, -27, 37],\n [-20, 5, 5, 60, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[15, -10, 76, 1, -19],\n [-12, -5, -33, -5, 5],\n [19, 25, -13, 22, -32],\n [-16, -20, -16, -3, -29],\n [8, -5, -1, -7, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-4, 4, 9, 2, -1],\n [8, -8, -2, 0, 10],\n [-28, 28, 31, 6, -23],\n [4, -4, 19, 5, 15],\n [24, -24, -26, -5, 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[[18, -18, 0, 6, -24],\n [-6, 6, 0, -2, 8],\n [9, -9, 0, 3, -12],\n [18, -18, 0, 6, -24],\n [3, -3, 0, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-3, -12, -9, 18, -18],\n [-5, -20, -15, 30, -30],\n [-3, -12, -9, 18, -18],\n [4, 16, 12, -24, 24],\n [-2, -8, -6, 12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0, 0],\n [-6, 15, 12, 12, 18],\n [10, -25, -20, -20, -30],\n [6, -15, -12, -12, -18],\n [2, -5, -4, -4, -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 5x5 matrix:\n[[-7, 1, -2, -3, -12],\n [25, 11, 4, -7, 17],\n [-6, -6, 12, 18, 30],\n [-19, 86, 49, -37, -14],\n [-12, -34, -10, 24, 10]]\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, 16, 10, 24, 8],\n [-21, 7, -6, -1, 9],\n [1, 9, 10, 19, 20],\n [4, -5, 28, 11, 3],\n [-1, 10, -6, 0, 0]]\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[[7, 24, 23, 2, -24],\n [-47, 26, 47, 38, -41],\n [-16, -36, -17, -14, 17],\n [18, -44, -42, -36, 38],\n [-48, -16, 18, 12, -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 5x5 matrix:\n[[4, 17, -3, 11, -6],\n [-4, 7, -9, 5, -2],\n [4, 23, -6, 15, -8],\n [-4, 7, -9, 5, -2],\n [-8, 20, -21, 14, -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[[-6, 5, 2, 1, -1],\n [1, 10, -17, -21, -14],\n [3, -9, 9, 12, 9],\n [21, -11, -17, -16, -5],\n [-55, 35, 35, 30, 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[[-2, 1, -4, 4, 6],\n [12, -6, 24, -24, -36],\n [0, 0, 0, 0, 0],\n [-2, 1, -4, 4, 6],\n [12, -6, 24, -24, -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[[-38, -10, -21, -6, -37],\n [-22, -19, -15, 9, -13],\n [1, 4, 10, -4, 2],\n [-6, -42, -5, 48, 37],\n [8, 13, -13, 5, 9]]\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 5x5 matrix:\n[[-6, 0, 2, 1, -10],\n [-8, 20, 16, -2, -10],\n [8, -2, -4, -1, 13],\n [-20, -10, 0, 5, -35],\n [0, 30, 20, -5, 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[[12, 4, -9, -27, -2],\n [-4, 0, 2, 11, 0],\n [-12, 4, 3, 39, -2],\n [-4, -16, 14, -13, 8],\n [-12, 12, -3, 51, -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[[52, -46, -44, 23, 13],\n [-12, -1, 17, -36, -73],\n [-60, 32, 58, -19, -11],\n [20, -36, -18, 32, -4],\n [12, -19, -5, 3, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, 8, 12, 8, 6],\n [14, -8, -14, -44, 5],\n [34, -23, -34, -14, -20],\n [10, -7, -10, 2, -8],\n [28, -18, -28, -36, -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 5x5 matrix:\n[[-10, 6, -6, 8, -12],\n [-15, -9, 9, 18, -24],\n [20, -24, 24, -12, 20],\n [30, -30, 30, -20, 32],\n [-15, 9, -9, 12, -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 5x5 matrix:\n[[4, -13, 18, 47, 2],\n [-32, -14, 17, 14, -16],\n [-62, 36, 12, -30, -31],\n [-4, 23, -8, -25, -2],\n [18, -36, -10, -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[[-6, -9, -18, 18, 15],\n [-4, -6, -12, 12, 10],\n [10, 15, 30, -30, -25],\n [-2, -3, -6, 6, 5],\n [8, 12, 24, -24, -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 5x5 matrix:\n[[-5, 4, -20, -8, 12],\n [12, -18, -8, 25, 46],\n [32, -27, 6, 24, -8],\n [-22, 26, -44, -44, -16],\n [-15, 19, -14, -29, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, -12, -3, -9, 15],\n [6, 24, 6, 18, -30],\n [-6, -24, -6, -18, 30],\n [0, 0, 0, 0, 0],\n [-2, -8, -2, -6, 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[[-12, 20, -4, -20, -24],\n [-12, 20, -4, -20, -24],\n [12, -20, 4, 20, 24],\n [0, 0, 0, 0, 0],\n [-18, 30, -6, -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[[65, -39, 8, -10, -24],\n [-38, 18, 24, 0, 4],\n [1, -14, -39, 8, 11],\n [-69, 36, -15, 12, 27],\n [13, 6, 1, -2, -3]]\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[[-7, -7, -2, -21, 16],\n [-24, -35, 23, -17, -8],\n [-2, -6, 4, -18, 4],\n [-8, -9, 2, -11, 7],\n [-28, -16, -17, -24, 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[[-40, -30, -5, 56, 44],\n [-21, -5, 29, 33, -27],\n [27, 21, 8, -39, -39],\n [-54, -34, 12, 78, 30],\n [34, 26, 10, -50, -50]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-12, -6, -18, -6, -6],\n [-4, -2, -6, -2, -2],\n [-2, -1, -3, -1, -1],\n [-10, -5, -15, -5, -5],\n [2, 1, 3, 1, 1]]\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[[-25, -25, 30, 10, 30],\n [25, 25, -30, -10, -30],\n [0, 0, 0, 0, 0],\n [-25, -25, 30, 10, 30],\n [-10, -10, 12, 4, 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[[8, -32, -14, -26, -38],\n [-11, -4, 10, 19, 0],\n [3, 4, 0, -5, 2],\n [-10, -6, 2, 19, 1],\n [-1, -34, -29, -1, -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[[1, 12, 21, -17, -30],\n [-7, -2, -21, 5, 42],\n [-3, -2, -21, 29, 6],\n [12, -21, 12, -8, -3],\n [17, -6, 42, -16, -69]]\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],\n [10, 5, 5, -20, -10],\n [10, 5, 5, -20, -10],\n [2, 1, 1, -4, -2],\n [-10, -5, -5, 20, 10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[10, -6, -17, -22, 8],\n [-10, -38, 3, 50, -36],\n [17, 70, 30, -4, -27],\n [34, 18, -2, 11, -68],\n [-14, 0, 10, 8, 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[[7, 16, 6, 49, 6],\n [5, -17, -43, -50, 4],\n [35, -4, -42, -9, 40],\n [-46, 23, -3, 20, -49],\n [9, 61, -29, -36, 72]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[16, -16, 0, 8, 4],\n [5, -38, 0, 22, -10],\n [-11, 22, 0, -12, 1],\n [0, 0, 0, 0, 0],\n [17, -6, 0, 2, 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[[-15, 5, 11, -3, 38],\n [1, 5, 13, 29, 14],\n [-15, 53, 5, -3, 14],\n [11, -41, 5, 19, 2],\n [3, -49, 5, 3, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-24, 20, -12, 4, -8],\n [6, -5, 3, -1, 2],\n [-36, 30, -18, 6, -12],\n [-36, 30, -18, 6, -12],\n [30, -25, 15, -5, 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[[0, 3, 4, 5, -5],\n [0, 9, 12, 15, -15],\n [0, 18, 24, 30, -30],\n [0, 18, 24, 30, -30],\n [0, -3, -4, -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[[-5, -2, 2, -4, -1],\n [-30, -12, 12, -24, -6],\n [5, 2, -2, 4, 1],\n [-25, -10, 10, -20, -5],\n [-30, -12, 12, -24, -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[[-10, -25, 0, 0, -20],\n [0, 0, 0, 0, 0],\n [-8, -20, 0, 0, -16],\n [2, 5, 0, 0, 4],\n [8, 20, 0, 0, 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 5x5 matrix:\n[[12, 12, 6, 12, 12],\n [-16, -16, -8, -16, -16],\n [-16, -16, -8, -16, -16],\n [12, 12, 6, 12, 12],\n [24, 24, 12, 24, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 16, 8, -4, 28],\n [5, 13, -21, -28, -13],\n [-3, 9, 7, 0, 19],\n [-4, -2, 14, 14, 16],\n [3, 9, -13, -18, -7]]\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, -7, -17, -18, -19],\n [68, 64, 15, -53, 33],\n [33, 0, -21, 6, 3],\n [-23, -11, 7, 10, -50],\n [16, -14, -24, 6, -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[[-30, 8, 9, 15, 60],\n [4, -48, 42, -10, 24],\n [44, 38, -28, 61, -12],\n [-14, -6, 2, -49, -49],\n [40, 44, 5, 71, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-16, -4, 20, -12, 4],\n [20, 5, -25, 15, -5],\n [-8, -2, 10, -6, 2],\n [-4, -1, 5, -3, 1],\n [8, 2, -10, 6, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-11, 13, -14, -14, 14],\n [-6, -18, 9, 27, -12],\n [-24, 24, -12, -30, -12],\n [25, 21, -13, -34, 36],\n [-10, -14, 7, 22, -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[[0, -21, -6, -13, 9],\n [0, -10, 12, -10, 0],\n [32, -14, 40, -38, -3],\n [-18, 8, -48, 28, 9],\n [-19, 24, -26, 34, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[14, 30, -15, 6, -2],\n [-2, -48, -54, 36, 43],\n [31, 12, 6, 28, -11],\n [11, 36, 12, -8, -18],\n [23, 12, 30, 12, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 8, 18, 5, 31],\n [-71, -7, -54, 15, 10],\n [66, -11, 56, -4, 17],\n [-7, 32, -12, 9, -1],\n [-10, -15, 6, -33, -34]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, 21, 6, 12, -12],\n [-5, 20, 1, 20, -20],\n [-15, 10, -5, 20, -20],\n [21, 36, 15, 12, -12],\n [-30, -5, -14, 20, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[57, -29, -13, 0, 5],\n [-37, -7, -15, -30, -23],\n [0, -3, -36, 9, -27],\n [50, -14, 29, 3, 2],\n [-21, -1, -3, -15, 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 5x5 matrix:\n[[-9, 2, -15, 8, 10],\n [8, -11, 24, -8, -30],\n [15, -8, 33, -16, -34],\n [-3, 30, -9, -20, -6],\n [0, 34, -12, -20, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[19, 13, -6, -6, -43],\n [11, -12, -14, 23, 0],\n [-8, 39, -4, -44, 6],\n [10, 17, 6, -11, 5],\n [7, -10, -2, 11, -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[[-12, 9, -30, -6, -27],\n [24, -18, 60, 12, 54],\n [23, 16, 5, -13, 1],\n [20, -15, 50, 10, 45],\n [-11, -25, 25, 19, 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 5x5 matrix:\n[[1, -34, -43, -31, -35],\n [10, 27, 36, 15, 25],\n [-29, 7, 6, 24, 19],\n [31, -36, -40, -61, -44],\n [66, -42, -42, -96, -60]]\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[[11, 9, -9, 12, -14],\n [-47, 17, -1, -10, 53],\n [24, -14, 14, -2, -31],\n [-41, 7, 3, -14, 48],\n [45, -24, 9, 3, -51]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[24, 0, 16, -24, 4],\n [36, 0, 24, -36, 6],\n [-12, 0, -8, 12, -2],\n [18, 0, 12, -18, 3],\n [30, 0, 20, -30, 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[[-18, 14, 9, -16, 0],\n [26, -5, -12, 38, -29],\n [8, -10, -34, 16, -48],\n [-12, -9, 16, -14, 14],\n [-2, -23, -6, -6, -1]]\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[[-30, 10, -30, -15, 20],\n [0, -6, 0, -33, 6],\n [-30, 16, -30, 18, 14],\n [18, -10, 18, -13, -8],\n [-6, -2, -6, -25, 8]]\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, -12, -24, 12, -4],\n [10, 6, 12, -6, 2],\n [-20, -12, -24, 12, -4],\n [20, 12, 24, -12, 4],\n [10, 6, 12, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-15, 24, -48, -6, 87],\n [40, 18, 49, 20, -23],\n [15, -14, 3, -2, -12],\n [15, 22, 36, 16, -15],\n [20, -34, -17, -12, -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[[-1, -11, 5, -6, 3],\n [-5, 0, -41, -19, 48],\n [6, 66, -30, 36, -18],\n [1, 31, -29, 10, 9],\n [5, 35, -1, 26, -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[[-23, 19, 10, 18, -19],\n [-20, 16, 6, 12, -16],\n [-30, 4, 7, -18, -24],\n [27, -1, -3, 24, 21],\n [-39, 15, 4, -12, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, 31, -19, 21, 6],\n [-6, -15, 17, -13, 12],\n [15, 27, -35, 25, -30],\n [18, 17, -31, 19, -36],\n [-27, -15, 39, -21, 54]]\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, -6, 18, -6, -18],\n [6, -2, 6, -2, -6],\n [24, -8, 24, -8, -24],\n [6, -2, 6, -2, -6],\n [-18, 6, -18, 6, 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[[-36, 18, -18, -24, 36],\n [-6, 11, -11, 8, 10],\n [30, -23, 23, 8, -34],\n [-24, 8, -8, -22, 22],\n [36, -22, 22, 18, -38]]\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, -3, 5, 1, -5],\n [0, 0, 0, 0, 0],\n [15, 15, -25, -5, 25],\n [6, 6, -10, -2, 10],\n [9, 9, -15, -3, 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[[13, 47, 70, -19, 20],\n [-32, -13, -3, -12, -6],\n [7, 41, 54, -6, 15],\n [3, 18, 25, -17, 21],\n [14, 30, 0, -9, 67]]\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[[12, -18, 6, 6, 3],\n [16, -24, 8, 8, 4],\n [4, -6, 2, 2, 1],\n [-24, 36, -12, -12, -6],\n [16, -24, 8, 8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[33, -30, 39, 3, -33],\n [6, -9, -30, -51, 39],\n [13, -2, -4, -10, 11],\n [-16, 23, -26, 1, 25],\n [-31, 38, 13, 73, -29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -13, -1, 26, 13],\n [-6, -15, -7, 38, 33],\n [-31, 46, -47, -29, 8],\n [7, -32, 33, 21, 14],\n [49, -29, 41, 2, -52]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 18, 30, 24, 0],\n [-8, 12, 20, 16, 0],\n [-6, 9, 15, 12, 0],\n [-8, 12, 20, 16, 0],\n [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[[-34, -33, -30, 17, 19],\n [18, 32, 36, -32, -14],\n [-8, -15, -9, -5, -32],\n [-28, -21, -7, -18, -5],\n [-28, -21, -7, -18, -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[[-8, 6, 8, 8, -10],\n [48, -18, -48, 0, 6],\n [34, -12, -34, 2, 2],\n [-8, 6, 8, 8, -10],\n [10, -12, -10, -22, 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 5x5 matrix:\n[[8, 33, 13, 16, -1],\n [-2, -5, 41, 42, -15],\n [-20, -49, -47, 16, 25],\n [35, 3, -28, -8, 21],\n [-9, 21, 19, 30, -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[[-12, -20, 12, 20, 8],\n [42, 50, 24, -20, -38],\n [4, 0, 18, 10, -6],\n [35, 45, 9, -25, -30],\n [-2, 0, -9, -5, 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[[14, 7, -2, -5, 4],\n [55, 11, 10, -17, -10],\n [-10, 19, -22, 1, 32],\n [0, 0, 6, 3, -6],\n [15, 24, -22, -9, 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[[0, 0, 0, 0, 0],\n [5, -25, -30, -30, -10],\n [3, -15, -18, -18, -6],\n [-5, 25, 30, 30, 10],\n [1, -5, -6, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[41, 50, 0, 18, -50],\n [24, 83, 13, 30, -65],\n [-16, 58, -10, 26, -30],\n [15, -20, -14, 25, 15],\n [18, 9, -61, -11, -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 5x5 matrix:\n[[-15, 34, -14, -13, -28],\n [-9, 38, -10, -23, -32],\n [-16, 26, -14, -5, -21],\n [15, 10, 10, -25, -10],\n [-5, -18, -2, 21, 16]]\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[[19, -5, -10, 10, 2],\n [-32, 4, -6, -22, 4],\n [-24, 6, 11, -13, -2],\n [36, -6, -1, 23, -2],\n [17, -1, 9, 13, -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[[-14, 29, -10, -17, -28],\n [28, -12, -16, 12, 4],\n [13, 1, -22, 26, -15],\n [15, 10, -22, 0, -17],\n [28, -12, -28, 42, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[4, -37, -45, 2, -47],\n [-3, -18, -27, -6, -30],\n [-8, 10, 6, -14, 2],\n [-5, 31, 36, -4, 37],\n [-26, 22, -6, -3, 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[[-13, 22, -18, 8, -13],\n [15, -41, 6, -8, -17],\n [-2, 2, 20, -16, 22],\n [2, 26, -11, 37, 21],\n [-21, 18, 6, -18, 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 5x5 matrix:\n[[5, 12, -5, -1, -1],\n [30, 16, -30, 22, -13],\n [-1, -4, 1, 1, 0],\n [28, 24, -28, 16, -11],\n [4, 0, -4, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[63, 43, -9, -26, -45],\n [-39, -24, 2, 8, 35],\n [-9, 3, -33, -15, 15],\n [-51, -35, -7, 28, 25],\n [-42, -24, -12, 8, 34]]\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 5x5 matrix:\n[[-30, -8, -1, -30, 29],\n [-10, -12, 23, 18, 5],\n [25, 9, -5, 18, -23],\n [-10, -6, 8, 0, 8],\n [25, 17, -25, -6, -19]]\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[[3, 15, -35, -31, 23],\n [8, 10, -13, -13, 2],\n [-10, 6, -32, -26, 34],\n [-32, -24, 4, 12, 24],\n [4, -10, 24, 23, -28]]\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, 14, 2, 18, -8],\n [12, -36, -8, -22, 22],\n [-8, 32, 8, 12, -20],\n [-10, 7, -1, 26, -3],\n [-6, 39, 11, 4, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-32, 30, 26, 22, 18],\n [-3, 16, 22, 18, 19],\n [-4, 14, 22, 24, 12],\n [42, -28, -16, -12, -10],\n [-19, -7, -5, 24, -39]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -2, 1, 2, 0],\n [-12, 4, -2, -4, 0],\n [-24, 8, -4, -8, 0],\n [30, -10, 5, 10, 0],\n [6, -2, 1, 2, 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[[-9, 18, -18, -12, -9],\n [-12, 24, -24, -16, -12],\n [6, -12, 12, 8, 6],\n [-12, 24, -24, -16, -12],\n [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[[-3, -33, -15, -9, -18],\n [-7, -26, 9, 5, -6],\n [8, -16, -24, -10, -2],\n [-34, -29, 0, -18, -28],\n [21, 17, 35, 35, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-10, 10, -12, -2, 8],\n [-15, 15, -18, -3, 12],\n [-30, 30, -36, -6, 24],\n [20, -20, 24, 4, -16],\n [-5, 5, -6, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, 5, -32, 16, 0],\n [-22, -1, 0, -7, 13],\n [12, 5, 46, -23, 45],\n [-4, 5, 10, -7, 29],\n [24, 8, 27, -8, 32]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, -9, -3, 9, 0],\n [4, 3, 1, -3, 0],\n [16, 12, 4, -12, 0],\n [20, 15, 5, -15, 0],\n [-4, -3, -1, 3, 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[[58, 32, 1, -54, -16],\n [64, 0, 36, -44, -50],\n [-28, 24, -6, 8, 14],\n [-4, -24, -12, 14, 11],\n [6, -32, 35, 10, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[30, 15, 20, -25, -5],\n [12, 6, 8, -10, -2],\n [-30, -15, -20, 25, 5],\n [12, 6, 8, -10, -2],\n [36, 18, 24, -30, -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[[-3, 2, -2, 4, -4],\n [6, -30, 0, -9, 36],\n [36, 28, 32, -46, -8],\n [30, 32, 28, -38, -16],\n [35, 20, 30, -45, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-14, -31, 0, 6, -43],\n [-31, -12, 6, 7, -38],\n [-83, -13, 53, 35, -17],\n [-52, -57, 24, 23, -55],\n [12, -3, 2, 10, -35]]\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[[27, -1, 19, 21, 12],\n [-11, -11, 1, -3, 5],\n [-33, -8, -1, -2, 40],\n [13, -4, 33, 38, -2],\n [23, -16, 9, 2, 31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[25, -10, -25, -20, 30],\n [5, -2, -5, -4, 6],\n [-10, 4, 10, 8, -12],\n [30, -12, -30, -24, 36],\n [10, -4, -10, -8, 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[[-16, 1, -13, 9, -8],\n [-50, -7, -53, 3, -46],\n [20, 0, 6, -8, 0],\n [-35, -37, -13, 26, -21],\n [25, -36, 34, -35, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-16, 24, -20, -4, 4],\n [0, 0, 0, 0, 0],\n [-12, 18, -15, -3, 3],\n [-4, 6, -5, -1, 1],\n [4, -6, 5, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-15, -12, -6, -6, -12],\n [-5, 26, -2, -22, -24],\n [20, 16, 8, 8, 16],\n [-25, 10, -10, -30, -40],\n [-10, -8, -4, -4, -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[[0, 0, 0, 0, 0],\n [-15, -20, 15, 0, 10],\n [9, 12, -9, 0, -6],\n [9, 12, -9, 0, -6],\n [18, 24, -18, 0, -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[[-15, -15, 18, -9, 3],\n [-10, -10, 12, -6, 2],\n [20, 20, -24, 12, -4],\n [-15, -15, 18, -9, 3],\n [-20, -20, 24, -12, 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[[36, 14, -12, 36, 22],\n [4, 14, 11, 12, 16],\n [-33, -12, 6, -36, -24],\n [-7, -40, 23, 4, 2],\n [-10, 1, 3, -10, -5]]\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[[-10, -38, 45, 7, 5],\n [24, -33, -9, 12, 24],\n [-30, -42, 16, -42, 16],\n [-25, -25, 47, -6, -5],\n [-33, -30, -6, -58, 17]]?\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[[9, -12, 30, -21, 24],\n [-11, -22, 10, -6, -6],\n [19, -18, 54, -38, 46],\n [-1, -28, 34, -23, 16],\n [6, -8, 20, -14, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-30, -24, 12, 36, -18],\n [5, 4, -2, -6, 3],\n [5, 4, -2, -6, 3],\n [5, 4, -2, -6, 3],\n [-5, -4, 2, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-40, -20, 2, 37, -19],\n [3, 4, 11, -17, 14],\n [56, -44, 0, 42, -42],\n [34, -42, 12, 26, -26],\n [-26, 20, 0, -41, 29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-13, 24, 9, -26, -3],\n [7, 20, -38, 10, 2],\n [-38, 25, -4, -28, -30],\n [16, -9, -29, 38, -10],\n [14, -22, 10, 36, -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 5x5 matrix:\n[[12, -20, -2, -4, -8],\n [24, 19, 28, 21, -23],\n [0, -2, -8, 2, 10],\n [-11, 26, 7, 7, 5],\n [19, 34, 30, 27, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 22, -20, 8, -6],\n [35, 25, 22, 2, -55],\n [-86, -28, 0, 2, 78],\n [-25, -31, -4, -2, 47],\n [4, -4, -14, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[18, 0, 22, 2, 2],\n [15, 0, 10, -10, 20],\n [15, 0, 10, -10, 20],\n [-20, 0, -20, 4, -12],\n [3, 0, 12, 12, -18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[17, 4, 0, -7, -15],\n [26, -64, 10, 24, 18],\n [-15, 16, 23, 22, 51],\n [11, -21, 14, 20, 61],\n [70, -26, -56, -60, -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[[4, -2, 1, 4, 6],\n [16, -8, 4, 16, 24],\n [24, -12, 6, 24, 36],\n [-4, 2, -1, -4, -6],\n [-4, 2, -1, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-34, -2, 10, -40, 0],\n [50, 12, -55, 14, -18],\n [-23, 62, 41, -41, 15],\n [1, 37, 40, 8, 34],\n [32, -2, -15, 34, 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[[-24, -3, 26, -7, 29],\n [-46, -3, -16, -70, 57],\n [-14, 14, -15, -46, 4],\n [3, 37, -19, -32, -41],\n [46, -8, -15, 83, -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[[0, 3, 9, -6, -15],\n [0, 2, 6, -4, -10],\n [0, -2, -6, 4, 10],\n [0, -1, -3, 2, 5],\n [0, 3, 9, -6, -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[[10, 6, -8, -4, 12],\n [15, 9, -12, -6, 18],\n [-10, -6, 8, 4, -12],\n [-30, -18, 24, 12, -36],\n [-10, -6, 8, 4, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, 20, 27, -9, -30],\n [-1, -2, 2, -4, -1],\n [-8, 4, 18, -10, -16],\n [-46, -4, 49, 29, -28],\n [-3, 17, 12, 5, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[36, -27, 9, 12, 5],\n [-40, 45, 7, -32, -54],\n [-50, 12, 5, -1, 4],\n [-47, 33, 26, -10, -58],\n [-57, -13, 6, 28, 45]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[20, -29, 0, 1, -8],\n [-5, 11, 0, -4, 2],\n [-25, 55, 0, -20, 10],\n [30, -11, 0, -31, -12],\n [25, -60, 0, 25, -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[[2, 2, -10, -2, -12],\n [5, 5, -25, -5, -30],\n [6, 6, -30, -6, -36],\n [-1, -1, 5, 1, 6],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-18, 18, 6, -9, 12],\n [-6, 6, 2, -3, 4],\n [6, -6, -2, 3, -4],\n [12, -12, -4, 6, -8],\n [-36, 36, 12, -18, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-15, 3, 16, -10, 13],\n [-11, -15, 30, -44, -3],\n [10, 3, 22, -19, 28],\n [22, -18, -24, 0, -42],\n [35, 9, 12, -6, 39]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -27, 3, -13, -9],\n [7, -35, 5, -16, -12],\n [15, 27, -33, -10, 18],\n [0, -42, 18, -10, -18],\n [-14, -14, 26, 12, -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[[-6, 12, 9, 3, -15],\n [32, 12, -9, 9, -9],\n [-24, 43, 21, 1, -23],\n [-32, 54, 18, -6, -6],\n [-14, 32, 12, 0, -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[[-14, 0, -23, 4, 22],\n [10, 31, -8, -12, -4],\n [-9, 1, -10, 54, 16],\n [15, -66, 83, 27, -53],\n [32, -2, 24, 40, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[21, 12, 0, -18, -36],\n [-13, -61, -27, 0, 42],\n [-35, 14, 28, 20, 18],\n [16, 0, -19, 7, 15],\n [-26, 18, 23, 19, 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[[-30, 18, -26, -42, 40],\n [-36, 21, -31, -45, 44],\n [-10, 4, -8, 4, 0],\n [-14, 8, -12, -16, 16],\n [-20, 8, -16, 8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -14, 32, -24, -6],\n [-12, -22, 28, -24, -18],\n [-2, -6, 10, -8, -4],\n [-4, 9, -28, 20, 1],\n [-10, 5, -30, 20, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 4, 18, -14, 10],\n [8, 12, 9, -8, 3],\n [-22, -6, -27, 22, -15],\n [-26, -22, -24, 22, -10],\n [-32, -8, -21, 21, -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[[26, -37, -3, 5, 19],\n [-44, 80, 6, -40, 0],\n [16, -22, 0, 2, 6],\n [16, 20, 26, -70, -10],\n [4, -16, 2, 20, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, -20, -63, -26, 0],\n [-32, 6, -12, 5, -14],\n [11, -19, -66, -25, 15],\n [6, 9, 6, 2, -5],\n [-32, 20, 20, 18, -20]]\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, -5, -23, -24, 48],\n [-14, 21, -20, -7, 25],\n [-10, -45, 20, 15, -5],\n [3, -25, -3, -8, 24],\n [-6, -28, 18, 14, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, -20, -16, -8, 0],\n [10, -25, -20, -10, 0],\n [0, 0, 0, 0, 0],\n [-2, 5, 4, 2, 0],\n [-10, 25, 20, 10, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-25, 4, -14, -6, 4],\n [-9, 0, -2, -8, -6],\n [33, 16, 18, 22, -12],\n [-21, -22, -16, -14, 24],\n [-3, 20, -2, 12, -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[[60, 27, -37, -11, 7],\n [36, -24, -32, 30, -14],\n [26, 36, -48, -58, 0],\n [16, 6, 30, -35, -75],\n [22, 36, 0, -56, -30]]\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, -30, -11, -23, 16],\n [16, 14, 25, -50, -34],\n [-4, -28, -20, -13, -5],\n [42, 36, 36, -89, 4],\n [39, 20, 24, -73, 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[[-22, -10, -26, -19, 22],\n [-30, 14, -50, -31, 14],\n [30, -14, 50, 31, -14],\n [-3, 28, -19, -8, -14],\n [-36, -6, -48, -33, 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[[-32, -24, 25, -13, -23],\n [24, 36, -42, 30, 36],\n [-12, -6, -11, -7, 11],\n [-6, 21, -17, 30, 11],\n [2, 21, -41, 18, 36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[30, -35, -45, -55, -20],\n [-12, 6, 33, 32, -2],\n [48, -18, 9, -6, -16],\n [-6, -53, -9, -25, -44],\n [-36, 40, 36, 50, 26]]\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[[-11, 66, 13, -15, 12],\n [-16, 3, 5, 6, -20],\n [10, 38, -1, -8, 26],\n [5, -3, 2, -9, 8],\n [11, 33, -4, -3, 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[[-29, 21, -16, -40, -18],\n [-16, -40, 29, -12, -21],\n [16, -12, -6, 33, 40],\n [-1, -25, 22, -28, 2],\n [-4, 2, -3, -17, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 20, 24, 0, 0],\n [-4, 20, 24, 0, 0],\n [-4, 20, 24, 0, 0],\n [-6, 30, 36, 0, 0],\n [-1, 5, 6, 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[[-31, 13, 32, -8, -15],\n [11, 13, 26, -39, 49],\n [-6, 8, 17, 0, -5],\n [80, -56, -34, -29, 63],\n [-24, 24, -4, 19, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[4, 2, -8, 4, 8],\n [0, 0, 0, 0, 0],\n [-4, -2, 8, -4, -8],\n [8, 4, -16, 8, 16],\n [2, 1, -4, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[27, -23, -20, 3, -23],\n [-24, -17, -6, -9, -31],\n [11, -7, 4, -45, 29],\n [6, -9, -30, -61, -9],\n [-24, -5, -12, -13, -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[[60, -16, 20, 12, -28],\n [-30, -6, -2, -33, 1],\n [55, -16, 19, 7, -26],\n [-12, 16, -12, 12, 24],\n [24, 0, 4, 12, -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[[0, 4, -8, 28, -24],\n [14, -19, -11, 0, 16],\n [-10, 13, 9, -4, -8],\n [-2, 4, -1, 9, -10],\n [2, 0, -7, 19, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-15, 3, 19, -2, 12],\n [9, -14, -11, -10, 0],\n [28, -40, -33, -27, -3],\n [-31, 10, 37, -2, 24],\n [19, -21, -31, -18, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-13, -10, 20, -11, 8],\n [70, 34, -20, -52, 54],\n [15, 31, -54, 27, -15],\n [-19, 28, -40, 33, -38],\n [-5, -22, 28, 7, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-14, 30, -12, -2, 44],\n [14, 13, 14, -2, -27],\n [-9, -34, -8, 10, 13],\n [-16, -16, -20, -9, 20],\n [1, -15, 14, 41, 28]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-64, -23, -7, -48, -24],\n [-6, 28, 6, 33, 28],\n [-38, 19, -12, -49, 26],\n [-2, -19, 12, 37, -18],\n [-20, 33, -11, -8, -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[[-8, 2, -2, 2, 4],\n [-12, 3, -3, 3, 6],\n [16, -4, 4, -4, -8],\n [-12, 3, -3, 3, 6],\n [16, -4, 4, -4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-21, -13, -1, 11, 21],\n [24, 16, 5, -12, -2],\n [3, 11, -2, 3, 41],\n [-27, -15, -7, 15, 14],\n [-27, -15, -12, 15, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[26, -29, 34, 37, -7],\n [4, 3, -14, -8, 6],\n [10, -5, 26, 16, 0],\n [-22, 1, 10, -16, -4],\n [14, -47, -21, -19, 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 5x5 matrix:\n[[2, 1, 1, 4, -6],\n [-2, -1, -1, -4, 6],\n [6, 3, 3, 12, -18],\n [10, 5, 5, 20, -30],\n [-2, -1, -1, -4, 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[[23, -20, -8, 14, -2],\n [-16, 1, -7, -20, 0],\n [10, -30, -33, 40, 34],\n [46, 10, 27, 14, -42],\n [56, 1, 43, 32, -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[[30, -12, -12, 30, 6],\n [15, -6, -6, 15, 3],\n [-15, 6, 6, -15, -3],\n [25, -10, -10, 25, 5],\n [20, -8, -8, 20, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[14, 6, 12, -26, 12],\n [40, 12, -9, -34, 12],\n [-24, -18, 3, 27, -12],\n [-24, 14, -3, 19, -4],\n [13, -5, -9, -2, -2]]\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 5x5 matrix:\n[[-36, 50, -54, 26, -26],\n [22, -31, -11, -29, 37],\n [20, -24, -26, -32, 50],\n [-14, 28, -19, 9, 6],\n [2, 2, -19, -9, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-7, 7, -16, 14, -22],\n [-38, 14, -2, 40, -14],\n [-28, 20, 11, 20, -5],\n [14, 8, 20, -25, 15],\n [-16, 10, 11, -7, 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[[-5, 13, 10, 42, 34],\n [36, -61, 3, -5, 5],\n [14, 17, 17, 27, -13],\n [-32, 50, -11, -28, -31],\n [0, 13, 15, 53, 37]]\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[[-5, 2, -1, 2, -6],\n [-5, 2, -1, 2, -6],\n [25, -10, 5, -10, 30],\n [30, -12, 6, -12, 36],\n [15, -6, 3, -6, 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[[-3, -17, 42, -22, 13],\n [11, -1, 38, -48, 35],\n [32, 27, -8, -43, 12],\n [-31, 29, 6, -35, 14],\n [18, 18, -19, -11, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-27, -24, 71, 42, -26],\n [-15, -27, 36, 54, -42],\n [12, -33, -10, -1, 6],\n [12, -3, -35, 12, -16],\n [13, 15, -41, -9, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -24, 30, -30, -18],\n [-1, 4, -5, 5, 3],\n [5, -20, 25, -25, -15],\n [4, -16, 20, -20, -12],\n [2, -8, 10, -10, -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 5x5 matrix:\n[[-2, 3, 2, 5, 17],\n [-1, -6, -14, 0, 21],\n [-6, 0, -12, 12, 66],\n [-1, 21, 40, 9, -24],\n [-1, -15, -32, -3, 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[[10, 6, 4, 2, 0],\n [-30, -18, -12, -6, 0],\n [0, 0, 0, 0, 0],\n [-30, -18, -12, -6, 0],\n [-30, -18, -12, -6, 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 5x5 matrix:\n[[-30, 24, 30, -30, 6],\n [5, -4, -5, 5, -1],\n [-25, 20, 25, -25, 5],\n [-30, 24, 30, -30, 6],\n [-15, 12, 15, -15, 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[[-3, 30, -30, -6, -6],\n [4, 40, 0, -2, -22],\n [2, 20, 0, -1, -11],\n [-2, -4, -8, -1, 5],\n [-4, -8, -16, -2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-10, 6, -12, 60, -38],\n [-13, -9, 6, 42, -23],\n [-15, -19, 18, 30, -13],\n [12, 32, -36, 12, -16],\n [19, 39, -42, -6, -7]]?\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[[-9, -15, -19, 9, 23],\n [-19, -11, -3, 7, -10],\n [-3, -3, -7, -13, 26],\n [93, 29, 0, 40, -20],\n [-87, -61, -32, -20, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -4, -10, -12, -4],\n [36, -18, 36, 6, -12],\n [-24, 18, 18, 34, 16],\n [-28, 19, 7, 27, 16],\n [-22, 13, -8, 9, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, 4, -16, 20, 9],\n [-17, -11, 24, -16, 1],\n [26, 18, 8, -32, -28],\n [-11, 25, 26, -34, -18],\n [9, 13, 40, -60, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-35, 70, 25, -30, 8],\n [-57, -22, -25, -16, -34],\n [-12, 17, -8, 12, 10],\n [9, -35, 23, 2, -12],\n [1, 8, 1, -4, 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[[6, -12, 30, 36, 24],\n [4, -8, 20, 24, 16],\n [-2, 4, -10, -12, -8],\n [4, -8, 20, 24, 16],\n [4, -8, 20, 24, 16]]?\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[[26, -32, 2, -7, -2],\n [-12, 14, 36, 41, -21],\n [9, -31, 24, 20, 9],\n [-37, 27, -6, -14, 24],\n [-12, 22, -50, 10, 32]]?\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, 32, -26, 9, 23],\n [-19, -12, -34, 39, 8],\n [4, -8, 24, -19, -13],\n [-6, 0, 0, -3, 9],\n [2, -16, 20, -9, -21]]?\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, -24, -16, 38, -22],\n [-8, -3, -44, 31, 13],\n [27, 33, -4, -36, 40],\n [-10, -6, -40, 32, 8],\n [-6, 0, -48, 30, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 5, -6, -21, 2],\n [8, -4, -29, 4, -13],\n [32, 12, 17, 13, 6],\n [-52, -25, 24, -51, -8],\n [-16, 0, 62, -48, 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[[-5, 37, 18, 8, -2],\n [-17, 10, -10, 1, -16],\n [-16, -3, 8, -3, 10],\n [-45, 11, 19, 10, -28],\n [13, 10, 25, 30, -64]]?\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, -14, -57, -16, 10],\n [-10, -11, -11, -3, -4],\n [-14, 0, 26, -1, 2],\n [32, -43, -25, -49, 26],\n [35, -39, -11, -53, 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[[-2, -12, -10, -4, -10],\n [-1, -6, -5, -2, -5],\n [3, 18, 15, 6, 15],\n [6, 36, 30, 12, 30],\n [-3, -18, -15, -6, -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, 48, -18, 26, 18],\n [11, 9, 8, 10, -8],\n [15, 18, 23, 2, -18],\n [-3, 12, -23, 36, 66],\n [24, 18, 29, 7, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-15, 12, -39, 45, 42],\n [32, -8, 4, -8, 16],\n [-15, 0, 15, -15, -30],\n [28, -10, 17, -22, -4],\n [-7, -2, 16, -17, -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 5x5 matrix:\n[[34, -38, 38, -22, -11],\n [17, 1, 24, -4, -16],\n [-11, -17, 2, -4, 19],\n [4, -41, 36, -17, 18],\n [-27, 7, -2, 8, 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[[28, 34, -10, -34, 24],\n [-19, -17, 1, 22, -10],\n [18, 0, -12, -21, 24],\n [11, -1, 17, -10, -14],\n [30, 36, -16, -37, 32]]\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 5x5 matrix:\n[[-10, -4, 24, -9, -12],\n [8, 20, 6, -18, 18],\n [18, 20, -24, -3, 28],\n [-32, -24, 60, -12, -44],\n [-10, -20, 0, 15, -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[[6, -6, 0, 5, -1],\n [24, -24, 0, 20, -4],\n [36, -36, 0, 30, -6],\n [18, -18, 0, 15, -3],\n [24, -24, 0, 20, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-34, -22, 9, 6, -4],\n [18, 20, 10, 2, 0],\n [-22, 7, -6, -9, -11],\n [30, -9, 44, 31, 17],\n [-23, -39, 22, 20, 7]]?\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, -30, -14, -22, 32],\n [-11, -30, -3, -14, 39],\n [-29, 6, 27, 22, 9],\n [12, 15, -4, 3, -23],\n [9, 21, 1, 9, -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 5x5 matrix:\n[[17, -1, -4, 49, -27],\n [22, -32, 30, 62, -30],\n [-4, 10, -3, 14, 9],\n [-11, 29, -17, 13, 21],\n [-28, 20, 5, -36, 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[[-4, 42, 39, -34, 13],\n [24, -60, -42, 12, -14],\n [20, -18, -3, -22, -1],\n [0, 36, 36, -36, 12],\n [16, -6, 6, -26, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-44, -8, -55, -3, -12],\n [4, 10, 11, -3, -6],\n [-27, -8, -38, -1, -6],\n [19, 39, 49, -11, -21],\n [2, -12, 17, 7, 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[[-22, -29, -20, 12, 41],\n [47, 57, 62, 30, -3],\n [-19, 39, -2, -18, -41],\n [-36, -33, -18, 18, 33],\n [21, -20, 2, -6, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[7, 17, -2, 32, 44],\n [13, -4, -2, 38, 35],\n [34, 9, 16, 34, 13],\n [-60, 18, -24, -60, -6],\n [-30, -18, -24, 0, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-18, 19, -2, 5, 1],\n [28, 0, 22, -20, -2],\n [0, 20, 6, -15, -18],\n [-32, -1, -41, 5, -24],\n [-10, -16, -19, 4, 36]]\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, -22, -9, -25, -36],\n [8, -4, -8, 10, 8],\n [-6, 6, 5, 1, 4],\n [10, -8, -9, 4, 0],\n [18, -24, -13, -20, -32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[24, 24, 9, 33, -30],\n [-16, -12, -4, -20, 24],\n [4, -1, -1, 3, -10],\n [12, 11, 4, 16, -16],\n [-24, -16, -5, -29, 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[[27, -2, -3, 47, 31],\n [-16, -3, 8, -40, -22],\n [64, -25, 24, 8, 46],\n [7, -10, 13, -1, 3],\n [-28, 6, -4, 20, -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 5x5 matrix:\n[[78, 6, 43, -53, -29],\n [-2, -26, 19, -8, -12],\n [-14, -36, 10, 16, -38],\n [-16, -11, 35, -23, 29],\n [-35, 46, -47, 40, 33]]\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 5x5 matrix:\n[[-40, 0, -16, 7, 11],\n [-1, -6, 11, 16, -58],\n [-27, -33, 41, 13, 17],\n [28, -2, 20, 1, -39],\n [-42, -26, -2, 20, 44]]\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, 35, -32, -24, 27],\n [-8, -27, 14, 16, -7],\n [-8, -25, 18, 16, -13],\n [-10, -34, 17, 20, -8],\n [-6, -14, 23, 12, -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[[-30, -12, 18, 18, -24],\n [-20, -8, 12, 12, -16],\n [10, 4, -6, -6, 8],\n [-25, -10, 15, 15, -20],\n [-5, -2, 3, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, 39, 6, -1, -24],\n [35, 18, 6, -26, -22],\n [14, -1, -28, 49, -40],\n [39, 12, -12, 27, -57],\n [-36, -21, -6, 3, 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[[6, 18, 30, -6, 18],\n [1, 3, 5, -1, 3],\n [10, -21, 5, 20, -24],\n [3, -8, 0, 7, -9],\n [19, -28, 20, 31, -33]]?\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[[9, 0, -6, 9, 12],\n [-15, 0, 10, -15, -20],\n [3, 0, -2, 3, 4],\n [18, 0, -12, 18, 24],\n [-6, 0, 4, -6, -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[[18, -8, -28, -10, 0],\n [4, -2, -12, -2, 2],\n [28, -11, -6, -17, -13],\n [-21, 8, -2, 13, 12],\n [7, -3, -8, -4, -1]]?\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, -7, -27, -33, -16],\n [21, -2, -24, -3, -23],\n [9, 32, 16, 14, 8],\n [-18, -24, 30, 19, 38],\n [2, 52, 16, 6, -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[[-6, -10, -12, -2, 4],\n [9, 15, 18, 3, -6],\n [18, 30, 36, 6, -12],\n [-15, -25, -30, -5, 10],\n [3, 5, 6, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-15, -3, -15, -9, -12],\n [-30, -6, -30, -18, -24],\n [-24, -12, 16, -8, 0],\n [39, 15, -1, 17, 12],\n [-36, -9, -26, -20, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[16, -4, -24, -4, -16],\n [-11, 5, 21, 11, 17],\n [-7, 1, 9, -1, 5],\n [-25, 1, 27, -13, 11],\n [15, 3, -9, 21, 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[[-33, 31, 14, 32, 7],\n [-20, 10, -17, 15, -23],\n [-18, 26, 34, 22, 32],\n [18, -16, -5, -17, -1],\n [6, -12, -21, -9, -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[[26, -14, 22, -1, -12],\n [-1, 7, -17, -4, -6],\n [7, -1, -1, -2, -6],\n [25, -15, 25, 0, -10],\n [-4, 4, -8, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[20, 12, 16, 4, -20],\n [-15, -9, -12, -3, 15],\n [-30, -18, -24, -6, 30],\n [-10, -6, -8, -2, 10],\n [25, 15, 20, 5, -25]]\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 5x5 matrix:\n[[-69, -22, 44, 2, 26],\n [61, 16, -6, 32, -18],\n [48, 24, 40, 60, -7],\n [-19, -24, 8, -13, -21],\n [35, -6, -12, 2, -35]]\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[[-7, -4, -4, -28, 12],\n [35, 12, -4, -26, 14],\n [-62, -58, 10, 19, 25],\n [-25, -48, 8, -21, 51],\n [-12, -36, -12, -47, 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 5x5 matrix:\n[[12, -36, 24, -36, 36],\n [-10, 30, -20, 30, -30],\n [8, -24, 16, -24, 24],\n [-12, 36, -24, 36, -36],\n [2, -6, 4, -6, 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 5x5 matrix:\n[[15, -17, 14, 10, -7],\n [28, 16, -20, 16, 10],\n [18, -6, 4, 1, -2],\n [-36, 12, -8, -2, 4],\n [-14, -6, 4, 29, -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[[-34, -26, -22, 24, 10],\n [-9, -15, -15, 18, 3],\n [6, -36, -42, 54, 0],\n [15, -21, -27, 36, -3],\n [-1, -17, -19, 24, 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[[-18, 15, -6, 12, 0],\n [2, -1, -1, -3, -6],\n [-20, 16, -5, 15, 6],\n [-60, 54, -30, 30, -36],\n [-14, 15, -13, 1, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 12, 8, 12, 10],\n [4, 12, 8, 12, 10],\n [-6, -18, -12, -18, -15],\n [-2, -6, -4, -6, -5],\n [-12, -36, -24, -36, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-5, -1, -4, 3, 5],\n [30, 6, 24, -18, -30],\n [10, 2, 8, -6, -10],\n [10, 2, 8, -6, -10],\n [-5, -1, -4, 3, 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[[-16, 10, 4, 22, -16],\n [-13, 6, 3, 18, -13],\n [15, 48, 3, -24, 15],\n [-14, 30, 6, 18, -14],\n [-5, 18, 3, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-27, 36, -13, 12, -54],\n [-48, 9, -44, -24, 1],\n [-15, 36, 5, 15, 12],\n [-21, 6, -17, -13, 46],\n [18, 39, 36, 43, -55]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[15, -6, 3, 51, -21],\n [11, 0, 3, 15, -7],\n [12, 0, 2, 18, -10],\n [-12, 3, -11, -21, -2],\n [37, 2, 6, 46, -28]]\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, 2, -26, 50, 35],\n [16, -12, 30, 16, -3],\n [0, -3, 31, -2, 18],\n [20, -9, 35, -18, -15],\n [-20, 31, 5, -8, 31]]\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 5x5 matrix:\n[[24, 12, -24, 48, 8],\n [38, 10, -26, 54, 6],\n [4, 24, -24, 40, 0],\n [2, -24, 15, -19, 13],\n [-61, 67, -14, -12, -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[[-12, -6, 4, 8, 0],\n [0, 0, 0, 0, 0],\n [-6, -3, 2, 4, 0],\n [-30, -15, 10, 20, 0],\n [36, 18, -12, -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 5x5 matrix:\n[[2, 13, -10, 5, 8],\n [-28, -15, 28, -19, -20],\n [60, 66, -36, 18, 36],\n [-28, -18, 16, -10, -14],\n [-12, 10, 22, -18, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-31, 27, 26, -18, -6],\n [16, 1, 10, -31, 52],\n [51, -21, -4, 20, -12],\n [-12, -20, -41, 11, 13],\n [-19, 3, -12, -23, 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[[12, 12, 24, -33, -27],\n [-16, -40, 5, 9, -2],\n [-10, -41, 7, -25, 6],\n [-3, 5, -14, 22, 13],\n [-2, -50, 26, -52, 16]]\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, -46, -16, -1, -4],\n [-18, -6, -10, 20, -24],\n [-13, 38, -16, 19, -16],\n [28, -32, 12, -23, 22],\n [9, -52, 30, -30, 26]]\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 5x5 matrix:\n[[-19, 8, -10, 10, 0],\n [-1, 20, -19, -6, 32],\n [22, -30, 41, 4, -42],\n [15, -23, -1, -24, -7],\n [5, -25, 14, -4, -29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[26, 34, -21, 12, -22],\n [-28, -42, 23, -6, 16],\n [-22, -32, 18, -6, 14],\n [-32, -44, 26, -12, 24],\n [-24, -12, 18, -36, 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[[11, -2, 7, 17, -28],\n [12, -15, -7, 9, 15],\n [-6, 18, -2, -20, -4],\n [36, -12, -4, 24, -24],\n [22, -10, 6, 28, -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[[12, 48, 4, 34, -16],\n [18, 48, 10, 31, -16],\n [-24, -30, -19, -13, 10],\n [-12, -12, -10, -4, 4],\n [-24, -12, -22, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -25, 11, -5, -5],\n [-16, -10, -6, 24, 50],\n [0, 10, -2, -4, -10],\n [0, -10, 2, 4, 10],\n [16, -50, 18, 0, 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 5x5 matrix:\n[[4, 12, 3, -20, 6],\n [-14, 9, 15, 2, -4],\n [4, -18, -12, 20, -4],\n [-36, 18, 36, 12, -12],\n [-10, -9, 3, 22, -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 5x5 matrix:\n[[-18, -26, -7, -19, -13],\n [-12, -20, -8, -12, -8],\n [18, 10, -13, 23, 17],\n [6, -2, -11, 9, 7],\n [0, 16, 20, -4, -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[[-8, -11, 21, 13, -19],\n [11, 3, -27, -18, -14],\n [2, -9, 33, 19, -14],\n [3, -13, 3, 0, -45],\n [-2, 13, -63, -37, 11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -3, 0, 2, 1],\n [4, 6, -8, 0, -2],\n [-10, 45, -40, -10, -15],\n [16, -12, 4, 6, 4],\n [-10, 33, -28, -8, -11]]\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, 26, -11, 67, 36],\n [7, 35, -4, 58, 26],\n [19, -5, -29, -8, -86],\n [-8, -22, 11, -25, -4],\n [-38, -40, 41, 23, 56]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 36, -28, 12, 12],\n [-19, -30, 47, 0, -54],\n [12, 34, -34, 10, 24],\n [19, 11, -34, 5, 42],\n [-17, -31, 44, -1, -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 5x5 matrix:\n[[4, -20, -12, 20, -24],\n [0, 0, 0, 0, 0],\n [1, -5, -3, 5, -6],\n [-1, 5, 3, -5, 6],\n [3, -15, -9, 15, -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 5x5 matrix:\n[[0, -36, -24, 30, 30],\n [-15, -5, 0, 5, 10],\n [-9, 3, 4, -2, 1],\n [15, 11, 4, -10, -15],\n [18, 36, 20, -31, -37]]\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[[33, -8, 42, -48, -4],\n [-15, 23, 23, 8, -47],\n [7, 20, 26, 8, -58],\n [36, -1, -4, -11, 19],\n [-20, 10, -19, 21, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 40, 18, 20, -39],\n [12, -54, 3, 18, 15],\n [10, -24, -26, -32, 37],\n [-10, 32, 17, 17, -30],\n [4, -8, 19, 33, -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 5x5 matrix:\n[[18, -36, 24, -30, 30],\n [-9, 18, -12, 15, -15],\n [0, 0, 0, 0, 0],\n [15, -30, 20, -25, 25],\n [18, -36, 24, -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[[0, 6, 4, 0, -1],\n [0, -24, -16, 0, 4],\n [0, 36, 24, 0, -6],\n [0, -36, -24, 0, 6],\n [0, 12, 8, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[20, -5, -11, 12, 20],\n [-2, 53, -29, 23, -14],\n [27, 39, -1, 12, 7],\n [-5, 20, -26, 17, -5],\n [21, 51, 3, 9, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, -30, -6, 6, -15],\n [29, -39, -4, 18, -13],\n [5, -17, -10, 16, -4],\n [34, -34, 0, 20, -8],\n [-11, 11, -5, 5, 7]]?\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[[-27, -56, -27, -10, -11],\n [-15, 2, 5, 11, -8],\n [-2, 32, -2, 7, -10],\n [-26, 28, -6, 10, -30],\n [10, -64, -50, -40, 8]]?\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[[-17, 13, 30, 4, -3],\n [34, 0, -16, 4, -2],\n [7, 6, -13, -15, -18],\n [11, 8, 9, 15, 28],\n [13, -16, -20, -2, -13]]\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, 21, 5, 1, -1],\n [-28, 24, -24, -3, -18],\n [30, -38, 5, 0, -34],\n [40, -46, 7, -10, -52],\n [-28, 28, -18, 17, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 16, 0, -20, -16],\n [3, -12, 0, 15, 12],\n [1, -4, 0, 5, 4],\n [4, -16, 0, 20, 16],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-7, -1, 0, 9, -3],\n [35, -15, 21, -26, 25],\n [35, -15, 21, -26, 25],\n [-9, -7, 6, 17, -1],\n [1, -17, 18, 15, 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[[4, 5, 4, 4, -1],\n [17, 21, 14, 11, 0],\n [-36, -44, -24, -12, -8],\n [7, 8, -2, -11, 11],\n [-35, -43, -26, -17, -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[[-45, -2, -19, 0, -35],\n [60, -16, 25, -12, 8],\n [-38, 3, -23, 7, -12],\n [33, -7, 13, -5, 9],\n [30, -16, 28, -20, -30]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[46, 5, -10, 20, 46],\n [7, 25, -13, -20, 7],\n [40, -12, 7, 27, 40],\n [-4, -28, 36, 8, -4],\n [-67, -14, 2, -11, -67]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-5, 20, 30, 15, -25],\n [4, -16, -24, -12, 20],\n [-2, 8, 12, 6, -10],\n [-3, 12, 18, 9, -15],\n [3, -12, -18, -9, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[2, 86, 12, 18, -30],\n [29, -4, -5, 19, 8],\n [48, -13, -34, -13, -20],\n [3, 13, -11, -20, -22],\n [18, 57, 11, 25, -9]]\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, -3, 26, -5, 14],\n [14, -21, 12, 16, 13],\n [-4, 6, 28, -14, 12],\n [18, -27, 4, 24, 11],\n [2, -3, 36, -8, 19]]\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[[58, -42, 86, -19, -21],\n [-26, 2, -46, 22, 12],\n [-37, 69, -28, -4, -16],\n [-6, 47, -11, 6, 32],\n [-1, 21, -12, 16, 32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-9, 12, -7, 1, 12],\n [-4, -6, -6, -14, -23],\n [-12, -8, -28, -28, -52],\n [14, -5, 23, 15, 21],\n [41, -12, -9, 55, 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 5x5 matrix:\n[[-23, 38, 34, -15, 13],\n [-28, -60, 40, 23, -17],\n [-12, 39, -3, 57, 29],\n [-3, -29, 19, -32, -20],\n [-30, -7, 42, 32, 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[[-8, 4, -10, 30, -10],\n [9, -19, -6, 50, 14],\n [18, -38, -16, 32, 32],\n [16, -35, -18, -4, 31],\n [-4, 6, -4, -72, -2]]\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 5x5 matrix:\n[[-6, -1, 5, 6, -4],\n [-36, -6, 30, 36, -24],\n [18, 3, -15, -18, 12],\n [-6, -1, 5, 6, -4],\n [18, 3, -15, -18, 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[[-5, -5, 6, -1, 5],\n [25, 25, -30, 5, -25],\n [0, 0, 0, 0, 0],\n [-20, -20, 24, -4, 20],\n [-30, -30, 36, -6, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, -12, -2, 48, -22],\n [1, -2, -1, 9, -3],\n [-5, 6, 3, -33, 21],\n [-5, 2, 1, -21, 27],\n [11, -8, 4, 33, -38]]\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, 20, 22, -4, -9],\n [-20, 2, -6, 17, -10],\n [-17, -5, -25, 8, -8],\n [-68, 2, -6, -30, 2],\n [-21, 17, 17, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[25, -26, 1, 9, -8],\n [-10, 12, -6, -6, 12],\n [20, -18, -9, 3, 9],\n [0, -6, 21, 9, -33],\n [-10, 18, -27, -15, 45]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[10, 0, 4, -2, -12],\n [-7, -12, -10, 11, 12],\n [23, -32, -10, 21, -18],\n [-8, 2, -2, 0, 9],\n [13, -22, -8, 15, -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[[10, 5, 25, 25, 10],\n [-7, -5, -24, -24, -8],\n [3, 3, 14, 14, 4],\n [5, -5, -20, -20, 0],\n [16, -4, -12, -12, 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[[6, -8, -6, 0, 10],\n [3, -4, -3, 0, 5],\n [0, 0, 0, 0, 0],\n [3, -4, -3, 0, 5],\n [6, -8, -6, 0, 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 5x5 matrix:\n[[-36, 0, -6, 18, -17],\n [2, -28, 34, -14, -5],\n [-38, 12, -2, 10, -15],\n [-5, -50, 2, -20, -2],\n [14, 2, 13, 28, -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 5x5 matrix:\n[[18, 1, 19, -18, 1],\n [28, -16, 8, -22, -12],\n [7, 41, 2, -35, -10],\n [5, 56, 23, -37, 5],\n [34, -13, 29, -26, -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[[17, -4, 7, 29, -3],\n [33, -14, 11, 19, 31],\n [-6, 26, 20, -13, -5],\n [-3, 8, -45, -11, -3],\n [-43, 5, 43, -28, -24]]\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[[3, -10, 14, -42, 17],\n [12, 40, -49, 35, -10],\n [12, 36, -37, 19, 2],\n [-48, 37, -46, 17, 47],\n [-1, -7, -2, -37, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-24, 17, -27, -5, 48],\n [-6, -25, -27, -5, -18],\n [6, 0, 49, 32, -18],\n [-15, -37, -69, -28, 2],\n [9, 0, 30, 7, 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[[52, 42, 34, 52, -56],\n [21, 0, 4, 2, 7],\n [18, -9, -3, 22, 4],\n [3, 9, 5, 28, -25],\n [-21, -18, -15, -6, 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[[-2, -10, 6, -6, -8],\n [1, 5, -3, 3, 4],\n [-6, -30, 18, -18, -24],\n [-6, -30, 18, -18, -24],\n [-5, -25, 15, -15, -20]]\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, -21, -16, 27, -4],\n [10, 15, 14, -27, 8],\n [18, -6, -10, 24, -12],\n [-3, 6, 7, -15, 6],\n [-17, -21, -19, 36, -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 5x5 matrix:\n[[-6, 2, -2, -4, -4],\n [-6, 2, -2, -4, -4],\n [6, -2, 2, 4, 4],\n [18, -6, 6, 12, 12],\n [3, -1, 1, 2, 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[[15, 0, 4, -21, -5],\n [1, -22, 12, 3, -4],\n [-38, 26, -24, 48, 17],\n [-22, 4, -8, 30, 8],\n [14, -38, 24, -12, -11]]?\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, 13, 0, 22, 15],\n [-24, 4, 8, -4, 40],\n [-22, -18, 24, 20, 42],\n [18, -2, 0, -11, -31],\n [49, -16, -22, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-32, -34, -2, 22, 8],\n [-32, -34, -2, 22, 8],\n [-4, -4, 0, -24, -4],\n [18, -9, -27, 52, 26],\n [-17, 13, 30, -57, -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 5x5 matrix:\n[[5, -1, 6, -6, -2],\n [-30, 6, -36, 36, 12],\n [-20, 4, -24, 24, 8],\n [20, -4, 24, -24, -8],\n [25, -5, 30, -30, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-19, -76, -26, 49, 4],\n [12, 19, 22, -21, -24],\n [56, -23, -30, -35, 40],\n [-1, -44, -32, 7, 22],\n [4, -27, -10, 45, 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 5x5 matrix:\n[[18, -30, 36, -30, 6],\n [12, -20, 24, -20, 4],\n [-12, 20, -24, 20, -4],\n [9, -15, 18, -15, 3],\n [12, -20, 24, -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[[44, 10, -20, 13, -5],\n [12, 16, -2, 24, -18],\n [-54, 6, -4, 47, -73],\n [16, -32, -26, 14, 14],\n [-37, -28, -19, 20, -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 5x5 matrix:\n[[33, 26, 39, -10, -49],\n [-48, 30, 0, -24, 17],\n [9, -53, -30, 37, 24],\n [16, -26, 2, 26, -10],\n [-17, -24, -31, 10, 36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1, -12, -18, 30, -20],\n [-4, 10, 15, 13, 4],\n [7, -18, -27, -21, -8],\n [-2, 2, 3, 17, -4],\n [-3, 8, 12, 8, 4]]\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, -24, -22, 4, -9],\n [14, -10, 6, -20, -7],\n [-11, -19, -29, 30, -16],\n [-19, 9, -6, 12, 14],\n [3, -37, -33, 22, -33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-15, 12, 6, -12, -15],\n [-5, 26, -1, -34, 1],\n [13, -24, -16, 1, -6],\n [-18, -2, 9, 7, -23],\n [7, -2, 5, 19, 18]]\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, -22, 12, 4, -2],\n [44, 10, -22, 30, -8],\n [-8, 26, -13, -7, 3],\n [-36, -18, 24, -24, 6],\n [-28, -8, 15, -19, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, 16, 20, 12, -4],\n [-18, 24, 30, 18, -6],\n [-6, 8, 10, 6, -2],\n [9, -12, -15, -9, 3],\n [-15, 20, 25, 15, -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 5x5 matrix:\n[[-10, 1, -29, -7, -22],\n [13, -14, -23, -36, 3],\n [43, 10, 24, 5, -1],\n [46, -24, 0, 10, 6],\n [-6, -5, -30, -75, 9]]\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[[-5, -16, 35, 14, -18],\n [0, -7, 20, 13, -6],\n [14, 21, -30, 5, 30],\n [12, 30, -60, -18, 36],\n [-6, 6, -30, -30, 0]]\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, -18, -18, 18, -12],\n [-36, 6, 48, 0, -4],\n [20, -10, -24, 8, -4],\n [-12, 12, 12, -12, 8],\n [-5, 10, 3, -11, 8]]\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[[75, 30, 76, 26, -6],\n [1, 5, -14, -5, 2],\n [-64, -23, -52, -22, 26],\n [-14, 20, -26, -11, -8],\n [-33, -19, -28, -18, 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[[18, 28, 4, 14, 0],\n [14, 12, -25, -16, 22],\n [13, 6, -38, -29, 32],\n [18, 12, -42, -30, 36],\n [-7, -10, 1, -3, -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[[9, 3, -3, 9, 0],\n [-18, -6, 6, -18, 0],\n [-15, 11, 25, -3, 0],\n [-15, 11, 25, -3, 0],\n [-30, 14, 40, -12, 0]]\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, 10, -5, 25, -30],\n [-12, -12, 6, -30, 36],\n [2, 2, -1, 5, -6],\n [12, 12, -6, 30, -36],\n [-8, -8, 4, -20, 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[[-6, -10, -5, -7, -5],\n [5, -8, -18, 7, 3],\n [38, 40, 0, 46, 30],\n [26, 34, 9, 31, 21],\n [-4, -2, 3, -5, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, 3, -3, -3, -6],\n [1, 3, -3, -3, -6],\n [-4, -12, 12, 12, 24],\n [4, 12, -12, -12, -24],\n [-3, -9, 9, 9, 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[[-17, 2, -10, -7, -5],\n [-27, 13, 48, -13, 11],\n [27, -15, -39, 5, -18],\n [-27, 13, 48, -13, 11],\n [26, 0, 25, 14, 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[[-14, 22, -11, 4, -6],\n [6, -8, 4, -16, 4],\n [6, -8, 4, -16, 4],\n [5, -6, 3, -20, 4],\n [-4, 6, -3, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-16, 24, -4, -12, 24],\n [28, -35, 0, 24, -41],\n [28, -21, -14, 30, -39],\n [-32, 6, 34, -42, 42],\n [16, -38, 18, 6, -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[[-39, -25, 5, -38, -12],\n [-21, 13, 6, 6, -66],\n [-18, -6, 3, -12, -18],\n [33, 7, -6, 18, 42],\n [9, 15, 0, 18, -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[[18, -10, 11, 3, -13],\n [65, -30, 0, 20, 10],\n [-22, 22, 0, 0, 12],\n [7, 6, -4, 8, 18],\n [38, -31, -7, 5, -3]]\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[[8, -12, 10, 12, -10],\n [-15, 24, -18, -27, 18],\n [14, -24, 16, 30, -16],\n [-26, 40, -32, -42, 32],\n [-18, 32, -20, -42, 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[[31, -13, -6, -13, -12],\n [-25, 38, -52, -15, 0],\n [-23, 29, -39, -10, 4],\n [-81, 39, -30, 45, 54],\n [52, -46, 30, 10, -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[[16, -8, -24, 24, -4],\n [20, -10, -30, 30, -5],\n [0, 0, 0, 0, 0],\n [16, -8, -24, 24, -4],\n [20, -10, -30, 30, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[18, -6, -46, 22, -36],\n [-21, -9, 43, -31, 30],\n [16, 20, -24, 28, -13],\n [4, -16, -20, 0, -19],\n [-23, -7, 49, -33, 35]]?\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 5x5 matrix:\n[[-11, 15, -55, 17, -48],\n [7, -32, 8, 3, -14],\n [-10, 27, -74, 19, -42],\n [-20, 27, -13, -22, 10],\n [16, -52, 26, 16, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 0, 18, 9, -6],\n [-4, 0, 12, 6, -4],\n [8, 0, -24, -12, 8],\n [10, 0, -30, -15, 10],\n [4, 0, -12, -6, 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[[10, 10, 12, 4, -8],\n [-10, -10, -12, -4, 8],\n [-10, -10, -12, -4, 8],\n [-25, -25, -30, -10, 20],\n [-20, -20, -24, -8, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, 30, -2, -1, -21],\n [0, 14, 19, -14, 5],\n [48, 0, 42, -24, 6],\n [16, 6, -49, 34, -47],\n [62, -24, -5, 11, -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[[-11, -6, 16, 16, 2],\n [-9, -18, 24, 0, -6],\n [2, 24, -22, 20, 13],\n [-5, 18, -10, 28, 13],\n [-2, 24, -18, 28, 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[[24, 6, -14, 21, 30],\n [-35, -21, 29, -2, -31],\n [7, 2, -16, 6, 13],\n [-5, -11, 9, 23, -21],\n [-15, -3, 6, -16, -12]]\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 5x5 matrix:\n[[0, 9, 3, 9, -6],\n [0, 12, 4, 12, -8],\n [0, -6, -2, -6, 4],\n [0, -15, -5, -15, 10],\n [0, 3, 1, 3, -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[[47, 25, 4, -3, -28],\n [-31, -44, -42, 8, 32],\n [26, 47, 25, -57, -27],\n [2, -42, 20, 48, 10],\n [-17, 19, 19, -40, 0]]?\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 5x5 matrix:\n[[0, 0, 0, 0, 0],\n [1, 3, 0, -1, 0],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [4, 12, 0, -4, 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[[8, 4, -8, 5, -6],\n [0, 24, 16, -12, 0],\n [-24, 30, 52, -36, 18],\n [0, -24, -16, 12, 0],\n [-4, -11, -2, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-18, 12, -3, -12, 3],\n [-24, 16, -4, -16, 4],\n [-12, 8, -2, -8, 2],\n [0, 0, 0, 0, 0],\n [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[[28, -26, -4, 16, 17],\n [19, -12, 6, 8, 27],\n [-28, 32, 12, -20, 0],\n [-15, 10, -15, -15, -15],\n [-47, 56, 47, -17, -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[[-3, -6, -16, 24, 4],\n [-33, 9, -11, -32, -25],\n [7, 9, 17, -12, -1],\n [36, -48, 4, -12, 32],\n [7, 24, 8, 38, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 38, 13, 30, 5],\n [0, 4, -1, 6, 4],\n [12, -40, -35, -6, 26],\n [2, -26, -1, -30, -15],\n [-12, 48, 33, 18, -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[[6, -5, -5, 4, -5],\n [6, -5, -5, 4, -5],\n [18, -15, -15, 12, -15],\n [-36, 30, 30, -24, 30],\n [30, -25, -25, 20, -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[[-17, -15, -56, -42, 17],\n [7, 10, 26, 12, 3],\n [-33, -2, -44, -27, 25],\n [-3, 9, 6, -9, 21],\n [-30, 8, -10, 9, 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[[36, -24, -30, -6, 6],\n [36, -24, -30, -6, 6],\n [-30, 20, 25, 5, -5],\n [-12, 8, 10, 2, -2],\n [-6, 4, 5, 1, -1]]\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[[0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [30, -20, 15, -5, -25],\n [12, -8, 6, -2, -10],\n [24, -16, 12, -4, -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[[-18, 10, 26, -30, 16],\n [48, 13, -11, 20, 38],\n [15, -20, -66, 31, -6],\n [-6, 15, 25, -28, 30],\n [6, -15, -39, 22, -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 5x5 matrix:\n[[0, 0, 0, 0, 0],\n [-2, 6, 4, -8, 0],\n [2, -6, -4, 8, 0],\n [-5, 15, 10, -20, 0],\n [-3, 9, 6, -12, 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[[-14, -6, 0, -8, 1],\n [24, 17, 32, -7, -10],\n [30, 51, 12, -27, 9],\n [-12, 46, -2, -26, 30],\n [18, -71, 21, 13, -57]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-16, 24, -24, -12, -24],\n [20, -30, 30, 15, 30],\n [-4, 6, -6, -3, -6],\n [-24, 36, -36, -18, -36],\n [-20, 30, -30, -15, -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[[-20, 24, -8, -4, 20],\n [25, -30, 10, 5, -25],\n [10, -12, 4, 2, -10],\n [20, -24, 8, 4, -20],\n [-15, 18, -6, -3, 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[[-64, -18, -24, 22, -24],\n [7, -11, 27, -6, 27],\n [-46, 0, -30, 50, -50],\n [7, -18, 39, -11, 41],\n [-10, -4, 6, 23, -7]]\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, 18, 9, -6, -18],\n [-8, 26, -7, 3, -31],\n [4, 32, 8, -6, -34],\n [-32, 4, -38, 22, -14],\n [12, 36, 18, -12, -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[[15, -20, 25, 30, -15],\n [-9, 12, -15, -18, 9],\n [-15, 20, -25, -30, 15],\n [-12, 16, -20, -24, 12],\n [-18, 24, -30, -36, 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[[16, 43, 0, 46, -45],\n [4, 11, 6, 14, -33],\n [6, 23, -4, 21, 22],\n [4, -15, -33, -21, 24],\n [-14, -28, 23, -24, -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[[22, -2, 24, 35, -8],\n [-25, -9, -33, -44, 16],\n [-16, -10, -24, -26, 8],\n [-14, -14, -24, -23, 8],\n [4, -13, -6, 22, -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[[7, -4, -10, 75, -11],\n [74, 10, 14, -26, 44],\n [-25, -1, -5, 2, 2],\n [-27, -9, -50, -5, -12],\n [28, -1, -22, 22, 13]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-37, -42, -47, 20, 17],\n [-16, 20, 4, -17, -13],\n [-16, 22, -2, 0, 2],\n [-48, -34, -62, 40, 38],\n [-27, -30, -2, -22, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[25, -15, -5, 5, -5],\n [-10, 6, 2, -2, 2],\n [15, -9, -3, 3, -3],\n [25, -15, -5, 5, -5],\n [30, -18, -6, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0, 0],\n [-2, -4, 6, 12, -6],\n [-4, -8, 12, 24, -12],\n [-3, -6, 9, 18, -9],\n [4, 8, -12, -24, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[36, 24, 24, 24, 30],\n [-12, -8, -8, -8, -10],\n [-30, -20, -20, -20, -25],\n [-36, -24, -24, -24, -30],\n [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[[17, -5, -1, 16, 12],\n [21, -15, -3, 28, 6],\n [-4, -20, -4, 16, -24],\n [3, 30, 6, -26, 33],\n [24, -15, -3, 30, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[28, 13, -4, -23, 6],\n [28, 15, -26, 16, -37],\n [-16, -19, 34, -30, 43],\n [15, 1, 7, -25, 12],\n [24, 9, -12, 6, -17]]?\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, -5, 0, 5, -20],\n [0, 6, 0, -6, 24],\n [40, 36, -40, -26, 34],\n [-4, 1, 4, -2, 15],\n [12, 9, -12, -6, 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[[47, 47, -35, 35, 0],\n [25, 13, -2, -3, 16],\n [-34, -16, -6, 1, -14],\n [8, 36, 12, 44, -26],\n [-34, -54, 11, -44, 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[[-21, -3, -6, 10, -17],\n [-62, 10, -17, 15, -20],\n [9, -7, -2, 2, -6],\n [21, -27, 15, -21, 30],\n [-24, 42, -24, 33, -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 5x5 matrix:\n[[2, -2, 0, 2, 4],\n [-2, 2, 0, -2, -4],\n [-1, 1, 0, -1, -2],\n [3, -3, 0, 3, 6],\n [5, -5, 0, 5, 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[[-8, -16, 8, -12, -16],\n [-8, -16, 8, -12, -16],\n [-12, -24, 12, -18, -24],\n [-6, -12, 6, -9, -12],\n [-12, -24, 12, -18, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[9, 15, 16, 21, -3],\n [-50, -3, -37, 10, -9],\n [-46, -21, -48, -15, 3],\n [1, -30, 20, -22, -9],\n [-36, -6, -46, 16, 22]]\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, -32, 4, -11, -44],\n [34, -23, 31, -26, -31],\n [-30, -20, 40, 7, 0],\n [12, 28, -38, -2, 14],\n [-6, 34, -50, 13, 26]]\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 5x5 matrix:\n[[8, 0, -2, -6, -12],\n [-16, 0, 4, 12, 24],\n [-4, 0, 1, 3, 6],\n [-8, 0, 2, 6, 12],\n [-12, 0, 3, 9, 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, -3, -3, -3, 1],\n [0, 0, 0, 0, 0],\n [-12, 9, 9, 9, -3],\n [-12, 9, 9, 9, -3],\n [-20, 15, 15, 15, -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[[39, 24, -20, 40, 22],\n [-27, -34, -6, 10, 6],\n [54, 52, 10, 15, 9],\n [24, 2, 34, 29, 10],\n [-9, -8, 34, -21, -17]]\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, 21, 17, 37, 32],\n [80, 52, 17, 13, 8],\n [-37, -17, 23, -8, -25],\n [63, 43, 22, 6, -8],\n [45, 37, 61, 25, 8]]\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 5x5 matrix:\n[[8, 4, 16, -12, 0],\n [-8, -4, -16, 12, 0],\n [-12, -6, -24, 18, 0],\n [6, 3, 12, -9, 0],\n [12, 6, 24, -18, 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[[34, 6, -50, 4, 24],\n [61, -46, 2, 48, 10],\n [-52, 47, 10, -38, -12],\n [9, 17, 6, 2, 2],\n [33, -44, -4, 5, 14]]\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 5x5 matrix:\n[[1, 20, -17, 16, -1],\n [3, 12, -11, 8, -11],\n [-4, 16, -12, 16, 20],\n [-2, -34, 29, -27, 3],\n [-3, -12, 11, -8, 11]]\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[[9, -15, 3, 3, -9],\n [15, -25, 5, 5, -15],\n [12, -20, 4, 4, -12],\n [-18, 30, -6, -6, 18],\n [15, -25, 5, 5, -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[[-24, -16, -14, 14, 24],\n [8, 0, 3, 21, 0],\n [-21, -10, -12, 6, 23],\n [-45, -30, -25, 10, 35],\n [19, 6, 11, -5, -25]]?\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, 32, 19, 48, -13],\n [-15, -20, 36, 48, 46],\n [-6, -7, 9, -4, -4],\n [-19, -13, 28, 25, 11],\n [2, -16, -5, -26, 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[[-2, 3, -1, 8, 0],\n [-8, 12, -4, 32, 0],\n [-28, -9, -5, 4, 0],\n [45, 26, 6, 18, 0],\n [18, 24, 0, 36, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-10, -9, 47, 46, 8],\n [-7, -6, 29, 24, 8],\n [11, 9, -40, -26, -16],\n [9, 36, 15, -20, 48],\n [9, 23, -16, -38, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 8, -2, 0, -12],\n [0, -6, -3, 24, 18],\n [0, -26, 2, 24, 48],\n [0, -4, 1, 0, 6],\n [0, 10, -4, 8, -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[[18, 12, 27, 24, -18],\n [-8, 11, 15, 15, 12],\n [-14, -13, -21, -27, 12],\n [-16, -17, -21, -37, 12],\n [-22, -5, -15, -15, 24]]\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, 6, 4, -12, 12],\n [8, 12, 8, -24, 24],\n [8, 12, 8, -24, 24],\n [-4, -6, -4, 12, -12],\n [12, 18, 12, -36, 36]]\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 5x5 matrix:\n[[-33, 43, -6, 31, -31],\n [27, -35, 5, -25, 25],\n [0, 2, 1, 4, -4],\n [-33, 43, -6, 31, -31],\n [-3, -5, -5, -15, 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 5x5 matrix:\n[[-3, 37, 25, 34, 7],\n [18, -6, -8, -26, 16],\n [-35, 61, 52, 23, -12],\n [-21, 22, 21, 12, -12],\n [41, -9, -17, -24, 35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-60, -15, -35, 40, -35],\n [-48, -22, -22, 36, -22],\n [-6, 21, -17, -5, -17],\n [-18, -7, -9, 13, -9],\n [42, 3, 29, -25, 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[[-22, 20, -20, 25, -4],\n [-43, -14, -35, 3, 22],\n [-21, 4, -15, -8, -15],\n [44, 24, 56, 19, -4],\n [-35, -22, -33, -10, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 8, -20, 4, 0],\n [6, 0, 18, -6, -9],\n [-1, 2, -5, 1, 0],\n [1, -6, 9, -1, 3],\n [-13, -6, -33, 13, 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 5x5 matrix:\n[[9, 26, 17, 26, 25],\n [12, 4, -8, 4, -28],\n [27, 30, 3, 30, -21],\n [-3, -2, 1, -2, 5],\n [-6, -20, -14, -20, -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[[8, 20, 24, -32, -32],\n [43, 16, 17, -54, -61],\n [35, 5, 0, -32, -32],\n [13, 0, 4, -12, -22],\n [24, 26, 30, -52, -54]]\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[[-38, 39, -9, -32, 57],\n [36, -33, 9, -3, -2],\n [-22, 18, -12, 17, -19],\n [38, -41, 1, 45, -73],\n [-10, 4, -20, 36, -45]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[26, -3, -28, 12, 5],\n [-36, 16, 0, -36, 20],\n [-9, 4, 0, -9, 5],\n [-16, 12, -16, -24, 20],\n [21, -13, 12, 27, -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[[-2, 15, -7, -7, 3],\n [0, 10, -50, -15, 5],\n [4, 17, 2, 4, 15],\n [-20, 23, 6, -17, 18],\n [-4, -23, 10, 6, 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[[5, 1, 1, 0, -3],\n [-30, -6, -6, 0, 18],\n [-15, -3, -3, 0, 9],\n [0, 0, 0, 0, 0],\n [30, 6, 6, 0, -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[[-24, -12, -12, -6, 0],\n [20, 10, 10, 5, 0],\n [20, 10, 10, 5, 0],\n [-20, -10, -10, -5, 0],\n [20, 10, 10, 5, 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[[15, 26, -9, -13, -4],\n [-4, -14, -13, -39, 18],\n [-15, -14, -5, -21, 24],\n [0, -26, -7, -25, 2],\n [-13, 38, 5, 19, 22]]?\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[[60, -1, -25, 64, 14],\n [-48, -26, 26, -28, 12],\n [-54, 0, 51, -69, -24],\n [48, 8, -9, 38, -2],\n [-60, -2, 41, -68, -18]]?\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 5x5 matrix:\n[[3, -58, -1, 8, -50],\n [28, 42, -44, -14, 86],\n [0, -36, -1, 14, -29],\n [8, 18, -14, -2, 32],\n [25, -4, -31, -22, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 12, 15, -15, -18],\n [16, 16, 20, -20, -24],\n [20, 20, 25, -25, -30],\n [8, 8, 10, -10, -12],\n [24, 24, 30, -30, -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[[-16, 28, -32, 0, 22],\n [2, -8, 14, -6, -15],\n [-8, -22, 32, 0, -37],\n [7, -43, 29, 39, -10],\n [-22, -6, -2, 26, -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[[7, 25, -16, 22, -42],\n [-26, -14, 8, 28, 12],\n [15, 24, -15, 6, -36],\n [-34, -13, 7, 44, 6],\n [35, 10, -5, -50, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-21, -6, -3, -2, 18],\n [-9, -6, 3, 4, 3],\n [-3, 6, -9, -10, 12],\n [-44, -24, 8, 12, 22],\n [-45, -30, 15, 20, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 7, -25, 4, -7],\n [-2, -2, 0, 6, -3],\n [-8, -9, -5, 32, -17],\n [10, 8, -10, -14, 5],\n [-8, -9, -5, 32, -17]]\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, -64, 52, 25, 37],\n [-55, 5, 15, -11, -27],\n [-82, 33, -18, -15, -24],\n [-48, 23, -20, -5, -14],\n [-6, -50, 46, 20, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-18, -24, -24, 6, -12],\n [-3, -4, -4, 1, -2],\n [6, 8, 8, -2, 4],\n [9, 12, 12, -3, 6],\n [-15, -20, -20, 5, -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[[0, 8, -16, -12, -12],\n [0, -6, 12, 9, 9],\n [0, 6, -12, -9, -9],\n [0, -12, 24, 18, 18],\n [0, 6, -12, -9, -9]]?\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, -4, 26, 36, 22],\n [5, -29, -23, -33, -34],\n [2, 16, -14, -21, -8],\n [5, -5, 10, -15, -25],\n [1, -1, 2, -3, -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[[-18, 9, 3, -18, 9],\n [30, -15, -5, 30, -15],\n [0, 0, 0, 0, 0],\n [-36, 18, 6, -36, 18],\n [-36, 18, 6, -36, 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 5x5 matrix:\n[[22, 16, 0, 3, 25],\n [16, 15, 0, -18, -2],\n [26, 20, 0, -3, 23],\n [16, 15, 0, -18, -2],\n [-18, -13, 0, -3, -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[[-21, -21, -2, -17, 2],\n [6, -40, 18, 62, -74],\n [-20, -57, 22, -16, -25],\n [35, 4, -8, 63, -41],\n [18, 38, -22, -20, 44]]?\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, -10, -24, 4, 24],\n [-25, 6, 1, -28, -26],\n [-39, 12, 1, -40, -26],\n [0, -11, -27, 14, 42],\n [-1, 13, 12, 2, 18]]\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[[-16, -12, 17, 0, -26],\n [12, 6, -9, 6, 18],\n [-32, -28, 39, 8, -54],\n [-2, 1, -1, -5, -2],\n [-10, -11, 15, 7, -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 5x5 matrix:\n[[-8, -20, 16, -4, 0],\n [-10, -25, 20, -5, 0],\n [8, 20, -16, 4, 0],\n [-2, -5, 4, -1, 0],\n [4, 10, -8, 2, 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[[18, -6, 15, -9, -6],\n [24, -8, 20, -12, -8],\n [30, -10, 25, -15, -10],\n [-36, 12, -30, 18, 12],\n [18, -6, 15, -9, -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 5x5 matrix:\n[[43, 60, 15, 31, -5],\n [-39, 9, -9, -30, -21],\n [-22, -31, -12, -17, 4],\n [9, 15, 13, 9, -5],\n [-53, -47, -9, -37, -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[[-5, 0, 9, -1, -8],\n [4, 1, -3, -2, 2],\n [4, 27, 11, -9, -27],\n [-1, 36, 17, -7, -38],\n [-14, 11, 17, 4, -22]]\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 5x5 matrix:\n[[-5, -20, -45, 8, -17],\n [34, -7, 17, 42, 48],\n [33, -23, 44, -18, 19],\n [3, -7, 60, -97, -17],\n [-17, 12, -1, 2, -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[[-31, 15, 10, 17, -28],\n [-14, 54, 10, 12, 26],\n [5, 30, 15, 7, 21],\n [-27, 36, 40, 32, -28],\n [1, -24, -15, -9, -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[[-54, -9, -16, -6, -43],\n [-36, 7, -29, 2, -43],\n [60, 12, 14, 24, 36],\n [3, -4, 11, -29, 16],\n [30, 11, 16, -50, 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[[0, 10, 0, -20, -26],\n [13, -11, -5, -19, -32],\n [-21, -3, -9, 21, 26],\n [-27, 9, -6, 18, 26],\n [2, -4, -7, -17, -28]]\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, 14, 7, -31, -55],\n [8, -2, 9, 0, -12],\n [10, -22, 64, 34, -20],\n [17, 6, -3, -25, 8],\n [-13, 16, -31, 3, -30]]\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, 12, 2, 18, -24],\n [-8, -8, 4, 4, -4],\n [-2, -20, 10, 28, -19],\n [38, 2, -7, 8, 10],\n [-20, 28, -10, -44, 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[[-11, -25, 6, 2, -29],\n [15, 56, -18, 13, 78],\n [24, -18, 0, 6, -30],\n [45, 16, -8, 1, 6],\n [-15, 36, -3, -12, 48]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[18, 6, -24, -6, 3],\n [-32, -16, -28, -7, -23],\n [-14, 5, -14, 5, -16],\n [28, 35, -25, -8, 28],\n [-38, 3, -30, -4, -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[[40, 19, -31, -13, -27],\n [-24, 22, 21, -6, 3],\n [62, 18, -49, -20, -26],\n [-44, -6, 35, 2, 39],\n [22, -6, -18, 8, -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[[9, 43, -24, 8, -14],\n [-9, 21, -14, 18, -23],\n [17, 43, -21, -15, -10],\n [-5, 29, -24, 36, -5],\n [31, 54, -27, 5, 8]]\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, 29, 2, -10, -52],\n [-36, 51, 38, -2, -20],\n [2, -10, -24, -5, -20],\n [30, -36, -22, 8, 46],\n [-2, -5, -14, -7, -32]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, 23, 24, 22, -30],\n [-28, -23, -18, 7, -13],\n [2, -22, -21, -23, 25],\n [-27, -44, -36, -17, 7],\n [9, -10, -15, -12, 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[[-7, -11, 43, 30, -37],\n [46, -22, 2, 0, -26],\n [21, 6, -26, -31, 24],\n [5, 6, -63, -59, 64],\n [10, 19, -45, -13, 27]]?\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[[-32, 17, -31, 19, -5],\n [-28, 16, -26, 17, -7],\n [-16, 19, -5, 13, -27],\n [32, -26, 22, -22, 26],\n [36, -21, 33, -22, 10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[45, 96, 30, 0, -30],\n [19, 33, -10, -36, 20],\n [-38, -4, -27, 18, 4],\n [-30, 30, -7, 42, -24],\n [-31, -42, -18, 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 5x5 matrix:\n[[-2, -8, 10, -6, -6],\n [27, -6, -15, -15, 3],\n [11, 6, -15, 1, 7],\n [25, 5, -25, -5, 10],\n [13, 14, -25, 7, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 2, 4, 8, -4],\n [0, 0, 0, 0, 0],\n [0, -1, -2, -4, 2],\n [0, -6, -12, -24, 12],\n [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[[12, 48, 54, -24, -24],\n [28, 0, 6, -8, -8],\n [4, 16, 18, -8, -8],\n [-28, 0, -6, 8, 8],\n [-22, -4, -9, 8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[35, -9, -2, -9, 19],\n [-73, 7, 28, 13, -29],\n [-13, 31, 37, 32, 5],\n [-32, -5, -4, 5, -17],\n [36, 8, 0, 12, 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[[2, 7, 24, -13, -16],\n [32, -38, 24, 2, -16],\n [24, -6, 72, -30, -48],\n [25, -25, 30, -5, -20],\n [-22, 28, -12, -4, 8]]\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[[-30, 36, 12, -6, -6],\n [10, -12, -4, 2, 2],\n [15, -18, -6, 3, 3],\n [20, -24, -8, 4, 4],\n [-20, 24, 8, -4, -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[[-4, -20, 27, 38, 27],\n [-17, 4, 19, 4, 7],\n [16, -20, -3, 26, 11],\n [12, -12, 10, 8, 17],\n [3, 16, -7, -36, -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[[-39, -8, 7, 16, 60],\n [0, -7, 18, 16, 6],\n [-24, -4, 4, 24, 32],\n [-8, 33, 36, 10, -6],\n [32, -44, -8, -24, -8]]\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, 10, -16, -1, 26],\n [31, 6, 6, 1, 0],\n [15, 29, 4, -39, 25],\n [30, -21, 12, 30, -33],\n [11, -10, -10, 37, 0]]\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[[16, -10, -24, 18, -12],\n [-18, 15, 28, -15, 14],\n [-4, -5, 4, -15, 2],\n [-7, -5, 8, -21, 4],\n [9, -15, -16, -3, -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[[12, -6, -15, 3, 15],\n [0, 0, 0, 0, 0],\n [16, -8, -20, 4, 20],\n [-8, 4, 10, -2, -10],\n [-4, 2, 5, -1, -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 5x5 matrix:\n[[-16, -60, -48, 44, 37],\n [-8, 42, 42, -28, -3],\n [-22, 49, 51, -32, 23],\n [-16, 3, 21, 4, -18],\n [-22, -4, 12, 8, 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[[11, -13, -2, -3, -7],\n [4, 10, -13, 21, -32],\n [-4, 8, -2, 6, -4],\n [-2, -14, 14, -24, 34],\n [-12, 6, 9, -9, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 15, -3, -9, -18],\n [20, 25, -5, -15, -30],\n [4, 5, -1, -3, -6],\n [4, 5, -1, -3, -6],\n [24, 30, -6, -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[[22, -28, 32, 0, 14],\n [17, -28, 19, -7, 14],\n [17, -28, 19, -7, 14],\n [22, -28, 32, 0, 14],\n [5, 10, 22, 18, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-36, 18, 6, -36, 36],\n [24, -12, -4, 24, -24],\n [-30, 15, 5, -30, 30],\n [0, 0, 0, 0, 0],\n [-18, 9, 3, -18, 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[[-8, 16, -24, 12, -20],\n [-4, 8, -12, 6, -10],\n [10, -20, 30, -15, 25],\n [-2, 4, -6, 3, -5],\n [-6, 12, -18, 9, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[24, 22, 7, -32, 2],\n [8, 8, 2, -10, 2],\n [-25, 2, 16, 28, 1],\n [25, 32, 19, -38, -1],\n [-22, -22, -12, 33, 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[[36, 0, -6, 30, 30],\n [-6, 0, 1, -5, -5],\n [0, 0, 0, 0, 0],\n [-24, 0, 4, -20, -20],\n [-30, 0, 5, -25, -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[[-6, -9, 9, 15, -6],\n [-12, -18, 18, 30, -12],\n [-2, -3, 3, 5, -2],\n [-12, -18, 18, 30, -12],\n [8, 12, -12, -20, 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[[-16, 16, 52, -7, 25],\n [-11, -19, -46, 22, -19],\n [18, -3, -10, -7, -7],\n [-44, 16, 24, 14, 18],\n [12, -11, -50, 7, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-50, 34, 1, -34, 31],\n [-30, 76, -45, -24, 53],\n [-9, -16, 32, 12, -9],\n [23, 8, 2, -20, 5],\n [-27, -30, 42, -6, -14]]?\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 5x5 matrix:\n[[-48, -4, 10, 18, -6],\n [27, 9, 8, 0, -9],\n [8, -39, 5, 8, 4],\n [-37, -6, -1, 2, 9],\n [-12, 8, -24, 18, -24]]\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, 37, -1, 30, 15],\n [6, 27, -5, 24, 7],\n [36, 33, 18, -12, 39],\n [36, 7, 2, -68, 25],\n [0, 14, -25, -2, -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 5x5 matrix:\n[[-20, 10, -5, 5, -15],\n [-16, 8, -4, 4, -12],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [-16, 8, -4, 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 5x5 matrix:\n[[5, 2, -2, -4, -3],\n [5, 2, -2, -4, -3],\n [15, 6, -6, -12, -9],\n [-25, -10, 10, 20, 15],\n [20, 8, -8, -16, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[26, 1, 30, -21, 18],\n [-24, -19, -11, 35, -9],\n [-36, 9, -39, 15, -21],\n [14, 19, 27, -39, 21],\n [38, 18, 12, -38, 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[[3, 6, -18, -12, -6],\n [3, 6, -18, -12, -6],\n [1, 2, -6, -4, -2],\n [3, 6, -18, -12, -6],\n [-5, -10, 30, 20, 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[[-2, -12, -8, 10, -2],\n [5, 30, 20, -25, 5],\n [1, 6, 4, -5, 1],\n [4, 24, 16, -20, 4],\n [4, 24, 16, -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[[22, 16, 12, 2, -14],\n [26, 2, 6, 10, -10],\n [42, 8, 12, 14, -18],\n [-22, 15, 3, -16, 2],\n [2, 24, 12, -10, -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[[23, 72, 38, -10, 24],\n [12, -7, -16, -9, -23],\n [-50, -48, -10, 6, 19],\n [-29, -33, -18, -25, 2],\n [-22, 19, 24, 21, 31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-21, -2, -28, 32, 0],\n [-14, -33, 19, -22, 18],\n [-51, -45, -38, -39, 64],\n [-27, 4, -33, 5, -5],\n [48, 24, 48, 18, -39]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[14, -10, 6, -17, 2],\n [14, -10, 6, -17, 2],\n [-7, 8, -16, 8, 4],\n [-29, 16, 8, 36, -12],\n [-25, 20, -20, 30, 0]]\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[[-44, 36, -22, -22, -8],\n [9, -6, 9, 0, -2],\n [11, -24, -16, 27, 30],\n [-23, 12, -27, 4, 11],\n [53, -42, 17, 36, 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 5x5 matrix:\n[[-4, -60, -40, 28, 4],\n [-4, -48, -36, 16, 4],\n [-7, -33, -12, 39, -9],\n [42, -18, 0, -18, 54],\n [-3, -9, -18, -15, 3]]\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, 20, 15, -11, -49],\n [36, -32, -14, 43, 57],\n [35, -9, 22, -1, -1],\n [27, 27, 6, -7, -35],\n [61, -5, 21, 5, 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[[0, -30, 25, 30, -30],\n [0, 6, -5, -6, 6],\n [0, -36, 30, 36, -36],\n [0, 30, -25, -30, 30],\n [0, 12, -10, -12, 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[[-12, -21, 30, 22, -24],\n [17, 34, -25, 20, 22],\n [-4, -45, 32, -23, -40],\n [5, 1, -1, -56, -2],\n [-27, -32, 29, 58, -18]]\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, -18, 31, 18, 24],\n [14, 7, 20, -2, -4],\n [7, 1, 22, -14, 14],\n [-38, -23, 28, 34, 20],\n [24, 15, 12, 6, -24]]\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[[-8, 25, 3, 1, 11],\n [-12, -16, -52, 7, 12],\n [-24, -10, -55, 8, -2],\n [-34, 10, -21, -7, 28],\n [34, -36, -16, 10, -14]]\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 5x5 matrix:\n[[12, -8, 20, -8, -24],\n [-3, 2, -5, 2, 6],\n [-15, 10, -25, 10, 30],\n [-9, 6, -15, 6, 18],\n [12, -8, 20, -8, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, -4, -23, 20, 38],\n [19, -9, 15, 1, -4],\n [16, -33, -1, -36, -24],\n [21, -36, -5, -5, 14],\n [-7, -20, -26, -1, 24]]\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, 6, -37, -30, -55],\n [-2, 0, -7, -4, -15],\n [-33, 46, -29, -27, 20],\n [-50, 20, -43, -50, -23],\n [18, -2, 35, 25, 61]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[37, -16, 9, 25, 10],\n [4, 20, -46, 18, 6],\n [51, -8, -13, 40, 10],\n [0, -24, 28, 4, 28],\n [15, 10, -30, 20, 5]]\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[[-5, 10, 5, -3, 3],\n [-6, 12, -1, -19, 12],\n [5, -10, -10, -8, 3],\n [4, -8, -21, -35, 18],\n [-6, 12, 4, -8, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[19, 12, -9, -8, 12],\n [26, -12, -18, -10, -12],\n [6, -12, -6, -2, -12],\n [4, 42, 6, -3, 42],\n [-2, 54, 12, -1, 54]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[14, 34, -30, 22, -10],\n [-6, -3, 9, 6, -6],\n [7, 17, -15, 11, -5],\n [11, 10, -18, -5, 7],\n [12, 6, -18, -12, 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[[12, -21, 26, -49, 22],\n [-3, -26, 1, -49, 37],\n [0, -6, -36, 8, -22],\n [0, -32, -24, -46, 18],\n [6, 19, 16, 28, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[34, 3, 15, -1, 8],\n [24, 33, -24, 39, -15],\n [22, 31, 14, -7, -16],\n [2, -32, 12, 4, 19],\n [0, 32, -37, 26, -17]]\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[[18, -18, -3, -15, -12],\n [-6, 21, -2, 8, 1],\n [12, 18, -8, -4, -14],\n [24, -4, -8, -16, -20],\n [30, 45, -20, -10, -35]]\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 5x5 matrix:\n[[3, -2, 11, -1, -17],\n [0, 8, -16, -4, 14],\n [0, -8, 16, 4, -14],\n [45, -18, -27, -35, 39],\n [-36, 17, 8, 26, -13]]\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, 1, 2, -4, 4],\n [1, 10, -18, 33, -12],\n [11, 13, 10, 2, 13],\n [31, -50, 18, -41, -28],\n [-9, 27, 18, -12, 39]]?\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, -4, 16, 18, 2],\n [5, 4, -5, -6, 2],\n [0, 0, 0, 0, 0],\n [30, 0, -33, -36, -12],\n [-15, -36, 12, 18, -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[[-1, -35, 0, 33, -19],\n [17, 15, 20, -21, 3],\n [16, -20, 20, 12, -16],\n [14, -61, 19, 51, -38],\n [13, 20, 15, -24, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-9, -24, -30, 24, -15],\n [-8, -22, -25, 21, -15],\n [3, 14, -5, -5, 20],\n [-9, -26, -25, 23, -20],\n [8, 22, 25, -21, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[20, -5, 25, -20, -5],\n [24, -6, 30, -24, -6],\n [24, -6, 30, -24, -6],\n [16, -4, 20, -16, -4],\n [-20, 5, -25, 20, 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[[8, 28, 0, -24, 4],\n [12, 42, 0, -36, 6],\n [21, 1, 0, -13, -7],\n [2, 36, 0, -26, 8],\n [19, 23, 0, -27, -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[[54, 25, 128, 23, -76],\n [45, -8, 74, -1, -34],\n [-56, -24, -36, 60, -16],\n [-36, -41, -26, 7, -26],\n [4, -14, -34, -76, 16]]\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[[5, -3, -3, 0, 2],\n [-30, 18, 18, 0, -12],\n [-10, 6, 6, 0, -4],\n [0, 0, 0, 0, 0],\n [-20, 12, 12, 0, -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 5x5 matrix:\n[[-15, 3, 8, 10, 16],\n [-10, -22, 28, 0, -4],\n [0, -18, 17, -5, -11],\n [-11, -35, 41, -3, -11],\n [6, 42, -44, 8, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[25, 28, -23, -23, -13],\n [-10, 32, -34, -34, 34],\n [-5, 28, -29, -29, 25],\n [-5, -8, 7, 7, 1],\n [5, 32, -31, -31, 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[[-10, -4, -6, 6, -2],\n [-6, 24, 24, -24, -30],\n [1, -4, -4, 4, 5],\n [-4, -28, -30, 30, 28],\n [22, 0, 4, -4, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[39, 32, 19, -42, 5],\n [23, 34, -9, -53, -13],\n [-2, -21, 23, 11, -25],\n [4, 12, -10, -25, -16],\n [-12, 24, -48, -6, 36]]\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[[22, -12, 21, -11, -12],\n [6, 55, -24, 51, 27],\n [0, 45, -29, 56, 15],\n [-10, 7, -5, -6, 16],\n [25, 19, 17, -3, 47]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, -6, 10, -25, -6],\n [-36, -6, 29, 4, 50],\n [50, 18, -22, 54, -5],\n [16, -15, 33, -14, 43],\n [-60, -15, 35, -43, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-9, 23, 42, 12, -28],\n [-13, -17, 21, 25, 10],\n [29, -26, 20, -21, -6],\n [-34, 21, 26, 25, -14],\n [53, 12, 33, -40, -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[[26, 0, 6, 27, -18],\n [6, 4, -16, -4, 5],\n [68, 8, -10, 2, -16],\n [-25, -25, 2, 32, 5],\n [-5, 25, 3, 20, -18]]\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, 9, -10, 9, 15],\n [21, -38, 32, -38, -48],\n [-39, 14, -8, 14, 12],\n [36, -7, 2, -7, -3],\n [-18, 9, -6, 9, 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[[-23, 24, 12, 9, 14],\n [45, -50, -20, -25, -25],\n [6, -2, -8, 8, -7],\n [-12, 4, 16, -16, 14],\n [12, -4, -16, 16, -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 5x5 matrix:\n[[30, -30, 10, 20, -10],\n [15, -18, 3, 8, -10],\n [-27, 12, -19, -28, -16],\n [9, -6, 5, 8, 2],\n [-24, 36, 0, -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[[-28, -33, -3, -4, -18],\n [-7, -2, 54, -7, 24],\n [28, 19, -6, 23, -6],\n [50, 40, 7, 48, 15],\n [-31, -36, -10, -9, -24]]?\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[[18, 3, -15, 24, 12],\n [30, -25, 25, 30, -20],\n [0, -6, 10, -2, -8],\n [30, -22, 20, 31, -16],\n [-18, 6, 0, -21, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[21, -8, -43, 2, 63],\n [27, 6, 43, -22, -17],\n [15, -16, 31, -42, -11],\n [9, 3, 48, -22, -38],\n [30, 28, 3, 26, 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[[36, -6, 6, 12, -30],\n [18, 7, 13, 8, 7],\n [12, -12, -8, 2, -32],\n [-60, -20, -40, -26, -16],\n [-36, -4, -16, -14, 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[[-24, -6, 24, 30, 36],\n [20, 5, -20, -25, -30],\n [20, 5, -20, -25, -30],\n [24, 6, -24, -30, -36],\n [4, 1, -4, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, -6, -9, -3, 6],\n [0, 0, 0, 0, 0],\n [-24, -12, -18, -6, 12],\n [16, 8, 12, 4, -8],\n [16, 8, 12, 4, -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[[-5, 30, -10, 5, 20],\n [-2, 12, -4, 2, 8],\n [6, -36, 12, -6, -24],\n [6, -36, 12, -6, -24],\n [-3, 18, -6, 3, 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[[-10, -31, 7, 12, -8],\n [20, 26, -32, 18, 28],\n [8, -10, -23, 31, 18],\n [6, -9, -18, 25, 14],\n [-8, 16, 26, -38, -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[[3, 14, 30, 19, -9],\n [29, -28, -24, -25, -8],\n [23, 5, 36, 32, -39],\n [2, -23, -14, 16, -50],\n [-48, 40, 44, 70, -30]]?\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, 29, -4, 19, -39],\n [64, -29, -22, -10, 56],\n [-1, 5, 32, 10, 8],\n [-62, 29, 48, 10, -42],\n [23, 44, 27, 46, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-23, 23, -36, -6, -26],\n [-23, 0, -15, -14, -7],\n [-29, -1, -18, -18, -8],\n [9, -10, 15, 2, 11],\n [-15, 9, -18, -6, -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[[13, 7, 18, -31, 8],\n [26, -12, 10, -32, 6],\n [-8, 9, 1, 7, 13],\n [-20, 6, 2, 23, -24],\n [8, -5, 3, -10, -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 5x5 matrix:\n[[-49, 37, 18, -36, -4],\n [34, -21, -72, 60, -37],\n [-39, 20, 74, -64, 43],\n [-20, 30, -8, -5, -30],\n [40, -40, -8, 25, 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[[-46, 24, -27, -11, 37],\n [41, -24, 35, 2, -47],\n [-27, 16, -35, 22, 23],\n [-4, 22, -33, -36, 3],\n [-1, 23, -41, -29, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 6, 6, -10, 12],\n [-6, -9, -9, 15, -18],\n [8, 12, 12, -20, 24],\n [-12, -18, -18, 30, -36],\n [-2, -3, -3, 5, -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 5x5 matrix:\n[[-4, 21, 1, -27, 6],\n [5, -18, 7, 20, -2],\n [13, -9, -34, -13, 28],\n [-2, 8, 13, -9, 0],\n [13, -29, -24, 21, 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 5x5 matrix:\n[[30, -25, -27, 14, 34],\n [57, -30, -39, 20, 4],\n [33, 2, -15, 44, -20],\n [-5, 13, 10, -1, -31],\n [-29, -7, 10, -40, 32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 4, 12, -7, 0],\n [4, -16, 36, 14, 0],\n [-20, -16, -36, 26, 0],\n [-6, -8, -6, 11, 0],\n [-16, -16, -24, 24, 0]]?\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[[6, -2, 8, 10, -4],\n [6, -2, 8, 10, -4],\n [-9, 3, -12, -15, 6],\n [0, 0, 0, 0, 0],\n [-15, 5, -20, -25, 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, 4, 0, 24, 16],\n [8, -2, 0, -12, -8],\n [4, -1, 0, -6, -4],\n [4, -1, 0, -6, -4],\n [12, -3, 0, -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 5x5 matrix:\n[[-2, -6, 4, 6, 10],\n [22, 6, 11, -16, 20],\n [9, 15, -7, -17, -19],\n [30, 18, 6, -30, 6],\n [-17, 9, -21, 1, -45]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[20, -20, 0, -24, -4],\n [-10, 10, 0, 12, 2],\n [25, -25, 0, -30, -5],\n [25, -25, 0, -30, -5],\n [-5, 5, 0, 6, 1]]?\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 5x5 matrix:\n[[1, -3, 0, -3, 1],\n [16, -8, 0, 27, 26],\n [17, -3, 0, 39, 29],\n [-5, -9, 0, -30, -11],\n [6, 14, 0, 42, 14]]\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[[-30, -52, -2, 27, 29],\n [-8, -66, 8, 23, 19],\n [-32, -7, 1, 32, 21],\n [-20, 25, -9, -30, 11],\n [-27, -22, 28, 67, 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[[-3, 9, 3, 18, -18],\n [-1, 3, 1, 6, -6],\n [2, -6, -2, -12, 12],\n [-2, 6, 2, 12, -12],\n [6, -18, -6, -36, 36]]?\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 5x5 matrix:\n[[-18, -3, 3, 18, -3],\n [15, 3, -4, -8, 7],\n [-18, -2, 0, 32, 6],\n [-18, -1, -3, 46, 15],\n [12, 3, -5, 2, 11]]\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[[4, -6, 5, -6, 4],\n [12, -18, 15, -18, 12],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [8, -12, 10, -12, 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[[6, -36, -42, 30, -36],\n [-8, 40, 32, -16, 39],\n [12, 11, 46, -56, 10],\n [-22, -9, 20, -10, 1],\n [-18, -16, -42, 54, -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 5x5 matrix:\n[[20, 21, -24, -19, -12],\n [-30, -29, 26, 21, 18],\n [-5, -6, 9, 7, 3],\n [-10, -10, 10, 8, 6],\n [15, 15, -15, -12, -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[[-43, 0, -2, -15, -40],\n [-5, 0, 2, 0, -5],\n [-24, 0, 16, 5, -25],\n [25, 0, -10, 0, 25],\n [15, 0, 26, 25, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[30, -12, -12, 12, 0],\n [20, -8, -8, 8, 0],\n [-10, 4, 4, -4, 0],\n [-25, 10, 10, -10, 0],\n [-25, 10, 10, -10, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -8, 0, -18, -31],\n [-1, 2, 31, 36, 32],\n [10, 30, 76, 54, -12],\n [4, 0, -14, 39, -18],\n [1, -40, -5, 10, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, 2, 4, -4, -12],\n [-6, -2, -4, 4, 12],\n [-18, -6, -12, 12, 36],\n [-12, -4, -8, 8, 24],\n [-15, -5, -10, 10, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, 49, -1, -48, -20],\n [34, 6, 49, 11, -33],\n [5, -25, 32, 23, -8],\n [-2, 24, 0, -28, 2],\n [2, 5, -20, -1, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 33, 18, -15, 15],\n [0, -11, -6, 5, -5],\n [0, 0, 0, 0, 0],\n [0, -66, -36, 30, -30],\n [-36, 3, -18, 15, 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[[-20, -47, 7, -30, -2],\n [23, 41, -13, 12, 5],\n [33, 21, -16, -49, -1],\n [20, 27, -14, -69, -12],\n [4, -34, 5, 55, 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[[-42, 39, -3, -48, 33],\n [18, -14, -3, 15, -10],\n [-10, 1, 19, -4, 7],\n [-6, -2, 21, -5, 10],\n [15, 0, -33, 6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 14, -29, -1, 64],\n [-29, 25, 0, -15, 10],\n [-31, 25, 17, -20, -26],\n [-67, 47, 26, -23, -2],\n [-43, 35, -6, -15, 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[[-10, 12, 18, 34, 52],\n [3, -34, -7, -39, -58],\n [18, 30, 12, -6, 9],\n [-4, 18, -6, 24, 29],\n [2, -4, 38, -2, 18]]?\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, -60, -20, 10, -5],\n [-5, -6, -8, -14, 13],\n [11, 18, 16, 22, -21],\n [-15, -42, -16, 2, 1],\n [18, 48, 20, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[6, 3, -15, 9, 12],\n [12, 6, -30, 18, 24],\n [8, 4, -20, 12, 16],\n [6, 3, -15, 9, 12],\n [-8, -4, 20, -12, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[45, 35, 55, 28, 61],\n [-15, 18, -15, 13, -10],\n [-20, -38, -56, -38, -66],\n [-45, -42, -75, -39, -84],\n [10, 12, -49, -9, -51]]\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, 11, 35, 35, -26],\n [27, 29, 17, 8, 8],\n [-5, -3, 19, 16, 4],\n [2, -18, 3, 12, -26],\n [-29, 13, -38, -47, 48]]\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[[2, -2, 4, 0, -12],\n [-1, 1, -2, 0, 6],\n [-5, 5, -10, 0, 30],\n [-1, 1, -2, 0, 6],\n [-5, 5, -10, 0, 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 5x5 matrix:\n[[-3, -9, -3, -6, 6],\n [20, 49, 19, 30, -30],\n [-2, 5, -1, 6, -6],\n [-34, -14, -26, 12, -12],\n [21, -3, 15, -18, 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 5x5 matrix:\n[[11, -12, 12, 4, 6],\n [20, 32, 7, -13, 21],\n [28, 43, 7, 26, 20],\n [10, -16, 8, 8, -12],\n [7, -1, 10, -27, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[15, 29, -23, -27, 44],\n [-11, -10, -43, 36, -11],\n [26, 19, 40, -63, 23],\n [2, 8, 45, -21, 9],\n [10, 0, -5, -15, -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[[-25, -26, 35, -34, 8],\n [26, 22, -34, 32, -4],\n [15, 3, -15, 12, 6],\n [22, -4, -18, 12, 16],\n [-3, -9, 7, -8, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[11, 2, -33, -11, -20],\n [10, 30, -55, 40, 23],\n [2, 2, 37, 18, 35],\n [-46, -12, 28, -4, -14],\n [45, 10, -15, 5, 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[[30, -14, -19, -7, 18],\n [-8, 47, 23, 38, -14],\n [14, 11, 30, 6, 32],\n [-16, -46, -11, -48, -1],\n [-4, 14, 30, 14, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 16, 12, -16, 12],\n [3, -4, -3, 4, -3],\n [-3, 4, 3, -4, 3],\n [9, -12, -9, 12, -9],\n [6, -8, -6, 8, -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[[45, 1, -6, -7, -24],\n [-24, 26, -26, 12, -30],\n [45, 1, -6, -7, -24],\n [-18, -2, 4, 4, 12],\n [10, 23, -29, 33, -45]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-39, 29, 22, -36, -3],\n [32, 24, -23, -16, 59],\n [25, 0, 36, -37, -22],\n [-52, -4, -11, 1, -17],\n [7, 16, -49, 15, 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[[-12, -9, -6, -27, -3],\n [-8, -6, -4, -18, -2],\n [-16, -15, -11, -42, -1],\n [8, -6, -8, -6, 14],\n [-24, -3, 3, -24, -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[[41, -21, -6, 29, 11],\n [11, -20, 5, 8, -31],\n [21, -53, -43, -33, -54],\n [-43, 31, -14, 4, 25],\n [6, 16, 14, 16, 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[[20, 48, -32, 64, 20],\n [5, 58, -51, 64, 16],\n [4, -41, 50, -39, -30],\n [-8, -25, 9, -37, -33],\n [-8, 39, -23, 40, -9]]\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[[3, 0, -6, 15, 3],\n [-3, 0, 6, -15, -3],\n [-5, 0, 10, -25, -5],\n [2, 0, -4, 10, 2],\n [-5, 0, 10, -25, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -24, 16, 12, -12],\n [4, -24, 16, 12, -12],\n [5, -30, 20, 15, -15],\n [-3, 18, -12, -9, 9],\n [-1, 6, -4, -3, 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[[6, 1, -38, 6, -14],\n [10, 28, 0, -26, 10],\n [29, 27, -29, -31, 3],\n [16, 1, -2, -12, 4],\n [-22, -28, 51, 20, 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[[-8, 12, 12, 2, -10],\n [8, -12, -12, -2, 10],\n [-12, 18, -36, 12, 21],\n [8, -12, 24, -8, -14],\n [-20, 30, -60, 20, 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[[-5, -30, -5, 20, -20],\n [-2, -12, -2, 8, -8],\n [3, 18, 3, -12, 12],\n [3, 18, 3, -12, 12],\n [3, 18, 3, -12, 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[[36, 23, -27, -12, -2],\n [45, 16, -38, 2, 4],\n [-17, -11, 29, 14, -16],\n [-6, -4, 24, 12, -20],\n [-16, -13, -3, 2, 17]]\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[[41, -12, -43, -43, -28],\n [-6, -8, 45, 20, 27],\n [39, -32, 13, 25, 8],\n [-5, 2, -40, -11, -15],\n [9, 2, -3, -63, -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 5x5 matrix:\n[[-6, 0, 45, -9, -3],\n [-2, -32, -6, -38, -4],\n [2, -20, -19, -1, 45],\n [26, -42, -56, 54, 30],\n [3, 24, -29, 21, -4]]\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, -44, -13, 9, 1],\n [-28, -42, -55, -17, -13],\n [12, -23, -7, 39, 1],\n [-18, 27, 24, -21, -12],\n [2, 27, 22, -33, -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[[0, 0, 0, 0, 0],\n [-6, 0, 12, 0, 6],\n [6, 0, -12, 0, -6],\n [-15, 0, 30, 0, 15],\n [-18, 0, 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[[-12, 2, 4, -4, -26],\n [-26, -14, 16, 17, -5],\n [26, 19, -18, -24, -9],\n [-18, -7, 10, 8, -11],\n [-16, -14, 12, 18, 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[[4, 36, 16, 45, 21],\n [-28, -28, 9, 46, -47],\n [-4, 30, 17, 43, 12],\n [-42, -36, -14, 29, -61],\n [-4, 0, -5, 23, -8]]\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 5x5 matrix:\n[[28, -28, 1, -24, 16],\n [18, -33, -21, 6, 0],\n [-21, -7, -10, -21, 25],\n [27, -13, -7, 6, -12],\n [-33, -24, -52, 28, 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[[33, -28, -6, 23, 12],\n [-1, -22, 12, -7, 2],\n [-7, -9, 9, -9, -1],\n [-3, 21, -9, 3, -3],\n [21, -2, -12, 19, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-10, 4, -2, -6, -4],\n [-25, 10, -5, -15, -10],\n [-15, 6, -3, -9, -6],\n [-20, 8, -4, -12, -8],\n [10, -4, 2, 6, 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[[10, -20, -5, 5, -15],\n [-12, 24, 6, -6, 18],\n [-12, 24, 6, -6, 18],\n [-12, 24, 6, -6, 18],\n [2, -4, -1, 1, -3]]\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[[10, -4, -10, 2, 12],\n [30, -12, -30, 6, 36],\n [-41, -34, -31, 11, -18],\n [12, -30, -48, 12, 30],\n [-5, -40, -55, 15, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-2, 8, -4, 8, -6],\n [-3, 12, -6, 12, -9],\n [5, -20, 10, -20, 15],\n [-1, 4, -2, 4, -3],\n [-2, 8, -4, 8, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, 24, -12, -20, 8],\n [-6, -18, 9, 15, -6],\n [0, 0, 0, 0, 0],\n [-4, -12, 6, 10, -4],\n [-2, -6, 3, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[15, -5, -25, -20, -20],\n [3, -1, -5, -4, -4],\n [-18, 6, 30, 24, 24],\n [6, -2, -10, -8, -8],\n [-15, 5, 25, 20, 20]]\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[[17, 6, 3, -17, -5],\n [-2, -11, -16, -15, 19],\n [4, -16, -4, -4, 22],\n [35, -1, 23, -8, 0],\n [33, 1, 37, 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[[-1, -3, 5, 4, 3],\n [5, 15, -25, -20, -15],\n [1, 3, -5, -4, -3],\n [-1, -3, 5, 4, 3],\n [5, 15, -25, -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[[-29, -29, 22, 2, 5],\n [-30, -30, 24, 0, 6],\n [46, 46, -32, -8, -6],\n [21, 21, -18, 2, -5],\n [54, 54, -36, -12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[16, 20, 12, -24, -12],\n [4, 5, 3, -6, -3],\n [4, 5, 3, -6, -3],\n [-12, -15, -9, 18, 9],\n [4, 5, 3, -6, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-37, -20, 27, 19, -29],\n [20, 34, -54, -8, 0],\n [2, -20, 27, 19, 6],\n [-19, 8, -20, 20, -31],\n [-24, 6, 0, -30, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-5, 4, -14, 13, 1],\n [-1, -34, -8, -12, -12],\n [5, 40, 18, 9, 17],\n [-5, 6, -16, 17, 4],\n [5, 2, 0, 10, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 9, 17, -12, 24],\n [-38, 49, 68, 40, 2],\n [36, -51, -14, 2, 22],\n [-20, 38, 22, -4, 4],\n [4, 6, -19, -22, 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 5x5 matrix:\n[[-22, -45, -16, -1, -32],\n [11, 27, -1, 14, -2],\n [13, 24, 11, 11, 7],\n [-24, -55, -10, 3, -38],\n [1, 26, -37, 21, -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[[-20, -8, -4, 12, 24],\n [0, 0, 0, 0, 0],\n [-30, -12, -6, 18, 36],\n [-5, -2, -1, 3, 6],\n [-30, -12, -6, 18, 36]]\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 5x5 matrix:\n[[-7, -8, -8, 10, 18],\n [30, 25, 1, 10, 14],\n [-17, -13, -3, 6, -20],\n [1, 10, -20, 2, -34],\n [-24, -17, -15, 18, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-14, 6, -6, -11, 41],\n [-34, 22, 12, -25, 5],\n [34, -20, -7, 19, -52],\n [24, -14, -3, 18, -23],\n [0, 2, 9, 6, -7]]\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],\n [16, -16, 4, 8, -12],\n [8, -8, 2, 4, -6],\n [-4, 4, -1, -2, 3],\n [24, -24, 6, 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[[-3, 5, -1, 5, -4],\n [-18, 27, -10, 31, -20],\n [12, -26, -4, -18, 24],\n [-15, -8, -49, 36, 24],\n [3, 1, 9, -7, -4]]\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, -13, 9, 12, -2],\n [25, 15, -25, -35, -14],\n [-26, -12, 37, 39, 46],\n [18, -1, -17, -16, -30],\n [-40, 5, 20, 25, 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[[-65, -40, 9, -17, 17],\n [41, -16, 11, 17, 15],\n [46, 14, -2, -2, 8],\n [-10, 64, -45, -22, -26],\n [68, 26, -18, 36, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-36, 36, -12, -30, 36],\n [25, -35, 6, 20, -33],\n [22, -2, 12, 20, -6],\n [55, -5, 30, 50, -15],\n [25, 25, 20, 25, 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[[12, -18, 3, -18, -15],\n [8, -12, 2, -12, -10],\n [20, -30, 5, -30, -25],\n [8, -12, 2, -12, -10],\n [-16, 24, -4, 24, 20]]\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, -30, 39, -12, 18],\n [8, 15, -19, 9, -24],\n [-44, 2, 5, 28, 10],\n [-54, 2, 10, 48, -10],\n [-20, 8, -4, 28, -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[[-9, -43, -24, -34, 29],\n [-7, -28, -28, 27, 29],\n [1, 2, -26, -31, -15],\n [-2, -26, -53, -12, 10],\n [6, 23, 24, 18, -14]]?\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, -38, 12, -3, -35],\n [-9, 61, -16, -19, 33],\n [27, -31, 4, 61, 30],\n [9, 20, -36, 11, 59],\n [-11, -28, 24, -21, -58]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-11, 3, 10, -8, 12],\n [-32, -16, -14, 16, -20],\n [-47, -25, 4, 16, -8],\n [-42, -46, 6, 36, -20],\n [9, 7, -15, 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 5x5 matrix:\n[[-4, 12, -6, -2, 5],\n [-4, 14, -20, -18, 6],\n [-2, -44, 37, 29, -10],\n [-28, -12, 14, 18, -11],\n [10, -39, 32, 22, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[16, 2, 10, 14, -4],\n [-6, 15, -5, -3, 6],\n [-50, 32, -34, -39, 24],\n [24, -15, 15, 22, -14],\n [-4, -41, -9, 15, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, 1, 2, 1, -2],\n [15, -5, -10, -5, 10],\n [12, -4, -8, -4, 8],\n [-15, 5, 10, 5, -10],\n [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[[-30, -12, -6, -30, 24],\n [15, 6, 3, 15, -12],\n [-25, -10, -5, -25, 20],\n [-15, -6, -3, -15, 12],\n [-30, -12, -6, -30, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, 36, -6, 24, -12],\n [3, -18, 3, -12, 6],\n [3, -18, 3, -12, 6],\n [-5, 30, -5, 20, -10],\n [-4, 24, -4, 16, -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 5x5 matrix:\n[[-8, -1, -12, -9, 21],\n [4, 51, 64, 47, 7],\n [6, -5, -8, -1, 28],\n [10, -38, -38, -24, -5],\n [-26, 27, 20, 3, -28]]\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, 2, 0, -34, 0],\n [18, -6, -10, -28, 10],\n [7, 16, -26, -2, 26],\n [33, -21, 15, -48, -15],\n [0, 27, -25, 16, 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 5x5 matrix:\n[[0, 0, 0, 0, 0],\n [12, -3, 6, 18, 12],\n [4, -1, 2, 6, 4],\n [4, -1, 2, 6, 4],\n [16, -4, 8, 24, 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[[25, 15, 10, -30, 25],\n [25, 15, 10, -30, 25],\n [-25, -15, -10, 30, -25],\n [-20, -12, -8, 24, -20],\n [20, 12, 8, -24, 20]]\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[[10, -8, -32, 37, -12],\n [25, -30, -20, 20, 5],\n [-35, 46, 4, 1, -21],\n [12, -12, -24, 27, -6],\n [8, -12, 8, -11, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-18, -20, -17, 12, -20],\n [-19, -50, -11, -11, 28],\n [-29, -12, -5, 28, -12],\n [-72, -52, -32, 70, 48],\n [-13, -34, -27, 3, 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[[16, -21, -17, -5, 43],\n [16, -23, 21, -7, -7],\n [52, -42, 48, 38, -2],\n [-64, 58, -40, -34, -24],\n [-6, 14, -24, 12, 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[[18, 35, -17, 30, -29],\n [-3, 35, -13, 35, -6],\n [54, 23, -33, 22, -67],\n [-14, -38, 22, -38, 26],\n [-5, -4, 14, -13, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-18, -18, -18, 15, 18],\n [30, 30, 30, -25, -30],\n [-24, -24, -24, 20, 24],\n [12, 12, 12, -10, -12],\n [-18, -18, -18, 15, 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[[-22, 2, -24, 40, 2],\n [9, 5, 4, -12, -3],\n [-14, -6, -8, 20, 4],\n [18, -6, 24, -36, 0],\n [1, -3, 4, -4, 1]]\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[[-8, -6, 12, 8, 10],\n [-4, -3, 6, 4, 5],\n [-20, -15, 30, 20, 25],\n [-16, -12, 24, 16, 20],\n [8, 6, -12, -8, -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[[-59, -23, -19, 54, 28],\n [-15, -16, 2, -21, 35],\n [0, 0, -1, -18, 7],\n [-18, 17, -3, -9, 13],\n [-23, 26, -14, 33, -17]]\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, -9, 7, 12, 28],\n [-8, -13, 17, -11, -33],\n [28, -36, 40, 0, 22],\n [-40, 49, -57, 10, -17],\n [60, -46, 58, -26, 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[[-28, 3, 25, -25, 41],\n [0, 0, 0, 0, 0],\n [8, 2, -10, 10, -10],\n [6, 9, -15, 15, -3],\n [-18, 3, 15, -15, 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[[11, 14, -10, 13, 10],\n [-28, 8, -16, -8, 4],\n [-22, 12, -18, -3, 7],\n [-26, -4, -4, -14, -4],\n [-14, 4, -8, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, -36, 22, 26, -52],\n [72, 25, -1, -9, 1],\n [-34, 6, -33, 6, 21],\n [-27, -18, 7, 28, -41],\n [37, -45, -11, 49, -65]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-21, -3, 22, 37, -27],\n [42, -30, -32, -22, 38],\n [-21, 15, 16, 11, -19],\n [-15, 30, 5, -20, -5],\n [24, -30, -14, 6, 16]]?\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, 0, 16, 20, 6],\n [2, -74, -37, 42, -64],\n [16, 46, 22, -28, 50],\n [-4, 52, 14, -44, 32],\n [22, -44, -32, 12, -34]]\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, -30, 30, -36, 36],\n [-5, -25, 25, -30, 30],\n [-4, -20, 20, -24, 24],\n [5, 25, -25, 30, -30],\n [1, 5, -5, 6, -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 5x5 matrix:\n[[4, -12, 4, 8, 8],\n [3, -9, 3, 6, 6],\n [5, -15, 5, 10, 10],\n [-3, 9, -3, -6, -6],\n [6, -18, 6, 12, 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[[19, -22, 24, 12, 15],\n [-1, 2, -20, 20, -11],\n [18, -20, 44, 16, 32],\n [2, -4, -20, -16, -20],\n [-50, 62, 3, 6, 21]]\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, 6, 15, 6, 15],\n [10, -20, -22, 0, 10],\n [-20, 8, 20, 8, 20],\n [-5, 26, 23, -4, -25],\n [15, -2, -12, -7, -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[[-18, -18, 3, -15, -6],\n [-36, -36, 6, -30, -12],\n [-24, -24, 4, -20, -8],\n [30, 30, -5, 25, 10],\n [-36, -36, 6, -30, -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[[-26, -20, -4, -30, 44],\n [26, -8, 26, 28, -26],\n [61, -58, 14, 45, -18],\n [-53, 33, 7, -39, 25],\n [-44, 43, -15, -33, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[6, 0, 12, 12, -24],\n [1, 0, 2, 2, -4],\n [0, 0, 0, 0, 0],\n [6, 0, 12, 12, -24],\n [-3, 0, -6, -6, 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[[0, -8, -7, 11, -14],\n [16, 32, 33, -29, 18],\n [8, -20, -15, 35, -54],\n [14, -13, -7, 31, -56],\n [20, 18, 22, -6, -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[[-6, -36, -12, -30, 24],\n [-6, -36, -12, -30, 24],\n [3, 18, 6, 15, -12],\n [0, 0, 0, 0, 0],\n [4, 24, 8, 20, -16]]?\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, 53, 2, 30, -18],\n [8, -31, 2, -4, 12],\n [-44, 13, -32, 46, -30],\n [-36, -7, -37, -21, -23],\n [-4, 12, -15, 47, -19]]?\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 5x5 matrix:\n[[36, -18, 36, -30, 12],\n [-12, 6, -12, 10, -4],\n [-18, 9, -18, 15, -6],\n [24, -12, 24, -20, 8],\n [36, -18, 36, -30, 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 5x5 matrix:\n[[6, 30, 8, -22, -4],\n [6, 36, 9, -24, -6],\n [10, 24, 9, -28, 2],\n [-2, 30, 4, -6, -12],\n [-4, -30, -7, 18, 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[[-30, -42, -12, 30, 6],\n [10, 26, 14, -16, -6],\n [25, 41, 15, -28, -7],\n [20, -20, -32, 4, 12],\n [0, -12, -10, 6, 4]]\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[[30, 2, 27, -6, -28],\n [-12, 12, -6, 12, 8],\n [18, 14, 21, 6, -20],\n [-12, -4, -12, 0, 12],\n [0, -24, -9, -18, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[43, 10, -36, 19, -29],\n [30, -51, -21, -42, 48],\n [15, -12, -2, 6, -36],\n [9, -26, -9, -30, 48],\n [-25, 19, 25, 14, -22]]\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, -6, -12, 8, 12],\n [5, 15, 30, -20, -30],\n [-13, -29, -23, -18, 8],\n [-6, -14, -14, -4, 8],\n [-3, -1, 26, -44, -38]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-14, -33, -1, -11, 15],\n [12, -65, -31, -6, 19],\n [-46, 31, 14, -1, 4],\n [24, -5, -13, -6, 10],\n [-6, -17, 18, -21, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[0, 0, 0, 0, 0],\n [-6, 12, 10, 2, 12],\n [6, -12, -10, -2, -12],\n [-9, 18, 15, 3, 18],\n [-6, 12, 10, 2, 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[[-4, -6, -8, 10, 4],\n [14, -6, -25, 9, 10],\n [-33, -46, -21, 15, -49],\n [2, 6, -3, 11, 22],\n [0, 18, 16, 2, 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[[22, 31, 3, 2, -9],\n [20, 46, 22, -23, 45],\n [-22, -32, -6, 8, -6],\n [-26, -43, -9, 4, -6],\n [-4, 33, 29, 11, 23]]\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, -31, 10, -38, -27],\n [-11, -16, 13, -26, -9],\n [17, 33, -15, 44, 26],\n [16, 15, -24, 34, 1],\n [13, 0, -27, 22, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-23, 40, -12, -7, 12],\n [46, -38, -39, -7, -32],\n [17, 9, -8, -1, -29],\n [48, -12, -33, -18, -42],\n [10, 2, 40, -27, 10]]\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 5x5 matrix:\n[[-16, -26, 2, 18, 34],\n [-30, 19, 41, -23, 23],\n [15, 10, -2, 1, -23],\n [-14, -4, -4, -12, 18],\n [-27, -4, 12, -13, 33]]\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 5x5 matrix:\n[[-36, -6, -18, -6, -24],\n [18, 3, 9, 3, 12],\n [18, 3, 9, 3, 12],\n [-12, -2, -6, -2, -8],\n [-24, -4, -12, -4, -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[[-48, 28, 48, 2, -38],\n [-36, 18, 36, -15, -27],\n [21, -11, -21, 6, 16],\n [-15, 9, 15, 2, -12],\n [-6, 10, 6, 36, -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[[-6, -30, -12, 36, 24],\n [-3, -15, -6, 18, 12],\n [-2, -10, -4, 12, 8],\n [-3, -15, -6, 18, 12],\n [-1, -5, -2, 6, 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[[-15, 45, -15, 0, 25],\n [15, 5, 45, -20, -35],\n [-3, 34, 12, -10, 0],\n [9, -17, 15, -4, -17],\n [-15, 25, -27, 8, 29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 13, 22, -19, -23],\n [-8, -23, -34, 25, 33],\n [16, -9, 2, -17, -11],\n [-20, 5, -10, 25, 20],\n [16, 16, 32, -32, -36]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[4, 24, 24, 20, 4],\n [-1, -6, -6, -5, -1],\n [-6, -36, -36, -30, -6],\n [-5, -30, -30, -25, -5],\n [2, 12, 12, 10, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-42, 19, 15, -3, -19],\n [-46, 22, 10, 1, -22],\n [-8, 11, -37, 26, -11],\n [-18, 6, 18, -9, -6],\n [36, -22, 18, -18, 22]]\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 5x5 matrix:\n[[-7, -22, -43, 16, 4],\n [-12, 14, -14, -12, -5],\n [11, -46, -45, 11, -7],\n [8, 28, 25, 17, -27],\n [1, -52, -25, -3, 38]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -13, -26, -16, 25],\n [-34, 24, -20, 6, 14],\n [29, -35, -12, -23, 16],\n [-42, 48, 12, 30, -18],\n [-6, 5, -2, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[23, 7, -16, 20, -21],\n [14, 1, 35, -18, -11],\n [31, 14, -3, 16, -21],\n [-7, -29, 0, -10, -24],\n [26, -14, 32, -16, -42]]?\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, 62, 42, -15, -33],\n [6, -50, -42, 42, 6],\n [-2, 32, 28, -31, -1],\n [18, 12, 20, -47, 11],\n [-2, 0, 5, -17, 54]]\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 5x5 matrix:\n[[6, -10, -4, -12, -12],\n [9, -15, -6, -18, -18],\n [-3, 5, 2, 6, 6],\n [-6, 10, 4, 12, 12],\n [15, -25, -10, -30, -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 5x5 matrix:\n[[-1, 1, 3, 1, -2],\n [2, -2, -6, -2, 4],\n [0, 0, 0, 0, 0],\n [-2, 2, 6, 2, -4],\n [1, -1, -3, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-45, 1, -29, -26, -34],\n [-15, -12, -1, -4, 1],\n [10, -60, -14, 56, -22],\n [-20, -17, -6, 6, -19],\n [-15, 72, 1, -72, 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[[30, -20, -15, 0, -17],\n [-7, 32, 37, -9, 2],\n [-23, 39, 45, 11, 7],\n [-4, -10, -4, 44, -6],\n [29, -41, -43, -1, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-23, -12, -5, 22, 35],\n [9, 5, 40, -55, 7],\n [11, -11, 28, -62, 6],\n [-17, 22, -3, 51, 4],\n [11, -16, -21, -1, 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[[-9, -9, 0, 3, 0],\n [-1, -21, 8, -21, -8],\n [9, -36, 18, -51, -18],\n [-8, 42, -20, 56, 20],\n [-15, -15, 0, 5, 0]]?\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, -18, -34, -16, 34],\n [-1, -6, -10, -33, 19],\n [-20, -20, -29, -22, 47],\n [10, -18, 7, -14, 47],\n [45, 1, 32, -43, 31]]\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[[3, -6, -30, 6, 18],\n [19, 35, 36, -26, 16],\n [-74, -8, 7, -7, -16],\n [18, 6, 9, -19, -2],\n [5, 40, -2, -9, 59]]\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, 28, -12, 20, -4],\n [-2, -4, -6, -10, 0],\n [31, -40, 21, -25, 6],\n [-18, 15, -18, 0, -3],\n [11, 5, 21, 25, 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[[41, 29, 37, -45, 8],\n [-13, 0, -11, 11, 4],\n [25, -2, -13, -3, 4],\n [5, 27, 34, -28, 7],\n [1, 2, 35, -19, -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[[20, -10, 5, -10, -20],\n [-14, 13, -11, 11, 24],\n [-6, 21, -24, 15, 36],\n [-38, 1, 13, 7, 8],\n [52, 10, -32, -2, 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[[56, 37, -20, -43, -19],\n [-16, -6, 20, 12, 15],\n [-12, 6, -34, -5, -26],\n [-36, -6, 6, 27, -13],\n [-34, -13, -23, 6, -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[[-34, 1, 3, -26, 24],\n [-11, 4, 12, 21, -29],\n [-26, 4, 12, 6, -14],\n [-6, -1, -3, -14, 16],\n [30, -5, -15, -10, 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[[-45, 9, 34, -12, 24],\n [-38, 16, 23, -18, 26],\n [-16, 24, -40, 0, 36],\n [-12, -16, 44, 0, -14],\n [36, 18, 10, -48, -21]]?\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[[29, 39, 11, 2, -61],\n [21, 11, 39, -5, 15],\n [-40, -46, 13, 25, 30],\n [36, 58, 5, 0, -50],\n [-30, -44, 8, 13, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[27, 7, -10, 29, 10],\n [-35, 11, 23, -33, -37],\n [14, 12, -1, 13, -15],\n [59, -3, -31, 55, 33],\n [74, -8, -41, 69, 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[[0, -15, 9, -6, -18],\n [0, -25, 15, -10, -30],\n [0, -25, 15, -10, -30],\n [0, 0, 0, 0, 0],\n [0, -10, 6, -4, -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[[-24, -46, 64, 15, -21],\n [-46, 2, 25, -62, 73],\n [14, -27, 26, 54, -68],\n [-36, -7, 24, -37, 27],\n [-40, -40, 65, -11, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-5, 3, 38, 9, 22],\n [-5, 5, 33, 12, 18],\n [15, 7, -2, 13, 6],\n [10, -6, 19, -8, 21],\n [-35, -15, -5, -29, -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[[56, -36, 10, 28, 6],\n [43, -27, -1, 26, 21],\n [-38, 24, -1, -22, -15],\n [4, -2, -7, 6, 15],\n [-30, 20, -15, -10, 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[[-35, 53, -35, -20, 48],\n [-9, 31, 0, 20, 30],\n [6, -4, 5, 6, -4],\n [6, 2, 0, 4, 0],\n [-34, 31, -40, -43, 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[[-22, 32, 21, 12, -19],\n [10, -10, 24, 11, -12],\n [14, -10, 23, 11, -9],\n [2, 26, 53, 29, -27],\n [-12, -4, -34, -18, 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[[-2, -82, 28, 20, 32],\n [28, -23, 26, 16, -13],\n [-37, -23, -28, 16, 61],\n [12, 12, 24, -15, -30],\n [-29, -1, -8, -18, 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 5x5 matrix:\n[[-16, -16, -24, 12, -8],\n [-4, -4, -6, 3, -2],\n [8, 8, 12, -6, 4],\n [-12, -12, -18, 9, -6],\n [8, 8, 12, -6, 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[[-13, 26, -32, 22, -28],\n [3, 2, -32, 38, -44],\n [9, -14, 38, -47, 50],\n [-29, 10, 26, -1, 22],\n [-9, -16, 16, 26, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[20, -24, -35, -12, 19],\n [-12, -20, -22, 33, -20],\n [-12, 4, 8, 15, -14],\n [0, 0, 0, 0, 0],\n [-24, 12, 21, 27, -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[[-12, -8, -24, 12, 24],\n [3, 2, 6, -3, -6],\n [15, 10, 30, -15, -30],\n [-12, -8, -24, 12, 24],\n [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, -2, -3, 4, -6],\n [0, 4, 6, -8, 12],\n [0, 2, 3, -4, 6],\n [0, 2, 3, -4, 6],\n [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[[-18, 6, -15, 6, -9],\n [-18, 6, -15, 6, -9],\n [-24, 8, -20, 8, -12],\n [-24, 8, -20, 8, -12],\n [6, -2, 5, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-15, 0, 39, 20, 25],\n [17, -41, 36, -17, -30],\n [4, -25, -6, 13, -56],\n [-18, -2, 42, 10, 26],\n [12, 22, -42, 35, -5]]\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[[-18, -3, -12, -18, 0],\n [6, 1, 4, 6, 0],\n [18, 3, 12, 18, 0],\n [30, 5, 20, 30, 0],\n [-30, -5, -20, -30, 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[[88, 25, -9, 5, -15],\n [9, -9, 19, -3, -21],\n [0, -1, -7, 15, 23],\n [41, 25, -25, 2, -4],\n [-80, 3, -23, -19, 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 5x5 matrix:\n[[0, 0, 0, 0, 0],\n [4, -12, 12, 2, 4],\n [-6, 18, -18, -3, -6],\n [-4, 12, -12, -2, -4],\n [6, -18, 18, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-32, 26, 29, 21, -5],\n [-40, 34, 25, 33, -25],\n [8, -3, 31, 6, 13],\n [-29, 27, 22, 33, -29],\n [52, -31, -24, 9, -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 5x5 matrix:\n[[8, 0, 16, -24, -24],\n [2, 0, 4, -6, -6],\n [-4, 0, -8, 12, 12],\n [10, 0, 20, -30, -30],\n [12, 0, 24, -36, -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[[-22, 10, 6, 9, -23],\n [3, 6, -4, -32, 18],\n [-16, 18, 44, 10, -36],\n [-12, -27, -66, 9, 15],\n [54, -33, -32, -28, 66]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[20, -20, -16, -24, -12],\n [20, -20, -16, -24, -12],\n [-20, 20, 16, 24, 12],\n [10, -10, -8, -12, -6],\n [-25, 25, 20, 30, 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[[-30, 12, 8, -36, -26],\n [41, 6, -12, 46, 35],\n [-28, 0, 8, -32, -24],\n [-9, -30, 4, -6, -7],\n [-12, -12, 4, -12, -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[[6, 60, -18, -69, 6],\n [21, 49, 50, -23, 0],\n [-5, 17, -49, -46, 12],\n [2, 0, -38, -23, 1],\n [-22, -40, -63, 7, 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[[35, -28, 38, 13, -18],\n [-5, -26, 32, -21, -54],\n [-10, -21, 27, -34, -65],\n [19, -29, -1, -30, 0],\n [-13, -5, 45, 64, -6]]?\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 5x5 matrix:\n[[-1, -2, 5, 38, -13],\n [-24, 50, -12, -20, -12],\n [-14, 27, 0, 37, -22],\n [11, -23, 39, -31, 45],\n [-14, 45, -56, 3, -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 5x5 matrix:\n[[-21, 19, 22, -35, -48],\n [13, -19, -20, -2, 17],\n [7, 39, 24, 31, -16],\n [53, -3, -26, -5, -20],\n [21, -43, -22, -25, -18]]\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, -27, 24, 21, 13],\n [3, -38, 28, 13, 17],\n [-26, -56, 58, 54, 36],\n [6, -29, -8, -17, -25],\n [19, 11, -16, -24, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-3, 4, 6, -5, -6],\n [9, -12, -18, 15, 18],\n [9, -12, -18, 15, 18],\n [-18, 24, 36, -30, -36],\n [12, -16, -24, 20, 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[[8, 21, -30, 9, 23],\n [-32, 19, -28, -5, -21],\n [3, -40, 42, -16, -28],\n [-19, 1, 3, -11, -21],\n [-25, 10, 18, 28, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, -74, -4, 42, 6],\n [-17, -13, -6, 0, -8],\n [-2, -28, -12, 27, 7],\n [20, -28, 8, 24, 14],\n [-42, 2, -28, -6, -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[[2, 44, -28, -2, 18],\n [-10, 20, -7, 4, 9],\n [-66, 12, 24, 47, 22],\n [4, 16, -11, -7, 3],\n [26, 44, -40, -16, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[57, -36, -9, 49, 23],\n [38, -26, -5, 40, 20],\n [-46, 20, 20, -23, -2],\n [1, -8, 1, 33, 19],\n [22, -4, -16, -2, -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[[3, -1, 10, 2, 1],\n [-6, -3, 0, -4, 28],\n [6, 2, 4, 4, -22],\n [18, -4, 52, 12, -6],\n [-15, -6, -6, -10, 61]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[5, 15, 10, 3, -6],\n [-53, 12, 6, 33, 43],\n [-17, -25, -42, -24, 2],\n [22, -12, -12, -21, -20],\n [-12, 29, 16, 15, 5]]\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[[-34, 11, -6, -26, 35],\n [42, -45, -48, 48, 45],\n [4, -10, -16, 8, 26],\n [12, -18, -12, 12, -18],\n [74, -37, -22, 68, 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[[27, 6, -21, -33, 0],\n [-20, 5, 5, 25, 10],\n [-23, -7, 20, 28, -2],\n [10, 6, -12, -12, 4],\n [-8, 2, 2, 10, 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[[37, 28, 5, 8, 16],\n [-12, 27, -39, -66, -24],\n [-15, 19, 5, -17, -25],\n [33, 28, 15, 6, 20],\n [51, -9, 12, 30, 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[[-24, 8, 22, 40, -12],\n [-24, -12, -3, 15, 18],\n [-6, 8, 25, 43, -12],\n [10, -8, -19, -31, 12],\n [10, -20, -34, -46, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-25, 46, -13, -13, -7],\n [30, 3, -2, -29, -33],\n [12, -18, 18, 13, 3],\n [13, 29, 1, -26, -32],\n [13, 38, -15, -43, -41]]?\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 5x5 matrix:\n[[-4, 12, -16, -12, -14],\n [-38, -43, 0, -14, -46],\n [26, -6, 73, 12, 59],\n [-18, 5, -20, -20, -11],\n [-1, -6, 47, -18, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -20, -24, 16, -4],\n [0, 0, 0, 0, 0],\n [-21, 25, 16, 6, 1],\n [-19, 31, 26, -4, 3],\n [17, -5, 8, -22, 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[[-34, 8, -18, 16, 26],\n [-24, 10, -22, 8, 18],\n [-5, 19, -36, -13, -8],\n [21, 3, 2, -19, -34],\n [48, -3, 3, -27, -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[[-39, -16, 9, -17, 18],\n [-19, 4, -8, 23, -14],\n [-5, -6, 2, -21, 20],\n [-16, 1, 15, -21, 22],\n [2, -4, 20, -30, 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, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [-6, -6, -3, 0, 9],\n [12, 12, 6, 0, -18],\n [4, 4, 2, 0, -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[[2, 6, -16, 4, 3],\n [-2, 0, 1, 3, -1],\n [30, -4, -12, 18, 9],\n [38, -11, -1, 22, 9],\n [54, -9, -18, 39, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-6, 0, 5, -2, 9],\n [2, -4, 1, -10, -15],\n [24, 15, -30, 48, 9],\n [12, 6, -14, 20, 0],\n [8, 5, -10, 16, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 8, 24, -24, 0],\n [0, -6, -18, 18, 0],\n [0, 8, 24, -24, 0],\n [0, -8, -24, 24, 0],\n [0, -8, -24, 24, 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[[10, -4, -12, 4, 10],\n [-20, 8, 24, -8, -20],\n [10, -4, -12, 4, 10],\n [-15, 6, 18, -6, -15],\n [15, -6, -18, 6, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-16, 24, 78, 20, -14],\n [32, 21, 55, -3, -33],\n [-2, 11, 34, 7, -8],\n [-18, -2, -2, 2, -1],\n [-14, 2, 42, 22, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -20, -2, -16, -4],\n [7, -1, 9, -5, -3],\n [-28, -26, -39, -4, 6],\n [18, 6, 24, -6, -6],\n [17, 19, 24, 5, -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[[2, -24, -3, -19, 22],\n [2, -24, -3, -19, 22],\n [-14, 16, 9, 17, -18],\n [-37, 7, 21, 18, -16],\n [45, 11, -24, -7, 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[[1, 44, -51, -3, 50],\n [-6, -27, -21, -45, 12],\n [17, 53, 2, 42, -6],\n [31, 16, 11, -8, -49],\n [-19, 1, -6, 18, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[18, -9, -9, 3, 15],\n [18, 1, -27, 21, 9],\n [24, -2, -30, 22, 14],\n [-24, 2, 30, -22, -14],\n [12, -11, 3, -7, 13]]\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 5x5 matrix:\n[[10, -23, -8, 18, 24],\n [36, 17, -28, -4, 14],\n [-14, -20, 16, 34, 22],\n [-2, -48, 1, 12, -20],\n [38, -28, -25, 40, 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[[0, -8, -8, 0, -8],\n [0, 24, 24, 0, 24],\n [0, 4, 4, 0, 4],\n [0, 0, 0, 0, 0],\n [0, -12, -12, 0, -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[[13, -41, -18, 6, -6],\n [-2, 42, 18, 28, 2],\n [-9, 13, -18, 38, -2],\n [8, 16, 21, 4, 1],\n [4, 54, 39, 19, 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[[-2, -7, 6, 0, -6],\n [-19, -33, 26, -3, -31],\n [-45, 8, 32, -15, -19],\n [14, 20, 24, 40, 27],\n [19, 34, -28, 5, 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[[-9, 27, 18, 15, 18],\n [-21, 9, 15, -25, -21],\n [-8, 12, 10, 0, 2],\n [-21, 9, 15, -25, -21],\n [-31, 33, 32, -15, -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[[-7, -6, 1, 11, -8],\n [1, 2, -7, -1, 4],\n [-5, -6, 11, 7, -10],\n [3, 6, -21, -3, 12],\n [20, 10, 40, -35, 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[[-14, -19, 36, 0, -14],\n [-20, -22, 26, -10, -2],\n [26, -24, 12, 34, 18],\n [-24, -7, 40, -10, -32],\n [-10, -33, 38, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[21, 45, -27, 24, 3],\n [-9, -9, 3, -12, 5],\n [4, -12, 12, 8, -12],\n [3, 27, -21, 0, 13],\n [4, -12, 12, 8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, 2, -4, -6, 5],\n [-4, -8, 16, 24, -20],\n [-2, -4, 8, 12, -10],\n [6, 12, -24, -36, 30],\n [-6, -12, 24, 36, -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[[-24, 32, 0, -8, -2],\n [30, -22, 0, 10, -11],\n [-6, -6, 0, -2, 10],\n [12, -8, 0, 4, -5],\n [24, 4, 0, 8, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-14, -5, -27, -18, -30],\n [30, -5, -15, -10, -30],\n [33, 0, 9, 6, 0],\n [24, 7, 39, 26, 42],\n [-26, -3, -21, -14, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-28, -1, 1, 39, 16],\n [-30, -4, 16, -15, 4],\n [-16, 5, 13, -6, 32],\n [-1, 83, 13, -46, 14],\n [-9, -41, -1, 14, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[14, -17, -31, 13, -44],\n [-4, 18, 0, 11, 10],\n [2, -6, 12, -34, -56],\n [-23, 16, -6, -17, -8],\n [28, 6, -20, 43, -30]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-36, -19, -40, 8, 26],\n [-25, -19, -13, 14, -2],\n [37, 29, 17, -22, 6],\n [-11, 0, -27, -6, 28],\n [3, 8, -13, -10, 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[[39, -20, -3, -8, -28],\n [17, 22, 29, -26, 40],\n [-8, -1, -43, 19, 8],\n [-36, 7, -35, 29, 4],\n [12, -34, 6, 2, -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[[23, -39, 30, 34, 3],\n [-21, -2, -52, 15, 0],\n [52, -31, 102, 7, 1],\n [40, 22, 32, 35, 38],\n [3, 35, 26, -26, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[36, 2, 36, 16, 43],\n [4, 1, -6, 6, -16],\n [0, -31, 24, -38, 22],\n [-4, -30, 24, -40, 27],\n [40, -13, 32, 6, 16]]\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, -30, 6, -12, -6],\n [-24, 30, -6, 12, 6],\n [-12, 15, -3, 6, 3],\n [-8, 10, -2, 4, 2],\n [24, -30, 6, -12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-17, 15, 0, -9, 11],\n [36, -30, -6, 18, -36],\n [-32, 30, -6, -18, 8],\n [25, -20, -7, 12, -31],\n [-12, 10, 2, -6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-20, 16, 2, -2, -35],\n [-15, -6, 18, -3, -15],\n [-9, 13, 44, 6, -22],\n [9, 18, -24, 3, 0],\n [1, 16, 26, 7, -11]]\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 5x5 matrix:\n[[-39, -10, 22, -47, 42],\n [55, 1, -13, 56, -44],\n [-54, 19, -25, -22, 0],\n [30, -23, 39, -11, 30],\n [-21, -33, -3, 42, -48]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-24, -24, 0, 27, 3],\n [1, 41, 42, -16, 6],\n [-30, 2, 18, 16, -5],\n [27, -13, 2, 1, 29],\n [21, 13, 28, -7, 28]]\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[[-47, -33, -34, -55, 60],\n [19, 4, 0, 18, -21],\n [22, 34, 18, 42, -48],\n [-20, -15, -25, -21, 21],\n [12, 18, 24, 18, -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[[-15, 6, 15, -3, -18],\n [-5, 2, 5, -1, -6],\n [0, 0, 0, 0, 0],\n [30, -12, -30, 6, 36],\n [5, -2, -5, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, -3, 4, -7, 3],\n [-9, 15, 3, 18, 6],\n [-27, 13, -25, 36, -20],\n [12, -4, 13, -15, 11],\n [-9, -17, -31, 0, -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[[-60, 19, 10, 31, -17],\n [-7, -20, -6, 33, -7],\n [-17, 9, 4, 4, -4],\n [-19, 21, 8, -10, -2],\n [-21, 2, 2, 17, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-28, -27, 2, -27, -31],\n [-52, -19, -30, -3, -7],\n [3, -6, 14, -3, -18],\n [10, 35, -30, 45, 55],\n [-57, -20, -38, -9, 0]]?\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[[-8, 12, 12, 24, -12],\n [6, -9, -9, -18, 9],\n [8, -12, -12, -24, 12],\n [8, -12, -12, -24, 12],\n [2, -3, -3, -6, 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[[-6, -12, 6, 10, 2],\n [18, 36, -18, -30, -6],\n [6, 12, -6, -10, -2],\n [12, 24, -12, -20, -4],\n [3, 6, -3, -5, -1]]?\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, -9, 15, -30, -18],\n [-17, -30, 29, -4, -24],\n [8, -20, 24, -24, -24],\n [-16, 11, -16, 26, 18],\n [7, -32, 37, -32, -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[[-50, -14, 7, 43, 2],\n [-15, 5, 11, -26, -7],\n [43, -5, -28, -35, -11],\n [-10, -6, -1, 31, 6],\n [9, -3, -9, -15, -6]]\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, 10, -15, 16, 6],\n [12, -5, 20, -9, -9],\n [29, 2, 46, 7, -10],\n [42, 41, -10, 8, -16],\n [-56, -16, -42, 8, 30]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[36, 36, -6, 36, -12],\n [-3, 6, -7, 3, 10],\n [6, 12, -6, 10, 4],\n [18, 18, -3, 18, -6],\n [0, -12, 10, -8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, -6, -4, -12, 2],\n [-5, -15, -10, -30, 5],\n [-6, -18, -12, -36, 6],\n [-2, -6, -4, -12, 2],\n [-5, -15, -10, -30, 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 5x5 matrix:\n[[-3, 3, 5, 6, 3],\n [-6, 6, 10, 12, 6],\n [12, -12, -20, -24, -12],\n [-18, 18, 30, 36, 18],\n [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[[42, 54, -6, -36, 66],\n [-24, -28, 12, 24, -34],\n [8, 16, 16, 0, 20],\n [-19, -23, 7, 18, -28],\n [20, 20, -20, -24, 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 5x5 matrix:\n[[40, -30, 40, 45, 30],\n [-20, 20, -30, 5, -10],\n [34, -1, 13, 19, 1],\n [44, 6, 6, 44, 2],\n [20, 4, -2, 39, 6]]\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, 10, 10, 15, 10],\n [12, 8, 8, 12, 8],\n [6, 4, 4, 6, 4],\n [9, 6, 6, 9, 6],\n [9, 6, 6, 9, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -12, -10, -8, -8],\n [0, -12, -10, -8, -8],\n [0, -36, -30, -24, -24],\n [0, 6, 5, 4, 4],\n [0, 30, 25, 20, 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[[-14, -4, -42, -2, -16],\n [-4, -14, -7, 21, 3],\n [54, -26, 18, 10, 38],\n [-42, 6, -24, 12, -26],\n [-10, 40, 19, 19, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-7, -3, 19, -24, 9],\n [-9, 3, 27, -36, 9],\n [-1, 3, 4, -6, 0],\n [1, -3, -4, 6, 0],\n [12, -12, -39, 54, -9]]\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 5x5 matrix:\n[[11, -17, -8, 15, 5],\n [-12, -10, 10, -22, -8],\n [-35, 6, 27, -59, -20],\n [-16, -3, 35, -16, -27],\n [-32, -17, 37, -52, -29]]\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, 9, 8, -13, 16],\n [1, -24, 10, 21, 6],\n [26, 15, -21, -3, 18],\n [9, -30, -39, 70, 17],\n [35, 42, -33, -21, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 16, -4, -22, 18],\n [-6, 16, 22, -7, 5],\n [-2, -18, -2, 21, -17],\n [8, -3, -22, -9, 8],\n [-2, -28, -6, 31, -25]]\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[[-2, -35, 19, 13, 2],\n [27, -11, 8, 23, 1],\n [2, -12, -34, 4, -38],\n [-22, 19, 21, -21, 30],\n [-33, -17, 0, -16, -6]]\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, -19, -3, 16, 6],\n [-9, 9, 1, -16, -2],\n [2, -41, -6, 44, 12],\n [-2, -13, -2, 12, 4],\n [2, -14, -2, 16, 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[[5, 5, 10, 0, -30],\n [-5, -5, -10, 0, 30],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [-5, -5, -10, 0, 30]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, 3, 1, -6, 3],\n [3, 9, 3, -18, 9],\n [3, 9, 3, -18, 9],\n [-3, -9, -3, 18, -9],\n [-4, -12, -4, 24, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 0, -8, 0, 24],\n [-18, 0, 12, 0, -36],\n [18, 0, -12, 0, 36],\n [-3, 0, 2, 0, -6],\n [-9, 0, 6, 0, -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[[24, 0, -24, 12, 36],\n [-8, 5, -2, 21, 33],\n [-24, 0, 24, -12, -36],\n [-32, 2, 28, -6, -30],\n [20, 0, -20, 10, 30]]\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 5x5 matrix:\n[[9, 3, -16, 20, -13],\n [33, -8, 47, -34, 1],\n [-30, -2, -32, -20, -6],\n [-7, -8, 3, -26, -31],\n [4, 2, -14, 22, -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 5x5 matrix:\n[[18, -14, -12, -30, 14],\n [-12, -8, 8, -6, 8],\n [-6, -22, 4, -30, 22],\n [-24, 16, 16, 36, -16],\n [-24, -28, 16, -30, 28]]\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[[6, 22, -6, -4, 2],\n [22, 41, 12, 16, -31],\n [-3, -2, -18, -6, 9],\n [-3, -3, -27, -6, 9],\n [12, 22, -6, 8, -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 5x5 matrix:\n[[-18, -22, 0, -16, 12],\n [-17, -19, -10, -10, 11],\n [-27, -14, 15, -36, -1],\n [-17, -12, 35, -36, -1],\n [9, 42, -15, 10, -32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[26, 12, 7, 25, -12],\n [-28, -12, -6, -26, 16],\n [-8, -12, -16, -16, -24],\n [10, 0, -5, 5, -20],\n [6, 0, -3, 3, -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, 0, 6, 30, -15],\n [8, 4, -6, -6, 4],\n [3, 24, -26, 14, -1],\n [10, 14, -17, -1, 4],\n [-28, 4, 2, 34, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[18, -27, 27, 3, 15],\n [-24, 12, 0, -34, -14],\n [0, 24, -36, 30, -6],\n [-12, 18, -18, -2, -10],\n [30, -33, 27, 20, 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[[-6, -12, 18, 12, -6],\n [0, 0, 0, 0, 0],\n [2, 4, -6, -4, 2],\n [12, 24, -36, -24, 12],\n [-12, -24, 36, 24, -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 5x5 matrix:\n[[-18, 6, -6, -3, -6],\n [-24, 8, -8, -4, -8],\n [24, -8, 8, 4, 8],\n [18, -6, 6, 3, 6],\n [18, -6, 6, 3, 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[[34, -27, 21, 34, -18],\n [36, 2, 34, -4, 28],\n [28, -10, 22, 12, 4],\n [-28, 10, -22, -12, -4],\n [-44, 12, -36, -14, -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[[-12, -12, -3, 9, -9],\n [-4, -4, -1, 3, -3],\n [12, 12, 3, -9, 9],\n [0, 0, 0, 0, 0],\n [4, 4, 1, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[30, 0, 29, -24, -16],\n [-41, -30, -24, 47, 24],\n [-30, -51, 39, 6, 3],\n [31, -7, 41, -29, -19],\n [7, 18, -45, 29, 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[[24, -30, -24, -60, 18],\n [-20, 14, 6, 12, -30],\n [-4, 12, 14, 38, 6],\n [-4, 26, 10, 10, 36],\n [2, 15, 5, 2, 33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-13, -54, 10, 24, -8],\n [27, -30, -6, 32, -56],\n [18, -9, 4, -17, -18],\n [-5, 30, 2, -32, 28],\n [-20, 21, 6, -28, 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[[-8, -20, 0, 4, 16],\n [12, 30, 0, -6, -24],\n [-6, -15, 0, 3, 12],\n [2, 5, 0, -1, -4],\n [-12, -30, 0, 6, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-21, 26, 27, 26, -12],\n [19, 80, 16, 40, -78],\n [11, -30, 45, 24, 66],\n [-38, 16, -14, -38, 6],\n [-17, -26, -31, -18, -12]]\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 5x5 matrix:\n[[-4, 18, -2, -6, -16],\n [19, -21, 8, 40, 41],\n [24, -30, -20, -17, -68],\n [16, -12, -10, 0, -6],\n [-10, 0, 2, -8, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 30, 12, 30, -12],\n [0, -25, -10, -25, 10],\n [0, 10, 4, 10, -4],\n [0, 5, 2, 5, -2],\n [0, 10, 4, 10, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, -3, 2, 6, 1],\n [-6, -9, 6, 18, 3],\n [8, 12, -8, -24, -4],\n [8, 12, -8, -24, -4],\n [10, 15, -10, -30, -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[[-9, 27, -15, 11, -17],\n [-25, -30, 18, -40, -32],\n [11, -49, 10, -3, 22],\n [54, 48, 6, 6, 54],\n [19, -43, -35, 27, 7]]\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[[-5, 5, 45, -45, -20],\n [6, 35, -46, 33, -3],\n [-10, 0, -27, 25, 17],\n [4, -9, 39, -34, -14],\n [-5, -2, -28, 27, 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 5x5 matrix:\n[[-7, -17, -16, -25, -14],\n [-14, -19, -15, -30, -21],\n [-4, -14, -14, -20, -10],\n [35, 10, -5, 25, 35],\n [-18, -18, -12, -30, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, 4, 1, 2, 5],\n [4, -8, -2, -4, -10],\n [-6, 12, 3, 6, 15],\n [4, -8, -2, -4, -10],\n [2, -4, -1, -2, -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[[-18, -8, -4, -6, 12],\n [0, 0, 0, 0, 0],\n [12, 4, -4, 8, -6],\n [12, 10, 26, -10, -15],\n [-6, 0, 12, -10, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[12, -12, 6, 0, 15],\n [-6, 24, 6, 6, 9],\n [20, -32, 4, -4, 14],\n [0, 0, 0, 0, 0],\n [-7, -2, -8, -3, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-36, 12, 6, -6, 18],\n [-18, 6, 3, -3, 9],\n [-30, 10, 5, -5, 15],\n [-18, 6, 3, -3, 9],\n [18, -6, -3, 3, -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[[-3, 0, 0, 0, -12],\n [-1, 0, 0, 0, -4],\n [1, 0, 0, 0, 4],\n [2, 0, 0, 0, 8],\n [6, 0, 0, 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 5x5 matrix:\n[[-23, -17, -5, 1, 9],\n [10, 22, 26, -30, -10],\n [27, 23, -18, 24, 22],\n [-17, -8, -13, 25, 55],\n [-27, -14, -14, 18, 48]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-25, -5, 0, -35, 35],\n [-10, 22, -40, 34, -10],\n [30, -18, 40, -6, -18],\n [-5, 11, -20, 17, -5],\n [-25, 28, -55, 31, 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[[0, 0, 0, 0, 0],\n [-5, -3, -5, 0, 0],\n [-5, -3, -5, 0, 0],\n [-30, -18, -30, 0, 0],\n [-5, -3, -5, 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[[-3, 12, -3, -6, 3],\n [-2, 8, -2, -4, 2],\n [3, -12, 3, 6, -3],\n [0, 0, 0, 0, 0],\n [1, -4, 1, 2, -1]]?\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, -29, -31, 2, -11],\n [-40, -5, -9, -13, -24],\n [-10, 16, 30, -47, 19],\n [-51, -78, -60, 0, 0],\n [-76, -20, -12, -37, -33]]?\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 5x5 matrix:\n[[-1, -4, 49, -39, 17],\n [28, 40, -4, 12, 28],\n [-6, -10, 28, -24, 4],\n [11, 14, 31, -21, 23],\n [39, 56, -11, 21, 37]]\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[[-9, 13, 0, -5, -6],\n [5, -1, 8, 1, 6],\n [15, -3, 24, 3, 18],\n [13, 3, 28, 1, 18],\n [-26, 22, -20, -10, -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 5x5 matrix:\n[[-18, 6, -40, 2, -2],\n [3, -3, 25, -5, 2],\n [42, -6, 20, 14, -2],\n [-47, 1, -2, -16, 4],\n [-14, 28, 11, -48, 3]]\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[[5, -16, -7, -1, -15],\n [6, 25, 16, 3, 4],\n [-12, 18, -8, 14, -8],\n [-7, 19, -1, 10, -3],\n [10, 36, 18, 10, -10]]\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, -10, 12, -4, -6],\n [-18, 15, -18, 6, 9],\n [30, -25, 30, -10, -15],\n [-6, 5, -6, 2, 3],\n [6, -5, 6, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-28, -8, 28, -42, -20],\n [-51, 55, -12, -4, -52],\n [12, 8, -2, -6, 10],\n [-40, 31, -36, -21, -74],\n [-3, -26, 2, -25, -16]]\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[[18, -9, 3, 18, 6],\n [-18, 9, -3, -18, -6],\n [6, -3, 1, 6, 2],\n [0, 0, 0, 0, 0],\n [-18, 9, -3, -18, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-19, 11, 9, 23, -14],\n [15, -14, -2, -21, 13],\n [4, -2, 16, 2, -2],\n [-4, -50, -12, -30, 26],\n [-31, -34, -20, -6, 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[[-41, -4, -14, 9, 56],\n [-20, -18, -31, -36, -12],\n [-25, -40, -25, -15, 10],\n [2, 27, 34, 54, 51],\n [-34, -39, -37, -30, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[16, -32, 19, -29, -15],\n [-24, 29, 14, 48, 7],\n [-16, -19, 26, 4, -9],\n [36, 49, -4, 2, 23],\n [8, 42, 16, -8, 38]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[28, 0, 14, 17, 7],\n [-12, -80, 50, -30, -3],\n [-51, -61, 12, 1, -3],\n [15, 13, -6, -22, 12],\n [-17, -19, 10, -52, -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[[-9, 33, -7, -15, -25],\n [15, -41, 14, 11, 37],\n [-3, 1, -4, 5, -5],\n [-3, 19, -1, -13, -11],\n [-3, 13, -2, -7, -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[[-37, 44, 5, -3, 16],\n [10, -34, -16, -3, -10],\n [19, -41, 0, -9, -26],\n [60, 20, 55, 20, -3],\n [27, -9, 18, 2, -14]]\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[[3, 7, 1, 3, 0],\n [9, -1, -13, -21, 0],\n [-1, -28, -19, -36, 0],\n [15, 24, -3, 0, 0],\n [-14, -18, 6, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[11, 19, -14, 8, 4],\n [-14, -7, 17, -20, -1],\n [-19, -50, 25, -4, -11],\n [14, 7, -17, 20, 1],\n [-1, 25, 0, -16, 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 5x5 matrix:\n[[-2, 12, -6, 40, -12],\n [-21, 3, 4, 22, -22],\n [-32, 12, 24, 35, -27],\n [-7, 6, 39, -18, 12],\n [38, 3, -25, 1, 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 5x5 matrix:\n[[5, -17, 8, -1, 21],\n [37, -25, -20, -2, -3],\n [-24, 4, 43, 9, -3],\n [25, -25, -15, -5, 20],\n [29, -5, -13, 5, -42]]\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, -34, 12, -4, 30],\n [-7, -24, -12, -10, 1],\n [34, -5, -58, 38, -33],\n [33, 17, -33, 39, -37],\n [-14, 24, 20, -16, 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[[10, -4, -12, 0, -6],\n [30, -12, -36, 0, -18],\n [-20, 8, 24, 0, 12],\n [-15, 6, 18, 0, 9],\n [25, -10, -30, 0, -15]]\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, -20, -5, 5, -35],\n [6, -8, 14, -38, 34],\n [-23, 16, -6, 21, -2],\n [-13, 12, -13, 37, -27],\n [-30, 16, 8, -14, 40]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-6, -29, -39, -49, -32],\n [-27, 19, 28, 47, 56],\n [-12, 12, 26, 40, 35],\n [-28, 50, 48, 58, 64],\n [-42, -44, -23, 4, 32]]\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[[-4, -14, -3, 11, -12],\n [-40, -12, -47, 28, -8],\n [56, 30, 56, -38, -3],\n [-48, -28, -56, 44, -26],\n [-16, 0, -6, -8, 44]]?\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 5x5 matrix:\n[[15, -20, 25, -30, 0],\n [12, -16, 20, -24, 0],\n [12, -16, 20, -24, 0],\n [12, -16, 20, -24, 0],\n [3, -4, 5, -6, 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 5x5 matrix:\n[[8, 36, 10, -10, -48],\n [-39, -14, 5, -24, 2],\n [19, 26, -11, 10, -26],\n [8, -23, -17, 20, 38],\n [-28, -49, -13, 2, 58]]\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, 10, -57, 46, -42],\n [-14, -23, 6, -41, 42],\n [-14, -12, -21, -7, 6],\n [-14, 14, -3, 42, -39],\n [-44, 45, -15, 76, -49]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[16, -19, -53, -19, -14],\n [-9, -18, -51, 21, -16],\n [26, 40, 32, -2, 0],\n [34, 17, -23, -13, -14],\n [29, 37, 24, -6, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[11, 14, 4, -6, 8],\n [13, 14, 6, -2, 5],\n [20, 24, 8, -8, 12],\n [15, 18, 6, -6, 9],\n [-6, 0, -6, -12, 9]]?\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 5x5 matrix:\n[[0, 12, 18, 9, -9],\n [0, 0, 0, 0, 0],\n [0, 20, 30, 15, -15],\n [0, -12, -18, -9, 9],\n [0, 16, 24, 12, -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[[-1, 6, 8, 1, 4],\n [-11, 10, 11, 11, 9],\n [-14, -4, -9, 14, 1],\n [26, -4, 1, -26, -9],\n [-10, -4, -8, 10, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[18, -23, -17, 0, -21],\n [-16, -6, -29, -22, 26],\n [6, 3, 21, 0, -7],\n [-14, -11, -36, -23, 24],\n [-18, 9, -15, -3, 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[[14, 15, 6, 31, 3],\n [6, 19, 30, 35, -9],\n [2, 41, 45, 65, -9],\n [18, -13, 5, -5, -7],\n [3, 7, -4, 11, 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[[-20, -24, -8, 24, -12],\n [-5, -6, -2, 6, -3],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [-15, -18, -6, 18, -9]]\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[[-20, -30, 2, 11, -6],\n [-21, -29, -14, -8, -45],\n [-9, -21, 8, -24, -25],\n [0, 16, 12, 12, 56],\n [-12, -23, -24, -1, -61]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, -8, -4, -4, 4],\n [18, 8, -20, 8, 12],\n [-30, -8, 32, -10, -20],\n [-24, 0, 24, -4, -16],\n [-6, -8, 8, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[24, 10, -6, -14, -27],\n [12, -6, 6, 6, -3],\n [-11, -22, 17, 27, 29],\n [-10, 16, -14, -18, -8],\n [14, 26, -20, -32, -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[[0, 0, 0, 0, 0],\n [-9, 6, 3, 12, -18],\n [-6, 4, 2, 8, -12],\n [6, -4, -2, -8, 12],\n [-15, 10, 5, 20, -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[[36, -54, 27, -33, 15],\n [-21, 36, -15, 20, -8],\n [27, -24, 23, -22, 14],\n [-24, 24, -20, 20, -12],\n [30, -42, 23, -27, 13]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-10, 0, -18, 13, -4],\n [21, 0, 27, -21, 3],\n [-8, 0, 0, 2, 4],\n [13, 0, 15, -12, 1],\n [-4, 0, 0, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-26, -10, -2, 0, 34],\n [-34, -15, -4, 18, 25],\n [-36, -27, 0, 49, -16],\n [-1, 1, -7, 35, -30],\n [10, 22, -20, 35, -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 5x5 matrix:\n[[6, -57, -73, 9, 54],\n [-57, 23, 18, 6, -45],\n [-3, 48, 55, -25, -28],\n [34, -19, -19, -8, 33],\n [-75, 9, -6, 3, -39]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, 0, 18, -12, -24],\n [6, 0, 18, -12, -24],\n [-5, 0, -15, 10, 20],\n [6, 0, 18, -12, -24],\n [4, 0, 12, -8, -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[[28, -12, -31, -19, -13],\n [-27, 5, 11, 29, 38],\n [-7, 9, 25, -5, -20],\n [-28, 4, 8, 32, 44],\n [15, -9, -24, -6, 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[[-24, 14, -12, 6, -22],\n [-28, -2, 28, 30, -2],\n [11, -20, 40, 12, 19],\n [-26, -3, 32, 27, -9],\n [-24, 0, 15, 27, 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 5x5 matrix:\n[[-25, 25, -10, -10, -20],\n [30, -30, 12, 12, 24],\n [10, -10, 4, 4, 8],\n [15, -15, 6, 6, 12],\n [-5, 5, -2, -2, -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[[-16, 3, -5, -9, -11],\n [22, -30, 17, 36, 23],\n [-24, -30, 6, 18, -6],\n [6, 42, -15, -36, -9],\n [-24, 16, -12, -24, -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[[-5, 5, -6, 3, 4],\n [-10, 10, -12, 6, 8],\n [20, -20, 24, -12, -16],\n [10, -10, 12, -6, -8],\n [5, -5, 6, -3, -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[[-36, -33, -17, -33, 43],\n [38, 0, 35, 24, -24],\n [-32, 12, -1, -18, -38],\n [-5, 0, -16, 9, 13],\n [-44, 4, -32, -24, 8]]\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 5x5 matrix:\n[[-28, 17, -1, 14, -27],\n [20, 8, 28, 18, -1],\n [-3, -11, 10, -1, 5],\n [39, -45, 66, 3, 42],\n [-11, 10, -23, -5, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, -3, -5, 3, 4],\n [-30, -15, -25, 15, 20],\n [-12, -6, -10, 6, 8],\n [24, 12, 20, -12, -16],\n [-12, -6, -10, 6, 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[[-75, 25, -74, 27, 24],\n [-50, 5, -54, 12, -1],\n [38, -25, 33, -20, -28],\n [23, -10, 31, -9, 34],\n [36, -26, 33, -20, -17]]\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, -2, -6, 0, -2],\n [0, -4, -12, 0, -4],\n [0, 12, 36, 0, 12],\n [0, 10, 30, 0, 10],\n [0, -4, -12, 0, -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[[-3, 3, 1, -3, -4],\n [12, -12, -4, 12, 16],\n [-6, 6, 2, -6, -8],\n [12, -12, -4, 12, 16],\n [-6, 6, 2, -6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -6, -22, -14, 7],\n [12, -6, -39, -27, 12],\n [12, -6, -39, -27, 12],\n [12, 14, 6, -2, -3],\n [-24, -36, -30, -6, 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[[-22, 7, -28, 18, -12],\n [-31, 47, 21, -74, -13],\n [28, -1, 28, -9, -18],\n [-22, -9, -18, 10, 38],\n [-18, 5, -9, -1, 9]]\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, 12, -18, -18, 14],\n [10, 6, 11, -11, -5],\n [-25, 12, -20, -1, 8],\n [-8, -30, -31, 5, 31],\n [11, -6, -1, -18, 11]]\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 5x5 matrix:\n[[-36, -24, -9, -12, 9],\n [54, -48, 48, 30, -30],\n [15, 3, 5, -7, 3],\n [36, -18, 25, 8, -11],\n [-30, -34, -7, -50, 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[[38, -17, 14, 35, -25],\n [-30, 17, 1, -8, -62],\n [-46, 3, 28, 27, -35],\n [44, -48, 15, 31, -3],\n [25, -9, 13, 31, 31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-9, -8, -11, -36, -21],\n [-6, 0, -18, -48, -52],\n [46, 54, -46, 11, 19],\n [0, -4, -16, -18, 14],\n [-22, -30, -2, -35, -9]]\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 5x5 matrix:\n[[7, -41, 6, -29, 6],\n [-15, 3, 18, -15, 18],\n [8, -50, 8, -36, 8],\n [23, -9, -26, 19, -26],\n [-5, 23, -2, 15, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-37, -8, 10, 16, 37],\n [-6, -3, 2, 6, 20],\n [-5, 5, -12, 8, -39],\n [54, 9, -6, -30, -36],\n [50, 4, 0, -26, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-16, -20, 4, 12, 20],\n [-16, -20, 4, 12, 20],\n [-8, -10, 2, 6, 10],\n [4, 5, -1, -3, -5],\n [-4, -5, 1, 3, 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 5x5 matrix:\n[[14, -26, -28, 38, -30],\n [-11, -7, -10, 17, -13],\n [-14, 26, 28, -38, 30],\n [34, -22, -20, 22, -18],\n [38, -2, 4, -14, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[23, 6, 24, 1, -7],\n [-30, -12, -57, -12, -9],\n [-13, -4, -30, -10, -7],\n [39, 10, 36, -1, -15],\n [4, -10, 25, 27, 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[[15, -34, 53, 9, 26],\n [4, 8, -17, 53, 33],\n [-14, -5, -28, -27, -19],\n [35, -5, 6, 37, -29],\n [-11, -12, -1, -39, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, 5, -4, -4, 5],\n [-8, -20, 16, 16, -20],\n [12, 30, -24, -24, 30],\n [-12, -30, 24, 24, -30],\n [2, 5, -4, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[39, 6, -1, 36, 8],\n [-36, -19, 8, -29, -17],\n [9, -5, 7, -30, -67],\n [-37, -22, 7, -2, 16],\n [27, 1, 1, 26, -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[[15, 2, 14, 9, 12],\n [-30, -12, -24, -12, -36],\n [50, -4, 52, 38, 24],\n [20, 12, 14, 5, 30],\n [25, 10, 20, 10, 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[[42, -36, -12, 5, 38],\n [0, -24, -36, 8, 16],\n [12, -30, -33, 8, 24],\n [36, -24, 0, 2, 28],\n [6, 6, 15, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[18, 9, -15, 6, 6],\n [18, 9, -15, 6, 6],\n [36, 18, -30, 12, 12],\n [-36, -18, 30, -12, -12],\n [-12, -6, 10, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[7, -22, 29, -19, -6],\n [47, -4, 15, 31, -6],\n [-36, 28, -42, -6, 0],\n [-6, -29, 30, 36, 72],\n [-14, -10, 11, -43, -24]]?\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[[12, -16, -8, -16, 4],\n [12, -16, -8, -16, 4],\n [-12, 16, 8, 16, -4],\n [-15, 20, 10, 20, -5],\n [-18, 24, 12, 24, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-11, -12, 19, -3, -10],\n [-44, -52, -6, 28, -10],\n [37, 22, -9, -12, 32],\n [36, 24, -3, -15, 27],\n [-3, -30, -5, 10, 24]]\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, 3, 7, -5, -30],\n [23, -14, 20, 20, 23],\n [-29, -7, 22, -29, -35],\n [-25, -30, 60, -28, -25],\n [20, -6, 8, 18, 16]]\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[[2, -6, 7, 23, -9],\n [-40, -24, -30, -6, 56],\n [36, 16, 13, -53, 10],\n [0, -21, 2, 10, 15],\n [-24, -5, -13, 15, 17]]\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[[-52, -23, 26, 7, -49],\n [1, -36, -17, -10, -7],\n [-28, 5, 23, -14, -9],\n [-16, -57, -12, -17, -19],\n [-6, -12, 14, 24, 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[[-20, -20, -16, 8, 20],\n [5, 5, 4, -2, -5],\n [-10, -10, -8, 4, 10],\n [20, 20, 16, -8, -20],\n [10, 10, 8, -4, -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[[-25, 10, -30, 5, 0],\n [-25, 10, -30, 5, 0],\n [0, 0, 0, 0, 0],\n [20, -8, 24, -4, 0],\n [20, -8, 24, -4, 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 5x5 matrix:\n[[-10, -21, -4, -24, -1],\n [-20, 15, -20, 0, -5],\n [29, -17, 28, 4, 7],\n [-12, -10, -8, -16, -2],\n [-2, 11, -4, 8, -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[[-18, -43, 50, -52, -9],\n [28, 14, -12, 19, 5],\n [-6, -30, 38, -37, -7],\n [-23, 26, -17, 14, -12],\n [-2, -15, 2, -6, 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 5x5 matrix:\n[[0, 0, 0, 0, 0],\n [-30, -36, -36, -36, -30],\n [-30, -36, -36, -36, -30],\n [-20, -24, -24, -24, -20],\n [30, 36, 36, 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[[-7, 7, -12, 1, 5],\n [-20, -40, -15, 5, 35],\n [-31, -6, -43, 6, 38],\n [-27, -12, -39, 6, 42],\n [-28, -28, -23, 5, 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[[16, 0, 32, -30, -26],\n [-37, -32, -33, 22, 39],\n [-3, -20, -28, 7, 35],\n [-29, -4, -9, 14, 1],\n [11, 42, -3, 35, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -14, -12, 14, 28],\n [-50, 12, -38, -23, 8],\n [-20, -16, -33, -3, 28],\n [-16, 10, 20, 20, 28],\n [24, -27, 3, 3, 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[[-2, -32, -25, 29, -5],\n [8, 30, 16, -32, 20],\n [-2, -18, -13, 17, -5],\n [6, -23, -27, 15, 15],\n [-16, 10, 28, 4, -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[[0, 30, 12, -66, 24],\n [4, 27, 4, -45, 22],\n [8, 29, -2, -35, 24],\n [10, 35, -3, -41, 29],\n [-6, -8, 7, -4, -7]]\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 5x5 matrix:\n[[24, 16, -23, 8, 0],\n [3, 38, 42, 4, 35],\n [22, -14, -68, 8, -32],\n [21, 7, -12, -40, -32],\n [-2, 12, 17, 3, 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[[-18, 7, -10, -15, -12],\n [-5, -18, -4, -38, -40],\n [-5, 21, 34, 11, 12],\n [-29, 30, 34, -16, -12],\n [-33, 31, 34, -11, -14]]?\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 5x5 matrix:\n[[-32, 2, 6, 32, 34],\n [-8, 33, -1, -12, 1],\n [-8, -32, 4, 28, 16],\n [-16, 1, 3, 16, 17],\n [6, -2, -1, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, 1, -17, 7, 2],\n [-32, -60, 13, -42, -15],\n [8, 39, -16, 24, -3],\n [-18, 8, -7, -4, -23],\n [39, 14, -7, 29, 43]]\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[[-46, -12, 11, 7, 46],\n [-41, -63, 25, -7, 23],\n [-21, -57, -12, 1, 5],\n [13, 23, -6, 30, 5],\n [6, -41, -8, -16, -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[[-8, 6, 2, 0, -12],\n [-12, 9, 3, 0, -18],\n [-12, 9, 3, 0, -18],\n [-4, 3, 1, 0, -6],\n [12, -9, -3, 0, 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[[-1, 8, 24, 16, -26],\n [-18, 0, -24, -24, 36],\n [-1, -4, -14, -10, 16],\n [-2, -8, -28, -20, 32],\n [21, -24, -48, -24, 42]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-16, 1, -2, 8, 32],\n [58, -55, 25, -2, 37],\n [-4, 14, -6, 24, 30],\n [-10, 12, -5, -8, -29],\n [34, -22, 11, -2, 1]]\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, 10, -7, 5, 1],\n [-10, -20, 11, -19, 1],\n [18, 0, 3, 9, -3],\n [-46, 10, -14, -16, 8],\n [4, -10, 7, -5, -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[[-15, -25, -20, 10, 5],\n [-6, -10, -8, 4, 2],\n [-9, -15, -12, 6, 3],\n [12, 20, 16, -8, -4],\n [-9, -15, -12, 6, 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[[1, 2, 2, 0, -2],\n [-3, -6, -6, 0, 6],\n [1, 2, 2, 0, -2],\n [-4, -8, -8, 0, 8],\n [5, 10, 10, 0, -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, -8, -36, -44, -2],\n [-28, 16, -14, -14, -31],\n [-23, 20, 29, 23, 19],\n [48, -37, 1, 14, 9],\n [-15, 11, 44, 47, 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[[-48, -16, -24, 51, -13],\n [8, 20, -22, -9, -25],\n [32, 30, -13, -11, -25],\n [42, 34, -9, -24, -23],\n [28, 30, -17, 6, -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 5x5 matrix:\n[[-16, 31, -14, 25, 33],\n [-33, 51, 24, 6, 18],\n [-27, 42, -12, 7, 35],\n [-4, -1, 44, -25, -33],\n [-10, 22, 4, 24, 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 5x5 matrix:\n[[0, -15, 5, -10, -25],\n [0, 9, -3, 6, 15],\n [0, -15, 5, -10, -25],\n [0, -12, 4, -8, -20],\n [0, -18, 6, -12, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 15, -6, -7, -24],\n [-4, -16, 2, 6, 41],\n [-20, -20, 10, 10, 25],\n [0, 18, 0, -6, -54],\n [-16, -4, 8, 4, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, -6, 18, -15, 18],\n [12, 6, -18, 15, -18],\n [-12, -6, 18, -15, 18],\n [0, 0, 0, 0, 0],\n [20, 10, -30, 25, -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 5x5 matrix:\n[[39, -15, 14, -8, -24],\n [5, -20, 18, -37, 6],\n [38, -14, -8, -8, 12],\n [42, -22, 22, -17, -34],\n [16, -6, 26, -1, -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[[-24, -8, -12, -4, 26],\n [-36, -7, -2, 4, -31],\n [12, 3, 14, 0, -27],\n [24, 13, -18, 14, 19],\n [12, 8, -14, 10, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -9, -18, 0, 12],\n [-20, 15, 30, 0, -20],\n [16, -12, -24, 0, 16],\n [24, -18, -36, 0, 24],\n [16, -12, -24, 0, 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[[-30, -25, -20, -20, -25],\n [18, 13, 16, 16, 17],\n [-12, -12, -4, -4, -8],\n [-6, -7, 0, 0, -3],\n [24, 19, 18, 18, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, -25, 10, -30, -5],\n [2, -10, 4, -12, -2],\n [4, 20, -32, 6, -14],\n [-8, -16, 40, 6, 22],\n [0, -8, 8, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1, -20, -16, 20, -12],\n [-14, 8, -54, -30, -28],\n [-37, 11, 45, -21, 46],\n [60, 22, 34, 13, -2],\n [-59, 11, -41, -39, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, -8, -5, 17, 3],\n [-24, 0, -30, -18, -30],\n [22, -2, 30, 23, 32],\n [-30, -10, -25, 10, -15],\n [-14, -2, -15, -4, -13]]\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 5x5 matrix:\n[[-4, -4, 26, 18, -8],\n [14, 14, -7, 21, -20],\n [8, 8, 18, 34, -24],\n [-4, -4, -30, -38, 24],\n [-4, -4, -30, -38, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-33, -36, 27, 10, 3],\n [-3, -24, 54, 13, 38],\n [-30, -30, 15, 5, -5],\n [-16, -30, 1, -27, -19],\n [52, 30, 2, -20, 22]]?\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[[-10, -8, -6, -4, -4],\n [36, 3, -30, -15, -9],\n [-17, -17, -37, -9, -23],\n [10, 49, 13, 57, -8],\n [29, -10, -4, -30, 11]]?\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 5x5 matrix:\n[[-16, 24, -22, 10, -22],\n [-14, 16, -15, 9, -21],\n [-23, -18, 13, 17, -50],\n [9, -26, 23, -5, 8],\n [-11, 14, -13, 7, -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[[-10, 10, -6, -10, -6],\n [55, -15, 30, 40, 10],\n [-16, 8, -9, -13, -5],\n [41, 7, 21, 23, -3],\n [-46, -2, -24, -28, 0]]?\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, -15, 3, 23, -21],\n [-17, -23, -7, 19, -6],\n [17, 32, 18, -34, 17],\n [-31, -14, -32, 11, -7],\n [6, -25, 25, 18, 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[[-8, 23, -5, 8, 16],\n [-16, -4, 0, -24, -8],\n [6, 59, 39, 28, -8],\n [13, -37, 3, -10, -20],\n [7, -39, -7, -14, -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[[-46, 10, 10, 32, -8],\n [-21, -63, -41, 26, -44],\n [5, -29, -42, 22, -40],\n [10, 14, 11, 18, -6],\n [47, 39, -1, -21, 13]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, 15, 33, 21, 30],\n [-29, -1, -29, -27, -43],\n [20, -30, -26, -10, -4],\n [45, -32, -25, 4, 10],\n [-62, -20, -22, -52, -44]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0, 0],\n [-6, -30, 6, 36, -30],\n [4, 20, -4, -24, 20],\n [3, 15, -3, -18, 15],\n [5, 25, -5, -30, 25]]?\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 5x5 matrix:\n[[2, -4, -4, -10, 12],\n [2, -6, -5, -21, 18],\n [-2, 10, 7, 43, -30],\n [3, -10, -8, -37, 30],\n [7, -8, -11, -2, 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 5x5 matrix:\n[[-16, -16, -4, -4, -4],\n [20, 20, 5, 5, 5],\n [-4, -4, -1, -1, -1],\n [8, 8, 2, 2, 2],\n [12, 12, 3, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, -20, 12, 22, -12],\n [16, -28, 12, -10, -12],\n [5, -13, 8, 16, -8],\n [10, -14, 4, -22, -4],\n [1, -5, 4, 14, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-59, -9, -37, -21, 24],\n [27, 21, 11, -28, 23],\n [5, 43, -15, -38, 31],\n [-13, -21, 1, -3, 6],\n [-32, 45, -36, -63, 54]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-30, 30, 6, -36, 18],\n [10, -10, -2, 12, -6],\n [30, -30, -6, 36, -18],\n [15, -15, -3, 18, -9],\n [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[[5, -29, 18, -29, -24],\n [0, -24, -12, -24, -24],\n [1, -13, 0, -13, -12],\n [-5, -19, -42, -19, -24],\n [4, -28, 12, -28, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -12, -3, 0, 18],\n [0, 4, 1, 0, -6],\n [0, 12, 3, 0, -18],\n [0, 12, 3, 0, -18],\n [0, -20, -5, 0, 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[[-6, -10, -21, -65, 54],\n [-30, 7, 22, 25, -16],\n [-5, -17, -30, -59, 43],\n [-23, 17, 9, 25, -24],\n [-14, 17, 20, 14, -5]]\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, -6, -16, -8, 18],\n [-11, -11, -22, -7, 21],\n [-20, 10, -10, -25, 30],\n [23, 5, 28, 22, -39],\n [16, 14, 30, 11, -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[[-25, 18, -26, -9, -10],\n [21, -20, 19, -23, 25],\n [37, -13, 31, -10, 39],\n [-19, 33, -23, 12, -7],\n [-11, -2, -6, 13, -22]]?\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, 12, 24, 0, 42],\n [3, 8, -8, 0, -3],\n [16, 38, -44, 0, -22],\n [5, 18, -12, 0, 1],\n [15, 33, -42, 0, -24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, 3, 3, -2, -6],\n [-5, -3, -3, 2, 6],\n [-25, -15, -15, 10, 30],\n [5, 3, 3, -2, -6],\n [15, 9, 9, -6, -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[[-15, -16, 11, -61, -36],\n [-3, -9, 11, -35, 9],\n [-21, -22, 9, -67, -8],\n [21, 3, 15, 33, 24],\n [-24, -7, -18, -18, -13]]\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, 0, 0, 0, 0],\n [3, -2, -3, -5, -5],\n [-12, 8, 12, 20, 20],\n [-15, 10, 15, 25, 25],\n [3, -2, -3, -5, -5]]?\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[[-29, 13, -27, 14, -6],\n [-16, 23, 0, 4, 6],\n [-8, -14, -24, 2, -6],\n [26, 3, 38, -8, 6],\n [-13, 24, 5, -8, 18]]?\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 5x5 matrix:\n[[0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [-2, 2, 6, 6, 0],\n [3, -3, -9, -9, 0],\n [6, -6, -18, -18, 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[[7, 9, 15, -26, -31],\n [10, 10, 20, -30, -30],\n [10, 10, 20, -30, -30],\n [-9, 1, -13, 2, -23],\n [-3, -5, -7, 14, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[11, -20, -35, -34, 17],\n [31, 1, -1, -25, 36],\n [2, -9, -2, 15, 4],\n [6, -5, -6, -5, 8],\n [-9, 14, -3, -32, -13]]\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[[-3, -6, 0, 3, -18],\n [-6, -12, 0, 6, -36],\n [-1, -2, 0, 1, -6],\n [-4, -8, 0, 4, -24],\n [-1, -2, 0, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[15, 18, 19, -15, -4],\n [-27, -18, 1, 3, -4],\n [5, 12, 21, -15, -6],\n [12, 18, 24, -18, -6],\n [-3, 9, 27, -18, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, 43, -55, 39, -2],\n [26, 21, -59, 19, -19],\n [4, 4, -37, 18, -41],\n [6, 45, -36, 37, -4],\n [6, 7, 1, 11, -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[[6, 6, 1, -1, 6],\n [6, 6, 1, -1, 6],\n [-24, -24, -4, 4, -24],\n [18, 18, 3, -3, 18],\n [-24, -24, -4, 4, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-18, 6, -30, -18, 12],\n [-19, -26, 6, 22, -23],\n [52, 52, 34, -2, -11],\n [-21, -23, -15, -1, 9],\n [20, 1, 25, 11, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[16, -18, 18, 36, -40],\n [7, 4, 3, -3, 8],\n [-27, 51, -18, -27, 12],\n [24, -22, 18, 24, -16],\n [21, -32, 9, 3, 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 5x5 matrix:\n[[-12, 2, -10, -2, -4],\n [-12, 2, -10, -2, -4],\n [18, -13, 15, 5, 14],\n [-18, -27, -15, 3, 18],\n [-36, 6, -30, -6, -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[[-6, 10, -74, -28, -12],\n [-17, -15, -42, -17, 1],\n [-16, -27, -18, -19, -22],\n [-7, 34, -14, 26, -31],\n [-5, -39, 6, -27, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[43, 23, 24, 21, 2],\n [23, 15, 54, 33, 16],\n [-34, -30, -54, -30, -26],\n [4, 10, -15, -12, 5],\n [35, 14, 6, 12, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, 42, -4, -16, -19],\n [8, -14, -8, 40, 33],\n [-19, -16, -6, 6, 1],\n [13, -18, 2, 18, 23],\n [-57, 0, 26, -20, -67]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-18, 0, -42, 12, 30],\n [-7, 4, -14, -3, -14],\n [-6, 6, 1, -11, -23],\n [7, 3, 20, -11, -30],\n [30, -8, 50, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-60, 0, -18, -48, -6],\n [-15, 0, -4, -13, -6],\n [-15, 0, -3, -15, -15],\n [-10, 0, -2, -10, -10],\n [5, 0, -2, 11, 32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[32, 66, -46, 30, 6],\n [15, 27, -8, 4, -17],\n [46, 15, -47, 15, -15],\n [-7, 8, 11, -3, -4],\n [-18, 24, -14, 22, 52]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -4, 2, -5, 3],\n [-5, -10, 5, -10, 5],\n [7, 26, -13, 23, -10],\n [1, -14, 7, -10, 3],\n [-7, -38, 19, -32, 13]]?\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 5x5 matrix:\n[[0, 12, 6, 2, 12],\n [0, -24, -12, -4, -24],\n [0, -6, -3, -1, -6],\n [0, -12, -6, -2, -12],\n [0, 18, 9, 3, 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[[-2, 11, -33, 7, -11],\n [-28, -26, -42, -2, -14],\n [0, -9, 21, -5, 7],\n [-6, -21, 27, -9, 9],\n [-6, -21, 27, -9, 9]]\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 5x5 matrix:\n[[-4, 8, 0, -6, -9],\n [72, 48, -36, -12, -6],\n [4, 20, 24, 20, 16],\n [-4, 12, -30, -40, -44],\n [28, 60, -12, -20, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -5, -5, 1, 0],\n [-4, -5, -5, 1, 0],\n [-4, -5, -5, 1, 0],\n [-24, -30, -30, 6, 0],\n [12, 15, 15, -3, 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[[-16, -16, 8, -20, -12],\n [-4, -4, 2, -5, -3],\n [0, 0, 0, 0, 0],\n [24, 24, -12, 30, 18],\n [12, 12, -6, 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[[0, 6, -15, -3, 15],\n [0, 6, -15, -3, 15],\n [0, 0, 0, 0, 0],\n [0, 2, -5, -1, 5],\n [0, -8, 20, 4, -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 5x5 matrix:\n[[0, 0, 0, 0, 0],\n [24, 18, -30, -6, -12],\n [20, 15, -25, -5, -10],\n [-24, -18, 30, 6, 12],\n [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[[-9, -28, 36, 2, -37],\n [15, -7, -12, 16, 14],\n [14, -10, 28, 14, -11],\n [-12, 31, 30, -8, -26],\n [53, -35, -14, 62, 27]]\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, -56, 69, 18, 13],\n [-30, 50, -85, -4, -35],\n [-17, 34, -34, -26, 18],\n [12, 8, 4, 48, -39],\n [-34, 58, -50, 18, -49]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[14, 61, 18, 3, 22],\n [16, 20, 0, 12, 8],\n [-30, 6, 18, -30, 0],\n [2, 46, 18, -6, 16],\n [-3, -40, -15, 4, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[48, 0, 24, 12, 12],\n [14, 24, 35, 7, 46],\n [24, 32, 22, 9, 8],\n [-29, -17, -36, -13, -40],\n [-10, 70, 10, -5, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[32, 28, 20, -20, -20],\n [44, 36, 30, -26, -24],\n [60, 60, 30, -42, -48],\n [14, 16, 5, -11, -14],\n [-50, -50, -25, 35, 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[[11, 12, -2, 5, 10],\n [-59, 21, 40, 15, 2],\n [5, 24, -6, -5, 6],\n [31, -18, -26, -15, -8],\n [-38, 30, 40, 30, 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[[6, 0, 4, 4, -10],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [9, 0, 6, 6, -15],\n [-15, 0, -10, -10, 25]]?\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, 3, -4, 11, 23],\n [-16, 8, 15, -5, -38],\n [-31, 5, 24, 16, -34],\n [-44, -39, 9, 33, -16],\n [7, 18, -2, -38, -36]]?\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, -34, 17, -1, 36],\n [-6, -3, 8, -10, -4],\n [0, -10, -27, 39, 38],\n [42, 33, -10, -4, -38],\n [-54, -37, 27, -15, 29]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[10, 2, -6, 22, 25],\n [-42, -6, -24, 57, 12],\n [-44, 6, -41, 3, -39],\n [-6, 8, -3, -14, -12],\n [2, 22, -42, 16, 12]]\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, -18, -9, -24, -6],\n [-45, 10, 10, 30, 20],\n [-12, 26, 5, 8, -18],\n [3, 26, 2, -2, -28],\n [15, -10, -4, -10, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-15, -7, -17, -11, 1],\n [2, 0, 6, -13, 12],\n [24, 12, 24, 30, -12],\n [-3, -3, 3, -27, 21],\n [-1, -3, 9, -40, 33]]?\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, 25, -26, -2, 50],\n [2, 16, -31, -24, 17],\n [7, 25, -26, -51, 3],\n [9, -21, 14, 20, -32],\n [11, 3, -25, -30, -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[[-24, -33, -33, 21, -24],\n [29, 29, 29, -13, 17],\n [-15, 12, 12, -24, 21],\n [1, 5, 5, -5, 5],\n [-23, 1, 1, -17, 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[[7, 9, -29, 24, -31],\n [25, -6, 10, -6, -1],\n [21, -15, 39, -26, 19],\n [-42, 2, 8, -7, 18],\n [8, 18, -58, 40, -40]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[28, 48, -22, -3, -7],\n [-6, -27, 6, 33, 3],\n [3, 27, -6, -24, 12],\n [9, 21, -10, 12, 16],\n [4, -9, 2, -7, -29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -4, -4, -2, -4],\n [0, -4, -4, -2, -4],\n [0, -12, -12, -6, -12],\n [0, -8, -8, -4, -8],\n [0, 24, 24, 12, 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 5x5 matrix:\n[[62, -28, 32, 16, 52],\n [26, 0, 3, 7, 9],\n [50, -24, 24, 10, 42],\n [-6, -24, 8, -14, 18],\n [33, 14, 20, 36, 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[[4, -4, 16, -24, 20],\n [24, -12, 0, -4, -4],\n [-36, 15, 24, -29, 37],\n [56, -26, -16, 14, -30],\n [44, -20, -16, 16, -28]]\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, 40, -16, -6, 6],\n [12, -9, 14, 2, 24],\n [2, -29, 6, 4, -18],\n [12, -9, 14, 2, 24],\n [28, -31, 34, 6, 48]]\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[[-36, -36, -36, -24, 0],\n [36, 36, 36, 24, 0],\n [30, 30, 30, 20, 0],\n [6, 6, 6, 4, 0],\n [-36, -36, -36, -24, 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[[3, 9, 18, 6, 6],\n [-3, -9, -18, -6, -6],\n [2, 6, 12, 4, 4],\n [-5, -15, -30, -10, -10],\n [1, 3, 6, 2, 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 5x5 matrix:\n[[28, -30, -4, 53, 57],\n [28, 14, -12, 63, 56],\n [-22, -33, 17, -12, -10],\n [-16, -48, 24, -32, -22],\n [-10, 25, 5, -15, -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[[-20, -12, -8, 24, 8],\n [25, 15, 10, -30, -10],\n [-5, -3, -2, 6, 2],\n [-20, -12, -8, 24, 8],\n [-10, -6, -4, 12, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 16, -12, 4, 12],\n [12, 16, -12, 4, 12],\n [15, 20, -15, 5, 15],\n [12, 16, -12, 4, 12],\n [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[[2, -1, 1, 1, -11],\n [-2, -26, -28, 2, 8],\n [0, 45, 45, -5, 5],\n [-5, 34, 29, -6, 31],\n [3, 3, 6, 1, -16]]?\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[[3, -41, -54, 39, 12],\n [-27, -32, 9, -5, 13],\n [9, 5, 9, 19, -29],\n [4, 45, 10, 5, -16],\n [3, -7, 0, -9, 6]]\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[[30, 30, -30, 0, 0],\n [-30, -30, 30, 0, 0],\n [-36, -36, 36, 0, 0],\n [36, 36, -36, 0, 0],\n [-36, -36, 36, 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[[30, 24, 0, 12, 6],\n [0, 0, 0, 0, 0],\n [27, 12, -9, -3, 6],\n [-21, -4, 12, 10, -5],\n [24, 0, -18, -18, 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[[4, 18, 28, -4, 16],\n [12, -6, 29, -8, 28],\n [-10, 20, -18, 8, -23],\n [36, -43, -15, 2, 27],\n [-20, 15, -21, 6, -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[[-9, 28, -51, 10, 21],\n [68, -18, -3, -12, -49],\n [49, -45, -28, -49, -8],\n [-55, 30, -35, 25, 65],\n [-1, -58, 17, -42, 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[[24, 16, 0, 0, -20],\n [-12, -30, 30, 6, -15],\n [42, 6, 30, 6, -60],\n [18, 34, -30, -6, 10],\n [-16, 4, -20, -4, 30]]?\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 5x5 matrix:\n[[-4, -10, -12, -46, 2],\n [48, 12, -18, 12, 30],\n [-8, -8, -6, -32, -2],\n [-20, -10, 0, -30, -10],\n [-8, -6, -3, -22, -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[[9, -7, -22, 21, 23],\n [38, 70, -12, 26, 10],\n [29, 25, -18, 15, 9],\n [23, 35, -30, 19, 7],\n [-39, -19, 37, -50, -49]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, 15, 0, 6, 9],\n [4, 1, 1, -3, 1],\n [-6, -24, 1, -13, -14],\n [-14, -17, -2, 0, -11],\n [-20, -32, -2, -6, -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[[4, -10, 0, -19, 24],\n [62, -48, -21, -12, -60],\n [6, 14, -15, 31, 12],\n [-64, 32, 36, -14, 24],\n [56, -47, -18, -20, -42]]\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, 24, 0, -20, -43],\n [-58, 59, 61, -30, -70],\n [-6, 0, -32, 26, 8],\n [33, -21, -17, 10, 12],\n [-10, 0, 16, -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[[40, -32, 32, 14, 14],\n [21, -39, 18, 52, 23],\n [32, -34, 28, 27, 17],\n [-6, 30, -4, -54, -20],\n [15, 9, 2, -32, -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[[-2, -1, -6, 6, -3],\n [-10, -5, -30, 30, -15],\n [10, 5, 30, -30, 15],\n [-4, -2, -12, 12, -6],\n [4, 2, 12, -12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -4, -10, -36, -6],\n [15, 12, 0, -12, -12],\n [-54, -48, -12, 0, 36],\n [-40, -36, -10, -4, 26],\n [-39, -36, -12, -12, 24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[34, 37, 7, -3, -33],\n [13, 15, -40, 16, 46],\n [-40, -6, -6, -10, 26],\n [-28, 8, -2, 20, 30],\n [-4, -24, 26, -4, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-28, -36, 16, 48, -20],\n [0, 0, 0, 0, 0],\n [-33, -39, 9, 54, -27],\n [18, 30, -30, -36, 6],\n [18, 22, -7, -30, 14]]?\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, 21, -5, -13, 30],\n [24, 18, -13, 6, 30],\n [-3, 31, 2, 12, -11],\n [16, 0, -4, -45, 25],\n [5, -63, -3, -51, 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 5x5 matrix:\n[[4, -8, 10, -44, 56],\n [22, 18, -43, -32, 14],\n [21, 17, -4, -35, 47],\n [-7, -8, 12, 8, 24],\n [-13, -16, 23, 2, 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[[-5, -2, 1, -4, 5],\n [-5, -2, 1, -4, 5],\n [-30, -12, 6, -24, 30],\n [0, 0, 0, 0, 0],\n [-5, -2, 1, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[36, 36, -20, -20, 24],\n [3, -2, -5, 0, 2],\n [12, 7, -10, -5, 8],\n [-6, -8, 2, 4, -4],\n [33, 26, -23, -16, 22]]\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[[-30, 36, 12, -33, -18],\n [28, -42, -16, 36, 22],\n [-34, 24, 4, -27, -10],\n [-8, -24, -16, 12, 16],\n [-4, -12, -8, 6, 8]]\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[[32, -3, 22, -35, 13],\n [-11, 12, -16, 5, 2],\n [22, -24, 32, -10, -4],\n [12, 33, -18, -35, 25],\n [33, -36, 48, -15, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, 22, 30, 4, -5],\n [12, -16, -30, 8, 10],\n [-21, 14, 33, -16, -14],\n [20, -8, -24, 16, 12],\n [-3, -10, -12, -4, 1]]\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 5x5 matrix:\n[[17, 37, -24, -26, 2],\n [-58, -42, -42, 30, -42],\n [37, 49, 0, -44, 14],\n [25, 41, -18, -25, 10],\n [-7, 17, -48, 5, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-11, -36, -27, 1, -35],\n [0, 76, -16, -70, 56],\n [25, -14, -1, 11, 21],\n [-14, -50, 7, 30, -39],\n [14, -16, 19, 30, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-11, 47, 5, 24, 15],\n [-26, 0, -66, -36, -42],\n [14, -46, 9, -16, -11],\n [-7, 55, 43, 48, 21],\n [-2, -30, -34, -32, -22]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, 14, -9, 17, 0],\n [-3, 0, 15, -13, -24],\n [8, 32, -17, -15, -28],\n [-8, -21, 20, 29, 16],\n [-13, -28, 40, 18, -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[[24, -3, -49, -29, -22],\n [30, 15, -25, -5, -10],\n [-12, 9, 39, 27, 18],\n [-18, -24, -14, -22, -8],\n [34, 12, -38, -14, -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[[0, -6, -8, 0, 6],\n [-12, 39, 6, -30, -21],\n [-4, 19, 10, -10, -13],\n [-6, 21, 5, -15, -12],\n [-6, 12, -7, -15, -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[[-9, -15, -2, 0, 21],\n [40, -24, 7, -34, 3],\n [-12, 12, -2, 12, -6],\n [15, 9, 3, -6, -18],\n [-25, -15, -5, 10, 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[[19, -36, -9, -20, -36],\n [-12, 8, -13, 28, 31],\n [9, 14, -58, -20, -24],\n [5, -36, -1, 26, 20],\n [-25, -10, 0, 0, -40]]?\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, 12, -2, -12, -12],\n [1, -6, 1, 6, 6],\n [-1, 6, -1, -6, -6],\n [-1, 6, -1, -6, -6],\n [1, -6, 1, 6, 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 5x5 matrix:\n[[-18, 12, 14, 32, -56],\n [-17, 15, -10, 29, -37],\n [5, -6, 13, -8, 4],\n [17, -12, -9, -30, 50],\n [0, -3, 19, 1, -13]]\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[[10, 4, -12, -10, -8],\n [-30, -12, 36, 30, 24],\n [10, 4, -12, -10, -8],\n [-25, -10, 30, 25, 20],\n [-20, -8, 24, 20, 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[[-20, 20, -24, -8, -24],\n [-20, 20, -24, -8, -24],\n [10, -10, 12, 4, 12],\n [10, -10, 12, 4, 12],\n [-25, 25, -30, -10, -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[[0, 0, 0, 0, 0],\n [2, -4, 10, 0, -4],\n [2, -4, 10, 0, -4],\n [-3, 6, -15, 0, 6],\n [-3, 6, -15, 0, 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[[-7, 20, -42, 36, 37],\n [3, -15, 18, -9, -18],\n [-9, 27, -54, 45, 48],\n [8, -22, 48, -42, -42],\n [5, -13, 30, -27, -26]]\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, -32, -8, 73, 8],\n [-5, -38, -23, 37, 20],\n [15, 0, 48, 15, -24],\n [-5, -40, 4, 35, 8],\n [20, -22, 23, 50, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[20, 20, -15, -20, -5],\n [4, 4, -3, -4, -1],\n [12, 12, -9, -12, -3],\n [-20, -20, 15, 20, 5],\n [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[[5, 12, -10, 24, -6],\n [11, 20, -16, 42, -6],\n [9, 12, -9, 27, 0],\n [1, 12, -11, 21, -12],\n [-24, 0, -6, -18, -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[[-8, 12, -4, -24, -32],\n [-3, -5, -25, -32, -17],\n [1, 7, -17, 30, -14],\n [1, -15, -7, -34, 12],\n [-1, 1, -3, -4, -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[[10, 16, 36, -16, -8],\n [-18, 24, -36, -24, 24],\n [9, 21, 36, -21, -6],\n [-6, 8, -12, -8, 8],\n [-5, -8, -18, 8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-12, -14, 2, 0, 14],\n [13, -78, -43, -43, -38],\n [-51, -1, 4, -33, 9],\n [-22, -20, 3, -22, -9],\n [-10, -9, 16, 12, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-4, 35, 40, -12, 23],\n [17, 12, -11, 20, -3],\n [2, -11, -26, -4, 31],\n [-30, -21, 30, -28, -27],\n [-39, -21, 39, -42, -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[[-26, 17, -22, -53, -26],\n [16, -13, -1, -11, -16],\n [-7, 27, 12, 38, 39],\n [-29, 10, -20, -65, -37],\n [33, 1, -8, -12, -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[[-18, -21, -35, 14, 23],\n [-38, -41, -46, -33, 14],\n [12, 26, 33, -18, 24],\n [-18, -8, -9, -35, 14],\n [4, 17, 11, -2, -8]]\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[[-4, -18, -1, 9, 23],\n [0, -6, -2, 3, 9],\n [-16, -12, 16, 6, 2],\n [-20, -12, 21, 6, -2],\n [8, -6, -12, 3, 17]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-36, -6, 12, -24, -30],\n [61, 26, 8, -1, 50],\n [-1, -4, 20, -28, 15],\n [-21, -50, -32, 46, 11],\n [-36, 12, 0, -9, -57]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[2, -2, -3, -2, -1],\n [4, -4, -6, -4, -2],\n [8, -8, -12, -8, -4],\n [8, -8, -12, -8, -4],\n [6, -6, -9, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[23, 6, -3, -4, -21],\n [-21, 18, 11, -22, 62],\n [59, 38, 3, -36, -10],\n [-20, -20, -30, 30, -35],\n [-14, 22, 4, -23, 53]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-20, -21, 2, 21, 8],\n [-36, 22, -12, -22, 4],\n [34, -8, 8, 8, -6],\n [-22, -30, 4, 30, 10],\n [-4, -18, 4, 18, 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[[6, 8, -4, -18, -4],\n [-12, -26, 10, 51, 15],\n [-21, 22, 4, -12, -21],\n [39, -38, -8, 18, 37],\n [6, -32, 4, 42, 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[[-14, 26, 33, 4, 22],\n [24, 24, 12, -24, 18],\n [36, 20, 2, -32, 14],\n [-50, -10, 15, 40, -5],\n [-4, -4, -2, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[36, 18, 30, -18, -30],\n [-6, -3, -5, 3, 5],\n [36, 18, 30, -18, -30],\n [0, 0, 0, 0, 0],\n [30, 15, 25, -15, -25]]?\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, -15, 10, 10],\n [12, 4, 6, -4, -4],\n [0, 0, 0, 0, 0],\n [-6, -2, -3, 2, 2],\n [-24, -8, -12, 8, 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 5x5 matrix:\n[[4, -6, 0, 0, -6],\n [-10, 15, 0, 0, 15],\n [-6, 9, 0, 0, 9],\n [0, 0, 0, 0, 0],\n [-2, 3, 0, 0, 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[[-20, -45, -9, 12, -9],\n [-8, -34, 19, 11, -23],\n [-2, 18, -14, -14, 26],\n [-14, -37, 3, 10, -13],\n [-10, -22, 0, 4, -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[[8, -32, -26, -20, 30],\n [-40, -8, 4, 44, -24],\n [-56, -16, 2, 60, -30],\n [26, 10, 1, -27, 12],\n [36, 12, 0, -38, 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 5x5 matrix:\n[[-10, 6, -26, 7, -25],\n [8, 12, 16, 20, -8],\n [27, 48, -21, 53, -26],\n [-3, -21, 11, -22, 14],\n [-16, -48, 8, -45, 5]]\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, 6, 27, 0, 18],\n [-5, 30, 30, -30, 15],\n [-5, 10, 17, -8, 10],\n [-15, 30, 51, -24, 30],\n [16, 4, -31, -14, -23]]\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[[-48, 18, -9, 38, -67],\n [-39, -14, 2, 58, -18],\n [20, 78, -34, -24, -18],\n [-57, -12, 0, 78, -36],\n [-17, -43, 20, 8, -6]]\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[[9, -27, -17, 12, -70],\n [15, 15, 25, 10, 53],\n [6, 6, 12, -6, 20],\n [-15, -15, 30, 19, 47],\n [-44, -12, -8, 28, 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[[-1, 3, 13, -1, 18],\n [-13, -11, -21, -3, -6],\n [-16, -7, -1, -5, 24],\n [-31, -17, -15, -9, 30],\n [6, -3, -21, 3, -36]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-26, 7, 14, 15, 2],\n [18, 4, -32, -22, 3],\n [-14, 13, -14, -3, 2],\n [1, 8, -9, -4, -22],\n [7, -29, 47, 21, 23]]\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[[-44, 6, -9, -20, -41],\n [-12, 60, 31, 49, 38],\n [-4, 36, 70, 14, 20],\n [-24, 21, 22, 2, -11],\n [-42, 31, -14, 23, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 16, 4, -12, 4],\n [-1, 5, 0, 6, -10],\n [-49, -21, 38, -40, -64],\n [-32, -14, 25, -27, -41],\n [-53, -29, 37, -33, -71]]\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[[-8, 35, -56, 1, -29],\n [12, 16, -22, -4, -6],\n [-12, 4, -2, -28, 32],\n [16, -4, 16, -32, 46],\n [-4, -39, 58, 9, 18]]\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[[-2, 1, -2, 5, 0],\n [2, -4, -16, -8, -12],\n [-1, 3, 14, 5, 10],\n [-2, 4, 16, 8, 12],\n [-10, 5, -10, 25, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[20, 20, 12, -12, -16],\n [0, 0, 0, 0, 0],\n [-20, -20, -12, 12, 16],\n [30, 30, 18, -18, -24],\n [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[[20, 15, -15, 5, 0],\n [-12, -9, 9, -3, 0],\n [-12, -9, 9, -3, 0],\n [-20, -15, 15, -5, 0],\n [-16, -12, 12, -4, 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[[3, 3, 5, -6, 5],\n [-18, -18, -30, 36, -30],\n [3, 3, 5, -6, 5],\n [18, 18, 30, -36, 30],\n [-3, -3, -5, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-24, -44, 4, 60, 36],\n [25, 13, -7, 13, 41],\n [1, 25, -31, -21, 17],\n [67, 28, -19, -4, 10],\n [-67, -27, 14, 8, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[2, -6, 6, 6, -4],\n [-12, -36, 28, 4, -8],\n [-7, -6, 3, -6, 2],\n [12, 18, -12, 6, 0],\n [27, 36, -23, 16, -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[[6, -6, 3, 6, -15],\n [-6, 6, -3, -6, 15],\n [6, -6, 3, 6, -15],\n [-2, 2, -1, -2, 5],\n [10, -10, 5, 10, -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[[10, -20, -40, 2, 0],\n [17, 12, -40, -3, -27],\n [-24, 16, 40, -5, 7],\n [11, 11, -5, 23, -28],\n [13, -29, -31, 42, -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[[-24, -12, 36, 24, -6],\n [-4, -2, 6, 4, -1],\n [8, 4, -12, -8, 2],\n [-16, -8, 24, 16, -4],\n [8, 4, -12, -8, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, 5, -4, 5, 5],\n [3, -15, 12, -15, -15],\n [-6, 30, -24, 30, 30],\n [3, -15, 12, -15, -15],\n [-1, 5, -4, 5, 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[[-1, -14, -3, 4, 6],\n [-10, 1, 2, -4, 4],\n [-27, 37, 39, -44, 4],\n [-1, -36, -7, 10, 15],\n [23, -13, -11, 16, -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[[20, 20, 4, -20, 24],\n [-25, -25, -5, 25, -30],\n [-5, -5, -1, 5, -6],\n [-30, -30, -6, 30, -36],\n [-30, -30, -6, 30, -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[[3, 5, -15, -29, 5],\n [-3, -23, 12, 11, 10],\n [-48, -12, 50, -8, 40],\n [8, 16, -20, -25, -8],\n [0, 6, -1, -9, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, -4, -6, -10, 10],\n [3, -12, 9, 33, -30],\n [3, 16, -3, -23, 20],\n [-4, -26, 6, 40, -35],\n [13, 4, 15, 31, -30]]?\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 5x5 matrix:\n[[12, 23, 4, 14, 12],\n [12, 23, 4, 14, 12],\n [20, 40, 7, 22, 21],\n [12, 33, 6, 6, 18],\n [24, 36, 6, 36, 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[[4, 8, -8, -2, 8],\n [-2, -4, 4, 1, -4],\n [8, 16, -16, -4, 16],\n [-8, -16, 16, 4, -16],\n [-2, -4, 4, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 14, -16, 36, 12],\n [0, 16, 16, -24, 0],\n [1, -17, -22, 35, 2],\n [2, 14, 4, -2, 4],\n [-3, 7, 22, -39, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, -20, -12, 12, 0],\n [-18, -22, -14, 6, 2],\n [0, -2, 2, 30, -8],\n [-10, -10, -10, -30, 10],\n [4, 3, 5, 27, -8]]\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[[39, 1, 30, -11, -14],\n [54, -8, 26, -11, -11],\n [-21, -5, -23, 10, 13],\n [1, 13, 27, 12, 1],\n [49, -17, 5, -15, -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[[-6, 24, 18, 18, 0],\n [-2, 8, 6, 6, 0],\n [2, -8, -6, -6, 0],\n [-1, 4, 3, 3, 0],\n [2, -8, -6, -6, 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 5x5 matrix:\n[[18, -24, -13, -37, -19],\n [7, -2, 18, 43, 50],\n [26, -13, -5, -33, -10],\n [-16, 5, 6, 22, 7],\n [19, -32, -15, -32, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-33, 2, 6, 22, 26],\n [3, -15, -31, -51, -32],\n [27, -23, -13, -34, -73],\n [48, 16, 4, 2, 30],\n [48, -33, 3, 11, -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[[11, 12, -2, 22, 7],\n [-28, -25, 28, -2, 12],\n [-35, -32, 31, -12, 10],\n [5, -13, 4, 28, -9],\n [12, -21, -24, -18, -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 5x5 matrix:\n[[-15, -23, -22, 44, 34],\n [44, -64, 16, 0, 4],\n [-29, 31, -19, 12, 5],\n [-35, 61, -34, -4, -18],\n [46, -22, 16, -40, -36]]\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[[17, -19, 33, -4, 1],\n [-26, -2, -16, 30, -10],\n [16, -7, -11, 4, 0],\n [49, 26, -4, -70, 27],\n [-42, -22, 10, 56, -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[[-7, -25, -1, 23, 4],\n [5, 9, 20, 2, -9],\n [15, 51, 46, -5, 11],\n [9, 27, 39, -24, -60],\n [3, 5, 37, 16, -14]]?\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[[-31, 12, 20, -19, 4],\n [54, -6, -10, 20, -16],\n [-9, -21, -35, 16, 16],\n [-26, -24, -40, 14, 24],\n [8, 15, 25, -11, -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[[-11, -22, -9, -29, 0],\n [-24, -26, -9, -42, 18],\n [8, -30, -46, 10, 12],\n [32, -12, -17, 21, -12],\n [-53, -5, 18, -62, -18]]\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, -20, 20, -20, 25],\n [20, -16, 16, -16, 20],\n [15, -12, 12, -12, 15],\n [30, -24, 24, -24, 30],\n [25, -20, 20, -20, 25]]?\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 5x5 matrix:\n[[19, -56, 19, -8, -49],\n [-23, 28, -23, -14, 11],\n [15, -14, 1, 16, -43],\n [-15, 24, 36, 26, 21],\n [-18, 40, -80, -41, 29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-24, 36, 30, 54, -42],\n [-14, 34, 22, 48, -30],\n [-5, -25, -5, -30, 5],\n [-32, -4, 22, 6, -34],\n [17, 7, -10, 3, 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 5x5 matrix:\n[[-23, 50, 22, 60, -10],\n [-15, 28, 42, 19, 14],\n [56, 14, -22, -38, 36],\n [-31, -4, -8, 56, -38],\n [-28, -2, -26, 49, -46]]\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[[-50, -5, 35, -10, -15],\n [56, 2, -37, 13, 15],\n [-28, 8, 13, -11, -3],\n [52, -2, -32, 14, 12],\n [-46, -1, 30, -11, -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[[26, 29, -22, -31, 30],\n [8, 28, -42, -36, 23],\n [-10, -22, 26, 17, -4],\n [-4, 20, -40, -22, 2],\n [0, -3, 6, 6, -5]]\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 5x5 matrix:\n[[15, -40, 35, 15, -15],\n [-12, 20, -24, -12, 10],\n [3, -26, 13, 3, -6],\n [9, -42, 27, 9, -12],\n [12, -8, 20, 12, -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 5x5 matrix:\n[[-1, -1, -4, -3, -1],\n [-2, -2, -8, -6, -2],\n [-3, -3, -12, -9, -3],\n [-3, -3, -12, -9, -3],\n [-5, -5, -20, -15, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[24, -15, -9, -14, -5],\n [3, -5, 2, -3, -5],\n [-27, 25, 2, 19, 17],\n [12, -10, -2, -8, -6],\n [-45, 45, 0, 33, 33]]\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, -6, 18, 8, -8],\n [-8, 3, -27, 14, 17],\n [50, 6, 1, -38, -10],\n [0, -18, 45, 6, -28],\n [22, 12, 3, -34, -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[[0, 0, 0, 0, 0],\n [-20, 20, 30, 30, 5],\n [-12, 12, 18, 18, 3],\n [-24, 24, 36, 36, 6],\n [-12, 12, 18, 18, 3]]\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[[3, 3, -24, -21, 18],\n [10, 18, -4, 6, 8],\n [-24, -44, 2, -22, -14],\n [-1, -5, -30, -31, 20],\n [10, 18, -4, 6, 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[[5, 30, -31, -15, -19],\n [16, -27, 14, 10, -12],\n [10, -40, 6, -10, 4],\n [13, -28, -6, -15, -5],\n [29, -33, -44, -45, -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[[-59, 7, 15, -6, 17],\n [-4, -13, 11, -31, -38],\n [-51, -12, -40, 30, 2],\n [-4, -34, 18, 10, -6],\n [34, -17, 49, -19, -7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, -32, -27, 20, -3],\n [-24, 8, -12, 20, -8],\n [-16, 32, 12, 0, -4],\n [6, -2, 3, -5, 2],\n [-48, -24, -54, 60, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-13, 22, -31, -1, 31],\n [5, -10, 14, 1, -5],\n [-48, 16, -17, -55, 6],\n [-63, 14, -10, -63, 15],\n [12, -14, 25, 34, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 22, -27, 12, -5],\n [2, -27, 7, 5, 21],\n [-6, -29, 26, 19, -6],\n [-13, 11, 0, -46, -1],\n [-24, -61, 32, -24, -4]]\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, 18, -15, -3, -3],\n [-4, 24, -20, -4, -4],\n [4, -24, 20, 4, 4],\n [2, -12, 10, 2, 2],\n [4, -24, 20, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[33, 30, 21, -7, -6],\n [6, -6, 14, -14, -10],\n [18, -18, 42, -42, -30],\n [15, 30, -5, 15, 10],\n [6, -15, 22, -24, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 4, 0, -4, 0],\n [16, 16, 0, -16, 0],\n [16, 16, 0, -16, 0],\n [4, 4, 0, -4, 0],\n [-20, -20, 0, 20, 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 5x5 matrix:\n[[12, -24, 12, 16, 12],\n [-12, 24, -12, -16, -12],\n [6, -12, 6, 8, 6],\n [18, -36, 18, 24, 18],\n [12, -24, 12, 16, 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[[-18, -30, -40, 34, -33],\n [15, 25, 30, -30, 30],\n [6, 10, -4, -20, 24],\n [-18, -30, -24, 42, -45],\n [-3, -5, 10, 14, -18]]\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, -31, -1, -26, -8],\n [38, 26, 14, 24, -4],\n [10, 2, -16, -1, 3],\n [27, 17, 11, 16, -2],\n [-30, -6, -6, -6, -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 5x5 matrix:\n[[-12, 36, -12, -24, 0],\n [4, -12, 4, 8, 0],\n [-8, 24, -8, -16, 0],\n [4, -12, 4, 8, 0],\n [8, -24, 8, 16, 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[[5, -2, 4, 3, -1],\n [-30, 12, -24, -18, 6],\n [-20, 8, -16, -12, 4],\n [-5, 2, -4, -3, 1],\n [-20, 8, -16, -12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[33, -6, -20, 21, 29],\n [15, -9, 1, -13, 17],\n [20, -8, 0, -26, 23],\n [-3, 14, -13, -6, -12],\n [1, -3, 1, 17, 4]]?\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[[-5, 5, 5, 4, -20],\n [-10, 10, -4, 0, -6],\n [15, 3, 14, -16, 5],\n [20, -25, 33, 20, -53],\n [20, -29, 25, 20, -37]]\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, 24, 1, -24, 38],\n [-5, -1, 21, -22, 20],\n [26, 28, -39, 1, 14],\n [-1, 10, 9, -22, 29],\n [-11, 8, 15, 2, 5]]\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[[5, 2, 6, 0, 2],\n [25, 10, 30, 0, 10],\n [20, 8, 24, 0, 8],\n [5, 2, 6, 0, 2],\n [10, 4, 12, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-13, -16, 25, -22, -38],\n [4, 52, 33, -18, -10],\n [9, 50, 9, 6, 24],\n [-7, -7, -16, 1, 7],\n [6, -6, -16, 4, 6]]?\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, -6, -12, -18, -6],\n [6, -6, -12, -18, -6],\n [-2, 2, 4, 6, 2],\n [-4, 4, 8, 12, 4],\n [-2, 2, 4, 6, 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 5x5 matrix:\n[[12, 4, -4, -4, 8],\n [6, -24, -30, -24, -12],\n [-32, -2, 20, 18, -16],\n [-12, -17, -10, -7, -16],\n [18, 6, -6, -6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-37, -31, -9, 39, 33],\n [25, 46, 18, 7, -32],\n [-24, -23, -17, 38, 63],\n [-29, -9, 1, 19, -5],\n [-25, 5, 11, 59, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[20, -10, 10, -10, 15],\n [16, -8, 8, -8, 12],\n [-24, 12, -12, 12, -18],\n [-12, 6, -6, 6, -9],\n [24, -12, 12, -12, 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[[-8, 40, 4, -32, -32],\n [56, -16, 5, 26, -7],\n [-12, 36, 3, -30, -27],\n [-24, 48, 3, -42, -33],\n [4, 4, 1, -2, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-47, -6, 17, -26, -1],\n [-54, -1, 13, -16, -4],\n [-13, 30, -11, 15, -7],\n [-64, -42, 52, -79, -10],\n [41, -15, -2, 6, -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[[6, -28, 12, 30, 33],\n [6, -13, 3, 12, 15],\n [12, -26, 6, 24, 30],\n [2, -16, 8, 18, 19],\n [-12, 11, 3, -6, -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[[27, 36, 12, 33, -27],\n [-19, -16, -10, -17, 26],\n [-14, 4, -10, -2, 31],\n [-1, 8, -2, 5, 8],\n [-1, -4, 0, -3, -1]]?\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, -16, 25, 25, -29],\n [18, 16, -25, -25, 29],\n [-18, -30, 21, 39, -33],\n [4, 30, 2, -32, 14],\n [18, -12, -33, 3, 21]]?\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[[16, -12, -8, -4, 8],\n [24, -18, -12, -6, 12],\n [-12, 9, 6, 3, -6],\n [16, -12, -8, -4, 8],\n [-20, 15, 10, 5, -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 5x5 matrix:\n[[-2, -30, 7, 1, 56],\n [-6, 32, -17, -5, -59],\n [-6, -34, 3, 9, 51],\n [-30, 20, -26, -11, -10],\n [14, -7, -8, 10, -44]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[15, 10, -36, -7, -11],\n [-3, 1, 9, 5, 4],\n [15, 0, -42, -19, -17],\n [0, -30, -18, -36, -18],\n [0, -5, -3, -6, -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[[-26, -26, -18, 2, -18],\n [-14, 4, -5, 5, 26],\n [40, 22, 23, -7, -8],\n [20, 24, 16, -4, 20],\n [62, 28, 35, -15, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[64, -42, -15, 20, -50],\n [-17, -2, -26, -29, 14],\n [2, -11, -6, -9, 19],\n [-11, 83, 56, 24, 36],\n [0, 12, 11, -6, 46]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[7, 49, 20, -8, 31],\n [-8, -20, -25, 12, -18],\n [-14, 28, 20, -22, -4],\n [9, -39, 20, -10, -9],\n [-43, 11, -15, -16, -45]]\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, -64, 34, 6, 58],\n [-34, -26, -13, 36, 3],\n [-21, 16, -22, 39, -28],\n [30, -20, 29, -27, 33],\n [-33, 18, -30, 24, -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[[-8, 20, 12, -8, -24],\n [-2, 5, 3, -2, -6],\n [10, -25, -15, 10, 30],\n [-6, 15, 9, -6, -18],\n [10, -25, -15, 10, 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[[-11, -21, 16, -11, -8],\n [20, 7, -10, -4, 48],\n [27, 10, -13, 7, 54],\n [-6, -62, 16, 26, -32],\n [23, -15, 0, 13, 46]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[2, -5, 2, 1, 0],\n [-6, 15, -6, -3, 0],\n [0, 0, 0, 0, 0],\n [12, -30, 12, 6, 0],\n [2, -5, 2, 1, 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[[12, 0, -12, 3, 6],\n [-24, 0, 24, -6, -12],\n [-8, 0, 8, -2, -4],\n [-20, 0, 20, -5, -10],\n [4, 0, -4, 1, 2]]\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[[-7, -4, 25, 15, -10],\n [-8, 4, 8, 12, -8],\n [5, 10, -35, -15, 10],\n [15, -15, 3, -18, 12],\n [-6, 3, 6, 9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[30, -8, -15, -16, 24],\n [-23, 0, -6, 12, -9],\n [19, -41, -45, -6, 60],\n [8, 9, 10, 1, 12],\n [14, 2, -20, -10, 6]]\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 5x5 matrix:\n[[-13, 26, 22, -26, -6],\n [-13, 30, -1, -17, 19],\n [21, -22, 17, -1, -18],\n [-4, -20, -62, 54, 8],\n [-16, 22, -42, 14, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-30, 0, 20, 30, 30],\n [0, 0, 0, 0, 0],\n [-6, 0, 4, 6, 6],\n [0, 0, 0, 0, 0],\n [-18, 0, 12, 18, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, 4, -12, -4, 12],\n [12, -6, 18, 6, -18],\n [-16, 8, -24, -8, 24],\n [-4, 2, -6, -2, 6],\n [-12, 6, -18, -6, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-24, -16, -19, 36, -7],\n [-26, -48, -78, 70, 8],\n [21, -2, -24, -5, 3],\n [-51, -33, -2, 10, 0],\n [-16, 11, 49, -23, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, 11, -66, -25, -40],\n [-18, 18, -12, 1, -5],\n [-1, -9, 9, 1, 5],\n [1, 19, -33, -6, -20],\n [-21, 19, -27, -19, -7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[31, 14, 14, -32, -33],\n [31, 14, 14, -32, -33],\n [15, 12, -6, 6, -9],\n [-50, -31, -2, 17, 42],\n [35, 19, 8, -23, -33]]\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, 0, 9, 15, -6],\n [-12, 0, 6, 10, -4],\n [0, 0, 0, 0, 0],\n [-12, 0, 6, 10, -4],\n [-12, 0, 6, 10, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[11, 12, -33, -16, -32],\n [34, -24, -6, -32, -32],\n [-19, 27, -18, 14, 3],\n [-10, 33, -39, 2, -19],\n [28, -21, -3, -26, -25]]\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[[-58, -28, -14, 60, 28],\n [-9, -28, -13, -2, -7],\n [13, 25, -79, -26, 13],\n [-39, -22, -55, 23, 22],\n [-24, -30, 0, 17, 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[[16, 16, 4, 12, 8],\n [14, 9, -29, -12, -18],\n [-2, -1, 6, 3, 4],\n [22, 19, -14, 3, -4],\n [-2, -7, -33, -24, -26]]?\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[[-6, -3, 2, 0, 1],\n [-36, -18, 12, 0, 6],\n [6, 3, -2, 0, -1],\n [-36, -18, 12, 0, 6],\n [24, 12, -8, 0, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, 6, 1, 18, -11],\n [-41, 12, -7, 9, 23],\n [-20, 0, -4, -12, 20],\n [9, -8, 1, -17, 3],\n [26, -2, 5, 10, -23]]?\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 5x5 matrix:\n[[9, -19, -28, -7, -23],\n [51, -17, -8, 22, -25],\n [30, 4, 49, 25, 32],\n [-25, 21, -21, -4, -19],\n [-50, -10, -36, -37, -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[[48, 38, 9, 33, -34],\n [-3, -5, -8, -2, 14],\n [6, 0, -4, 9, -3],\n [-15, 1, 12, -23, 5],\n [-6, -8, -12, -5, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[15, 29, 5, 35, 5],\n [4, -8, -24, -28, -12],\n [-17, 3, 18, 25, -2],\n [-28, -8, -18, -5, -28],\n [-41, -19, 24, 13, 6]]?\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, 4, -31, 15, 50],\n [10, 12, 7, 5, -30],\n [-25, 4, -26, 13, 41],\n [5, -24, 11, -20, 15],\n [-20, 24, -26, 26, 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[[-9, 18, -41, 38, -20],\n [-21, -35, 17, -31, 3],\n [19, -47, 22, -19, -28],\n [10, 60, -16, 36, 10],\n [3, -3, -24, 9, 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[[57, -25, 8, 48, -12],\n [-18, -50, -54, -54, -19],\n [-16, -24, -24, -22, 18],\n [39, -25, 0, 28, -7],\n [1, -4, 1, 2, 12]]?\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 5x5 matrix:\n[[30, -36, 30, -18, -30],\n [-25, 30, -25, 15, 25],\n [-10, 12, -10, 6, 10],\n [10, -12, 10, -6, -10],\n [10, -12, 10, -6, -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[[-2, -2, -3, 13, 25],\n [-11, -11, -7, -3, 12],\n [-5, -12, 8, 21, 31],\n [-30, -33, -8, -14, 13],\n [19, 4, 39, 28, -8]]\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[[-38, 32, -37, -19, 39],\n [-12, 4, 56, 36, 4],\n [-9, 9, -9, 37, -7],\n [-14, 18, 27, 21, -21],\n [-50, 44, -29, -20, 40]]\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, 28, 16, -7, 35],\n [22, 3, 5, 22, 5],\n [26, -20, 19, 34, -51],\n [-7, 8, 26, -36, 42],\n [-16, 7, 13, -27, 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[[-9, 27, 27, 22, 34],\n [39, -6, -6, -9, 13],\n [-36, 9, 9, 11, -7],\n [39, -15, -15, -16, 0],\n [-15, 21, 21, 18, 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[[-13, 5, 10, 23, 11],\n [17, -5, 8, -3, -46],\n [-42, -3, -6, 36, 30],\n [26, 5, 34, 10, -47],\n [-13, -1, -24, -15, 41]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[10, 6, 7, 0, 6],\n [40, 16, 32, -20, 6],\n [42, 30, 27, 12, 36],\n [-18, 2, -19, 32, 18],\n [28, 4, 26, -32, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-10, -24, 28, -1, 18],\n [-46, 11, -11, -10, -13],\n [-20, -21, -15, -36, -33],\n [36, 48, 16, 62, 60],\n [54, 42, 0, 40, 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[[-8, 24, -20, -4, 0],\n [-2, 6, -5, -1, 0],\n [2, 6, 7, 23, 0],\n [-10, 42, -23, 17, 0],\n [12, -48, 28, -16, 0]]?\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, 3, -17, 12, 23],\n [-1, 30, -11, 5, 17],\n [-10, -60, -22, 34, 10],\n [-35, 12, -3, 3, 26],\n [-34, -72, -22, 34, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 8, -12, -12, 0],\n [-2, -4, 6, 6, 0],\n [-5, -10, 15, 15, 0],\n [-3, -6, 9, 9, 0],\n [-2, -4, 6, 6, 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[[-2, 6, -10, 40, 6],\n [8, -9, -10, 5, 6],\n [13, -12, -25, 37, 15],\n [-22, 27, 20, 11, -12],\n [17, -21, -15, -10, 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[[12, -8, 20, 6, -48],\n [-6, 1, -1, -6, -6],\n [-12, 8, -20, -6, 48],\n [60, -14, 22, 56, 20],\n [30, -6, 8, 29, 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[[-15, -25, 15, 0, -5],\n [-9, -15, 9, 0, -3],\n [12, 20, -12, 0, 4],\n [-15, -25, 15, 0, -5],\n [18, 30, -18, 0, 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[[11, 3, 43, 9, 20],\n [-41, -30, -43, 31, 18],\n [-10, 24, 22, -5, -15],\n [21, -15, -30, -5, -15],\n [23, -9, -23, -8, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-10, 50, -67, 18, 3],\n [-1, 2, 53, 6, 12],\n [18, -20, -2, 15, 9],\n [3, 24, 9, 45, 27],\n [26, -54, 51, -12, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[5, -6, 1, -1, -6],\n [20, -24, 4, -4, -24],\n [-30, 36, -6, 6, 36],\n [15, -18, 3, -3, -18],\n [20, -24, 4, -4, -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[[20, -16, -12, 4, 20],\n [5, -4, -3, 1, 5],\n [25, -20, -15, 5, 25],\n [15, -12, -9, 3, 15],\n [5, -4, -3, 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[[-25, 30, -20, -10, 25],\n [20, -24, 16, 8, -20],\n [30, -36, 24, 12, -30],\n [25, -30, 20, 10, -25],\n [25, -30, 20, 10, -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[[-15, 44, 44, 6, 0],\n [3, -49, -16, -14, 20],\n [-27, 6, 63, -16, 27],\n [-14, 63, 44, 28, -36],\n [12, -21, -30, -4, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[22, 18, 18, -2, 18],\n [37, 13, 13, -12, 51],\n [-15, -35, -35, -10, 15],\n [-28, -32, -32, -2, -12],\n [-38, -22, -22, 8, -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[[50, -46, 18, -18, 34],\n [67, -61, 7, -1, 45],\n [-11, 15, 13, -11, -33],\n [-42, 41, -26, -20, -14],\n [-9, 21, -33, -3, -33]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, -6, 12, -12, -7],\n [-5, -10, 21, -20, -12],\n [0, 0, 0, 0, 0],\n [30, -10, 42, -20, -19],\n [18, 12, -18, 24, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-67, -10, 34, 43, 10],\n [19, -29, 22, 29, 29],\n [-47, -12, 26, 23, 12],\n [36, -14, 8, 36, 14],\n [35, -36, 22, 25, 36]]\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, 4, -2, -5, -14],\n [-1, 19, 4, -2, 28],\n [0, -16, -8, 0, -30],\n [3, -9, 2, 1, -14],\n [-39, 21, -48, 0, 54]]\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 5x5 matrix:\n[[-15, -10, -30, 0, 30],\n [-12, -8, -24, 0, 24],\n [15, 10, 30, 0, -30],\n [-18, -12, -36, 0, 36],\n [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[[6, 6, 28, 30, -2],\n [0, -6, -27, -30, 6],\n [-30, 2, 4, 10, -22],\n [30, 2, 14, 10, 18],\n [24, 2, 13, 10, 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 5x5 matrix:\n[[7, -21, 34, 30, -20],\n [4, 6, -14, -15, 13],\n [-21, 21, -24, -15, 3],\n [-1, 23, -42, -40, 30],\n [-9, -3, 12, 15, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 4, 8, 4, -8],\n [0, -3, -6, -3, 6],\n [0, 1, 2, 1, -2],\n [0, 5, 10, 5, -10],\n [0, 5, 10, 5, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 3, 21, -9, 10],\n [16, -5, -13, -7, -24],\n [8, -6, -24, 0, -26],\n [0, -1, -5, 1, -4],\n [-20, 5, 10, 10, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[14, 1, -20, 18, 21],\n [-11, 14, 19, 22, -5],\n [36, -18, -56, -4, 38],\n [11, -14, -19, -22, 5],\n [-7, 13, 13, 24, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0, 0],\n [-18, -26, 21, 5, 20],\n [-4, -3, 3, 0, 0],\n [4, -2, 0, 2, 8],\n [-4, 2, 0, -2, -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 5x5 matrix:\n[[13, -18, -4, -17, -31],\n [0, 0, 0, 0, 0],\n [4, -8, 0, -6, -10],\n [-11, 14, 4, 14, 26],\n [-13, 18, 4, 17, 31]]\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[[35, -30, 9, 24, 27],\n [10, 8, 15, -18, 16],\n [-5, -14, -15, 24, -13],\n [35, -34, 6, 30, 25],\n [-20, 0, -18, 12, -24]]\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, 13, 22, 30, 27],\n [6, -32, -26, -2, -12],\n [-4, -5, -14, -27, -18],\n [-33, -39, -21, 21, 15],\n [-25, -26, -23, -10, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, -16, 11, -15, -22],\n [-4, 3, -3, 0, 1],\n [8, -6, 6, 0, -2],\n [2, -33, 24, -27, -41],\n [-6, -20, 13, -21, -30]]?\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 5x5 matrix:\n[[-21, -35, -3, -39, 4],\n [37, 25, -51, -5, -8],\n [-23, -32, -4, -45, 6],\n [-2, -50, -29, -31, -6],\n [-25, 1, 29, 1, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0, 0],\n [-12, 30, 6, 18, -18],\n [-6, 15, 3, 9, -9],\n [10, -25, -5, -15, 15],\n [12, -30, -6, -18, 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[[-1, 32, 14, 30, -35],\n [-3, 1, -15, -5, 9],\n [4, -3, 19, 5, -10],\n [0, 0, 0, 0, 0],\n [-1, -13, -13, -15, 19]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, -20, -18, 36, -3],\n [7, -17, -23, 51, -5],\n [-11, -17, -3, 17, 24],\n [54, -6, 6, 12, -24],\n [18, -22, 10, 24, 24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-16, 0, -1, 6, 15],\n [10, -6, 2, 12, 4],\n [6, 14, -4, -40, -22],\n [-30, 12, 21, -24, -27],\n [43, -14, 42, 13, -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[[14, -60, -52, 60, -3],\n [72, -42, 6, 48, 36],\n [20, -28, -12, 32, 25],\n [-9, 1, -17, 24, 3],\n [23, 25, 23, 8, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-18, 15, 15, 15, -9],\n [-30, 25, 25, 25, -15],\n [-30, 25, 25, 25, -15],\n [24, -20, -20, -20, 12],\n [30, -25, -25, -25, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, 20, -1, 4, -48],\n [-9, -54, -13, 38, 42],\n [-45, -14, -6, 10, 18],\n [42, -2, 4, -4, -24],\n [53, -24, -8, 33, -3]]\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[[-30, 52, 32, -10, 44],\n [40, -36, 59, 32, -18],\n [7, 6, 31, 25, -12],\n [-13, 15, 46, -39, 36],\n [25, -9, -6, 67, 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[[15, -15, 25, -20, 35],\n [5, -9, 5, -16, 19],\n [-1, 3, 0, 6, -6],\n [-9, 9, -15, 12, -21],\n [3, -9, 0, -18, 18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -12, -3, -21, 9],\n [17, 4, 6, 12, -3],\n [14, 16, 6, 30, -12],\n [24, -24, 6, -30, 18],\n [-11, 8, -3, 9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, 3, -6, 8, 7],\n [-26, 29, -3, 26, -24],\n [0, -14, -12, 0, 34],\n [38, -37, 9, -38, 22],\n [50, -45, 15, -50, 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[[46, 47, -61, -29, -20],\n [-40, -28, 16, 10, 30],\n [48, 53, -51, -14, -45],\n [-60, -40, 24, 18, 40],\n [-10, -25, 43, 47, -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[[-8, -40, 4, -8, 34],\n [-28, -34, -18, 0, 1],\n [-25, -37, -11, 19, 11],\n [-7, -2, -11, -29, -11],\n [-33, -67, -11, 7, 33]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[22, 3, 18, -12, 34],\n [-21, -23, -16, 30, -57],\n [-39, 14, -46, -6, 17],\n [9, -26, 6, 18, -7],\n [-26, -29, -22, 36, -62]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, -2, 10, 2, -2],\n [-9, 11, -25, -1, 36],\n [-15, 2, -16, -4, -3],\n [22, 5, 11, 7, 35],\n [19, -3, 21, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[24, -16, -4, -16, -24],\n [30, -20, -5, -20, -30],\n [30, -20, -5, -20, -30],\n [-6, 4, 1, 4, 6],\n [12, -8, -2, -8, -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[[14, -10, -12, -41, -27],\n [-22, -17, 31, -12, 38],\n [23, 31, -47, 48, -22],\n [22, 13, -18, 17, -7],\n [-7, -16, 27, -32, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[16, 16, 14, -16, -12],\n [1, 2, -16, 5, -1],\n [2, 2, 17, -8, -2],\n [8, 18, 6, -14, -14],\n [-13, -23, -18, 22, 18]]?\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 5x5 matrix:\n[[23, -29, 38, 12, -39],\n [6, -38, 26, 34, 32],\n [12, -6, 15, -3, -33],\n [37, -29, 32, 19, -41],\n [-10, 12, 9, -27, -41]]\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, 46, 2, -32, 40],\n [17, -7, 19, -4, -4],\n [-14, -6, -26, 16, -8],\n [-12, 2, -16, 6, 0],\n [-9, 14, -1, -9, 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 5x5 matrix:\n[[-55, 90, -20, -4, -4],\n [-35, 26, -39, -12, -34],\n [31, -44, -7, -18, -21],\n [45, -39, 11, -18, -5],\n [13, -49, 6, 32, 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[[32, -19, -12, 38, -48],\n [-12, 4, 2, -10, 16],\n [24, -8, -4, 20, -32],\n [-20, -10, 40, 1, 11],\n [-12, 19, 40, -33, 23]]\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[[-13, -3, -2, -8, 7],\n [-7, 1, 20, 18, -39],\n [19, -1, -3, 9, -49],\n [-9, -1, 18, 16, -49],\n [-38, -8, -5, -23, 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[[46, -1, 25, -16, 5],\n [-6, 6, 22, 49, 66],\n [-15, -13, -11, -15, -29],\n [35, -73, 34, -45, 31],\n [8, 46, -15, 4, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-31, 17, 3, -36, -12],\n [92, 36, -44, 59, 6],\n [-30, -39, 23, 0, -5],\n [-88, -32, 40, -53, -26],\n [52, 67, -47, 8, -5]]\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, -12, 3, -15, 3],\n [6, 6, 9, 9, 57],\n [-49, -25, 48, -4, -21],\n [-5, -45, -31, 33, -22],\n [2, 42, -29, 41, 31]]\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, 10, 20, 8, -22],\n [-40, -19, -6, -5, 44],\n [-48, -21, -9, 24, 45],\n [48, 45, 29, -15, 22],\n [43, 38, -18, -14, -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[[26, -12, -11, -13, 41],\n [-31, -45, -20, -2, 59],\n [43, -11, -53, -40, 72],\n [55, 31, 28, -1, -21],\n [-29, -1, -13, 1, -10]]\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 5x5 matrix:\n[[-20, 0, 16, 19, 10],\n [-6, 2, 5, 5, 3],\n [-2, 14, 3, -3, 1],\n [22, -14, -19, -16, -11],\n [-12, -36, 6, 24, 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[[28, 24, 24, 26, -52],\n [16, 18, 16, 14, -32],\n [-4, 18, 8, -8, -4],\n [-14, 18, 4, -19, 10],\n [-12, 39, 16, -21, -4]]\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[[30, -18, -24, -30, -36],\n [-25, 15, 20, 25, 30],\n [-25, 15, 20, 25, 30],\n [30, -18, -24, -30, -36],\n [-20, 12, 16, 20, 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[[0, 45, -27, 0, 27],\n [19, 37, -25, -25, 30],\n [-41, -68, 55, 5, -25],\n [4, 22, -18, 20, -2],\n [-13, 41, -28, 49, -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[[-10, 8, 10, 6, 12],\n [30, -24, -30, -18, -36],\n [0, 0, 0, 0, 0],\n [-10, 8, 10, 6, 12],\n [25, -20, -25, -15, -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 5x5 matrix:\n[[-22, 0, 6, -20, -40],\n [-31, 36, -4, -38, -18],\n [-25, 37, -7, -30, -9],\n [18, 23, -15, 16, 51],\n [-17, 26, -6, -18, -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[[50, 42, -38, -20, 11],\n [-21, -20, 10, 11, -2],\n [-6, 26, -13, 3, -16],\n [8, -20, 47, -29, -68],\n [-6, 4, 43, -19, -52]]\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 5x5 matrix:\n[[-4, 11, 11, 21, 0],\n [4, -20, -11, -12, 9],\n [0, 27, 21, 21, -18],\n [30, 20, 33, 4, -53],\n [-33, -9, -30, -3, 48]]\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],\n [-14, -8, 16, 24, 0],\n [-4, -10, 26, 30, -6],\n [-18, 0, -8, 0, 8],\n [-34, 14, -54, -42, 26]]\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, -23, -30, -31, 12],\n [-10, 2, -4, 24, 26],\n [20, -4, 4, -34, -38],\n [49, -21, -20, -49, -26],\n [-4, -16, -24, -17, 33]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -4, -2, -12, 4],\n [-17, 7, 9, 33, -9],\n [-5, -5, 3, -3, 3],\n [-6, -14, 4, -18, 10],\n [-7, 17, 3, 39, -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 5x5 matrix:\n[[-39, -36, -36, 45, 30],\n [-18, -22, 6, 24, -12],\n [30, 30, 18, -36, -12],\n [10, 5, 27, -9, -28],\n [38, 32, 48, -42, -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 5x5 matrix:\n[[-35, -15, -47, 17, 36],\n [0, 11, -9, 12, -4],\n [-3, 22, -21, 19, -7],\n [15, 1, 24, -11, -13],\n [10, -4, 25, -32, -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[[0, 0, 0, 0, 0],\n [13, 20, -22, -7, 11],\n [4, -20, 24, -16, 8],\n [0, 34, -40, 18, -6],\n [-12, -25, 28, 3, -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[[-32, -24, -12, -18, 27],\n [-66, -42, -18, -48, 66],\n [21, 17, 1, 2, -6],\n [-21, 3, 43, -5, 1],\n [78, 46, -2, 42, -58]]\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, 24, 8, -20, -12],\n [0, 0, 0, 0, 0],\n [0, -6, -2, 5, 3],\n [0, 18, 6, -15, -9],\n [0, -6, -2, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-32, 36, -16, -45, 36],\n [-36, 24, 18, -6, 42],\n [-10, 33, -32, -53, 12],\n [10, 30, -22, -52, 6],\n [-3, 27, -6, -28, 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[[-12, -8, -15, -7, -4],\n [17, 6, 10, 22, 9],\n [-25, 9, -40, 0, -20],\n [14, -30, 10, 10, 24],\n [-14, 0, -5, -21, -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 5x5 matrix:\n[[-3, 3, 4, 2, -3],\n [-9, 9, 12, 6, -9],\n [-9, 9, 12, 6, -9],\n [-3, 3, 4, 2, -3],\n [6, -6, -8, -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[[14, 3, 18, 49, -1],\n [-32, -34, -44, -14, 34],\n [-24, -28, -38, 53, 45],\n [-1, -2, -4, 32, 11],\n [28, 26, 40, 4, -32]]\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 5x5 matrix:\n[[8, 8, 4, 2, 6],\n [54, 54, -7, -12, -19],\n [34, 34, 3, -2, 1],\n [4, 4, -10, -8, -18],\n [-24, -24, -4, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-33, 9, 18, 18, 24],\n [-18, 2, -4, -12, 40],\n [-31, 7, 10, 6, 36],\n [22, -10, -31, -42, 21],\n [-29, 13, 40, 54, -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[[-10, 6, -12, 6, 12],\n [1, -15, -18, 15, -3],\n [13, -44, -16, 21, -32],\n [-7, -6, -12, 9, 0],\n [32, -48, 0, 12, -42]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 9, -36, 51, -27],\n [6, 0, -18, 48, 0],\n [-6, 5, -12, 7, -15],\n [-12, 7, -6, -19, -21],\n [-16, 11, -18, -7, -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 5x5 matrix:\n[[-11, 18, 5, -9, -7],\n [17, -34, -15, 23, 5],\n [20, -42, -20, 30, 4],\n [30, -12, 30, -30, 54],\n [-18, -3, -30, 33, -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[[-46, 10, 42, -14, -26],\n [34, -22, -42, -14, 32],\n [-13, -17, -3, -37, 10],\n [-17, -13, 3, -33, 5],\n [5, -23, -21, -35, 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[[6, 2, 40, -4, 50],\n [14, 18, 37, -4, 40],\n [25, 20, 29, 9, 45],\n [-40, -30, 31, -34, 10],\n [-16, -27, 48, -13, 60]]\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, 2, -2, 10, 6],\n [0, 4, -4, 20, 12],\n [0, -5, 5, -25, -15],\n [0, 2, -2, 10, 6],\n [0, -3, 3, -15, -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 5x5 matrix:\n[[-17, -27, 18, 44, -33],\n [0, -10, 2, -7, 11],\n [-11, -6, -6, -19, 24],\n [23, 23, -10, -36, 22],\n [0, 9, 0, -15, 3]]\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[[-9, 40, 8, -11, 36],\n [-18, 42, 16, 26, 36],\n [15, 32, -32, 37, 12],\n [-40, 28, 55, 9, 27],\n [48, -11, -73, 9, -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 5x5 matrix:\n[[4, 3, -1, 1, 2],\n [8, 6, -2, 2, 4],\n [12, 9, -3, 3, 6],\n [12, 9, -3, 3, 6],\n [4, 3, -1, 1, 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 5x5 matrix:\n[[-20, -25, 0, 0, 25],\n [0, 0, 0, 0, 0],\n [-4, -5, 0, 0, 5],\n [-12, -15, 0, 0, 15],\n [8, 10, 0, 0, -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 5x5 matrix:\n[[-24, -14, -41, 35, 1],\n [11, -13, -27, -3, -13],\n [6, -14, -2, -40, 36],\n [14, -26, 20, 10, -46],\n [-5, 1, -20, 36, -32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[20, 10, 36, -2, -37],\n [-5, 10, 26, 18, -67],\n [-7, 6, 14, 14, -45],\n [-3, 6, 10, 43, -15],\n [21, 10, 30, 34, -7]]\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[[25, -81, 44, -58, 15],\n [-9, 18, -61, 2, 13],\n [-17, 12, 11, 8, 1],\n [29, -72, 31, -62, -5],\n [-9, 1, -38, -24, -7]]\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[[-15, -2, 8, -51, 24],\n [15, 6, 53, -29, 77],\n [-18, -6, -37, 3, -57],\n [-7, 1, 32, -58, 52],\n [3, 2, 6, -10, 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[[18, 0, -36, 0, -12],\n [-3, 0, 6, 0, 2],\n [3, 0, -6, 0, -2],\n [6, 0, -12, 0, -4],\n [9, 0, -18, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 18, 14, 4, 10],\n [-8, -42, -30, -20, -18],\n [-26, 30, 32, -28, 34],\n [14, -12, -14, 16, -16],\n [-16, 6, 10, -20, 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[[6, 30, -6, 24, -6],\n [-2, -17, -1, -17, 3],\n [-4, -6, 10, 2, 2],\n [-7, 0, 22, 17, 2],\n [5, 18, -8, 11, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-30, 30, 25, -20, -30],\n [-18, 18, 15, -12, -18],\n [-12, 12, 10, -8, -12],\n [-36, 36, 30, -24, -36],\n [-18, 18, 15, -12, -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 5x5 matrix:\n[[4, 26, -28, 6, 22],\n [30, 0, 3, -30, 21],\n [-8, -13, 22, 4, -6],\n [36, -6, 30, -36, 42],\n [-22, 0, 15, 24, 3]]\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[[-63, 46, 4, 58, 16],\n [55, -32, 3, -5, -13],\n [55, -51, 44, -7, 0],\n [0, -15, -45, -80, -25],\n [-21, 19, -38, -19, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-30, -9, 0, -9, 15],\n [0, -14, -20, -14, -10],\n [24, 3, -6, 3, -15],\n [6, 6, 6, 6, 0],\n [-20, -6, 0, -6, 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[[-36, 24, 6, 24, -36],\n [30, -20, -5, -20, 30],\n [-6, 4, 1, 4, -6],\n [12, -8, -2, -8, 12],\n [-30, 20, 5, 20, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -24, 30, -18, 6],\n [3, 12, -15, 9, -3],\n [2, 8, -10, 6, -2],\n [-5, -20, 25, -15, 5],\n [-1, -4, 5, -3, 1]]\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 5x5 matrix:\n[[-12, 4, 12, 20, 4],\n [6, -2, -6, -10, -2],\n [18, -6, -18, -30, -6],\n [-12, 4, 12, 20, 4],\n [15, -5, -15, -25, -5]]\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, -29, -23, -34, 76],\n [-10, 32, -10, 25, -11],\n [-18, -3, 8, 2, -13],\n [-20, 20, -5, 21, -11],\n [-20, 61, -23, 53, -31]]?\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 5x5 matrix:\n[[4, 0, 24, 24, 12],\n [-12, 6, 27, 30, -6],\n [-14, 4, -18, -16, -22],\n [-24, 10, 21, 26, -22],\n [-14, 4, -18, -16, -22]]\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[[-12, 12, 12, 6, 6],\n [-10, -26, -11, 2, -16],\n [18, -6, -11, -8, -2],\n [-4, -20, -10, 0, -12],\n [-14, 2, 7, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-22, 27, 19, -9, -12],\n [-27, -31, 16, 3, -13],\n [15, -36, -13, 8, 1],\n [-22, -17, 13, 6, 3],\n [16, 24, -11, -10, -5]]\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[[-17, -2, -23, -16, -4],\n [18, -36, -17, 17, 14],\n [-11, 22, 1, -14, -36],\n [-3, -30, -42, -5, -10],\n [22, -17, 4, 19, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[9, -32, -25, 41, -29],\n [-3, -6, -3, 5, -7],\n [-6, 15, 20, -8, 28],\n [-12, -9, -21, 0, -29],\n [6, -9, 5, 22, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, 18, -2, -38, 28],\n [15, -6, -5, -10, -32],\n [0, -6, 0, 10, -12],\n [15, 0, -5, -20, -20],\n [18, 18, -6, -54, 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[[30, -8, -41, -26, -77],\n [-22, -52, 42, 34, 54],\n [-20, 29, -5, -27, 8],\n [30, 21, -11, 0, 5],\n [11, -6, -16, -19, -20]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[33, -24, 6, -11, -5],\n [-3, 4, 6, 1, -1],\n [-24, 7, -42, 8, 12],\n [-12, 6, -12, 4, 4],\n [-33, 14, -42, 11, 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[[22, 34, -59, 3, 41],\n [8, -13, -11, 9, -5],\n [-26, 10, 18, 0, -20],\n [44, 38, -72, -4, 52],\n [-4, -22, 6, 6, 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[[29, 44, 28, 11, 0],\n [31, 33, -1, 4, -57],\n [-5, -28, -30, 14, -10],\n [-56, -11, -28, 20, 14],\n [19, 2, 38, 1, 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[[-16, 8, -32, -20, -12],\n [-12, -15, -29, -69, 21],\n [-13, 20, -24, 13, -60],\n [5, -4, 8, -5, -36],\n [28, -28, 52, -4, 24]]\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[[3, 7, 63, -44, 52],\n [-51, 25, 3, -8, 12],\n [-27, -3, 47, -37, 7],\n [-45, -4, 39, -11, 9],\n [-60, -26, -16, 27, -69]]\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[[-25, 20, 21, -21, -26],\n [9, 10, 19, -18, 13],\n [20, -26, 33, -22, 21],\n [-1, -22, -10, 13, -5],\n [24, -4, -58, 48, 26]]\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 5x5 matrix:\n[[5, 10, -15, 0, -20],\n [3, 12, 5, 12, -16],\n [-7, -29, -14, -30, 38],\n [-7, -23, 0, -18, 34],\n [10, 35, 5, 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[[-13, 0, -7, -3, 14],\n [36, -30, -41, 22, -1],\n [-57, 34, 47, -39, 14],\n [19, 2, -14, 35, -9],\n [6, -1, 19, -18, -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 5x5 matrix:\n[[-12, 24, -10, 40, -40],\n [-40, 15, -39, 20, 41],\n [-45, -37, 12, -13, 14],\n [-56, -3, 5, 32, -1],\n [-3, -37, 15, -25, -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[[-21, 8, -27, -32, -39],\n [-8, -34, 33, -31, -11],\n [-11, 1, 10, 49, 3],\n [-48, -32, 26, 4, -32],\n [-15, 28, -37, 4, -53]]?\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, 44, 50, 2, -20],\n [61, 27, -2, 32, 31],\n [-16, 5, 7, -35, 1],\n [37, 3, -23, 2, 37],\n [-50, -29, -7, -27, -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[[-11, 36, -36, -33, 13],\n [7, -41, 61, 6, -14],\n [16, 11, -12, -22, 40],\n [40, 22, -66, 30, 70],\n [-24, 9, 30, -52, -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 5x5 matrix:\n[[-3, 36, -32, 0, 12],\n [6, 12, 22, -40, -42],\n [9, 0, -26, 36, 38],\n [30, 0, 2, 6, 0],\n [-18, -18, 7, 6, 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[[1, -16, -9, 7, 21],\n [13, -46, -9, 10, 12],\n [-8, 44, 24, -22, -6],\n [3, -42, -33, 28, 20],\n [0, 18, 12, -9, -29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-19, -4, 10, 42, 9],\n [4, -11, 20, -12, -10],\n [-18, 7, 22, 58, 2],\n [-37, -11, 53, 52, -7],\n [39, 23, -57, -96, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-16, -4, -1, -12, 29],\n [1, -5, 31, 34, 5],\n [0, -14, 18, 17, 11],\n [-15, 47, -15, -16, -7],\n [-1, 5, -13, -14, -3]]\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, 3, -3, -6, -12],\n [-19, 24, 2, -22, 9],\n [-29, -8, -8, 0, -33],\n [-26, -4, -6, -2, -34],\n [9, -19, -3, 16, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-24, -8, -34, -4, -20],\n [-52, -18, -74, -3, -42],\n [-20, 24, -13, -33, -6],\n [-30, -5, -40, -9, -23],\n [16, -30, 5, -5, -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[[4, 7, 11, 6, 4],\n [-36, -49, 13, -12, 20],\n [-24, -30, 30, 0, 24],\n [24, 34, 2, 12, -8],\n [32, 46, 8, 18, -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[[38, -18, -4, 11, -6],\n [-38, 8, -19, -6, -17],\n [-14, -18, -40, -8, -23],\n [-16, 4, -12, 3, -17],\n [14, 0, 7, 8, -1]]\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[[-3, -31, -43, -19, -6],\n [-52, 8, -1, 25, -6],\n [12, 51, 32, 16, 19],\n [0, -15, -6, 14, 29],\n [-24, -1, -38, 14, 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[[-8, -30, 3, -5, 12],\n [-8, -30, 3, -5, 12],\n [18, 18, 7, 3, -16],\n [-48, -36, -22, -6, 40],\n [22, -12, 18, -2, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[30, 15, -12, 1, 19],\n [60, 40, 9, 33, 22],\n [42, 19, -21, -6, 28],\n [-54, -29, 7, -4, -25],\n [36, 26, 20, 22, 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[[18, 0, 18, -9, -12],\n [18, 0, 18, -9, -12],\n [0, 0, 0, 0, 0],\n [-30, 0, -30, 15, 20],\n [-24, 0, -24, 12, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[26, 21, -21, 20, -15],\n [11, 11, 0, 13, 23],\n [29, -38, 21, 29, 35],\n [3, -37, 31, 2, 8],\n [22, 10, 10, 20, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[18, 6, 9, -18, 9],\n [18, 6, 9, -18, 9],\n [-36, -12, -18, 36, -18],\n [-6, -2, -3, 6, -3],\n [36, 12, 18, -36, 18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[16, 18, 5, -2, 8],\n [8, -26, -29, -50, -24],\n [-24, -12, 6, 24, 0],\n [26, 28, 7, -5, 12],\n [-4, 18, 19, 32, 16]]\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[[8, -24, 0, 30, 10],\n [21, 27, -9, -45, -21],\n [-54, 22, 14, -10, 6],\n [-66, 18, 18, 0, 12],\n [35, 5, -11, -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 5x5 matrix:\n[[30, -8, 19, 56, -3],\n [-30, 20, -25, -20, -15],\n [18, -18, 18, -6, 18],\n [24, -8, 16, 40, 0],\n [36, -32, 34, 0, 30]]\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 5x5 matrix:\n[[-15, 55, 45, -5, 45],\n [-17, 43, 37, -3, 35],\n [-29, 0, 10, 5, -1],\n [16, -20, -20, 0, -16],\n [-10, 27, 23, -2, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0, 0],\n [-20, -20, -25, -20, 0],\n [20, 20, 25, 20, 0],\n [12, 12, 15, 12, 0],\n [12, 12, 15, 12, 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 5x5 matrix:\n[[-20, -28, 4, -8, 11],\n [-21, -33, 3, -12, 9],\n [-3, -15, -3, -12, -6],\n [41, 61, -7, 20, -20],\n [-32, -40, 8, -8, 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[[4, -2, 4, -1, -4],\n [26, -28, -29, 16, 29],\n [48, -36, 4, 6, -4],\n [12, -12, -10, 6, 10],\n [20, -28, -46, 22, 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[[3, 15, -6, 18, 15],\n [-4, -20, 8, -24, -20],\n [-6, -30, 12, -36, -30],\n [4, 20, -8, 24, 20],\n [-1, -5, 2, -6, -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 5x5 matrix:\n[[18, 4, -7, -11, -15],\n [22, 44, 39, -13, 15],\n [0, 11, 10, -10, -3],\n [6, -6, -15, -15, -25],\n [-20, -24, -7, 39, 33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 38, 62, 48, 0],\n [-5, -53, -44, -44, 26],\n [23, -3, 9, 8, 16],\n [22, -56, -65, -46, 2],\n [24, 4, -19, 0, -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 5x5 matrix:\n[[-5, 18, 16, -3, -30],\n [15, -15, 4, 9, 12],\n [25, -21, 12, 15, 12],\n [-10, 18, 8, -6, -24],\n [25, -18, 16, 15, 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 5x5 matrix:\n[[-34, -17, -20, 10, 12],\n [70, 34, 15, -17, -10],\n [24, 33, 31, 1, -2],\n [-58, -53, 23, -1, -32],\n [-25, -5, 5, -15, 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[[24, 8, 46, 30, -6],\n [-21, -6, -37, -25, 5],\n [-48, 8, -14, -30, 6],\n [-24, -8, -46, -30, 6],\n [-18, -12, -54, -30, 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 5x5 matrix:\n[[-5, -31, -1, 20, -28],\n [20, -26, 29, -5, -38],\n [10, 14, 10, -16, 8],\n [0, -36, 6, 18, -36],\n [5, -23, 10, 7, -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 5x5 matrix:\n[[13, 21, -8, -31, -23],\n [-23, 6, 5, 13, 25],\n [-23, 6, 5, 13, 25],\n [14, 15, -7, -26, -22],\n [-22, 0, 6, 18, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[21, 24, -12, 27, -48],\n [-37, 4, 40, 21, -20],\n [-61, -8, 60, 13, 0],\n [-6, -30, -6, -42, 66],\n [24, 12, -20, 8, -20]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-24, -4, 20, 8, -20],\n [0, 0, 0, 0, 0],\n [-36, -6, 30, 12, -30],\n [12, 2, -10, -4, 10],\n [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[[-5, -15, -5, -10, -20],\n [5, 15, 5, 10, 20],\n [-1, -3, -1, -2, -4],\n [-2, -6, -2, -4, -8],\n [6, 18, 6, 12, 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[[4, -27, 28, 0, 36],\n [-31, 9, -39, 33, -45],\n [-8, -27, 0, 12, 0],\n [-33, -1, 5, 40, 17],\n [-14, -16, -26, 16, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -31, 12, -8, -41],\n [46, -12, 36, 38, -30],\n [-44, 14, -16, -28, 6],\n [-1, -65, -14, -38, -39],\n [-20, -36, -24, -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[[-9, -29, 0, 1, 17],\n [-2, 13, -7, -6, -18],\n [28, 18, 26, 20, 28],\n [35, 60, 19, 13, -7],\n [-13, -28, -5, -3, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, -8, -6, -6, 2],\n [-6, -8, -6, -6, 2],\n [6, 8, 6, 6, -2],\n [6, 8, 6, 6, -2],\n [9, 12, 9, 9, -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[[48, 39, -4, -2, -11],\n [9, 7, 33, 19, -18],\n [26, 14, 16, -4, 14],\n [-36, -52, -6, -24, 32],\n [-16, -7, 54, 26, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -4, 6, 9, -13],\n [-26, -7, -52, 34, -52],\n [-10, -22, 3, 27, 16],\n [40, 40, -2, -10, -6],\n [8, -3, -7, 31, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, 16, 8, 0, 12],\n [8, 16, 8, 0, 12],\n [2, 4, 2, 0, 3],\n [0, 0, 0, 0, 0],\n [-12, -24, -12, 0, -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[[19, 39, 4, -25, -1],\n [22, 51, -2, -10, 2],\n [1, -15, -24, 27, 9],\n [-14, -13, 6, 18, -2],\n [-9, -51, -32, 35, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 5, 4, -1, 4],\n [-2, -6, 4, 10, 6],\n [2, 36, 20, -16, 18],\n [-6, 7, 32, 25, 38],\n [0, -5, -4, 1, -4]]\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[[32, 13, -29, 38, 21],\n [-11, -28, 18, -14, -17],\n [-74, 30, 52, -82, 2],\n [-3, -27, 14, -3, -1],\n [-27, -39, 39, -30, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[24, 18, 24, 6, -18],\n [16, 12, 16, 4, -12],\n [24, 18, 24, 6, -18],\n [8, 6, 8, 2, -6],\n [12, 9, 12, 3, -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[[16, -16, 32, -32, 11],\n [-12, 12, -24, 24, -8],\n [3, -3, 6, -6, 3],\n [7, -7, 14, -14, 4],\n [14, -14, 28, -28, 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 5x5 matrix:\n[[0, -4, -58, -58, 9],\n [-36, -27, -18, -6, -18],\n [-64, 32, 36, -12, -82],\n [-50, 11, 22, -3, -56],\n [-40, 6, 40, 24, -46]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1, 6, 6, -1, -2],\n [-14, 6, 12, 16, -16],\n [13, 0, -6, -17, 14],\n [-7, -10, -6, 13, -6],\n [-37, 40, 54, 33, -46]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -2, 10, 6, 18],\n [6, 6, 18, 22, 10],\n [-48, -10, -19, 4, -2],\n [-17, -1, -16, -3, -19],\n [23, 11, 14, 13, -7]]\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 5x5 matrix:\n[[-4, 10, 36, 28, -4],\n [0, 0, 0, 0, 0],\n [-36, 18, 36, 36, -36],\n [32, -14, -24, -26, 32],\n [-10, 4, 6, 7, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 12, 8, -32, 12],\n [14, -32, -12, -3, -2],\n [9, -51, -18, -60, -21],\n [4, -25, 11, -34, -20],\n [-6, 16, -6, -20, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, 12, 24, 26, -9],\n [-5, 12, -24, 34, -21],\n [4, -12, 12, -32, 18],\n [-5, 4, -48, 18, -17],\n [-3, 2, -30, 10, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -1, 12, 12, 7],\n [-24, -11, 42, -24, -28],\n [-22, -40, 29, -37, 3],\n [13, 9, -14, 13, 7],\n [26, -1, 19, -39, -50]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[14, 7, 12, -2, -30],\n [16, 35, -24, 38, -24],\n [12, 51, -28, 22, -48],\n [24, 4, 14, 16, -26],\n [3, -37, 27, -6, 26]]\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, 8, 10, 12, -8],\n [-25, 30, 5, 20, -20],\n [-16, 20, 12, 20, -16],\n [26, -32, -14, -28, 24],\n [18, -24, -30, -36, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-30, 17, 30, -13, 16],\n [-30, 32, -21, 41, -14],\n [-4, -4, -9, -42, -13],\n [4, -3, 39, 20, 32],\n [8, -3, 12, 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 5x5 matrix:\n[[-1, -2, -1, 0, 6],\n [2, 4, 2, 0, -12],\n [6, 12, 6, 0, -36],\n [1, 2, 1, 0, -6],\n [5, 10, 5, 0, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, -4, 13, -4, -7],\n [-14, 12, -40, 5, 20],\n [-37, -29, 23, 20, 15],\n [2, -1, 12, 21, -13],\n [12, 14, 30, -8, -32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[10, -10, 10, -40, -5],\n [-29, 8, 20, 18, 39],\n [24, -12, -4, -40, -26],\n [36, -12, -20, -32, -46],\n [-9, 6, -2, 22, 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[[-11, -13, -9, 11, -14],\n [6, -17, -22, -8, -12],\n [37, -29, -53, -41, -14],\n [-20, 30, 41, 27, 16],\n [22, 1, -5, -29, 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[[16, 40, 16, 36, 16],\n [0, 2, -8, -9, 12],\n [-2, -8, 10, 9, -20],\n [-19, -23, -25, -44, 10],\n [16, 22, -4, 8, 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[[18, -36, -24, -30, 18],\n [-18, 36, 24, 30, -18],\n [0, 0, 0, 0, 0],\n [-18, 36, 24, 30, -18],\n [-6, 12, 8, 10, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[26, 61, -25, 8, -40],\n [-24, 12, -39, 6, -36],\n [-13, -36, 36, 6, 16],\n [15, 59, -25, 15, -61],\n [-25, -29, 14, 8, -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[[0, -17, 10, -3, 18],\n [27, 1, -54, 13, -8],\n [21, 26, -12, 26, -16],\n [-31, 16, 28, -18, -18],\n [18, -9, -38, 5, 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[[4, 7, 0, 12, -8],\n [22, 44, -14, 34, -12],\n [-15, -2, 27, -5, 8],\n [36, 13, -88, -20, -6],\n [9, 9, -15, 0, 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 5x5 matrix:\n[[2, 6, -9, -12, 8],\n [-20, -8, 14, -12, -34],\n [4, 34, 44, 30, 8],\n [10, -3, 6, 27, 10],\n [10, -17, -16, 13, 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[[16, 0, 12, -12, 0],\n [-24, 0, -18, 18, 0],\n [8, 0, 6, -6, 0],\n [8, 0, 6, -6, 0],\n [-4, 0, -3, 3, 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 5x5 matrix:\n[[-1, -12, 34, 8, -2],\n [-14, 24, -4, 22, -28],\n [-2, 23, -11, -12, 12],\n [41, 33, -16, 12, 25],\n [-1, 17, -29, 16, -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[[-40, 30, 35, -25, 10],\n [16, -26, -15, 1, -18],\n [36, -6, -30, 36, 12],\n [-6, 29, 7, 12, 26],\n [-26, 23, 23, -14, 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 5x5 matrix:\n[[-23, -14, 10, -31, -26],\n [17, 11, -25, 34, 29],\n [22, 12, 28, 6, 4],\n [10, 7, -29, 29, 25],\n [0, 1, -27, 17, 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[[1, -4, -1, -2, 0],\n [6, -4, 4, -7, 10],\n [-19, 16, -11, 23, -30],\n [1, 4, 3, 0, 4],\n [5, -8, 1, -7, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-15, 16, 14, -13, 3],\n [31, -11, -30, -10, 18],\n [-25, -7, 2, 20, -24],\n [-16, 14, 32, 2, -6],\n [8, -10, -8, 9, -3]]?\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[[-42, -39, -2, -7, -38],\n [-24, -30, -8, -10, -20],\n [15, 30, 15, 15, 10],\n [3, 15, 11, 10, 0],\n [24, 3, -16, -11, 26]]\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[[-6, -12, -9, 6, 3],\n [4, 8, 6, -4, -2],\n [-10, -20, -15, 10, 5],\n [0, 0, 0, 0, 0],\n [-4, -8, -6, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 29, 23, -40, 8],\n [22, -4, -33, -16, -9],\n [15, -25, -8, 24, -53],\n [-1, -12, -11, 28, 28],\n [-24, 12, 29, 24, 71]]\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, -48, -52, 16, 51],\n [-7, 57, -16, -17, -30],\n [35, -25, 4, -55, 58],\n [-21, -12, 4, 44, -27],\n [23, 15, -4, -47, 30]]?\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, 27, 2, 16, -6],\n [-4, 8, -18, 2, -6],\n [25, 5, 15, 19, 25],\n [-1, -23, -11, -15, 3],\n [42, 36, -12, 48, 36]]\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[[5, 26, -44, 26, -37],\n [6, -7, 10, -28, 31],\n [15, -20, -22, -10, -3],\n [-4, -14, -4, 10, -20],\n [33, -30, 60, 52, 29]]?\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 5x5 matrix:\n[[-28, -3, 10, -12, -21],\n [28, -39, 18, 18, 32],\n [-10, -84, 40, 66, 19],\n [-9, -19, 10, 19, 2],\n [37, 44, -40, -5, 7]]\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, 4, -1, -6, -2],\n [-3, -12, 3, 18, 6],\n [0, 0, 0, 0, 0],\n [-3, -12, 3, 18, 6],\n [5, 20, -5, -30, -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[[32, -14, -24, 20, -10],\n [54, -24, -42, 34, -10],\n [-6, 3, 6, -4, -5],\n [31, -13, -21, 19, -20],\n [-33, 15, 27, -21, 0]]\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, 5, 15, -60, -10],\n [32, 43, -30, 15, -47],\n [30, 4, -7, 13, -21],\n [4, 45, -28, 7, -31],\n [-16, -34, 6, 46, 32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 25, 22, 16, 13],\n [6, 10, -20, 10, -2],\n [-15, 25, 30, 15, 15],\n [12, 0, -32, 4, -8],\n [-3, 15, 2, 11, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-24, 24, -4, 4, -16],\n [-24, 24, -4, 4, -16],\n [0, 0, 0, 0, 0],\n [24, -24, 4, -4, 16],\n [30, -30, 5, -5, 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 5x5 matrix:\n[[-1, -26, -53, -47, 17],\n [-23, -38, -17, -22, 30],\n [-11, 6, 71, 44, 12],\n [36, 30, 24, 8, -20],\n [5, -25, -51, -50, 17]]\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[[8, 19, 19, 12, 18],\n [18, 12, -3, 17, -9],\n [-18, 19, 12, 5, 28],\n [0, -12, 9, -11, 34],\n [15, 17, -6, 21, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[13, -9, 11, -21, -12],\n [-7, 53, -29, 7, -36],\n [-5, 3, -19, 16, -16],\n [-38, 17, 8, 39, 1],\n [43, 19, -31, -43, 15]]\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[[23, 40, -13, -9, -31],\n [42, 15, 15, 13, 19],\n [15, 30, -9, -19, -49],\n [32, 55, -19, -5, -27],\n [-40, -15, -17, 5, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-17, -40, 10, -10, -21],\n [3, -29, -28, -10, -26],\n [-20, 13, 42, -9, 10],\n [-42, -7, 10, 0, 23],\n [-21, -31, -52, -1, -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[[0, 2, 4, 2, -2],\n [0, 0, 0, 0, 0],\n [0, -12, -24, -12, 12],\n [0, 8, 16, 8, -8],\n [0, -2, -4, -2, 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 5x5 matrix:\n[[11, -3, 3, 3, -8],\n [-8, -21, -9, -14, -1],\n [-23, -3, -9, -11, 14],\n [41, 12, 18, 23, -23],\n [-36, 33, -3, 2, 33]]\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[[7, 19, 42, -34, -36],\n [2, -24, -46, 14, 24],\n [-7, 22, -67, 37, 40],\n [2, -14, 31, 6, -16],\n [-4, 4, -56, -18, 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[[-6, 9, -15, 0, 0],\n [-22, 48, 10, 60, -20],\n [-2, 6, 8, 12, -4],\n [-12, 30, 22, 48, -16],\n [-9, 15, -16, 6, -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[[6, 6, 5, 4, 5],\n [6, 6, 5, 4, 5],\n [-36, -36, -30, -24, -30],\n [-6, -6, -5, -4, -5],\n [6, 6, 5, 4, 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 5x5 matrix:\n[[-16, -12, 34, 28, 16],\n [-24, 60, -42, -60, 24],\n [1, 4, -6, -6, -1],\n [-1, 22, -25, -28, 1],\n [-16, 40, -28, -40, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0, 0],\n [-20, 16, 20, -8, 12],\n [0, 0, 0, 0, 0],\n [-5, 4, 5, -2, 3],\n [10, -8, -10, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[39, -21, -54, 0, 15],\n [8, 5, -20, 24, 37],\n [38, 3, -22, 6, 13],\n [-1, 16, 3, 23, 29],\n [8, 13, 9, 7, 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[[-2, 13, -11, -7, 17],\n [-26, -11, -17, 17, 5],\n [12, 12, 3, -12, 6],\n [26, 1, 24, -11, -17],\n [-36, -6, -30, 18, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[20, 0, 16, 20, 4],\n [20, 0, 16, 20, 4],\n [20, 0, 16, 20, 4],\n [30, 0, 24, 30, 6],\n [-5, 0, -4, -5, -1]]\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[[-20, 1, -29, -4, 26],\n [-19, -39, -3, 7, 26],\n [-5, -39, 3, -28, 34],\n [-27, -33, -7, 25, 54],\n [7, -32, 6, -53, 32]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-18, 19, 19, -15, -3],\n [-24, 28, 15, 19, 20],\n [-26, 25, 27, -23, -3],\n [26, -28, -26, 16, 1],\n [4, 8, 15, -49, -46]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[24, 18, 24, 18, -24],\n [-12, -9, -12, -9, 12],\n [16, 12, 16, 12, -16],\n [-8, -6, -8, -6, 8],\n [-4, -3, -4, -3, 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[[3, 5, -2, -11, -28],\n [-33, -11, -19, -18, 10],\n [33, -33, 33, 28, 45],\n [48, 3, 33, 24, -3],\n [3, -39, -8, 55, 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[[-40, -6, 8, 51, -33],\n [2, 11, -38, -33, -3],\n [53, -22, 34, -17, 48],\n [40, -1, 24, -4, 44],\n [-9, 19, 16, -11, -8]]\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[[-3, 4, -1, -6, 3],\n [-9, 12, -3, -18, 9],\n [0, 0, 0, 0, 0],\n [9, -12, 3, 18, -9],\n [-18, 24, -6, -36, 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[[-23, -34, 16, -19, -54],\n [1, 2, -2, -1, 6],\n [2, 2, 1, 5, -2],\n [13, 20, -11, 8, 36],\n [6, 6, 3, 15, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-5, 5, 23, -35, -19],\n [4, 20, -4, -20, -4],\n [-11, -30, 26, 5, -9],\n [0, -20, -12, 40, 16],\n [-6, -10, 18, -10, -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 5x5 matrix:\n[[18, -15, -6, 51, -24],\n [-41, -31, 37, 34, -8],\n [-38, -26, 26, 32, 0],\n [-2, 15, -11, -30, 20],\n [34, 7, -23, 14, -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[[12, -4, -25, 39, 29],\n [-18, 13, -20, 15, -17],\n [0, -21, -9, -28, -30],\n [-16, 18, 0, 6, -10],\n [0, -3, -6, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-31, -18, -9, 23, -30],\n [27, 26, 13, -21, 30],\n [-13, 10, 5, 8, -6],\n [33, 14, 7, -24, 30],\n [-3, 22, 11, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-18, -14, -5, 18, 12],\n [-2, -2, -12, 20, 40],\n [-8, -68, -6, 58, -20],\n [22, 2, -2, -2, 4],\n [23, -9, -10, 20, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[46, -49, -44, 2, -61],\n [40, -63, -43, 3, -86],\n [-51, 23, 54, 14, 47],\n [-36, -25, -15, 37, -22],\n [-27, 55, 40, -1, 86]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[20, -12, 12, 0, -4],\n [-5, 3, -3, 0, 1],\n [0, 0, 0, 0, 0],\n [-25, 15, -15, 0, 5],\n [30, -18, 18, 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 5x5 matrix:\n[[0, 0, 0, 0, 0],\n [15, 30, -5, -30, 30],\n [12, 24, -4, -24, 24],\n [-3, -6, 1, 6, -6],\n [18, 36, -6, -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[[-3, -6, -1, 6, -1],\n [25, 30, -5, 0, 15],\n [-5, -6, 1, 0, -3],\n [23, 18, -11, 24, 17],\n [14, 12, -6, 12, 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 5x5 matrix:\n[[4, -24, -4, 0, 12],\n [-1, 6, 1, 0, -3],\n [-2, 12, 2, 0, -6],\n [2, -12, -2, 0, 6],\n [-6, 36, 6, 0, -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 5x5 matrix:\n[[28, -2, 36, 16, 36],\n [34, -15, 47, -6, 11],\n [-1, -2, 9, 2, 15],\n [18, -13, 34, -8, 10],\n [-10, 2, -26, -12, -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[[-19, 30, -24, 7, -9],\n [54, -10, 8, 2, -10],\n [-1, -10, 8, -3, 5],\n [30, -30, 24, -6, 6],\n [-66, 0, 0, -6, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, 28, 44, 13, -39],\n [-26, -21, 18, -33, -18],\n [4, 2, 2, 50, -46],\n [-23, -30, -9, -43, 25],\n [4, -32, -48, -12, 36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[18, -3, 6, 9, -3],\n [-12, 2, -4, -6, 2],\n [-12, 2, -4, -6, 2],\n [-18, 3, -6, -9, 3],\n [-24, 4, -8, -12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-24, -24, 4, 28, 0],\n [12, 20, -30, 14, 28],\n [-26, -12, 6, 16, 30],\n [6, 4, -18, 16, 2],\n [-24, -4, -2, 18, 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[[-4, -8, -2, -3, -19],\n [-2, -31, 8, -6, -50],\n [-2, 11, -6, 1, 13],\n [-14, 5, -18, -5, -17],\n [0, 12, -4, 2, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 10, 6, -3, 20],\n [-4, -48, -1, 4, -18],\n [5, -42, 7, -8, 9],\n [-6, 6, -7, 3, -18],\n [4, -18, 2, -19, 6]]\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, -15, 13, -32, 17],\n [42, 1, 42, 59, 9],\n [-11, 12, 2, 45, -7],\n [-51, -12, -38, -51, 7],\n [-8, 14, -14, -2, -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[[36, -14, -16, 5, -11],\n [26, -20, -14, 1, -24],\n [13, -30, 18, -3, 4],\n [-35, 15, 15, -1, 11],\n [56, -27, -5, 27, 6]]\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 5x5 matrix:\n[[-2, 19, -40, 13, 33],\n [-7, -31, 10, -2, -6],\n [5, 5, 16, -8, -9],\n [-10, -30, 4, 8, -20],\n [7, 11, 14, -10, -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[[-13, 16, 2, 0, -3],\n [20, -16, 0, -8, -12],\n [-2, 10, 3, -7, -15],\n [-10, 22, 5, -9, -21],\n [-10, -6, -5, 17, 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 5x5 matrix:\n[[50, -20, -20, 15, 10],\n [10, -7, 3, 19, -19],\n [10, -7, 3, 19, -19],\n [0, 3, -7, -16, 21],\n [-4, 4, -4, -14, 16]]\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, -23, 16, 38, -26],\n [32, 28, -16, -44, 28],\n [-44, -32, 24, 54, -38],\n [26, 0, -20, -13, 21],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-23, -1, -35, -10, 16],\n [-21, 3, -45, 0, 12],\n [21, -3, 45, 0, -12],\n [7, 5, -5, 14, -8],\n [-24, -12, 0, -36, 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[[-5, 39, -44, -1, 7],\n [-40, -21, -4, -23, -2],\n [-65, -17, -24, -33, -8],\n [-25, -24, 14, -5, -29],\n [-25, -60, 34, -13, -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[[-11, 25, -38, -1, -23],\n [-16, -40, 52, 11, 5],\n [-10, 56, -49, 23, 12],\n [29, 19, -10, -2, 26],\n [-19, 29, -38, 12, -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 5x5 matrix:\n[[10, 5, -10, -7, -22],\n [34, 84, -2, -11, 6],\n [-20, -61, -32, -20, -12],\n [-34, -86, -6, 9, -22],\n [-12, 14, -43, -23, -7]]\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 5x5 matrix:\n[[-18, -10, 13, 43, 10],\n [-7, -24, 21, 53, 4],\n [-28, 27, -14, -10, 16],\n [33, -28, 10, 4, -14],\n [-23, 37, -4, -30, -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[[20, 8, -4, 28, 2],\n [-18, -5, -3, 10, 7],\n [-34, -11, -1, -6, 7],\n [4, 2, -2, 12, 2],\n [-24, -8, 0, -8, 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[[22, -13, 24, -7, -21],\n [22, -7, -27, 2, 43],\n [-20, 4, 3, -13, 6],\n [1, 4, 1, -1, -13],\n [-33, 8, 2, -3, 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 5x5 matrix:\n[[8, -12, 4, -12, 4],\n [-4, 20, -12, -12, -4],\n [-17, 15, -1, 39, -7],\n [-21, 21, -3, 45, -9],\n [14, 0, -8, -48, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[0, 0, 0, 0, 0],\n [2, -2, 10, 2, 0],\n [-1, 1, -5, -1, 0],\n [-5, 5, -25, -5, 0],\n [4, -4, 20, 4, 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 5x5 matrix:\n[[12, 4, -33, 26, 14],\n [-2, -13, 7, -7, -7],\n [-6, 22, 1, 20, 14],\n [0, -7, -3, 7, 1],\n [-3, 25, -3, 17, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-32, 59, -16, 10, -57],\n [20, -15, -15, 15, 25],\n [-16, 30, -11, 9, -28],\n [10, 29, -14, -8, -16],\n [8, -36, 4, 12, 32]]\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 5x5 matrix:\n[[3, -10, -33, 30, -3],\n [-5, 16, 35, -40, -7],\n [-49, -16, -26, -5, 61],\n [12, -12, -41, 43, -12],\n [-12, -1, -28, 5, -6]]\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, 0, -6, -6, -12],\n [7, 10, 27, -13, -6],\n [25, -2, -1, 7, 10],\n [-12, 0, -2, -2, -4],\n [31, 10, 31, -9, 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[[-24, 24, 44, 28, -22],\n [-24, 8, 18, -14, 50],\n [1, 37, -1, -20, 6],\n [-1, -68, 7, 39, -15],\n [1, 38, 16, 10, -39]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[8, 0, -11, -1, -39],\n [26, 4, -32, -31, 3],\n [20, -4, -24, -11, -17],\n [-5, 0, 6, 5, -1],\n [15, -32, -13, 32, -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[[43, 22, -72, 31, 38],\n [-5, 56, -13, 61, 45],\n [-30, 56, 24, 33, 27],\n [11, 23, 6, 46, 9],\n [-20, 7, -1, 5, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[10, -10, -12, 10, 2],\n [10, -10, -12, 10, 2],\n [25, -25, -30, 25, 5],\n [-25, 25, 30, -25, -5],\n [-20, 20, 24, -20, -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[[-18, -5, 5, 3, -61],\n [-33, 25, -49, -37, -10],\n [-18, -53, 40, 11, -34],\n [-42, -45, 37, 1, -45],\n [8, -15, 18, 8, 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[[19, 33, -34, -14, 15],\n [-10, -33, 26, 23, -16],\n [21, 18, -28, 3, 7],\n [-13, -24, 24, 11, -11],\n [-3, -18, 12, 15, -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[[-19, -21, -26, 17, -12],\n [0, -7, -4, 4, 2],\n [-3, 8, -16, -1, 6],\n [3, -18, 15, 6, -6],\n [8, 21, 4, -12, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, -6, 9, 12, -9],\n [-4, 2, -3, -4, 3],\n [8, -4, 6, 8, -6],\n [-4, 2, -3, -4, 3],\n [20, -10, 15, 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[[-15, 10, 10, 4, 15],\n [-10, 30, 25, 8, -5],\n [-5, 8, 7, -4, 18],\n [-26, -6, -1, 8, 25],\n [10, 12, 8, -4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, 12, -6, 4, 0],\n [-15, -30, 15, -10, 0],\n [9, 18, -9, 6, 0],\n [12, 24, -12, 8, 0],\n [-12, -24, 12, -8, 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 5x5 matrix:\n[[5, -30, 15, 10, -15],\n [-6, 36, -18, -12, 18],\n [-6, 36, -18, -12, 18],\n [5, -30, 15, 10, -15],\n [-3, 18, -9, -6, 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[[28, -10, 26, 34, 7],\n [-8, -31, 19, 52, 17],\n [-8, -8, 18, 24, -1],\n [-4, -22, -2, 20, 20],\n [36, -32, 19, 45, 35]]\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, 12, -6, 2],\n [3, -5, 6, -3, 1],\n [-12, 20, -24, 12, -4],\n [6, -10, 12, -6, 2],\n [3, -5, 6, -3, 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[[-16, 8, -12, -4, -12],\n [4, -2, 3, 1, 3],\n [0, 0, 0, 0, 0],\n [16, -8, 12, 4, 12],\n [4, -2, 3, 1, 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[[-3, -17, 2, 14, -6],\n [-39, -55, 1, 26, -11],\n [18, 36, 43, -40, 47],\n [45, 66, 0, -33, 15],\n [27, 30, 42, -27, 39]]\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, 1, 0, -2, -2],\n [12, 2, 0, -4, -4],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [36, 6, 0, -12, -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[[12, -4, -52, -14, -38],\n [8, 4, -12, -2, -6],\n [-18, -9, 15, -6, 12],\n [28, 9, -23, 19, -31],\n [2, -14, -38, -3, -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[[-8, 20, 0, 20, 24],\n [-12, 30, 0, 30, 36],\n [0, 0, 0, 0, 0],\n [-2, 5, 0, 5, 6],\n [-8, 20, 0, 20, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-20, -4, -12, 20, 24],\n [-15, -3, -9, 15, 18],\n [-20, -4, -12, 20, 24],\n [-25, -5, -15, 25, 30],\n [-10, -2, -6, 10, 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[[0, 29, -43, 34, 5],\n [13, -33, 29, -38, -11],\n [4, 30, -44, 42, 30],\n [-4, -1, 7, -2, -1],\n [24, 6, -42, 12, 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 5x5 matrix:\n[[14, -29, 31, 32, 28],\n [-6, -24, 24, 24, 45],\n [28, -12, 18, 16, -19],\n [-16, -6, -2, 3, 17],\n [21, 15, 18, -8, 9]]\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, 20, 12, -16, 5],\n [-9, -5, -24, -17, -17],\n [-11, -22, -17, 18, -10],\n [-25, -18, -48, -13, -50],\n [0, 1, 8, 8, 39]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-11, 10, -12, 16, -16],\n [-28, 18, -16, 33, -27],\n [-8, 4, -1, 12, -15],\n [-1, 0, 3, 7, -16],\n [34, -8, -12, -38, 38]]\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 5x5 matrix:\n[[18, 30, 36, 30, -24],\n [-6, -10, -12, -10, 8],\n [15, 25, 30, 25, -20],\n [-9, -15, -18, -15, 12],\n [6, 10, 12, 10, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-17, 36, 6, -15, 18],\n [51, -16, 12, -19, 34],\n [3, -13, -30, -11, 14],\n [8, 24, 3, -24, 36],\n [5, -1, 30, 3, -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[[-16, 0, -20, 4, -20],\n [4, 0, 5, -1, 5],\n [4, 40, 0, -36, 0],\n [-16, 8, -21, -3, -21],\n [10, -12, 14, 8, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0, 0],\n [24, -7, 28, 13, -24],\n [6, -18, -3, -3, 9],\n [20, -8, 22, 10, -18],\n [48, -14, 56, 26, -48]]\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[[34, -22, 54, 38, -29],\n [-22, 8, 48, 32, -14],\n [-52, 30, 24, 12, 6],\n [-1, -37, 12, 30, -36],\n [5, 36, -30, -42, 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[[-40, -7, 21, -21, -6],\n [22, 14, -5, 52, -1],\n [-12, -36, -2, -48, 14],\n [-18, -38, 4, -20, 20],\n [-34, 32, 10, -30, 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[[-47, -43, -28, -28, 28],\n [12, -43, -20, 26, 2],\n [21, 15, -48, 5, 16],\n [4, 44, 30, -11, 2],\n [29, -6, -30, 25, -36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[14, -26, 27, 6, 23],\n [33, -57, 63, 30, 60],\n [-7, -41, 31, 38, 36],\n [-20, 8, -16, 4, -12],\n [11, 44, -32, -45, -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[[27, 9, -7, -4, -6],\n [38, 11, -8, -5, -10],\n [-3, 24, -27, -9, 24],\n [15, 15, -15, -6, 6],\n [24, 33, -34, -13, 18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-42, 11, 42, -37, 6],\n [21, -6, -21, 8, -11],\n [25, -11, -25, 35, 3],\n [-12, -1, 12, -1, 6],\n [10, -9, -10, 11, -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[[6, -10, -8, -6, -2],\n [0, 0, 0, 0, 0],\n [3, -5, -4, -3, -1],\n [0, 0, 0, 0, 0],\n [-3, 5, 4, 3, 1]]\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[[38, -14, -18, 18, 9],\n [30, 10, -5, 30, -10],\n [38, -14, -18, 18, 9],\n [-2, -6, -2, -6, 5],\n [-32, -16, 3, -36, 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 5x5 matrix:\n[[-25, -5, -20, 25, 15],\n [-25, -5, -20, 25, 15],\n [20, 4, 16, -20, -12],\n [30, 6, 24, -30, -18],\n [5, 1, 4, -5, -3]]\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[[-8, 12, -20, 8, 0],\n [10, -15, 25, -10, 0],\n [-8, 12, -20, 8, 0],\n [4, -6, 10, -4, 0],\n [10, -15, 25, -10, 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[[-5, -25, 25, -10, 10],\n [-6, -30, 30, -12, 12],\n [-1, -5, 5, -2, 2],\n [-3, -15, 15, -6, 6],\n [2, 10, -10, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-40, 9, -22, -29, -36],\n [33, 24, 36, 21, 24],\n [4, 22, 14, 0, -5],\n [6, -27, -14, 5, 0],\n [-18, 15, -2, -13, -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[[39, 6, 26, -6, 23],\n [0, -9, -26, 3, 35],\n [56, -47, 6, 40, 63],\n [32, 8, -4, 33, 2],\n [20, 10, -22, 16, 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[[32, -14, 30, 4, -9],\n [-5, 20, 45, 10, 10],\n [-5, -4, -18, -3, -5],\n [-46, 34, -6, 2, 21],\n [28, -22, 3, -1, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-19, 29, 10, 32, -16],\n [-20, 28, 2, 28, -8],\n [-11, 13, -7, 10, 4],\n [-31, 41, -5, 38, -4],\n [6, 6, 48, 24, -48]]\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, 3, -12, 9, -3],\n [-20, -4, 16, -12, 4],\n [-20, -4, 16, -12, 4],\n [5, 1, -4, 3, -1],\n [-25, -5, 20, -15, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -12, 36, -12, 12],\n [-15, 11, 27, -4, 19],\n [30, -18, -66, 12, -42],\n [-25, 29, 13, 4, 21],\n [20, -18, -26, 2, -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[[10, -30, 10, -30, -30],\n [2, -6, 2, -6, -6],\n [-8, 24, -8, 24, 24],\n [4, -12, 4, -12, -12],\n [8, -24, 8, -24, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, -46, -38, -17, 8],\n [24, 28, -24, -17, 37],\n [-12, -41, -37, -19, 7],\n [9, -20, -21, -2, 19],\n [-27, 13, 12, 0, -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[[6, 9, 12, 12, -15],\n [36, 4, -13, 22, -5],\n [34, 11, 0, 28, -17],\n [-28, 8, 29, -6, -15],\n [6, -1, -5, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[36, 39, 18, -18, 18],\n [24, 21, 21, -6, -6],\n [20, 26, 5, -12, 0],\n [-8, -7, -7, 2, 2],\n [-13, -20, 1, 10, 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[[-9, -18, -5, -33, -10],\n [3, 6, -2, 6, -1],\n [-20, -40, 28, -20, 24],\n [18, 36, -34, 6, -32],\n [-10, -20, 14, -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 5x5 matrix:\n[[16, 24, -20, -8, 16],\n [12, 18, -15, -6, 12],\n [-4, -6, 5, 2, -4],\n [-20, -30, 25, 10, -20],\n [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[[5, 27, -1, -7, -18],\n [-9, 10, 17, 1, -11],\n [-16, 17, -4, 56, 36],\n [-19, -11, 31, 3, -5],\n [-14, -23, 26, -6, -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[[0, 0, 0, 0, 0],\n [-15, -15, -15, 12, 12],\n [-30, -30, -30, 24, 24],\n [-15, -15, -15, 12, 12],\n [10, 10, 10, -8, -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 5x5 matrix:\n[[-10, -5, -20, 10, -20],\n [2, 1, 4, -2, 4],\n [-10, -5, -20, 10, -20],\n [4, 2, 8, -4, 8],\n [8, 4, 16, -8, 16]]\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, -3, -38, -11, 34],\n [5, -15, 30, 25, -30],\n [-5, 15, -30, -25, 30],\n [-4, -24, 26, 32, -28],\n [-25, 3, -50, -21, 46]]?\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 5x5 matrix:\n[[-6, 0, 0, 15, -6],\n [2, 3, 15, -32, -1],\n [-14, 5, 25, -10, -19],\n [-14, 3, 15, 8, -17],\n [12, -6, -30, 24, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, 30, -6, 40, -18],\n [8, -5, 1, -28, -13],\n [18, -30, 6, -48, 12],\n [0, 0, 0, 0, 0],\n [-14, 20, -4, 40, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -32, -25, 3, 17],\n [-6, -25, -26, 20, 16],\n [-12, 62, 25, 5, -17],\n [10, -24, -24, -10, 18],\n [18, 25, 17, -41, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[14, 8, -4, 10, -7],\n [10, 8, -12, -18, 19],\n [7, 3, 2, 16, -14],\n [-5, -3, 2, -2, 1],\n [14, 6, 4, 32, -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[[1, -1, 2, 6, -4],\n [2, -2, 4, 12, -8],\n [-4, 4, -8, -24, 16],\n [3, -3, 6, 18, -12],\n [-1, 1, -2, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[31, 15, 78, 1, -18],\n [8, -26, 32, -8, 30],\n [23, 37, -8, 6, -20],\n [30, 1, 22, -5, 23],\n [-16, -11, -40, 10, 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[[2, -31, 1, 25, 4],\n [32, 3, 8, 11, 28],\n [6, 17, 2, -49, -5],\n [44, -45, 4, -21, 31],\n [-22, 14, -11, -26, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-29, -23, -34, 44, 1],\n [44, 28, 30, -14, -21],\n [9, 11, -13, 54, -38],\n [30, 2, 7, 12, -8],\n [19, 9, 20, -28, 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[[-2, 20, 40, -4, -15],\n [-12, -22, 24, -28, -20],\n [-7, 41, -13, 1, 6],\n [-20, 16, -8, -48, -18],\n [4, 10, 28, 32, 6]]\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 5x5 matrix:\n[[20, 11, -16, -2, 28],\n [-6, 19, -41, 3, -19],\n [-2, -32, 59, 9, -7],\n [-14, 23, -29, -41, 37],\n [16, 6, -6, -4, 27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[20, -24, -40, -10, -15],\n [-38, 38, 22, -15, 1],\n [40, 22, -70, 37, -28],\n [-12, 36, 16, 10, 10],\n [-10, 32, 26, 6, 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[[0, 25, -20, 45, -5],\n [-12, 16, -11, 27, -20],\n [-4, -23, 19, -42, -1],\n [24, -2, -2, 0, 34],\n [-12, -19, 17, -36, -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[[-10, -17, 37, -2, -24],\n [-40, 21, -24, 27, 10],\n [56, -7, -22, -1, 25],\n [-8, -4, 5, 5, -4],\n [-7, -30, 10, 28, -4]]\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, 4, 4, 16, -20],\n [42, 5, 3, -32, 33],\n [36, 18, 14, -32, 26],\n [-54, -9, -6, 42, -42],\n [-12, 26, 22, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, -5, 3, 1, 6],\n [-28, -17, 11, 15, 12],\n [-20, -20, -48, -8, -48],\n [-45, -19, -13, 13, -18],\n [8, -4, -4, -4, 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[[0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [-9, 0, 12, 18, -6],\n [0, 0, 0, 0, 0],\n [6, 0, -8, -12, 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[[6, 0, -6, 0, -6],\n [9, 0, -9, 0, -9],\n [-6, 0, 6, 0, 6],\n [3, 0, -3, 0, -3],\n [-12, 0, 12, 0, 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[[-22, -8, -17, -8, -9],\n [-18, 21, 18, 2, 47],\n [28, 3, 13, 6, -14],\n [28, -23, -21, -14, -52],\n [30, 20, 25, -16, 23]]\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, 10, -12, -2, 2],\n [0, 0, 0, 0, 0],\n [-3, 15, -18, -3, 3],\n [3, -15, 18, 3, -3],\n [6, -30, 36, 6, -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 5x5 matrix:\n[[4, 8, 24, 16, 12],\n [3, 6, 18, 12, 9],\n [-3, -6, -18, -12, -9],\n [-1, -2, -6, -4, -3],\n [2, 4, 12, 8, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, -6, -12, 18, 24],\n [8, 4, 8, -12, -16],\n [12, 6, 12, -18, -24],\n [-6, -3, -6, 9, 12],\n [-6, -3, -6, 9, 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[[35, 30, 29, 2, 37],\n [10, 15, -24, -28, -1],\n [-2, 4, -34, 2, -51],\n [-26, -1, 28, 24, -23],\n [-33, -34, -15, -2, -13]]\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 5x5 matrix:\n[[-32, -44, 20, -29, -3],\n [5, 19, -6, 20, 7],\n [2, 27, -1, 8, -1],\n [-53, -11, -12, 17, -20],\n [62, 25, 15, -5, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[42, 7, -58, -22, 2],\n [54, 32, 14, 10, -23],\n [42, 16, 5, 14, -17],\n [-20, -4, 21, -4, 26],\n [54, 30, 22, 18, -25]]\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, 6, 36, -36, 24],\n [0, 0, 0, 0, 0],\n [-6, -6, -36, 36, -24],\n [-3, -3, -18, 18, -12],\n [5, 5, 30, -30, 20]]\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[[-8, -9, 8, 18, -18],\n [-14, 8, -6, 24, -24],\n [12, -34, 28, -12, 12],\n [16, -39, 32, -18, 18],\n [-22, 18, -14, 36, -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[[-47, 17, 11, 27, -3],\n [3, -42, 47, -2, -11],\n [19, 32, -31, 0, 13],\n [-28, 7, -13, 33, 36],\n [-24, 42, -30, 10, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[21, 4, -8, -14, -24],\n [-26, -5, 11, 18, 30],\n [-12, -2, -2, 4, 12],\n [-18, -2, -26, -8, 12],\n [-9, -2, 10, 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 5x5 matrix:\n[[72, -42, 0, -36, 24],\n [-18, 18, 0, 18, -6],\n [0, 25, 0, 30, 0],\n [6, 24, 0, 30, 2],\n [-60, 30, 0, 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[[20, 6, 18, -10, -8],\n [-22, -21, -27, 17, 22],\n [18, -33, -3, 7, 28],\n [-44, 6, -30, 14, 0],\n [2, -9, -3, 3, 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[[4, -10, 21, -9, -5],\n [21, -6, -11, 8, 12],\n [8, 29, 18, -14, 8],\n [22, -19, -8, 14, -8],\n [21, -8, 10, -9, 27]]\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[[-84, 33, -10, 66, 21],\n [-11, -19, 11, 26, 18],\n [19, -35, 40, -4, -8],\n [-16, -26, 36, 28, 6],\n [2, 18, -28, -8, 4]]?\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 5x5 matrix:\n[[18, -14, 7, -11, 15],\n [9, 6, 21, -18, 4],\n [0, -40, 4, -18, -16],\n [8, -10, 0, 1, 20],\n [37, 22, -5, 1, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 8, 12, 13, 3],\n [-14, -4, -16, -17, -7],\n [-4, 48, -11, -9, -35],\n [-19, -2, -38, -44, -20],\n [15, -51, 50, 56, 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[[-6, 30, 60, 36, 0],\n [-2, -15, -25, -12, -1],\n [30, 0, -30, -36, 6],\n [34, 5, -25, -36, 7],\n [-1, 30, 55, 30, 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[[-16, -1, 2, -9, -1],\n [-18, -4, 12, -2, -30],\n [27, 7, -4, 18, -28],\n [-6, 21, -30, -21, 15],\n [-18, -28, 36, 7, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[48, 22, 28, -22, 36],\n [-15, 7, -4, -3, -15],\n [-51, 42, 1, -8, -33],\n [54, 11, 4, -39, 28],\n [15, 23, 14, -23, -5]]\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[[8, 20, 43, 10, 54],\n [-44, -6, -44, -4, -64],\n [20, -12, -17, -28, -4],\n [-11, 16, -17, -15, -14],\n [23, -61, 18, 14, 13]]\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, -6, 2, 8, -10],\n [9, 9, -3, -12, 15],\n [-12, -12, 4, 16, -20],\n [-18, -18, 6, 24, -30],\n [3, 3, -1, -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[[-6, 1, -16, -7, -2],\n [6, -11, 16, 13, -2],\n [17, -15, 46, 24, 4],\n [-2, -10, -6, 7, -8],\n [-11, 40, -28, -42, 18]]\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[[-17, -55, 23, -62, -9],\n [32, 22, 33, 14, 15],\n [-7, 7, 1, -6, -38],\n [-8, -26, 17, -36, -29],\n [31, 31, -8, 50, 15]]\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[[-30, -25, 20, -5, -10],\n [-18, -15, 12, -3, -6],\n [6, 5, -4, 1, 2],\n [-6, -5, 4, -1, -2],\n [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[[-31, -1, -8, 5, -31],\n [14, 8, 1, 5, 14],\n [-14, -8, -1, -5, -14],\n [-25, 21, -14, 25, -25],\n [15, 3, 3, 0, 15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[9, -16, 66, -17, -27],\n [-24, 35, -30, 18, 27],\n [40, -35, -34, 6, -11],\n [-39, 66, -18, 35, 39],\n [25, -34, 38, -17, -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 5x5 matrix:\n[[22, -32, 20, -16, -42],\n [-20, 24, -16, 0, 44],\n [-14, 14, -10, -8, 34],\n [-2, -6, 2, -24, 14],\n [-13, 10, -8, -16, 35]]\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, 12, 6, -8, 16],\n [-13, 12, -29, 19, 8],\n [-5, 30, -28, 2, 19],\n [15, -2, 6, 5, 8],\n [-12, 28, -30, 2, 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 5x5 matrix:\n[[-36, 10, -36, -56, -38],\n [18, -3, 32, 27, 18],\n [8, -9, 21, 13, 9],\n [14, -21, 8, 25, 18],\n [16, 35, -3, 19, 11]]\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 5x5 matrix:\n[[-35, -33, -30, -9, 15],\n [6, -9, 9, -27, 9],\n [-35, -33, -30, -9, 15],\n [-23, -32, -17, -26, 18],\n [33, 17, 32, -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[[36, -25, -28, 40, 3],\n [-12, 20, 14, -18, -8],\n [36, -15, -24, 36, -3],\n [-24, 0, 12, -20, 8],\n [-18, -15, 3, -9, 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 5x5 matrix:\n[[9, 27, 12, -15, 3],\n [9, 54, 29, -20, 2],\n [-46, 8, -36, 37, 47],\n [40, -35, 3, -29, -29],\n [-39, -18, -9, 43, 3]]\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[[-36, 1, -26, -8, 18],\n [4, -26, -18, -17, 9],\n [1, 58, -34, 45, -7],\n [37, 36, 24, 39, -30],\n [39, 47, 6, 45, -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[[2, 1, -3, -4, 1],\n [4, 2, -6, -8, 2],\n [-6, -3, 9, 12, -3],\n [-4, -2, 6, 8, -2],\n [-10, -5, 15, 20, -5]]?\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, -24, 4, -8, -16],\n [-9, 18, -3, 6, 12],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [12, -24, 4, -8, -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[[3, 33, -8, 9, 4],\n [20, -8, 3, 30, 30],\n [-29, -10, 40, -12, -2],\n [-8, -27, 46, 27, 20],\n [1, 2, -2, -12, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[13, -17, -9, 1, -26],\n [-20, -12, -41, -53, 19],\n [39, 19, 29, 16, -5],\n [5, -18, -19, -12, -18],\n [41, 12, 41, 34, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, 24, 11, -27, -14],\n [17, 6, -30, -1, 27],\n [11, 11, 3, 17, 16],\n [12, 36, 16, -12, -4],\n [1, -18, -29, -5, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-13, -39, -29, 95, 21],\n [-6, 13, 37, -68, -22],\n [6, -38, 6, 56, -22],\n [-14, -22, -14, 8, 17],\n [-13, -85, -15, 22, 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[[21, -91, -80, -33, 19],\n [11, 4, 5, 32, -14],\n [-3, 21, 20, 13, 3],\n [6, -32, -30, -16, -4],\n [-23, 61, 50, -2, -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[[-11, -17, -19, -4, -25],\n [-6, -36, 11, 45, 15],\n [-20, 34, 0, -4, 50],\n [-8, 8, -17, -21, -15],\n [15, -22, 12, 17, -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[[-18, 15, 0, 18, 9],\n [0, 0, 0, 0, 0],\n [24, -20, 0, -24, -12],\n [36, -30, 0, -36, -18],\n [18, -15, 0, -18, -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[[-10, 20, 4, -20, -14],\n [3, -5, -2, 6, 4],\n [-8, 10, 8, -16, -10],\n [11, -25, -2, 22, 16],\n [-15, 5, 26, -30, -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 5x5 matrix:\n[[18, -12, 6, -36, 6],\n [9, -6, 3, -18, 3],\n [6, -4, 2, -12, 2],\n [-6, 4, -2, 12, -2],\n [-9, 6, -3, 18, -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[[0, 0, 0, 0, 0],\n [0, 18, 3, -12, 9],\n [0, 6, 1, -4, 3],\n [0, -36, -6, 24, -18],\n [0, -36, -6, 24, -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 5x5 matrix:\n[[14, -28, -30, 60, -12],\n [26, -16, -30, 24, -12],\n [-22, 20, 30, -36, 12],\n [-10, 4, 10, -4, 4],\n [0, -7, -5, 17, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[24, -43, 7, -30, 74],\n [-10, 3, -6, 10, -4],\n [72, -46, -15, -30, 18],\n [47, -16, -21, -5, -28],\n [-41, 15, 18, 5, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-16, -27, -7, 16, 13],\n [-29, -27, -2, 20, 14],\n [-21, -33, -8, 20, 16],\n [-15, 21, 16, -4, -8],\n [-41, -18, 7, 20, 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 5x5 matrix:\n[[-18, -27, -45, 24, 27],\n [-24, -20, -12, -8, -12],\n [-24, -18, -6, -13, -18],\n [0, -6, -18, 15, 18],\n [0, 12, 36, -30, -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[[42, 2, -23, 21, 38],\n [7, 8, -22, -25, -17],\n [5, -32, 12, -2, 0],\n [26, -39, -16, -17, 3],\n [27, 3, -20, 15, 29]]\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[[-1, -1, 3, 3, 0],\n [-2, -2, 6, 6, 0],\n [-4, -4, 12, 12, 0],\n [-3, -3, 9, 9, 0],\n [-3, -3, 9, 9, 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[[21, 7, -16, -13, 15],\n [-22, 8, -13, -40, 12],\n [-21, 6, 23, 26, -27],\n [-48, 27, 5, -26, -1],\n [11, -41, 8, 22, 8]]\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[[-20, 20, 30, -5, -30],\n [-8, 8, 12, -2, -12],\n [24, -24, -36, 6, 36],\n [0, 0, 0, 0, 0],\n [-20, 20, 30, -5, -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[[0, -3, -24, -21, -6],\n [6, 9, 24, 0, -2],\n [-22, 35, 26, 3, 0],\n [23, -26, 3, 11, 3],\n [12, -18, 0, 12, 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[[5, 2, -9, 3, -18],\n [-31, 32, -15, 33, -18],\n [-33, 53, 28, 42, 30],\n [-26, 38, 12, 32, 12],\n [36, -2, 62, -18, 60]]\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, 1, 15, -18, -23],\n [-40, -5, -24, 24, -8],\n [-19, -4, -28, 15, -7],\n [-22, 3, 40, 6, 18],\n [14, -1, -31, 9, 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[[0, 0, 0, 0, 0],\n [15, -10, -15, 30, 10],\n [18, -12, -18, 36, 12],\n [-6, 4, 6, -12, -4],\n [-12, 8, 12, -24, -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 5x5 matrix:\n[[8, -8, -12, -6, -10],\n [-16, 16, 24, 12, 20],\n [16, -16, -24, -12, -20],\n [4, -4, -6, -3, -5],\n [-4, 4, 6, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, -41, 0, -6, 26],\n [1, -2, 0, -30, -15],\n [3, -15, 0, -36, -9],\n [-6, 32, 0, 60, 10],\n [-4, 23, 0, 30, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[45, -36, -43, -12, -13],\n [-62, 58, 52, -6, 46],\n [26, -4, 16, -4, -5],\n [34, -2, 16, -32, -25],\n [-36, -9, -22, 44, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-26, 0, -48, -16, 32],\n [-36, 38, 30, -9, 18],\n [-14, -4, -36, -10, 20],\n [-15, -8, -48, -12, 24],\n [-56, 36, -12, -22, 44]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, -12, -12, 12, 15],\n [-8, -8, -8, 8, 10],\n [-12, -12, -12, 12, 15],\n [-16, -16, -16, 16, 20],\n [-24, -24, -24, 24, 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[[17, 22, -38, 29, 31],\n [-18, -20, -36, 0, 40],\n [-36, -36, 24, 3, -3],\n [1, 10, -1, 46, 10],\n [25, 30, 41, 13, -45]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, 6, 5, -3, -5],\n [-4, -24, -20, 12, 20],\n [-4, -24, -20, 12, 20],\n [5, 30, 25, -15, -25],\n [-6, -36, -30, 18, 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[[16, 54, -41, -4, -8],\n [-42, 6, -18, -42, -12],\n [-18, -3, 50, 40, -19],\n [19, -35, 25, 19, 27],\n [46, 8, -2, 30, 53]]?\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[[75, 8, 28, 24, -56],\n [-8, -5, 16, 1, 35],\n [19, -6, 14, 16, -36],\n [23, -17, 30, 23, -2],\n [-21, 27, -27, -30, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -4, -12, 10, 8],\n [0, -12, -36, 30, 24],\n [0, -6, -18, 15, 12],\n [0, -12, -36, 30, 24],\n [0, 8, 24, -20, -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[[9, -18, 12, 3, -6],\n [15, -30, 20, 5, -10],\n [-15, 30, -20, -5, 10],\n [12, -24, 16, 4, -8],\n [-9, 18, -12, -3, 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[[-11, -16, 11, 34, 17],\n [-46, -18, -8, 4, 4],\n [-12, 18, -12, -26, -12],\n [27, -26, -25, -10, 35],\n [-2, -32, 2, 28, 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[[-11, -52, -27, 4, 23],\n [-25, 6, 28, 8, 16],\n [10, 13, 44, -26, -17],\n [-12, -21, -17, 51, 26],\n [4, 48, 35, -2, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[15, -6, -11, -15, -12],\n [-11, 4, 1, 9, 5],\n [-14, -3, -55, -4, -8],\n [9, -13, 18, -1, 41],\n [16, -4, -4, -14, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0, 0],\n [-25, -10, -25, 5, 25],\n [-10, -4, -10, 2, 10],\n [15, 6, 15, -3, -15],\n [20, 8, 20, -4, -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[[38, -30, -13, 16, -13],\n [30, -14, -17, 11, -35],\n [-18, -22, 26, 6, 27],\n [6, 18, -14, -12, -29],\n [-14, 24, -4, 6, 31]]\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[[-14, 14, -1, 13, 11],\n [-23, 8, -7, 31, 2],\n [4, -16, -4, 4, -16],\n [-2, -20, -8, 16, -22],\n [-10, 26, 5, -1, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-17, 26, 2, -3, 18],\n [-7, 55, -3, -10, 55],\n [-23, 42, -3, 10, 57],\n [-36, 37, 14, -25, 29],\n [-23, 51, -10, 24, 37]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[5, -4, 12, 26, -24],\n [-28, -51, -38, -54, -45],\n [-21, 22, -2, -12, 4],\n [36, -19, 16, 29, 18],\n [11, 23, -4, -8, 37]]\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, -24, -30, -30],\n [8, 12, -8, -10, -10],\n [12, 18, -12, -15, -15],\n [-16, -24, 16, 20, 20],\n [4, 6, -4, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[11, 0, -101, -59, -24],\n [-30, 31, 76, 47, 17],\n [18, -66, -30, -24, 0],\n [19, 33, -20, -9, -6],\n [-39, 11, 28, 17, 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[[5, -3, -6, 6, 0],\n [25, -15, -30, 30, 0],\n [25, -15, -30, 30, 0],\n [0, 0, 0, 0, 0],\n [5, -3, -6, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-9, -3, -18, 6, -6],\n [9, 3, 18, -6, 6],\n [-6, -2, -12, 4, -4],\n [6, 2, 12, -4, 4],\n [-15, -5, -30, 10, -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 5x5 matrix:\n[[-27, 9, 6, -17, 17],\n [10, 15, 18, -18, -23],\n [0, -31, -25, 31, 29],\n [25, -48, 18, 39, -2],\n [46, -24, 3, 4, -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[[-4, 24, -8, 8, 12],\n [-2, 12, -4, 4, 6],\n [-15, -20, -10, 5, -25],\n [18, 2, 16, -11, 16],\n [12, 38, 4, 1, 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 5x5 matrix:\n[[-3, 5, -7, 0, -5],\n [-10, 8, -26, 12, -10],\n [0, 26, 8, -36, -20],\n [6, -10, 14, 0, 10],\n [-10, 8, -26, 12, -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[[-15, -5, 5, 15, 30],\n [-9, -3, 3, 9, 18],\n [18, 6, -6, -18, -36],\n [18, 6, -6, -18, -36],\n [-15, -5, 5, 15, 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[[3, 3, -3, -5, 7],\n [-2, -3, 6, 3, -16],\n [-17, 42, 38, 14, 10],\n [6, 22, 24, 6, -27],\n [52, 11, -3, 19, -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 5x5 matrix:\n[[24, -6, 23, 11, -8],\n [12, -24, 8, 2, 24],\n [-18, 30, -13, -4, -28],\n [18, -36, 12, 3, 36],\n [18, 6, 19, 10, -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[[6, 18, 6, -9, 0],\n [4, 12, 4, -6, 0],\n [2, 6, 2, -3, 0],\n [0, 0, 0, 0, 0],\n [-6, -18, -6, 9, 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[[15, 0, 6, -6, 42],\n [12, 12, 0, -3, 60],\n [-12, -6, -8, 6, -72],\n [-2, 9, -12, 5, -20],\n [9, 8, -6, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[23, -13, 63, -5, -9],\n [-19, 21, -67, 10, -1],\n [-6, 11, 18, 8, -26],\n [-22, -12, 18, -7, 8],\n [24, 9, 0, 6, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[15, -12, 3, 18, -9],\n [-20, 16, -4, -24, 12],\n [-25, 20, -5, -30, 15],\n [25, -20, 5, 30, -15],\n [5, -4, 1, 6, -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[[16, -31, 31, 36, -12],\n [15, 1, 6, 6, -10],\n [7, -16, 27, 18, 12],\n [-7, -23, 14, 18, 3],\n [-9, 2, -13, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, 28, -82, 75, 56],\n [-25, 4, -2, 7, 12],\n [21, -20, 0, 41, -2],\n [46, -47, 56, -9, -52],\n [3, -11, 54, -28, -20]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-15, 30, 8, -7, 2],\n [-18, 40, 29, -2, 2],\n [-2, 11, 44, 21, -8],\n [-6, 32, -54, -59, 0],\n [-9, 18, 23, 7, 0]]\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, 33, 34, -41, 24],\n [-36, -36, -36, 36, -24],\n [-15, -15, -10, -25, 0],\n [-15, -15, -20, 55, -20],\n [9, 9, 8, -1, 4]]\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, -22, -11, 37, 35],\n [18, -10, -29, 36, 8],\n [58, 24, -11, -7, 11],\n [-65, -29, -2, 4, -40],\n [17, -9, -34, 27, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, -3, 14, 3, 6],\n [-21, -36, 18, 36, -18],\n [7, 12, -6, -12, 6],\n [-12, -27, 6, 27, -18],\n [22, 42, -16, -42, 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[[5, 0, -20, -5, 0],\n [43, 40, 12, -35, 32],\n [31, 25, -9, -26, 20],\n [-10, -10, -6, 8, -8],\n [34, 30, 2, -28, 24]]\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, 16, -20, 0, 0],\n [0, 0, 0, 0, 0],\n [4, 8, -10, 0, 0],\n [10, 20, -25, 0, 0],\n [4, 8, -10, 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[[-42, -17, -9, 23, -39],\n [-18, 2, 24, -5, 0],\n [6, 11, 27, -17, 21],\n [-4, -9, -23, 14, -17],\n [-12, 8, 36, -14, 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[[20, 5, 2, 12, 29],\n [-15, -21, 33, -9, 7],\n [-30, -27, 36, -18, -11],\n [15, -6, 21, 9, 38],\n [-25, 5, -25, -15, -55]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[19, 0, 8, -14, -31],\n [8, 17, -2, 12, -39],\n [4, 18, -4, 16, -34],\n [15, 20, 0, 10, -55],\n [18, -14, 12, -28, -8]]\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, -4, -52, 30, -14],\n [-15, -5, -21, 9, -11],\n [-12, -4, -23, 12, -15],\n [-19, -7, 17, 5, 19],\n [-28, 3, -11, 26, 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[[27, 9, 5, -21, -10],\n [5, 17, 12, -32, -1],\n [-5, -17, -12, 32, 1],\n [7, -5, -4, 8, -3],\n [28, -2, -3, -1, -11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-50, 37, 7, -31, -64],\n [-16, 24, 22, -16, -32],\n [-26, -38, -34, -16, -12],\n [34, -24, 0, 32, 40],\n [-2, 22, 28, 16, -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 5x5 matrix:\n[[42, -13, 26, -33, -23],\n [4, 17, 12, 0, -6],\n [-14, -10, -22, -3, 13],\n [22, -46, -19, -48, 1],\n [30, -10, 15, -30, -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[[0, 6, -12, 18, 30],\n [0, -5, 10, -15, -25],\n [0, -1, 2, -3, -5],\n [0, 4, -8, 12, 20],\n [0, 2, -4, 6, 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[[0, 2, 5, -6, -4],\n [0, -8, -20, 24, 16],\n [0, -2, -5, 6, 4],\n [0, -12, -30, 36, 24],\n [0, 2, 5, -6, -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[[10, -63, 42, -55, -7],\n [16, 25, -5, -3, 8],\n [-9, -49, 27, -35, 7],\n [16, 59, -28, 31, -1],\n [18, 51, -26, 35, -17]]\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, -15, -25, 40, -5],\n [0, -6, 42, -24, 54],\n [33, 16, 31, -46, 10],\n [-21, -12, -7, 22, 10],\n [-21, -11, -14, 26, 1]]\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 5x5 matrix:\n[[-20, -20, -20, 25, 15],\n [14, 16, 0, -13, -5],\n [-2, -4, 12, -2, -4],\n [26, 32, -16, -19, -3],\n [4, 4, 4, -5, -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[[5, -2, -43, 5, 3],\n [26, 8, 8, 10, 16],\n [2, 4, -4, -14, 0],\n [-23, -31, 19, -15, -30],\n [40, 14, -53, 0, 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[[-24, 18, -6, 0, -36],\n [-24, 18, -6, 0, -36],\n [8, -6, 2, 0, 12],\n [24, -18, 6, 0, 36],\n [8, -6, 2, 0, 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[[15, 48, -27, -18, -36],\n [24, -6, -36, 36, 18],\n [-18, 16, 26, -36, -24],\n [15, -21, -21, 36, 27],\n [-1, 6, 1, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, 2, 16, 9, 28],\n [-30, 50, 9, -15, 9],\n [-32, -28, -22, 8, -2],\n [7, 18, 17, 1, 34],\n [4, 14, 8, -3, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -4, -12, 0, -6],\n [0, -10, -30, 0, -15],\n [0, 12, 36, 0, 18],\n [0, 0, 0, 0, 0],\n [0, -12, -36, 0, -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[[6, -30, 6, -30, 24],\n [5, -25, 5, -25, 20],\n [2, -10, 2, -10, 8],\n [2, -10, 2, -10, 8],\n [4, -20, 4, -20, 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 5x5 matrix:\n[[-10, -15, 30, -15, 5],\n [8, 12, -24, 12, -4],\n [-2, -3, 6, -3, 1],\n [8, 12, -24, 12, -4],\n [10, 15, -30, 15, -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 5x5 matrix:\n[[-18, 9, 9, -15, -9],\n [24, -12, -12, 20, 12],\n [-6, 3, 3, -5, -3],\n [0, 0, 0, 0, 0],\n [-6, 3, 3, -5, -3]]\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, 9, -7, 9, -27],\n [-37, -14, 8, -24, 6],\n [-16, 4, -3, 0, -15],\n [13, 5, -4, 7, -14],\n [8, 16, -9, 20, -13]]\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[[5, -26, 13, -28, 26],\n [-27, 5, -23, 35, -22],\n [10, 34, -9, 18, -33],\n [10, -25, 21, -33, 37],\n [-30, -41, -11, -1, 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[[7, 27, 39, 15, 5],\n [8, -20, -84, -6, -40],\n [-12, -30, 18, 9, 27],\n [6, -18, -42, 12, -19],\n [-5, 13, 9, -24, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1, 2, 10, 11, 12],\n [0, 3, 16, 19, 20],\n [-3, -6, -34, -43, -44],\n [-10, -1, -12, -23, -20],\n [-3, 0, -2, -5, -4]]?\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, -24, -36, 6, 0],\n [-1, 4, 6, -1, 0],\n [6, -24, -36, 6, 0],\n [5, -20, -30, 5, 0],\n [5, -20, -30, 5, 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[[-21, 12, 26, 2, -35],\n [-66, -54, 60, 72, -78],\n [-2, 22, -4, -16, 2],\n [5, -2, 4, 0, -3],\n [-26, -10, 42, 22, -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 5x5 matrix:\n[[-33, -12, 24, 0, -18],\n [-15, 6, -12, -18, 0],\n [-30, -9, 18, -3, -15],\n [-27, -6, 12, -6, -12],\n [25, 11, -22, -3, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-36, -48, -14, -32, 8],\n [-22, -36, -8, -24, 16],\n [11, 18, 4, 12, -8],\n [18, 12, 8, 8, 16],\n [16, 24, 6, 16, -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[[16, -19, 0, -8, 8],\n [-29, 26, 3, 48, 54],\n [31, -14, -32, -7, -1],\n [-25, -3, 37, -12, -8],\n [-33, -6, 21, -2, 20]]?\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[[3, -30, 36, 4, 2],\n [-14, 24, 35, 20, 10],\n [6, 12, -54, -16, -8],\n [-7, 30, -14, 4, 2],\n [1, -6, 5, 0, 0]]\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, -33, -9, -2, 32],\n [35, -36, -11, 20, 79],\n [23, -63, 12, 2, 17],\n [33, -11, 7, 40, 49],\n [-22, -12, -19, -46, -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[[22, -7, 45, -32, -5],\n [7, -8, 25, -13, -4],\n [33, 35, -25, -25, 12],\n [-10, 8, -41, 18, 5],\n [35, 15, -10, -35, 5]]\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 5x5 matrix:\n[[-5, 1, 3, -6, -6],\n [20, -4, -12, 24, 24],\n [-15, 3, 9, -18, -18],\n [-20, 4, 12, -24, -24],\n [-10, 2, 6, -12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[21, -17, -20, 17, -12],\n [26, -26, -15, 25, -16],\n [-18, -18, 15, -3, 22],\n [-19, -17, -3, -8, 28],\n [17, 23, -17, 0, -22]]?\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 5x5 matrix:\n[[32, -7, -14, -12, -30],\n [33, -24, -34, 6, -46],\n [-2, -26, -10, -6, -18],\n [-3, 15, 30, -36, 18],\n [-14, 39, 15, 25, 39]]\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, -12, 24, 4, 8],\n [-18, 18, -36, -6, -12],\n [-9, 9, -18, -3, -6],\n [0, 0, 0, 0, 0],\n [-18, 18, -36, -6, -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 5x5 matrix:\n[[-54, 15, 33, -30, 3],\n [-26, -40, -26, -56, 34],\n [-32, -28, -18, -34, -14],\n [-4, -17, -17, -10, -7],\n [41, 13, -3, 43, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-11, -9, 23, -69, 5],\n [-33, 37, -31, 6, -30],\n [-10, -6, -30, 24, 4],\n [-28, 29, -46, 41, -21],\n [-37, 10, -45, 6, -8]]\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[[-21, 4, -1, -3, 10],\n [-10, -28, 11, 39, -18],\n [24, -17, 6, 20, -21],\n [1, -18, 10, 16, -18],\n [-21, 3, -2, 2, 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[[-16, 4, -12, -16, 24],\n [4, -1, 3, 4, -6],\n [8, -2, 6, 8, -12],\n [-24, 6, -18, -24, 36],\n [20, -5, 15, 20, -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[[8, 24, -16, -4, 34],\n [-4, -26, -14, -11, -19],\n [0, 22, 14, 17, 22],\n [-4, 22, 34, 29, 13],\n [-12, -34, -2, 3, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[33, 21, 37, 3, -27],\n [-6, 8, -12, 4, 12],\n [14, -10, 22, -6, -18],\n [5, -37, 3, -15, 18],\n [1, -36, -6, -14, 30]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[25, -10, 5, 15, 15],\n [-20, 8, -4, -12, -12],\n [5, -2, 1, 3, 3],\n [20, -8, 4, 12, 12],\n [-15, 6, -3, -9, -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[[-9, 8, 16, 16, 26],\n [1, -25, 33, 30, -19],\n [-43, 5, -11, 18, 5],\n [-16, 6, -6, 24, -2],\n [-6, -1, 4, 19, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 3, -3, -12, -15],\n [2, -8, 0, -10, -22],\n [-14, 28, -4, 14, 46],\n [12, -20, 4, -4, -24],\n [-1, -3, -1, -9, -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 5x5 matrix:\n[[30, 24, 3, -30, -21],\n [-13, -6, -29, 10, 3],\n [-23, -7, 2, 19, 26],\n [-25, 17, -52, 11, 4],\n [-15, -47, -9, 31, -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 5x5 matrix:\n[[4, -5, 1, 2, 1],\n [-16, 20, -4, -8, -4],\n [-16, 20, -4, -8, -4],\n [-8, 10, -2, -4, -2],\n [20, -25, 5, 10, 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[[27, -3, -17, 3, 5],\n [-23, 2, 11, 13, 6],\n [41, -12, -44, -31, -42],\n [33, -1, -12, -3, 9],\n [-42, 12, 50, -18, 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[[-16, 12, -12, -20, -20],\n [12, -9, 9, 15, 15],\n [4, -3, 3, 5, 5],\n [16, -12, 12, 20, 20],\n [24, -18, 18, 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, -10, -8, 26, 49],\n [50, -45, 30, -15, -5],\n [-30, 29, -14, -1, -15],\n [45, -42, 24, -6, 9],\n [-25, 21, -18, 15, 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[[12, -12, -9, -3, -3],\n [3, 29, 7, 13, 21],\n [0, 18, 18, 12, 6],\n [30, -10, 4, 8, -4],\n [-9, -39, -12, -20, -28]]?\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[[29, -48, 5, 11, 12],\n [17, 7, -20, -28, 0],\n [-10, 30, -26, -46, 3],\n [54, 0, -42, -54, 0],\n [-6, 36, -16, -24, -9]]\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],\n [11, 15, -14, 3, 27],\n [-10, 25, 15, -30, 30],\n [-6, 32, 10, -30, 42],\n [24, -26, -34, 48, -24]]\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[[-6, -1, 3, -3, 4],\n [-24, -4, 12, -12, 16],\n [24, 4, -12, 12, -16],\n [-12, -2, 6, -6, 8],\n [-6, -1, 3, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-8, 20, 38, -40, -44],\n [-12, 30, 46, -26, -22],\n [-20, -1, 26, -15, -21],\n [-31, -32, -3, 34, 29],\n [-17, 35, 63, -49, -50]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[25, 20, 0, -30, 10],\n [5, 4, 0, -6, 2],\n [30, 24, 0, -36, 12],\n [-20, -16, 0, 24, -8],\n [10, 8, 0, -12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[4, -3, 0, -10, -4],\n [-51, 20, -32, -2, -28],\n [-29, -35, -62, 1, -16],\n [57, -57, 0, -26, 13],\n [-13, 37, -6, 13, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 24, -12, -12, 8],\n [1, 6, -3, -3, 2],\n [4, 24, -12, -12, 8],\n [6, 36, -18, -18, 12],\n [4, 24, -12, -12, 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, -24, 16, 0, -12],\n [-8, 16, -20, -24, -6],\n [-3, 21, -21, -18, 0],\n [3, -1, 3, 6, 3],\n [12, 36, -24, 0, 18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-23, 44, 29, -19, -7],\n [2, -11, -18, 30, 1],\n [3, -6, -4, 5, 0],\n [38, -59, -8, 22, -17],\n [18, -15, 22, -50, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[12, 8, 24, 12, -24],\n [-18, -12, -36, -18, 36],\n [-12, -8, -24, -12, 24],\n [9, 6, 18, 9, -18],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-6, 24, -7, 2, -2],\n [-3, 54, 0, 15, 6],\n [12, -24, 16, 4, 8],\n [18, 12, 28, 22, 20],\n [0, 36, 3, 12, 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[[-14, 36, 22, -48, -32],\n [35, 30, 37, -12, -8],\n [-36, -36, -42, 18, 12],\n [-3, 12, 8, -15, -10],\n [-29, -24, -30, 9, 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 5x5 matrix:\n[[20, -8, -5, 7, -31],\n [-25, 10, -20, -7, 37],\n [-8, 2, -53, -3, 17],\n [-14, 11, 26, 11, -14],\n [-31, 19, 29, 9, 4]]\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 5x5 matrix:\n[[24, -40, -38, -23, -1],\n [26, -3, -6, -32, -1],\n [-3, 30, 2, 35, 13],\n [-38, 3, -4, 45, -32],\n [42, 32, 24, -36, 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 5x5 matrix:\n[[-2, 11, -5, 25, -7],\n [22, 26, 1, -5, -30],\n [-11, -8, 2, -10, 5],\n [14, -10, 1, -5, 14],\n [-3, 14, -5, 25, -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[[4, -11, 9, -15, 1],\n [5, 14, -6, -2, 2],\n [-44, -32, 0, 24, 16],\n [6, -21, 15, -9, -9],\n [-14, 1, -7, 15, 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[[-4, 0, 6, -2, -3],\n [-2, 0, 13, -36, -39],\n [2, 0, -13, 36, 39],\n [10, 0, -13, -2, 0],\n [-4, 0, 2, 12, 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 5x5 matrix:\n[[20, 15, 10, -20, 5],\n [4, 3, 2, -4, 1],\n [12, 9, 6, -12, 3],\n [24, 18, 12, -24, 6],\n [-4, -3, -2, 4, -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[[6, 4, -30, -17, -22],\n [-3, 1, -42, -12, -19],\n [18, -20, 48, -36, -28],\n [9, -21, 18, -36, -33],\n [-15, 28, -12, 58, 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 5x5 matrix:\n[[20, 3, -24, -30, -33],\n [4, 13, -11, -6, 12],\n [16, 22, -29, -24, 3],\n [20, 3, -24, -30, -33],\n [16, 10, -23, -24, -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[[-8, -13, 10, 20, -14],\n [-23, 4, 28, 24, -2],\n [-16, -3, 11, 12, -4],\n [34, 6, -15, -16, 6],\n [17, 19, 30, 16, -36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, -5, -2, -6, -5],\n [-5, -25, -10, -30, -25],\n [3, 15, 6, 18, 15],\n [-1, -5, -2, -6, -5],\n [-2, -10, -4, -12, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[20, 20, -24, 16, -8],\n [15, 9, -12, 3, 0],\n [25, 19, -24, 11, -4],\n [25, 31, -36, 29, -16],\n [10, -20, 18, -37, 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[[18, 41, 38, -46, -31],\n [30, 15, 15, -10, 5],\n [-4, -25, -27, 19, 21],\n [20, 39, 31, -57, -31],\n [-4, 7, 11, 3, -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[[-6, -4, -2, 6, 1],\n [-36, -24, -12, 36, 6],\n [-6, -4, -2, 6, 1],\n [30, 20, 10, -30, -5],\n [-18, -12, -6, 18, 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[[5, -27, -31, -19, 38],\n [5, -7, -11, -7, 10],\n [45, 2, -34, -24, -1],\n [-20, 18, 34, 22, -26],\n [-25, -5, 15, 11, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[10, 2, -3, 22, 17],\n [-47, 40, -22, 50, -24],\n [-7, -26, 0, 6, 6],\n [43, 18, 7, -44, 15],\n [32, 2, 13, -10, 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[[4, 6, -14, 4, 4],\n [-14, 4, 24, 0, -6],\n [-6, -13, -19, 12, -13],\n [-13, 9, -7, 14, -7],\n [-4, 27, -31, 20, 5]]\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 5x5 matrix:\n[[-15, -50, 33, -14, -39],\n [51, 18, -21, 24, -13],\n [9, -13, 5, -1, -26],\n [27, -4, -5, 8, -29],\n [3, -31, 3, -7, -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[[-12, -36, -18, -24, -30],\n [-31, -18, -29, -37, 10],\n [-21, 12, -14, -17, 35],\n [-1, 12, 2, 3, 15],\n [-37, -36, -38, -49, -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[[-4, -2, 0, -6, 5],\n [0, 0, 0, 0, 0],\n [16, 8, 0, 24, -20],\n [-16, -8, 0, -24, 20],\n [-8, -4, 0, -12, 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[[-25, 5, -20, 0, -10],\n [0, 0, 0, 0, 0],\n [20, -4, 16, 0, 8],\n [-10, 2, -8, 0, -4],\n [5, -1, 4, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-39, 22, -5, -31, 40],\n [-39, 32, -25, -25, 44],\n [3, 6, -15, 7, 0],\n [24, -17, 10, 17, -26],\n [-12, 1, 10, -13, 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 5x5 matrix:\n[[25, -15, 10, -20, 20],\n [25, -15, 10, -20, 20],\n [0, 0, 0, 0, 0],\n [-30, 18, -12, 24, -24],\n [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[[-46, -26, 29, -6, 10],\n [-21, 32, 31, -4, -29],\n [27, -2, -28, -2, 11],\n [9, 12, 23, 40, -31],\n [-29, -8, 27, 4, -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[[-4, 3, 2, 0, 1],\n [4, -3, -2, 0, -1],\n [-4, 3, 2, 0, 1],\n [12, -9, -6, 0, -3],\n [-20, 15, 10, 0, 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[[12, 3, 9, 11, 29],\n [-39, -22, -3, 2, 7],\n [6, -25, -23, -7, -25],\n [-24, 8, 24, 3, 32],\n [-13, 15, 24, -4, 20]]\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, 25, -20, -10, 20],\n [-25, -25, 20, 10, -20],\n [-25, -25, 20, 10, -20],\n [-20, -20, 16, 8, -16],\n [15, 15, -12, -6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, -3, 15, -9, 9],\n [-12, 4, -20, 12, -12],\n [15, -5, 25, -15, 15],\n [3, -1, 5, -3, 3],\n [6, -2, 10, -6, 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 5x5 matrix:\n[[3, 12, -18, 12, 6],\n [-4, -16, 24, -16, -8],\n [-5, -20, 30, -20, -10],\n [3, 12, -18, 12, 6],\n [-1, -4, 6, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[18, 30, -6, -12, -6],\n [22, -30, 16, 27, -4],\n [-31, 15, -13, -21, 7],\n [36, -20, 16, 26, -8],\n [23, 25, -3, -7, -7]]\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 5x5 matrix:\n[[-8, 7, -2, -7, -14],\n [19, -15, 16, 15, 22],\n [-24, -13, 30, 13, 6],\n [-2, -25, 34, 25, 30],\n [-32, -5, 22, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[10, -14, 46, 17, -23],\n [-1, 3, -3, 2, -3],\n [-8, -6, 0, -10, 8],\n [2, -8, 4, 23, -19],\n [38, 20, 41, -22, 18]]\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, 18, -24, 24],\n [24, 39, 30, -18, 42],\n [18, 32, 23, -16, 32],\n [8, 24, 12, -16, 16],\n [-8, -2, -8, -4, -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[[4, 10, 16, 28, 22],\n [60, -35, 32, 30, 7],\n [42, -34, 4, 12, 10],\n [-44, 37, -8, -2, 7],\n [-2, -14, -23, -26, -13]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 37, -18, 49, -29],\n [-6, -13, 37, 2, -6],\n [-6, 37, -18, 49, -29],\n [-2, -11, 27, -10, -18],\n [-13, 16, 13, 57, 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[[-4, 11, -18, -9, 1],\n [-2, -61, -47, -28, 8],\n [12, -10, -7, -13, -16],\n [-8, 23, 1, 6, 7],\n [16, 29, 37, 12, -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 5x5 matrix:\n[[5, -27, 28, 9, 21],\n [44, -56, 79, 5, 44],\n [-34, 36, -21, -6, -15],\n [29, -21, 53, 3, 30],\n [6, -38, -37, -1, -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[[6, 36, -12, -18, -12],\n [-2, -12, 4, 6, 4],\n [-3, -18, 6, 9, 6],\n [-5, -30, 10, 15, 10],\n [-3, -18, 6, 9, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[24, -24, 36, -18, 6],\n [-4, 4, -6, 3, -1],\n [24, -24, 36, -18, 6],\n [8, -8, 12, -6, 2],\n [-24, 24, -36, 18, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-17, -10, -18, 5, 0],\n [23, 40, 42, 13, -3],\n [-32, 15, -11, 34, -3],\n [-1, -30, -14, -35, 20],\n [20, 0, 6, 0, -17]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 10, -4, 6, 2],\n [11, 9, 5, -27, 40],\n [16, 24, 20, 16, 12],\n [18, 16, 26, 36, -16],\n [15, 36, 24, 36, 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[[15, -30, 5, -5, 20],\n [3, -6, 1, -1, 4],\n [-18, 36, -6, 6, -24],\n [0, 0, 0, 0, 0],\n [15, -30, 5, -5, 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[[10, -14, 6, 4, 24],\n [-49, -10, 14, 12, -35],\n [32, -19, -11, -26, 23],\n [-18, -20, 8, 0, -6],\n [8, 11, -2, 4, 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[[-18, 4, 22, 35, -10],\n [-24, -7, 23, 10, -15],\n [-13, -5, 11, 2, 11],\n [-22, -40, -22, 2, -11],\n [-50, -64, -12, -4, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-2, 5, 16, 5, 19],\n [-10, 10, 20, 5, 25],\n [-36, 12, -24, -14, -22],\n [-24, 9, -12, -8, -10],\n [2, 1, 8, 3, 9]]\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 5x5 matrix:\n[[24, 6, -2, 28, 11],\n [-5, -10, 15, 0, 40],\n [-3, -6, 9, 0, 24],\n [10, 2, 0, 12, 7],\n [-18, -6, 4, -20, -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[[-14, -41, -44, -23, 5],\n [-23, 40, -19, -7, 0],\n [54, 15, 32, 38, -30],\n [17, -25, -31, 2, -20],\n [-52, 2, 24, -18, 30]]\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, 10, 14, 40, 18],\n [4, 2, -26, -28, 0],\n [-7, -11, 23, 4, -15],\n [5, 13, -1, 28, 21],\n [-9, -15, 27, 0, -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[[-34, 39, -1, -49, -46],\n [-18, 27, -25, -17, -13],\n [70, -37, -37, 43, -2],\n [12, 10, -46, 30, 30],\n [8, 2, 20, -30, -53]]\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 5x5 matrix:\n[[51, -22, -36, -93, -30],\n [-42, 38, 36, 73, 13],\n [-42, 27, 27, 84, 12],\n [-52, 22, 57, 61, 12],\n [33, 35, -36, -22, -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 5x5 matrix:\n[[20, 1, -14, -12, -20],\n [55, -20, 0, -5, 50],\n [-17, -5, 4, -3, 0],\n [50, 3, -6, 6, 20],\n [11, 1, -1, 2, 5]]\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 5x5 matrix:\n[[-42, 18, -24, 12, 0],\n [-21, -20, 22, 31, 7],\n [-17, -30, 34, 37, 9],\n [32, -22, 28, -2, 2],\n [7, 26, -30, -27, -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[[-58, 12, 31, -25, -16],\n [-40, 2, -16, 36, -16],\n [56, -24, 7, -29, 24],\n [-52, 44, -23, 37, -44],\n [3, 9, 7, -13, -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 5x5 matrix:\n[[0, 6, -12, 3, -12],\n [0, 0, 0, 0, 0],\n [0, -12, 24, -6, 24],\n [0, -10, 20, -5, 20],\n [0, 4, -8, 2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, -1, -6, 11, -11],\n [-3, 7, 6, -20, 20],\n [-9, -17, 18, -3, 3],\n [-3, -3, 6, -5, 5],\n [-12, -16, 24, -14, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-22, 3, -23, 11, -10],\n [10, 0, 11, -5, 7],\n [12, -18, 6, -6, -24],\n [6, -4, 5, -3, -3],\n [14, -16, 9, -7, -19]]\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, 5, -50, -20, 25],\n [-35, -39, 12, 2, 8],\n [-30, -33, 6, 0, 9],\n [20, 26, -44, -16, 14],\n [5, 3, 24, 10, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-24, 20, -36, -25, -16],\n [-8, 20, 12, 3, 32],\n [-14, 4, -28, -20, -26],\n [14, -21, -6, 5, -24],\n [-2, 5, -14, -2, -4]]\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 5x5 matrix:\n[[42, 18, 33, -39, 12],\n [44, -14, 36, -28, -6],\n [-46, 0, -37, 35, -2],\n [-32, 6, -26, 22, 2],\n [28, -34, 24, -8, -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[[17, 15, 0, -4, 25],\n [5, 0, 15, -10, 25],\n [-19, -20, 11, -2, -15],\n [34, 35, -17, 2, 30],\n [24, 25, -13, 2, 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[[9, 15, -12, 18, 9],\n [-3, -5, 4, -6, -3],\n [-15, -25, 20, -30, -15],\n [-6, -10, 8, -12, -6],\n [15, 25, -20, 30, 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[[-24, 14, -11, 19, 4],\n [20, 10, -15, -5, -45],\n [-24, 8, -17, 21, -6],\n [-4, -49, 11, -5, 24],\n [-28, 33, 13, 13, 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 5x5 matrix:\n[[12, -6, -6, 12, 3],\n [24, -12, -12, 24, 6],\n [-16, 8, 8, -16, -4],\n [-12, 6, 6, -12, -3],\n [-16, 8, 8, -16, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 4, -2, -6, -12],\n [9, -6, 3, 9, 18],\n [-18, 12, -6, -18, -36],\n [-15, 10, -5, -15, -30],\n [-12, 8, -4, -12, -24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-30, -30, -25, 0, -10],\n [36, 36, 30, 0, 12],\n [-5, 5, -6, 1, 6],\n [-18, 42, -26, 6, 40],\n [-6, 54, -16, 6, 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[[10, 4, 0, 4, -2],\n [20, 26, 6, -28, -4],\n [39, 44, -14, 2, -23],\n [41, 31, -1, -2, -12],\n [10, 19, 5, -26, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[25, 27, -8, -44, -30],\n [0, 3, 4, -9, -28],\n [18, 8, 4, -36, -20],\n [27, 0, 6, -45, -3],\n [-5, -4, -4, 13, 0]]?\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 5x5 matrix:\n[[24, -48, 3, -14, -15],\n [-4, 26, 6, -44, 38],\n [-31, 44, 16, -14, -7],\n [-42, 18, 46, -17, -21],\n [21, -23, -14, 8, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, -5, 2, 1, 6],\n [8, -20, 8, 4, 24],\n [0, 0, 0, 0, 0],\n [10, -25, 10, 5, 30],\n [-12, 30, -12, -6, -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[[-12, -9, -2, -6, -18],\n [4, 3, -10, 10, 6],\n [-12, -9, -6, -3, -18],\n [44, 33, 2, 26, 66],\n [8, 6, -20, 20, 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[[-28, -14, 22, -2, -6],\n [-12, -12, 12, -9, -3],\n [22, 15, -19, 7, 5],\n [8, 8, -8, 6, 2],\n [18, 11, -15, 4, 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[[26, -5, -35, 19, 36],\n [48, -60, -24, 30, -30],\n [30, -25, -25, 20, 5],\n [12, 0, -18, 9, 21],\n [12, 10, -26, 10, 40]]?\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[[44, 32, 46, -28, -34],\n [10, 3, 12, 5, 14],\n [-14, 7, -24, 1, 62],\n [-14, 15, -28, -7, 70],\n [-14, 3, -22, 5, 58]]\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, 15, -10, -4, 5],\n [53, 1, 27, -11, -2],\n [14, 28, -20, 6, 18],\n [-81, 16, -60, -1, 15],\n [-16, -23, 8, -7, -18]]\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[[18, 5, 5, 14, 2],\n [-30, 1, -6, -14, 20],\n [12, 10, 5, 16, 18],\n [6, -17, -3, -14, -46],\n [12, -14, -1, -8, -42]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[10, 10, 25, -25, -25],\n [0, 0, 0, 0, 0],\n [-2, -2, -5, 5, 5],\n [8, 8, 20, -20, -20],\n [2, 2, 5, -5, -5]]\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[[-46, -15, -38, 21, 14],\n [-37, -60, -56, 12, -22],\n [-35, -14, -30, 5, -36],\n [-2, 18, 8, 12, 52],\n [7, -9, 0, -12, -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[[-13, 34, -39, -25, 13],\n [-4, 16, -12, -4, 4],\n [13, -34, 39, 25, -13],\n [4, -10, 12, 8, -4],\n [8, -23, 24, 14, -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[[-36, 8, 14, -21, -24],\n [41, -1, 45, -14, 43],\n [36, -25, 22, -9, 32],\n [34, 10, -8, 67, 2],\n [-6, 35, -28, 37, -14]]\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 5x5 matrix:\n[[-18, 26, 30, -28, 24],\n [-2, -2, 18, -8, 10],\n [4, -12, 12, 0, 4],\n [12, -14, -30, 22, -21],\n [14, -16, -36, 26, -25]]\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, 6, -3],\n [8, 4, 16, 26, -21],\n [4, -4, 8, 16, -24],\n [12, 28, 24, 28, 18],\n [-2, -18, -4, 2, -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 5x5 matrix:\n[[0, 20, 0, 16, 0],\n [0, 20, 0, 16, 0],\n [0, -20, 0, -16, 0],\n [0, -5, 0, -4, 0],\n [0, 20, 0, 16, 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[[23, 16, -19, -15, -15],\n [-26, -7, 13, 0, 30],\n [-27, -21, 24, 21, 15],\n [2, 11, -9, -16, 10],\n [-22, -2, 8, -6, 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[[-6, 15, -6, -3, 3],\n [-12, 30, -12, -6, 6],\n [-12, 30, -12, -6, 6],\n [8, -20, 8, 4, -4],\n [-8, 20, -8, -4, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[7, -3, -21, -33, 12],\n [-3, -7, 19, -29, -10],\n [-4, 20, -24, 27, -24],\n [1, -18, 32, -10, 19],\n [-4, 4, 8, 23, -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[[-18, 10, -16, -8, 1],\n [42, 43, -32, -42, 72],\n [15, 5, -10, -23, 31],\n [-26, 9, -16, 1, -13],\n [-32, -28, 28, 7, -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[[30, -35, -5, -16, 16],\n [17, -35, -4, -31, 24],\n [-36, 0, 8, -18, -4],\n [-7, -40, 3, -41, 16],\n [19, -10, -5, -5, 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 5x5 matrix:\n[[-25, -14, 5, 5, 8],\n [-18, 28, -2, -23, -27],\n [31, 20, -9, -6, -13],\n [-11, 33, -12, -18, -33],\n [-1, 8, 11, -16, -3]]\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[[-40, 20, 45, -25, 55],\n [9, 0, -15, 15, -15],\n [3, 0, -5, 5, -5],\n [-4, 8, -2, 10, 2],\n [-16, 8, 18, -10, 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[[-22, 2, 17, 26, -18],\n [6, 32, 33, 0, 39],\n [18, -3, 7, -21, 27],\n [-11, -15, -61, -30, 7],\n [-24, -19, -59, -19, -5]]\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, -44, 18, 26, -5],\n [-27, 8, -48, -25, -30],\n [-8, -8, -3, 27, -6],\n [-49, -14, -27, 2, -51],\n [2, 4, 3, 27, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-5, -6, -25, 16, -38],\n [-26, 12, -28, -40, 0],\n [4, 0, 1, -40, 34],\n [-31, 15, -26, -19, -16],\n [0, 0, -9, -48, 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 5x5 matrix:\n[[3, 24, 0, 9, 0],\n [14, 16, 0, -30, -16],\n [-5, -28, 0, -6, 2],\n [5, 40, 0, 15, 0],\n [-13, -20, 0, 24, 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[[-2, 10, 2, 8, -2],\n [-6, 30, 6, 24, -6],\n [-4, 20, 4, 16, -4],\n [0, 0, 0, 0, 0],\n [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[[6, 1, 7, -2, -33],\n [-6, -6, -13, -15, -21],\n [-6, -15, -43, 12, -3],\n [-8, 3, 10, -25, 6],\n [12, 4, 8, 28, 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[[-8, -1, 50, 37, -28],\n [12, -26, -8, 42, 24],\n [4, 8, 4, 40, 0],\n [0, 25, -20, -15, 0],\n [10, -25, -14, 19, 24]]\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, -2, 29, -10, -3],\n [2, 56, 31, -32, 62],\n [2, 34, 12, -20, 6],\n [7, 43, 14, -22, 37],\n [8, -32, -26, 24, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-25, 23, -13, 7, -3],\n [18, -7, -3, 12, 7],\n [17, -26, 62, -5, 28],\n [-30, 41, -51, 24, -11],\n [-63, 47, -21, -3, -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[[-34, 6, 58, 18, 24],\n [15, -33, 9, 21, 60],\n [-10, -25, 23, 7, 44],\n [-17, 23, -3, -19, -44],\n [-27, 25, 23, -5, -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 5x5 matrix:\n[[16, 1, -19, -7, 55],\n [-40, 29, 25, 13, -25],\n [-34, 32, 16, 10, 5],\n [10, -16, 0, -2, -25],\n [-36, 31, 19, 11, -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[[0, -2, -13, -27, -14],\n [14, 16, -11, -78, 10],\n [12, -10, 16, 63, -16],\n [-30, -30, 30, 84, -24],\n [10, -28, 53, 57, -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[[1, -1, -1, -3, -3],\n [1, -1, -1, -3, -3],\n [-2, 2, 2, 6, 6],\n [2, -2, -2, -6, -6],\n [5, -5, -5, -15, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-1, -36, 12, -17, -29],\n [-34, 2, -15, -25, 28],\n [14, 32, -15, 25, 60],\n [28, 28, 6, 34, -16],\n [7, 19, 6, 14, -33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, 7, -2, 2, -2],\n [16, -2, 5, 3, 8],\n [8, 32, 6, 2, -36],\n [-13, 2, -3, -3, -9],\n [31, 40, 8, 10, -25]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, -14, -42, 52, -26],\n [-9, -4, 3, -3, -7],\n [9, -2, -32, 8, -15],\n [12, -9, -63, -6, -21],\n [-15, -8, 8, 6, -13]]?\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 5x5 matrix:\n[[-3, -6, 12, -6, -18],\n [-5, -10, 20, -10, -30],\n [-1, -2, 4, -2, -6],\n [-4, -8, 16, -8, -24],\n [-4, -8, 16, -8, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[11, 24, 10, -16, 27],\n [-18, -4, -12, -32, 20],\n [4, 4, 20, -66, 69],\n [42, -6, 10, 63, -48],\n [-21, 4, -14, -4, -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[[-25, 30, 25, -5, -25],\n [20, -24, -20, 4, 20],\n [-5, 6, 5, -1, -5],\n [-5, 6, 5, -1, -5],\n [15, -18, -15, 3, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-12, -24, 0, -18, 24],\n [2, 4, 0, 3, -4],\n [6, 12, 0, 9, -12],\n [12, 24, 0, 18, -24],\n [-4, -8, 0, -6, 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 5x5 matrix:\n[[12, 6, 18, 18, -36],\n [-12, -6, -18, -18, 36],\n [-10, -5, -15, -15, 30],\n [-10, -5, -15, -15, 30],\n [-4, -2, -6, -6, 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[[4, 28, 16, 8, -28],\n [-4, -12, 4, -12, 12],\n [0, -4, -5, 1, 4],\n [-8, -48, -22, -18, 48],\n [-6, -2, 26, -22, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[24, -47, -35, 41, -19],\n [28, 28, 9, 25, -57],\n [-42, -1, -24, -48, 24],\n [-42, 14, -9, -63, -3],\n [-25, -17, 1, -20, 65]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 2, -5, -4, 4],\n [-27, 9, -20, -14, 19],\n [-45, 14, -24, -20, 33],\n [-30, 11, -36, -26, 18],\n [-28, 11, -40, -26, 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 5x5 matrix:\n[[-20, -2, -6, -19, 23],\n [-25, 17, -14, -40, 19],\n [5, 35, -10, -24, -23],\n [20, -34, 18, 49, -5],\n [5, -19, 8, 21, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[6, 2, -6, 2, 12],\n [15, 5, -15, 5, 30],\n [6, 2, -6, 2, 12],\n [3, 1, -3, 1, 6],\n [18, 6, -18, 6, 36]]\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 5x5 matrix:\n[[-66, 12, 0, 60, -6],\n [-2, -4, -24, 0, -22],\n [0, -12, -66, -5, -60],\n [50, -8, 6, -45, 10],\n [14, -8, -30, -15, -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 5x5 matrix:\n[[-17, -24, -10, 54, -18],\n [-15, 1, -2, -24, -21],\n [24, 14, 8, -12, 30],\n [12, 7, 4, -6, 15],\n [-28, -25, -12, 42, -33]]\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[[42, -33, 8, 5, -34],\n [33, 33, 26, 14, 11],\n [-23, -39, 1, -49, -39],\n [15, 18, 24, -21, -15],\n [-14, 0, -22, 20, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-32, 4, -40, -31, -29],\n [-31, 15, -33, 32, -4],\n [16, -6, 19, -2, 8],\n [-5, 17, -17, 0, -8],\n [28, 2, 15, -45, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -9, 9, -17, -19],\n [4, 14, -2, -29, -52],\n [15, 15, -3, -2, 35],\n [7, 19, 7, -26, -54],\n [10, 10, 10, -8, 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[[-32, -32, -14, 17, -27],\n [28, 46, -8, -19, 9],\n [8, 63, -39, 12, -22],\n [36, 15, 51, 3, 57],\n [-23, -31, -34, -35, -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[[23, 1, 11, 3, 9],\n [17, -36, 42, 29, 39],\n [-10, -17, 14, 21, 18],\n [-41, 0, -20, -3, -15],\n [35, 15, 2, -12, -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[[-27, -22, 22, 27, -23],\n [17, 26, -2, -13, 19],\n [34, -24, 36, -62, -6],\n [-23, 12, -54, 43, 6],\n [5, 20, -38, 5, 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 5x5 matrix:\n[[-31, 18, 3, 45, -58],\n [42, -21, -3, -60, 78],\n [-39, 50, -1, 5, -16],\n [24, 9, 9, -10, 22],\n [0, 20, -4, -40, 44]]\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[[13, 9, -40, 8, -34],\n [32, 19, -7, 26, -8],\n [27, 16, -5, 22, -6],\n [-10, -6, 4, -8, 4],\n [16, 9, 11, 14, 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[[-2, -2, 4, -6, 2],\n [-26, 30, 17, 20, 19],\n [15, -9, -15, 3, -12],\n [4, 4, -8, 12, -4],\n [-28, 36, 16, 28, 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[[-6, 12, -12, -24, -72],\n [-14, 14, 4, -4, -24],\n [-76, 61, 21, 20, -18],\n [26, -17, -28, -26, -48],\n [15, -9, 17, -4, 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 5x5 matrix:\n[[6, 12, 24, 18, -24],\n [-5, -10, -20, -15, 20],\n [5, 10, 20, 15, -20],\n [-5, -10, -20, -15, 20],\n [4, 8, 16, 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[[41, 12, 4, 12, -35],\n [-28, -15, -8, 3, 25],\n [17, 22, 20, -18, -9],\n [7, 20, 12, -30, -13],\n [-20, -22, -8, 27, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[21, -6, -2, 32, 14],\n [15, 2, -6, 36, 6],\n [-4, -5, -5, -4, -10],\n [-22, 21, 2, 7, 1],\n [24, 31, 17, 4, 25]]?\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[[3, 12, -12, -12, 3],\n [-4, -16, 16, 16, -4],\n [5, 20, -20, -20, 5],\n [1, 4, -4, -4, 1],\n [2, 8, -8, -8, 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[[-28, 19, -18, -57, 20],\n [-32, 29, 0, -51, 13],\n [20, 13, -6, 33, -28],\n [-4, 39, 6, 3, -24],\n [-16, 52, 12, -12, -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[[-30, 18, -12, -30, -36],\n [12, -22, 18, 30, 16],\n [1, 29, -26, -35, -2],\n [-36, -8, 12, 0, -40],\n [6, -48, 42, 60, 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 5x5 matrix:\n[[0, 9, 24, 7, -1],\n [-23, 16, -19, 9, -7],\n [29, -8, -43, -22, 7],\n [56, -9, -24, -29, 13],\n [-46, 4, 74, 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[[-9, -14, -1, 1, 15],\n [-24, 1, 18, -8, -10],\n [38, 28, -2, 5, -16],\n [-4, 6, -16, 13, 14],\n [46, 26, 3, 11, 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 5x5 matrix:\n[[-4, 4, -24, -13, 21],\n [-22, 17, 0, 10, 13],\n [-6, 7, -8, 5, -16],\n [10, -5, -12, -4, -25],\n [-20, 15, -10, 0, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[5, -29, -2, 28, 3],\n [20, 19, 19, -23, 12],\n [-5, -26, -9, 27, -3],\n [25, 35, 26, -40, 15],\n [10, -23, 3, 21, 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[[32, 22, 28, 0, -10],\n [-11, -3, -11, -27, -25],\n [14, 4, 16, 10, -20],\n [-22, -7, -24, -22, 13],\n [13, 18, 4, -1, 54]]\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, 2, 18, 5, -5],\n [24, 6, 54, 15, -15],\n [10, 20, -30, 8, 6],\n [36, 44, -24, 26, 2],\n [6, 14, -24, 5, 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[[-11, -16, 28, -21, -21],\n [-16, 42, -14, 14, -22],\n [-6, -6, -11, 15, 39],\n [-22, 18, 22, -16, -52],\n [-19, 20, -5, 10, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -20, 4, -24, -20],\n [0, 5, -1, 6, 5],\n [0, 0, 0, 0, 0],\n [0, -30, 6, -36, -30],\n [0, 0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-41, 28, -33, -30, 19],\n [-25, 10, -28, -14, 32],\n [41, -28, 33, 30, -19],\n [-60, 28, -42, -37, 39],\n [-38, 8, -6, -19, 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[[7, 11, 20, -5, -3],\n [15, 23, 48, 1, 5],\n [44, 0, -12, 18, 34],\n [48, 2, -22, -5, 13],\n [-32, -14, 2, 35, 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 5x5 matrix:\n[[-36, -15, -3, 6, 39],\n [-7, -8, 11, -17, 37],\n [2, 2, -2, 4, -9],\n [-33, -11, -10, 15, 20],\n [-21, -12, 9, -7, 41]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-66, -30, 6, 12, -36],\n [-36, -12, -10, 30, -28],\n [-24, -24, 20, 36, -40],\n [65, 23, 3, 4, 22],\n [-19, 9, -40, 43, -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 5x5 matrix:\n[[-8, 50, 10, 38, 0],\n [-12, -40, 0, -10, 34],\n [16, 6, -8, 0, -16],\n [-4, 6, 7, -27, -32],\n [0, -14, 2, -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[[32, -30, -10, -2, -4],\n [-68, 37, 19, 19, 30],\n [-23, 11, 37, 33, 26],\n [-21, -10, 45, 52, 46],\n [-36, 58, -14, -34, -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[[12, 16, 12, 46, -22],\n [-13, -14, -12, -51, 28],\n [15, -47, -17, -47, 40],\n [-20, 48, -4, -16, 19],\n [6, 12, -30, 9, -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[[-6, -30, 12, 30, -36],\n [-4, -20, 8, 20, -24],\n [-1, -5, 2, 5, -6],\n [3, 15, -6, -15, 18],\n [-4, -20, 8, 20, -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[[17, -5, 18, -7, 7],\n [48, -53, 33, -4, 47],\n [16, -7, 17, -12, 9],\n [2, 14, 12, -26, -6],\n [44, -36, 31, 28, 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[[2, -2, 7, 2, -4],\n [2, -34, 27, 34, -28],\n [4, 20, -1, -20, 10],\n [0, 24, -15, -24, 18],\n [-3, -17, 2, 17, -9]]\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 5x5 matrix:\n[[0, -2, 1, -4, -4],\n [24, 12, -10, 40, -4],\n [-2, 0, 27, 36, -11],\n [14, -4, -27, -36, -11],\n [8, -2, -17, -22, -5]]\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[[-25, -20, -30, 15, -5],\n [30, 24, 36, -18, 6],\n [30, 24, 36, -18, 6],\n [-10, -8, -12, 6, -2],\n [15, 12, 18, -9, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[16, 5, -2, -27, -32],\n [22, -6, -54, 30, -8],\n [6, -38, 2, -6, -12],\n [-12, 24, 30, -21, 3],\n [-17, -18, 3, 30, 34]]\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 5x5 matrix:\n[[-3, 9, -18, 0, 15],\n [-12, -6, -6, -10, -8],\n [-22, -18, 0, -20, -26],\n [-16, -15, 3, -15, -22],\n [-35, 0, -45, -25, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[7, -51, 49, 0, 16],\n [12, -24, 14, 13, 14],\n [6, -51, 1, 3, 53],\n [-8, 16, -14, -41, 12],\n [-41, -1, -5, -62, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-62, 1, -8, -12, 2],\n [-16, -2, -19, 7, -28],\n [-25, -18, 5, -12, -34],\n [-61, 2, -7, -20, 6],\n [8, 8, 26, 30, 52]]\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, -7, -24, 14, 5],\n [-13, 13, 3, 11, 24],\n [3, 30, -27, 15, 9],\n [-8, -12, 48, -24, -6],\n [-4, -5, -6, 8, 9]]\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[[50, 48, 19, 22, -35],\n [37, 49, 5, 18, -39],\n [27, 34, -1, -11, -21],\n [20, -50, -54, 8, 16],\n [29, 62, -11, -18, -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[[32, -28, -12, -36, -6],\n [40, -20, 36, -12, -54],\n [-18, 12, -6, 12, 15],\n [-34, 16, -34, 8, 49],\n [-35, 15, -40, 5, 55]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[6, 3, -15, 12, -18],\n [0, 0, 0, 0, 0],\n [4, 2, -10, 8, -12],\n [10, 5, -25, 20, -30],\n [-2, -1, 5, -4, 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 5x5 matrix:\n[[-12, -2, -12, 39, 42],\n [-9, 33, 28, 1, 9],\n [-4, -1, -40, -16, -10],\n [-1, -28, 29, 11, -19],\n [-4, -4, -37, -37, -40]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[36, -24, -6, -36, 30],\n [-12, 8, 2, 12, -10],\n [-12, 8, 2, 12, -10],\n [-24, 16, 4, 24, -20],\n [24, -16, -4, -24, 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 5x5 matrix:\n[[24, 36, -12, -30, 24],\n [-8, 30, -30, -55, -32],\n [15, 7, 2, 10, 29],\n [31, 11, 30, -10, 23],\n [30, 10, 24, 0, 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[[-45, 33, -36, -16, 13],\n [-30, 12, -24, 6, 12],\n [35, -17, 28, -2, -13],\n [15, -24, 12, 27, 0],\n [-15, 6, -12, 3, 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 5x5 matrix:\n[[31, 56, -24, -28, -29],\n [11, 4, -21, 34, -25],\n [-52, -43, 2, -9, 69],\n [39, 32, 7, -2, -49],\n [3, -4, -14, 28, -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[[5, -15, 10, -15, 30],\n [1, -3, 2, -3, 6],\n [0, 0, 0, 0, 0],\n [2, -6, 4, -6, 12],\n [-2, 6, -4, 6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-48, -18, -30, 6, 6],\n [18, 30, -6, 0, 18],\n [-10, 4, -12, 2, 8],\n [13, 1, 11, -2, -5],\n [12, 20, -4, 0, 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[[18, 0, -12, 6, -15],\n [-24, 0, 16, -8, 20],\n [24, 0, -16, 8, -20],\n [0, 0, 0, 0, 0],\n [12, 0, -8, 4, -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[[4, 20, -8, 16, 24],\n [2, 10, -4, 8, 12],\n [4, 20, -8, 16, 24],\n [5, 25, -10, 20, 30],\n [-1, -5, 2, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-46, 25, -45, -11, 42],\n [-6, -6, 13, -33, 23],\n [18, -26, 46, -38, 4],\n [-8, -2, -18, 40, -20],\n [-36, 7, -45, 45, 8]]\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, -24, 2, 11, 28],\n [-12, -6, 8, 2, 4],\n [8, -6, -42, 7, 24],\n [6, -3, -26, 4, 14],\n [-16, -6, 18, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-36, -5, 37, -1, 8],\n [-16, -40, 24, -42, 30],\n [20, 35, -27, 36, -27],\n [12, 5, -13, 4, -5],\n [-12, 15, 9, 18, -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[[-5, -30, 15, -25, -5],\n [1, 6, -3, 5, 1],\n [-5, -30, 15, -25, -5],\n [-4, -24, 12, -20, -4],\n [-3, -18, 9, -15, -3]]\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, -25, 0, 0, 10],\n [24, 30, 0, 0, -12],\n [24, 30, 0, 0, -12],\n [-4, -5, 0, 0, 2],\n [-24, -30, 0, 0, 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[[21, -17, 16, -20, 15],\n [-18, 12, -12, 15, -12],\n [24, -22, 20, -25, 18],\n [18, -12, 12, -15, 12],\n [6, -22, 16, -20, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-15, 20, -5, 25, 0],\n [6, -8, 2, -10, 0],\n [-18, 24, -6, 30, 0],\n [-3, 4, -1, 5, 0],\n [-12, 16, -4, 20, 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[[12, 12, -18, 18, 12],\n [12, 12, -18, 18, 12],\n [-4, -4, 6, -6, -4],\n [-12, -12, 18, -18, -12],\n [-8, -8, 12, -12, -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[[-38, -12, -18, 10, 4],\n [-3, -26, -2, 34, -15],\n [30, -11, -11, -14, 14],\n [-4, -20, -32, 36, 4],\n [13, -53, -21, 32, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[15, -1, -3, 10, -17],\n [27, -13, 1, 34, -37],\n [-6, 6, -2, -12, 10],\n [24, -10, 0, 28, -32],\n [-30, 2, 6, -20, 34]]\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[[-11, 10, -14, -20, 1],\n [-24, -25, 8, 23, 16],\n [-12, 21, -30, -35, 8],\n [18, 28, -5, -32, -28],\n [15, 46, -17, -60, -39]]\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[[12, 0, -20, -20, -24],\n [3, 0, -5, -5, -6],\n [-18, 0, 30, 30, 36],\n [3, 0, -5, -5, -6],\n [15, 0, -25, -25, -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 5x5 matrix:\n[[-2, -3, -4, 6, 0],\n [4, 6, 8, -12, 0],\n [-2, -3, -4, 6, 0],\n [4, 6, 8, -12, 0],\n [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[[51, -10, -29, 2, 1],\n [-12, -31, 13, -25, 37],\n [54, 12, -41, -5, -4],\n [12, -5, 1, 27, -21],\n [53, 8, -44, -25, 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[[-4, -2, 8, 12, -6],\n [2, 7, -22, -39, 3],\n [-14, -1, 10, 9, -21],\n [-8, -4, 16, 24, -12],\n [-4, 0, 2, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-36, -6, 24, 24, 18],\n [-18, -3, 12, 12, 9],\n [24, 4, -16, -16, -12],\n [-30, -5, 20, 20, 15],\n [-24, -4, 16, 16, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[18, -6, 0, 6, -15],\n [-18, 6, 0, -6, 15],\n [18, -6, 0, 6, -15],\n [-18, 6, 0, -6, 15],\n [-18, 6, 0, -6, 15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[11, 32, -8, 5, -6],\n [0, 16, -31, 24, -15],\n [17, 37, 7, -20, -9],\n [2, -49, 45, -11, 26],\n [11, 32, 35, -51, 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[[11, 43, -16, 3, -6],\n [-18, -58, 32, -6, -12],\n [23, 39, -28, 4, 12],\n [32, 1, -2, -4, -27],\n [-14, -5, -18, 6, 57]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-26, 10, -44, -26, -26],\n [15, 6, -12, 6, 15],\n [8, 10, -28, -2, 8],\n [10, -13, 46, 17, 10],\n [-44, -4, -8, -28, -44]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-22, 21, 15, -2, -17],\n [-23, 33, -15, 20, -19],\n [-16, 12, 20, -8, -12],\n [16, -21, 5, -10, 13],\n [11, -6, -20, 10, 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[[-20, 2, -22, 0, -8],\n [-28, 14, -10, 0, 16],\n [-6, -5, -17, 0, -16],\n [-26, 4, -26, 0, -7],\n [-12, -3, -21, 0, -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[[-2, 5, 2, -4, 6],\n [10, -25, -10, 20, -30],\n [-8, 20, 11, -10, 19],\n [-12, 30, 15, -18, 31],\n [-12, 30, 30, 12, 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 5x5 matrix:\n[[-4, 21, 18, 8, 19],\n [-33, -20, 7, 17, 30],\n [-13, -15, -15, -15, 5],\n [2, 3, -18, -28, 7],\n [-29, -12, 15, 33, 70]]\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 5x5 matrix:\n[[-22, 8, 60, 16, -64],\n [-47, 16, 1, -43, 1],\n [-25, 33, -20, -9, 19],\n [-9, 21, -11, 2, 11],\n [23, -16, -25, -5, 29]]\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, -24, -18, 0, -6],\n [-24, 24, 18, 0, 6],\n [-12, 12, 9, 0, 3],\n [-16, 16, 12, 0, 4],\n [-20, 20, 15, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, 30, -30, -6, 24],\n [-1, 5, -5, -1, 4],\n [4, -20, 20, 4, -16],\n [2, -10, 10, 2, -8],\n [5, -25, 25, 5, -20]]\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[[-12, -4, 16, -16, 8],\n [27, 9, -6, 36, -33],\n [3, 1, 18, 4, -13],\n [-12, -4, -24, -16, 28],\n [0, 0, -16, 0, 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[[11, 24, 7, -19, 37],\n [3, -8, -9, 5, -11],\n [11, 4, -8, -5, 8],\n [-9, -16, -3, 13, -25],\n [-24, 24, 42, -12, 30]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-24, 20, -28, -12, -36],\n [6, -6, 3, 1, 4],\n [-36, 32, -34, -14, -44],\n [-18, 22, 7, 5, 8],\n [-6, 10, 13, 7, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, -2, -4, -43, 4],\n [42, 20, 2, 8, -9],\n [-9, 9, 20, 19, -22],\n [-24, 8, 30, 23, -17],\n [-3, -7, -12, 40, 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[[-15, -18, 24, 0, -27],\n [-6, -6, 30, 0, -24],\n [-10, -12, 16, 0, -18],\n [14, 17, -19, 0, 23],\n [11, 16, 30, 0, -11]]\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, 8, -12, -12, 12],\n [12, 24, -36, 18, -30],\n [-21, 28, -42, -24, 20],\n [22, -40, 60, 24, -16],\n [27, -16, 24, 33, -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[[36, -13, 21, -24, 45],\n [-32, 20, -60, 27, -38],\n [20, -2, 34, 3, 4],\n [-26, -2, -18, -6, -8],\n [17, -11, 21, -18, 26]]\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[[10, -8, -4, 0, -12],\n [2, -12, 24, -20, 24],\n [-30, 37, -19, 25, 3],\n [35, -41, 17, -25, -9],\n [15, 1, -37, 25, -51]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-18, 12, 15, -12, 12],\n [22, -22, -19, 19, -10],\n [20, -6, -16, 9, -18],\n [0, -44, -4, 26, 28],\n [-14, 46, 15, -31, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, -66, 66, 84, 48],\n [23, 60, -19, -33, 0],\n [37, 17, 19, 4, -53],\n [-48, -15, -30, -27, -3],\n [-8, -25, 16, 33, 69]]\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 5x5 matrix:\n[[9, 50, 5, 6, -67],\n [-52, -23, -29, -31, -32],\n [-40, -38, -6, -8, 8],\n [-7, 60, -17, -8, -83],\n [-13, -17, -8, -19, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, 0, 6, 15, -6],\n [9, 0, 6, 15, -6],\n [-3, 0, -2, -5, 2],\n [6, 0, 4, 10, -4],\n [-12, 0, -8, -20, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[53, -47, 43, 0, -16],\n [19, 9, 27, -2, 4],\n [-10, -16, -20, 50, -14],\n [16, -30, -5, 59, -10],\n [33, -67, -8, 41, -13]]\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, -39, 18, -40, 37],\n [-6, 30, 3, 41, -27],\n [-22, -28, 23, -15, 31],\n [24, 60, -30, 54, -60],\n [-14, 1, 10, 16, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[20, 34, -9, -11, -33],\n [5, 4, -11, 6, -14],\n [5, 46, 14, -19, -34],\n [-10, -4, 22, -12, 23],\n [30, 42, -1, -29, -22]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, -3, 9, 3, -3],\n [-12, 0, -22, 8, -4],\n [-22, 13, 16, -33, 23],\n [26, -8, 13, 12, -10],\n [26, -11, 0, 23, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 4, -38, -44, 0],\n [50, -60, 35, -2, 52],\n [25, -15, -40, -52, 22],\n [-25, 33, -45, -14, -18],\n [-10, 12, 25, 10, -28]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -28, 28, 48, -24],\n [-6, -6, 10, 16, -12],\n [-6, 3, 2, 2, -6],\n [4, 28, -28, -48, 24],\n [-4, 8, -4, -8, 0]]\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[[-39, 30, 9, -28, -36],\n [7, 14, 5, 6, -8],\n [-23, -27, -3, -22, 26],\n [-41, 10, 16, -37, 6],\n [28, 7, -2, 24, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[10, 28, -8, -26, -22],\n [1, 16, -5, -14, -13],\n [12, 16, -4, -16, -12],\n [12, 38, -11, -35, -30],\n [8, 40, -12, -36, -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 5x5 matrix:\n[[3, 29, 36, -16, 24],\n [-4, 40, 50, -17, 14],\n [37, -13, -34, 9, 18],\n [15, 1, 4, -7, -8],\n [-13, 9, 26, -15, 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[[24, 24, -12, -24, -6],\n [16, 16, -8, -16, -4],\n [8, 8, -4, -8, -2],\n [-12, -12, 6, 12, 3],\n [-20, -20, 10, 20, 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[[-3, -3, 9, -6, 12],\n [-1, -13, 3, 4, 31],\n [6, -10, -18, 20, 12],\n [-1, -5, 3, 0, 13],\n [-2, -18, 6, 4, 44]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[25, -50, -15, 25, -20],\n [-30, 48, 16, -24, 22],\n [5, 8, 0, -4, -1],\n [30, 12, -6, -6, -12],\n [30, -48, -16, 24, -22]]\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 5x5 matrix:\n[[8, -1, -1, 22, -6],\n [-12, 1, 32, -12, -18],\n [26, 12, -32, 22, -26],\n [9, 11, -29, -10, -2],\n [18, -42, 30, 66, -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[[-35, 17, 0, -50, -19],\n [-4, 0, -8, 24, -14],\n [5, -5, 34, -26, -3],\n [14, -3, 4, 15, 7],\n [-16, 29, 21, -54, -9]]\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 5x5 matrix:\n[[0, 3, -10, -3, 8],\n [4, -24, 52, 12, -36],\n [12, -30, 16, -6, 4],\n [20, -45, 10, -15, 20],\n [8, -24, 24, 0, -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[[-8, -2, 8, -4, 8],\n [0, 0, 0, 0, 0],\n [24, 6, -24, 12, -24],\n [24, 6, -24, 12, -24],\n [-24, -6, 24, -12, 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[[16, 36, -9, -29, -54],\n [-24, -26, 3, 25, 64],\n [15, -63, -12, 6, -6],\n [-12, -10, -34, -16, 18],\n [-25, 33, -3, -1, 36]]\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, 10, 10, -4, -4],\n [6, -10, -10, 4, 4],\n [-15, 25, 25, -10, -10],\n [3, -5, -5, 2, 2],\n [3, -5, -5, 2, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[24, 0, -30, 12, -18],\n [8, 0, -10, 4, -6],\n [12, 0, -15, 6, -9],\n [-4, 0, 5, -2, 3],\n [-16, 0, 20, -8, 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 5x5 matrix:\n[[-30, 18, -30, 0, 6],\n [10, -6, 10, 0, -2],\n [5, -3, 5, 0, -1],\n [-25, 15, -25, 0, 5],\n [10, -6, 10, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-5, 54, -8, 8, -1],\n [0, -60, 14, -11, 5],\n [39, 8, -20, 15, 8],\n [-18, -66, 60, -30, 9],\n [24, -48, 8, -7, -18]]\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[[18, -18, -12, -18, 6],\n [12, -12, -8, -12, 4],\n [-6, 6, 4, 6, -2],\n [-36, 36, 24, 36, -12],\n [-24, 24, 16, 24, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[25, 30, 5, 15, -25],\n [6, 1, 2, -2, -7],\n [20, 55, 0, 40, -15],\n [29, 10, 9, -5, -33],\n [-26, -25, -6, -10, 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[[-2, -10, -26, -20, 0],\n [-50, 29, -5, -4, -46],\n [49, -18, 29, 12, 16],\n [5, -25, -42, -41, -18],\n [-41, 12, 5, 0, -60]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-14, -15, -13, -18, 22],\n [1, -1, 60, -34, -35],\n [-22, -24, 35, -43, -10],\n [-71, -54, 34, 7, -59],\n [21, 51, -17, 17, 9]]\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, -20, -35, 18, 7],\n [-31, 75, 41, -60, -1],\n [39, 16, -28, -12, 25],\n [-24, 46, 28, -36, -4],\n [-16, 42, 29, -26, -33]]\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 5x5 matrix:\n[[-2, 15, -13, 18, -21],\n [-20, -19, 30, 26, 6],\n [-14, 7, 1, 38, -25],\n [6, 55, -49, 26, -37],\n [8, -13, 8, -30, 26]]\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[[4, -16, -16, 24, 12],\n [6, -24, -24, 36, 18],\n [-3, 12, 12, -18, -9],\n [0, 0, 0, 0, 0],\n [-6, 24, 24, -36, -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[[36, 24, 3, 45, 22],\n [21, 12, -18, 32, 12],\n [17, 16, 48, 42, 17],\n [49, 50, 6, 6, 47],\n [-33, -30, -19, -37, -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 5x5 matrix:\n[[-20, -6, -8, 54, 0],\n [0, 3, 6, 15, 0],\n [-10, -12, -22, -18, 0],\n [5, 3, 5, -6, 0],\n [25, 20, 35, -5, 0]]\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, -18, 24, 12, 12],\n [0, 0, 0, 0, 0],\n [-18, -18, 24, 12, 12],\n [-3, -3, 4, 2, 2],\n [-15, -15, 20, 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[[-12, 24, 12, 0, -12],\n [15, -30, -15, 0, 15],\n [-9, 18, 9, 0, -9],\n [18, -36, -18, 0, 18],\n [-18, 36, 18, 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[[8, 40, -68, -32, 18],\n [14, -19, -33, -8, 7],\n [4, -17, -5, -12, 2],\n [-13, 24, -39, -1, -25],\n [5, -33, 10, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-34, 5, -30, -4, -1],\n [-31, -28, 1, 14, 16],\n [36, 41, -9, -16, -6],\n [-52, -47, 6, 32, 21],\n [-29, -39, 18, 34, 20]]\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, -6, 10, -8, 2],\n [20, 15, -25, 20, -5],\n [12, 9, -15, 12, -3],\n [16, 12, -20, 16, -4],\n [4, 3, -5, 4, -1]]\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, 18, 12, 0, -18],\n [-30, 18, 12, 0, -18],\n [-10, 6, 4, 0, -6],\n [-15, 9, 6, 0, -9],\n [10, -6, -4, 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 5x5 matrix:\n[[-10, -51, -16, -22, 20],\n [-60, 39, -6, -2, 0],\n [-4, -30, 8, -30, 14],\n [-26, 0, -38, 25, 1],\n [-5, -40, 7, -36, 18]]\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 5x5 matrix:\n[[-2, 0, 10, -25, -18],\n [51, -7, -10, 28, 9],\n [-20, -39, -7, -31, -25],\n [39, 21, -46, 15, 71],\n [24, -7, -9, -11, 1]]\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[[-31, 30, 17, 26, -13],\n [-10, 7, -33, 52, 26],\n [-38, 43, 63, 7, -50],\n [-20, 1, -17, 41, 4],\n [-1, -26, -53, 44, 29]]\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 5x5 matrix:\n[[10, 3, 15, -24, 5],\n [17, 37, 10, 14, -32],\n [-38, -37, -40, 40, 5],\n [-15, -28, -9, -3, 12],\n [15, 45, 20, -29, -27]]\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, -49, 57, 37, -7],\n [6, 2, 10, 8, -4],\n [-1, 30, -21, -5, -9],\n [-7, -11, -11, 2, -8],\n [-10, 46, -44, -28, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -43, -43, -5, 7],\n [-13, 5, 21, 11, 17],\n [9, -7, -17, -1, -1],\n [14, -8, -19, 20, 29],\n [-4, 7, 7, -23, -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[[54, -15, -15, -24, -33],\n [-48, 25, -3, 41, 13],\n [36, -15, -16, -17, -15],\n [0, -30, -8, -22, 42],\n [14, -30, -1, -31, 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 5x5 matrix:\n[[30, -25, 10, 15, -15],\n [18, -15, 6, 9, -9],\n [-36, 30, -12, -18, 18],\n [18, -15, 6, 9, -9],\n [-30, 25, -10, -15, 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[[4, 4, -6, 6, -3],\n [20, 20, -30, 30, -15],\n [-20, -20, 30, -30, 15],\n [20, 20, -30, 30, -15],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-4, 2, -5, 1, -9],\n [16, -12, -38, 14, -22],\n [2, -2, -12, 4, -10],\n [-29, 19, 29, -13, 0],\n [-19, 13, 27, -11, 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[[3, 18, 3, -9, 15],\n [6, 36, 6, -18, 30],\n [2, 12, 2, -6, 10],\n [-4, -24, -4, 12, -20],\n [1, 6, 1, -3, 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[[28, -12, -5, -12, -25],\n [-13, 40, 14, 5, 19],\n [-33, 27, -20, 7, 39],\n [7, 4, 26, 19, 11],\n [15, -62, -32, -11, -27]]\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 5x5 matrix:\n[[-9, 26, -41, 32, -11],\n [5, 13, 16, 29, -15],\n [-15, 21, 15, 9, -21],\n [-15, 25, -58, 25, -1],\n [28, -27, 10, -1, 17]]\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[[-17, 0, -3, -1, 15],\n [23, 27, 8, 3, 1],\n [-29, 45, 30, -1, 57],\n [-9, -33, 28, -5, -23],\n [-44, -24, -12, -4, 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[[-8, 24, -20, 8, 8],\n [4, -12, 10, -4, -4],\n [4, -12, 10, -4, -4],\n [8, -24, 20, -8, -8],\n [10, -30, 25, -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[[1, -5, 1, 2, 0],\n [-2, 10, -2, -4, 0],\n [-1, 5, -1, -2, 0],\n [1, -5, 1, 2, 0],\n [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[[6, 45, -22, -41, 10],\n [-2, -9, 6, 5, -4],\n [-10, 12, 32, -6, -30],\n [0, 15, 2, -3, -3],\n [-2, 18, 0, -34, -7]]\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[[13, 85, 7, -22, -15],\n [-11, 13, 11, -4, -4],\n [-54, -6, 30, -54, -45],\n [38, 2, -27, 10, 11],\n [-21, 51, 29, 0, -2]]\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 5x5 matrix:\n[[3, -15, -14, 30, 2],\n [15, -6, 5, -6, -3],\n [-9, 13, 3, -16, 10],\n [-14, 2, -14, 14, -52],\n [24, -6, -5, -12, 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[[0, 0, 0, 0, 0],\n [-6, 18, 6, 9, -12],\n [10, -30, -10, -15, 20],\n [10, -30, -10, -15, 20],\n [6, -18, -6, -9, 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[[7, -6, 1, -2, -9],\n [13, -4, -6, -13, -16],\n [-19, 12, 2, 11, 24],\n [-2, 6, -5, -5, 3],\n [3, 6, -9, -12, -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[[-9, -3, 0, 6, -6],\n [17, 14, -25, -23, -7],\n [12, -6, 30, 6, 30],\n [5, -5, 20, 6, 18],\n [-19, -8, 5, 15, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-18, 18, 6, -9, 15],\n [18, -18, -6, 9, -15],\n [-36, 36, 12, -18, 30],\n [12, -12, -4, 6, -10],\n [12, -12, -4, 6, -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[[12, -10, -8, -4, 10],\n [12, -10, -8, -4, 10],\n [30, -25, -20, -10, 25],\n [24, -20, -16, -8, 20],\n [6, -5, -4, -2, 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[[-28, -9, 3, -34, 29],\n [-30, 16, 39, 44, 4],\n [-45, 14, 39, 50, 0],\n [-27, -8, -6, 26, -26],\n [23, 11, -48, -32, -7]]\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[[59, -55, 7, -20, -12],\n [-8, 28, -1, -25, -24],\n [-59, 51, -11, 0, -6],\n [27, -31, 5, 10, 12],\n [-8, 8, -6, -30, -28]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-15, 3, -24, 24, -27],\n [-12, -8, -16, 20, -12],\n [-16, 27, -11, 3, -15],\n [-3, 8, 28, -29, 45],\n [10, -4, 21, -20, 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[[15, -10, 15, 0, -10],\n [-3, 2, -3, 0, 2],\n [9, -6, 9, 0, -6],\n [-9, 6, -9, 0, 6],\n [15, -10, 15, 0, -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[[-1, 5, -5, -1, 5],\n [-5, 25, -25, -5, 25],\n [3, -15, 15, 3, -15],\n [-4, 20, -20, -4, 20],\n [5, -25, 25, 5, -25]]\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 5x5 matrix:\n[[5, 6, 13, -19, 7],\n [-5, 6, -17, 41, -13],\n [-7, -12, -17, 20, -8],\n [1, 24, -5, 38, -10],\n [6, 12, 14, -14, 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 5x5 matrix:\n[[20, -8, -20, -12, -20],\n [0, 0, 0, 0, 0],\n [-10, 4, 10, 6, 10],\n [25, -10, -25, -15, -25],\n [20, -8, -20, -12, -20]]\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, 12, 6, 1, 6],\n [39, -30, -31, -2, -18],\n [-38, 22, 14, 15, -1],\n [-29, 18, 17, 24, -8],\n [-28, 4, -10, 19, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[20, 25, 17, -3, 38],\n [-1, -2, -1, -77, -3],\n [-78, -33, 15, -37, -1],\n [93, 29, 2, 24, 7],\n [-49, -16, 23, -11, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 13, 10, -13, -3],\n [36, -14, 36, -2, 2],\n [-12, 30, 26, -31, -7],\n [-24, 16, -14, -7, -3],\n [-36, 10, -42, 7, -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[[28, 33, 31, 6, -19],\n [0, 18, 1, -21, -9],\n [0, -3, 15, 10, -5],\n [-8, -3, 27, 6, -13],\n [-36, -42, -23, -1, 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[[-21, -29, 24, -10, 3],\n [-4, 16, -9, 16, 12],\n [21, 49, -39, 35, 12],\n [27, 55, -45, 38, 11],\n [17, 5, -9, -3, -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[[5, -55, 16, 17, 4],\n [35, 0, 40, -28, 24],\n [-21, 25, 24, -23, -2],\n [-29, 0, -8, 20, -40],\n [6, -15, -52, 49, -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 5x5 matrix:\n[[3, -9, -12, -9, -18],\n [-5, 15, 20, 15, 30],\n [-3, 9, 12, 9, 18],\n [0, 0, 0, 0, 0],\n [-4, 12, 16, 12, 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 5x5 matrix:\n[[48, -36, -51, 6, 12],\n [36, -23, -17, -29, -8],\n [-1, 4, -32, 0, -29],\n [20, -36, -19, -20, 14],\n [50, -16, -37, 4, -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[[-21, 15, -6, 3, -12],\n [-10, 8, 4, 4, -8],\n [-5, 4, 2, 2, -4],\n [5, -4, -2, -2, 4],\n [-20, 13, -16, -1, -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[[0, 0, 0, 0, 0],\n [-12, -30, 36, 0, 36],\n [-12, -30, 36, 0, 36],\n [-2, -5, 6, 0, 6],\n [12, 30, -36, 0, -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[[7, 3, -40, -12, 15],\n [-42, -31, 23, -54, 31],\n [6, 24, -30, 12, 48],\n [-16, 4, 17, 18, -15],\n [43, 13, 0, 42, -60]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, 36, -4, 0, -8],\n [-14, -6, -26, -24, -28],\n [3, 4, 4, 4, 4],\n [-18, -5, -35, -32, -38],\n [21, 9, 39, 36, 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[[-21, 0, 30, 12, -15],\n [28, 14, -1, 15, 18],\n [37, 24, 14, 32, 23],\n [-3, -8, -18, -16, -1],\n [5, 4, 4, 6, 3]]\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 5x5 matrix:\n[[19, -32, 27, 48, 39],\n [-5, -21, 18, 28, 21],\n [16, 12, -19, 17, 1],\n [-23, 38, -36, -43, -42],\n [46, 22, -26, 2, -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[[21, 9, 12, 0, 3],\n [29, 9, 12, 6, 15],\n [20, 29, 13, -13, -49],\n [38, 33, 55, -39, -53],\n [6, -8, 26, -14, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-26, 3, 2, -15, -48],\n [28, -2, 4, 18, 48],\n [-2, -5, -26, -9, 12],\n [0, 6, 30, 9, -18],\n [-4, 4, 18, 3, -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[[-18, -15, -18, 18, -15],\n [-36, -30, -36, 36, -30],\n [-6, -5, -6, 6, -5],\n [24, 20, 24, -24, 20],\n [-24, -20, -24, 24, -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 5x5 matrix:\n[[-17, 10, -2, -28, 2],\n [-18, -13, -49, -9, 23],\n [-23, -31, -3, 11, 53],\n [0, 3, 3, 39, 1],\n [-19, -4, -14, 16, 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[[-10, -15, -25, 15, 10],\n [-2, -3, -5, 3, 2],\n [-2, -3, -5, 3, 2],\n [-12, -18, -30, 18, 12],\n [6, 9, 15, -9, -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[[20, 20, -30, 25, -10],\n [8, 8, -12, 10, -4],\n [-4, -4, 6, -5, 2],\n [8, 8, -12, 10, -4],\n [20, 20, -30, 25, -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[[10, -10, 2, 6, -4],\n [15, -15, 3, 9, -6],\n [5, -5, 1, 3, -2],\n [-15, 15, -3, -9, 6],\n [15, -15, 3, 9, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-70, -6, 8, -25, 18],\n [-61, -42, 2, -14, 8],\n [-18, 48, 54, -12, -12],\n [-12, -5, 12, -3, -3],\n [87, 21, -2, 20, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[33, -48, -8, 9, 32],\n [23, -22, -26, -29, 14],\n [-16, 15, 21, 14, -19],\n [-1, -3, 7, 17, 7],\n [19, -27, -8, 10, 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[[-2, 15, -33, -5, 16],\n [18, 30, -18, 0, 6],\n [21, 2, 42, 9, -23],\n [-8, -6, -6, -2, 4],\n [-10, -13, 3, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-24, 4, 20, 24, 8],\n [36, -6, -30, -36, -12],\n [-36, 6, 30, 36, 12],\n [12, -2, -10, -12, -4],\n [6, -1, -5, -6, -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 5x5 matrix:\n[[-4, -19, 2, 9, 2],\n [13, 20, 9, -1, -9],\n [-15, 21, -27, -30, 15],\n [19, 38, 6, -28, 18],\n [-39, -34, -32, 10, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[9, -3, -18, 12, 18],\n [36, -12, -30, 30, 12],\n [-3, 1, 13, -7, -16],\n [-15, 5, 9, -11, 0],\n [18, -6, -1, 9, -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[[0, 18, 12, -3, 0],\n [0, 30, 20, -5, 0],\n [0, 6, 4, -1, 0],\n [0, -6, -4, 1, 0],\n [0, -24, -16, 4, 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 5x5 matrix:\n[[-4, -6, -3, 3, 2],\n [-16, -24, -12, 12, 8],\n [-8, -12, -6, 6, 4],\n [16, 24, 12, -12, -8],\n [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[[18, 31, 1, 26, -29],\n [-24, 5, 21, 2, 29],\n [18, -44, 26, -48, 40],\n [5, -28, 4, -27, 37],\n [40, -5, -16, -5, -14]]\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[[3, -24, -18, -15, -18],\n [-12, 34, 49, 30, 42],\n [0, 30, -25, -10, -10],\n [12, 28, -26, 0, -12],\n [-12, 26, 9, 1, 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 5x5 matrix:\n[[7, 25, -46, -48, 26],\n [30, 31, -38, -36, 54],\n [16, -9, -46, -50, -8],\n [27, -30, 24, 27, -9],\n [15, 1, 2, 4, 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[[11, -1, 11, -1, 4],\n [26, -1, 26, 2, 19],\n [3, -3, 3, -9, -18],\n [16, -1, 16, 0, 9],\n [-32, 2, -32, 0, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[11, 17, 32, -6, 13],\n [-17, -18, -23, 23, -11],\n [-5, -50, -35, -33, 5],\n [9, 9, 54, 0, 27],\n [-4, -15, -25, -8, -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[[6, -2, 6, 6, -2],\n [-15, 5, -15, -15, 5],\n [-3, 1, -3, -3, 1],\n [18, -6, 18, 18, -6],\n [3, -1, 3, 3, -1]]\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, 36, -36, 24, 24],\n [1, -6, 6, -4, -4],\n [-2, 12, -12, 8, 8],\n [-1, 6, -6, 4, 4],\n [3, -18, 18, -12, -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 5x5 matrix:\n[[48, -30, -22, -2, -32],\n [12, -30, -18, 12, 12],\n [-28, 34, 22, -8, 4],\n [-4, 19, 11, -9, -12],\n [4, -19, -11, 9, 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[[-10, -35, 29, -4, 43],\n [54, 63, -88, 1, -34],\n [-5, 22, -15, 6, 10],\n [-23, -42, 51, 10, -2],\n [46, 14, -48, 20, -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[[-4, -5, -5, 0, -3],\n [24, 30, 30, 0, 18],\n [-8, -10, -10, 0, -6],\n [-16, -20, -20, 0, -12],\n [4, 5, 5, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-58, -36, -33, -46, -15],\n [58, 4, 4, 12, -10],\n [-18, -12, 24, 18, -6],\n [-6, -5, -2, -3, 0],\n [27, -2, -2, -6, -35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[8, -11, 42, 4, 32],\n [-31, 21, -26, -2, -26],\n [-44, 26, -22, 8, -26],\n [63, -27, -20, -30, 0],\n [48, -21, 2, -36, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-34, -42, -12, -20, -11],\n [34, 18, 1, -19, -17],\n [16, 39, 18, 40, 28],\n [16, 0, -23, -19, -20],\n [-34, -42, -12, -20, -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[[-6, -18, 2, -30, -23],\n [36, 26, 3, 12, -6],\n [18, -6, 3, -30, -33],\n [24, 41, 25, 16, -9],\n [48, 18, -16, 16, 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[[-5, -15, -5, 0, -5],\n [-6, -18, -6, 0, -6],\n [-6, -18, -6, 0, -6],\n [5, 15, 5, 0, 5],\n [2, 6, 2, 0, 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 5x5 matrix:\n[[19, 4, -20, 13, -41],\n [-63, -47, 2, 32, 48],\n [-32, -10, 21, -8, 38],\n [-37, -40, -6, 25, 71],\n [7, 5, 25, -2, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-16, 60, 22, -20, 12],\n [30, 25, -18, -16, -3],\n [-12, -23, 1, 14, 51],\n [-51, 10, 15, -5, 38],\n [-25, 32, 33, 0, 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[[-7, 52, -13, 44, -27],\n [-24, 32, -38, 76, 18],\n [34, 12, -10, 8, -36],\n [-29, 12, -1, 14, 15],\n [23, -40, 33, -58, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, -31, -56, -1, -7],\n [-4, 3, -16, 51, -9],\n [-18, 49, -1, -16, -12],\n [31, -4, 23, 65, 26],\n [-34, -4, 21, 1, -36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[33, -1, -51, -47, 4],\n [-30, 12, 48, -4, -40],\n [-17, 11, 28, -19, -38],\n [-13, -22, 32, 12, -39],\n [21, -2, -30, -36, -13]]\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[[31, 3, -30, -31, 20],\n [-28, -34, -30, -28, 3],\n [-20, 47, 38, -45, -32],\n [18, -24, -6, -48, -18],\n [20, -82, -24, 38, 4]]?\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[[28, 6, 6, -8, 6],\n [-8, -4, 0, -4, -2],\n [30, 4, -30, -28, 4],\n [4, 1, -15, -6, 0],\n [42, 2, -24, -44, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, 0, -6, -3, 0],\n [-39, 30, 42, -24, -45],\n [-34, 20, 32, -14, -30],\n [-36, 32, 42, -27, -48],\n [-13, 2, 8, 1, -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[[20, -32, -14, 29, 11],\n [-41, -19, -27, 19, 35],\n [29, 1, 7, 1, -6],\n [103, 23, 52, -18, 49],\n [-35, -31, -35, 26, -49]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[7, 20, -37, 30, -6],\n [5, 5, 6, -19, -1],\n [24, 6, 13, -24, 17],\n [35, -28, 26, 18, 53],\n [-7, 22, -35, 6, -30]]\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[[-20, -8, 12, 4, -8],\n [-25, -10, 15, 5, -10],\n [-30, -12, 18, 6, -12],\n [10, 4, -6, -2, 4],\n [20, 8, -12, -4, 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[[6, 26, -51, -12, 15],\n [42, 1, 30, -81, 48],\n [0, 6, -30, -3, 6],\n [8, 15, 31, -2, -9],\n [6, 74, -24, 14, -12]]?\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 5x5 matrix:\n[[0, 5, 30, -15, 30],\n [-6, 2, 6, -12, -54],\n [3, 1, 9, 0, 39],\n [6, -4, -18, 18, 42],\n [-6, 11, 60, -39, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[5, -5, -25, -5, -15],\n [-6, 6, 30, 6, 18],\n [-4, 4, 20, 4, 12],\n [4, -4, -20, -4, -12],\n [3, -3, -15, -3, -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[[-30, -14, -6, 38, 22],\n [-11, 28, -16, 23, -22],\n [18, 20, 0, -16, -24],\n [-33, -7, -21, 12, 19],\n [5, -42, 22, -11, 36]]?\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, -20, -4, -6, 16],\n [-21, -25, 1, -22, 37],\n [-11, 18, 12, 16, 30],\n [-8, -13, -2, -25, -1],\n [-11, -2, 5, 3, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 5, 5, -2, 5],\n [18, -15, -15, 6, -15],\n [12, -10, -10, 4, -10],\n [12, -10, -10, 4, -10],\n [-30, 25, 25, -10, 25]]\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 5x5 matrix:\n[[11, 18, -24, 6, -37],\n [17, -12, 12, -5, -11],\n [3, -9, 9, -9, 21],\n [40, -24, 17, -26, 13],\n [11, 2, 36, -43, 25]]\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, -27, 39, -4, 7],\n [34, 8, 22, -30, 10],\n [44, 8, 38, -30, 32],\n [-24, 3, -38, 1, -50],\n [12, 14, 12, 18, 64]]?\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 5x5 matrix:\n[[-16, 2, -14, -18, 0],\n [8, 6, -2, -2, -20],\n [-20, 6, -22, -28, -10],\n [-36, 8, -36, -46, -10],\n [-20, 6, -22, -28, -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[[-17, -10, 7, -31, 17],\n [2, 17, 10, 92, 35],\n [-57, -6, -6, 42, -42],\n [-14, -17, -21, 57, -2],\n [1, -28, -28, 70, 32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 24, 16, 20, -16],\n [-1, 6, -4, 25, 4],\n [-8, -40, -32, -20, 32],\n [-3, -20, -12, -20, 12],\n [7, 40, 28, 30, -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[[24, 18, 36, -36, -36],\n [24, 18, 36, -36, -36],\n [12, 9, 18, -18, -18],\n [-24, -18, -36, 36, 36],\n [20, 15, 30, -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[[73, -17, -23, 36, -6],\n [-1, -30, 23, 10, 0],\n [-15, -21, 3, 0, -12],\n [-6, -32, -21, 6, -31],\n [-31, 7, 32, -14, 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 5x5 matrix:\n[[15, 6, -33, -3, -24],\n [-28, -2, 54, 10, 42],\n [-21, -13, 50, 2, 35],\n [-20, 15, 25, 15, 25],\n [-5, 21, -8, 12, 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[[-23, 14, -37, 8, 4],\n [-24, 0, -25, 7, 7],\n [-18, 12, -34, 12, 4],\n [59, 10, 44, -5, -17],\n [-14, -1, -5, -8, 2]]\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[[11, -3, 13, 21, -22],\n [-25, 15, 25, 15, 20],\n [20, -15, -40, -35, -5],\n [-15, 9, 15, 9, 12],\n [17, -9, -9, -1, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, -6, -12, -18, -24],\n [21, -29, 33, -9, 27],\n [-19, 26, -32, 6, -28],\n [18, -24, 36, 0, 36],\n [-19, 27, -23, 15, -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[[-17, 14, 33, 31, 18],\n [40, -22, -1, -28, -3],\n [-37, -32, 29, -53, -13],\n [24, -19, 21, -31, 9],\n [-19, 16, 3, 9, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[57, -42, -54, 0, -12],\n [-3, 6, 24, -22, 44],\n [79, 24, 8, 6, 6],\n [27, 5, -3, 13, -19],\n [-48, 3, 10, 2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-5, 0, 0, -15, 25],\n [0, 0, 0, 0, 0],\n [2, 0, 0, 6, -10],\n [3, 0, 0, 9, -15],\n [4, 0, 0, 12, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-22, -40, 29, 33, 17],\n [-18, -30, 36, 12, 18],\n [1, -1, -14, 14, -5],\n [26, 46, -40, -32, -22],\n [-12, -24, 6, 30, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 24, -12, 30, -30],\n [0, 12, -6, 15, -15],\n [0, -12, 6, -15, 15],\n [0, 20, -10, 25, -25],\n [0, 8, -4, 10, -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 5x5 matrix:\n[[16, 17, 20, -5, 31],\n [29, 4, -17, -38, -21],\n [1, 10, -10, 30, 20],\n [-29, 22, 9, 11, -20],\n [5, 10, 31, -76, -43]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[5, 1, 10, -16, -8],\n [9, -3, -31, 12, -4],\n [-3, -39, -8, -24, 28],\n [2, -18, -17, -4, 11],\n [-4, 28, 13, 20, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-30, -30, -20, 0, 10],\n [-18, -18, -12, 0, 6],\n [24, 24, 16, 0, -8],\n [-36, -36, -24, 0, 12],\n [-6, -6, -4, 0, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[15, 12, 6, -15, -12],\n [-5, -4, -2, 5, 4],\n [-15, -12, -6, 15, 12],\n [-10, -8, -4, 10, 8],\n [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[[-53, -51, 42, 9, -15],\n [-28, -34, -4, 2, -12],\n [-43, -54, 6, 18, -18],\n [19, 15, -45, -22, 1],\n [10, 0, -24, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 3, 6, -3, -5],\n [0, 0, 0, 0, 0],\n [20, -15, -30, 15, 25],\n [0, 0, 0, 0, 0],\n [12, -9, -18, 9, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[24, 12, -24, -20, -24],\n [6, 3, -6, -5, -6],\n [18, 9, -18, -15, -18],\n [-24, -12, 24, 20, 24],\n [24, 12, -24, -20, -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[[-17, -10, -11, 27, -26],\n [-49, 15, -11, 24, -46],\n [24, 13, -3, -25, 32],\n [-28, 22, -15, -4, -7],\n [15, -24, 18, 7, -1]]?\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[[-9, -14, -16, -21, -16],\n [-24, -35, -8, 22, 28],\n [-21, -25, -28, -28, -23],\n [0, -16, 4, 9, 19],\n [-27, -20, -28, -18, -21]]\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[[8, 20, 12, 0, -20],\n [-8, -20, -12, 0, 20],\n [-8, -20, -12, 0, 20],\n [10, 25, 15, 0, -25],\n [6, 15, 9, 0, -15]]\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, 0, -9, 8, 2],\n [-1, 20, -7, 4, -4],\n [-4, -4, 14, -12, -2],\n [5, -10, -10, 10, 5],\n [-1, 20, -7, 4, -4]]\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[[31, -33, -18, 2, -18],\n [-44, 48, 24, -6, 28],\n [-17, 3, 30, 40, -22],\n [0, -18, 24, 49, -38],\n [12, 0, -24, -34, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[29, -18, -19, 7, 3],\n [78, 20, 13, -40, 49],\n [-33, -12, -41, 47, -26],\n [-57, 42, 26, -5, -4],\n [0, 37, -15, 3, 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[[-28, -54, 44, 6, -1],\n [9, 3, 12, 0, 15],\n [8, 4, -10, -10, -21],\n [1, 7, -24, -8, -29],\n [20, 14, 4, -6, 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[[5, 15, 23, 14, -3],\n [23, 5, 19, 12, -4],\n [23, -13, -12, -7, -15],\n [-74, 46, 32, 18, 22],\n [-43, 1, -20, -13, 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 5x5 matrix:\n[[-24, 0, -30, 12, -18],\n [4, 0, 5, -2, 3],\n [24, 0, 30, -12, 18],\n [-16, 0, -20, 8, -12],\n [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[[3, -12, 28, -25, -15],\n [-8, -8, 52, -40, -10],\n [20, -28, 22, -28, -35],\n [27, -36, 24, -33, -45],\n [-28, 32, -8, 20, 40]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[58, -14, -2, 34, 48],\n [-45, 37, 21, -45, -47],\n [-14, -21, -15, -14, 4],\n [20, -21, -19, 46, 14],\n [-9, -34, -20, -3, 15]]?\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[[-23, 24, 16, -34, 9],\n [-42, 26, 22, -12, 34],\n [-37, -5, 25, 34, 47],\n [11, 4, -12, -6, -13],\n [-8, -7, 3, 24, 16]]?\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[[27, -9, -19, 11, -41],\n [-3, 16, 1, -12, 13],\n [-81, 36, 15, -18, 36],\n [-66, 31, -8, -43, 11],\n [54, -20, -10, 28, -34]]\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 5x5 matrix:\n[[7, -6, -11, -34, 13],\n [-1, 7, -9, -25, 16],\n [13, 25, 47, 3, 15],\n [4, 30, 46, 1, 20],\n [-23, -10, 25, -70, 42]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, -11, 4, 1, 14],\n [12, 4, -8, 16, -16],\n [12, 4, -8, 16, -16],\n [-30, 32, -10, -7, -38],\n [12, -10, 2, 5, 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[[-49, 4, -32, -25, 45],\n [31, 14, 23, 10, -30],\n [31, -40, 14, 29, -25],\n [9, 18, 9, -2, -10],\n [24, 30, 21, 1, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[11, -10, 11, -2, 2],\n [-4, 10, 24, -26, 12],\n [29, -30, 13, 10, -2],\n [-39, 45, 3, -33, 12],\n [33, -35, 11, 15, -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[[2, -6, 6, -2, 2],\n [-5, 15, -15, 5, -5],\n [6, -18, 18, -6, 6],\n [4, -12, 12, -4, 4],\n [-2, 6, -6, 2, -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 5x5 matrix:\n[[13, -24, -10, -12, 20],\n [5, -18, 22, -24, -8],\n [0, -19, 14, -14, 8],\n [3, 12, 6, -4, -24],\n [-18, 42, -60, 68, 36]]\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, -36, 15, 9, -12],\n [-14, -75, 9, 26, 4],\n [-10, 42, -22, -14, 0],\n [-28, -3, -4, 8, 28],\n [27, -3, 1, -7, -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[[-12, 8, 4, -20, 12],\n [12, -14, -16, -10, -3],\n [15, -10, -5, 25, -15],\n [-30, 28, 26, -10, 18],\n [39, -38, -37, 5, -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[[-87, 82, 44, 45, -19],\n [-1, -3, 27, 9, 31],\n [1, -4, 27, 11, 48],\n [27, -32, 32, 3, 73],\n [56, -64, -19, -29, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-13, 16, 37, -11, -1],\n [-37, -23, 19, -11, -13],\n [15, -6, -27, 9, 3],\n [-30, -15, 20, -10, -10],\n [-14, -16, -2, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[10, 5, -20, -20, 20],\n [8, 4, -16, -16, 16],\n [10, 5, -20, -20, 20],\n [6, 3, -12, -12, 12],\n [4, 2, -8, -8, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[18, 1, -18, -30, -27],\n [39, -35, -6, -27, -7],\n [57, 20, -60, -3, 10],\n [-51, 6, -20, -30, -13],\n [11, -21, 38, 53, 49]]\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 5x5 matrix:\n[[6, -56, -3, 9, -44],\n [-30, 12, -17, 1, -24],\n [16, -47, -34, 13, -14],\n [8, 6, -13, 6, 24],\n [-34, 23, -26, 8, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, 8, -6, 2, 2],\n [-12, -12, 9, -3, -3],\n [24, 24, -18, 6, 6],\n [20, 20, -15, 5, 5],\n [-24, -24, 18, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -21, -18, 3, -1],\n [16, 25, 30, -9, -15],\n [14, 52, 36, -4, 2],\n [1, -10, -18, 4, -11],\n [17, 13, 0, -1, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[50, -20, 30, -25, -10],\n [-50, 20, -30, 25, 10],\n [2, -8, 6, -10, -13],\n [6, 24, -14, 30, 45],\n [52, -16, 28, -20, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[30, -35, -23, 17, 1],\n [-22, 38, 16, 2, 24],\n [13, -2, 5, -5, -46],\n [-15, -20, -5, -19, 12],\n [22, 7, -13, 40, 38]]\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 5x5 matrix:\n[[-28, -1, 22, 12, -5],\n [-14, 5, 16, -4, -17],\n [-9, -7, 1, 16, 16],\n [23, 13, -7, -32, -28],\n [7, -8, -13, 12, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[29, 21, 16, 0, 30],\n [61, 34, 31, -3, 32],\n [-29, -10, -21, -9, -21],\n [-13, -15, 4, 18, 9],\n [-23, -29, -2, 18, -18]]\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 5x5 matrix:\n[[-17, 35, -8, 26, 42],\n [7, 15, -5, -8, -27],\n [31, -27, -2, 12, 32],\n [-18, 58, -12, -16, -12],\n [-10, 25, -6, 29, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[10, 17, 4, 10, 17],\n [-15, 2, 16, -4, 24],\n [5, 16, 8, 8, 22],\n [15, -12, -24, 0, -42],\n [15, 3, -12, 6, -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[[-16, 0, 15, 17, -27],\n [-31, -51, -3, 28, -15],\n [0, 12, 6, 2, -6],\n [-14, -3, -19, 31, 33],\n [-6, -27, 14, -10, -36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[10, -9, 9, -13, -4],\n [0, -4, -12, -20, 24],\n [-15, 11, -21, 7, 21],\n [-25, 23, -21, 35, 7],\n [25, -16, 42, 0, -49]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[39, -20, 10, -18, -7],\n [40, -2, -1, 70, -8],\n [-15, 38, 9, 47, 12],\n [-13, 24, -18, 51, -10],\n [-7, 8, 26, -19, 23]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-20, -15, -25, -5, 20],\n [0, 0, 0, 0, 0],\n [8, 6, 10, 2, -8],\n [24, 18, 30, 6, -24],\n [-4, -3, -5, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, -3, -21, -9, -5],\n [26, -4, -6, 32, -14],\n [-8, -6, 32, 6, 0],\n [-7, -5, -25, -26, -3],\n [-1, -4, 33, 17, -1]]\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, 3, -13, -24, 0],\n [14, 4, -24, -28, -10],\n [15, 6, -28, -30, -9],\n [-8, -13, 23, 12, -10],\n [-5, 11, -13, 6, 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[[38, -8, -24, -20, -10],\n [-12, 6, 4, 4, 4],\n [-39, 3, 30, 24, 9],\n [-1, -5, 6, 4, -1],\n [34, 5, -34, -26, -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[[30, -30, -15, -15, -5],\n [-36, 36, 18, 18, 6],\n [6, -6, -3, -3, -1],\n [-30, 30, 15, 15, 5],\n [24, -24, -12, -12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -12, -4, 8, -16],\n [-1, -3, -1, 2, -4],\n [-26, -36, 37, 10, 15],\n [14, 18, -22, -4, -12],\n [-10, -6, 26, -4, 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[[-10, -15, 25, -10, 0],\n [4, 6, -10, 4, 0],\n [0, 0, 0, 0, 0],\n [-8, -12, 20, -8, 0],\n [-6, -9, 15, -6, 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, -20, -2, 30, 8],\n [33, 4, 0, -20, 7],\n [-6, -36, -34, 26, 38],\n [16, -55, -18, 41, 14],\n [24, -32, -12, 13, 13]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[5, 4, 5, 3, 1],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [25, 20, 25, 15, 5],\n [-15, -12, -15, -9, -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[[0, 37, -39, 16, 46],\n [0, -11, 15, -14, -20],\n [0, -30, 18, 24, -12],\n [0, 21, -7, -32, -2],\n [0, 27, -19, -14, 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 5x5 matrix:\n[[-10, 16, -31, -5, -11],\n [-6, 12, -20, -20, -13],\n [0, 21, -2, 31, -1],\n [-20, 56, 22, -26, -38],\n [-6, 24, 28, -2, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-14, 4, -3, -11, -12],\n [-24, 2, -3, -9, -22],\n [5, 17, 23, -38, 27],\n [22, -6, -4, 18, 14],\n [4, -7, -3, 16, -2]]\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 5x5 matrix:\n[[-24, 54, -6, 30, 36],\n [2, 6, 10, 12, 2],\n [-26, 48, -16, 18, 34],\n [31, -12, 60, 41, -19],\n [-15, 18, -18, -3, 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 5x5 matrix:\n[[3, 28, 50, -32, -3],\n [-11, -5, 3, -4, 6],\n [30, -4, -22, 2, -20],\n [30, -6, -21, -3, -21],\n [5, -10, 1, -23, -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[[31, 2, -1, -39, -33],\n [15, -10, 15, -15, -25],\n [-8, -6, 8, 12, 4],\n [-11, 13, -19, 9, 23],\n [4, 20, -28, -12, 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[[24, 4, -6, 4, -48],\n [8, 2, -11, -46, 28],\n [17, 28, -4, -24, 7],\n [-15, 24, 20, 52, -3],\n [-5, 4, 4, 8, 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[[-54, 36, -8, 18, 6],\n [-25, 28, -27, -20, -1],\n [-66, 48, -18, 12, 6],\n [34, -28, 16, 2, -2],\n [-31, 34, -32, -23, -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[[-38, -3, 8, -1, -12],\n [40, 12, -16, 8, 0],\n [24, -20, 24, 24, 8],\n [-52, -6, 10, -13, -6],\n [-52, 34, -32, -12, -40]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -6, -8, 6, 6],\n [0, 0, 0, 0, 0],\n [30, -15, -20, 15, 15],\n [-36, 18, 24, -18, -18],\n [-6, 3, 4, -3, -3]]\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, 4, -4, -2, 1],\n [8, -8, 8, 4, -2],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [-20, 20, -20, -10, 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[[24, 4, 20, -20, 0],\n [36, 6, 30, -30, 0],\n [12, 2, 10, -10, 0],\n [-36, -6, -30, 30, 0],\n [30, 5, 25, -25, 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[[-20, 16, 35, -4, -25],\n [14, -6, -34, -13, 10],\n [10, 24, -8, 10, 8],\n [4, 0, -20, -20, -4],\n [15, 12, -23, 3, 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 5x5 matrix:\n[[-2, 22, 38, -14, -34],\n [-4, 3, -4, 6, 14],\n [-9, 28, 35, -6, -16],\n [-4, -27, -32, 40, 74],\n [-10, 46, 28, -18, -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[[28, -12, 7, 30, 21],\n [56, -12, 2, 32, 48],\n [-6, 6, -30, -19, 6],\n [6, -10, 43, 21, -15],\n [2, -2, 0, 1, 0]]\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[[5, 0, -6, -15, 18],\n [8, -3, -21, -30, 36],\n [14, 6, 6, -30, 36],\n [0, 10, 38, 20, -24],\n [5, 5, 13, -5, 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[[23, 33, 4, 20, 27],\n [24, -25, 5, 46, -21],\n [-42, -28, -17, -58, -20],\n [-8, 30, 46, 12, -22],\n [-16, 1, -9, -26, 27]]\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, 15, -22, -7, -11],\n [54, 19, 22, 19, 11],\n [36, 1, 28, 16, 14],\n [6, 41, -42, -9, -21],\n [-24, -31, 16, -2, 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 5x5 matrix:\n[[2, 4, 2, -10, -2],\n [1, 2, 1, -5, -1],\n [1, 2, 1, -5, -1],\n [-4, -8, -4, 20, 4],\n [-1, -2, -1, 5, 1]]\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, -19, -13, 3, 25],\n [-12, 39, 33, -15, -45],\n [10, -22, -24, 16, 20],\n [8, -29, -23, 9, 35],\n [-12, 12, 24, -24, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-23, 15, -15, 7, -13],\n [-34, -9, -25, 14, -1],\n [-24, 0, 3, 39, -24],\n [22, 27, 3, -34, 3],\n [1, -57, -6, 4, 35]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0, 0],\n [36, -16, -28, -24, 4],\n [-27, 1, 16, 9, -7],\n [-3, 16, 9, 14, 5],\n [39, 1, -22, -11, 11]]\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, 11, -3, 12, -37],\n [20, 12, 2, 12, -44],\n [5, -11, -7, -7, 14],\n [50, -11, -26, 4, -45],\n [25, 6, 2, 7, -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[[49, 13, 33, -40, 54],\n [-10, -36, 23, 25, -29],\n [-11, 3, -23, -16, 8],\n [13, -12, 14, -21, 20],\n [-4, -10, -4, -12, 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[[-4, -12, 0, 17, -7],\n [41, -38, -38, 31, -48],\n [9, -4, -10, 33, 52],\n [22, 21, -9, -36, -3],\n [-16, -27, 3, 11, -46]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[3, 24, -34, 36, -3],\n [-1, -3, 20, -15, 1],\n [2, -12, 38, -57, 29],\n [-28, 15, 8, 12, -35],\n [13, 0, -24, 38, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-15, 15, -9, -3, -6],\n [39, -1, 31, 4, 27],\n [39, -21, 27, 6, 21],\n [-27, 13, -19, -4, -15],\n [27, -13, 19, 4, 15]]?\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, 20, -20, 24, -12],\n [24, 10, 14, 24, -6],\n [24, -15, 39, -6, 9],\n [-24, -25, 1, -42, 15],\n [-4, 30, -34, 34, -18]]?\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, -25, 23, 28, 6],\n [-24, 40, -8, -34, 12],\n [-16, -5, -37, -10, -30],\n [24, -15, 33, 24, 18],\n [-24, 50, 2, -38, 24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-5, -13, -9, 0, -32],\n [5, -26, -30, 31, 14],\n [-3, 44, 52, -9, 48],\n [-25, -44, -53, 12, -59],\n [14, 36, 49, -25, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-48, -32, -20, -12, -6],\n [2, 13, 4, 28, -32],\n [10, 30, 16, 30, -44],\n [22, 3, 4, -12, 28],\n [38, 58, 34, 40, -53]]?\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, 12, 12, -30, 18],\n [0, -10, -10, 25, -15],\n [0, -6, -6, 15, -9],\n [0, 2, 2, -5, 3],\n [0, 6, 6, -15, 9]]\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[[-10, 6, 12, 6, 10],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [-15, 9, 18, 9, 15],\n [-15, 9, 18, 9, 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[[30, -37, 2, -5, -48],\n [49, -19, -11, 79, 20],\n [-43, -25, 25, 2, 18],\n [-5, -56, 15, -24, -48],\n [-89, 10, 34, -25, 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[[-4, -38, 20, 20, -28],\n [-2, 5, -29, -15, -17],\n [-3, 6, 20, 15, 13],\n [-2, -43, 31, 34, -29],\n [11, -67, 25, 35, -46]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-6, 15, 18, -15, -18],\n [2, -5, -6, 5, 6],\n [4, -10, -12, 10, 12],\n [-12, 30, 36, -30, -36],\n [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[[35, -51, -42, -53, 11],\n [-14, 21, -24, 6, -23],\n [-11, 25, 24, 27, 31],\n [-12, 29, 46, 36, 5],\n [9, 32, 25, 23, 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[[13, -7, 5, 2, 0],\n [14, 54, -34, 28, -32],\n [-4, 6, -4, 1, -2],\n [-46, -6, 2, -20, 16],\n [-8, 12, -8, 2, -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[[24, -20, 12, 8, 24],\n [6, -5, 3, 2, 6],\n [-6, 5, -3, -2, -6],\n [0, 0, 0, 0, 0],\n [-24, 20, -12, -8, -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 5x5 matrix:\n[[-24, 30, 30, 29, -19],\n [-37, 38, 26, 17, -21],\n [-9, -15, 0, -5, 10],\n [-16, 30, -40, -62, -8],\n [38, -5, -10, 6, -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 5x5 matrix:\n[[-7, -9, -16, -21, 14],\n [-10, -18, 44, 6, -16],\n [-16, -26, 34, -10, -6],\n [14, 22, -20, 14, 0],\n [23, 35, -18, 31, -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[[0, -1, -3, 6, -2],\n [0, 6, 18, -36, 12],\n [0, 6, 18, -36, 12],\n [0, -6, -18, 36, -12],\n [0, 6, 18, -36, 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[[25, 18, 16, -37, -13],\n [-33, -22, -4, 47, 15],\n [-16, 17, -36, -18, -28],\n [-16, -8, 24, 20, 4],\n [-17, 1, -18, 6, -8]]\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[[-9, -15, 9, -12, -6],\n [3, 5, -3, 4, 2],\n [12, 20, -12, 16, 8],\n [18, 30, -18, 24, 12],\n [-12, -20, 12, -16, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[24, 45, 28, 53, -22],\n [15, 54, 42, 65, -9],\n [30, -30, -44, -37, -40],\n [27, -27, -34, -27, -29],\n [30, 33, 24, 50, -18]]\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 5x5 matrix:\n[[10, 11, 15, -15, -60],\n [-52, 18, -1, 20, -4],\n [9, 7, 55, 15, -40],\n [56, -27, 47, -5, 36],\n [-46, 18, -58, -30, -16]]\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[[14, -10, 20, -5, -19],\n [-20, -4, 8, -9, -21],\n [16, 11, -7, 6, 3],\n [26, 38, -8, 4, -42],\n [7, -30, 7, 4, 46]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 4, 24, -24, -8],\n [-4, 4, 24, -24, -8],\n [-3, 3, 18, -18, -6],\n [0, 0, 0, 0, 0],\n [5, -5, -30, 30, 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[[-10, 13, -20, -30, 2],\n [19, 8, -7, 4, 25],\n [8, 1, 2, 30, 0],\n [-26, 14, -22, -6, -26],\n [-4, -11, 10, -48, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-32, -7, -16, -7, 62],\n [2, -2, 46, 29, -12],\n [17, -20, 52, -9, -16],\n [35, -83, 12, 5, -22],\n [-2, -19, -4, 65, -10]]\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 5x5 matrix:\n[[15, -25, 15, 12, 24],\n [27, -29, 27, -12, 24],\n [7, -9, 7, 0, 8],\n [-36, 32, -36, 30, -24],\n [-16, 22, -16, -3, -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[[-5, -1, 15, 31, 36],\n [3, -3, -9, -33, -36],\n [-5, -5, 15, 15, 20],\n [-6, 0, 18, 42, 48],\n [-6, -11, 18, -2, 4]]\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, -26, -32, -35, 46],\n [-16, 4, 2, -4, 0],\n [-2, -18, -34, -28, 34],\n [56, 2, -31, 16, -16],\n [-26, -12, 1, -21, 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[[-18, -3, 9, -12, -15],\n [30, 5, -15, 20, 25],\n [-24, -4, 12, -16, -20],\n [6, 1, -3, 4, 5],\n [-24, -4, 12, -16, -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 5x5 matrix:\n[[-39, -30, -51, -51, -34],\n [34, -8, 38, 57, 28],\n [-42, -12, -42, -34, -16],\n [-5, 70, -1, 0, 40],\n [-73, -16, -85, -55, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-10, 5, -27, 18, 20],\n [16, 4, 28, -16, -24],\n [9, -9, 30, -21, -21],\n [6, 9, 1, 2, -4],\n [-10, -25, 11, -14, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-24, 27, -45, -12, -36],\n [-7, 0, -15, -8, -9],\n [4, 27, 15, 20, 0],\n [-8, 30, -10, 8, -16],\n [-2, -24, -10, -16, 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[[0, 17, -5, 28, 15],\n [-22, 5, -33, -7, -35],\n [9, -40, -18, -40, -12],\n [17, 4, 40, 9, 28],\n [-30, -28, 0, -51, -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[[17, 24, 82, 18, 5],\n [-14, 37, 13, -8, -27],\n [-32, 6, -10, -7, -65],\n [-39, -14, -10, -58, -55],\n [-12, 14, 26, -18, -24]]?\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[[-5, -13, -2, -33, -2],\n [0, -12, 12, -42, -8],\n [21, 15, 48, 0, -18],\n [-20, -10, -50, 15, 20],\n [4, 8, 4, 18, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[10, 5, -40, 15, 20],\n [-21, -3, -1, -20, -3],\n [-16, 16, -27, 46, -8],\n [42, 6, -33, 30, 6],\n [5, -19, 40, -62, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -8, -10, 12, 24],\n [-3, -1, 1, -1, -5],\n [26, 18, 0, -2, 26],\n [-2, 4, 5, -6, -12],\n [7, 7, 2, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-37, -37, 62, -34, -27],\n [4, 11, -6, -20, 4],\n [40, 40, -30, -30, 5],\n [-22, -20, 30, 2, -7],\n [-66, -57, 100, -30, -29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[13, 4, 2, -9, 8],\n [13, 24, 42, 64, 7],\n [13, 10, 42, 29, 21],\n [-39, -34, -6, -28, -2],\n [-28, -4, 8, 38, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, -6, 0, 2, 12],\n [-6, -6, 8, 6, 6],\n [18, 3, 16, 7, -18],\n [-6, -6, 8, 6, 6],\n [6, 12, -24, -16, -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 5x5 matrix:\n[[15, -3, -18, -15, -3],\n [5, -1, -6, -5, -1],\n [15, -3, -18, -15, -3],\n [-5, 1, 6, 5, 1],\n [20, -4, -24, -20, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[24, 12, 36, -39, 9],\n [-13, -20, -33, 29, -15],\n [8, -8, 0, -6, -6],\n [-21, -12, -33, 35, -9],\n [-9, -24, -33, 26, -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[[12, 24, -8, 4, 24],\n [6, -48, 4, 28, 18],\n [-26, -12, 12, -26, -56],\n [6, -48, 4, 28, 18],\n [30, 0, -12, 36, 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[[22, -7, 45, -43, -4],\n [1, 1, -1, -2, -16],\n [13, -9, 19, -18, -14],\n [1, 15, 7, -18, -34],\n [16, -36, 10, 6, 18]]?\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, -18, -46, 26, 17],\n [44, -19, -33, 27, -24],\n [4, 45, 23, -23, 1],\n [-10, -47, 2, 14, -32],\n [-44, 11, 69, -37, -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 5x5 matrix:\n[[30, 15, -20, 10, -5],\n [-6, -3, 4, -2, 1],\n [18, 9, -12, 6, -3],\n [30, 15, -20, 10, -5],\n [18, 9, -12, 6, -3]]\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[[2, 8, 5, -23, -13],\n [-12, -9, -17, 34, 26],\n [-8, 4, -8, -4, 4],\n [-8, 4, -8, -4, 4],\n [16, 1, 19, -16, -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[[24, -14, -31, 34, 38],\n [-36, 26, 39, -36, -42],\n [-6, -2, 16, -25, -26],\n [-30, 34, 14, 7, 2],\n [-24, 30, 7, 14, 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[[5, 48, 8, -29, -50],\n [10, 39, -3, -30, -57],\n [-11, -21, 10, 23, 47],\n [16, -21, -35, -4, -25],\n [-3, 21, -12, 23, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, -23, 11, -14, 26],\n [1, -8, -41, 22, -21],\n [7, 56, -3, 38, -67],\n [-1, 9, 35, -17, 15],\n [-27, 1, 7, 21, -23]]\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[[2, -6, 4, 12, 2],\n [-5, 15, -10, -30, -5],\n [-1, 3, -2, -6, -1],\n [0, 0, 0, 0, 0],\n [6, -18, 12, 36, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-35, 11, -12, 16, -14],\n [36, 2, 1, -13, 27],\n [9, 11, -13, -13, 35],\n [63, -20, 30, -5, -10],\n [-20, -26, 9, -33, 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[[38, -12, -9, -42, -46],\n [30, -33, 3, 18, 28],\n [-8, -2, -21, -17, -6],\n [41, -36, -28, -30, -21],\n [17, 3, 17, -12, -11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, -3, 6, -4, 1],\n [-6, 18, -36, 24, -6],\n [0, 0, 0, 0, 0],\n [-2, 6, -12, 8, -2],\n [3, -9, 18, -12, 3]]?\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, 7, -1, 1, 4],\n [-5, 20, -9, 42, 28],\n [-13, -5, -12, 18, 12],\n [13, 17, -6, -24, 4],\n [30, 36, 15, -15, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-9, -18, -6, -4, 17],\n [-33, -28, 51, -11, -2],\n [20, 15, -23, 14, 5],\n [-41, -28, 50, -30, -15],\n [-7, -7, 25, 8, 2]]\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 5x5 matrix:\n[[-6, 50, -31, 0, -3],\n [-4, 8, 11, -38, 17],\n [-3, 3, 12, -33, 15],\n [6, -14, -14, 54, -24],\n [-6, 38, -16, -18, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[30, 30, -15, -22, 19],\n [-5, 14, -6, 29, -38],\n [18, 37, 9, 9, -18],\n [5, 26, 21, -7, 19],\n [36, 30, 33, -72, 99]]?\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 5x5 matrix:\n[[0, 24, 54, -37, 5],\n [14, 22, 32, -24, -10],\n [9, -3, -18, 11, -10],\n [0, 0, 0, 0, 0],\n [-55, -35, -10, 15, 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 5x5 matrix:\n[[3, 3, 4, 1, 0],\n [-18, -18, -24, -6, 0],\n [6, 6, 8, 2, 0],\n [9, 9, 12, 3, 0],\n [-6, -6, -8, -2, 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[[0, -8, 18, -14, 28],\n [-7, 8, 3, -14, 7],\n [7, -8, -3, 14, -7],\n [22, -36, 15, 25, 16],\n [-8, 16, -12, -4, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-36, 18, -30, -12, -24],\n [-24, 12, -20, -8, -16],\n [18, -9, 15, 6, 12],\n [-36, 18, -30, -12, -24],\n [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[[16, 16, -12, -24, 20],\n [-20, -20, 15, 30, -25],\n [12, 12, -9, -18, 15],\n [24, 24, -18, -36, 30],\n [-4, -4, 3, 6, -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[[12, -18, 0, -6, -30],\n [-11, -18, -6, -17, -19],\n [3, 30, 6, 21, 39],\n [21, 3, 6, 12, -6],\n [37, 2, 10, 19, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-36, 28, 20, 0, 10],\n [-3, -10, -14, -22, 19],\n [36, 8, -24, -3, -26],\n [54, 12, 4, 32, -60],\n [-36, -8, 24, -5, 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[[-18, 3, -9, 33, -36],\n [12, 4, 48, -14, -20],\n [42, 2, -12, -37, 2],\n [-44, -5, 33, 23, 26],\n [10, -2, -24, -11, 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[[-12, -12, -18, -15, 18],\n [0, 0, 0, 0, 0],\n [-8, -8, -12, -10, 12],\n [-4, -4, -6, -5, 6],\n [16, 16, 24, 20, -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[[54, -25, -5, -1, 18],\n [0, 37, 21, -21, -16],\n [32, -12, 5, 2, 20],\n [-28, 0, -50, 32, -72],\n [-46, 23, 9, 25, -7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-30, -30, -12, -30, 18],\n [30, 30, 12, 30, -18],\n [25, 25, 10, 25, -15],\n [-20, -20, -8, -20, 12],\n [-25, -25, -10, -25, 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[[-42, 48, 48, 12, 18],\n [-23, 32, 30, -2, 13],\n [7, -8, -8, -2, -3],\n [23, -32, -30, 2, -13],\n [7, -8, -8, -2, -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[[52, 23, -32, -5, 9],\n [22, 17, -27, -18, -37],\n [5, -17, 30, 0, 31],\n [9, -18, 60, -42, 0],\n [-38, -25, 1, 36, 13]]\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 5x5 matrix:\n[[-22, 0, -12, -36, 33],\n [-41, 21, 11, -21, -43],\n [7, -23, 4, -6, 42],\n [-24, 4, 15, -18, -22],\n [36, -30, 35, 45, -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[[-12, 3, -6, -18, 9],\n [-8, 2, -4, -12, 6],\n [-12, 3, -6, -18, 9],\n [20, -5, 10, 30, -15],\n [-24, 6, -12, -36, 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[[-21, 6, 0, 2, 15],\n [-18, 5, 8, 10, 11],\n [29, 9, 15, 34, -22],\n [33, 41, -21, 37, -15],\n [3, -6, -7, -14, -1]]\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, 53, 50, -28, -42],\n [-6, 14, 22, -17, -12],\n [-17, 31, 30, -16, -4],\n [12, -33, -21, -2, 7],\n [-17, 10, 1, -23, -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[[-54, -10, 39, -15, 17],\n [-6, -4, 3, 0, 1],\n [-30, 24, -7, -55, -28],\n [-36, 20, -4, -55, -27],\n [-12, 28, -2, -38, -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[[-23, 7, -12, 11, -22],\n [-50, 25, 13, 38, 5],\n [-23, 64, 21, 27, -5],\n [10, -36, -52, 60, -35],\n [2, -42, -36, 22, -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[[5, -21, -29, -3, 12],\n [-5, 27, 23, 11, -4],\n [-1, 12, -2, 11, 8],\n [-36, 22, 16, 8, 54],\n [21, -18, 15, -21, -57]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-39, -14, 5, 55, -39],\n [-36, -38, 56, 34, -18],\n [8, 16, 1, -16, 12],\n [-38, -25, -4, 49, 9],\n [-27, -22, -15, 45, -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 5x5 matrix:\n[[23, -4, -30, -21, 5],\n [14, 5, -25, -13, 12],\n [-17, 10, 15, 9, 4],\n [36, -18, -39, -54, -9],\n [-40, 14, 46, 38, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-11, -6, -5, -11, -9],\n [12, -18, -6, 12, -36],\n [-21, 9, 0, -21, 21],\n [14, 24, 14, 14, 42],\n [8, 3, 3, 8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[13, -38, 40, -60, 5],\n [-48, -12, -15, -30, 42],\n [4, -44, 5, -40, -13],\n [53, -11, 17, 8, -47],\n [-37, 38, -39, 44, 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[[-20, -8, 8, 4, 16],\n [30, 12, -12, -6, -24],\n [-30, -12, 12, 6, 24],\n [0, 0, 0, 0, 0],\n [25, 10, -10, -5, -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[[34, -35, -15, -6, 26],\n [-59, 54, -32, 14, 30],\n [25, -29, -43, 2, 40],\n [-42, 39, -19, 5, 27],\n [13, -7, 43, -30, 0]]\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, 25, 0, -10, -5],\n [4, -5, 0, 2, 1],\n [-16, 13, -10, 0, 7],\n [2, -20, -25, 21, 28],\n [28, -49, -20, 30, 29]]\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[[-62, 6, -3, 39, 7],\n [22, 13, -8, -22, 3],\n [30, 5, 7, -21, 2],\n [38, 10, -5, -31, 1],\n [24, 42, 18, -30, 24]]\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, 46, 12, 38, 26],\n [2, -16, -10, -5, -19],\n [-32, -18, -36, 14, 26],\n [-1, 33, 18, 9, 31],\n [6, -50, -20, 20, -40]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[13, -42, -13, -2, -13],\n [-2, 9, -24, -29, 56],\n [9, -18, -17, -8, 21],\n [-15, 18, -13, -37, 30],\n [-12, 33, 22, 12, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[32, -24, -12, 24, -48],\n [1, 13, 24, 2, 6],\n [-9, 15, 18, -6, 18],\n [36, -16, 6, 28, -48],\n [16, 10, 33, 14, -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[[4, -6, -10, -6, 2],\n [-10, 6, 18, 11, 2],\n [-12, -36, -12, -6, 36],\n [-2, -15, -9, -5, 13],\n [-10, 15, 25, 15, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 6, 6, -8, 4],\n [-3, -9, -9, 12, -6],\n [-5, -15, -15, 20, -10],\n [-2, -6, -6, 8, -4],\n [-3, -9, -9, 12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-30, -30, 42, 2, 3],\n [12, 12, -4, 12, 2],\n [18, 18, -18, 6, 0],\n [-30, -30, 34, -6, 1],\n [-12, -12, 8, -8, -1]]\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 5x5 matrix:\n[[13, -9, -8, -9, 3],\n [-6, -2, 8, 0, 14],\n [27, -16, -23, -17, -3],\n [9, 17, 34, 11, -25],\n [-15, -9, -24, -4, 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[[6, 12, -9, -6, -15],\n [-12, -24, 18, 12, 30],\n [-12, -24, 18, 12, 30],\n [8, 16, -12, -8, -20],\n [-10, -20, 15, 10, 25]]\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 5x5 matrix:\n[[6, 30, 30, -24, 12],\n [1, 5, 5, -4, 2],\n [0, 0, 0, 0, 0],\n [-6, -30, -30, 24, -12],\n [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[[-35, 36, -24, 4, 1],\n [36, -48, 41, -41, -11],\n [2, 86, 8, 5, 45],\n [18, 66, 8, 47, 59],\n [24, -18, 32, -34, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[10, 6, 1, 2, 26],\n [34, -30, -26, 32, 17],\n [18, -42, -29, 30, -28],\n [-14, 30, 21, -22, 18],\n [14, -18, -14, 16, -1]]\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, 25, 15, -25, -25],\n [12, -30, -18, 30, 30],\n [10, -25, -15, 25, 25],\n [-6, 15, 9, -15, -15],\n [-6, 15, 9, -15, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-8, -2, -11, -2, 11],\n [9, -7, 12, -3, -12],\n [12, 6, 30, 12, -12],\n [-13, -37, -46, -37, 10],\n [26, 21, 46, 20, -33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[24, 2, 22, -48, -22],\n [4, -3, -18, -20, -12],\n [23, -37, 27, 21, -23],\n [-16, 31, 15, 4, 29],\n [-6, 21, 25, 2, 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[[5, -11, 6, -36, -28],\n [-33, -9, -21, 32, 31],\n [-31, -28, -22, 9, 27],\n [44, -10, 26, -36, 0],\n [33, -35, 17, -43, 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[[-26, -3, 1, -1, 19],\n [28, -3, -2, 2, -20],\n [15, 36, 39, 15, -6],\n [15, 27, -39, -27, -22],\n [-21, 9, 14, 4, 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[[-6, 3, -22, -9, 24],\n [2, 13, -16, 3, 20],\n [10, 35, -30, 15, 40],\n [8, 1, 21, 12, -22],\n [0, -18, 30, 0, -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[[18, -12, 0, 0, 9],\n [36, -24, 0, 0, 18],\n [-18, 12, 0, 0, -9],\n [-36, 24, 0, 0, -18],\n [0, 0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-2, -36, 36, 38, 34],\n [-15, -57, 34, 41, 16],\n [0, -7, 4, 6, -29],\n [16, 26, 28, 66, -44],\n [22, 62, -18, -9, -47]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[27, 0, 12, -3, -24],\n [-21, -10, -1, 14, 22],\n [-12, -16, 8, 20, 16],\n [-39, -10, -9, 16, 38],\n [-18, 12, -18, -12, 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 5x5 matrix:\n[[6, 27, -6, 20, 3],\n [0, -24, 0, -16, -12],\n [20, 14, -20, 16, -28],\n [-20, -14, 20, -16, 28],\n [-14, -11, 14, -12, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-11, -22, -8, -4, 15],\n [34, 8, 14, -23, 25],\n [3, -10, 4, -6, -26],\n [10, -20, 4, -18, 0],\n [6, -4, 4, -6, -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[[-30, 6, 18, 42, 18],\n [25, -22, -66, 16, 19],\n [-30, 14, 42, 18, 2],\n [20, 0, 0, -40, -20],\n [-5, 4, 12, -2, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 9, -9, -6, 15],\n [6, 9, -9, -6, 15],\n [-12, -18, 18, 12, -30],\n [8, 12, -12, -8, 20],\n [0, 0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[4, -44, -8, 28, -26],\n [2, 43, 4, -24, 20],\n [27, -32, -20, 32, -36],\n [-39, 19, 16, -16, 4],\n [-45, 20, 20, -20, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 6, 27, -24, -6],\n [-19, -14, 0, -7, 23],\n [-12, -8, -8, 4, 12],\n [-5, -2, -16, 15, 1],\n [13, 8, 15, -11, -11]]?\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, 1, 21, 13, 6],\n [-20, -7, 17, -9, 0],\n [-28, -26, 4, 9, 63],\n [-32, 7, 35, 43, 22],\n [12, -23, -29, -40, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[24, 26, -8, 8, -24],\n [4, -18, -14, -12, -3],\n [-14, 27, 15, 11, 6],\n [16, 16, -4, 6, -15],\n [26, -5, -33, -15, -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[[5, -14, 15, 14, -3],\n [-18, 0, 15, 18, -12],\n [-37, 14, 15, 28, -17],\n [-9, 34, -20, 20, 17],\n [18, -24, 15, 6, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[16, -3, -2, 18, -10],\n [50, -21, 2, -4, -6],\n [-26, -32, 59, 36, 40],\n [-54, -3, 33, 18, 30],\n [-14, 17, -15, 2, -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[[0, 5, -4, 5, 1],\n [-4, -31, 9, -40, 6],\n [-16, 23, 3, -22, 30],\n [-4, -24, -6, -32, 10],\n [16, 10, -20, 54, -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[[8, -22, 21, 18, -18],\n [20, -20, 15, 10, -20],\n [-20, 20, -15, -10, 20],\n [-32, 4, 6, 12, 12],\n [-22, 15, -9, -4, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[16, 8, 0, -8, -12],\n [-26, 0, -12, 16, 10],\n [21, 4, 6, -12, -11],\n [-31, 56, -66, 32, -29],\n [-17, 24, -30, 16, -11]]\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, -39, 21, -6, 67],\n [-15, -30, -25, -34, 37],\n [6, 11, 12, 10, -20],\n [1, -13, 7, 8, 37],\n [-5, 24, 9, 10, -41]]?\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, 16, -4, 4, 32],\n [-15, 20, -16, -6, 7],\n [9, -12, -2, -8, -39],\n [-6, 8, -6, -2, 4],\n [-15, 20, -14, -4, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-18, 0, 9, 6, 12],\n [30, -3, 3, -13, 4],\n [-6, -3, 21, -1, 28],\n [-18, 6, -27, 12, -36],\n [36, -6, 18, -18, 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 5x5 matrix:\n[[6, 22, 17, 7, -9],\n [-12, 34, 5, -1, 5],\n [24, -8, 20, 12, -20],\n [-18, -6, -21, -11, 17],\n [6, -14, -1, 1, -3]]\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 5x5 matrix:\n[[38, -6, 40, 25, 33],\n [-20, 2, -40, 19, -5],\n [17, -8, 34, 8, 20],\n [13, 5, -1, 3, 1],\n [-23, -2, -28, 12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[17, -19, 12, -23, -3],\n [-12, 11, -5, 14, -2],\n [26, -39, 35, -40, -22],\n [25, -38, 29, -49, -21],\n [-16, -9, 11, -34, -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[[18, 30, -24, -18, 30],\n [23, -23, 1, -6, -32],\n [0, -30, 15, 9, -33],\n [-7, 1, 1, 6, 8],\n [14, -8, -2, -6, -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 5x5 matrix:\n[[0, 4, -20, 24, -4],\n [0, 1, -5, 6, -1],\n [0, -1, 5, -6, 1],\n [0, -5, 25, -30, 5],\n [0, 2, -10, 12, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-34, -2, -72, 3, 40],\n [38, -46, 15, -15, -49],\n [25, 25, 84, -1, -16],\n [-15, 33, 8, -55, -4],\n [-33, 55, 10, 41, 46]]\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, 6, 31, 32, 1],\n [-41, 2, 19, 26, 30],\n [-40, 16, 26, 8, 15],\n [6, 24, 22, -18, -35],\n [-23, 2, 7, 8, 18]]\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 5x5 matrix:\n[[-12, -38, -38, 2, 3],\n [-24, 12, 6, 12, 15],\n [-18, -54, -67, 18, -32],\n [-6, 48, 43, 11, 4],\n [8, 39, 35, -8, 1]]\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[[-9, 45, -39, -9, 51],\n [-18, 30, -30, -18, 36],\n [-24, 20, -24, -24, 26],\n [9, 35, -25, 9, 37],\n [-15, 25, -25, -15, 30]]\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 5x5 matrix:\n[[-1, -6, 42, -28, 6],\n [1, 6, -6, 4, -6],\n [0, 0, 18, -12, 0],\n [10, 60, -6, 4, -60],\n [10, 60, -6, 4, -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[[-15, 33, 3, 43, -25],\n [-3, 57, -9, 23, -41],\n [3, -9, -2, 4, 5],\n [12, -73, 4, -30, 51],\n [-33, 7, 29, 5, 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[[-9, -16, 9, 11, 12],\n [-10, 12, 44, -6, 54],\n [-26, -27, -8, 36, -27],\n [-19, -18, -10, 27, -27],\n [-1, 11, 17, -7, 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[[26, -2, 4, 32, 6],\n [-25, 13, 6, -2, -7],\n [3, 19, -28, 57, 13],\n [-14, -2, 10, 23, -21],\n [30, -16, -24, 5, 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[[8, -18, 32, -26, -14],\n [20, 25, 20, -55, -45],\n [22, 31, 19, -60, -50],\n [10, -2, 13, 9, 31],\n [-38, -43, -23, 28, -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[[-12, -3, 18, -9, 18],\n [34, -29, -35, -14, -16],\n [6, 66, -37, 23, -14],\n [-14, -17, 27, 0, 6],\n [14, -11, -15, -24, 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 5x5 matrix:\n[[20, -25, 10, 20, 10],\n [-16, 20, -8, -16, -8],\n [4, -5, 2, 4, 2],\n [-4, 5, -2, -4, -2],\n [20, -25, 10, 20, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-32, -14, 6, 4, -12],\n [38, 15, -7, -3, 16],\n [36, 19, -7, -8, 10],\n [-20, -25, 5, 20, 10],\n [-12, -2, 2, -2, -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[[8, 8, -20, -16, 20],\n [10, 10, -25, -20, 25],\n [8, 8, -20, -16, 20],\n [-6, -6, 15, 12, -15],\n [10, 10, -25, -20, 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[[-47, 3, -47, 7, 15],\n [42, 46, 0, 8, -32],\n [-14, -19, 4, -7, 11],\n [-2, 25, -21, -2, -12],\n [54, 8, 46, -12, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, 12, -2, 17, 14],\n [18, 2, -10, 8, 2],\n [3, 5, -1, 17, 5],\n [11, -21, -8, -58, -22],\n [-30, 8, 17, 13, 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[[0, -10, -10, -5, -10],\n [-6, 22, 1, 8, 16],\n [0, -10, -10, -5, -10],\n [0, 0, 0, 0, 0],\n [10, -26, 9, -8, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[30, 18, 24, -24, -36],\n [27, 14, 23, -19, -31],\n [-18, -2, -20, 4, 16],\n [9, 12, 3, -15, -15],\n [21, 6, 21, -9, -21]]\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[[-28, 9, -38, -5, -36],\n [-39, 39, 24, -10, 31],\n [8, -10, -7, 11, -10],\n [34, -23, 19, 26, 12],\n [-30, 18, -21, -17, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[20, -23, -4, 22, 1],\n [19, -19, -8, 20, 5],\n [-30, 6, 48, -24, -42],\n [17, -11, -16, 16, 13],\n [19, 0, -36, 14, 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[[-12, -19, 20, 32, 52],\n [-24, -8, 38, 2, -10],\n [-2, 26, -14, -44, 34],\n [2, 9, 8, -20, 24],\n [-30, 12, 34, -35, -6]]\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, -2, -46, -66, -5],\n [18, 4, -22, 14, -19],\n [-18, -24, 68, 60, 16],\n [-25, 29, 20, 14, 11],\n [27, -26, 31, 56, 3]]\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[[17, 0, 18, -38, -18],\n [6, 3, 15, -31, -5],\n [-7, -3, -7, -3, -3],\n [26, 18, 44, -22, 16],\n [-15, -15, -27, -7, -23]]\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, 0, -8, 12, -24],\n [0, 0, -10, 15, -30],\n [0, 0, 0, 0, 0],\n [0, 0, -6, 9, -18],\n [0, 0, 8, -12, 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, -17, -12, 11, 17],\n [-9, 9, -48, 37, -9],\n [-6, 6, 12, -10, -6],\n [30, -30, -27, 24, 30],\n [7, -7, -3, 3, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[19, -3, 12, -8, 13],\n [13, -2, 19, -14, 16],\n [-39, 18, -15, -30, 12],\n [2, 17, -45, -22, 19],\n [39, 9, -30, -24, 33]]\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 5x5 matrix:\n[[2, 6, -14, 2, -11],\n [15, -21, 18, -21, 9],\n [34, 2, -24, -6, -12],\n [24, -24, 4, -32, -8],\n [23, -9, 12, -5, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-24, 6, -30, 12, 15],\n [28, -2, 30, -4, 10],\n [-4, -2, -2, -4, -14],\n [-10, 5, -15, 10, 20],\n [24, 0, 24, 0, 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[[0, -1, -7, -4, 3],\n [-20, -11, 12, 0, -34],\n [-3, -16, -9, 15, -4],\n [-17, -8, 6, -17, -9],\n [-4, -16, -4, 3, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[24, -25, 3, 19, -26],\n [-25, 30, 0, -25, 30],\n [-21, 10, -12, -1, 14],\n [-5, -13, -15, 20, -8],\n [-10, 31, 15, -35, 26]]\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, -38, -14, 4, 26],\n [14, -17, 27, -46, -29],\n [-6, -10, 1, -4, 9],\n [-30, -13, -11, 17, 48],\n [12, 16, 14, -14, -24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-25, 0, 15, 0, -5],\n [-10, 0, 6, 0, -2],\n [-31, 30, 45, -36, -23],\n [19, 30, 15, -36, -13],\n [17, 15, 3, -18, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[20, -18, -46, 0, -14],\n [1, 31, 30, 36, 1],\n [-11, 5, -1, -19, 9],\n [5, 33, 17, 45, -11],\n [-11, 43, -4, 2, 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[[-16, 20, -20, 24, 16],\n [0, 0, 0, 0, 0],\n [-8, 10, -10, 12, 8],\n [4, -5, 5, -6, -4],\n [20, -25, 25, -30, -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[[-34, -14, 7, -26, -10],\n [-38, -13, 5, -31, -11],\n [34, 26, -8, 18, -4],\n [34, 17, -22, 23, 25],\n [0, 0, 0, 0, 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[[30, 18, -6, 12, -36],\n [30, 18, -6, 12, -36],\n [10, 6, -2, 4, -12],\n [25, 15, -5, 10, -30],\n [30, 18, -6, 12, -36]]?\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 5x5 matrix:\n[[0, 5, 15, -5, 25],\n [0, -5, -15, 5, -25],\n [0, 6, 18, -6, 30],\n [0, 6, 18, -6, 30],\n [0, 4, 12, -4, 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[[44, -29, 34, 23, 25],\n [-30, 18, -1, 7, 9],\n [56, 21, 9, -32, -1],\n [-22, -45, -13, 18, -11],\n [0, -12, -34, -22, -52]]\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, -26, 43, -19, -16],\n [-21, 14, -4, 10, -24],\n [-5, -24, 30, 7, -25],\n [-14, 16, -5, 6, -7],\n [-4, -22, 32, -24, -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[[0, -4, 4, -8, 24],\n [12, 9, 19, -2, -54],\n [-15, -10, -25, 5, 60],\n [3, 3, 4, 1, -18],\n [3, -3, 10, -11, 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 5x5 matrix:\n[[1, 3, 30, -6, -6],\n [-6, -21, 6, 5, 3],\n [-15, -13, -34, -46, 42],\n [-3, -23, 34, 18, -12],\n [8, -4, 20, 43, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-55, -44, 0, 48, 14],\n [-60, -15, -29, 22, 5],\n [26, -3, 9, -2, -11],\n [-24, -5, -13, 10, -1],\n [-14, 15, -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[[-6, 14, 14, -25, -9],\n [5, -9, -18, 28, 7],\n [4, -51, -6, -5, 17],\n [-18, -48, -48, -30, 0],\n [10, 18, 36, 4, 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[[-10, -15, 5, -5, 10],\n [8, 12, -4, 4, -8],\n [-4, -6, 2, -2, 4],\n [0, 0, 0, 0, 0],\n [6, 9, -3, 3, -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[[5, -4, -7, -4, 2],\n [-20, 22, 22, 10, -11],\n [20, -28, -16, -4, 14],\n [15, -6, -27, -18, 3],\n [-10, 18, 4, -2, -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[[4, 43, -45, -3, -42],\n [47, 51, -12, 25, -6],\n [5, -21, 24, 3, 26],\n [34, 32, -9, 15, -4],\n [17, -7, 16, 9, -18]]\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[[4, 2, 3, 18, 10],\n [-9, 24, -2, -12, 6],\n [-14, 20, -6, -36, -8],\n [-21, 36, -8, -48, -6],\n [8, -8, 4, 24, 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 5x5 matrix:\n[[-23, -7, 0, 29, -25],\n [-5, 19, -15, -6, 3],\n [-18, -21, 11, 22, -17],\n [-51, -58, 82, 33, -51],\n [19, -26, 27, -18, 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[[-51, -8, 17, 26, -37],\n [-23, 2, -1, 0, -15],\n [-41, 3, -8, 0, -28],\n [11, -3, 26, 8, 10],\n [-4, -14, -50, 18, -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[[0, -6, -12, 6, 10],\n [5, -20, 20, -30, 10],\n [-1, -2, -16, 12, 8],\n [0, 0, 0, 0, 0],\n [4, -10, 28, -30, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-28, 28, 12, 0, 20],\n [16, -13, 6, -3, -23],\n [-15, 17, 15, -2, 3],\n [-16, 20, 24, -4, -4],\n [30, -34, -30, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 24, -30, 36, 24],\n [10, -20, 25, -30, -20],\n [-2, 4, -5, 6, 4],\n [-6, 12, -15, 18, 12],\n [-2, 4, -5, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -44, -10, 2, 24],\n [21, 28, 3, -4, -3],\n [20, -17, -3, -10, 25],\n [-1, 6, -16, 27, 31],\n [14, 18, -8, 12, 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[[-44, -18, 58, -36, 13],\n [26, -31, -8, 20, 7],\n [-26, 11, 26, -16, -28],\n [2, 21, -18, 0, 6],\n [-12, 12, 2, -12, 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[[-28, 19, -7, 20, -28],\n [-8, -10, 12, 26, -35],\n [21, -12, 18, -15, -15],\n [-8, -4, -4, 16, 4],\n [-73, 55, -43, 41, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[18, 10, -32, -2, -6],\n [-14, 17, 6, -25, -3],\n [0, -8, -16, 30, 28],\n [10, -40, 23, 50, -1],\n [-12, -12, 31, 19, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-28, -28, -20, -2, -25],\n [6, 33, -15, -15, -12],\n [28, 28, 20, 2, 25],\n [-28, 0, -40, -18, -43],\n [-40, -24, -40, -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[[13, 20, -7, -11, -16],\n [6, -2, -19, -3, -35],\n [-9, -25, -11, 9, -19],\n [-3, -23, -22, 14, -10],\n [5, 13, 4, -8, -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[[4, -4, -22, -25, 0],\n [5, 2, -10, -5, 7],\n [-3, -10, -16, -30, -13],\n [-6, -8, -2, -15, -14],\n [-3, -10, -16, -30, -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[[-9, -18, -1, 57, 26],\n [-6, -13, -6, 51, 25],\n [15, 32, -49, 9, 21],\n [-24, 13, 16, 9, 0],\n [11, 27, -13, -48, -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[[-6, -15, -9, -6, 15],\n [-10, -25, -15, -10, 25],\n [-18, -23, -17, -10, 37],\n [14, -20, -4, -6, -15],\n [-16, -18, -14, -8, 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 5x5 matrix:\n[[9, -18, 21, -3, 6],\n [-2, 30, -22, -8, 3],\n [-6, -36, 18, 18, -12],\n [-8, 12, -16, 4, -6],\n [-7, 6, -11, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -30, 20, -3, 46],\n [24, 8, 20, 20, 35],\n [12, 6, 4, 3, -19],\n [-14, -54, 13, -24, 32],\n [74, 56, 35, 53, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-26, 16, -9, 26, 5],\n [-23, 65, 22, 57, 11],\n [-2, -12, -60, -20, -58],\n [-12, 20, 13, 18, 9],\n [-21, 20, -19, 30, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 2, -12, -12, -23],\n [7, -24, 19, -19, -21],\n [-13, 18, -13, 31, 54],\n [3, 32, -17, -7, -53],\n [-10, 52, -22, 19, -19]]\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[[-10, 2, 6, 15, 34],\n [8, 0, -2, -7, -18],\n [24, 8, 8, 4, -8],\n [25, 15, 20, 25, 30],\n [7, 9, 14, 22, 36]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-26, 64, 30, 16, -10],\n [17, 4, -1, 26, -9],\n [-13, 16, 51, -10, -13],\n [-2, -8, -44, -23, 10],\n [6, 16, -52, -7, -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[[40, 4, 58, -15, 20],\n [-10, -4, -32, 12, -22],\n [67, -5, 20, -33, -15],\n [21, 3, 40, 9, 7],\n [-20, 4, 2, -27, 32]]?\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 5x5 matrix:\n[[-52, 30, 9, 66, 43],\n [38, -53, 5, -4, -3],\n [1, -16, -9, 23, 22],\n [8, -54, 9, 18, -29],\n [-18, 11, -15, 20, 17]]\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, -18, 20, 8, -21],\n [10, -6, 8, -38, 38],\n [60, 36, -20, 22, -39],\n [-10, 12, -20, 24, -8],\n [-21, -6, 2, 22, -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[[15, -15, -3, 12, -6],\n [10, -10, -2, 8, -4],\n [-15, 15, 3, -12, 6],\n [0, 0, 0, 0, 0],\n [-10, 10, 2, -8, 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[[30, 45, -36, -27, -33],\n [30, 50, -35, -35, -25],\n [8, 15, -9, -12, -4],\n [10, 5, -14, 7, -27],\n [-24, -40, 28, 28, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-10, -7, 12, -3, -26],\n [8, 26, 14, -14, -14],\n [12, -33, -39, 3, 15],\n [3, 3, 1, -5, -7],\n [8, -4, 0, -20, -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[[16, 40, 16, -8, 8],\n [-10, -10, 20, 32, 28],\n [-13, -25, 2, 20, 10],\n [-8, -30, -28, -14, -26],\n [16, 40, 16, -8, 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[[47, 21, -34, 1, 35],\n [16, 4, -40, 0, -2],\n [2, 35, 13, -42, -25],\n [18, 46, -20, -50, -30],\n [27, 33, -22, -27, -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[[2, -4, 12, -12, -10],\n [2, -4, 12, -12, -10],\n [6, -12, 36, -36, -30],\n [-1, 2, -6, 6, 5],\n [5, -10, 30, -30, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, -9, -15, -3, 9],\n [-23, -20, -52, 0, -32],\n [12, 20, 10, -18, -4],\n [-31, -45, -28, 46, -15],\n [7, 19, -3, -19, -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 5x5 matrix:\n[[22, -56, -19, 55, -12],\n [24, 19, 12, -12, 6],\n [28, 10, 51, -13, 20],\n [-26, 1, -27, -1, -10],\n [25, -15, -28, 25, -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[[12, 13, -27, 33, -22],\n [42, 49, -27, -20, 23],\n [14, -20, 9, 8, -22],\n [27, 12, 8, -54, 23],\n [-18, 17, -19, -22, 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[[8, 8, 16, 12, 4],\n [10, 10, 20, 15, 5],\n [-8, -8, -16, -12, -4],\n [8, 8, 16, 12, 4],\n [6, 6, 12, 9, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[16, -50, -25, 40, -3],\n [-6, -30, -30, 30, -12],\n [25, -5, 20, -5, 15],\n [4, 20, 20, -20, 8],\n [-26, 0, -25, 10, -17]]\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 5x5 matrix:\n[[-14, -27, -23, 7, -7],\n [15, -3, 27, -15, -18],\n [16, -5, 9, -13, -15],\n [1, -7, -7, -1, -4],\n [-9, -2, 8, 4, 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[[-49, 14, -33, -19, 3],\n [15, 34, 9, 11, 29],\n [-28, -8, -21, -24, -11],\n [-33, 6, -14, 21, 0],\n [5, -18, 7, 13, -13]]\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[[-47, 2, -1, -4, 32],\n [-10, -36, -46, 28, -20],\n [-15, 6, 45, -21, 9],\n [-17, -12, 60, -22, -8],\n [-2, 10, -35, 11, 15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-33, 32, 5, -9, 18],\n [-9, 0, 13, 15, 34],\n [24, -23, -4, 6, -14],\n [3, 5, -11, -15, -28],\n [-42, 41, 6, -12, 22]]?\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 5x5 matrix:\n[[-2, -6, -6, -2, 6],\n [-4, -12, -12, -4, 12],\n [0, 0, 0, 0, 0],\n [4, 12, 12, 4, -12],\n [-6, -18, -18, -6, 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[[36, -12, 12, 6, -36],\n [-18, 6, -6, -3, 18],\n [-6, 2, -2, -1, 6],\n [-30, 10, -10, -5, 30],\n [18, -6, 6, 3, -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 5x5 matrix:\n[[-5, -5, -5, -10, -25],\n [2, 2, 2, 4, 10],\n [1, 1, 1, 2, 5],\n [1, 1, 1, 2, 5],\n [-5, -5, -5, -10, -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, 17, -4, 25, 7],\n [-20, 48, -22, 17, 2],\n [10, -4, 19, -25, -9],\n [8, -18, -24, 37, 37],\n [14, -22, 43, -29, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, 7, -69, 8, -35],\n [31, -64, 16, -11, -5],\n [-17, 38, -61, -3, -27],\n [-19, 47, -24, 16, -3],\n [-2, -13, 6, -29, -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[[13, 4, 25, -8, 30],\n [0, -50, 7, -13, -54],\n [14, 24, 22, 16, 20],\n [1, 4, 1, 4, 0],\n [-22, 20, -44, 2, 10]]\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, 21, 53, 38, 7],\n [1, 0, -11, -3, 33],\n [29, -1, 33, 6, -23],\n [26, 11, 43, 22, 45],\n [-32, 45, 8, 45, -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[[-16, 25, 12, -11, -8],\n [12, -36, -24, -18, 42],\n [-28, 30, 15, -17, -4],\n [33, -39, -28, -13, 29],\n [-56, 19, 8, -44, 47]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-22, -34, -16, 19, 8],\n [14, 26, 8, -14, -4],\n [0, 16, -8, -7, 4],\n [9, 3, 12, -3, -6],\n [-12, -4, -16, 4, 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[[26, -27, -7, 12, 11],\n [-14, 17, 9, -4, -5],\n [-2, 15, 28, 12, 4],\n [-6, 13, 16, 4, 0],\n [18, -31, -31, -4, 3]]\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 5x5 matrix:\n[[0, 0, 0, 0, 0],\n [18, 6, 18, -6, -18],\n [-24, -8, -24, 8, 24],\n [24, 8, 24, -8, -24],\n [-36, -12, -36, 12, 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[[-8, 35, -37, -22, -48],\n [3, -6, 6, 36, -21],\n [-15, -34, -14, 10, 1],\n [19, 35, 19, -4, 22],\n [2, -7, 9, 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 5x5 matrix:\n[[22, -44, 24, 1, -23],\n [-7, 21, -47, -26, 24],\n [-11, -58, 50, -33, -15],\n [-39, 25, -59, -66, 47],\n [-12, -30, 66, 58, -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[[4, 23, 1, 21, 1],\n [-9, 3, -39, 6, -3],\n [12, 21, 51, 15, 11],\n [16, 61, 11, 55, -2],\n [-4, -47, 23, -45, 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[[-5, 1, -8, 11, 0],\n [20, -15, -50, -4, -19],\n [9, 6, -7, -8, 16],\n [-35, 18, -7, -35, 13],\n [-43, 1, 11, 34, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, -18, -24, 30, 18],\n [2, 3, 4, -5, -3],\n [-2, -3, -4, 5, 3],\n [-10, -15, -20, 25, 15],\n [-6, -9, -12, 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[[-3, 0, -23, -6, 11],\n [32, 23, 33, 4, -42],\n [22, 41, -17, -16, 6],\n [-58, -23, -23, 4, 28],\n [23, 15, -13, -10, 6]]?\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 5x5 matrix:\n[[0, 0, -20, 30, -20],\n [0, 0, -12, 18, -12],\n [0, 0, -12, 18, -12],\n [0, 0, -12, 18, -12],\n [0, 0, 20, -30, 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[[30, 12, 48, -21, -15],\n [-43, 1, -55, 30, 8],\n [-26, 54, 14, 28, -32],\n [-5, 47, 19, -12, -38],\n [33, -61, 5, -10, 42]]\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[[8, 44, 1, 2, 30],\n [-25, -50, -13, 9, -33],\n [-16, 13, 35, 7, 37],\n [-20, -9, 39, 15, 4],\n [13, 23, -41, 2, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 23, -4, 1, -6],\n [18, -51, -40, -11, 0],\n [-14, -18, 13, 8, -32],\n [14, 17, 7, -23, -32],\n [-25, -60, 2, 5, 3]]\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[[-52, 7, -36, -19, -34],\n [-6, 20, 6, 16, -15],\n [54, -3, 42, 30, 15],\n [-18, -28, -30, -39, 19],\n [-24, -13, -18, 3, 22]]\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, -12, -12, -12, -12],\n [12, 32, 20, 20, 48],\n [21, 42, 33, 33, 54],\n [1, 12, 3, 3, 24],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 18, 22, 19, 17],\n [17, -7, 38, -11, 14],\n [5, -9, 18, -13, 0],\n [-22, 1, 5, 15, -10],\n [-11, 32, 11, 17, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -30, 7, -24, -31],\n [3, -1, -5, -2, -3],\n [3, -18, -6, -15, -21],\n [3, 8, -22, 7, 5],\n [23, -16, 5, -27, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -39, -11, 2, -29],\n [16, -45, 21, 20, -66],\n [17, -29, -33, -12, 8],\n [-19, 64, 8, -18, 55],\n [-17, 21, 47, 18, -31]]\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, -10, 20, 1, -31],\n [-12, 23, -16, 3, 14],\n [-10, -7, -1, 27, 45],\n [-2, 5, 4, 15, 3],\n [4, -4, 10, 8, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, 4, -1, 5, 2],\n [5, -4, 4, -1, -4],\n [48, -24, 42, 18, -36],\n [-12, 0, -12, -16, 8],\n [-16, 8, -14, -6, 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[[-30, 30, 30, 12, 0],\n [-20, 20, 20, 8, 0],\n [20, -20, -20, -8, 0],\n [5, -5, -5, -2, 0],\n [25, -25, -25, -10, 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[[-20, -14, -10, -13, 3],\n [44, 30, 6, 22, 18],\n [-42, -41, 7, -13, -27],\n [28, 32, -11, 5, 24],\n [-30, -27, -5, -14, -6]]\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[[-40, 20, 9, 29, -11],\n [-11, 20, 28, 6, -20],\n [-34, 28, -21, 40, 16],\n [-25, 36, 42, 16, -30],\n [0, 20, 27, 2, -18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-24, 22, -18, -24, -61],\n [57, -36, 24, -48, 18],\n [-23, 13, -6, -5, -29],\n [10, -10, 10, -12, 5],\n [-30, 38, -40, -2, -64]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, -12, 12, 0, -12],\n [-6, 6, -6, 0, 6],\n [-2, 2, -2, 0, 2],\n [8, -8, 8, 0, -8],\n [4, -4, 4, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-12, -2, 23, -9, -11],\n [21, -22, -15, -12, -18],\n [46, -24, -60, 14, 0],\n [2, 8, -3, 39, 9],\n [6, -9, 51, -75, -60]]\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 5x5 matrix:\n[[-6, 66, -3, -16, -19],\n [-2, -54, -32, 18, 54],\n [0, -36, 38, -32, -6],\n [-2, 14, 9, -44, 9],\n [20, -60, 17, -14, 13]]\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 5x5 matrix:\n[[-16, 2, 7, 24, -5],\n [28, 22, -25, -42, 30],\n [-4, 20, -8, 6, 15],\n [12, -24, 6, -18, -15],\n [-24, 0, 12, 36, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-22, -17, -25, -66, 51],\n [10, 10, 0, 30, -30],\n [10, 8, 10, 30, -24],\n [12, 6, 30, 36, -18],\n [-18, -14, -20, -54, 42]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-15, -10, -10, 20, 25],\n [0, 0, 0, 0, 0],\n [-9, -6, -6, 12, 15],\n [9, 6, 6, -12, -15],\n [15, 10, 10, -20, -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[[-18, 45, -48, 42, -3],\n [10, -33, 38, -32, 5],\n [-10, 45, -55, 45, -10],\n [2, -21, 28, -22, 7],\n [-14, -9, 25, -15, 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[[2, -1, 2, 5, 2],\n [-10, 5, -10, -25, -10],\n [-6, 3, -6, -15, -6],\n [4, -2, 4, 10, 4],\n [12, -6, 12, 30, 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[[-4, -12, 32, -6, 42],\n [6, 18, -2, 32, 6],\n [6, 18, -34, 16, -42],\n [5, 15, -19, 18, -21],\n [0, 0, 12, 6, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, -4, 10, -4, 12],\n [-15, 10, -25, 10, -30],\n [15, -10, 25, -10, 30],\n [3, -2, 5, -2, 6],\n [-6, 4, -10, 4, -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[[24, -6, 36, 0, 12],\n [-4, -19, 9, -20, 3],\n [4, 3, 3, 4, 1],\n [0, 4, -3, 4, -1],\n [-24, -2, -30, -8, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[18, -28, 9, -16, 0],\n [-3, 4, -2, 3, 1],\n [-12, 40, 10, 0, -32],\n [-6, -16, -22, 18, 38],\n [0, 12, 9, -6, -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 5x5 matrix:\n[[-2, -30, 11, 16, -15],\n [18, 60, -4, -14, 30],\n [38, 24, 38, 34, 12],\n [-40, -12, -46, -44, -6],\n [-16, -30, -7, -2, -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 5x5 matrix:\n[[-3, 0, -4, 6, -6],\n [-12, 0, -16, 24, -24],\n [-6, 0, -8, 12, -12],\n [12, 0, 16, -24, 24],\n [12, 0, 16, -24, 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 5x5 matrix:\n[[-14, 32, 10, -18, 4],\n [26, -44, -16, 2, -26],\n [2, 16, 14, -10, -26],\n [0, 22, 31, 22, -28],\n [19, -30, -4, 15, -22]]\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 5x5 matrix:\n[[1, -16, -11, 45, 21],\n [-10, -5, 0, -10, -45],\n [3, 3, 1, -1, 12],\n [2, 13, 8, -30, -3],\n [-3, -12, -7, 25, -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[[8, -26, 53, -18, -27],\n [66, 18, 12, 12, 12],\n [6, 12, 6, 18, 18],\n [6, 32, -35, 30, 37],\n [-27, -28, 43, -15, -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 5x5 matrix:\n[[66, -26, -10, 18, 36],\n [45, 1, -19, 13, 23],\n [-11, 2, 17, -34, -49],\n [0, -10, 2, 12, 25],\n [-12, -17, 21, -13, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-26, -22, -56, -20, -3],\n [-27, -18, -42, -3, 9],\n [15, 0, -10, -35, -30],\n [21, 18, 46, 17, 3],\n [-17, -10, -22, 3, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, 3, 12, 9, 12],\n [-2, 2, 8, 6, 8],\n [-4, 4, 16, 12, 16],\n [5, -5, -20, -15, -20],\n [-3, 3, 12, 9, 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[[-10, 6, 4, -4, -18],\n [-19, -12, 18, 26, -9],\n [9, 15, 20, -42, -24],\n [-10, 5, -52, 32, -6],\n [7, 27, -28, -26, -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[[-33, -10, -40, -42, 38],\n [42, 28, 28, 28, -60],\n [0, -3, 0, -1, 7],\n [42, 30, 14, 10, -50],\n [-6, -28, 50, 60, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-7, 62, 25, 10, 2],\n [32, 5, -35, 15, 9],\n [2, -31, -12, -9, 3],\n [-5, -21, -24, 1, 39],\n [30, -18, -39, 14, 4]]\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, -2, 10, 2, -2],\n [3, 3, -15, -3, 3],\n [6, 6, -30, -6, 6],\n [-5, -5, 25, 5, -5],\n [-3, -3, 15, 3, -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[[20, 24, -42, 55, 26],\n [33, -8, -49, 61, 31],\n [18, -68, 6, -12, -2],\n [3, -66, 15, -27, -9],\n [-8, -2, -6, 2, 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[[40, 5, 35, 35, 5],\n [12, -5, 9, 15, 11],\n [-28, -36, -32, -2, 44],\n [14, 18, 16, 1, -22],\n [-48, -6, -42, -42, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-24, -43, 5, -19, -17],\n [71, -24, 32, -17, -8],\n [-16, 16, -24, -8, 16],\n [1, -6, -18, -1, -2],\n [-32, -29, -49, 15, -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[[-3, -2, 3, -7, 10],\n [5, -10, -15, 29, -24],\n [42, 46, 43, 20, -17],\n [-19, -27, -11, -11, 25],\n [-8, 19, 18, -44, 27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[31, 3, -17, -45, -52],\n [-20, 0, -8, -48, -28],\n [39, -3, -7, 5, -19],\n [3, -21, -17, -53, -56],\n [-13, 41, 13, 17, 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[[26, -8, -31, -30, -14],\n [1, 24, 4, -25, -16],\n [13, 8, -10, 5, -5],\n [11, 16, -9, 7, -9],\n [20, -26, -26, -9, 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[[-6, 18, 30, 30, -30],\n [-6, 18, 30, 30, -30],\n [2, -6, -10, -10, 10],\n [-6, 18, 30, 30, -30],\n [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[[-1, 2, 3, -5, 4],\n [2, -4, -6, 10, -8],\n [2, -4, -6, 10, -8],\n [3, -6, -9, 15, -12],\n [-4, 8, 12, -20, 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[[8, 3, 17, 9, 38],\n [-16, 24, -14, 47, -31],\n [-8, -7, 37, -26, 31],\n [8, 11, 11, 28, 35],\n [-16, 2, 28, -9, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[25, 1, 16, -19, -30],\n [-15, 3, -2, 23, 16],\n [35, -11, 14, -31, 20],\n [13, -1, 16, 7, 19],\n [-24, -1, -17, 15, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-12, -21, 10, -19, 0],\n [-8, -10, -4, 10, -12],\n [-22, -20, 37, -49, 4],\n [-8, 8, 44, -56, 18],\n [-54, -60, 13, 5, -51]]\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 5x5 matrix:\n[[-14, -10, -28, 12, -9],\n [-43, 2, -8, -18, -13],\n [-44, -42, -56, 44, -17],\n [-9, 48, 24, -66, -6],\n [-24, 30, 12, -48, -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[[2, 12, -18, 11, -3],\n [-14, 10, 24, 6, 29],\n [-10, 17, 6, 13, 21],\n [8, 9, -6, 9, 14],\n [-8, 15, -12, 12, -2]]\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[[-2, 0, -14, -2, 14],\n [-4, 9, 8, -13, -26],\n [-4, 0, -28, -4, 28],\n [-2, 1, -10, -3, 8],\n [-6, 6, -18, -12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-40, 8, 28, -34, 44],\n [7, -9, 29, 8, 7],\n [6, 15, -45, 49, -22],\n [-3, 25, -48, 3, -10],\n [-12, -14, 15, 9, 5]]\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, 12, -16, -16, 24],\n [-36, -18, 24, 24, -36],\n [-36, -18, 24, 24, -36],\n [24, 12, -16, -16, 24],\n [-24, -12, 16, 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 5x5 matrix:\n[[40, 12, -50, 26, 50],\n [-35, -27, 7, -4, -24],\n [20, 27, 7, -37, 1],\n [6, 6, -5, -13, 3],\n [10, 3, -19, -5, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, -10, -12, -2, 4],\n [0, 0, 0, 0, 0],\n [-8, 10, 12, 2, -4],\n [4, -5, -6, -1, 2],\n [-16, 20, 24, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[30, 30, 25, -15, 0],\n [-12, -12, -10, 6, 0],\n [-30, -30, -25, 15, 0],\n [-24, -24, -20, 12, 0],\n [-18, -18, -15, 9, 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[[0, 0, 0, 0, 0],\n [-1, -4, -5, -5, -2],\n [-5, -20, -25, -25, -10],\n [-3, -12, -15, -15, -6],\n [-1, -4, -5, -5, -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[[4, 0, -20, 24, -16],\n [-2, 0, 10, -12, 8],\n [-3, 0, 15, -18, 12],\n [6, 0, -30, 36, -24],\n [1, 0, -5, 6, -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[[-8, -2, 8, 17, -14],\n [-6, -4, 6, 9, -13],\n [-6, -14, 6, -6, -23],\n [-8, -16, 8, -4, -28],\n [0, -8, 0, -12, -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[[-24, 24, 18, -30, 0],\n [-20, 20, 15, -25, 0],\n [4, -4, -3, 5, 0],\n [20, -20, -15, 25, 0],\n [12, -12, -9, 15, 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[[-5, -34, -12, -4, -19],\n [16, -3, 32, -3, -21],\n [24, 11, 32, 11, -11],\n [-11, -42, -26, -3, -17],\n [-13, -16, -26, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[40, -7, 2, -33, -32],\n [-16, 1, -8, 33, 20],\n [-42, -33, 62, -34, 31],\n [2, 4, -10, 13, 1],\n [-28, -24, 48, -34, 18]]\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[[5, 4, -3, -1, -5],\n [15, 12, -9, -3, -15],\n [15, 12, -9, -3, -15],\n [5, 4, -3, -1, -5],\n [-15, -12, 9, 3, 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[[16, -25, 4, 50, 6],\n [-5, -7, 27, -45, 16],\n [-9, 26, -13, 15, 6],\n [22, -2, -10, 54, 16],\n [22, 14, -10, -20, 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[[4, 1, 0, -3, 3],\n [-12, -3, 0, 9, -9],\n [4, 1, 0, -3, 3],\n [0, 0, 0, 0, 0],\n [-20, -5, 0, 15, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[15, 45, -5, -40, -35],\n [11, 9, 15, -22, -23],\n [9, 6, 23, 33, 1],\n [-13, 3, -8, 40, 21],\n [-45, 36, -12, 27, -9]]\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[[-30, 5, -5, 0, -30],\n [0, -11, -13, 6, -2],\n [-12, 13, 11, -6, -10],\n [-3, 6, 6, -3, -2],\n [-12, 35, 37, -18, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, -6, 18, 15, 6],\n [-18, 0, 24, 19, 8],\n [26, 4, -36, -29, -12],\n [-8, 14, 6, 3, 2],\n [3, -21, 3, 5, 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[[30, -25, 0, -10, -10],\n [0, 0, 0, 0, 0],\n [-6, 5, 0, 2, 2],\n [-36, 30, 0, 12, 12],\n [18, -15, 0, -6, -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 5x5 matrix:\n[[-5, 17, -46, 60, -3],\n [55, -4, 18, 11, 33],\n [22, -1, 14, -3, 15],\n [9, -12, 8, -11, 0],\n [-8, 14, -72, 86, -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[[-33, -28, -36, -44, 64],\n [6, -18, -12, -15, 24],\n [25, 21, 12, -15, -10],\n [-17, 46, -6, 0, -23],\n [21, 31, 26, 30, -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[[23, -35, -16, -16, -1],\n [-19, -29, 20, -28, 25],\n [5, 29, -10, 22, -17],\n [-31, -47, -16, -58, 8],\n [-10, 24, -22, 6, -22]]\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 5x5 matrix:\n[[-5, -3, 10, -7, 0],\n [-5, 5, 0, 15, -20],\n [-2, -2, 5, -5, 2],\n [9, -1, -10, -5, 16],\n [-1, 1, 0, 3, -4]]\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[[30, -12, 0, 0, 0],\n [-10, 4, 0, 0, 0],\n [30, -12, 0, 0, 0],\n [-25, 10, 0, 0, 0],\n [10, -4, 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[[-3, -6, 5, -3, 4],\n [0, 0, 0, 0, 0],\n [-15, -30, 25, -15, 20],\n [3, 6, -5, 3, -4],\n [-3, -6, 5, -3, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-29, -36, -23, -15, 28],\n [-43, -28, -8, -2, -9],\n [11, 8, -21, -11, 48],\n [-23, -50, -3, -10, -9],\n [30, 14, -4, -5, 25]]\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[[-25, 18, -22, -8, 28],\n [-20, -6, 17, -15, 21],\n [-33, 22, 12, -10, 18],\n [-44, 32, -15, -1, 63],\n [-26, 30, -33, -11, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[18, -4, -18, 28, 18],\n [15, 12, -15, -15, -8],\n [15, 8, -15, -5, -2],\n [-15, -4, 15, -5, -4],\n [-18, -4, 18, -8, -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[[-21, 7, 9, -12, -15],\n [-4, -6, 19, -18, -17],\n [21, -7, -9, 12, 15],\n [1, 5, -13, 12, 11],\n [-31, 13, 7, -12, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-26, 0, -10, -10, -54],\n [-16, -9, -11, -11, -9],\n [10, 4, 6, 6, 10],\n [-31, -28, -27, -27, 11],\n [-1, -16, -9, -9, 41]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, 0, -22, -7, -1],\n [12, 0, 14, -16, -10],\n [18, 0, -19, -14, -5],\n [24, 0, -12, -22, -10],\n [36, 0, 6, -39, -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[[-18, 11, 19, 3, 10],\n [2, -9, -1, -1, -10],\n [2, -9, -1, -1, -10],\n [-20, -15, 25, 1, -20],\n [-3, -39, 9, -3, -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[[6, -18, 30, 30, 24],\n [2, -6, 10, 10, 8],\n [-2, 6, -10, -10, -8],\n [2, -6, 10, 10, 8],\n [-1, 3, -5, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[24, 12, 4, 24, -24],\n [-18, -9, -3, -18, 18],\n [-24, -12, -4, -24, 24],\n [-36, -18, -6, -36, 36],\n [18, 9, 3, 18, -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[[-30, -18, 24, 12, 12],\n [-20, -12, 16, 8, 8],\n [0, 0, 0, 0, 0],\n [5, 3, -4, -2, -2],\n [-25, -15, 20, 10, 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 5x5 matrix:\n[[-10, -5, 24, -19, 6],\n [0, 0, 0, 0, 0],\n [10, -30, -38, 33, 8],\n [-2, -13, 0, 1, 6],\n [-8, 18, 28, -24, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-15, -9, 30, 21, -24],\n [45, -3, 20, -23, 30],\n [-49, -7, 11, 29, -12],\n [31, 10, -29, -29, 27],\n [8, -1, 8, 2, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-20, -10, -9, 9, -13],\n [2, 5, 19, -7, 45],\n [10, -10, 18, 0, 50],\n [18, 0, 10, -4, 22],\n [17, 45, 12, -27, 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[[10, -24, 16, 24, 15],\n [-23, 46, -34, -22, -16],\n [23, 18, 22, -22, -8],\n [-25, 26, -32, 4, -2],\n [-18, -12, -20, -44, -28]]?\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, 12, -2, -10, 40],\n [-10, -44, 36, 2, -28],\n [-60, -29, 9, -58, 39],\n [-9, 16, -6, -7, 36],\n [4, -3, 21, 18, 13]]\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[[-9, 44, -68, -71, 11],\n [52, 40, -2, -2, -34],\n [17, 34, -31, -36, -17],\n [-38, -28, -2, 10, 58],\n [-42, -4, -20, -22, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[15, 3, 18, -6, 3],\n [-6, -22, -52, -8, -22],\n [8, -14, -24, -11, -14],\n [9, 7, 22, -1, 7],\n [-8, 14, 24, 11, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, -16, -6, 1, 34],\n [-35, -31, -3, -8, 49],\n [19, 0, -6, -15, 9],\n [8, 9, -13, 26, -14],\n [-4, 16, 10, 30, -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[[-6, -12, -12, -18, 0],\n [0, 0, 0, 0, 0],\n [2, 4, 4, 6, 0],\n [0, 0, 0, 0, 0],\n [-5, -10, -10, -15, 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[[34, -1, -17, 31, 25],\n [30, 3, 7, 17, 35],\n [-24, 6, 42, -36, 0],\n [0, 6, 34, -16, 20],\n [34, 2, 0, 23, 35]]\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[[-30, -42, -11, 19, -14],\n [-18, 16, -1, 2, 12],\n [3, 18, -1, -13, 10],\n [-6, -16, -9, -6, -4],\n [54, 40, 14, -28, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[19, -38, 32, 71, 17],\n [19, -13, -20, 19, 23],\n [14, 5, -44, -14, 16],\n [-5, -1, 13, 1, -1],\n [-16, 7, 14, -32, 26]]\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, 15, 6, 2, -6],\n [-3, -20, -30, 1, 30],\n [-3, -30, -42, 1, 42],\n [3, 5, 12, -1, -12],\n [-3, 5, 0, 1, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-41, -4, -50, 0, -17],\n [-4, 4, 8, -16, -6],\n [-27, -4, -22, -16, -23],\n [5, 0, -14, 28, 19],\n [7, -20, 30, -40, -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[[0, 0, 0, 0, 0],\n [30, 0, 20, 30, 5],\n [-36, 0, -24, -36, -6],\n [-36, 0, -24, -36, -6],\n [24, 0, 16, 24, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[10, 5, 15, 0, 25],\n [2, 1, 3, 0, 5],\n [8, 4, 12, 0, 20],\n [-12, -6, -18, 0, -30],\n [12, 6, 18, 0, 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[[-18, 6, 9, -6, -15],\n [42, -26, 0, 8, 44],\n [-6, -10, 24, -8, 4],\n [-12, 4, 6, -4, -10],\n [27, -19, 4, 4, 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[[20, 25, 25, 25, 20],\n [24, 30, 30, 30, 24],\n [-24, -30, -30, -30, -24],\n [0, 0, 0, 0, 0],\n [24, 30, 30, 30, 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, 12, 12, 6, -10],\n [-20, 24, 24, 12, -20],\n [20, -24, -24, -12, 20],\n [20, -24, -24, -12, 20],\n [-10, 12, 12, 6, -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[[9, 0, 4, -1, -16],\n [-15, 30, 55, 20, 5],\n [2, 2, 5, 1, -5],\n [-1, 8, 16, 5, -4],\n [-3, -12, -26, -7, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-25, 8, 18, -21, 33],\n [-29, 24, 34, -41, 53],\n [12, -5, 3, -13, -17],\n [-29, 4, 30, -45, 33],\n [-13, -36, -8, -1, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 0, -24, -20, 0],\n [4, 0, -12, -10, 0],\n [-12, 0, 36, 30, 0],\n [-4, 0, 12, 10, 0],\n [-2, 0, 6, 5, 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[[-32, -1, -1, -8, -4],\n [18, 19, -28, 18, -14],\n [-8, -18, 25, -38, 12],\n [59, 11, -16, -16, -5],\n [32, 23, -37, -16, -20]]?\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 5x5 matrix:\n[[-33, -10, 10, -34, -25],\n [-9, 19, -42, 62, 11],\n [-18, 16, -45, 53, 7],\n [10, -18, 31, -59, -5],\n [-20, 3, -19, -7, -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 5x5 matrix:\n[[12, 18, -30, -6, -24],\n [-10, -15, 25, 5, 20],\n [0, 0, 0, 0, 0],\n [8, 12, -20, -4, -16],\n [6, 9, -15, -3, -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 5x5 matrix:\n[[-31, 47, 4, -2, 42],\n [-17, 30, 5, 4, 36],\n [14, -14, -8, 36, 12],\n [-17, 1, -28, 2, -42],\n [2, -5, -5, 6, -6]]\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[[5, -26, -38, -26, -14],\n [-17, 5, -8, -28, 0],\n [45, -5, -20, 40, 10],\n [21, -22, -25, 12, 7],\n [36, -8, -1, 26, -37]]?\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, -10, 13, 2, -15],\n [31, -30, 23, -18, -24],\n [-8, 40, -22, 22, 24],\n [-59, -10, 20, 25, -27],\n [-27, -22, -6, -19, 6]]\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[[-9, 13, -54, 1, -17],\n [-8, 7, -11, 23, -13],\n [-14, -38, 20, -61, 18],\n [-13, 15, -33, -22, -19],\n [-10, 2, -13, 4, -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[[-46, -6, 16, 50, 9],\n [24, -22, -13, -59, -37],\n [-20, 9, 26, 76, 39],\n [-44, 34, -24, -8, 4],\n [-42, -22, -1, -5, -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[[-27, -12, 33, -36, -21],\n [17, 7, -3, 26, 6],\n [13, -25, 1, 15, -16],\n [0, 36, -8, 5, 26],\n [15, 24, -45, 18, 33]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-30, 34, -22, -40, -27],\n [8, 16, 2, -4, -15],\n [-34, 36, -27, -60, -18],\n [-4, -28, 0, 0, 34],\n [-4, 42, -7, -16, -44]]\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[[-46, -56, -42, 28, -34],\n [34, 41, 33, -16, 22],\n [-10, -11, -15, -8, 2],\n [44, 54, 38, -32, 36],\n [11, 13, 12, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[18, -15, -3, 3, -3],\n [-30, 25, 5, -5, 5],\n [-36, 30, 6, -6, 6],\n [-12, 10, 2, -2, 2],\n [-18, 15, 3, -3, 3]]\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, -13, -20, 0, -5],\n [-16, 42, 40, 0, 10],\n [-12, -18, -24, 0, -6],\n [12, 18, 24, 0, 6],\n [-12, -7, -12, 0, -3]]\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 5x5 matrix:\n[[15, -28, 8, 35, 16],\n [9, 26, 36, -16, 9],\n [-32, 2, -24, -12, -20],\n [-25, -2, -4, 0, -9],\n [-15, 28, -8, -35, -16]]\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[[39, -8, -14, 10, 1],\n [18, -10, 1, 4, 6],\n [-28, 18, 5, -16, 4],\n [-39, -10, 11, 14, -25],\n [6, 20, -5, -20, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-24, 16, 12, -12, -4],\n [30, -20, -15, 15, 5],\n [36, -24, -18, 18, 6],\n [24, -16, -12, 12, 4],\n [-30, 20, 15, -15, -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[[-12, 15, 5, -8, -27],\n [-15, 15, -24, -51, -27],\n [0, 18, 0, 12, -6],\n [7, -10, 31, 47, 10],\n [10, -10, -28, -22, 26]]\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, -7, -25, 10, 0],\n [30, -7, 33, 24, 33],\n [-60, 36, -22, 4, 18],\n [-60, 26, -18, -24, -18],\n [12, -9, 50, -14, -6]]\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[[13, 19, 12, 3, 12],\n [4, -8, -87, 71, -28],\n [-46, -10, 9, -23, 22],\n [32, -10, 6, -10, -31],\n [-19, 3, 80, -48, 40]]\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, 0, -12, -20, -12],\n [12, 0, -9, -15, -9],\n [-16, 0, 12, 20, 12],\n [12, 0, -9, -15, -9],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[6, 0, -6, 22, 36],\n [-6, 0, -14, 16, 38],\n [-7, 0, -25, -19, -16],\n [-11, 0, 55, 23, 22],\n [23, 0, 11, 12, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -34, -48, 18, -2],\n [30, -36, 6, -30, 24],\n [-6, 3, -30, 32, -31],\n [-3, -29, -42, 17, -5],\n [-6, -22, -30, 10, 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[[-12, 8, 0, 6, -42],\n [16, -16, -8, -12, 44],\n [14, -24, -22, -18, 16],\n [12, -8, 0, -6, 42],\n [19, -24, -17, -18, 41]]\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, -18, -18, 6, -18],\n [9, 9, 9, -3, 9],\n [-9, -9, -9, 3, -9],\n [0, 0, 0, 0, 0],\n [-15, -15, -15, 5, -15]]\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[[-26, 14, -18, -12, -50],\n [-55, -29, 3, -33, -29],\n [-20, -43, -60, 30, -1],\n [23, 25, 45, -15, 17],\n [-42, 10, 16, -41, -50]]\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, -4, -60, -40, 6],\n [17, 14, -24, -52, -51],\n [58, 39, -14, -25, -57],\n [31, 5, -2, 9, -34],\n [43, 10, 56, 26, -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[[15, -15, 0, 3, -3],\n [5, -1, -5, -1, -5],\n [25, -21, -5, 3, -9],\n [20, -8, -15, -2, -16],\n [-30, 30, 0, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-18, -6, 30, 12, -12],\n [6, 2, -10, -4, 4],\n [-3, -1, 5, 2, -2],\n [-6, -2, 10, 4, -4],\n [-9, -3, 15, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, 6, 3, 1, 5],\n [-12, -24, -12, -4, -20],\n [15, 30, 15, 5, 25],\n [12, 24, 12, 4, 20],\n [-18, -36, -18, -6, -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 5x5 matrix:\n[[19, -36, 9, 13, -29],\n [-45, 24, -10, 9, 13],\n [55, 16, 7, -58, -17],\n [-24, -28, 1, 38, -14],\n [-4, 36, -7, -22, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-35, 32, -7, -28, 25],\n [26, -21, -41, -14, 33],\n [6, -51, -10, 17, -59],\n [38, -59, -33, 11, -21],\n [10, -31, -38, -5, 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 5x5 matrix:\n[[27, -20, 21, 0, 4],\n [0, -33, -39, 33, 45],\n [18, 10, 45, -23, -32],\n [2, 10, 20, 5, -22],\n [-27, 9, -21, 32, -3]]\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[[56, -1, -66, -1, 10],\n [-3, 13, 19, 19, -8],\n [-65, -31, 37, 19, 8],\n [58, 35, -44, -33, 4],\n [19, -29, -13, 33, -14]]\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 5x5 matrix:\n[[-37, -43, -32, -44, -20],\n [0, -14, -50, -66, -4],\n [-18, 0, -30, -30, 36],\n [27, 36, 15, 24, 27],\n [-17, -12, 31, 38, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, -34, 4, 18, 32],\n [6, 44, -5, -15, -49],\n [7, -40, -22, 36, 26],\n [28, -12, -8, 24, -6],\n [27, 28, 17, -11, -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[[-12, 30, -9, -9, 27],\n [17, 15, 0, 9, 7],\n [32, 24, 0, -18, -8],\n [-5, -11, 0, -57, -35],\n [32, 24, 0, -18, -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[[0, 14, 0, -4, 8],\n [20, 15, 20, -10, 20],\n [20, 22, 20, -12, 24],\n [6, 8, 6, -4, 8],\n [22, 13, 22, -10, 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[[30, 15, -25, 15, 30],\n [-17, -11, 12, -11, -24],\n [-1, 2, 3, 2, 6],\n [-26, -8, 26, -8, -12],\n [30, 30, -12, 30, 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[[35, -5, -40, -50, 5],\n [10, 2, -23, -22, 1],\n [-11, 5, 1, 8, -2],\n [2, -6, 17, 10, 1],\n [-15, 9, -6, 6, -3]]?\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 5x5 matrix:\n[[-40, 52, 11, 12, -3],\n [6, 33, -22, 34, -29],\n [-13, -11, 18, -18, 10],\n [6, -52, 13, -46, 36],\n [-27, -5, 15, -28, 0]]\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, 33, 16, 21, -2],\n [25, -41, -39, 42, 31],\n [-10, 2, 5, 27, -11],\n [7, -5, -4, -27, 0],\n [16, -41, -9, 12, -8]]\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 5x5 matrix:\n[[-20, -19, -45, 64, 25],\n [-30, 35, -73, 24, -3],\n [18, -22, 59, -24, 3],\n [-31, 57, 20, -19, 2],\n [-19, 45, -58, -1, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-13, -58, -17, 51, 5],\n [12, 0, -11, 5, -10],\n [-14, -12, 7, 6, 10],\n [-17, -26, -5, 10, 35],\n [-14, -28, -8, 14, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[22, -10, 18, 2, -1],\n [-7, -11, -3, 14, 49],\n [6, 6, -18, -12, 14],\n [-18, 24, -42, -22, -3],\n [-16, -20, 36, 34, 3]]?\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[[12, 26, -41, -10, -4],\n [-29, -52, 28, -10, -6],\n [-20, 3, 2, -49, 0],\n [22, 4, -19, 41, 1],\n [21, 13, -27, 25, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-17, -15, 12, 7, -7],\n [27, 29, -28, -13, 17],\n [21, 3, 12, -3, -9],\n [-19, -9, 0, 5, 1],\n [-30, -20, 10, 10, -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[[39, -49, -22, 4, 10],\n [-27, 33, 12, 0, -9],\n [-21, 11, -42, 44, -40],\n [21, -11, 42, -44, 40],\n [36, -36, 12, -24, 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[[0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [-18, 15, 3, 18, -15],\n [36, -30, -6, -36, 30],\n [12, -10, -2, -12, 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[[8, -3, 19, -20, 7],\n [-15, 1, 27, -8, 13],\n [21, -6, 12, -8, -4],\n [17, -28, -2, -36, 0],\n [-15, -28, 25, -58, 24]]\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[[5, 10, 21, -15, -21],\n [0, 16, 22, -28, -35],\n [-11, -6, 3, 5, 18],\n [2, -20, -37, 36, 41],\n [21, 2, -8, 7, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-14, 45, -9, 13, 29],\n [-50, 53, 11, 37, 13],\n [-20, 60, 4, -6, -24],\n [2, -14, -4, -2, -6],\n [-4, -19, 25, 5, -15]]\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, 8, 14, 12, 23],\n [32, 35, -7, 61, -42],\n [-22, -18, 38, -4, -11],\n [17, -5, -29, -25, 35],\n [1, -4, -8, -11, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 34, 1, -50, -22],\n [-38, -38, 2, 44, 28],\n [-33, 13, 9, -54, -18],\n [59, 53, -14, -26, 5],\n [-23, 1, 9, -34, -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[[29, 45, -53, 6, -74],\n [-36, -51, 27, 21, 33],\n [-19, -13, 8, 8, -3],\n [4, -9, -13, 13, -3],\n [-3, 7, 11, -10, 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[[-8, -40, -56, -16, -63],\n [17, 14, 43, -8, 45],\n [-41, -32, -37, -12, -14],\n [-81, -23, -28, -2, -38],\n [20, -3, -32, 10, -52]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 12, 8, 4, 0],\n [-12, -12, -8, -4, 0],\n [0, 0, 0, 0, 0],\n [6, 6, 4, 2, 0],\n [6, 6, 4, 2, 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[[-24, -2, 21, 3, -3],\n [6, -14, 0, 9, -9],\n [-10, 34, -3, -12, 17],\n [-20, 10, 15, 15, -5],\n [-24, 36, 10, 10, 6]]\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, -8, -48, 2, 38],\n [-37, -6, -60, 56, 16],\n [-48, -56, -6, 18, -8],\n [4, -58, 3, -20, 7],\n [-23, -48, 9, -4, -7]]?\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 5x5 matrix:\n[[6, 12, 9, -12, -18],\n [-2, -4, -3, 4, 6],\n [-6, -12, -9, 12, 18],\n [-4, -8, -6, 8, 12],\n [-12, -24, -18, 24, 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[[-52, -13, 27, -1, -1],\n [9, 12, -8, -10, -10],\n [24, -13, -9, -14, -27],\n [-25, 6, 12, 6, 16],\n [46, 15, -22, 22, 33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-14, -28, 15, 31, 8],\n [8, 16, -8, -18, -4],\n [12, 24, -8, -29, -2],\n [6, 12, -7, -13, -4],\n [-2, -4, 5, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-10, -8, 16, 1, 4],\n [-20, 6, 28, -4, 20],\n [-13, 11, 41, -11, 26],\n [-36, -19, 34, 5, 10],\n [9, -30, -31, 14, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[16, 22, -31, -24, -4],\n [22, -27, -23, 5, -9],\n [-48, -41, 25, 34, 37],\n [18, -41, -1, 20, -13],\n [-40, -34, 18, 41, 32]]?\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, 31, -56, 23, -9],\n [-31, 2, 20, -9, 4],\n [-21, 33, -34, -13, 18],\n [-23, -21, 40, -29, 6],\n [-22, 28, -32, -26, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[23, 26, 15, 48, 19],\n [2, 14, 20, 14, 20],\n [-10, 29, 10, 25, 27],\n [-30, -3, 15, -33, 15],\n [42, 12, 10, 48, 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[[40, -16, 10, 5, -12],\n [17, -16, -22, 24, -28],\n [-5, -8, 4, -5, 12],\n [-23, 16, 10, -16, 20],\n [21, -40, -42, 42, -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 5x5 matrix:\n[[-39, -3, -45, 18, 9],\n [-1, -5, -3, -2, 3],\n [-42, -18, -54, 12, 18],\n [11, -9, 9, -10, 3],\n [-22, 18, -18, 20, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 2, -2, -5, -7],\n [20, 36, -46, -30, -51],\n [-5, 4, -14, 0, -14],\n [13, 14, -10, -17, -16],\n [13, 16, -18, -10, -14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[17, 2, 14, 19, 10],\n [-6, 21, -27, 17, -22],\n [8, 3, 4, 13, -53],\n [-5, 89, -12, -10, -7],\n [16, -13, 9, 25, 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 5x5 matrix:\n[[46, 16, 40, 42, -72],\n [-2, -27, -72, 1, 6],\n [-28, 40, 30, -34, 18],\n [15, -12, 4, 17, -12],\n [-26, -38, -84, -20, 48]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-36, 6, 9, 36, 27],\n [0, 48, -42, 0, -6],\n [36, 18, -30, -36, -30],\n [6, -29, 23, -6, -1],\n [6, 27, -26, -6, -8]]\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, 0, 6, -4, 3],\n [-24, 0, 24, -16, 12],\n [6, 0, -6, 4, -3],\n [18, 0, -18, 12, -9],\n [30, 0, -30, 20, -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[[-40, 41, -1, -32, 34],\n [-37, 23, 9, -13, 4],\n [-5, 21, 45, -3, 26],\n [-16, 1, -39, -14, -8],\n [-47, 30, 1, -12, 7]]?\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, -17, -13, 6, 2],\n [-25, 25, -20, -5, 55],\n [28, -28, 21, 10, -66],\n [-50, -10, -39, 34, 6],\n [-18, -36, -10, 25, -43]]?\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[[8, 30, 16, 8, 5],\n [9, -45, 3, 9, -12],\n [-14, -22, -16, -1, -7],\n [23, -7, 13, -9, 6],\n [7, -3, 7, 4, -1]]\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, 28, 11, -15, -14],\n [-13, -5, -2, 27, 5],\n [39, 7, 25, -5, -32],\n [-31, 37, -20, -45, 23],\n [27, -1, 11, -19, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[20, 4, -9, 7, -22],\n [-16, -8, 3, 1, 2],\n [-6, -2, 2, -1, 4],\n [18, 14, 1, -8, 14],\n [-26, -6, 11, -8, 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[[-12, -24, 16, 12, -20],\n [12, 30, -12, -12, 18],\n [6, 3, -14, -6, 13],\n [0, -24, -16, 0, 8],\n [6, 39, 10, -6, 1]]\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 5x5 matrix:\n[[27, 21, 11, 41, 22],\n [3, 6, -33, -48, -33],\n [-3, 0, -23, -38, -25],\n [35, 31, -21, -1, -8],\n [-23, -22, 29, 24, 21]]\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, -4, -4, -24, 12],\n [24, -4, -4, -24, 12],\n [0, 0, 0, 0, 0],\n [12, -2, -2, -12, 6],\n [-30, 5, 5, 30, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-28, 38, -31, -8, 10],\n [0, -2, -5, -4, 12],\n [14, -18, 18, 6, -11],\n [18, -26, 16, 2, 3],\n [-18, 28, -11, 2, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-10, -24, 8, -39, -21],\n [-6, -36, 12, -54, -30],\n [-19, -6, 2, -18, -8],\n [-15, 18, -6, 18, 12],\n [42, -36, 12, -30, -22]]\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, 46, 22, 6, 46],\n [12, -21, -48, -21, -24],\n [-37, -12, 39, 16, -5],\n [22, 4, 28, 20, 0],\n [-51, -35, 4, -3, -26]]\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 5x5 matrix:\n[[12, -38, 28, 13, 11],\n [-16, 6, 7, 28, 31],\n [8, -18, 44, 31, -3],\n [-2, 12, 17, 17, -10],\n [0, -6, -27, -24, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, -8, -8, 4, 12],\n [3, 2, 2, -1, -3],\n [15, 10, 10, -5, -15],\n [-15, -10, -10, 5, 15],\n [-3, -2, -2, 1, 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[[-2, -18, 13, -25, -18],\n [-10, -12, 0, 5, 1],\n [0, -12, 10, -20, -14],\n [24, 24, 4, -20, -8],\n [0, -6, 5, -10, -7]]?\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 5x5 matrix:\n[[-17, -20, -30, -30, -14],\n [-26, -30, -42, -44, -18],\n [-13, -15, -21, -22, -9],\n [-34, -30, 6, -28, 30],\n [14, 15, 15, 20, 3]]\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 5x5 matrix:\n[[2, 20, -5, -45, 46],\n [-63, 1, -22, 30, 40],\n [28, -27, 3, -49, -2],\n [46, 51, 24, -10, -14],\n [-63, -17, -25, 27, 34]]\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 5x5 matrix:\n[[16, -8, 24, 16, -24],\n [-24, -4, 4, 4, 24],\n [30, -11, 35, 23, -42],\n [-40, -4, 0, 2, 42],\n [42, -1, 13, 7, -48]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-25, 3, -35, -18, -27],\n [24, 0, 36, 24, 30],\n [-50, 18, -60, -8, -37],\n [-35, 9, -45, -14, -31],\n [50, -18, 60, 8, 37]]\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[[-30, 0, -25, -10, 5],\n [24, 0, 20, 8, -4],\n [30, 0, 25, 10, -5],\n [-24, 0, -20, -8, 4],\n [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, 16, 12, 23, 17],\n [-6, -21, -47, -33, -6],\n [-12, -27, -51, -33, 0],\n [-30, 5, 15, -5, -20],\n [8, -21, -19, 10, 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[[-36, 30, 36, 0, -30],\n [18, -15, -18, 0, 15],\n [18, -15, -18, 0, 15],\n [-18, 15, 18, 0, -15],\n [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[[22, -37, -20, 43, 35],\n [-37, -34, -9, 10, 26],\n [-1, 36, 0, -59, -53],\n [-65, -30, -11, 20, 32],\n [15, -29, -21, 52, 36]]\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 5x5 matrix:\n[[11, -13, -8, 13, 14],\n [6, -12, -12, 2, 14],\n [-27, 0, 33, -2, -56],\n [-14, 19, 7, -21, -14],\n [21, 39, -18, -11, 46]]\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 5x5 matrix:\n[[6, -29, 51, -18, -16],\n [0, 6, -18, -63, 36],\n [-2, -7, 10, -16, 2],\n [10, 44, -17, -13, 36],\n [4, 25, 6, -2, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-25, -7, -6, 8, 3],\n [29, 6, -12, 5, 27],\n [8, -9, 22, -9, -26],\n [23, 9, 13, -11, 2],\n [45, 1, -5, -2, -8]]\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, -33, 2, 5, -3],\n [-4, 36, -8, 12, -4],\n [26, -42, 4, 2, -2],\n [-54, 6, 12, -38, 16],\n [39, -15, -6, 23, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-18, -2, 10, -24, -10],\n [24, 8, -8, 0, 8],\n [30, 3, -17, 42, 17],\n [12, 1, -7, 18, 7],\n [30, -1, -21, 66, 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[[4, -12, 0, 20, 16],\n [1, -3, 0, 5, 4],\n [4, -12, 0, 20, 16],\n [-5, 15, 0, -25, -20],\n [-5, 15, 0, -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[[13, -10, -4, -9, -6],\n [20, -44, -26, -32, -11],\n [36, -6, -30, 14, -31],\n [22, -19, 14, -33, 0],\n [-9, 12, 42, -17, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[9, 0, 6, -3, -12],\n [-9, 0, -6, 3, 12],\n [-3, 0, -2, 1, 4],\n [6, 0, 4, -2, -8],\n [-3, 0, -2, 1, 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[[-14, 24, -25, 22, 33],\n [31, 61, -36, 33, 60],\n [-26, -16, 18, 19, 5],\n [30, -3, 31, 20, 6],\n [-21, 32, -16, 17, 41]]\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[[-12, 3, -18, -6, -12],\n [12, -19, -6, 30, 8],\n [-12, -1, -24, 0, -13],\n [12, 5, 30, -6, 14],\n [0, -16, -24, 24, -4]]\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, -38, -19, 11, -6],\n [-36, 10, 16, -13, 8],\n [-70, -25, 25, -15, 40],\n [-42, 14, 20, -26, -2],\n [65, 19, -9, 1, -43]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[34, -16, 34, -8, -10],\n [27, -14, 27, -8, -7],\n [0, 0, 0, 0, 0],\n [-4, -24, -4, -32, 20],\n [-42, 12, -42, 0, 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 5x5 matrix:\n[[12, 14, -33, -31, 13],\n [28, 27, -66, 7, 9],\n [-40, 35, -3, -17, 12],\n [44, -24, -9, -1, -5],\n [-22, 21, 16, -1, 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 5x5 matrix:\n[[12, 41, 11, -41, -26],\n [-34, 40, 16, 12, 0],\n [-19, -7, -1, 23, 29],\n [27, -22, -6, -18, -15],\n [62, -38, -58, 14, -30]]\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[[-46, 26, -8, 23, -22],\n [15, -15, 5, -55, -30],\n [7, -17, 13, -48, -38],\n [28, -22, 16, 5, 20],\n [-42, 26, -10, 24, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-36, -4, 25, -15, 9],\n [40, 17, -34, 23, 5],\n [-22, 12, 8, -2, 23],\n [-26, 12, 14, -14, 19],\n [38, 8, -29, 3, -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[[20, 39, 16, 30, 39],\n [6, 3, -30, -3, 30],\n [-27, -36, 29, -2, -53],\n [5, -3, -3, 3, 33],\n [-3, -24, -14, -25, 5]]\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[[30, 25, -9, 32, 21],\n [-38, -31, -1, -32, -5],\n [2, 62, 42, 36, 1],\n [16, -60, -52, -27, 4],\n [4, -18, -30, 1, 26]]\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, -20, 20, -10, 10],\n [-4, 4, -4, 2, -2],\n [-4, 4, -4, 2, -2],\n [-16, 16, -16, 8, -8],\n [24, -24, 24, -12, 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[[-56, 7, 1, 30, -16],\n [-12, 4, 2, 0, -2],\n [-30, -4, -5, 36, -13],\n [32, -13, -7, 6, 4],\n [0, 7, 5, -18, 4]]\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[[-33, 19, -33, 31, -6],\n [24, -12, 24, -28, -2],\n [-3, 7, -3, -13, -19],\n [42, -26, 42, -34, 14],\n [39, -23, 39, -35, 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[[-12, -24, -12, -16, 16],\n [9, -18, 0, 12, 6],\n [-36, 24, -12, -48, 0],\n [30, -20, 10, 40, 0],\n [6, -28, -4, 8, 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[[-21, 10, 15, -2, -26],\n [-15, 9, 15, -3, -18],\n [20, -12, -20, 4, 24],\n [14, 2, 10, -6, 20],\n [-31, 16, 25, -4, -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[[-6, 15, 28, -1, 8],\n [-36, 5, -19, 11, -3],\n [-30, 15, 8, 7, 4],\n [6, -30, -61, 4, -17],\n [-12, 15, 23, 1, 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, -24, -12, 0, 36],\n [-9, -12, -6, 0, 18],\n [-12, -16, -8, 0, 24],\n [9, 12, 6, 0, -18],\n [-9, -12, -6, 0, 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[[-23, -15, 30, -24, -20],\n [4, 10, -10, -40, 28],\n [35, 35, -50, 4, 44],\n [-7, -13, 13, 25, -22],\n [8, 4, -9, 23, -2]]\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 5x5 matrix:\n[[-12, 8, 10, 12, 0],\n [36, -24, -30, -36, 0],\n [-12, 8, 10, 12, 0],\n [12, -8, -10, -12, 0],\n [-24, 16, 20, 24, 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[[-19, -11, 6, 1, 22],\n [5, 29, -10, -7, -26],\n [9, -16, 4, 5, 6],\n [-18, -30, 12, 6, 36],\n [6, -21, 6, 6, 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[[18, 0, 15, -12, -15],\n [24, 0, 20, -16, -20],\n [36, 0, 30, -24, -30],\n [18, 0, 15, -12, -15],\n [-24, 0, -20, 16, 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[[-1, -5, -2, 2, -6],\n [5, 25, 10, -10, 30],\n [-6, -30, -12, 12, -36],\n [6, 30, 12, -12, 36],\n [-2, -10, -4, 4, -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[[17, -7, -12, 7, 2],\n [41, 8, -15, 26, 38],\n [-17, -2, 9, -12, -14],\n [40, -8, -12, 10, 16],\n [-23, -26, 9, -33, -50]]\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[[-7, 10, 7, -14, -30],\n [-6, 3, -4, -6, -13],\n [14, -5, 0, -14, -13],\n [10, -7, -5, -4, 2],\n [10, -22, -40, -4, 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 5x5 matrix:\n[[6, -3, 0, -9, 12],\n [0, 0, 0, 0, 0],\n [-10, 5, 0, 15, -20],\n [4, -2, 0, -6, 8],\n [-8, 4, 0, 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[[-33, 1, 14, 8, -14],\n [57, 15, -14, 4, 34],\n [-58, -28, 32, -17, -51],\n [9, -7, 6, -9, -5],\n [6, 12, -16, 11, 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 5x5 matrix:\n[[24, 23, -3, -16, -25],\n [-11, 69, 29, -51, 37],\n [-53, -2, 9, -2, 25],\n [-24, 33, 27, -20, 71],\n [-22, -7, -13, 4, -32]]\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[[-50, 27, -28, -34, -37],\n [-28, -9, -14, 10, -20],\n [24, 21, 21, 8, 15],\n [8, -36, 1, 22, -2],\n [-12, 24, -12, -32, 27]]?\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 5x5 matrix:\n[[21, 3, -18, -27, -9],\n [-31, 47, -16, -27, 41],\n [-6, 2, -6, 26, 10],\n [13, -33, 31, 23, -30],\n [20, 22, -14, -22, -2]]\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, -40, -14, 10, 6],\n [-19, 12, 3, -29, -24],\n [25, -7, -2, 40, 32],\n [-24, -37, 32, -6, -2],\n [7, -11, -12, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-24, -6, 12, -3, 39],\n [23, 9, -19, -12, -25],\n [-12, 22, 3, -43, -19],\n [4, -10, 4, 25, -1],\n [13, 17, -14, -29, -28]]\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, 16, -2, 2, 15],\n [2, -1, 2, 3, -5],\n [10, -4, -4, -8, 6],\n [-10, 3, 18, 31, -37],\n [3, -1, -4, -7, 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[[48, -28, -11, -19, 9],\n [6, 10, 2, 28, -36],\n [6, 10, 2, 28, -36],\n [24, -8, -4, 4, -12],\n [6, -14, -4, -26, 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[[48, -13, 15, 63, 42],\n [-32, 8, -8, -44, -30],\n [15, -9, 15, 15, 15],\n [-3, -8, 12, 0, 21],\n [-50, 16, -32, -38, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-48, 36, -39, -16, 4],\n [-38, 18, -14, 2, 7],\n [-28, 48, 3, 20, 26],\n [-26, -27, -23, -18, -18],\n [22, -15, 8, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[24, 16, -16, 8, 16],\n [24, 16, -16, 8, 16],\n [-24, -16, 16, -8, -16],\n [-12, -8, 8, -4, -8],\n [24, 16, -16, 8, 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[[-30, 30, 30, 30, 25],\n [30, -30, -30, -30, -25],\n [-30, 30, 30, 30, 25],\n [6, -6, -6, -6, -5],\n [-12, 12, 12, 12, 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[[-1, -6, 3, -4, 5],\n [3, 18, -9, 12, -15],\n [-4, -24, 12, -16, 20],\n [-5, -30, 15, -20, 25],\n [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[[-3, 0, 3, 10, -5],\n [-36, -9, 36, 15, -30],\n [-32, -10, 32, -10, -20],\n [25, 5, -25, -25, 25],\n [-8, -1, 8, 15, -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[[22, -50, 9, 2, -23],\n [22, -7, 23, 40, -45],\n [9, 18, -4, 44, 1],\n [9, -4, 27, 6, -10],\n [26, -25, 23, 32, -49]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, 6, 28, 4, 12],\n [40, 16, -12, 2, 6],\n [-32, -16, -8, -4, -12],\n [-16, -8, -4, -2, -6],\n [28, 4, -48, -4, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[10, 0, -12, -2, 0],\n [-20, 0, 24, 4, 0],\n [10, 0, -12, -2, 0],\n [-20, 0, 24, 4, 0],\n [-25, 0, 30, 5, 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 5x5 matrix:\n[[27, -37, -7, 46, 7],\n [-15, 6, -12, 3, 60],\n [60, -56, 23, 8, -66],\n [7, 29, 29, -49, -9],\n [-39, 67, 11, -61, 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[[10, -22, 56, -23, 14],\n [29, 2, -3, -27, 2],\n [21, 24, -10, -6, -28],\n [2, 18, -10, 40, -12],\n [12, 13, 43, -19, -36]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, 6, -15, -38, 2],\n [49, 7, -6, -3, 49],\n [-16, 23, -33, 16, -4],\n [-4, -13, 21, 11, -5],\n [50, 42, -48, 57, 65]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, -36, 20, -11, -67],\n [3, 44, -6, 32, 59],\n [-12, 26, 8, 8, -2],\n [0, 45, -13, 17, 63],\n [24, -31, 3, 26, -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[[-11, -21, 3, 17, 21],\n [7, -15, -30, 47, 9],\n [4, 4, -17, 12, -14],\n [-2, -6, -1, 7, 6],\n [-10, 10, 26, -39, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-20, 15, -27, 7, 38],\n [-12, 5, -1, -1, 12],\n [12, -29, -35, -14, 13],\n [30, 24, -12, 13, 2],\n [-52, 22, 10, 20, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 10, -21, 27, -16],\n [13, -12, -13, -41, -4],\n [6, 60, 44, 5, -40],\n [9, 24, 21, -22, -20],\n [-5, -26, 11, -10, 32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-20, 41, -34, -8, -36],\n [-8, -15, 34, -13, 18],\n [20, -3, 14, 29, -10],\n [-4, -3, -10, -10, 8],\n [0, -17, -10, -14, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-10, 14, -44, 20, -6],\n [1, -17, -10, 28, 1],\n [-17, 16, -22, -16, 0],\n [-6, 61, -44, -8, 3],\n [-20, 19, -58, 13, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[20, 8, 15, 18, 3],\n [-23, 4, -9, -24, -4],\n [6, 24, 18, 0, 0],\n [28, 16, 24, 24, 4],\n [31, 4, 18, 30, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-38, -19, 7, 23, -33],\n [2, -1, -8, -14, -3],\n [8, -44, 20, 52, -12],\n [72, 6, 3, -3, 52],\n [48, -8, 14, 24, 33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[23, -8, 19, 4, 20],\n [1, -32, 13, -12, -4],\n [16, 8, 8, 8, 16],\n [21, 4, 13, 8, 20],\n [-20, 16, -20, 0, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, 4, 12, -24, 12],\n [12, -6, -18, 36, -18],\n [10, -5, -15, 30, -15],\n [4, -2, -6, 12, -6],\n [-10, 5, 15, -30, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[52, 75, -30, -13, -1],\n [19, 36, -65, 22, -2],\n [-2, 3, -12, -9, -13],\n [-28, -42, 40, -14, -6],\n [13, 18, -11, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[26, -2, 24, -37, 9],\n [-7, -14, 9, -6, -4],\n [3, -25, 30, -27, -2],\n [-12, 1, -9, 28, -5],\n [-35, -34, 9, 21, -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[[-24, -28, -38, 7, -36],\n [-10, 31, -12, 12, -6],\n [-20, 29, -26, 17, -15],\n [-40, 29, -48, 28, -9],\n [16, 6, 38, -7, 78]]\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 5x5 matrix:\n[[3, -6, 13, 40, 12],\n [-3, 15, -28, 35, 42],\n [-1, -12, 3, -10, 0],\n [-6, 3, -29, -20, 21],\n [4, 27, -1, 45, 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[[8, 6, -12, -4, 2],\n [24, 18, -36, -12, 6],\n [-24, -18, 36, 12, -6],\n [-4, -3, 6, 2, -1],\n [-12, -9, 18, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[0, 0, 0, 0, 0],\n [-6, -6, -12, -24, 36],\n [0, 0, 0, 0, 0],\n [3, 3, 6, 12, -18],\n [-2, -2, -4, -8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -4, -12, 8, 2],\n [-2, 2, 18, -20, -1],\n [-6, -12, -54, 48, 6],\n [10, 10, 30, -20, -5],\n [-6, -10, -42, 36, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[18, 18, -21, 18, 0],\n [0, 24, 20, 16, 24],\n [-36, -36, 42, -36, 0],\n [-6, -30, -13, -22, -24],\n [15, -6, -35, 1, -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 5x5 matrix:\n[[3, 6, -1, -4, -5],\n [-15, -36, 1, 22, 32],\n [-17, -38, 3, 24, 33],\n [-19, -46, 1, 28, 41],\n [-4, 2, 8, 2, -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[[0, 0, 0, 0, 0],\n [-3, -5, -1, 4, 1],\n [9, 15, 3, -12, -3],\n [3, 5, 1, -4, -1],\n [-3, -5, -1, 4, 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[[0, 12, 4, 16, -20],\n [0, 18, 6, 24, -30],\n [0, 3, 1, 4, -5],\n [0, 15, 5, 20, -25],\n [0, 18, 6, 24, -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[[-14, -48, -44, -12, 13],\n [36, -27, -12, 17, 12],\n [18, -5, 0, 1, -1],\n [38, -20, -4, -8, 19],\n [5, 57, 56, 9, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[11, -12, 6, 7, -6],\n [-9, 15, -36, -4, 17],\n [12, -9, -18, 9, 3],\n [-15, 15, 0, -10, 5],\n [14, -12, -12, 10, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[52, -18, 31, -10, 30],\n [-41, 16, -34, 2, -26],\n [32, -21, -15, -25, -6],\n [-1, -24, 11, 46, -36],\n [12, 12, 30, -9, 41]]\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[[13, 9, -12, 21, 18],\n [31, 14, -41, 16, -2],\n [-20, -36, 7, 14, 64],\n [34, -54, -11, 52, -6],\n [-31, -25, 6, -23, 35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[3, 29, 14, 4, -11],\n [8, 15, 3, 12, -9],\n [22, -19, 39, -44, 21],\n [10, -29, 33, -52, 27],\n [24, -23, 25, -28, 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 5x5 matrix:\n[[-12, -10, -6, -10, -2],\n [24, 20, 12, 20, 4],\n [-24, -20, -12, -20, -4],\n [-36, -30, -18, -30, -6],\n [-18, -15, -9, -15, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-18, 17, -28, -2, -6],\n [-17, 17, -19, -3, -8],\n [1, 2, -19, 11, -6],\n [15, -15, -9, 8, 10],\n [15, 14, -19, -16, -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 5x5 matrix:\n[[-28, -16, 18, 13, 26],\n [-12, -12, -30, -36, -56],\n [14, 13, -2, -18, -12],\n [-18, -7, 10, -10, 4],\n [8, 12, 44, 47, 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[[-21, 4, -29, 30, 12],\n [-7, 13, 16, -25, -10],\n [-16, 9, -9, 5, 2],\n [3, 3, 12, -15, -6],\n [4, -11, -17, 25, 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 5x5 matrix:\n[[-62, -44, 36, -24, -2],\n [-21, -30, 28, -10, -15],\n [1, -34, 24, -34, -5],\n [33, 2, 4, 12, -21],\n [-3, -16, 17, -1, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-24, -18, 36, -18, -6],\n [40, 14, -24, 2, 2],\n [12, 21, -45, 30, 9],\n [12, -15, 36, -33, -9],\n [8, 22, -48, 34, 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, 36, -36, -30, 0],\n [16, -24, 24, 20, 0],\n [12, -18, 18, 15, 0],\n [-16, 24, -24, -20, 0],\n [-20, 30, -30, -25, 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[[-12, 5, -14, -5, 7],\n [0, 15, -20, -15, -5],\n [-54, -36, 15, 36, 51],\n [-18, -6, -3, 6, 15],\n [-48, -28, 8, 28, 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[[-25, 30, -30, 30, -30],\n [25, -30, 30, -30, 30],\n [-5, 10, -10, 15, -18],\n [25, -10, 10, 15, -30],\n [40, -36, 36, -21, 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[[-5, 25, -5, 5, 30],\n [-5, 25, -5, 5, 30],\n [-5, 25, -5, 5, 30],\n [1, -5, 1, -1, -6],\n [6, -30, 6, -6, -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[[12, 4, -36, -6, -30],\n [-9, -3, 26, 8, 24],\n [-2, 51, 47, -3, 52],\n [4, -7, -19, 0, -17],\n [2, -36, -36, 5, -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 5x5 matrix:\n[[15, -11, 20, 24, 5],\n [10, -10, 8, 0, -10],\n [-10, 9, -10, -6, 5],\n [30, -30, 24, 0, -30],\n [-25, 21, -28, -24, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, 6, -2, 4, -6],\n [13, 30, -2, 14, -42],\n [-17, -30, -2, -11, 48],\n [-15, 30, -30, 35, 0],\n [24, 24, 12, 1, -54]]\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[[-7, -24, 24, 24, -33],\n [-1, -9, 6, 9, -15],\n [-13, -26, 36, 26, -27],\n [13, 13, -30, -13, 3],\n [7, -15, -6, 15, -39]]\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[[26, -18, 20, -19, 8],\n [-35, 39, -8, -1, -8],\n [6, 28, -26, -22, 2],\n [44, -31, 2, -12, 9],\n [8, 24, -26, -25, 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[[6, 23, 23, 27, -70],\n [6, 28, 44, 54, -6],\n [-14, 3, 35, -1, 1],\n [4, -17, -36, -20, -4],\n [-8, -12, 7, -3, 50]]\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[[23, -9, -27, -6, -33],\n [29, -38, -33, 45, -11],\n [22, 5, -18, -42, -19],\n [14, 34, -4, -31, 3],\n [46, -4, -31, 20, 25]]?\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, -21, -14, 23, -36],\n [-5, -26, -23, 27, 0],\n [9, -57, 16, 29, 42],\n [12, 16, -36, -12, 4],\n [-52, 9, -63, 44, -92]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-28, -4, -11, -11, -3],\n [16, -2, 2, 32, 6],\n [-24, -3, -9, -12, -3],\n [-16, -1, -5, -14, -3],\n [24, 0, 6, 30, 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 5x5 matrix:\n[[19, 13, -30, 24, -15],\n [-21, 6, 14, -4, -3],\n [-36, -24, -21, 1, 44],\n [23, 26, 0, -22, -47],\n [28, 7, -9, -17, -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[[6, 24, -18, -18, 30],\n [6, 24, -18, -18, 30],\n [3, 12, -9, -9, 15],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[24, -36, 18, -30, 6],\n [-24, 36, -18, 30, -6],\n [0, 0, 0, 0, 0],\n [12, -18, 9, -15, 3],\n [-8, 12, -6, 10, -2]]?\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[[-12, 30, 24, -12, -30],\n [-10, 25, 20, -10, -25],\n [8, -20, -16, 8, 20],\n [-4, 10, 8, -4, -10],\n [-4, 10, 8, -4, -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[[-19, -36, 1, 8, 8],\n [15, 20, 11, -24, -8],\n [18, 42, -12, 9, -6],\n [10, 0, 26, -44, -8],\n [-3, -2, -5, 9, 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[[32, 10, -2, -82, 24],\n [10, -29, 23, 26, 5],\n [-38, 3, -25, 18, -35],\n [7, 26, -1, 1, 15],\n [-29, 34, -29, 8, -18]]?\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 5x5 matrix:\n[[-4, -1, 19, 11, 32],\n [8, 31, 2, -23, -12],\n [-59, -3, -5, 49, 3],\n [-23, -50, -34, 34, -29],\n [-16, -15, -23, 13, -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[[7, -30, 0, -3, 8],\n [19, 42, 32, -15, 24],\n [20, -24, 16, -12, 24],\n [17, -42, 8, -9, 20],\n [-26, 42, -18, 15, -31]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-34, -23, 5, 12, 12],\n [4, -13, 40, -35, 52],\n [-1, -35, -17, 43, -13],\n [-33, 15, -10, 2, -15],\n [-34, -8, 11, -5, 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 5x5 matrix:\n[[-3, -8, 1, 24, -33],\n [-7, 8, 13, 8, 19],\n [35, -26, -53, -74, -3],\n [32, -42, -52, -40, -44],\n [-6, 18, 6, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-5, -34, -29, -1, -17],\n [-25, 6, -9, 29, -12],\n [-23, 18, -7, 19, 4],\n [-5, -27, -33, -11, -3],\n [-36, 7, -32, 20, 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[[12, -28, -12, 9, 15],\n [-8, 22, 14, -12, -18],\n [-16, 14, -5, -5, 1],\n [-4, 6, 13, -22, -22],\n [-16, -6, -17, -9, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-18, -3, 33, -42, -33],\n [-10, 20, 14, -6, -27],\n [-4, -19, 11, -24, 0],\n [6, -24, -6, -6, 21],\n [4, 9, -9, 16, 4]]?\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[[-12, -29, 17, -1, 2],\n [33, -11, 35, -28, -25],\n [3, 22, -39, 20, 11],\n [7, 29, -30, 11, 5],\n [10, -33, 22, -8, -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[[-29, 5, 33, -7, 4],\n [-45, 33, 31, 29, -21],\n [23, 21, 19, 15, -38],\n [-11, -29, 13, -41, 39],\n [12, -8, -13, -1, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-15, 2, 15, 24, 20],\n [23, -36, -8, -39, -41],\n [-15, 24, 15, 18, 30],\n [30, -20, -55, -25, -55],\n [-30, 30, 50, 26, 58]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[50, -11, 9, -33, -21],\n [16, -24, 17, 6, 3],\n [26, -43, 15, -5, -4],\n [-26, 2, -4, 15, 21],\n [2, 17, -18, -19, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-24, -26, 20, 30, -38],\n [18, -75, -14, 85, 13],\n [48, -17, 26, 39, 19],\n [75, -2, -21, 13, 75],\n [12, -72, -9, 71, -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[[-26, -8, -1, -27, -15],\n [12, -10, -2, 6, 8],\n [-34, -26, 35, -27, -21],\n [28, -2, 14, 30, 16],\n [16, 21, -12, 18, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, -12, 12, 4, 8],\n [-1, 6, -6, -2, -4],\n [-5, 30, -30, -10, -20],\n [-4, 24, -24, -8, -16],\n [-4, 24, -24, -8, -16]]?\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, -6, 6, -12, -9],\n [12, 8, -8, 16, 12],\n [-18, -12, 12, -24, -18],\n [-12, -8, 8, -16, -12],\n [6, 4, -4, 8, 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[[-12, -4, 0, -12, 16],\n [-12, -4, 0, -12, 16],\n [-15, -5, 0, -15, 20],\n [9, 3, 0, 9, -12],\n [-18, -6, 0, -18, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-30, 12, 36, -18, -24],\n [5, -2, -6, 3, 4],\n [25, -10, -30, 15, 20],\n [-20, 8, 24, -12, -16],\n [10, -4, -12, 6, 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[[-24, 6, -36, 6, 30],\n [8, -2, 12, -2, -10],\n [-20, 5, -30, 5, 25],\n [-24, 6, -36, 6, 30],\n [8, -2, 12, -2, -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[[-23, -17, -26, -18, -24],\n [-34, -3, -35, -23, -23],\n [6, 26, 12, 36, 8],\n [-10, 3, -8, 19, -14],\n [-11, -17, -13, 2, -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[[-48, 21, 10, -39, -7],\n [22, -41, 0, 17, -17],\n [16, 14, -37, 23, -36],\n [-43, 13, 23, -50, 5],\n [6, -6, 15, -11, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 4, 15, 7, 6],\n [13, -12, -35, -16, -13],\n [11, 16, -10, -7, -11],\n [10, 40, 10, 0, -10],\n [-30, 0, 60, 30, 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[[-4, 48, -13, -26, 51],\n [38, -53, 35, 28, -31],\n [-40, 18, -48, -16, -12],\n [-14, 44, -30, -27, 42],\n [-29, 30, -2, -6, 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[[36, 10, 42, 20, 36],\n [9, 11, 12, 4, 0],\n [1, 22, 5, -2, -22],\n [-9, -28, -15, -2, 18],\n [11, 4, 13, 6, 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 5x5 matrix:\n[[0, -23, 23, 4, -6],\n [34, 31, -12, -21, 0],\n [32, -12, 28, 2, -16],\n [-106, -38, 0, -24, 50],\n [40, 41, -12, 54, -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 5x5 matrix:\n[[66, 36, 46, -7, -31],\n [6, 1, 6, -2, -6],\n [30, 0, 34, -13, -37],\n [-42, -32, -22, -1, 7],\n [24, 24, 8, 4, 4]]\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[[-72, 18, -5, -36, -73],\n [-63, 15, -35, -17, -54],\n [18, -5, 34, -1, 8],\n [21, -5, 27, 2, 18],\n [15, -3, 2, -5, -7]]\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 5x5 matrix:\n[[-19, 8, 28, 1, 19],\n [31, -12, -31, 0, -9],\n [7, -2, 0, 4, 7],\n [-28, 12, 33, 13, 10],\n [-16, 4, 15, -33, 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[[-17, -34, 34, -18, -10],\n [-21, -23, 44, 63, 45],\n [7, 2, 8, -4, -15],\n [16, 24, -40, -32, -20],\n [-16, -37, 58, 9, -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[[3, 6, 4, 6, 3],\n [0, -18, -9, -14, -5],\n [-39, -28, 9, 0, -38],\n [21, 19, 21, 29, 13],\n [9, -3, -12, -13, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 66, -2, -12, -18],\n [-15, 39, 24, 9, 24],\n [3, -60, 11, 18, 42],\n [12, -24, -2, -6, -6],\n [2, 44, -20, -18, -38]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -5, 30, -10, 15],\n [0, 3, -18, 6, -9],\n [0, 6, -36, 12, -18],\n [0, 3, -18, 6, -9],\n [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[[-28, 6, 2, -14, -16],\n [-6, 2, -6, -8, -2],\n [-2, 0, 4, 2, -2],\n [32, -6, -10, 10, 20],\n [30, -5, -15, 5, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[0, 6, 0, 18, 15],\n [0, -10, 0, -30, -25],\n [0, 0, 0, 0, 0],\n [0, 6, 0, 18, 15],\n [0, -6, 0, -18, -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[[11, -21, -1, -15, -17],\n [-7, -15, 16, -33, -14],\n [-8, 24, -4, 24, 20],\n [-22, -6, 28, -42, -8],\n [-14, -6, 19, -30, -7]]\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 5x5 matrix:\n[[16, -22, 0, 7, 22],\n [-19, 14, 19, -5, 1],\n [16, -54, 64, 21, 4],\n [-63, -20, 17, 46, -56],\n [-31, 44, -43, -6, -54]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, 33, -40, -46, 4],\n [0, -14, 21, 16, 5],\n [-11, -12, -2, -16, 67],\n [-91, -47, -72, 44, 47],\n [-31, -25, -10, -18, 108]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-36, 0, 0, -18, -24],\n [18, 0, 0, 9, 12],\n [12, 0, 0, 6, 8],\n [36, 0, 0, 18, 24],\n [12, 0, 0, 6, 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[[-3, 22, 31, 2, 1],\n [7, -12, -46, -21, -5],\n [-12, 15, 28, -8, -20],\n [-3, 18, -44, -41, -23],\n [18, -17, 30, 4, 16]]\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[[-18, 15, -24, -15, 41],\n [28, -25, -25, 27, 0],\n [-19, 32, 34, -20, -9],\n [14, -18, 67, 8, -77],\n [5, -64, -32, 10, -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[[3, 24, -6, -30, -3],\n [2, 4, -16, 4, -14],\n [5, 22, -28, -14, -23],\n [5, 19, -31, -8, -26],\n [-3, -21, 9, 24, 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[[25, 37, -4, -1, 20],\n [36, 24, -7, -1, 17],\n [32, -64, -8, -15, -43],\n [-48, -3, 13, 8, 3],\n [52, -54, -21, -16, -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[[24, -15, 18, 0, -33],\n [39, 34, -1, -50, 16],\n [-55, 19, -31, -14, 53],\n [-34, 8, -16, -20, 26],\n [23, 1, 7, 14, -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 5x5 matrix:\n[[12, 10, 0, -7, -3],\n [-12, -24, -6, -17, -3],\n [36, 21, -6, -10, -15],\n [32, 33, 2, 1, -6],\n [-12, 19, 15, 25, 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[[8, -20, -8, 4, 4],\n [-8, 20, 8, -4, -4],\n [8, -20, -8, 4, 4],\n [-2, 5, 2, -1, -1],\n [-6, 15, 6, -3, -3]]?\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, 8, 9, 21, 9],\n [15, -6, 5, -8, -6],\n [-40, -26, -75, -33, -21],\n [-1, -2, 0, -9, -3],\n [11, 4, 25, -10, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[0, -29, -44, 6, -28],\n [-3, 24, 29, 7, 4],\n [-1, 39, 13, -25, 4],\n [-15, -50, -9, 16, -17],\n [8, 38, 41, 3, 29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[10, 21, -11, 5, -5],\n [-40, -51, -21, 43, -2],\n [16, 47, 7, -39, 17],\n [2, -11, 2, 17, -4],\n [-36, -62, -12, 34, -12]]\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 5x5 matrix:\n[[8, 8, -6, 10, 6],\n [4, 4, -3, 5, 3],\n [-12, -12, 9, -15, -9],\n [-16, -16, 12, -20, -12],\n [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[[14, -19, 1, 14, 17],\n [-4, 23, -5, -34, -22],\n [-56, 2, 19, 20, 0],\n [-12, -10, 7, 20, 10],\n [-32, -3, 9, 66, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, 3, 3, 5, -1],\n [30, 15, 15, 25, -5],\n [12, 6, 6, 10, -2],\n [-30, -15, -15, -25, 5],\n [36, 18, 18, 30, -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[[6, -24, 6, 24, 30],\n [2, -8, 2, 8, 10],\n [0, 0, 0, 0, 0],\n [3, -12, 3, 12, 15],\n [-6, 24, -6, -24, -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[[-46, -12, -25, 2, -11],\n [0, -5, 1, 18, 4],\n [-44, -2, -40, -14, 6],\n [28, -21, 15, 0, 6],\n [-6, -3, 31, 43, -33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-15, 15, 12, 3, -3],\n [15, -15, -12, -3, 3],\n [25, -25, -20, -5, 5],\n [-20, 20, 16, 4, -4],\n [5, -5, -4, -1, 1]]\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[[12, -22, 29, -31, -21],\n [2, 36, 2, -8, 22],\n [-6, 4, -14, 16, 6],\n [8, -38, 21, -19, -29],\n [-2, 48, -8, 2, 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[[5, 6, -2, -5, -5],\n [10, 12, -4, -10, -10],\n [-15, -18, 6, 15, 15],\n [5, 6, -2, -5, -5],\n [15, 18, -6, -15, -15]]\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, -22, 19, 40, -49],\n [-45, -14, -14, 5, -23],\n [-30, -14, 30, 38, -44],\n [36, 16, 45, 12, -7],\n [-3, -6, -20, -5, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[7, -21, 13, 25, -35],\n [14, -17, 2, 7, -34],\n [-17, 46, 1, 15, 13],\n [12, 14, 0, 19, -48],\n [-7, 1, 11, 21, -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[[8, -8, -20, -12, 24],\n [0, 0, 0, 0, 0],\n [4, -4, -10, -6, 12],\n [8, -8, -20, -12, 24],\n [12, -12, -30, -18, 36]]\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 5x5 matrix:\n[[35, -2, -56, 27, 49],\n [24, -24, -12, -6, -6],\n [31, -10, -40, 15, 29],\n [31, 2, -54, 28, 50],\n [-29, 2, 46, -22, -40]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[29, -45, -9, -26, -10],\n [3, 19, 40, -40, 4],\n [-14, -14, -38, 4, -19],\n [-25, 33, 15, -26, -7],\n [46, -40, 17, -14, 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 5x5 matrix:\n[[-1, -5, 40, -22, 35],\n [6, 10, -40, 20, -38],\n [5, 10, -50, 26, -46],\n [2, 1, 20, -8, 23],\n [5, 5, -25, 2, -42]]\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 5x5 matrix:\n[[6, -8, 10, 0, -12],\n [-6, 8, -10, 0, 12],\n [18, -24, 30, 0, -36],\n [15, -20, 25, 0, -30],\n [6, -8, 10, 0, -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[[-5, 9, 16, 12, -17],\n [29, 1, -6, -24, -23],\n [31, -17, -6, -72, 9],\n [6, 8, 23, 12, -20],\n [-31, 2, 12, 18, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, 21, 22, -16, 18],\n [-12, -3, -10, -6, -8],\n [12, -9, -22, 17, -7],\n [0, 36, 32, -9, 37],\n [-20, -5, -22, -8, -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 5x5 matrix:\n[[18, -35, 8, 46, 29],\n [3, -19, 24, -3, -17],\n [-7, -9, -7, 0, 12],\n [-10, -4, 5, -16, -7],\n [9, 48, -20, -2, -8]]\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, 18, -15, -6, 15],\n [12, 36, -30, -12, 30],\n [-8, -24, 20, 8, -20],\n [0, 0, 0, 0, 0],\n [4, 12, -10, -4, 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[[53, 87, -12, 15, 19],\n [-19, 0, 33, 0, -20],\n [-10, 6, 21, 0, -29],\n [28, 57, -4, -1, 0],\n [-38, -66, -6, -30, 8]]\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[[-33, 13, -44, 12, -8],\n [0, 15, -23, -28, -59],\n [-9, 18, 22, -27, -5],\n [-18, 0, -26, 20, 10],\n [-33, 28, 15, -17, 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[[-14, 4, -27, -3, -28],\n [-23, -9, -36, 11, 6],\n [14, -11, 2, 16, 10],\n [32, -22, -9, 18, -8],\n [33, 21, 39, 8, -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[[27, 26, -21, -6, -37],\n [-1, -52, 44, -42, 28],\n [-3, 40, -42, 42, -26],\n [-8, -24, 4, 0, 4],\n [-26, 19, -25, 48, 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[[12, -8, -8, -4, -4],\n [0, 0, 0, 0, 0],\n [-36, 24, 24, 12, 12],\n [-30, 20, 20, 10, 10],\n [30, -20, -20, -10, -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 5x5 matrix:\n[[-45, -9, -56, -16, 32],\n [12, 38, 26, -5, -2],\n [40, 24, 56, 6, -32],\n [-18, -5, -21, -12, 3],\n [8, 21, 15, 1, 3]]\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[[19, 27, -33, 30, 44],\n [2, -12, 18, -50, 0],\n [49, -16, 13, -52, -25],\n [2, 11, -23, 37, 24],\n [9, -8, 2, -8, -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 5x5 matrix:\n[[-33, 54, 21, -5, 30],\n [-12, 21, -33, 13, -15],\n [-27, 21, -38, 8, 30],\n [28, -44, -38, 6, -27],\n [14, -13, 15, -33, 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[[19, 24, 0, 16, -24],\n [-24, -28, 44, 18, 28],\n [-10, -14, -26, -31, 14],\n [0, 2, 38, 33, -2],\n [19, 22, -38, -17, -22]]\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, 50, 43, 16, 11],\n [-31, 17, 1, -1, 6],\n [-28, 7, -22, -58, 7],\n [-33, 56, 37, 21, 19],\n [19, 24, -3, 5, 35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-21, -32, 33, -13, 30],\n [4, -6, 16, 6, 12],\n [-13, -48, 13, -17, 22],\n [-8, 3, -14, -19, -16],\n [-23, 56, -5, 35, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[13, -19, -11, -3, 21],\n [-54, 18, 48, -15, -33],\n [9, 35, -9, 21, -29],\n [-17, 11, 7, -27, -3],\n [-11, -8, 10, -9, 4]]?\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 5x5 matrix:\n[[-25, 15, -30, 10, 5],\n [10, -6, 12, -4, -2],\n [15, -9, 18, -6, -3],\n [25, -15, 30, -10, -5],\n [-20, 12, -24, 8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-10, 11, -10, 0, -2],\n [-50, 59, -55, 22, -5],\n [0, 6, 0, 8, 0],\n [5, 2, 11, -10, -5],\n [0, 10, 4, 0, -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[[15, 12, 0, 15, 12],\n [-20, -16, 0, -20, -16],\n [-25, -20, 0, -25, -20],\n [5, 4, 0, 5, 4],\n [-20, -16, 0, -20, -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[[-13, 0, 3, -13, -3],\n [-17, -2, 4, -19, -4],\n [0, -10, -23, 18, 19],\n [-22, 8, -42, 42, 34],\n [14, 38, 7, 38, -5]]\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 5x5 matrix:\n[[-23, 22, -14, -12, -5],\n [18, -12, 24, 24, 6],\n [-9, 16, 13, 16, 1],\n [-3, -8, -29, -32, -5],\n [-24, 26, -7, -4, -4]]\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, 2, 2, -12, 4],\n [8, 4, 4, -24, 8],\n [-4, -2, -2, 12, -4],\n [-4, -2, -2, 12, -4],\n [-8, -4, -4, 24, -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[[-18, 27, 30, -15, -54],\n [34, 16, -10, 10, 4],\n [-38, -17, 25, -44, -4],\n [72, 36, -15, 9, 6],\n [-40, -19, 15, -20, -4]]?\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 5x5 matrix:\n[[8, 12, 12, 16, -8],\n [4, 6, 6, 8, -4],\n [8, 12, 12, 16, -8],\n [-10, -15, -15, -20, 10],\n [-8, -12, -12, -16, 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 5x5 matrix:\n[[-36, 19, -25, -1, 27],\n [-16, 3, -24, -17, 7],\n [19, -65, 37, -3, 30],\n [-16, 10, 13, 26, 26],\n [-47, 16, -44, -18, 33]]\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, -12, -5, -10, -25],\n [1, -8, 16, -20, 11],\n [47, 17, 12, -2, 9],\n [-27, 42, 8, 5, 32],\n [22, 43, 7, 8, 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 5x5 matrix:\n[[-30, 21, 7, -5, -27],\n [12, 13, -35, 8, 2],\n [0, 26, -42, 12, -12],\n [18, 21, -27, -33, 15],\n [0, -16, 36, -24, 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[[6, 5, 3, 1, -5],\n [36, 30, 18, 6, -30],\n [36, 30, 18, 6, -30],\n [0, 0, 0, 0, 0],\n [-6, -5, -3, -1, 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 5x5 matrix:\n[[-15, 0, -18, -12, -3],\n [10, 0, 12, 8, 2],\n [-25, 0, -30, -20, -5],\n [-10, 0, -12, -8, -2],\n [-20, 0, -24, -16, -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[[-5, 1, -4, -3, 2],\n [-12, 8, -12, -8, 12],\n [6, -4, 6, 4, -6],\n [13, 3, 8, 7, 2],\n [-34, 18, -32, -22, 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[[15, 3, 49, -20, -10],\n [-28, 32, 32, 34, -19],\n [-24, 36, 24, 54, -21],\n [10, -10, -12, -8, 6],\n [-55, 25, 25, 0, -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[[23, 16, -7, -19, 18],\n [-5, 32, -17, -23, -15],\n [-4, 34, -8, -24, -19],\n [-1, 27, -22, -21, -6],\n [4, 11, -59, -14, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-20, -16, 33, 10, -13],\n [6, -4, -33, 8, 27],\n [12, 8, -24, -4, 12],\n [0, 8, 21, -10, -21],\n [18, 12, -36, -6, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1, 36, -41, -30, 7],\n [30, 0, 30, -36, -6],\n [-8, -18, 13, 24, -2],\n [-33, -18, -12, 54, 3],\n [-22, 18, -43, 12, 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[[1, -15, 22, -3, -17],\n [-28, -5, -26, -26, 32],\n [-18, 29, -28, -6, 62],\n [-11, -20, -7, -12, -16],\n [11, 30, 17, 42, 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 5x5 matrix:\n[[35, 48, 3, 42, -4],\n [55, 26, -14, 26, -29],\n [33, 8, -37, 38, -4],\n [6, 18, -13, 40, 15],\n [-13, 26, -25, 23, 49]]\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 5x5 matrix:\n[[-10, 17, -22, 9, -11],\n [44, -15, -9, 11, -16],\n [-4, -1, 5, -3, 4],\n [38, -23, 10, 1, -3],\n [20, -21, 21, -7, 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[[27, 18, -45, 6, 15],\n [-15, -18, 21, 14, -13],\n [6, -12, -18, 36, -6],\n [-16, -28, 18, 34, -19],\n [-20, -20, 30, 10, -15]]?\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[[-33, -6, 12, 28, -21],\n [-9, -18, 21, 4, -3],\n [11, -10, 9, -12, 9],\n [27, -18, 15, -28, 21],\n [3, -42, 45, -12, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, -1, -27, 0, -18],\n [6, 6, -27, -9, -9],\n [-12, 12, 30, -14, 34],\n [4, -17, 3, 22, -20],\n [-12, -9, 51, 14, 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[[-4, 2, 2, 5, -1],\n [-8, 4, 4, 10, -2],\n [-24, 12, 12, 30, -6],\n [16, -8, -8, -20, 4],\n [20, -10, -10, -25, 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[[-2, 5, 14, 15, -17],\n [22, 25, -7, 18, -6],\n [12, -38, -12, -42, 38],\n [15, 22, -3, 18, -9],\n [-2, -12, 14, 0, -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 5x5 matrix:\n[[3, 13, -5, -35, -4],\n [27, 27, 15, -15, 24],\n [-15, -5, -15, -25, -20],\n [9, 21, -3, -45, 0],\n [-21, -10, -19, -25, -26]]\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[[6, 12, -10, 14, 10],\n [-37, 22, -5, 1, -31],\n [-33, -17, 20, -31, -34],\n [-29, 49, -5, 19, -14],\n [-58, 42, 6, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, -8, 12, 0, 24],\n [-8, 8, -12, 0, -24],\n [2, -2, 3, 0, 6],\n [-8, 8, -12, 0, -24],\n [2, -2, 3, 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 5x5 matrix:\n[[-16, -39, 23, 45, 14],\n [-12, 22, -2, -16, 14],\n [-8, 39, -10, -36, 17],\n [-17, -13, -10, 42, -7],\n [12, 37, 3, -62, 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[[24, 18, 12, -6, -6],\n [4, 3, 2, -1, -1],\n [-12, -9, -6, 3, 3],\n [4, 3, 2, -1, -1],\n [24, 18, 12, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[46, 22, -23, -15, -36],\n [-27, 25, 62, 47, 21],\n [53, 58, 8, -1, 1],\n [56, -6, -32, -28, 0],\n [16, 7, 2, -4, 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 5x5 matrix:\n[[0, 0, 0, 0, 0],\n [10, 8, -8, -4, 12],\n [10, 8, -8, -4, 12],\n [25, 20, -20, -10, 30],\n [15, 12, -12, -6, 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[[0, -12, 4, 12, 8],\n [0, 6, -2, -6, -4],\n [0, -18, 6, 18, 12],\n [0, 30, -10, -30, -20],\n [0, -24, 8, 24, 16]]?\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[[-33, 6, -27, -23, 19],\n [-41, 10, -38, -36, 20],\n [24, -12, 33, 39, -3],\n [7, -2, 7, 7, -3],\n [2, 8, -13, -23, -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[[-20, 9, 20, -34, 8],\n [16, -17, 36, 29, -23],\n [-4, -5, 32, -5, -9],\n [9, -14, 31, 18, -19],\n [24, 12, -48, 30, 18]]\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, 7, 0, -12, -28],\n [-12, 0, -14, -12, 14],\n [-6, 6, -2, -12, -22],\n [-11, 7, -7, -18, -21],\n [30, -12, 25, 42, 23]]\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 5x5 matrix:\n[[11, 67, -5, -16, 18],\n [-14, 19, -10, 11, 5],\n [28, -34, 38, -36, -16],\n [17, -29, -3, 14, 12],\n [-26, 21, 29, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 60, 22, 14, -16],\n [-12, -13, 5, -1, -12],\n [42, 37, -9, 29, -26],\n [-11, -5, 10, 4, -23],\n [-10, 3, 15, 9, -34]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[32, 2, 40, 26, -28],\n [-15, 16, -25, -11, 22],\n [18, -16, 28, 1, -28],\n [11, -24, 21, -21, -30],\n [3, -31, 13, -34, -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[[66, -27, 9, -21, -31],\n [-27, 29, -22, 0, 3],\n [1, 1, 1, -43, 27],\n [15, -22, 44, -6, -26],\n [3, 13, -23, -27, 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[[-21, 9, 20, 16, -17],\n [9, -18, 18, 0, -12],\n [-3, -18, 26, 1, -26],\n [-52, 26, -20, -13, -24],\n [23, -10, 38, 31, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, -6, 4, -6, 6],\n [-24, 12, -8, 12, -12],\n [-12, 6, -4, 6, -6],\n [12, -6, 4, -6, 6],\n [36, -18, 12, -18, 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[[9, 18, 9, 0, 12],\n [6, 12, 6, 0, 8],\n [-9, -18, -9, 0, -12],\n [6, 12, 6, 0, 8],\n [6, 12, 6, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -31, -3, -22, -35],\n [-4, 0, -38, 18, 34],\n [-26, 25, -2, 56, 67],\n [-28, 13, -23, 46, 60],\n [-12, 3, -22, 24, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, 18, -15, 18, 15],\n [12, 24, -20, 24, 20],\n [-15, -30, 25, -30, -25],\n [-15, -30, 25, -30, -25],\n [-6, -12, 10, -12, -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[[12, 3, -18, 9, 3],\n [-8, -2, 12, -6, -2],\n [-12, -3, 18, -9, -3],\n [24, 6, -36, 18, 6],\n [16, 4, -24, 12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[30, -34, 14, -22, -4],\n [-51, 37, -3, 40, 12],\n [-24, 0, 16, 21, 10],\n [-27, 5, 13, 23, 10],\n [18, 10, -22, -17, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[28, 28, -27, 2, 27],\n [6, 9, 46, 17, 3],\n [-13, 30, 24, 31, -2],\n [6, 7, -63, -15, 10],\n [19, 4, 16, 1, 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[[38, 0, -10, 46, 26],\n [30, -28, -30, 54, 8],\n [-37, -6, 5, -41, -28],\n [16, 18, 10, 8, 19],\n [30, 48, 30, 6, 42]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[14, -11, 6, -25, -13],\n [8, -4, 4, -24, -8],\n [-8, 24, 1, -61, 3],\n [2, -9, -1, 28, 0],\n [10, -9, 4, -13, -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[[-3, 33, -22, 12, 14],\n [-9, 34, -14, 23, 16],\n [-3, -7, 10, 4, -2],\n [-15, 40, -10, 35, 20],\n [-18, 33, 0, 39, 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[[-16, 20, 8, 12, -8],\n [-12, 27, 4, 1, 6],\n [24, -54, -8, -2, -12],\n [12, 15, -11, -29, 36],\n [-20, -11, 16, 39, -46]]\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, 15, 49, 32, 12],\n [34, -17, -39, -24, -12],\n [48, -26, -56, -34, -18],\n [-10, -13, 3, 6, -6],\n [-4, 22, 14, 4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[38, 14, 6, -76, 10],\n [-12, -31, 21, 45, -4],\n [-26, 5, -9, -23, -12],\n [34, 10, 19, 17, 46],\n [-4, 17, -14, -42, -6]]\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 5x5 matrix:\n[[42, -54, 9, 3, -14],\n [-6, 18, 9, -21, 26],\n [40, -50, 10, 0, -10],\n [-18, 24, -3, -3, 8],\n [-6, 6, -3, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-17, 23, 55, 7, -8],\n [18, -42, -36, -6, -48],\n [-6, 20, 26, 6, 17],\n [16, -14, 32, 22, -48],\n [-10, -13, -61, -25, 18]]\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, 12, 30, 18, 6],\n [-3, -2, -5, -3, -1],\n [18, 12, 30, 18, 6],\n [-18, -12, -30, -18, -6],\n [12, 8, 20, 12, 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[[-9, -6, 6, 9, -9],\n [-3, -2, 2, 3, -3],\n [-12, -8, 8, 12, -12],\n [-12, -8, 8, 12, -12],\n [9, 6, -6, -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[[-20, 24, -16, 20, 12],\n [0, 0, 0, 0, 0],\n [-30, 36, -24, 30, 18],\n [-30, 36, -24, 30, 18],\n [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[[6, -3, -2, 4, 3],\n [-36, 18, 12, -24, -18],\n [6, -3, -2, 4, 3],\n [-12, 6, 4, -8, -6],\n [-18, 9, 6, -12, -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[[-21, -23, 15, 40, 13],\n [-3, -31, 35, 34, 29],\n [5, 8, -3, -10, -1],\n [2, 39, -32, -38, -12],\n [-14, -27, -25, 5, -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[[5, 0, -5, -4, 4],\n [-10, 0, 10, 8, -8],\n [-15, 0, 15, 12, -12],\n [-10, 0, 10, 8, -8],\n [15, 0, -15, -12, 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[[-25, 8, 19, 0, 22],\n [12, 10, 6, 10, 2],\n [-38, -34, -10, -41, -11],\n [23, 8, 7, 6, -8],\n [-32, -20, -10, -21, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 6, -10, 8, 12],\n [9, -9, 15, -12, -18],\n [15, -15, 25, -20, -30],\n [9, -9, 15, -12, -18],\n [-6, 6, -10, 8, 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[[6, -15, 34, -9, -34],\n [2, -44, -5, 26, 12],\n [-27, 20, -29, -7, 13],\n [6, -21, -22, 27, 46],\n [-36, 46, 2, -42, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, -9, -9, 0, -15],\n [-8, 12, 12, 0, 20],\n [-8, 12, 12, 0, 20],\n [10, -15, -15, 0, -25],\n [4, -6, -6, 0, -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[[-10, 15, -25, 15, 20],\n [6, -9, 15, -9, -12],\n [-12, 18, -30, 18, 24],\n [2, -3, 5, -3, -4],\n [6, -9, 15, -9, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[23, -14, -30, 48, 18],\n [-24, 9, -36, 6, -30],\n [7, -1, 30, -18, 12],\n [-23, 11, -6, -18, -24],\n [32, -17, -12, 42, 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[[-3, 12, -9, -9, 15],\n [-4, 16, -12, -12, 20],\n [-1, 4, -3, -3, 5],\n [3, -12, 9, 9, -15],\n [-2, 8, -6, -6, 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, -13, 6, -2, -9],\n [-20, 14, -31, 36, -14],\n [-20, 6, -34, 44, -26],\n [-16, 32, -17, 8, 20],\n [-10, 27, -8, -2, 23]]?\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 5x5 matrix:\n[[-12, -2, -2, -12, -2],\n [-36, -6, -6, -36, -6],\n [-24, -4, -4, -24, -4],\n [36, 6, 6, 36, 6],\n [36, 6, 6, 36, 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 5x5 matrix:\n[[-20, -30, -30, -15, 0],\n [-4, -6, -6, -3, 0],\n [24, 36, 36, 18, 0],\n [-4, -6, -6, -3, 0],\n [-24, -36, -36, -18, 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[[-12, 38, -26, -20, 6],\n [-9, -52, -8, -6, -18],\n [6, -27, 2, -6, -48],\n [9, 16, 16, 14, 18],\n [-15, 8, -2, 14, 84]]\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, -12, -30, 0, 18],\n [9, -13, -15, 1, 25],\n [16, -19, -10, -8, 21],\n [1, 1, 60, -53, 46],\n [10, -11, -39, 24, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[16, -49, -8, 3, -9],\n [-12, 24, 32, -26, 46],\n [-19, 6, 22, -27, -30],\n [67, -32, -26, 49, 8],\n [-17, 20, -6, 1, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[24, -6, 6, 18, -36],\n [-4, 1, -1, -3, 6],\n [4, -1, 1, 3, -6],\n [-24, 6, -6, -18, 36],\n [8, -2, 2, 6, -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[[-34, -39, 27, 30, -21],\n [38, 10, 2, -53, 26],\n [-2, 43, -53, 1, 27],\n [-2, -18, 6, -33, 30],\n [20, -25, 41, -19, -15]]\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[[12, 20, 24, -9, -22],\n [-12, 39, 14, 15, -18],\n [-9, -16, -18, 18, 8],\n [3, -2, 2, 6, -8],\n [-3, 2, -2, -6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-80, 35, -49, 23, 49],\n [36, -13, 23, -7, 15],\n [-36, 52, -34, -8, 42],\n [29, 59, 6, 36, -20],\n [-1, 53, -15, -5, 12]]\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, 41, -48, -13, 22],\n [-6, -14, 27, 4, -17],\n [-24, -8, 36, -6, -26],\n [5, -27, 32, -45, -66],\n [62, 22, -33, -20, -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 5x5 matrix:\n[[34, 12, -24, 6, 19],\n [40, 15, -28, 7, 23],\n [-10, -12, 0, -6, -15],\n [40, 3, -30, 9, 15],\n [34, -3, -34, 1, 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[[-8, 24, 8, 20, 16],\n [-8, 24, 8, 20, 16],\n [2, -6, -2, -5, -4],\n [-6, 18, 6, 15, 12],\n [2, -6, -2, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-7, 2, 7, 6, -2],\n [-8, 2, 11, 7, -4],\n [-12, 6, -15, 9, 12],\n [-22, 10, -17, 17, 16],\n [1, -2, 17, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-30, -15, 16, -20, -38],\n [7, 13, -29, -23, 24],\n [29, 19, -21, 43, 20],\n [-17, -12, 17, -9, -22],\n [9, -5, 13, -9, 24]]\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[[-65, 12, 28, 13, 11],\n [40, -19, -17, -27, -9],\n [30, -12, -18, -6, -23],\n [13, -20, -26, -13, 44],\n [-38, 2, 24, -8, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, 12, -12, 45, -33],\n [36, 37, 26, 23, 8],\n [-41, -15, -34, -32, -3],\n [8, 13, -6, 43, -28],\n [-23, -36, -20, 7, -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[[2, 18, -13, -12, -15],\n [21, -32, 7, 1, 5],\n [-34, 16, -11, 1, -3],\n [-61, 74, -9, -19, 9],\n [-8, 6, 24, 35, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, -27, -44, -30, 0],\n [12, 6, 0, 28, 32],\n [12, 30, 34, 36, 4],\n [-16, -6, -28, -12, -8],\n [7, 21, 25, 22, -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[[-5, 12, 25, -21, 26],\n [-16, 11, 11, 0, -27],\n [21, -29, -9, 12, -17],\n [-22, 48, 44, -12, -12],\n [44, -7, -4, 9, 39]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -31, 36, -22, 39],\n [37, -37, -1, -28, -7],\n [8, -13, 0, -13, 21],\n [26, 27, -47, 79, -32],\n [-1, -4, 3, -11, 6]]\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, -8, -20, 24, 12],\n [36, 12, 30, -36, -18],\n [12, 4, 10, -12, -6],\n [18, 6, 15, -18, -9],\n [-30, -10, -25, 30, 15]]?\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, 5, 25, 15, 25],\n [16, -17, 8, -15, 2],\n [-11, -7, 27, 3, 23],\n [-23, 23, -9, 21, -1],\n [12, 16, -44, 0, -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[[20, 20, 8, -8, 0],\n [25, 25, 10, -10, 0],\n [10, 10, 4, -4, 0],\n [-30, -30, -12, 12, 0],\n [-15, -15, -6, 6, 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 5x5 matrix:\n[[56, -16, -6, 30, 58],\n [1, 25, -26, -7, -28],\n [-3, -3, 3, -3, -33],\n [21, 5, -14, 7, -4],\n [3, 3, -5, -1, -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[[15, 34, -24, -26, 40],\n [1, 5, -10, 15, -5],\n [21, 25, -32, -26, 15],\n [-9, -3, 18, -3, 15],\n [-1, 8, 10, -23, 30]]?\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[[-8, 33, -6, 8, 35],\n [-22, 55, 16, 9, 28],\n [6, 15, 15, -27, -15],\n [16, -53, -22, 8, -35],\n [9, -37, -56, 48, -32]]\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, -4, 12, 10, -20],\n [18, -16, 7, -42, -12],\n [-6, -18, -42, -4, -11],\n [18, 4, 8, 19, -7],\n [24, 14, 37, 16, -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[[10, -1, 0, -5, -26],\n [0, 33, -12, -33, -57],\n [-18, -4, 18, 11, 43],\n [4, -33, 6, 32, 51],\n [24, 30, -72, -30, -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[[27, 17, -7, 3, 11],\n [11, 3, -5, 7, 8],\n [-33, -23, 3, -17, -19],\n [36, -4, -30, 20, 28],\n [15, -23, -39, -17, 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[[0, -12, 6, -12, 6],\n [0, -10, 5, -10, 5],\n [0, 4, -2, 4, -2],\n [0, 10, -5, 10, -5],\n [0, -2, 1, -2, 1]]\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[[10, 0, 11, -1, -9],\n [-40, 25, -27, 27, 8],\n [-48, 35, -29, 37, 4],\n [-46, 15, -26, 36, 15],\n [-32, 20, -27, 15, 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[[-25, 15, 10, 5, 30],\n [-25, 15, 10, 5, 30],\n [30, -18, -12, -6, -36],\n [15, -9, -6, -3, -18],\n [-20, 12, 8, 4, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, -12, 0, 0, 9],\n [-6, 8, 0, 0, -6],\n [-6, 8, 0, 0, -6],\n [12, -16, 0, 0, 12],\n [-15, 20, 0, 0, -15]]?\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, -15, 22, -18, -10],\n [-1, 2, 16, 14, -5],\n [-18, -11, 22, 38, -20],\n [-7, 31, 0, 28, 25],\n [8, -12, -10, -8, -10]]\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 5x5 matrix:\n[[-20, -15, -24, 4, -11],\n [48, 9, 3, -9, 5],\n [11, -46, 17, 16, 55],\n [-20, 10, -28, -44, -74],\n [-2, 2, -16, 39, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-19, -1, 9, 5, -10],\n [34, 21, -12, 22, 25],\n [-35, 1, 33, -11, 4],\n [-11, -12, 5, -19, -7],\n [0, -1, -14, 20, -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[[26, -42, -14, -22, 12],\n [-5, 9, -1, 1, 0],\n [21, -31, -23, -28, 17],\n [33, -51, -27, -36, 21],\n [1, -1, -3, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-28, -28, 14, -38, -30],\n [22, -33, 21, -17, 25],\n [48, -17, -5, -9, 19],\n [29, 37, -52, -7, -59],\n [7, -25, 13, 0, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -6, -36, -18, 0],\n [0, -1, -6, -3, 0],\n [0, 1, 6, 3, 0],\n [0, 3, 18, 9, 0],\n [0, 4, 24, 12, 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[[14, 29, -16, -40, -33],\n [2, -4, 8, 19, 3],\n [-17, -35, 18, 54, 39],\n [-2, -2, 4, -24, 6],\n [-9, 3, -18, -35, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[4, 20, 16, -32, -4],\n [5, 21, 20, -16, 11],\n [0, 1, 0, -6, -4],\n [4, 12, 16, 16, 28],\n [4, 12, 16, 16, 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[[44, 8, -26, -2, 4],\n [24, -1, -8, 6, 0],\n [10, -43, 49, 23, -34],\n [30, 12, -25, -13, 4],\n [-14, 2, 1, 17, 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[[6, 0, -1, -4, -12],\n [-12, 4, 6, -12, 0],\n [12, 1, -1, -13, -30],\n [-24, 12, 16, -44, -24],\n [-18, 0, 3, 12, 36]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[8, -2, -24, -35, -11],\n [55, 36, -9, 30, -18],\n [11, -6, -45, -3, -15],\n [-8, -1, 20, 22, 8],\n [34, 31, -8, 26, -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 5x5 matrix:\n[[-24, 31, -26, 2, -9],\n [-18, 9, -9, 24, 4],\n [36, 41, 26, 4, 29],\n [54, 8, 30, -10, 10],\n [6, 19, -3, -17, -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[[39, 2, -37, -10, 3],\n [1, 2, 9, -35, -27],\n [42, -15, -38, -21, -25],\n [31, -4, -36, 14, 15],\n [6, -4, -9, 8, 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[[35, -5, 5, -10, 25],\n [2, 0, 8, -6, 6],\n [5, 0, 20, -15, 15],\n [-2, 1, 19, -13, 10],\n [34, -5, 1, -7, 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[[23, 9, -2, -47, -33],\n [-21, -15, -32, 44, 33],\n [-8, -3, 17, 27, 10],\n [6, 18, 20, -54, -10],\n [2, 3, 35, 12, -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 5x5 matrix:\n[[-10, -10, 5, 10, 25],\n [-14, -12, 27, 6, -5],\n [-27, 0, 14, 3, -7],\n [-4, 9, -22, 0, 16],\n [-9, -3, 26, -3, -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 5x5 matrix:\n[[6, -4, -2, 12, 4],\n [3, -2, -1, 6, 2],\n [-12, 8, 4, -24, -8],\n [0, 0, 0, 0, 0],\n [6, -4, -2, 12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-9, -3, 3, 9, 6],\n [-3, -1, 1, 3, 2],\n [-18, -6, 6, 18, 12],\n [0, 0, 0, 0, 0],\n [18, 6, -6, -18, -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[[-3, 1, 1, 5, 2],\n [-15, 5, 5, 25, 10],\n [10, 4, -12, -6, 8],\n [-39, -9, 39, 33, -18],\n [17, 9, -23, -7, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-20, 26, 48, -29, 24],\n [-52, -27, -3, 30, 42],\n [40, -8, 0, 15, -12],\n [24, -20, -27, 34, -30],\n [28, -21, -35, 13, -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[[3, 12, -3, 3, 15],\n [6, 24, -6, 6, 30],\n [3, 12, -3, 3, 15],\n [-5, -20, 5, -5, -25],\n [-5, -20, 5, -5, -25]]\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, 21, -6, -8, 10],\n [30, 15, -30, 10, -5],\n [54, 48, -24, -12, 18],\n [-12, 1, 22, -14, 11],\n [30, 29, -10, -10, 13]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, 43, -12, 16, -22],\n [-4, 16, 12, 46, -26],\n [-13, -39, 14, 21, 22],\n [22, 30, -30, -23, -15],\n [-21, 19, 6, 69, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[14, -5, -21, 22, -23],\n [13, -10, -17, 24, -21],\n [14, 10, -28, 12, -24],\n [6, 0, -10, 8, -10],\n [4, -10, -2, 12, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-20, -5, -20, -10, -25],\n [-14, -5, -6, 4, -15],\n [-21, -6, -17, -5, -25],\n [30, 15, -10, -40, 25],\n [24, 9, 8, -10, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, -13, -9, 12, 0],\n [9, -36, 12, 30, 6],\n [3, 30, -16, -25, -17],\n [16, -1, 45, -3, 9],\n [13, 4, 0, -4, -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 5x5 matrix:\n[[-3, 14, 2, 24, 54],\n [-11, 10, -26, 22, 5],\n [33, 25, 1, 7, -23],\n [-14, 6, -6, 30, 46],\n [-12, -7, -1, -5, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0, 0],\n [8, 16, -24, -8, -8],\n [6, 12, -18, -6, -6],\n [-2, -4, 6, 2, 2],\n [4, 8, -12, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[30, 35, 20, -20, 50],\n [12, 14, 8, -8, 20],\n [2, -17, 12, -8, -6],\n [14, -32, 36, -26, 0],\n [21, -19, 38, -29, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, -12, -12, -9, 18],\n [2, -4, -4, -3, 6],\n [-4, 8, 8, 6, -12],\n [4, -8, -8, -6, 12],\n [-6, 12, 12, 9, -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[[2, -6, -8, -18, -28],\n [9, 17, 8, 15, -11],\n [12, 28, 9, 17, -16],\n [5, 37, -6, -11, -17],\n [-19, 5, -15, -24, 45]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-18, -18, 9, 12, 6],\n [-6, -6, 3, 4, 2],\n [30, 30, -15, -20, -10],\n [36, 36, -18, -24, -12],\n [-6, -6, 3, 4, 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[[18, -36, 6, -6, -12],\n [-3, 6, -1, 1, 2],\n [-3, 6, -1, 1, 2],\n [0, 0, 0, 0, 0],\n [-6, 12, -2, 2, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-28, -39, -6, -36, 40],\n [-42, -27, -2, 12, 34],\n [13, 1, 7, -6, -27],\n [-20, -18, -8, -6, 32],\n [8, 13, 28, -33, -34]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[28, -21, 2, -8, -15],\n [0, 0, 0, 0, 0],\n [40, -27, 10, -8, -25],\n [7, -21, -37, -20, 15],\n [-2, -6, -18, -8, 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[[0, 0, 0, 0, 0],\n [8, -8, 24, 12, -20],\n [-8, 8, -24, -12, 20],\n [-4, 4, -12, -6, 10],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-17, -3, 16, 2, -20],\n [0, 18, 24, 18, -6],\n [-30, -39, 37, -36, 29],\n [-4, -12, 18, -14, 28],\n [-9, -15, 15, -15, 18]]\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 5x5 matrix:\n[[-8, -8, -1, -3, -9],\n [-39, 26, 13, 49, 26],\n [-24, 9, 18, 13, 46],\n [61, 19, -13, -70, -12],\n [-15, -39, -6, -15, -33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -2, -24, 14, -13],\n [-36, 16, 14, -6, 43],\n [-22, 10, 14, -6, 29],\n [-7, 3, 0, 0, 7],\n [32, -4, -30, -2, -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[[1, -7, 8, -12, 15],\n [-35, -13, 44, 24, -3],\n [4, 11, -4, 6, -21],\n [45, 22, -56, -26, -8],\n [-27, -1, -12, 48, -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[[20, 1, 26, 7, 16],\n [-5, -6, 5, 4, 19],\n [30, 5, 32, 7, 10],\n [-25, -6, -23, -4, -1],\n [0, -1, 2, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-25, 25, 67, -9, -15],\n [-20, 4, 15, -10, 3],\n [-40, -3, -11, 7, 33],\n [15, -13, -24, -17, -6],\n [15, 14, 40, -10, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-72, 33, 21, -3, -15],\n [66, -28, -35, 14, 25],\n [18, 9, -18, 33, 24],\n [-24, -1, 1, -16, -10],\n [-12, -11, -7, -20, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-24, 2, -20, 7, -10],\n [2, 14, 0, -16, 10],\n [14, -4, 12, -1, 4],\n [16, -24, 16, 20, -8],\n [-26, -12, -20, 23, -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[[12, -1, -23, 13, 3],\n [-42, 10, 9, -26, -30],\n [-36, 8, 14, -24, -24],\n [6, -2, 5, 2, 6],\n [-24, 8, -20, -8, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, -27, 72, -16, -51],\n [-5, 33, -72, 20, 44],\n [43, -27, 21, 22, 30],\n [-31, 47, -75, -8, 21],\n [36, -54, 78, 46, -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[[3, -9, -18, -18, 33],\n [6, -29, -14, 19, 11],\n [5, -25, -10, 20, 5],\n [-3, 14, 8, -7, -8],\n [1, -7, 2, 14, -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[[-6, -1, 27, -13, 5],\n [3, 0, -17, 7, -2],\n [0, -2, -14, 2, 2],\n [-9, -12, -33, -9, 18],\n [-9, -8, -5, -13, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, -14, 14, 36, -21],\n [-6, 0, 6, 0, -11],\n [12, -6, -24, -18, 34],\n [-22, -14, 4, -23, -10],\n [-28, -10, 36, 22, -19]]\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, -21, 12, 19, 1],\n [2, -10, 6, 8, 0],\n [-18, -12, 9, 3, -3],\n [-18, -12, 9, 3, -3],\n [22, 26, -18, -12, 4]]\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[[-33, -60, 18, -45, -39],\n [-60, -6, -24, -60, -66],\n [17, 26, -34, 14, 16],\n [12, -33, 48, 12, 15],\n [35, -24, 42, 33, 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[[1, 9, -42, -17, -60],\n [20, -24, 0, -15, -15],\n [-30, -6, 48, 25, -5],\n [-18, -27, -17, -10, 35],\n [-25, 6, 9, 10, -50]]?\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 5x5 matrix:\n[[10, 0, -15, -6, -3],\n [22, 30, 21, -18, 21],\n [1, 5, 6, -2, 4],\n [3, 20, 34, -4, 18],\n [0, -20, -29, 6, -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[[8, -8, 23, 20, -11],\n [27, -21, 18, 12, 27],\n [19, -19, 2, 6, 43],\n [-17, 12, -37, -26, -22],\n [39, -40, 17, 24, 12]]?\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 5x5 matrix:\n[[30, 30, -25, 15, -10],\n [-12, -12, 10, -6, 4],\n [-6, -6, 5, -3, 2],\n [-24, -24, 20, -12, 8],\n [-36, -36, 30, -18, 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[[0, 0, 0, 0, 0],\n [-20, 24, 12, 12, -4],\n [-15, 18, 9, 9, -3],\n [-15, 18, 9, 9, -3],\n [20, -24, -12, -12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-5, -24, -2, -8, 3],\n [30, 14, 12, -4, -31],\n [-55, 6, -22, 20, 60],\n [15, -38, 6, -20, -20],\n [-20, 34, -8, 20, 25]]?\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[[-19, -31, 0, -7, -63],\n [5, -39, 8, 17, -59],\n [10, 27, 0, 0, 56],\n [11, -7, 12, 11, 21],\n [-4, 33, -8, -14, 46]]\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[[-26, -16, 26, -10, -33],\n [-18, 13, -22, 17, -15],\n [33, 28, 14, -26, 23],\n [-6, -18, 2, 8, -19],\n [-26, 17, 30, -27, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-15, 18, -14, 38, -24],\n [12, -35, -37, -36, -20],\n [37, 15, 14, 47, 11],\n [-55, 28, -18, 28, -38],\n [48, -18, -9, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[16, -24, 12, -12, -16],\n [24, -36, 18, -18, -24],\n [0, 0, 0, 0, 0],\n [4, -6, 3, -3, -4],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-19, -1, 4, 37, 15],\n [-20, -3, 1, 31, 15],\n [-14, -30, -12, -42, -6],\n [11, 25, -12, 3, 9],\n [-14, -41, -1, -43, -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[[0, -5, -5, 5, -6],\n [0, -20, -20, 20, -24],\n [0, 20, 20, -20, 24],\n [0, -30, -30, 30, -36],\n [0, 15, 15, -15, 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[[-8, 22, -5, 21, -27],\n [6, -12, 0, -8, 12],\n [-13, 20, 5, 7, -15],\n [17, -4, -25, 29, -21],\n [2, -28, 20, -44, 48]]\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[[-66, -6, 21, -43, 45],\n [12, 3, -21, 4, -12],\n [6, -1, 12, 7, -1],\n [6, 2, -15, 1, -7],\n [12, -1, 15, 12, -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[[-25, -15, -25, 5, -20],\n [3, 1, -3, -11, 6],\n [10, 4, -5, -28, 17],\n [39, 21, 21, -39, 42],\n [-3, -1, 3, 11, -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 5x5 matrix:\n[[-30, 45, -18, 21, -12],\n [21, 21, -3, 6, 3],\n [0, -15, 0, -9, -18],\n [-18, 57, -16, 27, 6],\n [19, 19, 1, 8, 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 5x5 matrix:\n[[18, -24, -30, -30, -24],\n [9, -12, -15, -15, -12],\n [6, -8, -10, -10, -8],\n [0, 0, 0, 0, 0],\n [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[[2, -15, -10, 18, 7],\n [11, -4, -16, 22, -17],\n [-19, 18, 18, -40, 21],\n [6, 11, -14, 6, -19],\n [-3, 1, 42, -28, 6]]\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, 20, 12, -4],\n [-6, -6, 18, 10, -1],\n [6, 6, 12, 8, -5],\n [-6, -6, 28, 16, -3],\n [30, 30, -15, -5, -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 5x5 matrix:\n[[-38, -21, 11, 58, 58],\n [-10, -10, -17, 2, 3],\n [86, 70, 34, -50, -30],\n [56, 43, 10, -42, -29],\n [13, 29, 35, 30, 43]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-38, 30, 34, 6, 18],\n [-5, 5, 5, 1, 1],\n [-16, 20, 18, 4, -2],\n [-40, 20, 30, 4, 34],\n [23, -15, -19, -3, -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, 48, 36, 0, -15],\n [-16, -15, 27, -18, 40],\n [17, 24, 9, 6, -20],\n [-6, -7, -3, -6, 16],\n [-38, -61, -39, 2, 13]]\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, 29, -25, -25, 4],\n [35, 13, -37, -27, 27],\n [25, 53, -33, -41, 14],\n [-16, 26, -12, -14, -5],\n [40, 32, -40, -40, 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[[31, -23, -36, -10, 30],\n [30, 26, -11, 14, -7],\n [29, -3, 1, 27, 47],\n [-52, -15, 43, 11, 37],\n [40, 18, -39, -12, -35]]\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, 2, -34, -4, -34],\n [-13, 20, 5, -12, 2],\n [-23, 13, -26, -3, -54],\n [24, -36, -18, 18, -2],\n [11, -22, -1, 18, -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[[-5, 25, -5, 0, -10],\n [6, -30, 6, 0, 12],\n [-3, 15, -3, 0, -6],\n [-5, 25, -5, 0, -10],\n [5, -25, 5, 0, 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 5x5 matrix:\n[[59, -19, 5, 21, -14],\n [55, 5, 31, -18, 34],\n [7, 13, -5, -8, 2],\n [23, -33, 11, 26, -12],\n [-60, 0, -6, -3, 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[[0, 0, 0, 0, 0],\n [0, 1, 2, -3, -1],\n [0, -3, -6, 9, 3],\n [0, 4, 8, -12, -4],\n [0, 6, 12, -18, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-5, 0, 0, 0, -8],\n [-45, -28, -28, 28, 26],\n [10, 14, 14, -14, -33],\n [-15, -8, -8, 8, 4],\n [40, 28, 28, -28, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 36, 6, 36, 12],\n [5, -30, -5, -30, -10],\n [-3, 18, 3, 18, 6],\n [1, -6, -1, -6, -2],\n [-2, 12, 2, 12, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, 6, 6, 18, 18],\n [2, -4, -4, -12, -12],\n [2, -4, -4, -12, -12],\n [3, -6, -6, -18, -18],\n [2, -4, -4, -12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-24, 36, 12, 30, 18],\n [24, -36, -12, -30, -18],\n [-24, 36, 12, 30, 18],\n [-12, 18, 6, 15, 9],\n [-20, 30, 10, 25, 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[[-45, -4, 12, 22, 0],\n [30, 23, -26, -6, 23],\n [-3, 43, -36, 20, 45],\n [62, 2, -5, -35, -18],\n [22, -57, 29, -32, -32]]\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[[-7, -12, 17, -3, 21],\n [-10, 0, 14, 6, 6],\n [-12, -27, 33, -9, 45],\n [-10, 15, 5, 15, -15],\n [13, -12, -11, -15, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, -3, 3, 1, -6],\n [-1, 3, -3, -1, 6],\n [3, -9, 9, 3, -18],\n [-4, 12, -12, -4, 24],\n [0, 0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[15, 9, 6, -6, -3],\n [-20, -12, -8, 8, 4],\n [4, 12, 20, 8, -28],\n [-21, -15, -13, 6, 11],\n [-18, -6, 2, 12, -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 5x5 matrix:\n[[-14, -2, 2, 12, -2],\n [30, -6, -10, -32, 10],\n [-34, -46, -18, 4, 18],\n [11, -19, -13, -22, 13],\n [12, -24, -16, -26, 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 5x5 matrix:\n[[3, -19, -23, -9, -16],\n [0, 5, 25, 0, 5],\n [3, -9, 27, -9, -6],\n [4, -18, 6, -12, -14],\n [-5, 21, -15, 15, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[28, 8, -8, 4, 16],\n [-9, -3, -4, -10, -6],\n [79, 26, -18, 18, 46],\n [-57, -18, 6, -22, -34],\n [10, -16, -36, -46, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[38, 26, 5, 29, 28],\n [-24, 5, -25, -24, -27],\n [24, 50, -10, 8, 2],\n [-11, -29, 25, -3, 1],\n [20, -2, 10, 20, 22]]\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, -7, -4, -13, -19],\n [14, -7, -20, -23, -11],\n [-2, -4, 0, -6, -12],\n [2, 4, 0, 6, 12],\n [-7, -7, 4, -8, -23]]\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 5x5 matrix:\n[[10, 0, -8, -2, 6],\n [20, 0, -16, -4, 12],\n [-25, 0, 20, 5, -15],\n [-25, 0, 20, 5, -15],\n [15, 0, -12, -3, 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[[39, 12, -5, 27, 27],\n [-54, 0, -6, -42, -36],\n [21, 84, -59, 9, 35],\n [9, -36, 45, -24, 29],\n [12, -60, 46, 18, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[6, -18, -5, -4, -4],\n [-31, -4, 37, 1, 48],\n [0, -18, -27, -24, -24],\n [0, 0, 20, 14, 20],\n [-42, 6, 35, -6, 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[[-11, -4, 41, -47, -41],\n [7, -62, -22, 0, 29],\n [-2, 32, -4, 16, 14],\n [4, -27, 7, -19, 26],\n [-7, -52, -7, -15, 31]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, 49, -37, -9, -46],\n [15, -13, 32, 29, -2],\n [35, 14, 37, 36, -26],\n [5, 10, -14, 9, -21],\n [16, -16, -14, 11, -1]]?\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, -48, 36, 18, 7],\n [0, 43, -30, -3, -14],\n [-28, 20, -28, 24, -23],\n [-15, -31, 18, 30, -7],\n [38, 34, 12, 24, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[24, 4, -24, 4, -24],\n [-12, 1, 24, -7, 10],\n [24, 4, -24, 4, -24],\n [-27, -12, -3, 8, 32],\n [-12, -5, 0, 3, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-15, 15, 35, -10, 40],\n [6, -24, -8, 28, 20],\n [-6, -3, 17, 8, 34],\n [3, -21, -1, 26, 28],\n [-3, -6, 10, 10, 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 5x5 matrix:\n[[-2, -12, -11, 18, -13],\n [-1, -16, -8, 24, -14],\n [-5, -4, -21, 6, -13],\n [-6, -20, -29, 30, -27],\n [-8, -20, -37, 30, -31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, -36, -33, -9, 48],\n [2, -15, -1, 3, 35],\n [2, -13, -2, 2, 29],\n [8, -10, -29, -13, -10],\n [-12, 42, 30, 6, -66]]\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, 25, -30, 30, 15],\n [4, 10, -12, 12, 6],\n [10, 25, -30, 30, 15],\n [2, 5, -6, 6, 3],\n [10, 25, -30, 30, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[10, -16, 2, -32, -8],\n [-15, -16, -31, -29, 21],\n [-21, -20, -62, -43, 39],\n [-3, -8, -47, -28, 24],\n [34, 24, 44, 36, -36]]\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[[-17, -7, -36, 31, -22],\n [-8, 4, -6, 31, -14],\n [3, 5, 12, 3, 2],\n [-4, -8, -18, -7, -2],\n [-6, -6, -18, 3, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-9, 6, -18, 3, -9],\n [12, -8, 24, -4, 12],\n [3, -2, 6, -1, 3],\n [6, -4, 12, -2, 6],\n [6, -4, 12, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, 4, 11, -4, 14],\n [-66, 24, -30, 48, -36],\n [32, -8, 18, -22, 22],\n [4, 4, 7, -1, 9],\n [-41, 24, -10, 33, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 0, -24, 36, -12],\n [-4, 0, -8, 12, -4],\n [-16, 4, -12, 26, -4],\n [-10, 6, 10, -3, 8],\n [-4, -2, -18, 23, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, 4, 5, 6, 3],\n [-3, -12, -15, -18, -9],\n [13, 22, 20, 12, 18],\n [-10, 10, 25, 50, 5],\n [-1, -14, -20, -28, -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[[-9, 24, 7, -24, 2],\n [6, -30, -12, 27, -6],\n [13, -44, -15, 42, -6],\n [-37, -4, -25, -18, -26],\n [-3, 36, 17, -30, 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[[0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [-4, 4, -2, 1, -2],\n [12, -12, 6, -3, 6],\n [-8, 8, -4, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[21, 19, -9, 15, -14],\n [-6, 6, 30, 6, -36],\n [-41, -29, 37, -22, -1],\n [12, 18, 12, 15, -33],\n [4, 6, 4, 5, -11]]\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, 6, -36, -24, -18],\n [2, -20, 29, -32, 8],\n [-16, -2, -1, -27, -7],\n [-2, 27, -16, 60, -1],\n [4, 5, 25, 36, 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 5x5 matrix:\n[[14, 16, -6, -17, 9],\n [29, 26, -3, 25, -30],\n [-44, 8, 24, 11, -45],\n [-44, -2, 16, 21, -39],\n [79, 16, -28, 0, 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 5x5 matrix:\n[[10, -30, -20, -5, 0],\n [5, 55, 20, 10, 5],\n [9, 15, 0, 3, 3],\n [2, -6, -4, -1, 0],\n [25, -5, -20, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-34, -1, 59, -15, 57],\n [-16, 3, -22, 9, 1],\n [20, 7, -59, 21, -37],\n [-18, -24, 56, -4, 26],\n [-42, 10, -7, 10, 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 5x5 matrix:\n[[0, -16, -13, 32, -10],\n [-25, -29, -16, 18, 1],\n [25, 21, -22, -2, 15],\n [-20, -14, 21, -4, -11],\n [20, 18, 43, -4, -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 5x5 matrix:\n[[15, 16, -4, -26, 2],\n [10, 36, -8, -38, 10],\n [-30, 6, 0, 21, 9],\n [23, -16, -6, -11, -1],\n [9, 2, 4, -7, -7]]\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, 1, 19, -14, -11],\n [-4, -6, -10, 12, 1],\n [22, 19, 21, 7, -4],\n [-18, -26, -20, 16, -7],\n [-5, -11, 5, -12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, 30, -36, 30, 30],\n [0, 0, 0, 0, 0],\n [2, -5, 6, -5, -5],\n [-2, 5, -6, 5, 5],\n [2, -5, 6, -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[[-12, 0, 6, 36, -6],\n [-12, 0, 6, 36, -6],\n [6, 0, -3, -18, 3],\n [-6, 0, 3, 18, -3],\n [-12, 0, 6, 36, -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[[24, -30, 30, -24, -54],\n [-12, 0, -6, 12, 18],\n [10, 5, 2, -10, -12],\n [-30, 15, -24, 30, 54],\n [-10, 15, -14, 10, 24]]\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, 0, 12, 12, -12],\n [2, 0, 6, 6, -6],\n [-6, 0, -18, -18, 18],\n [2, 0, 6, 6, -6],\n [2, 0, 6, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-36, 12, -6, -60, -6],\n [-26, 12, -1, -35, 4],\n [-2, -4, -5, -15, -12],\n [30, -10, 5, 50, 5],\n [4, -6, -4, -5, -11]]?\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, 24, -36, -12],\n [0, 0, 0, 0, 0],\n [-16, -16, 16, -24, -8],\n [8, 8, -8, 12, 4],\n [20, 20, -20, 30, 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[[0, 0, 0, 0, 0],\n [6, 0, -1, 4, 0],\n [-18, 0, 3, -12, 0],\n [36, 0, -6, 24, 0],\n [36, 0, -6, 24, 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[[6, -6, -3, -5, 0],\n [-24, 24, 12, 20, 0],\n [-12, 12, 6, 10, 0],\n [6, -6, -3, -5, 0],\n [-24, 24, 12, 20, 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[[-5, -10, -15, 5, 0],\n [6, 12, 18, -6, 0],\n [-6, -12, -18, 6, 0],\n [2, 4, 6, -2, 0],\n [-3, -6, -9, 3, 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[[-59, 10, 8, -12, 47],\n [-34, 8, -15, 22, 6],\n [26, -10, 26, -48, 11],\n [46, 19, -11, 0, -32],\n [-11, -12, 2, -20, 6]]?\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[[32, -42, -8, 13, 19],\n [-24, 6, 9, -83, -39],\n [-1, 9, 0, 4, 16],\n [3, -27, -33, -72, 6],\n [-22, 48, 14, 21, 12]]?\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 5x5 matrix:\n[[20, 5, 15, 5, 30],\n [20, 5, 15, 5, 30],\n [24, 6, 18, 6, 36],\n [-20, -5, -15, -5, -30],\n [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[[-1, -11, -39, 17, -6],\n [-1, -11, -39, 17, -6],\n [-16, -5, -16, 6, 18],\n [26, 7, 22, -8, -30],\n [9, 9, 31, -13, -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[[12, 12, -36, 24, 6],\n [10, 10, -30, 20, 5],\n [6, 6, -18, 12, 3],\n [4, 4, -12, 8, 2],\n [12, 12, -36, 24, 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 5x5 matrix:\n[[12, 3, -15, -6, 18],\n [4, 1, -5, -2, 6],\n [-24, -6, 30, 12, -36],\n [0, 0, 0, 0, 0],\n [-12, -3, 15, 6, -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[[-24, 12, -40, 9, 18],\n [8, -4, 14, -2, -6],\n [-20, 10, -19, 29, 15],\n [-8, 4, -12, 5, 6],\n [4, -2, 1, -10, -3]]?\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 5x5 matrix:\n[[-9, 19, -15, 8, -26],\n [-3, 1, 27, -16, -14],\n [4, -6, -8, 5, 14],\n [2, -2, -10, 6, 8],\n [-5, 11, -11, 6, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-20, -50, 16, 4, 45],\n [23, 17, -10, 2, -18],\n [3, 37, -8, -6, -32],\n [-3, 23, -6, -2, -16],\n [26, -6, -18, 20, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-46, 17, -7, 7, -50],\n [-20, -10, 20, 18, -10],\n [-18, 68, -79, 2, -38],\n [37, -14, -10, 11, -2],\n [-33, 31, -26, -26, -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[[0, 0, 0, 0, 0],\n [-15, -6, -9, -6, -3],\n [-5, -2, -3, -2, -1],\n [25, 10, 15, 10, 5],\n [30, 12, 18, 12, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-26, -9, -25, 4, -4],\n [30, 9, -3, 18, 0],\n [58, 6, 31, -13, 14],\n [-66, 0, 2, -3, -14],\n [14, -3, -6, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0, 0],\n [36, -36, 36, 36, -30],\n [0, 0, 0, 0, 0],\n [24, -24, 24, 24, -20],\n [24, -24, 24, 24, -20]]?\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[[-20, -30, 15, -25, -55],\n [-20, -36, 14, -22, -46],\n [21, 30, -16, 27, 60],\n [-4, -18, 1, 1, 7],\n [-3, -18, 0, 3, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-5, -2, 6, 4, 6],\n [-5, -2, 6, 4, 6],\n [5, 2, -6, -4, -6],\n [10, 4, -12, -8, -12],\n [-25, -10, 30, 20, 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[[-17, 16, -15, 36, -25],\n [-37, -4, 2, -10, 29],\n [-1, -13, -15, 1, -5],\n [-13, -13, 20, -24, 26],\n [-3, -18, 29, 5, -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[[-15, -42, 5, 2, 15],\n [56, 49, -9, -28, 26],\n [47, 56, -64, -31, -2],\n [20, -5, 4, -12, 26],\n [38, 26, 17, -6, 16]]\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, 48, 21, 30, -3],\n [-20, 61, 0, 25, 1],\n [12, -27, -8, -15, 1],\n [-12, -21, 48, 15, -9],\n [-20, 37, 20, 25, -3]]\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 5x5 matrix:\n[[-14, -38, 38, 26, -5],\n [56, 15, -64, -25, 16],\n [16, -48, 15, 26, -2],\n [-12, 35, -12, -5, -22],\n [-12, 12, 4, -4, -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[[-25, -15, -12, 24, -10],\n [-24, -2, -10, 0, 0],\n [24, -12, 12, -12, 27],\n [-5, -11, 2, 25, -3],\n [-15, 3, 6, -15, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, -11, -4, 22, 5],\n [-36, 7, -18, -21, -33],\n [0, 59, -34, -21, 7],\n [-2, 14, 2, -15, 4],\n [-1, 35, -14, -9, -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[[-2, -4, -1, -4, 1],\n [-12, -24, -6, -24, 6],\n [-20, -20, -24, -4, -8],\n [22, 14, 32, -10, 16],\n [9, 3, 15, -9, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[36, -54, 18, 0, -48],\n [-6, 0, 9, -9, 10],\n [10, -12, 1, 3, -14],\n [16, -21, 4, 3, -22],\n [6, 0, -9, 9, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-10, 10, -15, 15, 25],\n [2, -2, 3, -3, -5],\n [10, -10, 15, -15, -25],\n [-10, 10, -15, 15, 25],\n [12, -12, 18, -18, -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[[0, 0, 0, 0, 0],\n [15, -5, -20, -30, 30],\n [15, -5, -20, -30, 30],\n [12, -4, -16, -24, 24],\n [-3, 1, 4, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, 20, 9, -44, 40],\n [-17, 0, -38, -1, -36],\n [-29, 24, -86, 15, -62],\n [2, -3, 26, -13, 7],\n [30, 6, 36, 48, 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 5x5 matrix:\n[[14, 11, -35, -3, 18],\n [-29, -1, -19, -33, 15],\n [-8, 3, -19, -15, 12],\n [12, 3, -3, 9, 0],\n [7, -2, 14, 12, -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[[8, 10, 6, 6, 12],\n [-8, -10, -6, -6, -12],\n [-20, -25, -15, -15, -30],\n [8, 10, 6, 6, 12],\n [-24, -30, -18, -18, -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[[4, 0, -10, 2, -6],\n [6, 18, 6, -12, -30],\n [12, 0, -30, 6, -18],\n [-3, -15, -10, 11, 22],\n [12, -18, -51, 21, 3]]\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 5x5 matrix:\n[[20, 20, -8, 4, -20],\n [20, 20, -8, 4, -20],\n [-25, -25, 10, -5, 25],\n [20, 20, -8, 4, -20],\n [30, 30, -12, 6, -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[[16, 8, -8, -4, -16],\n [20, 10, -10, -5, -20],\n [4, 2, -2, -1, -4],\n [-4, -2, 2, 1, 4],\n [20, 10, -10, -5, -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[[-4, 40, 46, 26, 4],\n [0, 21, 27, 12, -3],\n [4, 30, 44, 14, -14],\n [16, -34, -22, -32, -34],\n [-8, 3, -7, 8, 19]]\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[[9, -18, 18, -12, -3],\n [-18, 36, -36, 24, 6],\n [6, -12, 12, -8, -2],\n [6, -12, 12, -8, -2],\n [6, -12, 12, -8, -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[[1, -5, 5, -4, 10],\n [4, -10, 20, 14, 0],\n [-2, 10, -10, 8, -20],\n [5, -5, 25, 40, -30],\n [0, 2, 0, 6, -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[[-24, 11, 3, 6, 14],\n [84, 14, -36, -12, -46],\n [48, 42, -38, 0, -24],\n [-72, -9, 39, 0, 36],\n [30, 35, -24, -3, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, 8, -12, 10, 4],\n [-6, 24, -36, 30, 12],\n [4, -16, 24, -20, -8],\n [-4, 16, -24, 20, 8],\n [-5, 20, -30, 25, 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[[0, -2, -6, -12, -2],\n [-8, 13, 17, 36, 3],\n [-8, 4, -10, -18, -6],\n [4, -3, 2, 3, 2],\n [16, -15, -1, -6, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-23, 41, -28, 27, 39],\n [5, 6, -18, 11, -2],\n [1, 25, -1, 17, 16],\n [-31, -5, 11, 33, -6],\n [-29, 10, 25, 23, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[14, -30, -4, 6, -9],\n [12, -10, 8, -16, 1],\n [-18, 26, 13, -18, 8],\n [-10, 12, -15, 26, -1],\n [5, -6, 10, -17, 1]]\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, 10, -10, -30, 0],\n [-8, -8, 8, 24, 0],\n [-12, -28, 12, 4, -16],\n [-4, -20, 4, -20, -16],\n [-4, -24, 4, -28, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [2, 0, 0, 2, -10],\n [6, 0, 0, 6, -30],\n [-1, 0, 0, -1, 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[[-19, 28, -21, -15, -2],\n [42, 12, 27, -24, 75],\n [8, 13, 8, 0, 37],\n [-2, 2, -6, -10, -10],\n [2, -5, 4, 6, 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[[4, 5, -6, 3, -1],\n [3, -18, 3, -18, 6],\n [-13, 20, 7, 24, -8],\n [-24, 28, 16, 36, -12],\n [17, -15, -13, -21, 7]]\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, 0, 0, -42, 32],\n [24, 12, 6, 48, -36],\n [20, -44, -22, 13, -12],\n [12, 12, 6, 27, -20],\n [-8, 44, 22, 8, -4]]\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, -7, -25, 26, 28],\n [27, 3, -35, 46, 44],\n [5, 1, 11, -6, -4],\n [-15, 27, 48, -20, -23],\n [15, -9, -19, 14, 16]]\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, 0, 10, 3, -3],\n [6, -3, 15, -9, -15],\n [-28, 7, -11, 17, 5],\n [-30, 21, 5, 36, -5],\n [-18, -30, 12, 39, -10]]\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 5x5 matrix:\n[[-3, 29, -18, -4, 59],\n [12, 36, 18, -9, 45],\n [-8, -38, -6, 3, -67],\n [24, 10, 54, 13, 19],\n [10, 36, 12, -4, 58]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -48, -27, 6, 18],\n [0, -40, -21, 26, 30],\n [0, -26, -12, 40, 36],\n [0, 44, 24, -16, -24],\n [0, 9, 6, 12, 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 5x5 matrix:\n[[-18, -56, -32, 2, 2],\n [-22, -8, 7, 26, -5],\n [-16, -6, 11, 7, -4],\n [-16, -50, -16, -23, 1],\n [34, 0, -32, -22, 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 5x5 matrix:\n[[7, 62, 7, 16, 32],\n [-1, 6, -11, -12, 14],\n [-7, -18, -3, 2, -15],\n [-10, -12, -12, -4, -6],\n [-6, 28, -4, 12, 10]]\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[[-22, 20, -22, 8, 0],\n [-17, 20, -19, 6, -2],\n [3, -30, 15, 0, 12],\n [-6, 10, -8, 2, -2],\n [-3, 30, -15, 0, -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[[-4, 10, -6, -6, 6],\n [-12, 30, -18, -18, 18],\n [-2, 5, -3, -3, 3],\n [0, 0, 0, 0, 0],\n [-10, 25, -15, -15, 15]]?\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[[-4, 1, -10, 9, -5],\n [-4, 5, 18, -3, 7],\n [28, -16, 7, -36, 8],\n [36, -22, -1, -42, 6],\n [20, -11, 8, -27, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-11, 13, -32, 4, -36],\n [-8, -2, 6, 8, -2],\n [-24, 12, -28, 16, -44],\n [-19, 2, -3, 16, -19],\n [-3, -3, 8, 4, 4]]\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, -42, -2, 46, -6],\n [23, -32, -31, -1, 1],\n [-34, 42, 78, 16, -6],\n [8, -11, -34, -19, 4],\n [-40, 48, 48, -20, 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[[2, -20, 8, 8, 44],\n [4, 38, 5, 0, -25],\n [-18, -18, -11, -16, 7],\n [27, 1, 13, 26, 2],\n [-20, -10, -14, -20, -8]]?\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, -5, -1, 18, -2],\n [0, -2, -34, 6, 16],\n [16, 5, 16, 9, -34],\n [-13, 2, -60, -1, 22],\n [-13, -3, 2, -10, 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[[-10, 44, -22, -22, -25],\n [6, -41, 29, 26, 32],\n [44, -27, 6, 9, -12],\n [38, -23, -16, 26, 14],\n [14, -18, 21, 36, 39]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-9, -42, -24, -33, 23],\n [-28, 31, -1, 1, 1],\n [12, 36, -17, -12, -10],\n [23, 53, 27, 52, -36],\n [20, 5, -13, 13, -12]]\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 5x5 matrix:\n[[6, 0, 2, 5, -5],\n [30, 0, 10, 25, -25],\n [0, 0, 0, 0, 0],\n [6, 0, 2, 5, -5],\n [-12, 0, -4, -10, 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[[28, 20, -38, -26, -4],\n [-12, -9, 12, 9, 6],\n [-8, 2, 7, 1, 8],\n [-19, 1, 50, 23, -17],\n [0, -33, -6, 15, -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[[1, -2, -5, -5, -1],\n [-10, 20, 36, 34, -6],\n [1, -2, 9, 11, 15],\n [9, -18, -24, -21, 15],\n [13, -26, -23, -17, 35]]\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 5x5 matrix:\n[[20, -24, 24, 8, 24],\n [25, -30, 30, 10, 30],\n [30, -36, 36, 12, 36],\n [-30, 36, -36, -12, -36],\n [5, -6, 6, 2, 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[[10, 21, 6, -15, 7],\n [30, -26, -26, 6, -16],\n [36, -46, 40, 40, 0],\n [38, -90, 38, 64, -10],\n [28, 14, 47, 3, 17]]\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 5x5 matrix:\n[[27, 18, -6, -15, -9],\n [33, -5, 24, -8, -24],\n [-35, 22, -42, -11, 25],\n [-24, 60, -72, -66, 12],\n [-47, -1, -24, 11, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[18, 42, 12, -42, 60],\n [-17, 7, -9, -14, 18],\n [7, 23, 5, -24, 34],\n [-12, -8, -7, 5, -8],\n [-18, -22, -11, 19, -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[[-15, 27, -40, 15, 11],\n [-5, -15, 20, 5, -15],\n [15, -27, 40, -15, -11],\n [4, -24, 34, -4, -16],\n [4, -24, 34, -4, -16]]\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, 10, -4, -4, -4],\n [30, 30, -12, -12, -12],\n [-20, -20, 8, 8, 8],\n [-5, -5, 2, 2, 2],\n [-20, -20, 8, 8, 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 5x5 matrix:\n[[14, 13, -9, -1, -1],\n [22, 13, 10, 17, 17],\n [20, 18, -11, 0, 0],\n [-30, -17, -16, -25, -25],\n [-42, -31, 1, -17, -17]]\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 5x5 matrix:\n[[-1, -27, -36, -14, -25],\n [-10, 10, 6, -10, 19],\n [-11, -2, -16, 11, 0],\n [-36, 8, -28, 16, 22],\n [-5, 15, 12, 20, 13]]\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[[-31, -28, -29, -54, -27],\n [45, 72, 1, -26, -39],\n [-47, -66, -15, 1, 6],\n [-1, -16, -4, -13, -36],\n [59, 46, 41, 23, 18]]?\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, -18, 9, 12, -9],\n [18, 18, -9, -12, 9],\n [0, 0, 0, 0, 0],\n [12, 12, -6, -8, 6],\n [24, 24, -12, -16, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, 3, 4, 1, -13],\n [10, 7, 12, 5, -45],\n [4, -12, -10, 2, 19],\n [-6, -5, -8, -3, 29],\n [-12, -2, -8, -6, 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[[1, -48, 64, -1, -20],\n [55, -16, 79, -6, 31],\n [-14, -33, 28, 48, -2],\n [-4, 48, -37, -45, 11],\n [25, -3, 51, -22, 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[[-31, 10, -7, -31, 37],\n [-4, 8, -9, -8, 59],\n [57, -40, -40, 48, 17],\n [-30, 13, 46, -14, -80],\n [15, -11, -56, -6, 31]]\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[[13, -23, -14, -2, 8],\n [20, -11, -7, -9, 0],\n [38, 5, -40, 10, -11],\n [29, -24, -34, 4, 5],\n [-46, 3, 8, 22, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[20, -48, 9, 45, 14],\n [-22, 19, -4, -12, 34],\n [24, -29, -2, 22, -4],\n [-22, 19, -4, -12, 34],\n [-40, 55, 4, -44, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[45, 17, -44, 40, 19],\n [-2, 27, 3, 1, -17],\n [29, 7, -26, 34, 13],\n [-9, 13, 4, -25, -10],\n [-31, 12, 33, -19, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 40, 5, 50, -25],\n [3, -35, 1, -46, 23],\n [0, -48, -6, -60, 30],\n [24, 0, 43, -18, 9],\n [9, 15, 18, 12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-9, -3, -9, -6, 3],\n [-9, -3, -9, -6, 3],\n [12, 4, 12, 8, -4],\n [-6, -2, -6, -4, 2],\n [-15, -5, -15, -10, 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[[-9, -6, -3, 18, 27],\n [5, 43, 18, -9, 14],\n [-11, 8, 2, 23, 19],\n [-9, 25, 7, -10, 12],\n [-8, -51, -23, -7, -17]]\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[[-31, 38, 31, -12, 20],\n [-26, 19, 20, 0, 10],\n [15, -33, -21, 24, -24],\n [23, 7, -7, -22, 7],\n [8, -2, 2, 50, -53]]\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[[3, -17, -24, 26, -2],\n [-24, 27, -33, -57, -36],\n [6, 32, -48, -32, -46],\n [26, -9, 17, 37, 16],\n [39, -9, 3, 51, 9]]\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[[8, -31, 0, -31, 28],\n [-15, 21, 33, 21, -3],\n [7, -8, -17, -8, -1],\n [6, -21, -2, -21, 18],\n [18, -45, -22, -45, 30]]\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 5x5 matrix:\n[[5, 44, -33, 9, -60],\n [7, -36, 29, 38, 23],\n [52, -27, 1, -21, 47],\n [-20, -39, 38, -13, 29],\n [53, 23, -38, -15, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, 6, -12, -12, -9],\n [6, -4, 8, 8, 6],\n [-9, 6, -12, -12, -9],\n [-6, 4, -8, -8, -6],\n [-12, 8, -16, -16, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -22, 21, -58, -22],\n [-16, 10, -28, -8, -32],\n [29, 41, -8, 54, 24],\n [-25, -45, 14, -26, 4],\n [4, 4, 5, -42, -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 5x5 matrix:\n[[-8, 25, -30, 11, 26],\n [11, -44, 32, -11, -39],\n [12, -45, 10, -24, -13],\n [-32, -14, -52, 5, -33],\n [8, 30, -32, 34, 50]]\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 5x5 matrix:\n[[-2, -2, 5, -1, -12],\n [40, -16, 25, -27, 18],\n [21, -26, -10, -1, 27],\n [2, -36, -15, 55, -4],\n [7, -18, 12, 23, -19]]\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 5x5 matrix:\n[[3, -8, 18, 9, -12],\n [-33, 22, -18, 27, -30],\n [-17, 16, -22, 5, -4],\n [-25, 19, -20, 16, -17],\n [-22, 11, -2, 25, -29]]\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, -4, 6, -2, -12],\n [16, 8, -12, 4, 24],\n [-24, -12, 18, -6, -36],\n [-4, -2, 3, -1, -6],\n [12, 6, -9, 3, 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 5x5 matrix:\n[[34, 60, -30, -22, -12],\n [1, 62, -60, -61, -16],\n [-22, -20, 32, 0, 20],\n [-39, -6, -8, -29, 6],\n [17, -16, 35, 12, 17]]\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, 4, -24, 20, -16],\n [-12, 2, -12, 10, -8],\n [12, -2, 12, -10, 8],\n [-18, 3, -18, 15, -12],\n [36, -6, 36, -30, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-21, -51, 19, -11, 48],\n [31, 92, 2, 26, -74],\n [-26, -30, -2, -4, 38],\n [10, -17, -14, -18, -6],\n [27, 19, 10, 26, -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[[-3, -31, 22, -31, -8],\n [14, 6, 36, 6, 16],\n [-16, -18, -30, -18, -20],\n [4, 11, 1, 11, 6],\n [8, 35, -11, 35, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-36, 37, -10, -22, -5],\n [-6, 32, -12, -14, -6],\n [-12, 34, -12, -16, -6],\n [36, 18, -12, 0, -6],\n [30, -40, 12, 22, 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[[53, 33, -71, -8, 20],\n [-3, 37, 22, 50, -50],\n [21, 72, 6, 78, -75],\n [-19, 36, -14, 20, 3],\n [-18, -30, 33, -9, -3]]\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, 16, 6, 4, -80],\n [28, 2, -11, -7, 55],\n [-11, 28, -6, -11, -49],\n [-18, -8, 4, 22, 2],\n [-24, -28, 16, 26, -6]]\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[[9, 6, 24, 18, -15],\n [26, 5, 21, 6, 14],\n [14, 25, 13, 0, 24],\n [-21, -31, -27, -9, -20],\n [-26, -5, -21, -6, -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, -10, 0, 5, -30],\n [1, -2, 0, 1, -6],\n [5, -10, 0, 5, -30],\n [-2, 4, 0, -2, 12],\n [5, -10, 0, 5, -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[[13, 3, -8, 1, -4],\n [11, -22, 7, -17, -12],\n [-24, 33, 27, 36, 48],\n [19, -2, 27, 7, 20],\n [25, 12, -17, 7, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-30, -24, 42, 4, -40],\n [-6, 6, -11, 6, -1],\n [-17, 8, 23, -19, -15],\n [-21, -6, 16, 3, -22],\n [7, 38, -12, -32, 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[[-38, 10, 24, -26, 24],\n [-38, -14, 6, -53, 41],\n [-15, 31, 10, 12, -4],\n [16, 45, 8, 40, -22],\n [8, 37, 26, -5, 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[[2, 32, 30, 26, 8],\n [11, 53, -6, 20, 20],\n [13, 44, -33, 5, 20],\n [12, 44, -16, 28, 4],\n [8, 4, -28, 30, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[38, -32, 0, -15, 37],\n [22, -34, -22, 0, 30],\n [25, -25, 4, 34, 40],\n [-17, 17, 2, -39, -31],\n [-9, -33, -50, 16, 12]]?\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, 0, 12, 0, 2],\n [-18, 0, 18, 0, 3],\n [36, 0, -36, 0, -6],\n [6, 0, -6, 0, -1],\n [12, 0, -12, 0, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-21, -16, 4, 5, -27],\n [-32, -2, 18, 10, -4],\n [-8, -8, 0, 2, -11],\n [-3, -22, -14, 1, -17],\n [-3, 6, 6, 1, 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[[-10, 19, -22, -23, -35],\n [31, -49, 10, 7, 35],\n [37, -52, 6, 2, 58],\n [-4, 19, -36, -39, -19],\n [12, 0, -46, -52, -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[[-32, 30, 24, -48, -36],\n [-24, 22, 20, -36, -24],\n [-4, 2, 10, -6, 6],\n [-12, 9, 18, -18, 0],\n [4, 2, -26, 6, -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[[12, 10, -6, 2, 2],\n [-12, -10, 6, -2, -2],\n [36, 30, -18, 6, 6],\n [-6, -5, 3, -1, -1],\n [-18, -15, 9, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -33, 27, 5, -25],\n [-6, -43, 0, 28, 33],\n [-15, -34, -15, 40, 51],\n [31, 34, 12, -13, -15],\n [10, -4, 36, 18, -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[[-16, -24, -6, 18, 24],\n [-25, 49, 12, -14, -22],\n [75, -19, -7, 25, -28],\n [-11, -29, -7, 21, 24],\n [14, -18, -10, 10, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[5, 0, 5, -3, -1],\n [-25, 0, -25, 15, 5],\n [10, 0, 10, -6, -2],\n [-25, 0, -25, 15, 5],\n [25, 0, 25, -15, -5]]\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, -12, 12, 16, 24],\n [-3, 9, -9, -12, -18],\n [-1, 3, -3, -4, -6],\n [5, -15, 15, 20, 30],\n [3, -9, 9, 12, 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 5x5 matrix:\n[[15, 5, 0, -10, -10],\n [12, 4, 0, -8, -8],\n [15, 5, 0, -10, -10],\n [6, 2, 0, -4, -4],\n [9, 3, 0, -6, -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[[8, 18, -44, 24, 0],\n [-8, 5, 2, -4, -10],\n [-9, 16, -41, 24, -16],\n [14, 30, -54, 16, 2],\n [-25, -25, 18, -14, -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[[25, -15, -30, -10, -30],\n [-25, 15, 30, 10, 30],\n [0, 0, 0, 0, 0],\n [-20, 12, 24, 8, 24],\n [15, -9, -18, -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 5x5 matrix:\n[[-12, 20, 28, -12, 32],\n [-24, 25, 26, -6, 31],\n [-36, 30, 24, 0, 30],\n [-40, 30, 20, 4, 26],\n [-36, 30, 24, 0, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[33, -12, 8, -13, -14],\n [8, 10, -12, -30, 34],\n [-30, -8, 22, 19, 8],\n [-29, -10, 32, -7, 48],\n [11, -17, 18, 18, -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[[-36, 34, 56, 22, 57],\n [4, 54, 0, 18, 26],\n [-4, -26, 40, 26, 21],\n [-40, -78, 32, -34, -24],\n [0, 18, 2, 7, 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[[10, -10, 4, 2, -10],\n [15, -15, 6, 3, -15],\n [-30, 30, -12, -6, 30],\n [20, -20, 8, 4, -20],\n [-10, 10, -4, -2, 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 5x5 matrix:\n[[12, -18, 15, 3, -6],\n [48, -42, 27, -9, 0],\n [26, -14, 5, -11, 7],\n [22, -18, 11, -5, 1],\n [22, -28, 22, 2, -7]]\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[[-9, -10, -19, 5, -24],\n [1, -4, 1, 5, -1],\n [-20, 5, -34, 23, -5],\n [-3, 19, -1, -14, 14],\n [-5, 4, -9, -17, -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[[0, 4, -9, 28, -25],\n [-4, 22, -30, 30, -28],\n [24, -23, 18, -9, -23],\n [14, -28, 33, -34, 17],\n [-20, 30, -33, 38, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[14, 1, 0, 2, 32],\n [-16, -35, -12, -30, -62],\n [-20, -35, -20, -30, -50],\n [-4, -18, -8, -15, -18],\n [-4, -19, -4, -16, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-18, 39, 9, 3, -9],\n [16, 0, -20, 11, -41],\n [-26, 48, 18, -9, 1],\n [21, -26, -21, 22, -21],\n [16, -11, -11, -18, -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[[13, 33, 25, 28, -48],\n [0, -30, -25, -25, 30],\n [-22, -27, -25, -22, 12],\n [-35, -14, -15, -11, -6],\n [1, 4, 5, 3, 6]]\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, 3, 24, 2, 16],\n [-18, -51, -8, -4, -6],\n [-32, -33, -12, 1, 17],\n [11, -45, 10, -5, -11],\n [-34, -24, -4, 6, 46]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-18, 36, -6, -24, 12],\n [-6, 12, -2, -8, 4],\n [-9, 18, -3, -12, 6],\n [-9, 18, -3, -12, 6],\n [3, -6, 1, 4, -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 5x5 matrix:\n[[3, 14, 14, -32, -3],\n [8, -26, -28, 43, 9],\n [43, -58, 10, 2, -18],\n [-16, 0, -20, 38, 9],\n [-50, 72, -4, -14, 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[[-2, -12, 2, 2, -6],\n [-1, -6, 1, 1, -3],\n [3, 18, -3, -3, 9],\n [5, 30, -5, -5, 15],\n [4, 24, -4, -4, 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[[-2, 8, -6, -2, -6],\n [-3, 12, -9, -3, -9],\n [-2, 8, -6, -2, -6],\n [-5, 20, -15, -5, -15],\n [-2, 8, -6, -2, -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 5x5 matrix:\n[[-3, -9, -12, -3, 15],\n [-2, -6, -8, -2, 10],\n [0, 0, 0, 0, 0],\n [2, 6, 8, 2, -10],\n [2, 6, 8, 2, -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[[-22, 12, -36, -8, -1],\n [-14, -12, 12, -16, 19],\n [-28, -6, -8, -22, 20],\n [0, 9, -16, 5, -9],\n [34, 15, -4, 31, -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[[33, 4, -10, -25, 12],\n [-16, -33, -23, -16, -32],\n [-40, -27, -5, 0, -32],\n [-15, 43, 53, 21, 36],\n [-12, -27, -15, -30, -24]]\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, -17, -9, 16, 13],\n [-3, 10, -14, -19, -21],\n [-29, 29, -13, -33, -12],\n [-39, 25, -14, -25, -3],\n [-24, -20, -14, 32, 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 5x5 matrix:\n[[-9, -12, 0, -9, -9],\n [3, 4, 0, 3, 3],\n [-12, -16, 0, -12, -12],\n [-15, -20, 0, -15, -15],\n [15, 20, 0, 15, 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[[-3, 5, -1, 1, -4],\n [6, -10, 2, -2, 8],\n [-12, 20, -4, 4, -16],\n [6, -10, 2, -2, 8],\n [15, -25, 5, -5, 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[[42, 10, 12, -6, -16],\n [-33, -26, -24, 6, 2],\n [-26, -9, -10, 7, 14],\n [-44, -2, -6, 8, 26],\n [-30, 4, -1, 17, 43]]\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[[-8, 38, -10, 2, 8],\n [23, -17, -13, -72, 17],\n [20, 9, 37, -80, 7],\n [-53, 46, 12, 62, -24],\n [30, -6, -43, 10, 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[[16, -4, -2, 9, 4],\n [10, -2, -2, 12, 4],\n [-11, 3, 1, -3, -2],\n [8, 0, -4, 30, 8],\n [-11, 3, 1, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[12, 15, 18, 18, -6],\n [-37, 15, -13, -38, 26],\n [10, -12, -2, 8, -8],\n [-19, 13, -3, -18, 14],\n [16, -29, -10, 10, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-10, -7, -16, 0, 16],\n [-40, 24, -10, 4, 42],\n [-38, 25, -5, 2, 37],\n [-4, -2, 26, -28, -22],\n [2, 1, 5, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, -3, 13, 41, -51],\n [12, -8, 7, 9, -13],\n [18, 39, -33, 7, -21],\n [-53, 42, -24, 9, 7],\n [14, 6, -13, -20, 31]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[13, 56, -15, -55, -17],\n [7, 52, -17, -50, -19],\n [29, -18, 11, -9, 0],\n [-12, -40, 12, 44, 16],\n [-31, -30, 3, 48, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[18, 30, 30, -14, -31],\n [-10, -50, -30, -10, 35],\n [-16, -20, -24, 16, 24],\n [-10, 25, 0, 30, -5],\n [22, 5, 24, -34, -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 5x5 matrix:\n[[-12, 8, 20, -24, 24],\n [-18, 12, 30, -36, 36],\n [12, -8, -20, 24, -24],\n [18, -12, -30, 36, -36],\n [-3, 2, 5, -6, 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[[-36, 24, 36, -30, 30],\n [-36, 24, 36, -30, 30],\n [-12, 8, 12, -10, 10],\n [12, -8, -12, 10, -10],\n [-18, 12, 18, -15, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, 6, -80, -26, -12],\n [-52, 32, 46, 42, -14],\n [20, -12, 2, -36, -16],\n [62, -18, -14, -39, 28],\n [22, 29, 3, -48, -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[[9, 3, 3, -6, 12],\n [-6, -2, -2, 4, -8],\n [12, 4, 4, -8, 16],\n [-3, -1, -1, 2, -4],\n [-6, -2, -2, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, 12, -8, -8, 4],\n [0, 0, 0, 0, 0],\n [5, 30, -20, -20, 10],\n [-6, -36, 24, 24, -12],\n [-3, -18, 12, 12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-7, 19, -33, 13, -4],\n [7, 17, -73, 18, -5],\n [23, -5, -15, -10, -7],\n [-2, -43, 21, -28, -26],\n [-1, -14, -30, 19, 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[[10, -10, -8, -4, 4],\n [25, -25, -20, -10, 10],\n [5, -5, -4, -2, 2],\n [0, 0, 0, 0, 0],\n [25, -25, -20, -10, 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 5x5 matrix:\n[[20, 15, 0, 15, 20],\n [-8, -6, 0, -6, -8],\n [12, 9, 0, 9, 12],\n [-16, -12, 0, -12, -16],\n [-20, -15, 0, -15, -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[[20, 15, -20, 30, 15],\n [24, 18, -24, 36, 18],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [8, 6, -8, 12, 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 5x5 matrix:\n[[-41, -38, 32, 36, 40],\n [-21, -35, 1, -15, -9],\n [14, 35, 14, 32, 40],\n [-44, -78, -48, 4, -52],\n [27, 24, -27, -21, -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[[20, 0, 24, 0, -4],\n [30, 0, 36, 0, -6],\n [-25, 0, -30, 0, 5],\n [0, 0, 0, 0, 0],\n [-5, 0, -6, 0, 1]]\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[[0, 0, 0, 0, 0],\n [-12, -6, 9, 0, 18],\n [12, 6, -9, 0, -18],\n [0, 0, 0, 0, 0],\n [-24, -12, 18, 0, 36]]\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 5x5 matrix:\n[[18, -7, -11, 19, 0],\n [-10, 0, 17, -16, 14],\n [-16, 9, 2, -13, -10],\n [24, -16, 4, 16, 24],\n [-42, 18, 21, -42, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[11, 4, -10, -11, -4],\n [-16, -14, 12, 21, 5],\n [-1, 16, 6, -9, 2],\n [35, -5, -20, -30, -15],\n [-22, -2, 8, 23, 9]]\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, -10, -15, -40, -10],\n [-22, -44, -16, -14, -2],\n [23, 2, 12, 20, 10],\n [-21, -14, -4, 10, 0],\n [36, 32, 13, -1, 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[[7, 18, 8, 21, 7],\n [-29, 15, -25, -11, -29],\n [-21, 45, -15, 21, -21],\n [18, 18, 18, 30, 18],\n [12, 12, 12, 20, 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 5x5 matrix:\n[[0, 4, 10, -10, 10],\n [0, -10, -25, 25, -25],\n [0, -10, -25, 25, -25],\n [0, 8, 20, -20, 20],\n [0, -10, -25, 25, -25]]\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, 27, 15, 8, 0],\n [59, 47, -30, -32, -22],\n [23, 50, 17, 7, -5],\n [-11, -7, 16, -1, -27],\n [12, -14, -28, -33, -39]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, -4, -6, -3, -4],\n [-30, 20, 30, 15, 20],\n [-30, 20, 30, 15, 20],\n [-30, 20, 30, 15, 20],\n [-12, 8, 12, 6, 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[[12, 2, 12, 8, -6],\n [0, 0, 0, 0, 0],\n [36, 6, 36, 24, -18],\n [30, 5, 30, 20, -15],\n [-30, -5, -30, -20, 15]]?\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, 12, -24, -16, 4],\n [-20, 20, -33, -25, 10],\n [-16, -3, -15, -1, -11],\n [24, 22, 12, -16, 34],\n [0, -25, 15, 25, -25]]\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, -4, 4, 5, -2],\n [0, 0, 0, 0, 0],\n [4, 4, -4, -5, 2],\n [20, 20, -20, -25, 10],\n [24, 24, -24, -30, 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[[-7, 6, -2, -13, 19],\n [-30, 9, -23, -15, 0],\n [-8, -60, 44, 49, -28],\n [-8, -2, -19, -3, 3],\n [-58, -12, 6, 6, -36]]\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, -18, -9, 6, -15],\n [-2, 12, 6, -4, 10],\n [5, -30, -15, 10, -25],\n [3, -18, -9, 6, -15],\n [-2, 12, 6, -4, 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[[36, 45, -3, 12, 12],\n [24, 21, 22, -25, 20],\n [4, 3, 5, -6, 4],\n [-24, -18, -30, 36, -24],\n [0, 15, -40, 55, -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[[-3, -9, 6, -6, 18],\n [1, 3, -2, 2, -6],\n [-2, -6, 4, -4, 12],\n [1, 3, -2, 2, -6],\n [6, 18, -12, 12, -36]]\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 5x5 matrix:\n[[43, -14, 45, 1, 47],\n [29, -2, 45, -4, 41],\n [15, -1, 27, 9, 31],\n [-6, 21, 24, -34, -2],\n [22, 16, 66, -22, 46]]\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, -4, -30, -29, 47],\n [-20, 6, -22, -39, 9],\n [3, 5, -1, 9, 22],\n [19, -1, 19, 39, 4],\n [-6, 33, 6, -8, -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[[-12, -11, 15, 12, 53],\n [10, 9, 21, 11, 35],\n [11, 4, -6, -14, 6],\n [48, 25, -21, -48, -7],\n [-19, -12, 0, 11, -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[[15, 3, 6, 9, -12],\n [0, 0, 0, 0, 0],\n [10, 2, 4, 6, -8],\n [5, 1, 2, 3, -4],\n [-15, -3, -6, -9, 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[[21, 37, -30, 48, 35],\n [3, 31, -30, 39, 20],\n [18, 18, -12, 24, 22],\n [18, -6, 12, -6, 8],\n [21, -23, 30, -27, 0]]\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, 0, 0, 0, 0],\n [-15, 6, 3, 0, -9],\n [-5, 2, 1, 0, -3],\n [-10, 4, 2, 0, -6],\n [30, -12, -6, 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[[-10, -19, -8, -5, -20],\n [5, -40, -18, -3, -45],\n [5, 14, 6, 3, 15],\n [20, 29, 12, 9, 30],\n [-15, 30, 14, -1, 35]]\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 5x5 matrix:\n[[-5, 21, 40, -5, -32],\n [-1, -3, -6, -1, 4],\n [-24, 18, 31, -24, -34],\n [-22, 6, 8, -22, -16],\n [5, 15, 30, 5, -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[[30, 30, -5, -30, 15],\n [30, 30, -5, -30, 15],\n [12, 12, -2, -12, 6],\n [6, 6, -1, -6, 3],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[17, 52, 21, 13, -12],\n [6, 54, -5, -8, -6],\n [17, 75, 27, 43, -1],\n [-31, -30, -27, 46, 26],\n [20, 22, 20, -21, -18]]\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, 2, 15, -32, -8],\n [24, 27, -30, -12, -18],\n [22, 33, -37, -18, -32],\n [-19, -28, 41, -14, 53],\n [11, 24, -41, 18, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-20, -12, 24, 12, -24],\n [10, 6, -12, -6, 12],\n [-10, -6, 12, 6, -12],\n [-30, -18, 36, 18, -36],\n [-30, -18, 36, 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[[-21, -14, -22, -9, 20],\n [9, -30, 3, -27, -15],\n [20, -20, 15, -16, -9],\n [-26, 12, -22, 8, 6],\n [28, 0, 26, 2, -6]]\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, -3, -3, 0, -1],\n [11, 3, 3, 6, 5],\n [-38, -12, -12, -12, -12],\n [-39, -18, -18, 18, 6],\n [-10, 3, 3, -36, -23]]\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, -30, 6, 6, -30],\n [32, 20, 28, -36, 4],\n [8, 30, 2, -14, 26],\n [2, 15, -1, -5, 14],\n [-16, 10, -18, 14, 18]]\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, -6, -18, 6, 6],\n [-12, 2, 26, -22, 28],\n [-18, -3, -3, -3, 12],\n [-18, -5, -17, 7, 2],\n [26, 5, 9, 1, -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[[-4, -4, 13, -3, 10],\n [11, 13, -11, -5, -23],\n [7, 9, -5, -3, -11],\n [-4, -6, -10, 9, 5],\n [11, 13, -18, 0, -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[[-10, 10, 20, 8, 38],\n [-20, -23, 20, -10, 7],\n [0, 15, -15, -51, -36],\n [9, 7, -25, -37, -48],\n [-7, 11, 10, -8, 17]]\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[[2, 2, -14, 4, 25],\n [-26, -24, 9, 2, -43],\n [-3, -12, 26, -28, 11],\n [-1, -8, 35, -34, 4],\n [-7, 4, -17, 18, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[30, 25, 25, -10, -15],\n [36, 30, -25, 23, -3],\n [-12, -10, 56, -38, -12],\n [24, 20, -2, 6, -6],\n [54, 45, -10, 17, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[27, 54, 51, 22, -27],\n [38, -28, -36, 3, 4],\n [53, -24, 30, -87, 71],\n [-27, -36, -18, -28, 31],\n [-10, -12, -12, -37, 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[[-11, 34, 49, -29, -44],\n [12, -28, -44, 28, 40],\n [2, -38, -42, 18, 36],\n [7, -8, -17, 13, 16],\n [-29, -24, 11, -31, -16]]\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, -3, -15, -15, 9],\n [5, -1, -5, -5, 3],\n [5, -1, -5, -5, 3],\n [5, -1, -5, -5, 3],\n [25, -5, -25, -25, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, -6, -32, 28, 0],\n [4, -6, -20, 16, 4],\n [6, 0, -18, 18, -6],\n [1, 15, 17, -7, -21],\n [-6, 6, 26, -22, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[29, 30, -34, 31, -30],\n [20, 15, -31, 13, -15],\n [37, -10, -28, -16, -9],\n [8, -45, -9, -56, 28],\n [6, -30, 16, -33, 13]]\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[[-8, 31, -6, 21, 58],\n [26, -3, 42, -23, 32],\n [20, -13, -30, 31, 28],\n [4, -10, 14, -15, -27],\n [46, -27, 20, -7, 32]]?\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, -19, -13, 6],\n [58, 14, 32, 0, -24],\n [51, 20, 13, -7, 0],\n [13, 27, 21, 35, -6],\n [40, 28, 6, 2, 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[[-1, 21, -20, -40, 20],\n [36, -36, -30, 30, 30],\n [-23, -9, -7, 5, 2],\n [6, 31, -28, -45, 58],\n [36, -48, -17, 43, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-42, -33, 12, 30, 3],\n [44, 26, -13, -31, 2],\n [-10, -25, 2, 8, 11],\n [32, -12, -11, -21, 20],\n [18, -3, -6, -12, 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[[-12, 10, -15, -16, 19],\n [-45, 25, 33, 11, -8],\n [-15, 15, 3, -9, 12],\n [-6, -14, -54, -16, 16],\n [36, 14, 45, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-37, 5, 21, -9, -5],\n [10, -10, -8, -10, -12],\n [0, 12, -8, 20, 36],\n [-14, 23, -28, 31, 12],\n [-50, 4, 24, -18, -43]]\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[[-18, -21, -41, -7, -30],\n [-6, 53, 73, -29, 60],\n [15, 5, 14, 15, 12],\n [-49, 26, 5, -50, 18],\n [37, -10, 11, 32, -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[[9, -4, 12, -24, -1],\n [-37, -13, -36, -6, 14],\n [1, -18, 15, -22, 1],\n [-23, -2, -42, 12, 12],\n [35, -25, 42, -18, -6]]\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 5x5 matrix:\n[[-25, -29, -35, -17, 15],\n [20, 2, 4, -1, -14],\n [-32, -22, -7, -34, 18],\n [-33, -13, -24, 2, 23],\n [2, 22, 46, -8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[50, 19, 2, -13, -35],\n [-13, -24, -45, -5, -38],\n [75, 43, 51, -46, 20],\n [20, 7, -12, 21, -45],\n [-35, -37, -59, 4, -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[[3, 28, -45, 0, -39],\n [20, 32, -28, 7, -30],\n [0, 0, -22, -13, -2],\n [47, 4, 7, 41, -17],\n [-45, -12, -26, -43, 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[[0, -4, -4, -5, -5],\n [0, 4, 4, 5, 5],\n [0, 20, 20, 25, 25],\n [0, 8, 8, 10, 10],\n [0, 24, 24, 30, 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[[-9, 0, 0, 12, -6],\n [9, 0, 0, -12, 6],\n [9, 0, 0, -12, 6],\n [-15, 0, 0, 20, -10],\n [3, 0, 0, -4, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[7, -40, -18, 11, -6],\n [-7, 40, 18, -11, 6],\n [18, -17, 12, 2, -11],\n [5, -18, -7, 7, -4],\n [30, 37, 54, 2, -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[[-27, -4, 16, 13, -9],\n [6, 21, 17, -1, -9],\n [-3, 32, -29, 28, -23],\n [-19, 52, -8, 21, -33],\n [10, -59, 23, -15, 31]]\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, -6, 31, -64, -2],\n [48, 52, -6, -20, -40],\n [-25, -19, -19, 36, 21],\n [74, 68, 2, 8, -60],\n [-13, -20, 26, -42, 10]]?\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[[25, -1, -38, 3, 37],\n [-35, -1, 42, 3, -43],\n [11, 1, -10, -3, 11],\n [5, 7, 26, -21, -19],\n [-25, -11, -18, 33, 7]]?\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 5x5 matrix:\n[[1, 37, 11, 7, 46],\n [-18, -52, -32, 8, -36],\n [-77, -1, 21, -41, -31],\n [-28, 26, 25, -31, 8],\n [-7, 1, 9, 17, -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[[0, -24, -4, -24, -16],\n [0, 0, 0, 0, 0],\n [0, 18, 3, 18, 12],\n [0, -18, -3, -18, -12],\n [0, -12, -2, -12, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[21, -14, 21, 5, -37],\n [-23, -66, 45, -54, -36],\n [-4, -58, 66, -42, -86],\n [17, 12, -11, 24, 6],\n [64, -20, 12, 46, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-25, 10, -15, -10, 15],\n [20, -8, 12, 8, -12],\n [25, -10, 15, 10, -15],\n [25, -10, 15, 10, -15],\n [-10, 4, -6, -4, 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[[4, -5, 1, -6, -14],\n [-28, 28, -23, -14, 3],\n [-5, 9, 45, 0, -35],\n [27, -37, 41, -9, -17],\n [5, -1, 5, 13, 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 5x5 matrix:\n[[0, 24, 18, -6, -6],\n [1, 22, 22, -11, -11],\n [2, -4, 8, -10, -10],\n [1, -10, -2, -3, -3],\n [-2, 24, 7, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-20, 6, 54, 8, -14],\n [4, -12, 58, -38, -20],\n [28, -5, -50, 0, 27],\n [-34, -44, -44, 16, 40],\n [-33, 9, 62, 57, 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[[-24, -35, -50, -1, -13],\n [-28, 0, -13, 7, -45],\n [-20, -37, -28, 23, -17],\n [34, -3, 0, -33, 37],\n [-29, 8, -37, -36, -57]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[28, -20, 14, -20, -14],\n [19, -8, 16, 5, -16],\n [36, -36, 6, -60, -6],\n [-25, 14, -17, 5, 17],\n [15, -6, 13, 5, -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[[-25, 30, -20, -25, -10],\n [5, -6, 4, 5, 2],\n [-10, 12, -8, -10, -4],\n [5, -6, 4, 5, 2],\n [-30, 36, -24, -30, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, -6, 0, 15, -3],\n [-11, 2, -18, -5, -17],\n [-8, -4, -24, 10, -26],\n [42, -24, 36, 60, 24],\n [21, -12, 18, 30, 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 5x5 matrix:\n[[32, -40, 2, 12, 12],\n [-27, 16, 19, -18, 12],\n [-17, -10, 35, -18, 30],\n [-17, 40, -21, -10, -16],\n [8, 14, -24, -8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 42, -7, -1, 24],\n [9, -1, -5, 15, -10],\n [-16, -38, 23, -52, 21],\n [-17, 3, 11, -21, 22],\n [-12, 30, 5, -7, 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[[-24, -12, -12, -8, 8],\n [-6, -3, -3, -2, 2],\n [36, 18, 18, 12, -12],\n [-30, -15, -15, -10, 10],\n [36, 18, 18, 12, -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[[-6, 12, 0, -2, -10],\n [-3, 6, 0, -1, -5],\n [9, -18, 0, 3, 15],\n [-3, 6, 0, -1, -5],\n [15, -30, 0, 5, 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[[12, 4, 10, -12, 2],\n [-6, -2, -5, 6, -1],\n [24, 8, 20, -24, 4],\n [0, 0, 0, 0, 0],\n [18, 6, 15, -18, 3]]\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[[38, -2, 31, 7, -50],\n [34, -31, 24, 22, -18],\n [10, -25, 8, 18, 14],\n [22, -43, 18, 32, 18],\n [-9, -24, -5, 17, 43]]\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 5x5 matrix:\n[[-16, 20, 4, 16, 4],\n [-16, 20, 4, 16, 4],\n [-24, 30, 6, 24, 6],\n [16, -20, -4, -16, -4],\n [8, -10, -2, -8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, -5, -6, 2, -5],\n [10, 25, 30, -10, 25],\n [-2, -5, -6, 2, -5],\n [-6, -15, -18, 6, -15],\n [-2, -5, -6, 2, -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 5x5 matrix:\n[[9, -27, -41, -52, 28],\n [-39, -42, -1, 18, 5],\n [14, -33, -14, 31, -34],\n [-27, -3, 11, 2, 14],\n [49, 21, -17, -20, -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[[0, 0, 0, 0, 0],\n [16, 16, 4, -12, -20],\n [20, 20, 5, -15, -25],\n [16, 16, 4, -12, -20],\n [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[[-3, 5, 31, -1, 25],\n [6, -3, -6, -12, 6],\n [-2, 6, 42, -6, 38],\n [7, -1, 13, -19, 27],\n [1, -3, -21, 3, -19]]\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, 10, 1, -10],\n [-18, 20, -8, 7, -2],\n [23, -2, -13, 37, -40],\n [-24, -25, -14, 10, -2],\n [37, 23, 21, -16, 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[[20, 30, 30, 30, 25],\n [-14, -40, -28, -30, -40],\n [-21, -22, -28, -27, -15],\n [23, 6, 24, 21, -5],\n [-37, -8, -38, -33, 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[[-2, 8, -2, 1, 18],\n [2, 7, -4, -1, 18],\n [-30, 15, 12, 15, 18],\n [26, -14, -10, -13, -18],\n [42, -38, -10, -21, -66]]\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, 21, 14, 1, 17],\n [20, 3, 22, -6, 32],\n [33, -17, 33, 22, 34],\n [-8, 12, 0, 6, -4],\n [-54, -30, -6, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 12, -10, -2, 0],\n [0, 0, 0, 0, 0],\n [30, 30, -25, -5, 0],\n [36, 36, -30, -6, 0],\n [-30, -30, 25, 5, 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[[5, 0, 4, -3, -2],\n [-20, 10, -4, 6, 14],\n [-10, -10, -20, 12, -2],\n [20, -15, -2, -3, -17],\n [-25, 10, -8, 9, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, -4, 10, -4, 8],\n [-15, -10, 25, -10, 20],\n [6, 4, -10, 4, -8],\n [-15, -10, 25, -10, 20],\n [12, 8, -20, 8, -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[[-15, 25, 30, 25, 0],\n [-6, 10, 12, 10, 0],\n [12, -20, -24, -20, 0],\n [18, -30, -36, -30, 0],\n [-15, 25, 30, 25, 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[[3, -3, 6, 0, 12],\n [-3, 3, -6, 0, -12],\n [-6, 6, -12, 0, -24],\n [-2, 2, -4, 0, -8],\n [2, -2, 4, 0, 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 5x5 matrix:\n[[-9, 10, -15, -6, -12],\n [17, -10, -15, -2, 6],\n [18, -20, 30, 12, 24],\n [19, -6, -42, -10, -3],\n [37, -26, -12, 2, 21]]\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, 27, 10, 6],\n [28, 28, -36, 4, 6],\n [-30, -30, -13, -26, -20],\n [20, 20, -23, 4, 5],\n [18, 18, -34, -2, 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[[45, -5, -35, -11, 1],\n [-1, 61, 1, 31, -49],\n [-17, 39, 15, 6, -43],\n [-26, 18, -6, 9, 8],\n [-16, 30, 12, 25, -18]]\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, 14, 13, -46, -42],\n [18, -10, -34, -24, -27],\n [6, -11, -46, 19, 27],\n [9, -24, -20, -32, 7],\n [-14, 41, 47, 17, -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 5x5 matrix:\n[[-20, 13, 10, -4, -6],\n [4, -5, -18, -28, 36],\n [-62, 25, -24, -33, -58],\n [27, 25, 52, 40, -27],\n [-53, 23, -8, -16, -53]]\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, -9, 9, -9, -2],\n [18, -15, 15, -9, 3],\n [24, -26, 26, -12, 9],\n [-30, -35, 35, 15, 45],\n [24, -8, 8, -12, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, -9, 0, -3, 12],\n [-35, 25, -15, -15, -10],\n [-20, 8, -12, -16, 8],\n [-25, 21, -9, -7, -14],\n [-22, 11, -12, -15, 4]]?\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, 11, -1, 11, 1],\n [-9, -36, 18, -35, 0],\n [21, 16, 28, -24, -27],\n [-7, -9, -9, 16, 29],\n [-3, 28, 4, 7, -74]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-10, 0, 52, 16, -10],\n [1, 2, 32, 20, -20],\n [48, -38, 6, 39, -42],\n [-34, 48, -36, -2, 20],\n [12, -16, -2, 44, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[45, 7, -21, -20, 50],\n [21, -39, -7, 38, -17],\n [24, 30, 10, -26, 23],\n [37, -6, -3, 5, 13],\n [3, 11, 3, -10, 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[[-8, 24, 8, 20, 12],\n [-12, 36, 12, 30, 18],\n [-2, 6, 2, 5, 3],\n [12, -36, -12, -30, -18],\n [-10, 30, 10, 25, 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[[-3, 1, 16, -19, 5],\n [51, -54, 0, 24, -27],\n [1, -22, 8, 28, 15],\n [-48, 38, 14, -18, 36],\n [-60, 74, -4, -42, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[15, 25, -24, 18, -20],\n [-9, -3, 12, -18, 12],\n [-24, -7, -41, 27, -26],\n [-8, 17, 31, -53, 30],\n [-21, 14, -49, 21, -30]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, -10, 1, 9, -13],\n [0, -26, 8, 38, -28],\n [3, -39, 29, 25, -13],\n [-8, 6, -11, 45, -33],\n [18, 26, -24, 18, -9]]\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 5x5 matrix:\n[[-4, 10, 12, 0, 8],\n [-2, 5, 6, 0, 4],\n [12, -30, -36, 0, -24],\n [6, -15, -18, 0, -12],\n [8, -20, -24, 0, -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[[6, 6, -6, 10, 8],\n [-15, -15, 15, -25, -20],\n [-6, -6, 6, -10, -8],\n [-15, -15, 15, -25, -20],\n [-9, -9, 9, -15, -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[[6, -27, -3, -24, 12],\n [-2, -4, 1, -2, 3],\n [6, 25, -3, 16, -16],\n [14, -24, -7, -26, 7],\n [36, -6, -18, -24, -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[[0, 3, 4, -6, -2],\n [6, 3, -1, -3, -4],\n [-8, -8, -4, 12, 8],\n [-8, 4, 12, -12, 0],\n [36, 0, -30, 18, -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[[2, 28, -26, -30, 18],\n [-2, 8, -6, -10, 6],\n [18, 28, -22, -28, 2],\n [0, 24, -2, -37, 0],\n [17, 27, -27, -24, 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[[-18, -15, 27, -6, 0],\n [-24, 0, -24, -48, -20],\n [6, 3, -3, 6, 2],\n [0, 2, -6, -4, -2],\n [-18, -11, 15, -14, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0, 0],\n [-10, 4, 4, -4, -2],\n [0, 0, 0, 0, 0],\n [-10, 4, 4, -4, -2],\n [20, -8, -8, 8, 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[[-8, 14, 47, 4, -47],\n [10, -16, 63, 33, -47],\n [-8, -21, -48, 14, 59],\n [-12, 20, 40, -24, -7],\n [8, -15, 13, 0, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[21, -13, -13, 16, 1],\n [3, 10, 4, -13, -12],\n [-48, 37, 63, 55, -27],\n [7, -34, -6, 5, -32],\n [-22, 20, 34, 36, -16]]\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, 19, 33, 3, 15],\n [-17, 11, 7, -23, -5],\n [2, 25, -9, 3, 20],\n [14, -9, 17, 5, -4],\n [-8, -27, 13, -11, -26]]\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, -10, -33, 38, 6],\n [-21, -7, -8, -29, -19],\n [-44, 25, 38, -40, 4],\n [-8, -47, 17, -11, -71],\n [-43, -3, 65, -33, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[33, 2, 3, -5, -35],\n [16, -26, -12, -2, -4],\n [-20, 7, 2, 31, 16],\n [-21, 3, -54, -27, 6],\n [-6, -24, -32, 4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 24, -8, -16, -24],\n [22, -18, -8, 12, -17],\n [12, -24, -2, 16, -1],\n [16, -24, -4, 16, -6],\n [22, -6, -10, 4, -24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-15, -18, 60, -12, -90],\n [-36, 42, -7, -35, -18],\n [-51, 54, -12, -42, -18],\n [-1, 12, -19, -2, 24],\n [-7, 12, 23, -26, -48]]\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, 3, 5, 0, -4],\n [20, -12, -20, 0, 16],\n [-20, 12, 20, 0, -16],\n [25, -15, -25, 0, 20],\n [-5, 3, 5, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[15, 32, -5, 2, -9],\n [-29, -22, -3, -8, -33],\n [-15, -30, -9, 2, -21],\n [-33, -7, 10, -17, -21],\n [-11, -17, -2, -1, -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[[-23, 6, 28, -22, -29],\n [25, -38, -20, 43, 26],\n [12, 7, -13, -73, 17],\n [5, 14, 22, -1, 8],\n [26, -10, 14, -5, 31]]\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[[-27, -13, -21, -12, 12],\n [28, 12, 16, 22, -26],\n [50, -11, 39, 32, -12],\n [7, 5, -3, 16, -24],\n [17, -15, 19, 5, 13]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[17, -23, 17, 31, 14],\n [15, -6, -34, -21, -17],\n [-15, 34, -18, -47, -15],\n [11, -8, 6, -18, 21],\n [31, 23, 25, -32, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 0, -18, -12, 15],\n [10, 0, 30, 20, -25],\n [-8, 0, -24, -16, 20],\n [0, 0, 0, 0, 0],\n [-8, 0, -24, -16, 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[[-16, 33, 2, -18, 23],\n [9, 13, 16, -17, 23],\n [-54, 13, -18, 24, -21],\n [16, -34, 17, 19, -15],\n [7, -48, 20, 37, -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 5x5 matrix:\n[[0, 0, 0, 0, 0],\n [25, -41, 10, 21, 18],\n [-6, 16, -9, -9, -3],\n [16, -24, 4, 12, 12],\n [-11, -1, 16, 3, -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[[-6, 6, -18, 6, 15],\n [-20, -8, 12, 4, 6],\n [-64, -25, 12, 26, 27],\n [4, -1, -4, 2, -3],\n [6, 15, -36, 6, 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[[0, 0, 0, 0, 0],\n [6, -15, -9, 12, 0],\n [12, -30, -18, 24, 0],\n [-2, 5, 3, -4, 0],\n [12, -30, -18, 24, 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[[-4, 0, 4, 24, 4],\n [5, 0, -5, -30, -5],\n [-2, 0, 2, 12, 2],\n [-1, 0, 1, 6, 1],\n [-4, 0, 4, 24, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[5, 13, 4, 20, 21],\n [9, 41, 22, 0, -27],\n [-8, -20, -3, -26, -18],\n [10, 8, -21, 38, 14],\n [11, 41, 19, 18, -1]]\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, -14, 8, 10, 22],\n [-17, -2, -16, 13, -22],\n [39, 12, 6, -51, -30],\n [13, -12, 4, -33, -24],\n [-40, -3, -9, 60, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[5, -22, -38, -34, 16],\n [-2, -35, 16, 49, 15],\n [-33, -6, 42, -6, -48],\n [-19, -4, 29, 5, -27],\n [-13, -28, 9, 5, -7]]\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[[9, 15, -15, -3, 12],\n [-15, -25, 25, 5, -20],\n [6, 10, -10, -2, 8],\n [-9, -15, 15, 3, -12],\n [-6, -10, 10, 2, -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[[24, -12, 20, 8, 24],\n [-6, 3, -5, -2, -6],\n [-6, 3, -5, -2, -6],\n [24, -12, 20, 8, 24],\n [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, -42, 0, 17, -7],\n [44, -41, -24, -5, -19],\n [-5, 11, 13, -3, 2],\n [10, -7, 6, 27, 16],\n [-15, -1, -15, 5, 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 5x5 matrix:\n[[-12, 18, 14, -4, -9],\n [6, 48, -20, 38, -32],\n [26, -2, 7, -13, -3],\n [15, 9, -14, 40, -24],\n [-33, 29, -60, 22, 19]]\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 5x5 matrix:\n[[-10, -30, -2, 34, 5],\n [-10, -14, 8, -2, 0],\n [11, 30, -12, -23, -12],\n [26, 26, 22, -2, 33],\n [14, 6, 18, 10, 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[[41, -58, 46, 54, -12],\n [-59, 2, -24, -46, 28],\n [-6, 40, 8, -8, 15],\n [3, -6, 10, 18, 10],\n [-24, 18, 20, 11, 45]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-18, -12, -12, 12, 18],\n [-3, -2, -2, 2, 3],\n [3, 2, 2, -2, -3],\n [-12, -8, -8, 8, 12],\n [18, 12, 12, -12, -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[[5, -9, 48, -5, 17],\n [-1, 23, -13, -54, -15],\n [-52, 36, -24, -12, -14],\n [-5, -5, 31, -2, -2],\n [-1, -1, 8, 1, 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, -36, 14, 14, 9],\n [-51, 20, 41, -29, 9],\n [-41, 0, 10, 1, 8],\n [-9, 78, -16, -43, -24],\n [-13, 2, -7, 1, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -4, 14, -16, 60],\n [6, 14, 1, 16, -30],\n [10, 22, 3, 24, -42],\n [-8, -8, -12, 0, -24],\n [-20, -30, -20, -20, 0]]\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[[-7, 8, -8, 7, 4],\n [11, 8, 24, -3, -28],\n [-20, -8, -40, 8, 44],\n [-3, -12, -12, -3, 18],\n [-18, 0, -32, 10, 32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-25, -20, -15, 15, 25],\n [30, 24, 18, -18, -30],\n [20, 16, 12, -12, -20],\n [-30, -24, -18, 18, 30],\n [30, 24, 18, -18, -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[[3, -16, 16, 19, -20],\n [6, -23, 20, 26, -25],\n [-6, 5, 4, -2, -5],\n [6, -20, 16, 22, -20],\n [-6, -10, 24, 18, -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[[-5, 20, -20, 30, 15],\n [-9, 4, -8, -4, 1],\n [14, -24, 28, -26, -16],\n [-25, 36, -44, 34, 23],\n [-9, 4, -8, -4, 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[[-2, 26, 59, -24, 6],\n [-16, -5, 13, -13, -8],\n [-12, -12, -51, 24, -18],\n [-26, 56, 63, -18, -18],\n [-33, 51, 35, -14, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[16, 10, -10, 18, -26],\n [31, 22, -16, 36, -56],\n [22, 12, -16, 24, -32],\n [-19, -4, 22, -18, 14],\n [0, -14, -18, -6, 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[[30, 30, 0, 10, -5],\n [-12, -12, 0, -4, 2],\n [-24, -24, 0, -8, 4],\n [36, 36, 0, 12, -6],\n [36, 36, 0, 12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, 6, 0, -12, -10],\n [-12, 9, 0, -18, -15],\n [-4, 3, 0, -6, -5],\n [-12, 9, 0, -18, -15],\n [8, -6, 0, 12, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[20, 0, 10, 0, 25],\n [20, 0, 10, 0, 25],\n [8, 0, 4, 0, 10],\n [4, 0, 2, 0, 5],\n [-8, 0, -4, 0, -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 5x5 matrix:\n[[-9, 0, 0, 12, -3],\n [-3, 0, 0, 4, -1],\n [3, 0, 0, -4, 1],\n [-3, 0, 0, 4, -1],\n [15, 0, 0, -20, 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[[-1, 12, 1, -21, -16],\n [11, 17, -2, -27, -28],\n [-8, 38, -10, -12, 10],\n [-37, -56, 1, 11, -15],\n [-50, -55, -4, 2, -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 5x5 matrix:\n[[-12, -17, -27, 37, 39],\n [-38, -1, -35, 45, 67],\n [-6, 1, -30, 34, 42],\n [-19, 12, 11, -13, -1],\n [43, -22, 19, -21, -53]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-18, 10, 31, 27, -5],\n [53, -20, 11, -57, -34],\n [10, 36, 35, -1, 6],\n [-10, 4, -1, 11, 6],\n [-47, 24, -19, 49, 40]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[15, 6, 3, -12, 0],\n [20, 8, 4, -16, 0],\n [-15, -6, -3, 12, 0],\n [-5, -2, -1, 4, 0],\n [15, 6, 3, -12, 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[[8, 15, 26, 5, -3],\n [10, 22, 17, -3, 4],\n [-4, 0, -38, -40, 14],\n [-8, -18, -16, 10, -2],\n [-12, -23, -38, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, -11, -13, -7, -29],\n [1, -18, 46, -10, -15],\n [4, 39, 9, 25, 50],\n [-12, -29, 13, -19, 2],\n [9, -13, 9, -7, -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[[-18, -11, 12, 11, 10],\n [-24, 42, 6, -42, -60],\n [18, -23, -6, 23, 34],\n [8, 3, -5, -3, -2],\n [26, -37, -8, 37, 54]]\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, -15, 27, 33, 18],\n [-4, 9, -5, -1, -15],\n [1, -10, 28, 36, 31],\n [5, 8, -5, 0, -28],\n [-25, 15, -3, 3, 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[[24, 18, 12, 6, 6],\n [-8, -6, -4, -2, -2],\n [12, 9, 6, 3, 3],\n [-12, -9, -6, -3, -3],\n [-24, -18, -12, -6, -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[[-41, 70, -26, -4, 19],\n [-27, 40, 8, 23, -18],\n [48, -10, -2, -3, 43],\n [55, -35, 19, 11, 16],\n [45, -15, -9, -13, 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[[19, -5, 13, 33, 38],\n [15, -3, 6, 21, 24],\n [31, -5, 7, 37, 42],\n [12, 6, -33, -28, -34],\n [20, -4, 8, 28, 32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-20, 12, 20, -16, -24],\n [25, -15, -25, 20, 30],\n [0, 0, 0, 0, 0],\n [-25, 15, 25, -20, -30],\n [10, -6, -10, 8, 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[[37, -24, -36, 11, 6],\n [-12, -31, 6, -31, 34],\n [27, -43, -30, -10, 28],\n [-19, 50, 24, 21, -38],\n [6, -46, -12, -28, 40]]\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, -11, -12, -5, 8],\n [-19, -7, 11, -1, 24],\n [5, -19, -20, 0, 25],\n [54, -4, -51, -16, -25],\n [-78, 10, 80, -14, 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[[-13, 3, -13, 12, -26],\n [-11, 6, -16, 14, -22],\n [-30, -18, 6, 0, -60],\n [16, 6, 2, -4, 32],\n [9, 9, -7, 4, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, -4, 9, -25, -10],\n [6, -14, 44, 9, 19],\n [-38, 21, 49, -7, -2],\n [-14, 10, -29, -16, -17],\n [18, 19, 44, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[28, 0, 4, -16, 12],\n [7, -14, -40, 27, 13],\n [30, 4, 16, -26, 10],\n [-33, 4, 7, 10, -17],\n [20, -16, -44, 24, 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[[-5, 10, -5, -5, 15],\n [-1, 2, -1, -1, 3],\n [4, -8, 4, 4, -12],\n [3, -6, 3, 3, -9],\n [5, -10, 5, 5, -15]]\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, 13, -6, -20, 10],\n [9, 11, 24, -25, 2],\n [-1, 9, -18, -10, 10],\n [-5, -7, -12, 15, -2],\n [6, 6, 18, -15, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, 20, -16, -8, -16],\n [-7, -5, -24, 18, -8],\n [-8, -15, 19, 2, 15],\n [17, 20, 19, -28, -1],\n [36, 50, 2, -44, -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[[12, 24, 36, 18, 24],\n [-2, -4, -6, -3, -4],\n [-4, -8, -12, -6, -8],\n [-4, -8, -12, -6, -8],\n [4, 8, 12, 6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, -24, -29, 9, -38],\n [0, 24, 14, 0, 20],\n [-14, -18, 0, -14, -8],\n [36, -48, -34, 30, -28],\n [-5, 27, 9, -2, 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[[0, 0, 0, 0, 0],\n [20, 8, -12, -20, 20],\n [5, 2, -3, -5, 5],\n [-30, -12, 18, 30, -30],\n [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[[-27, 39, -27, 19, -20],\n [-31, 48, -26, 21, -20],\n [5, -17, -26, -2, -9],\n [21, -42, -8, -12, 0],\n [-1, 9, 18, -1, 9]]?\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 5x5 matrix:\n[[17, 9, 5, 23, -11],\n [47, -31, 45, -1, -43],\n [23, -69, 25, -29, -32],\n [-62, 50, -60, -22, 63],\n [2, 20, -12, -43, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[13, -10, -35, 7, 11],\n [-23, -40, -5, 13, -1],\n [33, 15, -42, 0, 15],\n [-33, -15, 42, 0, -15],\n [21, 5, -32, 2, 11]]\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[[17, 4, -3, 19, 21],\n [-12, -1, 3, -14, -15],\n [-13, -45, -18, -1, -12],\n [-30, -18, 0, -30, -36],\n [-5, -34, -15, 5, -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[[-35, -18, 14, -17, 27],\n [1, -12, -4, -8, -12],\n [23, 0, -48, 12, -13],\n [-20, -28, -12, -18, 6],\n [-29, -20, 12, -18, 17]]\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, -24, 4, -8, -20],\n [0, -6, 1, -2, -5],\n [0, -12, 2, -4, -10],\n [0, -6, 1, -2, -5],\n [0, -30, 5, -10, -25]]\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, 20, -40, 0, 12],\n [11, -15, 38, 4, -13],\n [3, 5, -6, 2, 1],\n [4, 0, 4, 2, -2],\n [13, -5, 22, 6, -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[[13, -37, -34, -18, 25],\n [14, -33, -21, 0, 20],\n [24, -24, 2, 2, 20],\n [19, 18, 18, -18, 1],\n [26, 35, 14, -57, 2]]\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, 9, 7, 2, 10],\n [-15, -6, -14, -6, -9],\n [-5, -9, -11, -4, -11],\n [-19, -9, -19, -8, -13],\n [3, -24, -20, -6, -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[[8, 8, -4, 4, -4],\n [-4, -4, 2, -2, 2],\n [-2, -2, 1, -1, 1],\n [-10, -10, 5, -5, 5],\n [6, 6, -3, 3, -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[[-1, -29, -4, 23, -14],\n [4, -31, 0, -12, -1],\n [8, -8, -36, -15, -2],\n [3, 18, 4, -31, 15],\n [9, -27, -24, -24, 0]]?\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, -54, -28, 32, -4],\n [-18, 13, 6, -20, 20],\n [16, -32, 8, 18, -25],\n [20, 4, 16, -4, -38],\n [-12, -15, -46, 36, 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[[26, 30, 45, 7, -30],\n [18, 6, 21, -9, -18],\n [5, -26, -4, 21, 33],\n [-22, -22, -41, -31, 6],\n [-20, 10, -25, -45, -30]]\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[[-12, 27, -30, 18, -12],\n [-8, 18, -20, 12, -8],\n [-19, 50, -55, 33, -22],\n [11, 26, -25, 15, -10],\n [-10, 8, -10, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, -6, 20, 23, -22],\n [6, -12, 15, 21, -19],\n [10, 0, 25, 25, -25],\n [-6, 12, -15, -21, 19],\n [-10, -36, -25, -7, 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[[8, 35, -35, -6, -14],\n [17, 11, -11, -42, -20],\n [2, -14, 14, -12, 0],\n [-5, -30, 30, 0, 10],\n [19, 23, -23, -42, -24]]\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, 36, -18, 36, -30],\n [9, -18, 9, -18, 15],\n [12, -24, 12, -24, 20],\n [-18, 36, -18, 36, -30],\n [-15, 30, -15, 30, -25]]\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 5x5 matrix:\n[[30, 10, -10, 0, -25],\n [18, 6, -6, 0, -15],\n [-36, -12, 12, 0, 30],\n [6, 2, -2, 0, -5],\n [-12, -4, 4, 0, 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[[-24, -24, -24, -18, -18],\n [40, -12, -20, 1, -11],\n [-19, 17, 43, 10, 21],\n [23, -13, -39, -7, -18],\n [11, -54, -64, -28, -43]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, -18, 6, -18, -18],\n [-6, -36, 12, -36, -36],\n [4, 24, -8, 24, 24],\n [6, 36, -12, 36, 36],\n [-4, -24, 8, -24, -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[[0, 0, 0, 0, 0],\n [2, -8, 10, 8, -12],\n [5, -20, 25, 20, -30],\n [-4, 16, -20, -16, 24],\n [-3, 12, -15, -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[[6, 4, -2, 4, -10],\n [18, 12, -6, 12, -30],\n [-18, -12, 6, -12, 30],\n [-9, -6, 3, -6, 15],\n [6, 4, -2, 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 5x5 matrix:\n[[-12, 12, -4, -22, -4],\n [-18, 9, 12, 21, -24],\n [24, -18, -4, 8, 20],\n [12, -6, -8, -14, 16],\n [-18, 10, 10, 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[[4, -29, 8, -48, 36],\n [-16, -7, -23, -6, -12],\n [-22, 12, -24, 24, -38],\n [-1, -1, -6, 0, -1],\n [-27, -7, 17, -18, -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[[13, -41, 1, -3, 14],\n [-6, 30, 18, -6, -12],\n [9, -27, 3, -3, 9],\n [4, 10, 38, -16, -7],\n [-3, -9, -31, 13, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[9, -33, 21, 6, -6],\n [-8, -29, 13, 8, 2],\n [49, 7, 13, -10, -22],\n [-19, -12, 0, 6, 8],\n [-20, -20, 4, 8, 8]]\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[[-12, -12, -4, -4, 10],\n [-6, -6, -2, -2, 5],\n [-30, -30, -10, -10, 25],\n [-24, -24, -8, -8, 20],\n [6, 6, 2, 2, -5]]\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, 62, -2, 8, -40],\n [0, -20, 5, 10, -6],\n [-48, 78, 48, 60, 12],\n [24, 8, -34, -48, 2],\n [35, -33, -29, -32, -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[[24, 36, 12, -13, 31],\n [4, 32, 40, 7, -29],\n [24, 64, 36, 2, 6],\n [20, 7, 16, -30, 15],\n [36, 65, 26, -7, -50]]\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[[30, -18, 6, 14, -8],\n [-5, -30, -23, 38, -28],\n [-10, 12, 2, -12, 8],\n [5, -6, -1, 6, -4],\n [-20, 42, 16, -46, 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[[12, -36, 36, 6, 30],\n [-10, 30, -30, -5, -25],\n [10, -30, 30, 5, 25],\n [10, -30, 30, 5, 25],\n [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[[4, -4, 12, -24, 24],\n [27, 15, -3, 6, -12],\n [14, 0, 14, -28, 26],\n [-2, -5, 8, -16, 17],\n [-19, -9, -1, 2, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[5, -8, -50, -61, 24],\n [-30, -2, -35, -49, 31],\n [0, -4, -34, -44, 17],\n [-15, -14, 1, 26, 17],\n [45, -8, -2, 11, -16]]\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[[-1, -12, 8, 10, 15],\n [44, 27, -32, -36, -5],\n [-1, 31, -9, -28, -42],\n [38, 16, -33, -22, 6],\n [10, 20, -33, -14, -18]]\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, 16, -24, -4, 8],\n [0, -12, 18, 3, -6],\n [0, 4, -6, -1, 2],\n [0, 20, -30, -5, 10],\n [0, -12, 18, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[21, -2, -30, -46, 37],\n [-18, 18, 2, 19, -32],\n [-3, 31, -30, -23, -10],\n [6, 38, 20, 14, -3],\n [57, -64, 24, -39, 57]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-36, 24, 30, 36, 6],\n [-3, -7, 10, 12, 5],\n [9, 3, -15, -18, -6],\n [3, 31, -30, -36, -17],\n [-30, 20, 25, 30, 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[[-19, -1, 23, 0, 3],\n [16, -53, 37, -1, -12],\n [0, -18, 21, 1, -6],\n [-24, 16, 4, -4, 16],\n [-6, -7, 8, -4, 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[[18, 1, 0, 16, -10],\n [37, -50, -6, -65, 16],\n [-30, 21, 29, 46, -9],\n [24, -25, 38, -5, -32],\n [-10, 29, -18, 13, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-15, 5, 25, 10, 30],\n [18, -6, -30, -12, -36],\n [-9, 3, 15, 6, 18],\n [-18, 6, 30, 12, 36],\n [6, -2, -10, -4, -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[[-3, -17, 21, -45, -25],\n [-12, 2, -56, 18, 60],\n [26, -33, -32, -3, -5],\n [34, -5, 32, 21, -55],\n [-21, 31, 67, -45, -40]]\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[[-17, 26, 2, -7, 7],\n [41, -58, 12, 6, -16],\n [-40, 40, -12, -20, 20],\n [10, 28, 12, 30, -14],\n [-20, 42, -7, 10, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 0, 24, -30, 24],\n [2, 0, -8, 10, -8],\n [-1, 0, 4, -5, 4],\n [-6, 0, 24, -30, 24],\n [5, 0, -20, 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[[-9, -12, 12, 6, -12],\n [-36, -8, 0, -12, -28],\n [-27, 17, -26, -25, -4],\n [21, -5, 10, 11, 6],\n [4, -13, 14, 6, -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 5x5 matrix:\n[[-6, -18, 3, 36, 6],\n [11, 6, -19, -30, 1],\n [9, -36, -36, 30, 19],\n [13, 12, -20, -42, -1],\n [-9, -18, 9, 42, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[15, -5, 24, -2, 15],\n [-3, -2, 8, -10, 5],\n [-24, 36, -8, 20, -12],\n [-38, -7, 6, -28, 18],\n [-2, -29, -23, -27, -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[[13, -8, -29, -41, 23],\n [23, 34, 0, -25, 15],\n [-43, -20, -30, 5, -33],\n [11, -46, -2, -3, 25],\n [-20, 22, 36, 46, -36]]?\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, 12, -30, -24, -12],\n [8, 8, -20, -16, -8],\n [6, 6, -15, -12, -6],\n [-10, -10, 25, 20, 10],\n [0, 0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-24, 37, 24, 7, 17],\n [0, 1, 8, 3, -3],\n [3, -3, 10, 4, -7],\n [-6, 13, 36, 13, -7],\n [-12, 18, 8, 2, 10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[21, 48, -41, -60, 22],\n [11, 15, -47, 14, 19],\n [44, 53, -41, -20, 11],\n [-30, 2, 19, -21, 22],\n [6, -29, -58, -27, -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[[-25, 0, -30, -25, 15],\n [5, 0, 6, 5, -3],\n [10, 0, 12, 10, -6],\n [5, 0, 6, 5, -3],\n [-15, 0, -18, -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[[-14, 13, -25, -21, 33],\n [26, 26, 18, -36, 2],\n [5, 20, -6, -15, 4],\n [23, -7, 34, -3, -19],\n [-24, 3, -33, 9, 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[[12, 0, 6, -9, 3],\n [0, 0, 0, 0, 0],\n [4, 0, 2, -3, 1],\n [-16, 0, -8, 12, -4],\n [-8, 0, -4, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-18, -6, -18, 0, 12],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [-9, -3, -9, 0, 6],\n [-9, -3, -9, 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 5x5 matrix:\n[[12, 30, -36, -6, 6],\n [-22, -25, 18, 11, 31],\n [4, -5, 12, -2, -19],\n [-12, -20, 20, 6, 8],\n [-16, -20, 16, 8, 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[[1, 6, -13, -5, -37],\n [-47, 4, -23, -7, 61],\n [-5, 17, 21, 24, 20],\n [-12, -33, -54, -57, 53],\n [67, -13, 49, 14, -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[[-23, -34, 9, -21, -20],\n [16, -67, -13, -14, 13],\n [53, 0, -19, 26, 33],\n [-34, 45, 7, -21, 0],\n [48, -45, -13, 19, 14]]\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[[-8, -10, -2, -6, 0],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [-8, -10, -2, -6, 0],\n [20, 25, 5, 15, 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 5x5 matrix:\n[[-39, 30, 18, -11, -22],\n [21, -21, -9, -4, 10],\n [42, -42, -18, -8, 20],\n [-1, -3, 1, -8, -2],\n [30, -36, -12, -18, 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[[-19, -38, 4, 23, 7],\n [36, -26, -28, -16, 14],\n [-33, 20, 16, 17, -17],\n [14, 35, 20, -22, 6],\n [-44, -38, -30, 42, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[7, 13, -45, -26, -8],\n [-6, -21, -14, -4, -26],\n [5, 11, -23, -14, 0],\n [-15, -42, 21, 18, -30],\n [-1, -7, -21, -10, -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[[-9, -4, 7, -5, 41],\n [-20, 4, 26, 14, -3],\n [34, -19, -3, -32, 5],\n [19, 20, -10, -39, 23],\n [-23, 51, 18, -37, 82]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[25, 58, 13, -47, -37],\n [17, 22, -1, -29, -39],\n [6, 24, 29, -13, -5],\n [22, 54, -20, -46, -60],\n [15, 40, 12, -32, -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[[-18, 57, 3, 36, 25],\n [34, -5, -15, 16, 15],\n [-48, 42, 18, 6, 0],\n [34, -35, 11, -8, -7],\n [30, 3, 21, 21, 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 5x5 matrix:\n[[-36, -9, 26, 29, 24],\n [29, 6, -10, -24, -30],\n [1, 4, -10, -11, -35],\n [-32, -30, 44, 34, 60],\n [26, 15, -30, -24, -29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-14, 22, 2, 4, 23],\n [-35, 0, 19, 22, 27],\n [-3, 3, 9, -6, 12],\n [-30, -46, 2, 52, -28],\n [23, 13, 3, -34, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[38, 17, -5, -39, -53],\n [10, -38, 20, -9, 27],\n [2, 39, -11, 8, 12],\n [-20, 13, -11, 22, -8],\n [5, -4, -2, -30, -33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[11, 4, -27, 24, 4],\n [-36, 1, -12, 27, 26],\n [-28, -8, -9, 15, 4],\n [51, 18, 9, -18, 0],\n [7, 3, 24, -24, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, 24, 22, -32, 1],\n [9, -18, -40, 41, 8],\n [39, 3, -36, 13, 16],\n [-7, 19, 0, -3, 6],\n [9, -24, 22, -18, -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[[-11, -44, 33, -29, -10],\n [31, -41, 30, -34, -19],\n [50, -36, 28, -34, -16],\n [50, -24, 22, -26, -4],\n [-46, -14, 11, -2, 6]]\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, 36, -30, -30, 34],\n [-7, 1, -9, 5, 6],\n [19, -13, 33, -5, -26],\n [-3, 21, -21, -15, 22],\n [-6, 6, -12, 0, 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[[0, 0, 0, 0, 0],\n [8, 4, 8, -12, 0],\n [0, 0, 0, 0, 0],\n [24, 12, 24, -36, 0],\n [-20, -10, -20, 30, 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 5x5 matrix:\n[[-6, 11, 7, 6, 13],\n [72, 39, 69, -10, -26],\n [-4, 2, -24, 34, -20],\n [35, -11, 13, -24, -29],\n [4, 6, 37, 17, 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[[-28, -5, 7, 45, -19],\n [-3, 36, -17, 12, -1],\n [-31, 4, -3, 8, -33],\n [-15, -18, 6, -16, -21],\n [-20, -49, 22, -13, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[24, 0, 30, -36, -12],\n [-4, -6, -7, 6, 2],\n [24, -30, 20, -36, -12],\n [-4, -18, -11, 6, 2],\n [28, -6, 33, -42, -14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, 15, -18, 15, 3],\n [-4, 10, -12, 10, 2],\n [4, -10, 12, -10, -2],\n [8, -20, 24, -20, -4],\n [-6, 15, -18, 15, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-22, -3, 13, 1, 20],\n [0, -5, 7, 9, 4],\n [8, -8, 8, 16, 0],\n [-22, -3, 13, 1, 20],\n [8, 2, -6, -2, -8]]\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, 5, 18, -24, 31],\n [16, -25, 52, -2, -25],\n [4, 6, 73, -23, -4],\n [-17, 2, -54, 14, 11],\n [21, -50, -13, 19, -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[[-14, 4, 12, 14, 4],\n [-11, 27, 21, -28, -14],\n [-5, 11, 48, -36, -15],\n [-22, 24, -48, 42, 12],\n [-13, -6, -3, 35, 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 5x5 matrix:\n[[-3, 1, -5, 0, -2],\n [18, -6, 30, 0, 12],\n [12, -4, 20, 0, 8],\n [-9, 3, -15, 0, -6],\n [6, -2, 10, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-10, 29, 18, 46, 20],\n [-33, -14, -42, 14, 23],\n [-1, -43, -10, -22, -36],\n [-20, -8, -55, -12, 32],\n [15, 17, 54, 18, -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[[-6, 3, -5, -24, -9],\n [-18, 30, -22, -9, -6],\n [-4, 10, -6, 8, 2],\n [18, -27, 21, 18, 9],\n [12, -18, 14, 12, 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[[-23, 20, 2, 19, 16],\n [-30, 24, 0, 24, -3],\n [1, 12, 2, 11, -32],\n [9, -8, 2, -9, 30],\n [-40, 52, 8, 48, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-46, 6, -19, 33, 16],\n [14, 37, 40, 15, -26],\n [0, -30, -33, -33, 30],\n [34, -3, 32, 7, -46],\n [-21, 12, -7, 13, 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[[5, -3, 0, 4, 4],\n [-15, 9, 0, -12, -12],\n [10, -6, 0, 8, 8],\n [-10, 6, 0, -8, -8],\n [-30, 18, 0, -24, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-24, 24, 24, -12, -18],\n [-16, 16, 16, -8, -12],\n [-24, 24, 24, -12, -18],\n [-24, 24, 24, -12, -18],\n [16, -16, -16, 8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-27, -35, -18, -3, -4],\n [-26, -19, -52, 9, 44],\n [-55, -43, -26, 21, 12],\n [56, 39, 24, -26, -15],\n [-6, 15, 20, 22, 1]]?\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[[29, -18, -7, 8, 3],\n [9, -18, -23, -46, 20],\n [-35, -12, -7, 12, 16],\n [-14, -12, -32, 22, 4],\n [-45, 0, -5, -10, 15]]\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[[-15, -9, 9, -15, -3],\n [24, 15, 2, 1, -4],\n [35, 46, -19, 38, -33],\n [-10, -33, -2, -5, 44],\n [-8, 2, -4, 6, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 43, 45, -18, 75],\n [47, 37, 33, -22, 25],\n [45, 5, -3, 6, -35],\n [5, -41, -45, 6, -69],\n [-11, 2, 12, 52, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 18, -3, 18, -6],\n [0, -36, 6, -36, 12],\n [0, 24, -4, 24, -8],\n [0, 18, -3, 18, -6],\n [0, -30, 5, -30, 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[[29, 13, -15, 9, 38],\n [-29, 20, 40, -11, -30],\n [0, 60, 6, 20, 4],\n [-7, -8, -17, 9, -16],\n [-56, 5, 43, -24, -53]]\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 5x5 matrix:\n[[-22, -5, 9, -9, 6],\n [14, -8, -41, -16, 14],\n [-6, 25, 2, -9, 25],\n [8, 0, -26, -12, 14],\n [10, -37, -22, 1, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-46, -2, -8, -40, -8],\n [-9, 45, 31, 0, 39],\n [46, 18, 14, 32, 22],\n [-22, 6, -6, -32, 2],\n [24, 27, 16, 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[[21, 13, -14, 1, -26],\n [61, -36, -48, 44, 11],\n [43, -3, -29, 16, -5],\n [19, -31, -12, 27, -6],\n [-6, -45, -15, 37, -19]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-20, 8, 16, -8, 24],\n [-10, 4, 8, -4, 12],\n [-10, 4, 8, -4, 12],\n [-10, 4, 8, -4, 12],\n [-20, 8, 16, -8, 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 5x5 matrix:\n[[-20, 25, 25, 45, -38],\n [-4, -35, -2, -11, -7],\n [-7, -66, -5, -35, -19],\n [-9, -22, 5, -5, -21],\n [4, -46, -12, -26, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, -4, 16, 12, -20],\n [6, 2, -8, -6, 10],\n [15, 5, -20, -15, 25],\n [-6, -2, 8, 6, -10],\n [-6, -2, 8, 6, -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[[46, 15, 7, -17, -33],\n [-38, -5, -21, -31, 1],\n [18, -2, 14, 25, 6],\n [-4, 2, 17, 45, 34],\n [4, -2, -6, -10, -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[[44, -1, -19, -11, -14],\n [43, -23, -15, 3, -7],\n [46, -62, 18, 6, 2],\n [13, -49, 27, 9, 9],\n [21, 2, -16, -2, -7]]\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, -12, 18, 0, 18],\n [4, 8, -12, 0, -12],\n [5, 10, -15, 0, -15],\n [-4, -8, 12, 0, 12],\n [-4, -8, 12, 0, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-10, 0, 0, -12, 6],\n [20, 0, 0, 24, -12],\n [30, 0, 0, 36, -18],\n [20, 0, 0, 24, -12],\n [-5, 0, 0, -6, 3]]\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[[1, 5, -13, 7, -15],\n [5, 38, 0, -17, 3],\n [-9, 30, 0, -9, -3],\n [-3, 13, 15, -15, 17],\n [-13, -26, 36, -11, 37]]\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, -27, -16, 38, -41],\n [21, -10, -20, 32, -51],\n [-55, -31, 32, -10, -4],\n [-39, -13, 10, -10, -35],\n [-12, -26, -14, 30, -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[[36, 2, -54, -32, 12],\n [-30, 15, -1, 18, -6],\n [-24, 18, -13, 20, 1],\n [18, -5, -5, -2, 10],\n [6, -5, 4, -6, -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[[30, -15, 25, 5, -20],\n [30, -15, 25, 5, -20],\n [-12, 6, -10, -2, 8],\n [-36, 18, -30, -6, 24],\n [36, -18, 30, 6, -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 5x5 matrix:\n[[-4, 0, 8, -6, -8],\n [-4, 0, 8, -6, -8],\n [-6, 0, 12, -9, -12],\n [2, 0, -4, 3, 4],\n [10, 0, -20, 15, 20]]\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[[-3, 9, -24, 12, 6],\n [44, 20, 16, 0, -24],\n [-66, -30, -24, 0, 36],\n [-54, -28, -12, -4, 28],\n [29, 8, 22, -6, -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 5x5 matrix:\n[[18, 10, 6, -4, 10],\n [-9, -9, -24, 6, -9],\n [40, 36, 18, -2, 17],\n [37, 1, 10, -16, 30],\n [19, 23, 18, 0, 8]]\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[[50, 18, 7, 39, 24],\n [16, -15, 9, 12, 11],\n [-26, 31, 20, 16, 17],\n [6, -32, -19, -38, -24],\n [-4, 39, -7, 9, -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[[6, -8, 2, -4, -12],\n [21, -15, 18, 6, -30],\n [-2, -19, -19, -32, -16],\n [10, 4, 18, 20, -4],\n [1, 3, 4, 6, 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[[14, 4, 10, -16, 3],\n [8, 6, 10, -10, 2],\n [-2, 18, 20, -2, 1],\n [20, 2, 10, -22, 4],\n [-12, 4, 0, 12, -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[[-2, -3, -19, -20, 50],\n [-33, -12, 6, 6, -6],\n [-10, -19, 36, 31, -34],\n [-11, 4, -2, -12, 32],\n [-43, -27, 29, 22, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[5, -6, 10, 26, -8],\n [-40, -15, -17, -28, 46],\n [9, 9, 21, 38, -31],\n [-15, 3, -3, -10, 8],\n [8, 18, 10, 8, -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[[-36, 11, -11, 27, -9],\n [48, -13, 9, -36, 17],\n [30, -3, 11, -18, 11],\n [27, -22, 36, -24, -22],\n [-24, 14, -30, 18, 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[[-12, 6, 12, 4, 10],\n [-36, 18, 36, 12, 30],\n [18, -9, -18, -6, -15],\n [0, 0, 0, 0, 0],\n [-6, 3, 6, 2, 5]]\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, -30, -5, -25, 5],\n [18, 18, 3, 15, -3],\n [-30, -30, -5, -25, 5],\n [-18, -18, -3, -15, 3],\n [36, 36, 6, 30, -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[[-30, 10, 30, 20, -5],\n [-30, 10, 30, 20, -5],\n [-12, 4, 12, 8, -2],\n [36, -12, -36, -24, 6],\n [-30, 10, 30, 20, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-17, -13, -12, -51, 32],\n [-42, 26, -12, -16, 12],\n [30, -16, 11, 6, -7],\n [-24, 32, -21, 1, 13],\n [40, -28, 26, 8, -18]]\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[[-15, 25, 10, -29, 12],\n [9, -15, 17, -1, 2],\n [-3, 5, -4, -1, 0],\n [15, -25, 40, -11, 8],\n [-9, 15, -17, 1, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[3, 18, -5, -2, 8],\n [18, -12, 25, 23, 8],\n [-19, 6, -10, -9, -24],\n [-30, 12, -34, -32, -20],\n [-10, -36, -5, -11, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[17, 11, 21, -7, -18],\n [-40, 5, 13, -10, 20],\n [-21, -21, -33, 15, 24],\n [21, -7, -12, 9, -9],\n [27, 1, 3, 3, -18]]\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],\n [-2, -3, -4, 2, 0],\n [-12, -18, -24, 12, 0],\n [8, 12, 16, -8, 0],\n [-6, -9, -12, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-16, 26, -18, 6, -24],\n [-7, 8, -5, -2, -16],\n [-3, -8, 7, -6, -2],\n [11, -3, 0, 11, 29],\n [27, -14, 7, -6, 7]]\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[[-39, 6, 6, -23, -33],\n [-4, -14, -4, -18, 22],\n [-47, -19, -20, -10, -25],\n [-26, -12, -12, -6, -12],\n [15, 17, 16, 0, -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[[0, 0, 0, 0, 0],\n [-5, 3, -6, -4, -2],\n [-25, 15, -30, -20, -10],\n [10, -6, 12, 8, 4],\n [-5, 3, -6, -4, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-20, -20, -25, -30, 10],\n [12, 12, 15, 18, -6],\n [-8, -8, -10, -12, 4],\n [12, 12, 15, 18, -6],\n [-24, -24, -30, -36, 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[[-52, -28, 32, -26, 32],\n [12, -2, -2, -3, -17],\n [-32, -50, -13, 1, 36],\n [62, 66, -22, 20, -73],\n [-26, -36, -6, 5, 50]]\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, 36, 0, -6],\n [12, 6, -12, 0, 2],\n [12, 6, -12, 0, 2],\n [18, 9, -18, 0, 3],\n [18, 9, -18, 0, 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[[27, -3, 9, 9, -12],\n [-25, 5, -7, 5, 20],\n [21, -4, 6, -3, -16],\n [5, -5, -1, -25, -20],\n [54, -6, 18, 18, -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 5x5 matrix:\n[[-15, 25, 36, -9, 25],\n [-20, 31, 44, -10, 31],\n [3, 9, -4, 9, 17],\n [-20, -4, 10, -4, -14],\n [32, -16, -31, 4, -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 5x5 matrix:\n[[24, -19, -7, -7, 23],\n [0, 5, 11, 2, -13],\n [4, 21, 43, -2, -17],\n [0, -3, -3, 3, -9],\n [-17, 30, 34, 3, -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 5x5 matrix:\n[[30, 28, 6, -12, 26],\n [21, 30, 13, -10, 27],\n [33, -3, -22, -8, 0],\n [24, -14, -26, -4, -10],\n [-45, 10, 35, 10, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[13, -3, -1, 3, -36],\n [20, -8, 10, -26, -11],\n [-19, 3, 39, -21, 52],\n [9, 17, -35, 41, -23],\n [15, 2, -15, 9, -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[[-15, -9, 18, 9, 12],\n [35, -3, 12, -15, 8],\n [-33, 29, 23, 16, 10],\n [-6, -17, 49, 8, 32],\n [-5, -32, 13, 5, 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[[-16, -14, 32, -8, -54],\n [5, 4, 12, -28, 66],\n [-47, -64, -2, -11, -35],\n [-10, -10, -22, 8, -20],\n [8, -20, 20, 41, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[10, -8, 10, -2, 4],\n [-4, 33, -23, 0, -4],\n [-4, 23, -13, 26, 20],\n [-8, -12, 4, 4, 0],\n [9, 0, 3, -12, -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[[36, 0, 30, 12, -12],\n [6, 0, 5, 2, -2],\n [-36, 0, -30, -12, 12],\n [-18, 0, -15, -6, 6],\n [24, 0, 20, 8, -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[[-19, 1, 12, 28, -12],\n [-38, -23, 9, 2, -28],\n [-5, 20, 15, 50, 0],\n [5, 5, 0, 4, 4],\n [0, 0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[36, 30, -9, -19, -21],\n [45, 34, -19, 3, -51],\n [-10, -10, -1, 18, -6],\n [20, 14, -49, 13, -21],\n [-16, -14, 9, 13, 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[[31, -15, 33, -7, -76],\n [10, -20, -20, 3, 3],\n [14, -22, 16, 0, -71],\n [64, -6, 34, -13, -31],\n [-23, 21, 4, -1, 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[[-6, -12, 18, 13, -4],\n [26, -16, -18, -21, 4],\n [-18, -7, 40, 22, 22],\n [-41, 11, 26, 43, 18],\n [-2, -13, 2, 11, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[22, 6, 46, 16, -34],\n [20, 30, -25, 20, -5],\n [-24, -18, -19, -20, 25],\n [-12, 0, -34, -8, 22],\n [-4, -24, 54, -8, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[23, 19, 67, -36, -41],\n [55, 57, 13, 3, -17],\n [14, 22, 28, -38, -36],\n [-5, 3, 55, 30, -2],\n [-26, -50, -42, -40, 10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-18, -30, -6, -30, 12],\n [3, 5, 1, 5, -2],\n [15, 25, 5, 25, -10],\n [3, 5, 1, 5, -2],\n [-6, -10, -2, -10, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1, -3, -16, 2, 1],\n [11, 8, 41, -27, -26],\n [-2, 29, 4, 2, -4],\n [9, -12, 15, -21, -18],\n [2, 33, -16, -10, -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[[38, 32, -38, 32, 34],\n [20, 10, 10, -10, 15],\n [-4, -4, 16, -12, 10],\n [24, 24, -36, 32, 30],\n [-27, -22, 21, -18, -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 5x5 matrix:\n[[-29, 5, -2, 41, -20],\n [-3, -13, -30, 7, 20],\n [-12, -2, -12, 32, -8],\n [26, 3, 17, -30, 2],\n [16, -20, -38, -12, 36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-36, -6, -42, -7, -18],\n [-79, -6, -60, -27, -49],\n [31, 53, -32, -19, -3],\n [16, 19, -5, 26, 50],\n [-18, 8, -7, -33, -46]]\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, -11, 43, -32, -19],\n [-10, 35, 35, -30, -20],\n [1, -13, -22, 16, -16],\n [7, -37, 8, -4, -16],\n [14, -66, -21, 20, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -1, -9, 12, 13],\n [0, 1, 2, -1, -1],\n [3, 4, 4, -5, -1],\n [-29, -32, -16, 27, -13],\n [31, 30, 7, -22, 21]]\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[[42, 72, 24, -4, 26],\n [20, -12, 38, -26, -32],\n [-30, -24, -27, -11, 11],\n [-2, -30, 10, 6, -29],\n [15, 24, 21, -57, 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 5x5 matrix:\n[[-1, 0, 34, 2, 43],\n [6, 8, -6, -71, -8],\n [5, -36, 36, 43, -9],\n [13, 8, -28, 54, -17],\n [16, 4, 14, -29, 14]]\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, 5, 10, 6, 1],\n [30, 30, 30, 0, 24],\n [-30, -30, -5, 30, -39],\n [10, 10, 10, 0, 8],\n [-30, -30, 0, 36, -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[[-12, -6, -8, -2, -6],\n [-44, 56, -12, -16, -22],\n [0, -9, -2, 1, 0],\n [-4, 19, 2, -3, -2],\n [36, -54, 8, 14, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -4, -1, -3, 6],\n [20, -20, -5, -15, 30],\n [4, -4, -1, -3, 6],\n [-12, 12, 3, 9, -18],\n [-12, 12, 3, 9, -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[[-4, -4, -10, -4, -2],\n [-16, 0, -18, -14, 0],\n [-18, 22, 10, -13, 11],\n [8, -24, -24, 4, -12],\n [12, -12, -3, 9, -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[[-5, -9, 67, -16, 4],\n [20, -40, 4, -34, 30],\n [-9, 32, -7, 5, -15],\n [20, -24, -4, 20, 4],\n [13, 10, 41, 47, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-32, 6, -2, -20, -1],\n [-47, 20, 24, -2, 18],\n [-57, -38, 52, 7, 5],\n [-1, 37, -1, 2, 20],\n [-5, -46, 40, 27, -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[[-6, 1, -1, 0, 6],\n [12, -2, 2, 0, -12],\n [12, -2, 2, 0, -12],\n [12, -2, 2, 0, -12],\n [18, -3, 3, 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[[6, -6, 6, 6, -1],\n [12, -12, 12, 12, -2],\n [-6, 6, -6, -6, 1],\n [6, -6, 6, 6, -1],\n [-30, 30, -30, -30, 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 5x5 matrix:\n[[25, -39, -33, -17, 11],\n [17, -45, -9, 29, -26],\n [18, -28, -17, -28, 23],\n [-8, -12, 42, 28, -18],\n [-25, 45, 36, -13, 16]]\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[[-2, -22, 16, 2, -6],\n [-23, -16, 29, 51, 32],\n [-1, 11, -17, -31, -13],\n [-40, 24, -23, -5, 12],\n [-42, 4, -5, 4, 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[[12, -12, 9, 18, 3],\n [-12, 12, -9, -18, -3],\n [8, -8, 6, 12, 2],\n [24, -24, 18, 36, 6],\n [-16, 16, -12, -24, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 4, 12, -8, 12],\n [9, -16, -6, -22, 12],\n [-6, -6, 24, -42, 42],\n [-7, -2, 22, -32, 34],\n [16, -9, -34, 27, -37]]\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, -54, 3, -12, 24],\n [19, 66, -8, 2, -28],\n [11, -46, -7, -32, -2],\n [-35, -30, 19, 36, 41],\n [20, 40, -16, -24, -44]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-36, -36, 12, 6, -12],\n [-24, -24, 8, 4, -8],\n [12, 12, -4, -2, 4],\n [30, 30, -10, -5, 10],\n [-12, -12, 4, 2, -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[[-2, 4, -8, -8, 10],\n [-3, 6, -12, -12, 15],\n [2, -4, 8, 8, -10],\n [1, -2, 4, 4, -5],\n [-6, 12, -24, -24, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[13, -5, 23, -24, 20],\n [-10, 29, -23, -15, 19],\n [3, 46, -18, -1, 29],\n [-18, -28, -16, 37, -50],\n [20, 42, 10, -28, 54]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-39, -10, -27, -29, 9],\n [16, 64, -16, 34, -20],\n [-10, -9, -7, -10, -8],\n [-42, -49, -15, -41, -10],\n [-3, -12, 3, -3, -9]]\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, -30, 24, -36, -30],\n [30, 17, 32, 42, 23],\n [-25, 0, -38, -18, -5],\n [-25, -20, -22, -42, -25],\n [-10, 21, -32, 18, 19]]\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[[23, -18, 23, 25, -4],\n [9, -11, -5, 26, -44],\n [-40, 25, -45, -49, 46],\n [-24, 12, -48, -36, 63],\n [-30, 20, -21, -44, 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 5x5 matrix:\n[[23, -6, 12, 52, 8],\n [-19, 24, -19, -20, 8],\n [-64, 20, 18, -12, -36],\n [7, -3, 6, 16, -1],\n [-4, -10, -3, -18, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[48, 0, -12, -12, 24],\n [-20, 18, -4, 14, -10],\n [-20, 6, 2, 8, -10],\n [0, -60, 30, -30, 0],\n [-40, 0, 10, 10, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[18, 36, -38, 15, 14],\n [-21, -10, -2, -49, 13],\n [-34, -28, 48, -4, 8],\n [30, 2, -34, -28, -28],\n [-15, -24, 8, -69, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[10, -6, -42, -44, -14],\n [-19, 37, 19, 26, 17],\n [-15, 33, 6, 12, 12],\n [16, -40, 5, -2, -11],\n [17, -39, -3, -10, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 12, 18, 4, -18],\n [8, -41, -14, 15, 26],\n [12, -3, 33, 18, -24],\n [8, -1, 16, 7, -12],\n [28, -20, 20, 11, -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 5x5 matrix:\n[[1, 18, -23, 31, -15],\n [-3, 22, 14, 13, -7],\n [6, -12, -24, -2, -7],\n [12, -32, 6, -24, 17],\n [-10, 2, -33, 26, 6]]\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[[17, 5, -12, -7, 12],\n [73, 49, -36, -59, 60],\n [-45, -42, 15, 52, -46],\n [-12, -12, 2, 24, -28],\n [50, 35, -23, -47, 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[[-4, -12, -12, 6, 10],\n [8, 24, 24, -12, -20],\n [8, 24, 24, -12, -20],\n [8, 24, 24, -12, -20],\n [-4, -12, -12, 6, 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[[31, -36, 35, -43, 15],\n [-13, 22, 3, 23, 25],\n [-23, 30, -27, 39, -3],\n [32, -54, 36, -78, -30],\n [18, -21, 42, -36, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, -6, 24, -12, -36],\n [-4, -4, 16, -8, -24],\n [-3, -3, 12, -6, -18],\n [-2, -2, 8, -4, -12],\n [-3, -3, 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 5x5 matrix:\n[[0, 0, 0, 0, 0],\n [24, 54, 12, 42, -12],\n [17, 27, 16, 32, -1],\n [10, 0, 20, 22, 10],\n [15, 30, 10, 27, -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[[-4, 11, -16, -14, -11],\n [-2, -17, 17, 13, 12],\n [-24, -33, 14, 4, 11],\n [-40, -25, -10, -20, -5],\n [0, 9, -10, -8, -7]]\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, -6, -42, -60, -30],\n [2, 4, 8, 15, 5],\n [19, 11, -23, -15, -20],\n [32, 22, -26, -5, -25],\n [-32, -22, 26, 5, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-36, 2, 19, 3, 39],\n [-7, 34, -2, -41, -15],\n [23, -6, -19, -28, -18],\n [19, -13, -24, -11, 3],\n [-56, 19, 48, 53, 36]]\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 5x5 matrix:\n[[1, 8, -20, 22, 19],\n [1, 30, -30, 39, 14],\n [-5, -29, -1, 9, 10],\n [1, -12, -18, 11, 49],\n [-22, 18, -6, 58, 32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-25, -17, 23, -9, 12],\n [16, 14, -10, 18, 22],\n [10, -31, 14, 0, 1],\n [-36, -10, 24, -12, 14],\n [-4, 23, -11, 3, 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[[2, -8, 10, -6, 12],\n [-1, -14, 3, -3, 4],\n [-4, -2, -12, 6, -14],\n [7, -19, 31, -18, 37],\n [-3, -6, -7, 3, -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[[10, -31, 13, -23, 4],\n [1, -7, 13, -1, 16],\n [1, -10, 22, 0, 28],\n [11, -32, 8, -26, -4],\n [-3, 9, -3, 7, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, -12, -12, 18, 0],\n [0, 0, 0, 0, 0],\n [-20, -20, -20, 30, 0],\n [8, 8, 8, -12, 0],\n [-8, -8, -8, 12, 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[[-7, -21, -30, 24, 14],\n [8, 19, 33, -18, -23],\n [-7, 7, -8, 60, -6],\n [10, 8, 31, -30, -26],\n [2, 10, 13, 6, -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[[36, 12, -4, 12, -9],\n [0, -46, -38, -10, -41],\n [81, 0, -24, 27, -36],\n [15, -18, -2, 15, -3],\n [-25, -20, -12, -15, -10]]\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, -60, 0, 3, 7],\n [-8, 46, 26, -14, 2],\n [-9, -27, 3, 0, 4],\n [18, -36, -36, 18, -6],\n [39, 12, -48, 21, -15]]\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, -24, 18, 34, -29],\n [16, 16, -40, -32, 24],\n [-17, -20, 32, 34, -27],\n [7, 20, -44, -30, 25],\n [-6, -12, 30, 20, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-10, 11, 10, -11, -22],\n [11, 2, 8, 20, 26],\n [9, -33, -33, 6, 21],\n [7, -17, -1, 26, 25],\n [-12, -12, -2, -2, -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[[-24, -6, 6, 18, -6],\n [12, 3, -3, -9, 3],\n [6, 9, 9, 3, -15],\n [-26, -9, 3, 17, -1],\n [34, 16, 2, -18, -8]]?\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[[-31, -66, -46, -27, -7],\n [-22, 23, 24, -59, -6],\n [-18, -28, 0, 10, 40],\n [33, 17, 2, 36, 11],\n [4, -26, -20, 2, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 4, -12, 24, -12],\n [4, 4, -12, 24, -12],\n [-1, -1, 3, -6, 3],\n [1, 1, -3, 6, -3],\n [-1, -1, 3, -6, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[24, -13, -28, 24, -36],\n [-37, 19, 0, 17, 9],\n [36, 6, 0, -36, 36],\n [24, -14, -3, -6, -12],\n [-35, 23, 9, 1, 27]]\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[[-7, -10, 2, -12, 0],\n [1, -2, 10, 0, -24],\n [-3, 0, -12, -3, 30],\n [15, 16, 12, 23, -38],\n [16, 20, 4, 26, -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[[21, 30, 51, 31, -47],\n [11, 8, 48, 36, -46],\n [0, -3, 43, 27, -30],\n [-6, 10, -44, -27, 29],\n [2, 51, -17, -10, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-36, -6, -18, 0, 18],\n [36, 6, 18, 0, -18],\n [18, 3, 9, 0, -9],\n [-30, -5, -15, 0, 15],\n [-24, -4, -12, 0, 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[[25, 20, -25, 30, 20],\n [20, 16, -20, 24, 16],\n [10, 8, -10, 12, 8],\n [0, 0, 0, 0, 0],\n [-30, -24, 30, -36, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-28, -18, 40, 46, -30],\n [-32, -26, 8, -24, -3],\n [-26, -39, 20, 37, -7],\n [25, 26, -14, 12, 3],\n [-20, 10, 40, 14, -36]]\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 5x5 matrix:\n[[6, -11, -21, -1, -35],\n [-5, 25, 5, 14, -29],\n [-13, 46, -6, 0, 17],\n [-6, 21, 1, -18, 32],\n [2, -12, -12, 15, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, -6, -3, 9, -18],\n [8, 12, 1, 3, -48],\n [-10, -14, -12, 22, -16],\n [-14, -42, 9, 13, -40],\n [14, 20, 10, -14, -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 5x5 matrix:\n[[-4, 3, -3, 5, -6],\n [-12, 9, -9, 15, -18],\n [-20, 15, -15, 25, -30],\n [0, 0, 0, 0, 0],\n [8, -6, 6, -10, 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 5x5 matrix:\n[[5, 15, 10, 30, 5],\n [-3, -9, -6, -18, -3],\n [6, 18, 12, 36, 6],\n [1, 3, 2, 6, 1],\n [4, 12, 8, 24, 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[[24, -24, 0, 12, -15],\n [34, -31, 9, 23, -13],\n [-32, 28, -12, -24, 9],\n [14, -13, 3, 9, -6],\n [-18, 19, 3, -7, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-41, 29, 3, 45, -47],\n [5, -20, 20, -39, 7],\n [-9, -48, -54, -63, 3],\n [-42, 4, -11, 9, -43],\n [-25, -13, -43, -21, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-15, -5, 32, 27, 9],\n [20, 16, -14, 11, 5],\n [15, 1, -28, -20, 0],\n [30, 22, -22, 15, 9],\n [5, 23, 18, 37, -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 5x5 matrix:\n[[6, 3, 0, -3, 4],\n [0, 0, 0, 0, 0],\n [18, 9, 0, -9, 12],\n [-30, -15, 0, 15, -20],\n [-6, -3, 0, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[24, 4, 20, -14, -18],\n [-30, 16, -25, 21, 33],\n [-6, 26, -5, 8, 18],\n [0, 6, 0, 1, 3],\n [0, 24, 0, 4, 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[[-3, 3, 18, -15, 0],\n [-9, 29, 54, 5, 30],\n [1, 3, -6, 15, 6],\n [0, 4, 0, 10, 6],\n [0, 4, 0, 10, 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[[4, -20, 20, 16, 0],\n [-5, 25, -25, -20, 0],\n [-2, 10, -10, -8, 0],\n [-3, 15, -15, -12, 0],\n [-4, 20, -20, -16, 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 5x5 matrix:\n[[-1, -6, 4, -6, 1],\n [-3, -18, 12, -18, 3],\n [2, 12, -8, 12, -2],\n [3, 18, -12, 18, -3],\n [-1, -6, 4, -6, 1]]\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 5x5 matrix:\n[[26, 22, 2, -12, 4],\n [30, 18, 0, -30, 6],\n [-17, -7, 1, 24, -4],\n [-9, -15, -3, -12, 0],\n [12, -12, -6, -54, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, -13, -3, 22, -8],\n [17, -45, 20, 17, 5],\n [-70, 14, -27, 0, 31],\n [76, -34, 12, 11, -44],\n [-31, 32, 29, 24, 27]]\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, -35, 24, 18, 14],\n [0, -1, 30, 9, -5],\n [0, -16, -14, 1, 11],\n [0, -2, -16, -4, 4],\n [0, 1, 8, 2, -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[[-5, -15, -13, 11, 6],\n [-14, -32, -40, 21, 16],\n [14, -44, 8, 7, 36],\n [12, -3, -12, -33, 33],\n [-15, -40, -9, 53, -7]]\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, -5, -8, 13, 6],\n [-4, -30, -27, 15, 36],\n [8, -10, -16, 26, 12],\n [-24, -35, -17, -26, 42],\n [-12, 5, 14, -31, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-11, 7, 10, -18, 8],\n [28, 2, -24, 30, 8],\n [47, 16, -54, 49, 40],\n [-10, 4, -12, -2, 16],\n [-1, -1, 17, -10, -11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 0, -16, 24, -12],\n [9, 0, -12, 18, -9],\n [3, 0, -4, 6, -3],\n [12, 0, -16, 24, -12],\n [-3, 0, 4, -6, 3]]\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[[4, 6, -12, -10, 10],\n [-10, -15, 30, 25, -25],\n [4, 6, -12, -10, 10],\n [-10, -15, 30, 25, -25],\n [-12, -18, 36, 30, -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[[3, 41, -22, -1, -1],\n [-19, 24, -21, -6, 31],\n [-13, 37, -26, -5, 23],\n [0, 46, -26, -2, 4],\n [2, -11, 7, 1, -4]]?\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, 0, 0, 0, 0],\n [25, -20, 5, 15, 0],\n [25, -20, 5, 15, 0],\n [5, -4, 1, 3, 0],\n [10, -8, 2, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, -13, -2, 61, -3],\n [-13, -37, -7, 13, 3],\n [28, 38, 24, 6, -38],\n [16, 9, 12, 50, -40],\n [43, 53, 35, -19, -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[[-4, -5, 3, -2, 2],\n [-20, -25, 15, -10, 10],\n [-4, -5, 3, -2, 2],\n [0, 0, 0, 0, 0],\n [-4, -5, 3, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 6, -5, 3, 10],\n [-47, -4, 35, 8, -20],\n [-1, -2, -7, -64, -36],\n [-20, 40, 15, -25, 10],\n [12, -3, -3, 51, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[52, -30, -82, 7, 17],\n [22, -30, -32, 8, 30],\n [-1, -16, -10, 20, 29],\n [26, 6, 12, -14, -13],\n [42, -13, -30, -44, -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[[5, 12, 10, -40, 10],\n [6, -19, 19, -28, -14],\n [-2, 46, -9, -51, 38],\n [1, -27, 1, 56, -24],\n [-13, 46, -24, -60, 42]]\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 5x5 matrix:\n[[-6, 14, -3, -3, -35],\n [-30, 2, -15, -9, -25],\n [0, 0, 0, -20, 44],\n [-30, 7, -15, -44, 40],\n [12, -4, 6, 28, -36]]\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[[-1, 30, -2, -2, -4],\n [-5, -40, -5, 10, 0],\n [-21, 22, -26, 22, -20],\n [-3, -24, -3, 6, 0],\n [26, -20, 32, -28, 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[[-18, -36, -24, -7, -30],\n [33, 33, -12, 55, 45],\n [5, 29, 44, -41, -12],\n [-20, -18, -7, -10, 0],\n [-40, -24, -10, -42, -22]]\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, -10, 10, 4, 0],\n [4, 4, 0, -8, 20],\n [5, 5, 0, -10, 25],\n [8, 28, -25, -16, 15],\n [-18, -66, 60, 36, -30]]\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 5x5 matrix:\n[[-10, -15, -5, -15, -5],\n [0, 0, 0, 0, 0],\n [4, 6, 2, 6, 2],\n [-10, -15, -5, -15, -5],\n [-8, -12, -4, -12, -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[[-19, -10, -6, 16, -21],\n [-16, -16, 3, 4, -3],\n [19, 26, -11, 4, -10],\n [-43, -42, 7, 12, -10],\n [23, 18, 1, -12, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[17, -71, 32, 5, -18],\n [5, 5, -27, -60, 16],\n [-39, 17, -15, 12, -20],\n [16, 32, -3, 3, 22],\n [10, -30, 0, -30, 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[[22, -24, 4, -43, 23],\n [-26, -3, 16, -8, 20],\n [7, -9, 18, 10, 8],\n [-15, 3, 6, -4, -5],\n [52, -9, -20, -15, -25]]\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, -3, -4, 3, 6],\n [-10, 6, 8, -6, -12],\n [5, -3, -4, 3, 6],\n [15, -9, -12, 9, 18],\n [20, -12, -16, 12, 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[[21, 27, 21, -5, 28],\n [57, 3, 1, -33, 36],\n [18, 0, 0, -12, 15],\n [-78, 6, 8, 44, -31],\n [15, 27, 21, -1, 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[[-3, -19, 18, -33, -36],\n [19, -33, -15, -52, -58],\n [-39, 1, 18, 3, -12],\n [13, 7, 26, 5, 22],\n [-60, 0, 6, 6, -24]]\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[[28, -20, 14, -36, 18],\n [-12, 12, -10, 12, -6],\n [-1, 8, -9, -6, 3],\n [-8, 4, -2, 12, -6],\n [-6, 0, 2, 12, -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 5x5 matrix:\n[[-44, -4, 43, 63, -2],\n [-40, 1, 29, 27, -19],\n [-10, -1, -8, -30, -21],\n [13, 30, -26, 12, 6],\n [1, -28, 30, -24, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 9, 18, -15, -12],\n [-12, -9, -18, 15, 12],\n [16, 12, 24, -20, -16],\n [-8, -6, -12, 10, 8],\n [16, 12, 24, -20, -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[[-16, -13, 8, 3, 4],\n [-4, -1, -17, -35, 31],\n [19, -4, 39, -1, -28],\n [-23, -25, 9, 8, -4],\n [-30, -40, -14, -38, 24]]\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[[-23, -6, 10, -7, -25],\n [12, 8, -4, 0, 12],\n [31, -26, -22, 35, 41],\n [10, 14, -6, -10, 38],\n [-9, 1, 10, 0, -45]]\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[[-9, 12, 0, 9, 3],\n [12, -16, 0, -12, -4],\n [-6, 8, 0, 6, 2],\n [0, 0, 0, 0, 0],\n [-9, 12, 0, 9, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-1, -23, 10, 20, 12],\n [-1, 13, -6, -10, -8],\n [-32, 2, -8, 25, -26],\n [13, -7, 6, -5, 14],\n [-25, 1, -6, 20, -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[[-22, -3, -10, 0, -15],\n [-6, 3, -34, 8, 11],\n [-45, 23, 5, 47, 3],\n [-25, -5, 33, -5, -33],\n [-51, 8, 11, 23, -24]]\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[[12, 3, 9, -6, 6],\n [-8, -2, -6, 4, -4],\n [16, 4, 12, -8, 8],\n [-4, -1, -3, 2, -2],\n [-8, -2, -6, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[19, -10, -10, -14, 18],\n [7, -12, -3, -15, 26],\n [8, -42, 9, -15, 52],\n [20, -28, -5, -21, 42],\n [22, -5, -12, -8, 5]]\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[[-19, 6, -4, -5, 7],\n [-5, -3, -11, 17, 5],\n [-1, 8, 8, -29, -5],\n [-5, -3, -11, 17, 5],\n [33, 2, 30, 23, -31]]?\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[[-3, -9, -10, -2, -6],\n [3, -7, -12, 0, 10],\n [-6, 23, 12, 3, 9],\n [-3, -44, -63, -6, 9],\n [12, 7, 44, 1, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, 17, -20, -2, -11],\n [-10, -11, -20, 22, 9],\n [-4, 28, -35, -2, -18],\n [2, 7, 0, -6, -5],\n [12, 18, 20, -28, -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 5x5 matrix:\n[[1, 1, -8, -3, -6],\n [20, -1, -34, -4, -29],\n [8, 5, -46, -16, -35],\n [8, -1, -10, 0, -9],\n [10, 4, -44, -14, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, -52, 4, -34, -52],\n [-30, -40, -26, -24, -28],\n [-15, -9, 3, -12, -45],\n [-1, 3, -5, 9, 4],\n [5, 69, 25, 39, 10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-29, -48, 8, -45, -77],\n [27, 35, 15, 12, 42],\n [-6, 6, -19, 36, 37],\n [-47, -40, -33, 39, -6],\n [5, 14, -25, 28, 28]]\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[[-22, 6, -29, -2, -12],\n [-5, 12, 20, 14, 3],\n [24, -12, 0, 56, -3],\n [-30, 4, -38, -16, -17],\n [37, -39, -1, -10, -1]]\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, -10, 28, 34, 24],\n [-13, 18, -26, -22, -24],\n [27, -4, 18, 44, 30],\n [30, 4, 6, 40, 24],\n [12, 45, -68, -27, -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[[-21, -10, 21, 8, -2],\n [-20, 19, 14, -16, -35],\n [2, -23, -8, 6, 3],\n [38, 44, -30, -20, 4],\n [-9, -35, -3, 7, -7]]\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, -8, 2, 0, 8],\n [-18, 24, -6, 0, -24],\n [-12, 16, -4, 0, -16],\n [-3, 4, -1, 0, -4],\n [-6, 8, -2, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-14, -29, 16, -30, 22],\n [3, 28, -20, 48, 0],\n [23, 31, -12, 22, -37],\n [-6, 9, -16, 10, 3],\n [-28, -8, -16, 8, 38]]\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[[-19, -28, -25, 15, -19],\n [18, 2, -15, 4, 10],\n [55, 14, 4, -1, 15],\n [-5, -26, -32, 17, -13],\n [34, 0, -2, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-20, -20, 10, 15, -15],\n [-12, -12, 6, 9, -9],\n [8, 8, -4, -6, 6],\n [-8, -8, 4, 6, -6],\n [-24, -24, 12, 18, -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[[13, 23, 15, -1, 18],\n [-13, 35, 7, -27, 21],\n [25, -15, -8, 44, -3],\n [-4, -18, 5, -11, -15],\n [-9, -35, 13, -27, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 0, 0, 15, 0],\n [3, 2, 39, -26, 6],\n [2, 8, -6, 0, 0],\n [4, 3, 18, -8, 3],\n [17, -1, 21, 27, 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[[17, -40, -13, -11, -34],\n [-18, -68, -24, -46, -24],\n [48, -22, -27, 22, -18],\n [31, 18, -14, 33, 16],\n [8, -18, -1, -6, -22]]\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 5x5 matrix:\n[[2, -15, 10, -13, -11],\n [-12, -1, 5, 0, 14],\n [-6, 17, -10, 15, 17],\n [-8, -3, 5, -2, 8],\n [-14, -28, 25, -23, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-20, 20, -8, -8, -20],\n [25, -25, 10, 10, 25],\n [-10, 10, -4, -4, -10],\n [0, 0, 0, 0, 0],\n [-5, 5, -2, -2, -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 5x5 matrix:\n[[-6, -30, -18, -75, 18],\n [-15, -30, -12, -57, 3],\n [24, 18, 0, -6, 30],\n [15, 20, 0, 45, -5],\n [2, 3, 6, -14, 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 5x5 matrix:\n[[0, 0, 0, 0, 0],\n [-8, 0, -16, -4, 20],\n [2, 0, 4, 1, -5],\n [4, 0, 8, 2, -10],\n [2, 0, 4, 1, -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 5x5 matrix:\n[[18, 32, 22, 23, -5],\n [-3, -32, -35, -12, -8],\n [4, -10, -28, -18, -4],\n [2, -10, -28, -21, -1],\n [10, 44, 40, 17, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[10, -10, -12, -12, -4],\n [-30, 30, 36, 36, 12],\n [-5, 5, 6, 6, 2],\n [10, -10, -12, -12, -4],\n [5, -5, -6, -6, -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 5x5 matrix:\n[[-6, 8, -11, 0, 25],\n [-31, -12, -32, 23, 28],\n [8, -38, -21, 2, -27],\n [-3, -10, -14, 3, 4],\n [-14, 45, 38, 4, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -30, 12, 0, -22],\n [3, 30, -21, 3, 29],\n [6, 40, -22, 2, 34],\n [-6, -35, 17, -1, -28],\n [-9, -45, 18, 0, -33]]\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[[-2, 7, -1, -7, 13],\n [0, 1, 0, -4, 8],\n [-18, 51, -9, -15, 21],\n [12, -34, 6, 10, -14],\n [16, -43, 8, 4, 0]]\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[[29, 7, 14, -21, -55],\n [3, 1, 0, -4, -1],\n [21, 15, -4, 14, -23],\n [39, 13, 14, -17, -69],\n [-4, 0, -4, 4, 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[[0, 18, 6, -12, 3],\n [0, 36, 12, -24, 6],\n [0, 24, 8, -16, 4],\n [0, 12, 4, -8, 2],\n [0, -18, -6, 12, -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[[1, -1, 2, -2, -1],\n [-1, 1, -2, 2, 1],\n [-2, 2, -4, 4, 2],\n [-1, 1, -2, 2, 1],\n [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[[28, -33, 6, 5, 12],\n [18, -45, 72, -39, -6],\n [-4, 15, 9, -5, -2],\n [-68, 15, -32, 4, -14],\n [16, -39, 57, -29, -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[[0, 3, 6, 2, 4],\n [0, -12, -24, -8, -16],\n [0, 6, 12, 4, 8],\n [0, 6, 12, 4, 8],\n [0, -6, -12, -4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[27, 0, 23, 0, -8],\n [-8, 20, -12, 20, -8],\n [38, 40, 22, 40, -32],\n [45, 36, 29, 36, -32],\n [-14, 8, -14, 8, 0]]\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, 25, 30, 30, 5],\n [-36, 30, 36, 36, 6],\n [-36, 30, 36, 36, 6],\n [-6, 5, 6, 6, 1],\n [6, -5, -6, -6, -1]]\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 5x5 matrix:\n[[-24, -12, -12, -24, 30],\n [22, 9, 12, 25, -27],\n [8, -8, 10, 26, -7],\n [12, 6, 6, 12, -15],\n [-32, -8, -20, -44, 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[[-8, -12, 4, -2, -6],\n [4, 6, -2, 1, 3],\n [8, 12, -4, 2, 6],\n [20, 30, -10, 5, 15],\n [-12, -18, 6, -3, -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[[33, -20, -34, 4, -15],\n [-17, -4, -24, -34, -43],\n [-45, 9, 14, -12, 39],\n [14, 7, 14, -11, -7],\n [-1, 9, 24, 48, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, -4, 36, 23, -16],\n [-25, 10, 25, -38, -14],\n [4, 42, 12, 30, -24],\n [-7, -3, -3, -24, 3],\n [9, 8, 27, 14, -34]]\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 5x5 matrix:\n[[-3, 0, -30, 22, -2],\n [-29, 0, 18, 0, 32],\n [29, 0, -18, 0, -32],\n [-5, 0, -36, 27, -1],\n [30, 0, -36, 12, -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[[-17, -4, -10, -7, -5],\n [-20, 14, 14, 20, -20],\n [2, 4, 6, 7, -1],\n [-41, -21, -41, -6, 32],\n [-21, -14, -26, 4, 34]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[7, 3, -5, 25, 3],\n [40, 15, -30, -8, -33],\n [9, -9, -16, -3, -36],\n [-14, -34, -19, 48, -47],\n [-5, 18, 46, -29, 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 5x5 matrix:\n[[0, 6, -3, -9, 3],\n [0, -10, 5, 15, -5],\n [0, 4, -2, -6, 2],\n [0, -12, 6, 18, -6],\n [0, 8, -4, -12, 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[[-31, -51, 28, -21, 41],\n [-52, -60, 14, 2, 54],\n [-58, -69, 8, 3, 35],\n [-52, -66, 46, -36, 56],\n [-28, -4, -9, 12, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, 6, 10, -2, -4],\n [50, 33, 7, -41, 8],\n [30, 21, 19, -17, -4],\n [18, 9, -33, -33, 24],\n [36, 24, 8, -28, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-4, -24, 8, 3, 8],\n [6, 38, 0, 1, -18],\n [-56, -54, 28, 22, 43],\n [-29, -23, 4, 7, 25],\n [1, 33, 16, 9, -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[[-6, 34, 13, 1, -25],\n [-24, -32, -11, 25, 5],\n [24, -24, -10, -18, 30],\n [-18, -42, -15, 21, 15],\n [6, 30, 11, -9, -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[[4, -20, -12, 16, 24],\n [-1, 5, 3, -4, -6],\n [1, -5, -3, 4, 6],\n [4, -20, -12, 16, 24],\n [-2, 10, 6, -8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[18, -46, 10, 14, 22],\n [3, 35, 12, 15, -8],\n [-5, 39, -2, 4, -9],\n [-12, 23, -6, -16, -25],\n [59, -9, -7, 76, 58]]?\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, 1, 0, -38, -6],\n [42, -42, 28, -50, -32],\n [18, -16, 10, -11, -10],\n [78, 10, -26, 13, -1],\n [-36, -14, 26, -27, -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[[-21, -13, 11, 19, -19],\n [-6, 17, 6, -21, -8],\n [-21, 11, 16, -8, -20],\n [42, 10, -2, 30, 66],\n [-18, -26, -17, -17, -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[[20, -24, -16, -4, 4],\n [30, -36, -24, -6, 6],\n [-5, 6, 4, 1, -1],\n [30, -36, -24, -6, 6],\n [20, -24, -16, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, -16, 24, 8, -24],\n [-22, -19, 19, 26, 34],\n [26, 18, -18, -32, -40],\n [18, 20, -20, -20, -28],\n [1, -25, 38, -16, -70]]\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[[7, 50, 21, -1, 9],\n [-12, -51, -27, -6, -9],\n [14, 46, 28, 10, 8],\n [-10, -56, -26, -2, -10],\n [-17, -25, -26, -19, -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[[-37, 7, 24, -35, 50],\n [-21, 6, -76, 39, -52],\n [10, 0, -12, 14, -8],\n [-1, 12, 35, -20, 22],\n [-11, 28, 78, -49, 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[[33, 12, -27, 27, -40],\n [45, -12, -3, 3, -32],\n [-32, 34, 5, -1, 9],\n [27, -10, 16, -28, -63],\n [-60, 26, 42, -62, -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 5x5 matrix:\n[[11, -19, -29, 17, 20],\n [-49, 61, 11, -19, -30],\n [34, -46, -26, 22, 30],\n [-8, 2, -38, 16, 15],\n [1, -9, -39, 19, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[50, -5, 34, -31, -18],\n [-26, -27, -21, -27, 11],\n [-26, -1, -31, 91, -27],\n [-49, 5, -30, 10, 27],\n [-37, -25, -34, 16, -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 5x5 matrix:\n[[-12, 24, 0, 36, -18],\n [0, 0, 0, 0, 0],\n [12, -24, 0, -36, 18],\n [6, -12, 0, -18, 9],\n [-2, 4, 0, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[3, 3, 19, 10, 12],\n [-25, 9, 27, -18, -20],\n [-41, 21, 55, -24, -22],\n [-14, 6, 32, -5, -7],\n [-9, -12, 23, -9, -27]]\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[[-51, 6, -21, -24, 18],\n [-36, -4, -10, -18, 4],\n [-11, 30, 17, -26, -28],\n [22, -24, -15, 31, 29],\n [-27, -28, -19, 0, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, 15, -21, -17, -21],\n [18, -40, 14, 8, 42],\n [-32, 35, 17, 19, -27],\n [-24, 45, -9, -3, -45],\n [-31, 5, 50, 45, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-17, -38, -2, 41, -6],\n [-14, -29, -4, 32, -8],\n [19, 36, 4, -17, -18],\n [-8, 21, -34, -44, -8],\n [24, 18, 35, -9, 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[[3, 3, 6, 6, 0],\n [3, -27, 19, 14, -46],\n [18, -12, 49, 44, -46],\n [4, -14, -5, 0, -18],\n [-15, 9, -56, -46, 44]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 7, 14, -4, -28],\n [4, 8, -18, 10, 2],\n [-6, -8, 11, -7, 5],\n [0, 2, -8, 4, 4],\n [6, 1, 17, -7, -19]]?\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, 34, 36, 36, 2],\n [4, 27, 26, 22, -5],\n [15, -5, -15, -30, -25],\n [-8, 14, 20, 28, 14],\n [22, 4, -10, -32, -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[[46, -9, -24, -9, 23],\n [-36, 40, 44, -32, -28],\n [49, -73, -19, 65, 34],\n [-32, -10, -6, 23, 20],\n [-35, -22, 33, 41, -19]]\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 5x5 matrix:\n[[35, -2, 16, -51, 41],\n [8, -17, 2, -9, 17],\n [-19, -30, 0, 39, -37],\n [-21, -33, -2, 42, -36],\n [10, -9, 6, -12, 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[[-13, 36, 4, 21, -12],\n [13, 24, -6, 27, 18],\n [-30, 0, 12, -18, -36],\n [2, -24, 0, -18, 0],\n [-38, -24, 16, -42, -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[[-45, 10, -7, -16, -6],\n [-24, -16, -22, -2, 10],\n [-63, -10, -12, -11, -7],\n [-27, 22, -20, -27, -3],\n [9, 4, -44, -16, 23]]\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[[12, -19, -9, -24, -27],\n [19, -32, -4, -8, -2],\n [-9, 29, 0, -19, 29],\n [-10, 18, 23, 6, 17],\n [-28, 34, 58, 26, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, -40, 11, -41, 12],\n [9, -3, -21, 3, -18],\n [9, -25, 22, -32, -36],\n [16, -38, 7, -39, -18],\n [2, 8, -23, 15, 6]]?\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[[38, 19, 10, 26, 2],\n [-26, -22, -22, -35, 13],\n [32, -29, 10, -12, 49],\n [20, 55, -13, 17, 12],\n [40, 2, 10, 15, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0, 0],\n [12, -10, -12, 0, 8],\n [-6, 5, 6, 0, -4],\n [18, -15, -18, 0, 12],\n [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[[-33, -14, -6, 43, 13],\n [19, 10, 6, -21, -7],\n [12, 24, 27, 21, 0],\n [-36, -24, -18, 30, 12],\n [-10, 4, 9, 29, 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 5x5 matrix:\n[[-4, -4, 4, -12, 10],\n [-2, -2, 2, -6, 5],\n [-2, -2, 2, -6, 5],\n [-2, -2, 2, -6, 5],\n [-12, -12, 12, -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[[-2, 27, 36, 2, 24],\n [50, -30, -10, -11, 7],\n [-10, 6, -6, 10, -24],\n [57, 34, 36, -36, 50],\n [-14, 21, -20, -26, 0]]\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[[8, 20, -24, 16, 0],\n [-8, 4, 12, -4, 30],\n [-6, -19, 20, -14, -5],\n [-16, -32, 44, -28, 10],\n [-10, -21, 28, -18, 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[[0, 0, 0, 0, 0],\n [12, 0, 6, -3, 6],\n [-24, 0, -12, 6, -12],\n [-12, 0, -6, 3, -6],\n [4, 0, 2, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[10, 10, -10, 1, -20],\n [4, -52, 44, 22, 32],\n [9, -32, 29, 22, -3],\n [12, 2, -4, 4, -14],\n [-25, -39, 43, 14, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -4, -2, -18, 16],\n [6, 2, 0, -30, 22],\n [-6, -5, -2, 30, -25],\n [-15, 21, 8, 19, -29],\n [-6, 24, 10, -14, 4]]\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 5x5 matrix:\n[[18, 36, -24, 12, 0],\n [-15, -30, 20, -10, 0],\n [9, 18, -12, 6, 0],\n [-6, -12, 8, -4, 0],\n [-6, -12, 8, -4, 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[[-5, 23, 44, -12, -19],\n [-44, -21, 12, 13, -13],\n [-44, 15, 46, -7, -17],\n [36, 22, -26, -26, 6],\n [-45, -78, -26, 61, 8]]\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[[30, 12, 24, 0, 9],\n [-12, 12, 10, 7, -12],\n [-10, -28, -36, -10, 9],\n [4, -20, -22, -9, 12],\n [6, -24, -26, -11, 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[[27, 9, 20, -18, 8],\n [36, 12, 25, -21, 7],\n [30, 10, 20, -16, 4],\n [-6, -2, -15, 23, -25],\n [42, 14, 25, -17, -1]]\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 5x5 matrix:\n[[0, 30, 16, -44, 18],\n [0, -9, -3, 18, -3],\n [0, 21, 19, -10, 23],\n [0, -9, -12, -6, -15],\n [0, -18, -24, -12, -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[[0, 0, 0, 0, 0],\n [2, 5, 3, 0, 2],\n [12, 30, 18, 0, 12],\n [6, 15, 9, 0, 6],\n [4, 10, 6, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[10, 7, -2, -5, -1],\n [-48, -12, 6, 30, 18],\n [-10, -25, 5, 0, -10],\n [36, 0, -3, -25, -19],\n [-34, 5, 2, 25, 21]]\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[[7, 7, 6, -21, 27],\n [-8, 4, 38, -24, 10],\n [-14, -14, -12, 42, -54],\n [13, -17, -31, 21, -2],\n [-4, 30, 14, -30, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 12, 6, -24, -27],\n [-6, 4, -18, 12, 16],\n [-7, 6, -23, 14, 19],\n [0, 12, -18, 0, 3],\n [6, 0, 12, -12, -15]]\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[[4, 0, -4, -1, 5],\n [-24, 0, 24, 6, -30],\n [-8, 0, 8, 2, -10],\n [4, 0, -4, -1, 5],\n [-20, 0, 20, 5, -25]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-28, -24, -7, 20, -22],\n [-28, -16, 7, 4, -3],\n [0, 16, 12, 16, -16],\n [-6, -22, -29, 32, -38],\n [34, 34, 11, -16, 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[[28, 14, 1, 61, 3],\n [36, -26, 18, 20, -54],\n [-4, -18, 61, -13, -19],\n [-46, -9, 37, -49, 24],\n [2, 11, 16, 12, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -2, 4, 6, -6],\n [-30, -14, -37, -8, -2],\n [18, 0, 39, 30, -24],\n [0, -8, 16, 24, -24],\n [12, -2, 30, 26, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[29, 33, -19, 3, -66],\n [58, 16, 16, -46, -82],\n [-12, -13, -24, 42, 19],\n [41, -31, 50, -67, -17],\n [-29, -18, 23, -15, 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 5x5 matrix:\n[[10, 18, -31, 1, -2],\n [-5, -41, -9, -34, 34],\n [32, 15, -20, 22, -4],\n [18, -7, -28, -26, 0],\n [14, -4, -1, 21, 14]]\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 5x5 matrix:\n[[24, 20, 23, 30, -25],\n [34, 50, 12, 10, -4],\n [1, -15, 16, 25, -24],\n [1, 5, -3, -5, 5],\n [15, 15, 12, 15, -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 5x5 matrix:\n[[-46, -50, 35, 48, 15],\n [10, -1, -11, 15, 12],\n [20, 12, -18, 0, 6],\n [8, -5, -10, 21, 15],\n [-14, 0, 15, -18, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-18, 4, 14, 1, 1],\n [21, -41, 22, 15, 13],\n [-5, 29, -22, -10, -12],\n [17, 7, -30, -9, -3],\n [-20, 1, 43, 17, -7]]\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, 10, -2, -2, -4],\n [-36, -30, 6, 6, 12],\n [36, 30, -6, -6, -12],\n [18, 15, -3, -3, -6],\n [12, 10, -2, -2, -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[[20, -13, -4, 13, 9],\n [10, -12, 20, 12, -34],\n [-30, 18, 12, -18, -24],\n [5, -9, 22, 9, -38],\n [5, -1, -10, 1, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-55, -7, 38, 1, 7],\n [10, -1, -17, 16, 1],\n [-10, -20, 24, -38, -15],\n [34, -5, -31, 28, 0],\n [16, 25, -25, -26, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[34, 9, -3, 24, 15],\n [14, 8, 0, 12, 6],\n [-60, 5, 28, -10, -33],\n [-27, 34, 36, 30, -21],\n [12, -10, -23, -22, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[22, -12, 8, 8, -3],\n [-8, 33, -29, -1, 1],\n [47, -18, 16, 22, -9],\n [-19, -17, 31, 1, -3],\n [22, 16, -20, 8, -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[[-6, -4, -2, 8, -1],\n [54, 48, 6, 12, -3],\n [66, 60, 6, 24, -5],\n [-30, -30, 0, -30, 5],\n [18, 13, 5, -17, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[0, 20, -16, -5, -12],\n [11, -12, 14, 14, 16],\n [14, 12, -4, 11, 4],\n [28, 24, -8, 22, 8],\n [-24, 8, -16, -26, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[20, 0, 30, 50, -38],\n [25, -54, 20, -44, -51],\n [32, 3, 19, -4, 33],\n [-1, 38, -7, 19, 60],\n [2, -14, 4, -6, -22]]\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 5x5 matrix:\n[[-66, -75, 15, 9, 30],\n [-4, 12, -1, -30, -58],\n [-6, 1, -39, 20, -46],\n [-32, -40, -38, 50, 4],\n [0, -14, 12, 17, 56]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[24, -22, 21, -4, -33],\n [9, 6, 3, -12, -24],\n [24, 4, -4, 18, 12],\n [-24, 4, -12, 10, 36],\n [-21, 4, -7, -1, 16]]\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, 2, 0, -8, -2],\n [6, 6, 0, -24, -6],\n [-3, -3, 0, 12, 3],\n [-5, -5, 0, 20, 5],\n [-5, -5, 0, 20, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, 5, 5, -2, -3],\n [-7, -13, -1, 14, -17],\n [-2, -5, 10, 13, -28],\n [0, -1, 8, 7, -18],\n [-13, -21, -27, 4, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[0, -26, -30, 8, -6],\n [31, 9, -15, -8, -19],\n [-25, -9, -5, 20, 7],\n [-32, 5, -25, 53, -7],\n [-6, 34, 10, 20, -6]]\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, -5, 30, -14, -22],\n [27, -6, 18, 6, -34],\n [39, -34, -14, 22, -50],\n [-16, 0, 3, -11, 12],\n [-33, 24, 6, -15, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[22, 33, -44, -47, -18],\n [-28, -15, -16, -6, -48],\n [-30, -33, 28, 24, 2],\n [-7, 9, -38, -67, -17],\n [10, 21, -36, -19, -38]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-35, 10, 25, 35, 45],\n [7, -29, -13, 7, 6],\n [-19, 17, 17, 13, 18],\n [-10, 26, 14, -2, 0],\n [16, 7, -8, -22, -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[[12, 12, 4, -4, -12],\n [12, 27, 19, -16, -21],\n [12, 17, 9, -8, -15],\n [36, 11, -13, 8, -21],\n [-12, 13, 21, -16, -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[[4, -4, -24, -16, -4],\n [6, -6, -36, -24, -6],\n [1, -1, -6, -4, -1],\n [-6, 6, 36, 24, 6],\n [-6, 6, 36, 24, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-19, -28, 48, -26, -18],\n [-31, 5, 48, -23, 0],\n [10, -57, 12, 1, -22],\n [8, 7, 1, -39, -28],\n [44, -20, -59, 24, -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 5x5 matrix:\n[[-39, -5, 14, 38, 6],\n [-30, 20, 0, 55, 20],\n [-19, -13, 26, 10, -14],\n [-26, 13, 7, 44, 11],\n [35, -1, 0, -38, -16]]\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, -7, 10, -32, -2],\n [5, 1, 12, 12, -26],\n [-13, 37, -34, -36, -20],\n [27, 10, -3, 44, -19],\n [0, 10, -10, -4, -4]]\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 5x5 matrix:\n[[0, 0, 0, 0, 0],\n [25, -30, 25, 30, -25],\n [20, -24, 20, 24, -20],\n [20, -24, 20, 24, -20],\n [-30, 36, -30, -36, 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[[-10, -13, -4, -3, 8],\n [40, 35, 5, 20, -25],\n [-26, -27, -6, -11, 18],\n [-38, -12, 9, -29, 15],\n [36, 6, -12, 30, -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[[-24, 0, 36, 12, 30],\n [-20, 36, 0, -20, 1],\n [-8, 18, -3, -11, -2],\n [-36, 18, 39, 3, 33],\n [-32, 12, 38, 6, 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[[-27, -23, -24, 23, 14],\n [4, 2, 2, -21, -24],\n [10, -2, 23, -18, 14],\n [-40, -10, -32, 59, 44],\n [20, 6, 23, -33, -14]]\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 5x5 matrix:\n[[-12, -9, 3, 12, -15],\n [4, 3, -1, -4, 5],\n [-20, -15, 5, 20, -25],\n [24, 18, -6, -24, 30],\n [-16, -12, 4, 16, -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[[29, 52, -21, 30, 29],\n [30, 73, -53, 50, 23],\n [7, 3, -6, -20, -10],\n [14, 68, -13, 4, 10],\n [4, -19, -24, -2, -15]]\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[[-50, 55, 61, -8, -13],\n [12, -15, -15, 12, 15],\n [-44, 50, 54, -16, -22],\n [-26, 25, 31, 16, 17],\n [8, -10, -10, 8, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[31, 34, -12, 11, -12],\n [-26, -35, 18, -13, 15],\n [7, -6, 28, 23, 12],\n [-9, -8, 14, 24, 6],\n [-4, 0, 2, 13, 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[[-12, -4, -6, 26, -22],\n [9, 3, 18, 12, -6],\n [-6, -2, -6, 6, -6],\n [-15, -5, -21, 1, -5],\n [-12, -4, -24, -16, 8]]\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, 11, 45, 51, 44],\n [-37, 66, 43, -4, -19],\n [-5, -10, 54, 17, 55],\n [35, -44, 16, 1, 53],\n [29, -10, -50, -43, -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[[6, -8, -2, 6, 2],\n [12, -16, -4, 12, 4],\n [15, -20, -5, 15, 5],\n [-9, 12, 3, -9, -3],\n [-15, 20, 5, -15, -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[[0, 0, 0, 0, 0],\n [5, -30, 10, 5, -20],\n [-6, 36, -12, -6, 24],\n [-5, 30, -10, -5, 20],\n [-5, 30, -10, -5, 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[[12, -32, 36, 0, 12],\n [32, -52, 54, 14, -10],\n [-14, -16, 6, 48, 34],\n [12, -32, 18, 66, -6],\n [8, -28, 15, 61, -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[[0, -10, -50, 5, -35],\n [-34, 10, 19, 4, 50],\n [-18, 16, 22, -25, -19],\n [-10, -9, 26, -4, -13],\n [0, 25, 34, -39, -36]]\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 5x5 matrix:\n[[-28, 16, -4, 34, -12],\n [14, -6, -16, -46, 8],\n [-37, 39, -38, 2, 6],\n [-31, 29, -10, 36, 1],\n [52, -52, 16, -64, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-19, -14, 23, 12, -17],\n [5, 6, -1, 4, -1],\n [-1, 1, 5, 6, -5],\n [33, 22, -45, -28, 35],\n [-4, 4, 20, 24, -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[[-12, 30, 30, 36, 12],\n [6, -15, -15, -18, -6],\n [12, -30, -30, -36, -12],\n [12, -30, -30, -36, -12],\n [2, -5, -5, -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[[19, -2, 26, -37, -18],\n [19, -42, -25, 20, -6],\n [34, -36, 22, -11, 6],\n [-11, -7, -22, 19, -12],\n [28, -12, -1, 5, 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 5x5 matrix:\n[[24, 16, 0, 8, 16],\n [-30, -20, 0, -10, -20],\n [-24, -16, 0, -8, -16],\n [-6, -4, 0, -2, -4],\n [-12, -8, 0, -4, -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[[12, 60, -2, 16, 44],\n [-9, 27, 5, 23, 20],\n [-21, 27, 4, 52, 23],\n [-24, -8, 31, -24, -12],\n [66, 42, -48, 24, 46]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[31, -15, -8, -1, -8],\n [-11, 9, 16, -25, 13],\n [34, -12, 10, -10, 4],\n [53, -14, 37, -13, 20],\n [-34, 11, -15, 6, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[54, -6, 4, 44, -42],\n [-48, -2, 22, -4, 8],\n [0, -5, -1, 13, -1],\n [20, 3, 3, 3, -15],\n [80, 3, -9, 24, -42]]?\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, 30, 12, -6, 30],\n [-36, 30, 12, -6, 30],\n [24, -20, -8, 4, -20],\n [-36, 30, 12, -6, 30],\n [-36, 30, 12, -6, 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 5x5 matrix:\n[[52, 32, -2, 21, -22],\n [10, 6, 8, -11, 14],\n [35, 11, 3, 19, 4],\n [31, 23, 13, -18, 14],\n [-9, -1, -19, 26, -42]]\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[[17, 22, -15, -30, 28],\n [-17, -23, 18, 36, -37],\n [-14, -18, 12, 24, -22],\n [-21, -26, 15, 30, -24],\n [-9, -13, 12, 24, -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[[6, -11, 3, 17, 20],\n [6, -3, 3, 7, 8],\n [-36, -18, -18, 3, 6],\n [24, -16, 12, 33, 38],\n [18, 3, 9, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 4, 7, 1, -7],\n [-2, 20, 1, -1, -1],\n [28, 0, -34, -6, 34],\n [2, 8, -3, -1, 3],\n [22, -10, -26, -4, 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[[0, 12, -36, -6, -18],\n [0, -10, 30, 5, 15],\n [0, 12, -36, -6, -18],\n [0, 4, -12, -2, -6],\n [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[[-34, 50, -10, -19, 15],\n [-33, -30, 51, 51, -57],\n [-9, -4, 14, 12, -13],\n [-15, -28, 26, 35, -41],\n [-21, -38, 34, 39, -44]]?\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, 10, 13, -7],\n [-4, 14, -16, -16, 10],\n [3, -12, 6, 3, -3],\n [0, -4, -16, -24, 12],\n [6, -29, -8, -24, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -30, 36, 24, 24],\n [0, -10, 12, 8, 8],\n [0, -15, 18, 12, 12],\n [0, 0, 0, 0, 0],\n [0, -10, 12, 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[[-1, 2, -4, -3, -6],\n [-5, 10, -20, -15, -30],\n [-2, 4, -8, -6, -12],\n [2, -4, 8, 6, 12],\n [4, -8, 16, 12, 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[[1, -3, 11, -7, -9],\n [2, -6, 14, -4, -10],\n [1, -3, -17, 28, 19],\n [-2, 6, 6, -21, -10],\n [-5, 15, -27, 0, 17]]\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 5x5 matrix:\n[[-42, 40, -60, 34, -2],\n [-53, 46, -69, 35, -21],\n [-5, 16, 8, -51, 23],\n [56, -46, 62, -16, 38],\n [-25, 17, -19, -7, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, 5, -6, -2, -4],\n [-3, 3, -12, -6, -27],\n [-1, 5, 8, 6, 37],\n [-22, 40, -34, -8, 9],\n [19, -33, 34, 10, 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[[18, -55, 0, 19, -18],\n [-20, 66, -24, 10, 8],\n [2, -27, 16, 13, -36],\n [12, -27, 2, -8, 13],\n [-16, 28, 16, -6, -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[[3, -12, 6, -9, -15],\n [-2, 8, -4, 6, 10],\n [5, -20, 10, -15, -25],\n [1, -4, 2, -3, -5],\n [4, -16, 8, -12, -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[[40, 45, 5, -25, -35],\n [0, 0, 0, 0, 0],\n [-24, -42, -14, 6, 22],\n [0, -15, -11, -9, 1],\n [10, -15, -18, -22, -7]]\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 5x5 matrix:\n[[-11, 15, 38, -45, 54],\n [-2, -12, -25, 27, -36],\n [27, 9, 6, 1, 10],\n [-12, 0, 6, -10, 8],\n [30, 0, -15, 25, -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[[-4, 28, -15, 22, -44],\n [-31, 7, 17, -27, 8],\n [9, -49, -32, -29, -44],\n [1, -9, -36, 3, -92],\n [2, 28, 28, 33, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 4, -6, 10, -4],\n [-8, 4, 1, -4, 8],\n [-44, 18, 8, -25, 42],\n [-36, 30, -3, -9, 42],\n [32, -8, -9, 22, -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[[5, -4, 25, 13, 12],\n [14, -28, 2, 19, -30],\n [-21, 12, 7, 9, 0],\n [-21, 0, -12, 12, -30],\n [-18, -12, 20, 39, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 32, 7, 10, -17],\n [-36, -4, -49, -10, -11],\n [-36, 4, -50, -8, -16],\n [-16, 8, -23, -2, -11],\n [12, -4, 17, 2, 7]]?\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 5x5 matrix:\n[[-27, 11, -15, -14, 5],\n [56, -7, 40, 70, -16],\n [-10, -2, 5, -6, 21],\n [38, -9, 12, 24, 2],\n [-56, 9, -29, -55, 10]]\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 5x5 matrix:\n[[-36, -15, -33, -20, -24],\n [9, 45, -13, 45, -4],\n [-30, -9, -31, -12, -27],\n [48, 12, 36, 28, -10],\n [6, -3, 3, 2, -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[[-20, -11, -12, 20, -23],\n [29, 14, 37, -29, 16],\n [-31, 11, -13, 31, -12],\n [-14, -11, -14, 14, -15],\n [26, -13, -4, -26, 18]]\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 5x5 matrix:\n[[0, 6, -18, -24, -6],\n [0, 1, -3, -4, -1],\n [0, 0, 0, 0, 0],\n [0, 5, -15, -20, -5],\n [0, 4, -12, -16, -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[[-2, 12, 2, -12, 4],\n [25, -26, -1, 6, -14],\n [27, 24, 9, -54, 0],\n [25, 5, 5, -30, -5],\n [24, 11, 6, -36, -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[[33, -31, 21, -14, -41],\n [3, -21, -39, 26, 19],\n [-6, 6, -3, 2, 7],\n [-36, 36, -18, 12, 42],\n [12, 0, 33, -22, -29]]\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 5x5 matrix:\n[[-5, -50, -45, -15, -30],\n [18, 22, 15, 22, 12],\n [-29, 38, 36, 10, 42],\n [-12, 12, 11, 5, 16],\n [34, -52, -50, -10, -52]]\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[[-22, 87, 18, 33, -30],\n [13, 66, -25, 46, -76],\n [15, -9, -19, -3, -14],\n [14, -21, 44, -3, 40],\n [20, -15, -20, 5, -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[[23, 37, -61, 13, -18],\n [25, 3, -25, 22, 1],\n [-28, -6, 20, -37, -37],\n [-6, 60, -12, -36, -36],\n [-17, -71, 21, 18, 23]]?\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 5x5 matrix:\n[[-14, 4, -34, -10, -40],\n [8, -4, 24, 8, 28],\n [4, 4, -4, -4, -4],\n [4, 1, 4, 0, 5],\n [11, 5, 5, -3, 7]]\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 5x5 matrix:\n[[-27, 6, -35, -15, -9],\n [23, -4, 25, 15, 11],\n [7, -2, 11, 3, 1],\n [-5, 4, -19, 3, 7],\n [-2, 1, -5, 0, 1]]\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, 32, -10, -34, -38],\n [2, -2, 19, 10, 5],\n [-24, -12, -12, 6, 12],\n [-16, -10, 4, 11, 12],\n [54, 32, -3, -31, -37]]\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 5x5 matrix:\n[[36, 10, 8, -2, 5],\n [9, -38, -1, -8, -1],\n [-24, -10, -4, 26, -13],\n [33, 20, 9, 14, 0],\n [9, -8, 2, 10, -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[[24, -16, -8, 16, 8],\n [-6, 4, 2, -4, -2],\n [-36, 24, 12, -24, -12],\n [24, -16, -8, 16, 8],\n [12, -8, -4, 8, 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[[1, -6, 0, 5, -3],\n [-3, 18, 0, -15, 9],\n [0, 0, 0, 0, 0],\n [4, -24, 0, 20, -12],\n [5, -30, 0, 25, -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[[3, -26, -28, -18, 21],\n [12, -12, -5, -27, -20],\n [51, 34, -21, -33, -35],\n [-12, 8, -2, 26, 28],\n [39, 24, -41, -17, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-22, 0, 19, -9, 14],\n [-19, -1, -38, 34, -12],\n [42, 18, -6, 18, 6],\n [6, -12, -57, 27, -39],\n [-7, 23, -8, 40, 24]]?\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, -46, -18, 34, 20],\n [15, 13, -3, -19, -20],\n [30, 6, -30, -42, -60],\n [20, 29, 10, -23, -15],\n [10, 7, -4, -13, -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 5x5 matrix:\n[[-36, -22, -2, 24, 28],\n [-73, -5, -46, 29, -15],\n [34, 2, 4, -8, 6],\n [-5, -18, 16, 18, 36],\n [-28, -26, 6, -44, -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[[10, 3, 1, -2, 0],\n [9, -3, -1, 16, -4],\n [11, -25, 15, 26, -26],\n [10, -5, 15, -20, -10],\n [-26, 3, 7, -44, 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[[9, 64, 61, 36, -42],\n [24, -20, -12, -27, 21],\n [25, -14, -7, -14, 16],\n [31, -87, -74, -19, 19],\n [-2, 3, 3, 7, -29]]\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 5x5 matrix:\n[[7, 51, -8, 39, 37],\n [-4, -48, 3, -38, -40],\n [10, 6, -17, 0, -14],\n [6, -6, -11, -8, -18],\n [-9, 3, 16, 7, 21]]\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[[31, -3, 6, 23, 12],\n [-2, 16, 24, -6, 20],\n [-18, 39, 54, -24, 42],\n [24, 18, 36, 12, 36],\n [-9, 2, 0, -7, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[20, 0, 16, -8, 16],\n [15, 0, 12, -6, 12],\n [0, 0, 0, 0, 0],\n [-20, 0, -16, 8, -16],\n [5, 0, 4, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[42, 44, 43, 9, -45],\n [-57, -96, -88, -10, 51],\n [-6, -70, -57, 4, 10],\n [18, -22, -18, 23, -18],\n [27, 60, 51, 11, -32]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-11, 26, 22, -4, 14],\n [0, -22, 11, 22, -30],\n [-21, 49, 31, -13, 33],\n [-49, 24, 9, 1, 22],\n [10, 23, 20, -9, 11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[14, 4, 0, -36, 20],\n [15, 2, -16, 14, -38],\n [31, 5, -27, 9, -56],\n [12, 3, -3, -21, 6],\n [-19, -5, 3, 39, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -3, 0, -17, 3],\n [39, 8, 39, -24, 31],\n [18, -3, 18, -49, 21],\n [24, 1, 24, -37, 23],\n [27, 6, 27, -14, 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 5x5 matrix:\n[[-1, 16, -15, 2, 6],\n [15, -3, 2, -29, 28],\n [18, -4, -14, -16, 44],\n [-22, 35, -35, 15, 26],\n [-22, 11, -11, 9, 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 5x5 matrix:\n[[1, -24, 4, 31, -14],\n [-20, -26, 5, 1, -16],\n [-34, -44, -1, 43, -10],\n [-48, -20, -15, 33, -5],\n [-14, -50, 20, -2, -7]]\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 5x5 matrix:\n[[-17, 4, 29, -23, 27],\n [24, 12, -12, -12, 12],\n [0, 0, 0, 0, 0],\n [6, 8, -6, -14, 10],\n [14, 6, 16, -8, 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[[-24, 12, 18, -24, 24],\n [-20, 10, 15, -20, 20],\n [16, -8, -12, 16, -16],\n [16, -8, -12, 16, -16],\n [16, -8, -12, 16, -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[[0, -18, 0, -2, 8],\n [2, 43, 11, 11, -33],\n [-46, 4, 32, -6, -19],\n [-16, -25, 7, -7, 10],\n [26, -19, 10, 15, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-26, -35, -13, 6, 0],\n [-22, -22, 19, -34, 7],\n [70, -3, 7, -24, 36],\n [12, -15, -32, 15, -23],\n [14, 57, -19, 38, -44]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, 6, 18, 17, 3],\n [-6, 27, 40, 27, 28],\n [11, 54, 68, 37, 10],\n [3, 66, 76, 37, 22],\n [2, -21, -36, -27, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 41, -53, 27, 22],\n [10, 27, -33, 31, 32],\n [7, -12, 9, 28, 44],\n [-3, -32, 45, 15, 31],\n [5, 35, -50, -10, -25]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -4, -24, 35, -12],\n [27, -18, 7, -15, -8],\n [-42, 28, 18, -20, 24],\n [-39, 26, 21, -25, 24],\n [3, -2, -27, 40, -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 5x5 matrix:\n[[0, 0, 0, 0, 0],\n [24, -6, 36, 18, 12],\n [8, -2, 12, 6, 4],\n [-4, 1, -6, -3, -2],\n [-16, 4, -24, -12, -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[[-6, 9, -15, -9, 18],\n [12, -18, 30, 18, -36],\n [-2, 3, -5, -3, 6],\n [6, -9, 15, 9, -18],\n [4, -6, 10, 6, -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[[-6, 12, 9, -18, -9],\n [10, -20, -15, 30, 15],\n [0, 0, 0, 0, 0],\n [-4, 8, 6, -12, -6],\n [10, -20, -15, 30, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-38, 18, -55, -20, 22],\n [10, 43, -5, -36, -4],\n [12, 7, 14, -4, -8],\n [-28, -17, -21, 14, 9],\n [-30, -33, -27, 24, 18]]\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 5x5 matrix:\n[[25, -30, -20, 15, 30],\n [-30, 36, 24, -18, -36],\n [25, -30, -20, 15, 30],\n [5, -6, -4, 3, 6],\n [-15, 18, 12, -9, -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[[-10, 4, 0, -12, -6],\n [25, -10, 0, 30, 15],\n [30, -12, 0, 36, 18],\n [10, -4, 0, 12, 6],\n [-25, 10, 0, -30, -15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-28, 5, 38, -35, 40],\n [-38, -9, 36, -47, 52],\n [-15, -2, 37, -27, 26],\n [38, 29, -28, 51, -52],\n [37, 43, -35, 58, -54]]\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, 24, 0, -42, 33],\n [48, 24, 0, -24, 42],\n [20, 4, 0, 4, 11],\n [30, 24, 0, -36, 36],\n [13, 20, 0, -38, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0, 0],\n [-30, 10, -15, -25, 0],\n [30, -10, 15, 25, 0],\n [-12, 4, -6, -10, 0],\n [12, -4, 6, 10, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, -24, 4, 24, -8],\n [4, 12, -2, -12, 4],\n [8, 24, -4, -24, 8],\n [4, 12, -2, -12, 4],\n [-12, -36, 6, 36, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-10, 2, 2, 0, -8],\n [30, -6, -6, 0, 24],\n [20, -4, -4, 0, 16],\n [25, -5, -5, 0, 20],\n [-15, 3, 3, 0, -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[[26, 22, -21, -39, 18],\n [-32, -20, 1, 33, -16],\n [-38, -10, -48, -14, -4],\n [-4, -10, -28, 14, -23],\n [-42, -2, 2, 8, 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[[-39, 12, -58, -22, -24],\n [5, 4, 2, 14, 2],\n [32, 0, 38, 30, 19],\n [4, 30, -24, -10, 8],\n [41, -28, 76, 0, 27]]?\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[[-16, 29, 17, -51, -55],\n [29, 27, -19, 29, 60],\n [-1, -43, -6, -5, -15],\n [7, -37, -18, -23, -23],\n [7, 69, 7, -8, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[36, 12, 13, 21, -50],\n [5, 10, -10, 30, -25],\n [18, -12, 32, -48, 14],\n [7, -10, 20, -36, 17],\n [-14, -4, -6, -6, 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 5x5 matrix:\n[[-4, 0, -14, 11, 9],\n [5, -13, 11, -4, 5],\n [0, -16, -8, 12, 20],\n [7, -31, 9, 4, 23],\n [-3, 23, 1, -9, -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[[-10, -29, 0, 1, -25],\n [-9, 6, 6, 0, 24],\n [-26, 26, 6, -28, 64],\n [28, -4, -12, 8, -48],\n [-16, 10, -3, -29, 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[[-6, 4, -8, 12, 2],\n [-3, 2, -4, 6, 1],\n [0, 0, 0, 0, 0],\n [-6, 4, -8, 12, 2],\n [-15, 10, -20, 30, 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 5x5 matrix:\n[[1, 1, -4, -5, 6],\n [-5, -5, 20, 25, -30],\n [1, 1, -4, -5, 6],\n [4, 4, -16, -20, 24],\n [5, 5, -20, -25, 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[[20, 20, -8, 20, 12],\n [5, 5, -2, 5, 3],\n [30, 30, -12, 30, 18],\n [0, 0, 0, 0, 0],\n [25, 25, -10, 25, 15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[20, -24, -24, -12, 16],\n [-5, 6, 6, 3, -4],\n [-25, 30, 30, 15, -20],\n [5, -6, -6, -3, 4],\n [-25, 30, 30, 15, -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[[-13, -28, -11, 36, 27],\n [26, 26, 22, -47, -34],\n [-10, 17, 36, -9, -52],\n [-7, -22, 15, 23, -3],\n [20, 23, 30, -40, -42]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-20, 0, -16, 0, 8],\n [-5, 0, -4, 0, 2],\n [30, 0, 24, 0, -12],\n [5, 0, 4, 0, -2],\n [20, 0, 16, 0, -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[[5, -22, -2, 22, -8],\n [45, 12, -21, 24, -42],\n [-10, 14, 18, -6, -36],\n [15, 4, -20, 28, -38],\n [0, -25, -4, 29, -15]]\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, 6, 36, 36, 30],\n [0, -3, -18, -18, -15],\n [0, -1, -6, -6, -5],\n [0, 3, 18, 18, 15],\n [0, 5, 30, 30, 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[[-26, 4, -6, 10, 5],\n [32, -4, 4, -16, -8],\n [16, -2, 2, -8, -4],\n [-8, 4, -12, -8, -4],\n [-18, 3, -5, 6, 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[[-3, 3, 48, -58, -4],\n [-11, -37, 25, -78, -41],\n [-3, -6, 27, -36, 0],\n [-5, -19, 24, -38, 4],\n [9, 33, -25, 62, 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[[-43, -12, 44, 8, -22],\n [29, 31, -23, -11, 34],\n [17, -44, -54, -10, -20],\n [34, 34, 0, -24, 18],\n [-26, -38, -36, -4, -6]]\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[[14, -28, -10, -22, 6],\n [-32, 17, -43, -15, 25],\n [-12, 33, -16, -36, 54],\n [20, -39, -2, -6, -8],\n [-18, -4, -18, 2, -34]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-17, -12, -13, 31, -19],\n [-39, -35, -40, 5, 15],\n [21, -19, 4, -23, -21],\n [-8, 2, 3, 29, -22],\n [5, 12, -2, 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[[17, 1, 12, -35, -36],\n [2, 19, 1, -10, 19],\n [1, 18, 28, -4, 6],\n [18, -14, -35, 15, -12],\n [18, -30, -43, 7, -32]]\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[[-2, -4, 9, 11, -18],\n [-6, -6, 18, 12, -42],\n [-31, 37, 45, 49, -27],\n [12, -6, -15, 14, 42],\n [-2, -6, 12, 18, -22]]?\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, -63, -9, -16, -47],\n [-24, 7, -28, 26, 26],\n [20, -37, 31, -20, -27],\n [4, 66, 15, 6, 37],\n [16, 9, 27, -12, -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[[20, 21, -3, 21, -13],\n [-24, -21, 15, -33, -31],\n [-9, -12, -3, -15, -13],\n [-50, -57, 3, -75, -59],\n [35, 30, -21, 39, 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[[-24, 3, 12, -36, 27],\n [-2, -5, -5, 9, 0],\n [-14, 0, 5, -17, 15],\n [-24, -18, -12, 12, 18],\n [0, -7, -8, 16, -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[[4, 13, 5, -7, -3],\n [22, -16, 10, -36, 16],\n [27, -19, 16, -37, 14],\n [-7, -14, -5, 16, -1],\n [18, -22, 16, -10, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-18, 43, 42, 54, 11],\n [25, -30, -18, -38, -8],\n [26, -9, 18, -10, -1],\n [-15, 9, 0, 12, 3],\n [13, -31, -48, -44, -13]]\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[[5, 5, 6, -18, 4],\n [-22, -22, -42, -4, -28],\n [16, 16, 33, 16, 22],\n [-16, -16, -27, 16, -18],\n [21, 21, 39, -2, 26]]?\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[[-2, -1, 6, 3, -5],\n [13, 4, -36, -18, 24],\n [-4, 3, 6, 3, 7],\n [-6, -8, 24, 12, -32],\n [2, -9, 6, 3, -29]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-5, 4, 6, 4, 2],\n [-10, 8, 12, 8, 4],\n [10, -8, -12, -8, -4],\n [10, -8, -12, -8, -4],\n [-30, 24, 36, 24, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, 7, 35, 36, -6],\n [-8, 1, 29, 28, -2],\n [10, 22, -13, -4, -13],\n [10, 25, -10, 0, -15],\n [-8, -5, 23, 20, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 4, -12, -6, -6],\n [-10, 10, -6, -13, -5],\n [8, 12, -12, -26, -13],\n [-24, -2, -6, 22, 8],\n [38, -14, -14, 13, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0, 0],\n [-8, -20, 0, 0, 16],\n [-8, -20, 0, 0, 16],\n [-8, -20, 0, 0, 16],\n [-8, -20, 0, 0, 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 5x5 matrix:\n[[24, -28, -8, 0, -12],\n [12, -14, -4, 0, -6],\n [-1, -23, -3, 20, 3],\n [-9, 25, 5, -12, 3],\n [-26, 40, 10, -8, 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[[40, 13, 34, 12, 35],\n [-8, -8, -6, 12, 8],\n [-4, 5, -12, 51, 48],\n [4, -50, 22, 39, 47],\n [-52, -16, -48, 15, -15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, -5, 1, 9, 9],\n [-8, -3, 9, 1, -1],\n [-5, -21, 0, 40, 41],\n [-20, 1, 25, -15, -21],\n [11, 19, -8, -32, -31]]?\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, -15, 0, -6, -12],\n [-22, 5, -18, 2, 4],\n [-24, -15, 0, -6, -12],\n [2, 20, -18, 8, 16],\n [16, 35, -24, 14, 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[[-3, -12, -15, -9, -6],\n [-2, -8, -10, -6, -4],\n [1, 4, 5, 3, 2],\n [-6, -24, -30, -18, -12],\n [-4, -16, -20, -12, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-24, 4, -6, 12, 8],\n [4, 1, 6, -12, 7],\n [-12, 6, 9, -18, 24],\n [-16, 6, 6, -12, 22],\n [-16, 4, 0, 0, 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[[12, 10, -8, -4, 12],\n [-36, -30, 24, 12, -36],\n [24, 20, -16, -8, 24],\n [-24, -20, 16, 8, -24],\n [-30, -25, 20, 10, -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[[0, 6, -12, 12, 8],\n [0, 9, -18, 18, 12],\n [0, -12, 24, -24, -16],\n [0, -9, 18, -18, -12],\n [0, -12, 24, -24, -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 5x5 matrix:\n[[-24, -2, 29, -55, 33],\n [-32, 6, 37, -31, 21],\n [-28, -14, 9, 21, -16],\n [-38, -36, 3, 11, -16],\n [15, 31, 2, 44, -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[[16, -20, 8, 24, -16],\n [21, -20, 2, 21, -16],\n [-41, 20, 22, -9, 16],\n [17, 10, -34, -27, 8],\n [24, -30, 12, 36, -24]]?\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, -29, 27, -9, 11],\n [17, 35, -29, 21, 17],\n [-30, -18, 30, -72, -6],\n [25, 27, -29, 24, -11],\n [-16, -30, 26, -24, -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 5x5 matrix:\n[[-6, -48, -40, -26, 4],\n [12, -36, 1, 10, -33],\n [36, -2, -35, -33, -25],\n [6, -19, 46, 27, -64],\n [-45, -27, 16, -11, -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 5x5 matrix:\n[[3, 35, 3, 2, -65],\n [11, 50, -7, 6, -85],\n [9, 28, -4, 4, 41],\n [-22, 37, -40, -35, -60],\n [-24, -38, -1, -21, 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 5x5 matrix:\n[[-3, 60, 9, 10, 21],\n [25, 33, -8, -19, -4],\n [-46, 14, 33, 44, 22],\n [-21, -58, 14, 22, -14],\n [21, 34, -11, -20, 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[[-14, -44, -9, 10, 29],\n [-31, -28, -11, -28, 14],\n [-9, 12, 1, -24, -8],\n [-8, 30, -3, -30, -31],\n [36, 24, 51, 6, 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[[18, -30, -24, 36, 36],\n [-18, 30, 24, -36, -36],\n [-6, 10, 8, -12, -12],\n [-12, 20, 16, -24, -24],\n [12, -20, -16, 24, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 46, -3, -4, -29],\n [33, 28, 31, 36, -9],\n [-60, -23, -33, -41, 15],\n [-15, -31, -16, 1, 35],\n [39, 23, 36, 35, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[9, 1, -37, -38, -13],\n [12, -4, 2, -24, 58],\n [3, 5, -28, -36, -2],\n [27, -21, 3, 6, 27],\n [-27, 23, -11, -16, -29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-24, 18, 18, -12, 30],\n [-12, 9, 9, -6, 15],\n [-16, 12, 12, -8, 20],\n [-16, 12, 12, -8, 20],\n [20, -15, -15, 10, -25]]\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, -6, -10, 6, -12],\n [-42, 18, 22, -18, -4],\n [18, -18, -14, 18, 44],\n [22, -15, -14, 15, 25],\n [-36, 18, 20, -18, -14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 3, -26, 28, 36],\n [25, -15, 5, 10, -30],\n [24, -12, -16, 32, 0],\n [27, -15, -5, 22, -18],\n [-2, 0, 10, -12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-14, 4, -38, 31, 16],\n [27, 0, 45, -36, -27],\n [-19, 2, -43, 35, 20],\n [16, -20, 28, -20, -26],\n [8, 28, 36, -34, 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 5x5 matrix:\n[[-6, 17, 6, 28, -20],\n [12, -25, 42, -20, 13],\n [-18, 12, 9, 6, -12],\n [-20, 11, 21, 6, -14],\n [-44, 45, -9, 34, -38]]\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 5x5 matrix:\n[[15, -5, 10, 0, 20],\n [3, -1, 2, 0, 4],\n [-15, 5, -10, 0, -20],\n [6, -2, 4, 0, 8],\n [6, -2, 4, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, 12, 0, -6, 18],\n [5, 20, 0, -10, 30],\n [3, 12, 0, -6, 18],\n [-1, -4, 0, 2, -6],\n [5, 20, 0, -10, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, 15, 9, 0, -18],\n [-18, -30, -18, 0, 36],\n [-12, -20, -12, 0, 24],\n [-15, -25, -15, 0, 30],\n [-3, -5, -3, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-67, -23, -50, 58, -26],\n [-13, -5, -3, 12, 7],\n [13, 9, 34, -6, 42],\n [9, 1, 11, -8, 13],\n [-4, 4, 0, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 10, 41, -45, -21],\n [25, -43, 42, -25, -18],\n [4, -46, 19, -13, -19],\n [-15, 23, -9, 14, -7],\n [-24, 48, -60, 36, 36]]?\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[[2, 27, 22, 14, -20],\n [32, 21, -20, -14, 24],\n [-4, 0, -26, -18, -10],\n [-12, -18, -24, -16, -4],\n [-5, -45, -10, -5, 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[[60, -14, -32, -52, 40],\n [32, 3, -31, -5, 34],\n [-24, -3, 43, -15, -26],\n [-4, -7, 25, -25, -12],\n [26, -15, -26, -20, 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 5x5 matrix:\n[[-20, 32, 0, 27, -11],\n [6, 12, 14, 9, -3],\n [-7, 25, -12, 24, 3],\n [-39, 21, -16, 18, -15],\n [4, -25, 45, -30, -22]]\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[[36, 2, -46, 56, -16],\n [0, 7, 37, -20, -2],\n [-26, -9, 47, -36, 4],\n [-17, 4, 21, -32, 11],\n [-21, 14, 13, -46, 22]]?\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[[9, -48, -17, 16, -3],\n [0, 27, 21, -27, 15],\n [12, 25, 11, -25, 1],\n [-15, 13, -26, 43, -35],\n [-12, 14, -14, 26, -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[[25, -5, 30, -20, 0],\n [30, -6, 36, -24, 0],\n [25, -5, 30, -20, 0],\n [25, -5, 30, -20, 0],\n [15, -3, 18, -12, 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[[-30, -15, 25, 30, -30],\n [-30, -15, 25, 30, -30],\n [24, 12, -20, -24, 24],\n [6, 3, -5, -6, 6],\n [18, 9, -15, -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 5x5 matrix:\n[[-24, -34, -8, -10, 8],\n [18, 22, 5, 8, -6],\n [18, 36, 9, 6, -6],\n [6, 5, 1, 3, -2],\n [-24, 8, 4, -16, 8]]\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, -20, -5, 25, -15],\n [24, -24, -6, 30, -18],\n [-16, 16, 4, -20, 12],\n [-4, 4, 1, -5, 3],\n [-16, 16, 4, -20, 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[[3, 29, -12, -8, -26],\n [-22, 1, -15, -28, 2],\n [4, 23, 6, -5, -31],\n [-32, -7, -3, -38, 0],\n [-13, -7, 6, -14, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[23, 9, 53, -42, -30],\n [-23, -21, -17, 22, 14],\n [-26, -27, -17, -2, 14],\n [-11, -17, 11, -6, -2],\n [-17, -24, 10, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[30, 25, 20, -40, -7],\n [9, -10, 34, 0, 0],\n [-9, -8, -22, 20, 29],\n [-19, 8, -30, 3, -17],\n [27, 9, 30, -28, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[80, 39, -2, 36, 16],\n [-43, 1, -14, -14, -7],\n [34, -11, 2, 10, 6],\n [-16, -10, -34, -1, 34],\n [33, -6, -12, 12, 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[[12, 20, 8, -16, 2],\n [-38, -22, -51, -9, 13],\n [-24, -52, -25, 23, -14],\n [24, 24, 24, -12, -4],\n [44, 48, 62, 5, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-35, -49, 16, 76, -19],\n [-10, -16, -2, 23, -3],\n [3, 37, -34, -12, -7],\n [26, 90, 10, -36, -40],\n [-10, -31, 25, 10, 7]]\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 5x5 matrix:\n[[-3, 50, -19, -60, 24],\n [-1, -38, 6, 25, 23],\n [2, 36, -17, -27, -25],\n [6, 49, 22, -2, -34],\n [3, -18, -20, 8, 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[[-21, -16, -13, 4, -12],\n [1, -6, -22, 13, -27],\n [12, 43, -16, 31, 12],\n [4, 22, 5, 5, 29],\n [1, -13, 20, -20, 3]]\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[[3, -6, -6, 18, 12],\n [-3, 6, 6, -18, -12],\n [3, -6, -6, 18, 12],\n [4, -8, -8, 24, 16],\n [-4, 8, 8, -24, -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 5x5 matrix:\n[[-19, 27, -4, -10, -9],\n [29, -7, 15, -20, 36],\n [-37, 17, -12, 13, -39],\n [-59, 25, -15, 19, -62],\n [33, -25, 34, -23, 37]]\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[[-55, -15, -45, -25, -15],\n [38, 6, 5, -2, 33],\n [-13, -36, 20, -8, -8],\n [-3, 22, -7, 9, -4],\n [-46, 10, -2, 16, -52]]?\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, -5, -2, -6, -6],\n [-2, 5, 2, 6, 6],\n [-8, 20, 8, 24, 24],\n [6, -15, -6, -18, -18],\n [-4, 10, 4, 12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-10, 3, 17, 4, -11],\n [42, 35, -1, 28, 49],\n [-40, -42, -24, -28, -54],\n [46, 12, 43, 44, 14],\n [12, 31, -16, 24, 19]]\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[[12, 24, -12, 4, 0],\n [-8, -7, 2, -2, -4],\n [17, 25, -11, 5, 4],\n [13, -19, 17, 1, 20],\n [-30, -33, 12, -8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-67, -26, -13, 6, 17],\n [-42, -45, 45, 32, 43],\n [-90, -51, 22, 19, 54],\n [-20, -45, 50, 39, 34],\n [-4, -5, 4, 13, -6]]\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, 24, 3, 2, -25],\n [23, -2, 2, 16, 26],\n [8, -5, 5, 34, -4],\n [-10, -2, -4, -24, -2],\n [-32, 20, 0, -16, -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[[-8, 6, 62, 11, 15],\n [39, -17, 32, 13, -2],\n [-43, 27, 34, -14, 0],\n [17, -27, 4, 49, 54],\n [39, -7, 34, -10, -31]]\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, -3, -3, -1, 6],\n [-20, 15, 15, 5, -30],\n [-4, 3, 3, 1, -6],\n [12, -9, -9, -3, 18],\n [-24, 18, 18, 6, -36]]?\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 5x5 matrix:\n[[38, -44, -11, -22, -8],\n [27, -28, -16, 5, -8],\n [24, 45, 18, 34, -11],\n [2, -14, -2, 22, -10],\n [10, -11, -44, 24, 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[[34, 22, 2, -24, 11],\n [-13, -11, -2, 24, -25],\n [9, -23, 37, 66, 36],\n [42, 42, -20, -60, -23],\n [33, 1, 33, 18, 62]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[20, -19, -3, 2, -25],\n [-35, -25, 36, -23, 18],\n [13, 20, -11, 16, 25],\n [-16, 18, -6, -4, -2],\n [-23, 16, 5, -5, 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[[-20, -20, 16, -8, 12],\n [-10, -10, 8, -4, 6],\n [5, 5, -4, 2, -3],\n [-30, -30, 24, -12, 18],\n [-5, -5, 4, -2, 3]]?\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, -16, -32, -3, -33],\n [-33, -6, -4, -4, -48],\n [-43, 20, -36, 53, 24],\n [-16, 30, 0, 19, -3],\n [29, 24, 34, -10, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[38, -19, -4, -58, 30],\n [-59, -7, 14, 24, -9],\n [45, -27, -19, -57, 21],\n [-25, 21, 2, 52, -27],\n [4, -45, -48, -10, -24]]?\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, 12, -18, -24, -18],\n [-8, -4, -8, 4, -8],\n [20, 20, 12, -28, 12],\n [19, 7, 21, -5, 21],\n [-5, -5, -3, 7, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 8, -10, -2, -4],\n [4, 4, -5, -1, -2],\n [16, 16, -20, -4, -8],\n [4, 4, -5, -1, -2],\n [-12, -12, 15, 3, 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[[-4, -8, 8, 20, 24],\n [1, 2, -2, -5, -6],\n [6, 12, -12, -30, -36],\n [2, 4, -4, -10, -12],\n [-3, -6, 6, 15, 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[[-10, 68, -21, -2, 18],\n [29, -10, 46, -23, -27],\n [-20, -12, 11, 25, 39],\n [19, 23, 21, -15, -14],\n [-15, -20, -37, -11, -13]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[16, 56, -3, 3, 16],\n [11, 38, 55, -9, 29],\n [-20, 7, -10, 36, -11],\n [16, 42, -25, 40, 7],\n [-12, 11, 58, 26, 15]]\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[[80, -62, 29, 61, 9],\n [-52, 41, -7, -40, 6],\n [-50, 31, -37, -36, -26],\n [2, 6, -30, -4, -32],\n [-58, 51, -7, -42, 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[[4, -22, -38, -27, -9],\n [1, -2, 0, -6, 0],\n [-19, -14, -28, -48, -2],\n [1, -12, -22, -15, -5],\n [-18, 4, -20, 12, -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[[-6, 0, 51, 18, -9],\n [-3, 12, -15, 0, 0],\n [10, -4, 39, 12, 7],\n [-15, -12, -36, -18, -15],\n [2, -2, -6, -3, 2]]\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 5x5 matrix:\n[[-20, 0, 12, 24, -4],\n [20, 0, -12, -24, 4],\n [-5, 0, 3, 6, -1],\n [-20, 0, 12, 24, -4],\n [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[[38, -55, -46, -33, 29],\n [50, -12, -64, -14, -4],\n [-17, -43, 18, -18, 28],\n [6, 10, -12, 4, -12],\n [0, 16, -8, 8, -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[[6, 3, -3, -1, -8],\n [30, -3, 3, -11, 2],\n [-48, 12, -12, 20, -20],\n [30, -9, 9, -13, 16],\n [-30, 15, -15, 15, -30]]\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 5x5 matrix:\n[[9, 18, -15, -3, 0],\n [-18, -36, 30, 6, 0],\n [6, 12, -10, -2, 0],\n [-3, -6, 5, 1, 0],\n [-18, -36, 30, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 10, 8, 0, 0],\n [0, -30, -24, 0, 0],\n [0, 25, 20, 0, 0],\n [0, 20, 16, 0, 0],\n [0, -30, -24, 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 5x5 matrix:\n[[-15, 12, 84, -46, -46],\n [-11, -34, -14, -17, -22],\n [17, 16, -65, 67, 68],\n [22, -1, -3, 1, 28],\n [-16, -11, 8, -31, -50]]\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[[3, 4, 12, -25, -5],\n [32, 28, -10, -15, 14],\n [-16, -32, -16, 15, 20],\n [-2, -2, -9, 20, 3],\n [-6, -14, -15, 20, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, -7, -3, 14, 3],\n [24, 57, -51, 15, 42],\n [-12, -33, 51, -24, -33],\n [-2, -33, 36, -26, -33],\n [6, 17, -40, 21, 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[[8, -44, -4, 40, 0],\n [-18, 13, 19, -10, -20],\n [-2, 54, -4, -50, 10],\n [-13, 50, 9, -45, -5],\n [-23, 19, 24, -15, -25]]\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[[-22, -26, -16, -6, 24],\n [-34, -38, -8, -18, 32],\n [-18, -21, -11, -6, 19],\n [-33, -39, -24, -9, 36],\n [-18, -24, -34, 6, 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 5x5 matrix:\n[[-49, 31, -6, -7, -67],\n [29, 4, -24, -13, 7],\n [-13, 4, 39, 24, 1],\n [15, 40, 23, 8, -20],\n [-2, 25, -38, -22, -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 5x5 matrix:\n[[14, 46, 19, -32, -32],\n [28, 45, 60, -42, 49],\n [-8, -21, -24, 36, 29],\n [-11, -35, -32, 46, 29],\n [17, 20, 71, -70, 12]]\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, 18, -6, 0, -6],\n [10, -3, -29, -24, -11],\n [0, -3, 21, 16, 9],\n [-19, 12, 11, 12, 2],\n [-9, 9, -18, -12, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-10, -5, 15, -10, -20],\n [-8, -4, 12, -8, -16],\n [-4, -2, 6, -4, -8],\n [8, 4, -12, 8, 16],\n [-2, -1, 3, -2, -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[[-18, 16, -55, 28, -29],\n [-38, -29, 0, 9, 12],\n [-24, -38, 37, -10, 31],\n [36, 30, 6, -6, -6],\n [-17, -8, -51, 6, -33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[11, -32, 5, -14, -29],\n [-45, 75, 30, 35, 15],\n [-29, 20, 43, -16, -1],\n [-6, -7, 19, -7, -22],\n [-12, -7, 31, -21, -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 5x5 matrix:\n[[1, -9, 3, 12, 14],\n [24, 51, -2, 6, -20],\n [-20, -39, 4, -12, 12],\n [-7, 9, -22, -11, -26],\n [-44, -66, 1, -45, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, -3, 6, 0, -4],\n [18, 18, -36, 0, 24],\n [-9, -9, 18, 0, -12],\n [-3, -3, 6, 0, -4],\n [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[[10, -2, -12, 0, -10],\n [15, -3, -18, 0, -15],\n [15, -3, -18, 0, -15],\n [15, -3, -18, 0, -15],\n [-25, 5, 30, 0, 25]]\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[[5, -6, 4, 5, 6],\n [-16, 17, -8, -33, 44],\n [-12, 19, -6, -31, 38],\n [44, -22, 28, 42, -20],\n [-19, -38, -8, 13, 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[[3, 1, 7, 56, -3],\n [23, -41, 2, -10, 6],\n [-32, 43, -9, -17, -33],\n [46, -56, 12, 2, 72],\n [-1, 13, 8, -62, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[60, 42, 57, -16, 56],\n [-30, -12, -17, -2, 10],\n [-24, -9, -6, -5, 16],\n [6, 12, -35, 10, -2],\n [18, 15, -6, 3, 6]]?\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[[-10, -6, 2, -10, -6],\n [0, 0, 0, 0, 0],\n [20, 12, -4, 20, 12],\n [-10, -6, 2, -10, -6],\n [-25, -15, 5, -25, -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[[0, 0, 0, 0, 0],\n [0, -12, 4, -8, -8],\n [0, -18, 6, -12, -12],\n [0, -30, 10, -20, -20],\n [0, 12, -4, 8, 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 5x5 matrix:\n[[-12, -12, 6, 8, -6],\n [-6, -6, 3, 4, -3],\n [-30, -30, 15, 20, -15],\n [-36, -36, 18, 24, -18],\n [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[[-8, 0, -20, 0, 16],\n [-2, 0, -5, 0, 4],\n [6, 0, 15, 0, -12],\n [-12, 0, -30, 0, 24],\n [-2, 0, -5, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, -1, 9, -11, 11],\n [-18, -30, -6, 30, -18],\n [-3, -23, 23, -13, 21],\n [12, 26, -4, -14, 4],\n [-6, 8, -26, 28, -30]]\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 5x5 matrix:\n[[-5, 22, -11, -1, 2],\n [-15, 13, 27, -10, -16],\n [-35, -12, 12, -37, 42],\n [60, -30, -46, 50, -12],\n [-20, -31, 26, -25, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-55, 6, -23, 26, 10],\n [7, 12, 0, 7, -13],\n [16, 52, 2, -26, -50],\n [-5, -24, 2, -5, 23],\n [27, -60, 16, 9, 45]]\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, -38, -28, -27, 22],\n [0, -38, -32, -20, 36],\n [0, -48, -40, -26, 44],\n [0, -28, -16, -28, 0],\n [0, 56, 44, 35, -42]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 23, 19, 8, -10],\n [-16, -19, 21, -22, 0],\n [-4, 13, 4, 2, 44],\n [20, 60, 5, 40, -20],\n [16, -6, -26, 12, -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 5x5 matrix:\n[[12, 16, -16, -32, -20],\n [-36, 24, 8, 8, 20],\n [18, -3, -9, -15, -15],\n [21, 1, -13, -23, -20],\n [-18, -6, 14, 26, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[39, -40, 18, -5, -45],\n [18, -15, 18, 6, -18],\n [9, 5, 44, 33, 1],\n [-15, 15, -8, 1, 17],\n [54, -60, 12, -18, -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[[12, -20, -12, 0, 20],\n [9, -15, -9, 0, 15],\n [-18, 30, 18, 0, -30],\n [6, -10, -6, 0, 10],\n [-15, 25, 15, 0, -25]]\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, -36, 14, -18, 21],\n [20, -28, 32, -14, 29],\n [3, -8, -18, -4, -8],\n [-5, 8, -2, 4, -4],\n [-19, 32, 2, 16, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, -20, -20, -24, -8],\n [12, 30, 30, 36, 12],\n [-8, -20, -20, -24, -8],\n [12, 30, 30, 36, 12],\n [10, 25, 25, 30, 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[[13, 9, 12, 17, -21],\n [22, 16, 21, 30, -36],\n [-5, -15, -15, -25, 15],\n [-13, -19, -21, -33, 27],\n [-6, 12, 9, 18, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[56, 16, -36, 0, 38],\n [-28, 28, 78, -8, -16],\n [50, 16, -12, 26, 35],\n [-9, 6, -9, -21, 12],\n [-7, 26, 9, -59, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[49, 35, 17, 13, 49],\n [9, -16, -8, -3, -18],\n [27, 29, -4, 21, 55],\n [16, 3, -23, -14, -2],\n [11, 13, -16, 1, 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[[8, 0, -4, -24, -8],\n [-6, 0, 3, 18, 6],\n [10, 0, -5, -30, -10],\n [6, 0, -3, -18, -6],\n [10, 0, -5, -30, -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[[42, 44, -30, -48, -24],\n [-27, -18, -13, 17, -8],\n [-3, 3, -17, -5, -13],\n [24, 25, -16, -28, -17],\n [-12, -14, 10, 19, 26]]\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 5x5 matrix:\n[[41, -8, 2, 7, -23],\n [-24, -8, 12, 12, 12],\n [-6, -2, 3, 3, 3],\n [-13, -26, 29, 34, 4],\n [22, -10, 7, 11, -13]]\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, 2, 23, 6, 5],\n [18, -24, -10, 4, 16],\n [-8, 8, 8, 0, -4],\n [-11, 14, 7, -2, -9],\n [14, -44, 26, 20, 42]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, 7, -27, 5, 16],\n [8, 14, 15, -36, 25],\n [4, 22, 1, 16, -61],\n [2, 1, -17, -5, 27],\n [27, 26, 9, -13, 6]]\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[[-8, 3, -15, 1, 9],\n [0, -14, -10, -2, 22],\n [-2, 13, 5, 2, -17],\n [32, -54, 30, -10, 30],\n [-16, 41, -5, 7, -37]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, 1, -1, 36, -18],\n [13, 17, -3, -16, 13],\n [-27, -21, 9, -22, -2],\n [0, -56, 6, 6, -8],\n [-32, -17, -3, -7, 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 5x5 matrix:\n[[18, -12, 60, 0, -21],\n [-12, 13, 34, -3, -17],\n [-29, -14, 5, 25, 22],\n [-10, -44, -22, 42, 32],\n [1, -7, -32, 10, 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[[30, -42, -42, -12, 48],\n [12, 28, 21, -16, -34],\n [3, -17, -15, 2, 20],\n [8, 8, 5, -8, -10],\n [20, 4, -1, -16, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, 4, 28, -11, 26],\n [-6, 45, 0, -36, 3],\n [-3, 24, -22, -13, -18],\n [-6, 19, 8, -16, 21],\n [-1, -18, -4, 17, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[18, 0, 12, 6, 12],\n [12, 0, 8, 4, 8],\n [18, 0, 12, 6, 12],\n [-18, 0, -12, -6, -12],\n [3, 0, 2, 1, 2]]\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[[-25, 13, -34, 27, 30],\n [-8, -6, -24, 32, 14],\n [11, 19, -6, 3, 0],\n [15, -8, -4, 17, -7],\n [31, -38, 30, -5, -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[[-40, -22, 24, -18, 42],\n [-32, -20, 0, -12, 44],\n [-14, -5, 30, -9, 3],\n [46, 28, -6, 18, -60],\n [-18, -3, 66, -15, -11]]\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, 37, 28, 19, 15],\n [0, -2, 2, 2, 2],\n [-22, -3, -2, 1, -1],\n [0, -16, -24, -22, -16],\n [-44, -30, -40, -31, -26]]\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[[-8, 0, 8, 0, 20],\n [-8, 0, 8, 0, 20],\n [12, 0, -12, 0, -30],\n [-4, 0, 4, 0, 10],\n [2, 0, -2, 0, -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 5x5 matrix:\n[[-24, -29, -29, -11, -5],\n [-19, -15, 12, -42, 14],\n [-25, -34, -29, -13, -7],\n [33, 4, 18, 10, 6],\n [-29, 2, 5, -7, -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[[-50, -4, 30, 18, 4],\n [10, -10, -15, 9, -8],\n [45, 18, -15, -33, 6],\n [-35, -16, 10, 28, -6],\n [10, -10, -15, 9, -8]]\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, 0, 0, 0, 0],\n [7, -19, 4, 9, -5],\n [2, -18, 20, 34, -14],\n [-18, 42, 0, -6, 6],\n [11, -31, 8, 17, -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[[2, 18, -5, 20, 6],\n [-16, 38, -1, -41, -35],\n [21, -12, 84, -21, 18],\n [41, -18, -20, 40, 14],\n [-60, 48, -27, -2, -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[[24, -20, 20, 24, -4],\n [6, -5, 5, 6, -1],\n [-36, 30, -30, -36, 6],\n [-6, 5, -5, -6, 1],\n [-30, 25, -25, -30, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-5, 2, -4, -5, 6],\n [-15, 6, -12, -15, 18],\n [30, -12, 24, 30, -36],\n [30, -12, 24, 30, -36],\n [30, -12, 24, 30, -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[[-5, -6, 1, 3, -1],\n [20, 24, -4, -12, 4],\n [10, 12, -2, -6, 2],\n [-15, -18, 3, 9, -3],\n [-15, -18, 3, 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[[2, -46, 5, -43, 21],\n [-22, 13, -27, 5, 0],\n [4, 22, 22, 34, -24],\n [-22, -47, 3, -35, 10],\n [-16, 33, 1, 40, -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[[-30, -20, -15, -10, 25],\n [-12, -8, -6, -4, 10],\n [-18, -12, -9, -6, 15],\n [12, 8, 6, 4, -10],\n [36, 24, 18, 12, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-34, 24, -6, 8, 13],\n [-16, 21, -30, -16, 25],\n [-16, -5, -16, -2, -21],\n [34, -6, 20, -2, 17],\n [-20, 28, -34, -18, 34]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-14, -32, 16, 14, 2],\n [-25, 20, -10, -25, -5],\n [4, -14, 7, 11, 2],\n [-23, -14, 7, -2, -1],\n [-45, -18, 9, -10, -3]]\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 5x5 matrix:\n[[21, -12, 10, 0, 40],\n [-11, -34, 3, 12, 24],\n [3, 0, -10, 6, -23],\n [5, -18, 5, -2, -1],\n [-8, -1, -12, 21, 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[[27, 15, 0, 1, -4],\n [-8, 15, 0, -4, -9],\n [-3, -18, 0, 3, 9],\n [2, -9, 0, 2, 5],\n [-18, -24, 0, 2, 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 5x5 matrix:\n[[-16, -1, -7, 16, -27],\n [-1, 2, 2, 10, -9],\n [38, 13, 11, -8, 26],\n [-7, -1, -11, -2, -10],\n [-24, -12, -12, -12, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, -38, 26, 11, 24],\n [3, 7, -10, -16, 6],\n [36, -31, 8, 48, 7],\n [-24, -26, 38, -7, 12],\n [-35, 19, 8, 5, -30]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-10, 5, 10, -10, 25],\n [-24, -4, -16, -12, 24],\n [20, 14, 40, 2, 4],\n [30, 5, 20, 15, -30],\n [-34, -7, -26, -16, 31]]?\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, -64, 30, -7, 36],\n [-32, -38, -20, 6, -18],\n [-10, -46, 56, 1, 66],\n [-22, -66, 28, -21, 30],\n [22, 58, -35, 4, -42]]\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 5x5 matrix:\n[[16, 50, -6, -24, 24],\n [16, 26, -30, 0, 36],\n [-25, -52, 1, -3, -6],\n [29, 35, -2, 39, -12],\n [-8, 18, -14, -56, 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[[-20, 0, 4, -8, -4],\n [5, 0, -1, 2, 1],\n [-10, 0, 2, -4, -2],\n [30, 0, -6, 12, 6],\n [10, 0, -2, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[48, 31, -56, -45, -27],\n [-29, -46, -17, 20, -26],\n [-10, 8, -18, 12, -2],\n [8, 62, -8, 6, 28],\n [36, 42, 12, -14, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, -18, -6, 15, 6],\n [14, -28, 4, 18, -4],\n [12, -44, -8, 34, 8],\n [17, -46, -2, 33, 2],\n [-12, 44, 8, -34, -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[[-5, 20, -25, -30, -15],\n [5, -20, 25, 30, 15],\n [-6, 24, -30, -36, -18],\n [-3, 12, -15, -18, -9],\n [-5, 20, -25, -30, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-7, 18, -32, 16, 19],\n [20, -5, 20, 15, 10],\n [24, 7, 4, 35, 30],\n [24, 7, 4, 35, 30],\n [-24, 6, -24, -18, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 22, 28, 20, -18],\n [29, 1, 19, -18, -28],\n [-11, 16, 19, 16, -11],\n [-5, -20, -35, -8, 31],\n [13, -3, 3, -10, -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 5x5 matrix:\n[[-37, 31, 8, -10, 39],\n [-8, -11, -18, -2, -2],\n [-20, 18, -6, 38, -18],\n [53, -41, -3, -3, -38],\n [57, -49, -2, -28, -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[[-31, 5, 28, 34, -13],\n [6, 2, -2, 1, 6],\n [29, 23, 10, -13, 15],\n [-6, 17, 28, -2, -12],\n [33, 26, 10, -1, 25]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[30, -11, 4, -17, 10],\n [-18, 19, -6, 36, -40],\n [1, -14, 0, -36, 46],\n [-12, -1, 54, 6, 6],\n [-34, 5, 40, 13, 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 5x5 matrix:\n[[-6, -2, 6, 5, -3],\n [6, 2, -6, -5, 3],\n [-24, -8, 24, 20, -12],\n [-12, -4, 12, 10, -6],\n [12, 4, -12, -10, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, 40, -26, 18, 48],\n [-1, -17, 31, -6, -51],\n [-13, 12, 55, 11, -6],\n [-6, -49, 19, -23, -18],\n [4, 22, -12, 10, 6]]?\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, -26, 56, 14, -14],\n [27, -42, 72, 18, -12],\n [6, 4, -12, 0, -4],\n [25, -50, 62, 16, -2],\n [-8, 48, -5, -3, -26]]\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 5x5 matrix:\n[[-54, -9, -23, -13, 24],\n [-21, -44, -16, 14, -26],\n [25, 81, 25, -20, -2],\n [2, -6, -40, 41, -52],\n [-23, 3, -7, -17, 54]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-41, -34, 27, 15, 56],\n [6, -5, 24, 19, 0],\n [45, 25, -20, 5, -50],\n [10, -20, 28, 48, 12],\n [4, 0, -7, 3, -2]]?\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 5x5 matrix:\n[[-24, 21, -29, -23, -10],\n [2, -18, -13, 4, -25],\n [-7, -2, -29, -2, -14],\n [16, -14, 52, 6, 2],\n [14, 4, -12, 24, 38]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-30, -32, -29, -10, 29],\n [-38, -28, -20, 6, 22],\n [3, 48, 12, -15, -51],\n [4, 2, -22, 2, 18],\n [-14, -32, -32, 15, 49]]\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 5x5 matrix:\n[[-24, 24, 30, 12, -30],\n [0, 0, 0, 0, 0],\n [-24, 24, 30, 12, -30],\n [-4, 4, 5, 2, -5],\n [-4, 4, 5, 2, -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[[2, -14, 13, 6, -2],\n [24, -54, 48, 0, 12],\n [-34, -9, 13, 54, -44],\n [26, -49, 43, -6, 16],\n [-14, 22, -19, 6, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-23, -20, 18, -15, -19],\n [6, -73, -20, -48, -37],\n [-68, -32, 5, -21, -1],\n [33, -14, 18, -17, -47],\n [55, 51, 20, 31, -2]]\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, -2, 5, 4, -2],\n [-4, -4, 10, 8, -4],\n [4, 4, -10, -8, 4],\n [-4, -4, 10, 8, -4],\n [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[[15, 30, 3, 18, 54],\n [19, 26, 5, 24, 54],\n [-7, -18, -1, -8, -30],\n [7, -12, 4, 11, -6],\n [-24, -36, -6, -30, -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[[8, 18, 14, -6, -10],\n [-7, -22, -11, 9, 5],\n [3, -2, 7, 3, -9],\n [-13, 2, 27, -21, 3],\n [-11, -51, 28, 15, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[16, -12, 16, 16, 12],\n [16, -12, 16, 16, 12],\n [-24, 18, -24, -24, -18],\n [-16, 12, -16, -16, -12],\n [-24, 18, -24, -24, -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[[-8, -4, -24, -8, 20],\n [0, 0, 0, 0, 0],\n [-2, -1, -6, -2, 5],\n [6, 3, 18, 6, -15],\n [-10, -5, -30, -10, 25]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-28, -8, -48, 20, 12],\n [-18, -8, -30, 10, 11],\n [17, 2, 30, -15, -4],\n [-7, 18, -18, 25, -20],\n [-7, -22, -6, -15, 26]]\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[[1, 5, -4, 4, 2],\n [-4, -20, 16, -16, -8],\n [-6, -30, 24, -24, -12],\n [-3, -15, 12, -12, -6],\n [-2, -10, 8, -8, -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[[12, 20, 24, -34, 4],\n [6, -8, -24, 19, -16],\n [-24, -22, -12, 32, 10],\n [0, 3, 6, -6, 3],\n [12, 8, 0, -10, -8]]\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, -9, -3, -1, 12],\n [40, 31, -72, 29, 7],\n [-40, -22, 33, 0, -13],\n [-55, -16, 30, 15, -34],\n [-15, -25, 52, -32, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, 0, -3, -8, -7],\n [-34, -18, 30, 18, 34],\n [17, 8, -9, 0, -13],\n [-46, -25, 42, 25, 46],\n [13, 16, -18, 12, 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[[21, 23, -3, -10, -8],\n [-27, -33, 5, 10, 12],\n [3, -13, 5, -15, 7],\n [-18, -12, 0, 15, 3],\n [-30, -20, 0, 25, 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[[0, -16, -5, -6, 21],\n [-22, 8, 3, 23, 15],\n [-39, -30, -6, 61, 16],\n [0, -24, -15, -10, -13],\n [-76, -4, -3, 67, 73]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-60, 42, 6, -38, 6],\n [-14, 73, 0, 10, 0],\n [26, 14, 12, 26, -22],\n [-9, -35, 17, -18, -26],\n [14, -30, -10, 3, 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[[0, -5, 0, 1, 4],\n [0, -15, 0, 3, 12],\n [0, -10, 0, 2, 8],\n [0, -15, 0, 3, 12],\n [0, 10, 0, -2, -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[[-39, 12, -21, -45, 12],\n [-22, -3, -37, -20, -17],\n [29, -21, 32, 10, -5],\n [31, -7, 38, 25, 7],\n [39, -4, 11, 60, -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 5x5 matrix:\n[[4, -13, 15, 11, -1],\n [24, 15, 52, 37, -19],\n [2, -5, 6, -1, 0],\n [28, 23, 31, 35, -31],\n [-47, -85, -25, -55, 63]]\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[[-55, 35, 40, -55, -20],\n [12, -33, 6, 12, -12],\n [0, 0, 0, 0, 0],\n [42, -38, -24, 42, 8],\n [23, -9, -20, 23, 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 5x5 matrix:\n[[-19, 29, -1, 12, 5],\n [-31, 11, -19, 48, 35],\n [-7, -22, -16, 30, 26],\n [32, 2, 26, -60, -46],\n [-34, 18, -18, 48, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-30, -45, 51, -27, -12],\n [-14, -27, 29, -21, -8],\n [-2, 9, -7, 15, 4],\n [16, -12, 4, -36, -8],\n [-4, -27, 25, -33, -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[[8, 5, -46, 26, -3],\n [5, 20, 55, -50, 10],\n [62, 59, -27, -12, 41],\n [0, -16, -37, 38, -2],\n [-18, -8, -50, 28, -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[[-10, 5, 20, -30, -10],\n [-6, 3, 12, -18, -6],\n [-6, 3, 12, -18, -6],\n [12, -6, -24, 36, 12],\n [4, -2, -8, 12, 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[[20, -24, 20, -16, -20],\n [8, -16, 4, 8, -12],\n [-40, 56, -35, 14, 45],\n [-7, 2, -11, 20, 3],\n [24, -32, 22, -12, -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 5x5 matrix:\n[[19, 43, -12, 19, -28],\n [-6, -10, -34, -14, 18],\n [11, 23, 3, 13, -11],\n [23, 51, -32, 19, -8],\n [14, 30, -8, 14, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-14, 5, -16, 37, -29],\n [4, -31, 27, 17, -30],\n [15, 34, -24, -9, 30],\n [24, -34, 38, -7, 13],\n [-7, -18, 8, 27, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-23, 28, -8, -10, -22],\n [-25, 20, 2, -22, 0],\n [9, -9, 0, 15, -6],\n [-13, -22, 26, 20, 0],\n [7, 13, -16, -3, -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[[-5, 0, 0, 20, -20],\n [-1, 0, 0, 4, -4],\n [1, 0, 0, -4, 4],\n [-1, 0, 0, 4, -4],\n [1, 0, 0, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[36, 14, -30, 24, -57],\n [-18, -45, -6, 18, -57],\n [26, 39, -18, -6, 2],\n [-9, -12, 6, -6, 18],\n [32, 18, -12, 20, -24]]?\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, -4, -28, -32, -19],\n [-10, 19, 7, -22, -13],\n [-24, 6, -39, -24, -3],\n [-15, -4, 17, -4, -12],\n [5, -11, 13, 14, 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[[0, 16, 8, 0, 4],\n [0, 4, 2, 0, 1],\n [0, 8, 4, 0, 2],\n [0, 4, 2, 0, 1],\n [0, 12, 6, 0, 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[[-9, -30, 7, -38, 7],\n [18, -24, 26, -46, -10],\n [-7, 28, -19, 45, 3],\n [11, 4, 7, -1, -7],\n [-19, -26, -3, -26, 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[[-26, 28, 10, 4, -8],\n [-19, 18, 6, 2, -4],\n [-34, 12, 0, -4, 8],\n [32, 0, 6, 8, -16],\n [-24, 16, 4, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, 8, -7, 0, 0],\n [19, 0, 9, 20, 18],\n [-6, 30, -28, 30, -34],\n [16, 0, 8, 20, 14],\n [-1, 28, -23, 40, -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 5x5 matrix:\n[[-4, -22, 8, -10, 6],\n [12, -36, 12, 0, 30],\n [-12, -32, 12, -20, 2],\n [4, 56, -20, 20, -22],\n [-32, -6, 4, -30, -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 5x5 matrix:\n[[10, -2, 0, 10, -2],\n [-30, -30, 20, 15, 10],\n [25, 31, -20, -20, -9],\n [-9, 9, -4, -18, 1],\n [-13, -19, 12, 14, 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[[-5, -14, 8, -19, 6],\n [-36, -16, -4, -12, 20],\n [45, -1, 12, -13, -18],\n [51, 21, 34, 5, -32],\n [4, -31, 16, -44, 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[[51, 46, 4, 10, -14],\n [46, 43, 2, 10, -15],\n [-43, -37, -8, -15, 13],\n [-2, -1, 6, 20, -11],\n [-25, -33, 8, -15, 25]]\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[[42, -60, -20, 42, -50],\n [27, -42, -20, 33, -35],\n [3, 6, 20, -15, 5],\n [-17, 30, 20, -27, 25],\n [9, -18, -15, 18, -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[[-6, 20, -4, -28, 14],\n [-8, 34, -12, -44, 20],\n [-4, -27, 34, 18, 2],\n [-6, 42, -24, -48, 18],\n [-10, -7, 30, -10, 16]]\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[[-3, 0, -15, -3, 0],\n [-11, -4, -30, -7, 6],\n [-23, -16, -15, -7, 24],\n [-20, -16, 0, -4, 24],\n [-12, -8, -10, -4, 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[[-33, -4, 4, -13, 11],\n [30, -5, -29, 24, -30],\n [-6, -19, -6, 10, -2],\n [15, -8, 7, 9, 3],\n [42, 22, -23, 12, -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 5x5 matrix:\n[[24, -33, 9, -15, -21],\n [10, -16, 4, -8, -12],\n [10, -7, 3, -1, 1],\n [12, -21, 5, -11, -17],\n [-9, 0, -2, -4, -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[[18, 18, 12, -30, 0],\n [-3, -3, -2, 5, 0],\n [15, 15, 10, -25, 0],\n [15, 15, 10, -25, 0],\n [6, 6, 4, -10, 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 5x5 matrix:\n[[-30, 0, -32, -11, -6],\n [-12, -7, 19, 61, 32],\n [-4, -11, 15, 21, 32],\n [16, 10, -14, -50, -36],\n [-2, 14, -12, 9, -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[[24, 16, 8, -24, 4],\n [-12, -8, -4, 12, -2],\n [-12, -8, -4, 12, -2],\n [-6, -4, -2, 6, -1],\n [-24, -16, -8, 24, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-4, -16, 24, 24, -4],\n [2, 8, -12, -12, 2],\n [-5, -20, 30, 30, -5],\n [2, 8, -12, -12, 2],\n [4, 16, -24, -24, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[0, 9, -3, 1, 25],\n [-6, -18, 60, -48, -30],\n [-7, -4, 27, -30, -15],\n [12, -4, -16, 33, 15],\n [-5, -11, 6, -12, -45]]\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[[22, 0, -16, 18, -38],\n [20, 1, 21, -12, 0],\n [-33, -12, -8, 13, 9],\n [20, 40, -30, -24, 12],\n [-43, -12, -43, 37, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-15, -31, 13, 21, -40],\n [41, 7, -38, -40, 19],\n [-7, 28, 16, 35, 25],\n [-15, 13, 1, -43, 20],\n [13, -35, -3, 37, -44]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 11, 3, -32, -15],\n [-11, -2, 9, 14, 0],\n [7, 19, 2, 2, -5],\n [-6, 19, 16, 8, -11],\n [1, 7, 0, 14, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-59, -37, -24, 47, 18],\n [60, 44, 17, -43, -23],\n [-11, -17, 28, 0, 25],\n [45, 33, -29, -5, -27],\n [-51, -1, -19, 28, -7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -16, 0, 16, 12],\n [0, 8, 0, -8, -6],\n [0, 20, 0, -20, -15],\n [0, 20, 0, -20, -15],\n [0, 12, 0, -12, -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[[18, 14, 28, 32, -40],\n [19, 11, 5, -21, 22],\n [-19, -11, -5, 21, -22],\n [25, 15, 10, -20, 20],\n [1, -1, -10, -24, 28]]\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, -1, 0, -1, 5],\n [-25, 5, 0, 5, -25],\n [30, -6, 0, -6, 30],\n [10, -2, 0, -2, 10],\n [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[[-30, -15, -30, -36, 3],\n [10, -19, -14, 4, 19],\n [6, -30, 16, -15, 25],\n [36, 2, 28, 27, 11],\n [38, 36, 64, 9, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, 4, -3, -6, 4],\n [0, 0, 0, 0, 0],\n [-4, -16, 12, 24, -16],\n [2, 8, -6, -12, 8],\n [-3, -12, 9, 18, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, -10, -12, 8, 4],\n [-24, -30, -36, 24, 12],\n [16, 20, 24, -16, -8],\n [16, 20, 24, -16, -8],\n [-20, -25, -30, 20, 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[[23, 9, -12, -12, 1],\n [36, -25, -44, -15, -35],\n [15, 18, 0, -9, 12],\n [2, 21, 12, -3, 19],\n [14, -8, -16, -6, -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[[-21, -37, 23, 11, -1],\n [-33, 5, 3, 17, 17],\n [51, -16, 47, -13, -49],\n [-74, -4, -10, 36, 36],\n [-33, -28, -9, 2, 32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-24, 5, 3, 6, 21],\n [26, 28, -40, -45, -1],\n [5, 4, -7, 0, -4],\n [-24, 7, 3, -15, 30],\n [-50, 13, 7, -21, 58]]\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 5x5 matrix:\n[[-5, -2, 2, -2, 0],\n [-10, -4, 4, -4, 0],\n [20, 8, -8, 8, 0],\n [0, 0, 0, 0, 0],\n [-10, -4, 4, -4, 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[[-24, 12, 36, -6, 0],\n [-12, 6, 18, -3, 0],\n [8, -4, -12, 2, 0],\n [16, -8, -24, 4, 0],\n [-4, 2, 6, -1, 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 5x5 matrix:\n[[42, -4, -3, 26, 37],\n [30, -2, -20, 28, 18],\n [33, 17, -41, 29, 43],\n [19, 25, -54, 17, 38],\n [-14, -16, 32, -24, -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[[-2, -14, -25, 6, 19],\n [34, 16, 16, -2, 22],\n [37, 13, -25, -6, 43],\n [-5, 4, -5, -5, -8],\n [-14, 1, 5, -3, -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[[4, -8, 8, -20, 0],\n [2, -4, 4, -10, 0],\n [3, -6, 6, -15, 0],\n [5, -10, 10, -25, 0],\n [-6, 12, -12, 30, 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 5x5 matrix:\n[[25, -10, 25, -25, 25],\n [30, -12, 30, -30, 30],\n [-20, 8, -20, 20, -20],\n [5, -2, 5, -5, 5],\n [25, -10, 25, -25, 25]]\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[[-29, -33, -39, 15, 25],\n [-11, -14, -21, 14, 16],\n [-12, 1, 14, -5, -3],\n [30, 36, 42, -12, -24],\n [3, 6, -1, 20, 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, -4, -6, 2, 5],\n [0, 0, 0, 0, 0],\n [-4, 4, 6, -2, -5],\n [-16, 16, 24, -8, -20],\n [4, -4, -6, 2, 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[[18, -15, 48, 48, 24],\n [-14, 20, 47, 44, 36],\n [-14, 3, 62, 64, 32],\n [1, -5, 44, 45, 22],\n [-10, 34, 26, 18, 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 5x5 matrix:\n[[-62, 30, -24, 6, -33],\n [-20, 32, 39, -34, 38],\n [0, -32, -75, -13, -61],\n [30, 6, 69, -7, 60],\n [26, -6, 30, 16, 25]]\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[[30, 6, -38, 8, 6],\n [-9, -9, 17, 4, -15],\n [-26, 14, 18, -24, 30],\n [14, -2, -14, 8, -6],\n [-34, 10, 30, -24, 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 5x5 matrix:\n[[-12, 0, -8, -6, -12],\n [6, 0, 4, 3, 6],\n [-36, 0, -24, -18, -36],\n [-12, 0, -8, -6, -12],\n [-12, 0, -8, -6, -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[[-35, -6, -6, 15, 42],\n [27, 26, -42, -31, -12],\n [13, -16, 42, 11, -33],\n [18, 10, -12, -14, -15],\n [-30, -2, -12, 10, 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 5x5 matrix:\n[[-18, -3, -26, 19, -9],\n [24, -18, 42, 15, 45],\n [20, 0, 30, -15, 15],\n [-26, 3, -40, 14, -24],\n [-30, 15, -50, -5, -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[[28, -3, -2, -42, -42],\n [12, -18, 1, -18, -18],\n [8, 30, -4, -12, -12],\n [-4, -42, 5, 6, 6],\n [-28, -24, 5, 42, 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[[-2, 1, 4, -1, 3],\n [-10, 5, 20, -5, 15],\n [2, -1, -4, 1, -3],\n [-6, 3, 12, -3, 9],\n [-8, 4, 16, -4, 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[[2, -40, 36, -30, -47],\n [38, -18, -1, 2, -11],\n [7, 27, -29, 7, 20],\n [17, 8, -4, 18, 1],\n [15, -13, 18, 23, -7]]\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[[21, 36, 21, 9, 12],\n [-27, 7, 30, 33, 18],\n [28, -8, -7, -39, -7],\n [41, 12, 10, -26, 25],\n [35, -72, -14, -94, 19]]?\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 5x5 matrix:\n[[-2, 1, 0, -5, -1],\n [-4, 2, 0, -10, -2],\n [-8, 4, 0, -20, -4],\n [8, -4, 0, 20, 4],\n [-10, 5, 0, -25, -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[[12, -12, -12, 4, 4],\n [-7, 39, 39, 11, 7],\n [-2, 42, 42, 16, 11],\n [-2, 18, 18, 6, 4],\n [-19, 3, 3, -13, -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 5x5 matrix:\n[[8, -42, -1, -4, 17],\n [8, -12, -6, 8, 6],\n [1, -24, 3, -8, 9],\n [13, 18, -16, 28, -4],\n [-18, 42, 11, -12, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-6, -30, -18, -12, 18],\n [5, 25, 15, 10, -15],\n [-5, -25, -15, -10, 15],\n [-3, -15, -9, -6, 9],\n [-5, -25, -15, -10, 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[[10, -25, 5, 25, 0],\n [-2, 5, -1, -5, 0],\n [-10, 25, -5, -25, 0],\n [-2, 5, -1, -5, 0],\n [-10, 25, -5, -25, 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 5x5 matrix:\n[[29, -26, -29, 13, -19],\n [0, -30, -1, -4, -31],\n [26, 11, -20, 11, 30],\n [-17, 3, 21, -14, 9],\n [15, -25, -18, 8, -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[[6, 0, -6, -8, -8],\n [6, 0, -6, -8, -8],\n [9, 0, -9, -12, -12],\n [9, 0, -9, -12, -12],\n [6, 0, -6, -8, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[27, -12, -23, 27, -9],\n [-48, -30, 42, -21, 42],\n [-10, 14, 0, -11, -8],\n [9, -33, 10, 16, 25],\n [41, 20, -5, 6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-40, -12, 46, 36, 28],\n [20, -15, -20, -15, 10],\n [4, 11, -6, -5, -14],\n [12, 19, -16, -13, -26],\n [-12, -26, 17, 14, 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 5x5 matrix:\n[[-22, -21, 23, 26, 77],\n [-1, 51, -21, 28, -48],\n [-20, 10, -2, 15, -7],\n [24, -13, -29, -22, 1],\n [-20, 42, 20, 45, -10]]\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 5x5 matrix:\n[[-24, 0, -12, -3, 0],\n [-32, -6, -10, 5, 6],\n [28, 3, 11, -1, -3],\n [-24, -12, 0, 15, 12],\n [20, 15, -5, -20, -15]]\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[[-2, -1, 0, 3, -4],\n [2, 1, 0, -3, 4],\n [-6, -3, 0, 9, -12],\n [6, 3, 0, -9, 12],\n [-6, -3, 0, 9, -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[[8, 6, -15, 0, 27],\n [-22, 6, 30, -18, -36],\n [-24, 12, 30, -24, -30],\n [18, -4, -25, 14, 31],\n [17, -1, -25, 11, 34]]\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, 7, 84, 42, 25],\n [36, 1, -47, -31, -23],\n [24, 7, -29, 3, 1],\n [42, -6, 49, -3, -14],\n [-24, -55, -3, 9, -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[[10, 20, 28, -68, 22],\n [-41, -9, 33, 6, -30],\n [-33, -13, 13, 30, -30],\n [-22, -36, 18, -2, -5],\n [12, 55, -19, 24, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-15, -5, 8, -7, 7],\n [-25, -10, 35, -25, 9],\n [-6, 24, -3, -16, -3],\n [-12, 8, 10, -16, 2],\n [-1, -1, 5, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -18, -18, -9, 12],\n [0, 6, 6, 3, -4],\n [0, -6, -6, -3, 4],\n [0, 0, 0, 0, 0],\n [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[[29, 14, -24, 43, -24],\n [12, 13, -9, -9, -6],\n [-26, -29, -9, -30, 17],\n [-2, -24, -19, 7, -5],\n [11, 6, -29, -4, -7]]?\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, 0, 12, 6, 6],\n [-5, 0, 10, 5, 5],\n [-2, 0, 4, 2, 2],\n [-4, 0, 8, 4, 4],\n [5, 0, -10, -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[[53, 20, 71, 4, 51],\n [21, -36, -5, 36, 15],\n [-10, 39, 20, -35, -4],\n [-18, 9, 14, -33, -14],\n [65, -19, 51, 43, 65]]\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, 38, -20, -33, 8],\n [-15, 25, 10, -1, 10],\n [-54, -13, 14, 13, -13],\n [-19, 27, 14, 2, 12],\n [3, -28, 8, 20, -3]]\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[[-14, 5, 31, -15, 7],\n [25, 0, 13, 37, 52],\n [-19, 8, 27, 28, 18],\n [24, -10, 1, 18, 31],\n [27, -4, -2, 29, 37]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-9, 3, 0, -9, 3],\n [18, -6, 0, 18, -6],\n [6, -2, 0, 6, -2],\n [3, -1, 0, 3, -1],\n [18, -6, 0, 18, -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 5x5 matrix:\n[[14, -41, -20, 12, 7],\n [14, -29, -20, -32, 5],\n [-10, -12, -12, 30, 9],\n [-7, 27, 30, 56, -10],\n [-31, -7, -34, -4, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[27, 15, -24, -33, 0],\n [-22, 2, 16, -14, -16],\n [35, 15, -30, -30, 5],\n [19, 7, -16, -13, 4],\n [-25, -13, 22, 28, -1]]\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[[-3, -12, 6, -5, -1],\n [11, -16, 14, 5, -7],\n [-21, -1, -3, -23, 7],\n [-24, 15, -33, 4, 14],\n [35, -12, 38, 2, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-49, -48, 14, -6, -62],\n [-24, 2, -6, 15, 6],\n [-21, -28, 24, -39, -36],\n [39, 27, -24, 12, 32],\n [-14, -51, 37, -4, -70]]\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[[41, -26, 38, -5, 2],\n [13, -44, -15, 21, -13],\n [-19, -26, -14, 15, -26],\n [19, -11, 47, -13, -8],\n [12, 32, 34, -24, 18]]\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[[42, 58, -13, -6, -9],\n [-15, 19, -24, -31, 12],\n [-29, -35, -7, -25, 33],\n [8, 5, -3, 62, -60],\n [19, 4, 10, -53, 59]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, 2, -2, -10, 12],\n [-6, -24, -12, 30, -36],\n [-23, 18, 24, 15, -18],\n [-26, 28, 32, 10, -12],\n [-4, 6, 6, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1, 1, -49, -20, 5],\n [7, -7, 24, -5, 23],\n [9, -9, 12, -15, 33],\n [-3, 3, -37, -10, -5],\n [-1, 1, -27, -10, 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[[-9, -12, 9, 15, -18],\n [-15, -20, 15, 25, -30],\n [0, 0, 0, 0, 0],\n [6, 8, -6, -10, 12],\n [-9, -12, 9, 15, -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[[6, -36, -12, -6, 0],\n [1, -6, -2, -1, 0],\n [3, -18, -6, -3, 0],\n [-5, 30, 10, 5, 0],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-30, -30, 15, 10, 0],\n [24, 24, -12, -8, 0],\n [30, 30, -15, -10, 0],\n [30, 30, -15, -10, 0],\n [24, 24, -12, -8, 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[[8, 40, -1, -13, 18],\n [-75, 20, 6, 41, -16],\n [36, 23, -6, -23, 33],\n [50, -33, -5, -2, -17],\n [58, -23, -3, -12, -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[[38, 38, -30, 31, -19],\n [-15, -14, -25, 9, 27],\n [-6, -6, 54, -35, -23],\n [0, -22, -8, 33, 3],\n [-10, -32, -38, 48, 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 5x5 matrix:\n[[-6, -12, 12, -9, -15],\n [6, 12, -12, 9, 15],\n [-2, -4, 4, -3, -5],\n [4, 8, -8, 6, 10],\n [6, 12, -12, 9, 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[[23, -31, -42, 13, 3],\n [-9, -15, 18, -7, 13],\n [-20, 10, 42, -18, 8],\n [-13, -7, 12, 7, 6],\n [4, -14, -12, 8, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-8, -3, 14, -9, -16],\n [12, -6, -12, 30, 24],\n [-3, 12, -6, -24, -6],\n [21, 7, -36, 25, 42],\n [17, 2, -26, 26, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-18, -12, -36, -30, -12],\n [9, 6, 18, 15, 6],\n [0, 0, 0, 0, 0],\n [6, 4, 12, 10, 4],\n [-9, -6, -18, -15, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-14, -29, -2, -8, -6],\n [-10, -10, 26, 8, 6],\n [-21, 5, 0, 3, 3],\n [-17, 13, 40, 19, 33],\n [13, 29, -18, -1, 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 5x5 matrix:\n[[0, 36, -24, 0, -24],\n [3, -21, 10, -6, 16],\n [-12, 12, 8, 24, -16],\n [0, 12, -8, 0, -8],\n [6, -42, 20, -12, 32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, -2, 5, -1],\n [0, 0, -6, 15, -3],\n [0, 0, -2, 5, -1],\n [0, 0, 0, 0, 0],\n [0, 0, 6, -15, 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[[-2, -4, 0, -1, 0],\n [-10, -20, 0, -5, 0],\n [-6, -12, 0, -3, 0],\n [0, 0, 0, 0, 0],\n [2, 4, 0, 1, 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[[-30, -16, 28, -24, 10],\n [5, -2, -28, -10, 3],\n [5, 7, 17, 17, -6],\n [-10, -10, -14, -22, 8],\n [-5, -9, -27, -23, 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[[-12, -12, 20, 16, 8],\n [12, 12, -20, -16, -8],\n [12, 12, -20, -16, -8],\n [6, 6, -10, -8, -4],\n [-18, -18, 30, 24, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-16, -26, 3, 8, 23],\n [-15, 0, 40, 11, -6],\n [46, 27, -5, 26, -12],\n [37, 8, -5, 27, 7],\n [7, -18, 12, 48, 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[[15, 0, 0, -6, -24],\n [-1, -8, -20, -22, -12],\n [8, -6, -15, -20, -23],\n [14, 2, 5, 0, -19],\n [-3, -4, -10, -10, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[24, -4, -32, -7, 1],\n [-12, 2, -12, -7, 3],\n [-12, 2, 44, 14, -4],\n [12, -2, 20, 10, -4],\n [-42, 7, 18, -2, 3]]\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 5x5 matrix:\n[[13, 18, -21, -16, -22],\n [10, 36, -18, 8, -28],\n [3, 6, -5, -2, -6],\n [18, 12, -28, -34, -24],\n [10, 24, -17, -3, -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[[24, -4, -5, -4, 26],\n [-33, -51, 30, 36, 23],\n [0, 44, -31, -27, -49],\n [18, 26, -21, -20, -12],\n [9, -13, 8, 6, 23]]\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, 6, -30, -26, 4],\n [0, 3, 5, 3, -4],\n [-16, -6, 30, 26, -4],\n [0, 9, 15, 9, -12],\n [4, -12, -30, -20, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -4, 8, 8, 4],\n [6, -6, 12, 12, 6],\n [2, -2, 4, 4, 2],\n [3, -3, 6, 6, 3],\n [1, -1, 2, 2, 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[[1, 34, -14, 45, -9],\n [57, 10, 30, 5, 11],\n [-40, -11, -15, -15, 2],\n [-11, -20, -12, -5, -25],\n [7, 20, -4, 25, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-19, -28, 35, 10, -15],\n [-50, -44, 31, 66, -47],\n [-11, -32, 43, 11, -15],\n [-28, -16, 14, 13, -20],\n [-25, -58, 62, 56, -37]]\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[[30, -5, 20, -5, 25],\n [-30, 5, -20, 5, -25],\n [-6, 1, -4, 1, -5],\n [-6, 1, -4, 1, -5],\n [6, -1, 4, -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[[8, -13, -27, -13, -1],\n [22, 11, -2, 11, -7],\n [18, 23, 20, 23, -7],\n [-18, -1, 14, -1, 5],\n [14, 2, -9, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[6, -74, -4, -48, -30],\n [-14, -11, 4, 3, 0],\n [3, 13, 0, 34, 18],\n [-41, -36, 20, -3, -6],\n [-15, 36, 4, 19, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0, 0],\n [6, -6, 15, 12, -9],\n [6, -6, 15, 12, -9],\n [2, -2, 5, 4, -3],\n [-4, 4, -10, -8, 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[[-21, -27, 10, 12, -45],\n [-47, -32, -21, 73, 29],\n [13, 3, 16, -32, -49],\n [20, -1, 7, -52, -8],\n [4, 0, 55, 16, -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, 19, -51, 28, 10],\n [-40, -32, 46, -37, -18],\n [-39, -29, 42, -35, -23],\n [-17, -9, 11, -13, -20],\n [16, 12, 12, 9, 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[[-27, 24, -15, 6, 39],\n [0, 13, -16, 1, 20],\n [-7, 15, -11, 11, 25],\n [20, -10, -4, -17, -19],\n [-27, 9, 9, 18, 18]]?\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, 35, -32, -11, 0],\n [28, 40, -9, 5, -28],\n [31, 15, -11, 34, -32],\n [40, 0, 1, 55, -44],\n [10, -10, 36, 6, -16]]\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[[3, -24, 15, 15, 18],\n [-5, 35, -25, -10, -25],\n [-2, 10, -10, 8, -6],\n [-6, 33, -30, 15, -21],\n [-1, 2, -5, 13, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[32, 0, -4, -16, -32],\n [33, 6, -6, -24, -39],\n [6, 4, -2, -8, -10],\n [-23, 6, 1, 4, 17],\n [-17, -6, 4, 16, 23]]\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 5x5 matrix:\n[[-6, 0, 2, -12, -8],\n [15, 0, -5, 30, 20],\n [3, 0, -1, 6, 4],\n [9, 0, -3, 18, 12],\n [9, 0, -3, 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 5x5 matrix:\n[[33, 59, -1, -13, 69],\n [-28, -21, 15, -7, -19],\n [47, 6, -49, 25, 35],\n [-71, -30, 27, -23, -53],\n [-41, 11, 14, -22, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -30, -24, 10, 14],\n [8, 10, 36, 6, -56],\n [-6, 10, -6, -8, 21],\n [-6, 25, 12, -11, 3],\n [6, -45, -36, 15, 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 5x5 matrix:\n[[20, -9, -14, -12, 4],\n [-21, 15, 30, -3, -18],\n [-39, 24, 56, -11, -34],\n [46, -17, -22, -38, 0],\n [-33, 20, 10, 46, 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 5x5 matrix:\n[[-11, -9, -23, -14, -21],\n [33, -11, -19, -31, -4],\n [-3, 31, 41, 41, -4],\n [11, -13, 43, 8, 15],\n [25, -12, -30, -34, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[23, 37, 3, 4, 25],\n [-15, -32, -1, -5, -21],\n [-7, 17, -7, 2, 10],\n [-32, -30, -28, -42, -16],\n [48, -9, 30, 9, -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[[-18, -6, 0, -3, -6],\n [0, 0, 0, 0, 0],\n [-30, -10, 0, -5, -10],\n [-30, -10, 0, -5, -10],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-26, 24, -24, 22, 4],\n [-4, 38, 0, 10, -36],\n [-32, -50, 16, -30, -22],\n [17, -5, -34, 5, 41],\n [-7, 55, -26, 25, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, -34, -4, -43, 59],\n [30, -38, -67, -32, 56],\n [24, 14, -2, -7, -9],\n [-24, 12, 50, 9, -17],\n [-30, 2, 49, 5, -5]]\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 5x5 matrix:\n[[16, 9, -3, 24, -8],\n [-18, 20, 0, 6, 0],\n [-36, 38, 10, 38, -22],\n [-17, 21, -20, 28, 4],\n [43, -22, -21, -8, 18]]\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, -15, 11, 29, 14],\n [10, 9, -17, -20, -11],\n [6, 6, -14, -14, -8],\n [4, 3, -3, -6, -3],\n [-19, -15, 19, 31, 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[[-6, 0, -12, 24, 12],\n [0, 0, 0, 0, 0],\n [3, 0, 6, -12, -6],\n [1, 0, 2, -4, -2],\n [-6, 0, -12, 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[[36, 0, -42, 0, -18],\n [8, 50, -3, 36, 43],\n [5, 41, 0, 30, 4],\n [-36, 24, 61, 38, 5],\n [-37, -40, 61, 1, -64]]\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, -18, -12, -12, 6],\n [1, -6, -4, -4, 2],\n [2, -12, -8, -8, 4],\n [1, -6, -4, -4, 2],\n [5, -30, -20, -20, 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[[42, 48, 30, 0, 6],\n [23, 28, 25, 2, -7],\n [33, 36, 15, -2, 15],\n [21, 18, -15, -7, 39],\n [-29, -34, -25, -1, 1]]\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 5x5 matrix:\n[[17, -9, 8, 14, -4],\n [-21, 1, -6, 7, -4],\n [-38, 14, -20, -6, 8],\n [35, -15, 22, 4, -12],\n [42, -6, 10, 4, 8]]\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, -15, -16, -10, 1],\n [50, -5, -1, -5, 12],\n [22, -24, -32, -16, 46],\n [-10, -9, -37, 11, 0],\n [-10, 12, -25, 31, 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[[-17, 1, -22, 29, -16],\n [-21, 3, -26, 27, -8],\n [-10, 5, -10, -5, 20],\n [23, -4, 28, -26, 4],\n [17, -4, 20, -14, -4]]\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, -32, -17, 32, -30],\n [20, -24, -4, 24, -24],\n [-2, -14, -14, 14, -12],\n [-35, 18, -19, -11, 16],\n [-13, 32, 17, -32, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, 18, -84, 8, 22],\n [31, -3, -38, 1, 26],\n [15, 18, -78, -3, 15],\n [-24, 12, -40, 24, 12],\n [-13, -12, -2, 41, 33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, -4, 6, 2, -10],\n [24, -8, 12, 4, -20],\n [6, -2, 3, 1, -5],\n [6, -2, 3, 1, -5],\n [18, -6, 9, 3, -15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-27, -3, 15, 3, -30],\n [6, -1, -10, -4, 20],\n [-6, 1, 10, 4, -20],\n [12, 3, 0, 2, 0],\n [-15, -2, 7, 1, -14]]\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[[2, -95, 41, -11, -62],\n [5, -11, -55, -6, 28],\n [-12, -42, -30, 14, 0],\n [23, -13, -16, 42, -40],\n [-11, 6, -38, -3, 36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[33, -3, -7, 33, -33],\n [-23, -11, 17, -23, 39],\n [-11, -17, 19, -11, 33],\n [3, -15, 13, 3, 15],\n [1, -23, 21, 1, 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[[7, 10, 21, 0, 13],\n [-7, -22, -35, 0, -23],\n [3, -12, -10, 0, -8],\n [-8, -2, -13, 0, -7],\n [6, 18, 29, 0, 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[[-16, -8, 0, 12, 24],\n [-12, -6, 0, 9, 18],\n [-8, -4, 0, 6, 12],\n [0, 0, 0, 0, 0],\n [-12, -6, 0, 9, 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[[-20, -10, 30, -18, 60],\n [-2, 56, -60, 12, -18],\n [-21, -40, -16, -8, 43],\n [28, 10, 1, -18, -18],\n [-10, 29, -7, 15, -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, -3, 33, -22, -24],\n [25, 21, -11, 24, -2],\n [15, 18, 24, -9, -3],\n [-10, -21, 1, -23, 22],\n [25, 27, -21, 42, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-36, 24, 6, 18, -6],\n [24, -16, -4, -12, 4],\n [6, -4, -1, -3, 1],\n [-24, 16, 4, 12, -4],\n [-12, 8, 2, 6, -2]]\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, -14, -22, 44, 12],\n [6, -30, 42, 16, -18],\n [10, 24, 25, -44, -28],\n [-17, 23, -4, 0, -25],\n [-3, -7, -2, 12, 3]]\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[[-31, 19, -2, -17, 6],\n [37, -22, 2, 21, -6],\n [15, -18, 6, -1, -18],\n [-30, 36, -12, 2, 36],\n [-32, 23, -4, -14, 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 5x5 matrix:\n[[-2, -6, 8, -12, 2],\n [-2, -6, 8, -12, 2],\n [1, 3, -4, 6, -1],\n [-3, -9, 12, -18, 3],\n [2, 6, -8, 12, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[0, 60, -42, -12, -30],\n [-10, 32, -18, 6, -32],\n [22, 0, -18, -18, 36],\n [-20, -44, 50, 22, -11],\n [12, 4, -6, -18, 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 5x5 matrix:\n[[-33, 33, 36, 24, 9],\n [-7, -8, 34, 31, -14],\n [-8, -8, 22, 43, -22],\n [-26, 44, -16, -4, 20],\n [6, 3, -16, -24, 11]]\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 5x5 matrix:\n[[-10, 2, -12, 11, 8],\n [5, 2, 8, 1, 3],\n [9, 0, 12, -6, -3],\n [25, 10, 40, 5, 15],\n [1, -8, -4, -18, -19]]\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[[1, -28, -22, -29, 10],\n [24, 7, 26, 37, -21],\n [-2, -22, 27, 18, -9],\n [13, 17, 9, 0, -14],\n [-21, -15, 26, 40, 5]]\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, -6, -9, -15, -6],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [0, 2, 3, 5, 2],\n [0, -10, -15, -25, -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[[29, 6, 6, -7, 1],\n [45, 14, -6, 18, -16],\n [7, 28, 4, 17, 1],\n [35, 17, 3, 2, 0],\n [31, 10, 10, -16, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[36, 6, -18, -36, 18],\n [-2, -12, 18, 18, 0],\n [6, -34, 48, 42, 6],\n [-31, 24, -27, -9, -18],\n [-3, -18, 27, 27, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[10, 2, 14, -10, -8],\n [-15, -3, -35, 22, 12],\n [-20, -4, -36, 24, 16],\n [-25, -5, -25, 20, 20],\n [-30, -6, -46, 32, 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 5x5 matrix:\n[[-6, 3, 18, 0, 18],\n [12, -6, -36, 0, -36],\n [12, -6, -36, 0, -36],\n [-10, 5, 30, 0, 30],\n [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[[20, -3, 10, -9, -3],\n [-10, 9, -14, -9, -9],\n [31, -26, -2, 6, 38],\n [5, 14, -74, -54, -4],\n [-40, 25, 16, 9, -38]]\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, 15, 15, 8, -27],\n [-5, 12, 15, 10, -18],\n [-3, 12, 25, 22, -6],\n [0, 0, 0, 0, 0],\n [-10, 18, 10, 0, -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[[-40, 6, -49, -4, 2],\n [-5, -7, -12, 29, 7],\n [-15, -11, -16, -3, 1],\n [-15, 32, -18, -22, -5],\n [5, -41, 4, 35, 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[[15, 11, -22, 17, 5],\n [-18, -18, 24, -30, 6],\n [15, 13, -21, 21, 0],\n [9, 15, -9, 27, -18],\n [12, 6, -19, 8, 11]]\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[[-13, -12, 1, -15, -12],\n [-25, 0, -5, 30, 30],\n [6, -16, 6, -48, -44],\n [33, 12, 3, -9, -12],\n [38, 12, 4, -15, -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[[-14, -5, 4, -21, 21],\n [-14, 36, 82, -28, 24],\n [-19, 24, 45, -20, -2],\n [11, 0, -9, 16, -14],\n [13, -33, -63, 17, -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 5x5 matrix:\n[[0, 0, 0, 0, 0],\n [6, 6, 3, 1, 1],\n [-30, -30, -15, -5, -5],\n [0, 0, 0, 0, 0],\n [18, 18, 9, 3, 3]]\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[[-8, -10, 8, -10, -4],\n [-16, -20, 16, -20, -8],\n [4, 5, -4, 5, 2],\n [12, 15, -12, 15, 6],\n [-8, -10, 8, -10, -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[[46, 0, 32, 18, -30],\n [19, 41, -7, 10, 6],\n [12, 36, 12, -4, 36],\n [31, -13, 11, 20, -48],\n [-35, 8, -58, 2, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[18, 34, 13, -33, 14],\n [-30, -38, -17, 27, 0],\n [-16, 4, -37, -6, -13],\n [-33, -24, -27, 9, 6],\n [-5, -32, 12, 33, -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[[26, 55, 25, -64, -31],\n [23, 14, -11, -43, -3],\n [-10, 3, 33, 12, 41],\n [-23, -49, -24, 57, 24],\n [3, -40, -55, 13, -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[[2, 0, 27, 46, 59],\n [-4, 4, 19, 38, 47],\n [23, 11, -5, -28, -33],\n [12, 4, 25, 34, 45],\n [1, 2, 15, 26, 33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, -49, -3, -21, -9],\n [33, -22, 4, -13, 0],\n [-15, 10, 26, 25, -6],\n [41, -28, -6, -27, 2],\n [12, -8, -1, -14, 0]]?\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[[-22, -44, -24, 6, -30],\n [13, 19, 30, -5, 23],\n [21, 47, 6, -21, 45],\n [-3, -10, 62, 16, 10],\n [53, 51, 58, -7, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[14, -6, 15, -7, 13],\n [12, -4, 13, -3, 23],\n [32, -11, 26, 14, 20],\n [13, 22, -6, -27, -13],\n [-23, 19, -12, -73, 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[[0, 0, 0, 0, 0],\n [2, -2, 10, 12, -8],\n [-2, 2, -10, -12, 8],\n [5, -5, 25, 30, -20],\n [5, -5, 25, 30, -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[[15, 0, 65, 25, -60],\n [26, -12, -2, -54, 18],\n [-3, 30, 13, -7, -40],\n [-33, 9, -6, 66, -9],\n [34, -24, 20, -42, 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 5x5 matrix:\n[[-20, 12, 24, -12, -4],\n [-30, 55, -25, -30, 5],\n [28, 19, -43, 18, 25],\n [2, 6, -6, 1, 4],\n [0, 42, 30, 12, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 20, -30, -30, -5],\n [0, -16, 24, 24, 4],\n [0, -4, 6, 6, 1],\n [0, 20, -30, -30, -5],\n [0, 24, -36, -36, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-36, -24, 6, 12, 18],\n [-12, -8, 2, 4, 6],\n [-18, -12, 3, 6, 9],\n [12, 8, -2, -4, -6],\n [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[[-4, 16, -2, 26, 18],\n [-6, 28, -6, 46, 34],\n [9, 2, -24, 8, 26],\n [5, -14, -2, -22, -12],\n [16, -8, -34, -6, 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[[3, -18, 12, 18, 6],\n [0, 0, 0, 0, 0],\n [-6, 36, -24, -36, -12],\n [-5, 30, -20, -30, -10],\n [-2, 12, -8, -12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-6, -4, 21, 6, 11],\n [24, -38, 6, -6, 10],\n [-24, 8, 44, 16, 20],\n [12, -7, -17, -7, -7],\n [-36, 42, 16, 14, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[18, 6, -33, 13, -6],\n [20, -27, -46, -31, 19],\n [-21, -8, -1, -16, -42],\n [-22, 23, 17, 25, -47],\n [-3, -60, -42, -82, 18]]?\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[[-30, 36, 24, 30, -24],\n [-36, 36, 32, 40, -32],\n [-20, 24, 16, 20, -16],\n [12, -18, -8, -10, 8],\n [-12, 9, 12, 15, -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[[3, 0, -4, -3, -1],\n [-9, -2, 6, 10, -3],\n [-3, -14, -38, 10, -41],\n [-9, 4, 24, 7, 15],\n [-6, -2, 2, 7, -4]]\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, -8, -8, -6, -8],\n [6, -8, -8, -6, -8],\n [18, -24, -24, -18, -24],\n [15, -20, -20, -15, -20],\n [-3, 4, 4, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[5, -6, 3, 3, 3],\n [-32, 54, -18, 24, -30],\n [-40, 61, -23, 12, -33],\n [-40, 61, -23, 12, -33],\n [-32, 54, -18, 24, -30]]\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 5x5 matrix:\n[[14, -12, 24, 14, 14],\n [-36, -36, 20, 29, 3],\n [-15, 18, -32, -20, -18],\n [-31, -30, 16, 24, 2],\n [24, 36, -28, -31, -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[[-1, 18, -7, -18, -15],\n [-4, 0, -4, -12, -6],\n [7, 6, 5, 16, 6],\n [-11, 6, -13, -38, -21],\n [3, 30, -7, -16, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-7, 16, -1, -19, -36],\n [-12, 18, 52, -30, -16],\n [-27, 36, 61, -8, -9],\n [26, -14, -2, 35, 43],\n [-28, 22, -12, 24, -6]]\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 5x5 matrix:\n[[0, -6, -8, -12, -10],\n [0, -9, -12, -18, -15],\n [0, 6, 8, 12, 10],\n [0, -15, -20, -30, -25],\n [0, -9, -12, -18, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-7, 33, 8, 26, -34],\n [-23, 5, 1, -3, -3],\n [31, -58, -31, -21, -15],\n [-30, -18, -15, -12, -12],\n [-18, 8, -4, 8, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-30, -30, 30, -15, 20],\n [-36, -36, 36, -18, 24],\n [-30, -30, 30, -15, 20],\n [-30, -30, 30, -15, 20],\n [6, 6, -6, 3, -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[[-4, -14, 14, -16, 12],\n [25, 13, 27, -54, -41],\n [-11, -5, 3, -3, -11],\n [-27, -10, -10, 32, 1],\n [0, 4, -30, 43, 38]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 35, -16, 16, 9],\n [-18, 32, -22, 20, 12],\n [11, 31, -1, 21, -3],\n [26, 4, 2, 42, -12],\n [-6, 44, -4, -3, 6]]\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, 16, 24, 0, 12],\n [-3, -4, -6, 0, -3],\n [3, 4, 6, 0, 3],\n [12, 16, 24, 0, 12],\n [15, 20, 30, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-19, -31, -9, 33, 25],\n [-5, 19, -1, -11, -19],\n [-32, -65, -3, 60, 60],\n [52, 70, 48, -80, -40],\n [3, 15, -51, -1, -41]]\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, 34, -16, 18, 44],\n [-46, 76, -34, 18, 80],\n [6, -28, 40, 28, -16],\n [28, 2, 20, 6, -4],\n [42, -18, -3, -33, -36]]\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[[10, 4, -32, 49, -48],\n [-8, -8, -12, 2, -38],\n [-8, 34, -33, 54, -32],\n [21, -14, 0, -4, 2],\n [7, -8, -9, 37, -20]]?\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[[12, -24, -6, -36, -6],\n [9, 37, 28, 33, 23],\n [30, 6, 24, -18, 18],\n [8, 6, 9, 0, 7],\n [3, 5, 5, 3, 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[[4, 16, -24, 24, -12],\n [-4, -16, 24, -24, 12],\n [-3, -12, 18, -18, 9],\n [-2, -8, 12, -12, 6],\n [5, 20, -30, 30, -15]]?\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[[-12, -18, 0, 24, 18],\n [2, 3, 0, -4, -3],\n [0, 0, 0, 0, 0],\n [-12, -18, 0, 24, 18],\n [-6, -9, 0, 12, 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[[40, 11, -1, 0, -8],\n [-26, -35, -8, -9, -20],\n [10, 33, -5, -4, 22],\n [9, -67, -12, -15, -67],\n [-50, -32, 2, -1, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, -12, -10, -6, 10],\n [3, -18, -15, -9, 15],\n [5, -30, -25, -15, 25],\n [-3, 18, 15, 9, -15],\n [4, -24, -20, -12, 20]]\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[[25, -5, -56, -49, 28],\n [-11, -14, 61, 89, 3],\n [-21, -28, 43, 57, -21],\n [-47, 13, 70, 35, -42],\n [-7, 13, -30, -65, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, -19, -13, -26, 19],\n [-9, -5, -7, 1, -34],\n [-12, -6, 18, -39, -9],\n [0, 27, 29, 22, -30],\n [7, 8, -8, 30, -3]]\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, 10, 0, -40, 23],\n [19, 18, -11, -2, 5],\n [-26, -20, 10, 12, -14],\n [29, 15, -5, -4, 24],\n [1, -19, 18, 2, 26]]?\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 5x5 matrix:\n[[2, -5, 4, 0, -2],\n [-4, 10, -8, 0, 4],\n [-8, 20, -16, 0, 8],\n [-12, 30, -24, 0, 12],\n [-6, 15, -12, 0, 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[[22, 24, 10, 4, -19],\n [38, 26, 25, -7, -22],\n [-4, -18, 5, -13, 13],\n [22, -6, 25, -23, 2],\n [2, -6, 5, -7, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, -7, -9, 15, -12],\n [-19, 0, -38, 13, -11],\n [-38, -20, -4, 56, -32],\n [22, 2, -2, -18, 13],\n [-56, 6, -40, 17, -13]]\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[[21, 21, -25, 11, -14],\n [5, 23, -35, 20, 28],\n [25, 5, -7, 27, -6],\n [16, -5, 22, 18, -9],\n [12, 10, -8, 18, 6]]?\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 5x5 matrix:\n[[16, -14, -6, 8, 7],\n [-17, 13, 9, -4, 4],\n [-50, 40, 24, -16, 1],\n [-2, -2, 6, 8, 22],\n [28, -22, -14, 8, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -22, 16, -9, -9],\n [-16, 21, -2, -2, 17],\n [27, 31, -10, 33, 24],\n [32, 12, -8, 28, 8],\n [-27, -8, 16, -22, 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[[33, -21, -46, -5, 34],\n [-13, 12, 10, 3, -3],\n [20, -30, 30, -10, -30],\n [-45, 51, 24, -9, -36],\n [-31, 44, -20, 1, 9]]\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 5x5 matrix:\n[[1, 14, 22, -8, 23],\n [14, 24, 28, 10, 21],\n [-35, -12, -22, 5, -9],\n [38, -20, -12, -20, -24],\n [-6, -10, 0, -29, 7]]\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 5x5 matrix:\n[[-48, 67, 40, 30, 66],\n [86, -43, -9, -60, -25],\n [-14, 22, 10, 8, 18],\n [14, -36, -16, -3, -35],\n [60, -27, -8, -44, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0, 0],\n [-24, 16, -12, -4, 16],\n [-12, 8, -6, -2, 8],\n [-36, 24, -18, -6, 24],\n [-24, 16, -12, -4, 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 5x5 matrix:\n[[2, 2, -19, -11, -16],\n [28, -20, -2, 14, -8],\n [-6, 0, 24, 12, 21],\n [-8, 4, 10, 2, 10],\n [-22, 16, 0, -12, 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[[0, 2, 2, -6, 2],\n [0, 8, 8, -24, 8],\n [0, 8, 8, -24, 8],\n [0, -10, -10, 30, -10],\n [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[[15, -30, 30, 30, -15],\n [15, -30, 30, 30, -15],\n [6, -12, 12, 12, -6],\n [-12, 24, -24, -24, 12],\n [-18, 36, -36, -36, 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[[5, 6, 5, -2, -1],\n [30, 36, 30, -12, -6],\n [5, 6, 5, -2, -1],\n [30, 36, 30, -12, -6],\n [-5, -6, -5, 2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 20, -8, -4, 20],\n [-3, -15, 6, 3, -15],\n [6, 30, -12, -6, 30],\n [-4, -20, 8, 4, -20],\n [2, 10, -4, -2, 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[[6, -9, -15, 30, 0],\n [-28, 2, -30, 0, 0],\n [2, 5, 15, -18, 0],\n [-10, 15, 25, -50, 0],\n [2, 5, 15, -18, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[21, -2, 12, 13, -10],\n [-72, -24, 40, -18, 34],\n [12, 30, -48, -3, 3],\n [-7, -21, -2, -19, -14],\n [-37, -26, -12, -39, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, -12, 24, -4, 4],\n [4, -6, 12, -2, 2],\n [2, -3, 6, -1, 1],\n [12, -18, 36, -6, 6],\n [10, -15, 30, -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[[33, 1, -24, -40, 22],\n [3, 22, -39, -16, -5],\n [25, 31, -66, -30, -9],\n [30, 35, -97, -48, -29],\n [26, -12, -14, -18, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[13, 12, -13, 0, 21],\n [10, -2, -15, -14, -12],\n [-14, -23, 15, -15, -43],\n [5, 9, -2, 5, 20],\n [1, 13, 0, 17, 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 5x5 matrix:\n[[18, -2, -19, 2, -8],\n [-18, 17, 4, 1, 23],\n [-36, 44, -2, 4, 56],\n [-12, -17, 31, -5, -13],\n [30, 5, -40, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-30, -5, 20, 0, 25],\n [12, 2, -8, 0, -10],\n [0, 0, 0, 0, 0],\n [6, 1, -4, 0, -5],\n [24, 4, -16, 0, -20]]\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, -6, 6, 0, -36],\n [-9, 3, -3, 0, 18],\n [15, -5, 5, 0, -30],\n [-6, 2, -2, 0, 12],\n [18, -6, 6, 0, -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[[44, -2, 60, -25, 6],\n [7, 4, 17, -21, -17],\n [-46, -9, -37, 1, -53],\n [36, -6, 44, -7, 18],\n [-22, -18, -28, 34, 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[[-49, 59, 14, -45, 11],\n [24, -42, -12, 18, 6],\n [-8, 50, 16, -78, -34],\n [17, -10, -1, 9, -13],\n [3, -8, -3, -15, 3]]\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, -21, 31, -10, 25],\n [33, 8, -40, -34, -7],\n [80, 8, -50, -90, -4],\n [-35, -3, 40, 35, 21],\n [-74, 12, 48, 84, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-14, 20, 18, 34, 2],\n [-44, 14, -34, 19, -5],\n [37, -40, 11, -32, 0],\n [20, 10, 30, 5, 5],\n [18, 36, 6, -18, 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 5x5 matrix:\n[[30, 6, 45, 35, 30],\n [0, -24, -20, -30, -10],\n [2, -22, 19, -3, 18],\n [-20, -26, -18, -31, -7],\n [-24, 48, 8, 38, -2]]\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 5x5 matrix:\n[[83, 2, -16, -17, -3],\n [54, -10, -2, -6, -3],\n [-7, 17, -30, -6, -15],\n [-37, -27, 68, 28, 37],\n [2, 9, 21, -27, 25]]\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, -22, 13, -3, -6],\n [41, -2, 53, 16, 31],\n [-15, -12, 21, 15, 24],\n [-18, -26, 35, 15, 30],\n [30, 8, 13, -23, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-18, 12, -1, 6, 6],\n [32, -32, 44, 8, -56],\n [27, -6, 38, 12, -42],\n [36, -24, 50, 12, -60],\n [-11, -10, 24, 12, -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[[12, 12, 25, 17, 3],\n [21, 12, 9, -19, 49],\n [18, 18, 35, 3, 37],\n [12, 15, 35, 19, 9],\n [-23, -9, 2, 6, -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[[8, -8, -4, 8, 0],\n [-2, 2, 1, -2, 0],\n [-3, -18, -9, 24, -18],\n [-2, -12, -6, 16, -12],\n [-40, -2, -1, 14, -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[[-46, -3, 5, -28, 11],\n [-29, 28, -18, -23, -20],\n [21, 17, -34, 35, -61],\n [27, 30, -34, 25, -56],\n [31, 26, -35, 27, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 0, 0, 0, 6],\n [6, 0, 0, 0, 9],\n [12, 0, 0, 0, 18],\n [0, 0, 0, 0, 0],\n [10, 0, 0, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[1, 20, 0, 21, -29],\n [2, -23, 36, -33, -17],\n [-2, -19, 18, -27, -9],\n [6, 8, 6, 12, 2],\n [-3, 6, -18, 9, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 0, 18, -8, 17],\n [-5, 19, 15, 25, -8],\n [12, -12, -36, -4, -20],\n [2, -16, -6, -24, 13],\n [-4, -10, 12, -22, 23]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[15, -15, -18, -9, 3],\n [20, -20, -24, -12, 4],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [-20, 20, 24, 12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[14, 28, -42, 19, 29],\n [30, -54, 50, 5, 35],\n [-2, -2, -20, -7, -9],\n [-8, 20, -42, 2, -10],\n [-4, -44, 43, -1, -11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[10, 39, 13, 4, -23],\n [-24, 27, 14, -3, 16],\n [-32, -24, -25, 22, 15],\n [-26, -42, 13, 19, 31],\n [8, 27, -29, 55, -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[[-14, -36, 15, -21, 0],\n [-4, 24, 38, -44, 20],\n [-3, -18, -23, -1, -26],\n [14, 33, -26, -4, -22],\n [4, 46, -7, -47, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[19, 10, 22, -8, 7],\n [9, 3, -6, -10, 5],\n [-22, -24, 16, -23, 1],\n [16, 26, 33, -11, -17],\n [16, 26, 36, -4, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, -15, 9, -6, 3],\n [8, 20, -12, 8, -4],\n [-2, -5, 3, -2, 1],\n [-2, -5, 3, -2, 1],\n [10, 25, -15, 10, -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 5x5 matrix:\n[[10, 22, 8, -18, 22],\n [-2, 26, 24, -14, 42],\n [0, 0, 0, 0, 0],\n [2, 12, 8, -8, 16],\n [13, 2, -12, -8, -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[[-33, 4, 9, 23, 19],\n [51, -8, -13, -37, -35],\n [-54, -18, -3, 32, -37],\n [45, 4, -23, -21, 5],\n [0, -24, 3, -15, -72]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[0, 12, -19, 22, 38],\n [0, 6, -11, 8, 22],\n [0, -2, 7, 4, -14],\n [0, 12, -23, 14, 46],\n [0, 12, -13, 34, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 0, 0, 12, 0],\n [0, 0, 0, 0, 0],\n [24, 0, 0, 24, 0],\n [16, 0, 0, 16, 0],\n [-16, 0, 0, -16, 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[[7, 3, -12, 10, 4],\n [17, 16, 10, -2, -18],\n [17, 44, -46, 12, 52],\n [-20, -17, -2, -4, 14],\n [6, 14, 8, -8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-54, -22, -32, 55, -15],\n [24, 14, 7, 0, 17],\n [7, -8, -15, 20, 32],\n [-5, 40, -2, -5, -28],\n [-24, -24, -5, 13, -10]]?\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 5x5 matrix:\n[[-27, 11, 8, -9, -12],\n [-26, 0, -20, 28, 30],\n [-30, 5, -10, 15, 15],\n [-13, 0, -10, 14, 15],\n [-66, 24, 12, -12, -18]]\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, -25, -20, 25, 10],\n [0, -25, -20, 25, 10],\n [0, 10, 8, -10, -4],\n [0, -15, -12, 15, 6],\n [0, 10, 8, -10, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[16, 12, -42, -6, 34],\n [18, 30, -24, 24, 32],\n [14, -24, 21, -27, 18],\n [-3, -31, 21, -31, -8],\n [-15, 29, -3, 41, -24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[48, -33, 34, -20, -19],\n [-1, -20, -30, 64, 32],\n [22, -1, 17, 4, 11],\n [31, -45, 8, -10, -45],\n [26, -15, 7, 28, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[15, 28, 16, 3, 8],\n [-25, -9, -23, 15, -12],\n [-5, -44, -14, -14, -7],\n [-45, -18, -20, 4, -9],\n [-35, 37, 17, 2, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-31, 0, -39, 3, 23],\n [2, -7, -12, 40, 6],\n [-3, 25, -12, 2, 17],\n [4, -4, 16, -24, -12],\n [7, 24, -2, 8, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[25, 15, -20, -30, 0],\n [-5, -3, 4, 6, 0],\n [-5, -3, 4, 6, 0],\n [-5, -3, 4, 6, 0],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[55, 5, 5, 35, 25],\n [19, 19, -11, 18, 10],\n [-8, 20, -16, 2, -2],\n [23, 9, -3, 17, 11],\n [-16, 2, -4, -9, -7]]\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[[-13, 30, -26, 2, 6],\n [-46, 18, -40, 60, -3],\n [9, 3, -6, 12, 8],\n [-30, -6, -8, -8, -23],\n [-10, 9, -4, 9, 3]]\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[[-15, -3, -9, -12, 9],\n [30, 6, 18, 24, -18],\n [-15, -3, -9, -12, 9],\n [-15, -3, -9, -12, 9],\n [-20, -4, -12, -16, 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 5x5 matrix:\n[[8, -22, 14, 6, 2],\n [24, -12, -3, 9, 24],\n [-4, -19, 18, 2, -11],\n [12, -15, 6, 6, 9],\n [4, 31, -28, -4, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[14, 8, 0, -7, 5],\n [-24, -36, 36, -6, 30],\n [22, 20, -12, -5, -5],\n [13, 13, -9, -2, -5],\n [-30, -32, 24, 3, 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[[-7, 5, -16, -6, 7],\n [10, -33, -29, 22, 51],\n [6, -25, 42, 32, 25],\n [15, 14, -32, -34, -46],\n [21, -16, 16, 24, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-9, -3, 21, -30, -6],\n [-6, -6, -12, 36, 18],\n [34, 18, -36, 20, -14],\n [1, 3, 15, -34, -14],\n [-14, -10, -2, 28, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[22, 6, -20, -31, -14],\n [50, 32, 32, 22, 10],\n [72, 30, 0, -30, -30],\n [15, 0, -42, -45, -12],\n [-16, -5, -12, -7, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[18, 17, -3, -4, 3],\n [4, 34, 42, 56, 30],\n [-13, 4, 8, 18, 7],\n [-42, -2, -24, 4, -3],\n [-47, -3, -7, 22, 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[[-6, -22, -9, -46, -30],\n [0, 4, -6, 4, 0],\n [-2, 8, -26, 0, -10],\n [-5, 2, -38, -18, -25],\n [1, -6, 16, -2, 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[[-1, 15, -59, -28, 36],\n [11, 35, -61, 9, -34],\n [-16, -18, 31, 29, -26],\n [-5, -21, 32, -23, 46],\n [-26, 2, -30, 10, 4]]?\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, 10, -16, 6, 8],\n [8, 20, 16, -12, 8],\n [-13, -30, -18, 15, -13],\n [-5, -10, -2, 3, -5],\n [-16, -25, 16, -3, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-10, -5, -20, -10, -5],\n [10, 5, 20, 10, 5],\n [-4, -2, -8, -4, -2],\n [-12, -6, -24, -12, -6],\n [-6, -3, -12, -6, -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[[-8, 17, 8, -9, 1],\n [32, 2, -5, -41, 48],\n [-26, 2, 14, 10, -20],\n [-37, -31, 4, 40, -36],\n [-10, -12, 7, 1, -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 5x5 matrix:\n[[-28, -24, -48, 24, 52],\n [28, 30, 36, -16, -44],\n [-14, 63, 6, -14, -42],\n [16, 3, 6, 2, -4],\n [13, 36, 24, -14, -39]]\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[[14, -7, -2, -1, 32],\n [4, -14, -22, 32, 38],\n [-60, -20, 25, 43, -43],\n [-27, -19, -17, 60, 10],\n [20, 2, -22, 8, 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[[34, 22, -11, 23, 16],\n [-24, -2, 34, -30, -20],\n [10, -45, -15, -5, 40],\n [-4, -14, 1, -7, 6],\n [-14, -30, 9, -21, 8]]\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[[-3, 59, 13, 41, 37],\n [-7, 5, -5, 40, 67],\n [14, 22, 3, 13, 18],\n [2, -6, -7, -1, 2],\n [-4, 10, -21, 28, 39]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, -26, 22, -22, 3],\n [34, -19, 27, -21, 12],\n [-36, -9, 5, -13, -63],\n [-35, -19, 8, 33, -28],\n [27, 12, -13, 23, 74]]\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 5x5 matrix:\n[[57, -6, 19, 25, -36],\n [20, -18, 0, 30, -45],\n [29, 0, 18, 5, 14],\n [41, 16, 26, -5, -19],\n [43, 23, 23, -15, 7]]\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 5x5 matrix:\n[[18, 75, 39, -31, 18],\n [-36, -75, -36, 16, 18],\n [10, 42, 22, -47, 34],\n [-18, 42, 1, 5, 12],\n [6, 63, 40, -12, 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[[-5, -4, -25, 13, -28],\n [6, -22, -22, -8, -14],\n [-7, -24, -23, -5, -12],\n [-1, 6, 11, -1, 10],\n [-9, 6, -25, 23, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[9, 24, -39, 29, 34],\n [-8, 53, 24, -24, -7],\n [29, -31, -13, 1, 7],\n [12, 21, 30, -36, -15],\n [-7, -10, -61, 61, 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 5x5 matrix:\n[[-5, 14, 10, 11, -5],\n [-12, -2, 3, -12, 18],\n [-6, 40, -28, -49, -16],\n [-38, -32, -26, 23, 21],\n [-10, -12, 12, 14, 16]]\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, 6, 5, 2, 6],\n [0, -30, -25, -10, -30],\n [0, -36, -30, -12, -36],\n [0, 0, 0, 0, 0],\n [0, -24, -20, -8, -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[[13, 22, -9, 15, -26],\n [2, -45, 20, -28, 34],\n [-24, 5, -45, 58, 16],\n [-6, 1, 22, -4, -8],\n [73, 12, -1, -53, -36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-10, 30, 25, -25, -10],\n [0, 0, 0, 0, 0],\n [-10, 30, 25, -25, -10],\n [-6, 18, 15, -15, -6],\n [-12, 36, 30, -30, -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 5x5 matrix:\n[[-32, 12, 12, -20, -8],\n [32, -15, -15, 25, 14],\n [48, -18, -18, 30, 12],\n [20, -12, -12, 20, 14],\n [-34, 12, 12, -20, -7]]\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[[2, 42, 26, -4, 0],\n [35, 30, 67, 29, -52],\n [80, -9, -1, 69, 25],\n [-58, -2, 3, -65, -27],\n [22, 6, 42, 36, -44]]?\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, -14, 48, 12, 6],\n [16, 2, -32, -20, -10],\n [8, 1, -16, -10, -5],\n [16, -11, 0, -18, -9],\n [2, -16, 36, 0, 0]]\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[[-30, 36, 9, -58, -36],\n [30, -30, 15, 22, 36],\n [5, -9, -21, -5, 38],\n [-24, -5, -28, 22, -28],\n [-37, 46, -40, -13, -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 5x5 matrix:\n[[6, -4, 6, 8, 8],\n [18, -12, 18, 24, 24],\n [-9, 6, -9, -12, -12],\n [18, -12, 18, 24, 24],\n [-3, 2, -3, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[14, 10, 2, 25, 1],\n [-41, 3, 27, 7, 15],\n [18, -22, -8, -26, -24],\n [3, 7, 5, 17, 3],\n [0, -16, 22, 4, -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[[-11, -8, -48, -13, 7],\n [-17, 42, -8, -38, -24],\n [-3, -40, 8, -4, 7],\n [11, 18, 58, 8, -8],\n [15, -16, 7, 20, 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 5x5 matrix:\n[[12, -18, 12, 14, 4],\n [49, 4, 9, 33, -12],\n [14, -26, 20, 20, 0],\n [-15, -37, 14, 0, 20],\n [-52, -5, -16, -39, 26]]\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[[35, -8, 31, -15, 5],\n [-27, 0, -6, -20, 1],\n [24, -14, 22, 42, 10],\n [11, -10, 26, -40, 5],\n [11, -29, 18, 33, 9]]?\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 5x5 matrix:\n[[2, 0, 6, 6, 4],\n [6, 0, 18, 18, 12],\n [-3, 0, -9, -9, -6],\n [0, 0, 0, 0, 0],\n [-2, 0, -6, -6, -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[[2, 0, -10, -6, -4],\n [-4, -1, 4, 6, -1],\n [-40, -15, -40, 30, -55],\n [28, 11, 36, -18, 43],\n [-4, 0, 20, 12, 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 5x5 matrix:\n[[-14, -5, 8, 17, 0],\n [-8, -12, -30, -44, 19],\n [36, 24, -23, 6, -7],\n [-36, -16, -18, -24, 10],\n [48, 18, 8, 38, -1]]\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[[19, -26, 2, 19, 12],\n [1, 1, -19, 1, 18],\n [41, -61, -1, 3, -4],\n [9, -43, -12, 26, -15],\n [-27, 17, -15, 23, 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[[-37, 9, 31, 0, -35],\n [32, -31, -50, 19, 8],\n [-11, -5, 45, -21, -2],\n [4, 34, -12, -1, 37],\n [65, 12, -17, -30, 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[[12, -12, 6, -18, 12],\n [-20, 20, -10, 30, -20],\n [8, -8, 4, -12, 8],\n [-16, 16, -8, 24, -16],\n [16, -16, 8, -24, 16]]\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[[38, 19, 11, -21, 55],\n [-40, 74, 0, -14, 30],\n [2, 1, 13, -1, 9],\n [-2, -47, -21, 11, -67],\n [-40, 18, 8, 6, -18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[19, -9, -9, -25, -29],\n [4, 6, 1, 5, 1],\n [33, 27, 0, 12, -12],\n [0, 30, 11, 39, 27],\n [-27, -3, 7, 15, 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[[-10, -10, 26, -6, -15],\n [8, -10, 6, 0, -12],\n [12, -32, 8, -16, -14],\n [-16, 11, 26, 12, -33],\n [-40, 14, 31, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[48, 2, -4, 0, 6],\n [32, -27, -6, -40, 19],\n [16, -39, -6, -56, 23],\n [48, 2, -4, 0, 6],\n [-8, -6, 0, -8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[20, 20, -15, 10, 5],\n [12, 12, -9, 6, 3],\n [-12, -12, 9, -6, -3],\n [20, 20, -15, 10, 5],\n [-8, -8, 6, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-9, -3, -7, -16, 16],\n [3, -3, 1, -2, 8],\n [-29, -2, -26, -12, -13],\n [27, -18, 6, 24, 3],\n [18, -56, -32, 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 5x5 matrix:\n[[-2, 24, -2, 2, -14],\n [14, -21, 18, -17, -57],\n [-9, 30, -22, 9, 41],\n [-2, -15, 12, 5, -3],\n [6, -2, 4, -8, -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[[38, 28, -2, 10, 44],\n [15, 30, -15, 5, 30],\n [10, 32, -19, 4, 28],\n [-8, -4, -1, -2, -8],\n [33, 30, -6, 9, 42]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-50, -17, -11, -21, -20],\n [-38, -12, 2, -20, -18],\n [29, 4, 1, 16, 21],\n [-1, -1, -18, 8, 44],\n [23, -14, 21, 9, -4]]\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[[14, 10, 6, -15, -13],\n [-14, -18, -15, 27, 15],\n [2, 2, -29, 13, 9],\n [-1, 14, 39, -33, -11],\n [-2, -18, 11, 11, -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[[-29, 11, -4, -17, 7],\n [2, -42, 33, -6, 30],\n [-30, -45, 42, -28, 48],\n [0, -30, 21, -4, 24],\n [48, -30, 30, 20, -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 5x5 matrix:\n[[-8, 9, 41, 44, -24],\n [-24, -38, -1, -19, 48],\n [-16, -33, 7, 14, 16],\n [26, -15, -28, -8, 2],\n [15, -17, -7, -9, 19]]\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[[14, 0, -12, 16, 12],\n [13, 21, -41, 29, 47],\n [14, -14, 16, -12, -30],\n [-7, 3, 0, -2, 3],\n [-1, -3, 2, 4, 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[[-20, 10, -17, -31, -8],\n [-19, 15, -20, -19, 10],\n [-8, 0, -4, -20, -16],\n [30, -30, 36, 18, -36],\n [-24, 20, -26, -22, 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[[2, 2, -8, -12, 8],\n [2, 2, -8, -12, 8],\n [3, 3, -12, -18, 12],\n [2, 2, -8, -12, 8],\n [-6, -6, 24, 36, -24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-13, -4, 20, -30, 18],\n [3, -16, 1, -16, 6],\n [-1, 10, -3, 13, -6],\n [3, 56, -5, 60, -18],\n [-23, -34, -6, -29, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, 6, 15, 3, 6],\n [4, 8, 20, 4, 8],\n [5, 10, 25, 5, 10],\n [-5, -10, -25, -5, -10],\n [4, 8, 20, 4, 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[[6, -6, -18, 18, 18],\n [-10, 10, 30, -30, -30],\n [-4, 4, 12, -12, -12],\n [-6, 6, 18, -18, -18],\n [6, -6, -18, 18, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, -5, 5, 0, 0],\n [-12, -30, 30, 0, 0],\n [12, 30, -30, 0, 0],\n [-4, -10, 10, 0, 0],\n [6, 15, -15, 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 5x5 matrix:\n[[-10, -8, 23, -9, -13],\n [65, 32, -12, 74, 45],\n [41, 10, -11, 21, 58],\n [-3, -14, -21, 14, 0],\n [-18, 4, -42, -16, -12]]\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 5x5 matrix:\n[[18, 30, -12, -6, 0],\n [3, 5, -2, -1, 0],\n [-9, -15, 6, 3, 0],\n [9, 15, -6, -3, 0],\n [-12, -20, 8, 4, 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 5x5 matrix:\n[[0, 34, -8, -28, 13],\n [-2, -35, -30, 40, -46],\n [-17, -23, -48, 10, -35],\n [30, 38, -6, 19, -24],\n [-9, -40, -52, 43, -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[[6, 5, 2, -1, -3],\n [-6, -5, -2, 1, 3],\n [-30, -25, -10, 5, 15],\n [-12, -10, -4, 2, 6],\n [-18, -15, -6, 3, 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[[-25, 30, -25, 25, 15],\n [-5, 6, -5, 5, 3],\n [20, -24, 20, -20, -12],\n [-30, 36, -30, 30, 18],\n [-20, 24, -20, 20, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, -36, -24, 2, 2],\n [-3, -18, -12, -4, -4],\n [-2, -12, -8, -31, -31],\n [1, 6, 4, -27, -27],\n [-2, -12, -8, -16, -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[[-64, -25, -55, -24, 16],\n [7, -20, 2, 18, 6],\n [-40, -3, -45, -57, 17],\n [-20, -25, -37, -52, 2],\n [30, -21, 27, 45, -15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, -2, 6, -6, -8],\n [-4, -1, 3, -3, -4],\n [-12, -3, 9, -9, -12],\n [-12, -3, 9, -9, -12],\n [-4, -1, 3, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 0, -5, 1, 9],\n [16, 8, 3, 1, -15],\n [4, 8, -2, 2, -6],\n [5, -2, 3, -1, -3],\n [-7, 22, -13, 7, -3]]\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 5x5 matrix:\n[[-8, 23, -29, 17, 17],\n [-8, -17, 45, 7, -21],\n [18, 25, 25, -50, -16],\n [12, -23, 5, 43, 19],\n [20, -10, 34, 5, -1]]\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[[5, 20, -15, 20, 25],\n [25, 40, -23, 36, 45],\n [2, 8, -6, 8, 10],\n [-17, -23, 12, -20, -25],\n [31, 49, -28, 44, 55]]\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[[-1, -22, 27, -4, 10],\n [24, -21, -27, 6, -3],\n [38, -37, -9, -10, -11],\n [10, -38, 12, 4, 14],\n [-16, 8, 42, -16, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 18, 36, -36],\n [0, 0, 6, 12, -12],\n [0, 0, 18, 36, -36],\n [0, 0, 6, 12, -12],\n [0, 0, 6, 12, -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[[21, 50, -1, -8, -56],\n [-18, -36, 18, 24, 24],\n [-39, -20, 49, 62, -16],\n [21, 12, -33, -40, 14],\n [6, 28, 34, 32, -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[[-12, -6, -5, 0, 4],\n [12, 6, 1, 6, -26],\n [24, 12, 18, -12, 36],\n [16, 8, 4, 4, -20],\n [-8, -4, 4, -11, 43]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-28, -20, -24, -4, 0],\n [14, 10, 12, 2, 0],\n [-8, -8, -2, 2, -8],\n [-12, -12, -3, 3, -12],\n [-22, -10, -31, -11, 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[[18, 1, 24, -16, -9],\n [-3, -23, -27, -53, 30],\n [4, 19, 12, 16, -31],\n [16, 22, -4, -18, -17],\n [14, 15, 35, 9, -39]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[25, 5, -5, -10, 5],\n [-2, 8, -2, 20, 14],\n [-39, -19, 11, -10, -27],\n [9, 13, -5, 22, 21],\n [61, 29, -17, 14, 41]]\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[[-6, -34, 8, -18, 6],\n [-12, -19, -40, 0, 14],\n [52, -2, 0, -52, 0],\n [42, 54, 12, -6, -15],\n [28, 31, 24, -7, -13]]\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[[-21, 33, -21, -18, 27],\n [12, -26, 16, 10, -24],\n [-44, 14, -26, 34, 24],\n [19, -15, 7, 38, 3],\n [22, -36, 32, -34, -54]]?\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[[5, -3, 22, 27, 9],\n [27, -2, 18, 5, 7],\n [-46, -2, -36, -18, -6],\n [-3, 38, 14, 35, -47],\n [57, -13, 32, -1, 25]]\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, 2, -5, -14, 18],\n [-24, 16, -10, -32, 24],\n [-24, -20, -1, 4, 24],\n [-18, 10, -7, -22, 18],\n [-36, -16, -5, -8, 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[[12, 35, -13, -23, -8],\n [-13, 35, 12, -2, -23],\n [-38, 4, 24, 26, -25],\n [-1, -13, -22, 25, -6],\n [8, 40, -2, -7, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-13, -14, 17, -6, -15],\n [13, 16, -3, 1, -20],\n [21, 30, -21, 9, 0],\n [-48, -63, 45, -18, 0],\n [1, -2, 3, -2, -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[[10, 4, -6, -12, 10],\n [6, 9, -2, -18, 7],\n [26, 17, -14, -42, 27],\n [15, -27, -17, 36, 10],\n [6, 9, -2, -18, 7]]\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 5x5 matrix:\n[[9, -15, 18, 6, -6],\n [15, -25, 30, 10, -10],\n [12, -20, 24, 8, -8],\n [-9, 15, -18, -6, 6],\n [-6, 10, -12, -4, 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[[-26, -6, 18, -52, 26],\n [5, 6, -16, 2, 12],\n [-8, 21, 4, -17, 15],\n [28, 12, 36, -16, -4],\n [-32, -36, 8, -25, 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[[0, -1, 3, -1, -6],\n [0, 0, 0, 0, 0],\n [0, 3, -9, 3, 18],\n [0, -4, 12, -4, -24],\n [0, -6, 18, -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[[-6, 19, 19, 17, 10],\n [12, -33, 9, -7, 14],\n [0, 37, 31, 4, 36],\n [25, -30, 11, -1, 40],\n [6, 18, 68, 14, 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[[22, 6, -12, -4, -2],\n [28, 4, -12, 0, -8],\n [-33, -9, 18, 6, 3],\n [16, 8, -12, -8, 4],\n [-14, -12, 15, 14, -11]]\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, 0, 4, 6, 10],\n [-2, 20, 16, -27, 18],\n [18, -30, 12, 54, -18],\n [-14, 28, -28, -54, 18],\n [-24, -20, 0, 24, -32]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0, 0],\n [36, -30, -30, 24, -36],\n [12, -10, -10, 8, -12],\n [6, -5, -5, 4, -6],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[5, -5, -1, 1, -1],\n [-5, 5, 1, -1, 1],\n [10, -10, -2, 2, -2],\n [-10, 10, 2, -2, 2],\n [-15, 15, 3, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-6, 11, -5, -22, -38],\n [3, -28, 25, 29, 28],\n [-1, -19, 20, 13, 2],\n [-1, -29, 30, 21, 6],\n [2, 23, -25, -14, 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[[-12, -12, 30, 18, -24],\n [10, 10, -25, -15, 20],\n [-4, -4, 10, 6, -8],\n [-6, -6, 15, 9, -12],\n [-4, -4, 10, 6, -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[[-3, -15, -33, 0, 30],\n [8, -6, -9, 7, 4],\n [-5, 15, 27, -2, -18],\n [16, -21, -54, 45, 61],\n [32, -8, -14, 46, 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[[12, 36, -12, 24, 30],\n [-1, -18, 11, 18, -10],\n [2, -12, 10, 28, -4],\n [13, 42, -15, 22, 34],\n [10, 48, -22, -4, 34]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[15, 5, -14, 10, 19],\n [-9, 1, 4, 0, -7],\n [-27, 3, 12, 0, -21],\n [48, -12, -14, -10, 30],\n [-18, -8, 19, -15, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[15, -6, -9, 9, 9],\n [-5, 2, 3, -3, -3],\n [-25, 10, 15, -15, -15],\n [-10, 4, 6, -6, -6],\n [-10, 4, 6, -6, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[24, -20, 20, 8, -24],\n [-24, 20, -20, -8, 24],\n [24, -20, 20, 8, -24],\n [18, -15, 15, 6, -18],\n [-30, 25, -25, -10, 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 5x5 matrix:\n[[-3, 17, -12, 22, -11],\n [30, 18, 1, 8, -8],\n [13, 33, 43, -30, -45],\n [37, 1, 2, -2, 9],\n [-17, -23, 2, -14, 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[[17, 2, -11, 50, 3],\n [13, 22, 27, 6, -4],\n [-39, 7, -26, 6, 27],\n [0, -29, -37, 20, 2],\n [-17, 36, 5, 30, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[25, 25, 30, 15, 0],\n [5, 5, 6, 3, 0],\n [-25, -25, -30, -15, 0],\n [20, 20, 24, 12, 0],\n [-30, -30, -36, -18, 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 5x5 matrix:\n[[4, 9, 27, -59, -12],\n [72, -43, -22, 15, 60],\n [38, -39, -21, 11, 39],\n [0, -26, -11, 12, 17],\n [10, -20, -4, -42, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-60, -3, 12, -60, -55],\n [-21, -6, -18, 0, -1],\n [-2, -8, -17, -13, -1],\n [3, 2, 23, -7, -18],\n [14, 10, -2, -26, 14]]\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 5x5 matrix:\n[[-34, -14, -43, 42, 13],\n [42, 0, 48, -54, -6],\n [18, -37, 19, -40, 42],\n [35, 54, 50, -20, -68],\n [33, 27, 36, -39, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-37, 6, -8, 49, 1],\n [-16, -22, 6, 7, -27],\n [8, -28, 12, -26, -30],\n [-26, 0, -4, 32, -4],\n [-5, 24, -10, 20, 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 5x5 matrix:\n[[35, -11, 3, 13, -8],\n [15, 21, -11, 19, -16],\n [-20, -6, -36, 24, 10],\n [-21, 41, -17, 9, -12],\n [27, 37, 9, 7, -28]]\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, 3, -6, -3, 15],\n [0, 2, -4, -2, 10],\n [0, -2, 4, 2, -10],\n [0, 5, -10, -5, 25],\n [0, -4, 8, 4, -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[[-17, 11, 12, 9, -1],\n [-37, 15, 12, 13, -21],\n [14, -18, -24, -14, -18],\n [-3, 12, 18, 9, 21],\n [-37, 15, 12, 13, -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, 36, 36, 18, -36],\n [10, 30, 30, 15, -30],\n [12, 36, 36, 18, -36],\n [-4, -12, -12, -6, 12],\n [-8, -24, -24, -12, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0, 0],\n [-6, 18, 12, 24, 30],\n [5, -15, -10, -20, -25],\n [4, -12, -8, -16, -20],\n [2, -6, -4, -8, -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 5x5 matrix:\n[[-1, -19, -1, 35, -23],\n [4, 4, 22, 4, -16],\n [3, -4, 1, 8, -5],\n [17, -2, 12, 10, -9],\n [25, 1, 40, 19, -31]]\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, -31, -24, -20, -28],\n [39, 25, 33, -8, 15],\n [37, 28, 27, 0, 29],\n [-30, -21, 8, -70, -22],\n [-13, -13, -7, -4, -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[[0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [-24, 36, -36, 0, -18],\n [-16, 24, -24, 0, -12],\n [24, -36, 36, 0, 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[[0, 1, -2, -14, -14],\n [0, 2, -4, -28, -28],\n [-18, 4, 10, 34, 25],\n [-38, 11, 16, 36, 17],\n [28, -10, -8, 0, 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 5x5 matrix:\n[[1, 5, 10, -9, 13],\n [12, 30, 35, 17, 11],\n [11, 26, 27, 22, 3],\n [-3, -8, -36, 3, 0],\n [-8, -16, -7, -29, 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[[-17, -4, -4, -14, 8],\n [-60, -65, -32, -26, -21],\n [-20, -11, -24, 64, -37],\n [-24, -42, -46, 16, -36],\n [18, 9, -31, 58, -30]]\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, 12, -22, 30, 14],\n [-22, 36, -18, 50, 18],\n [1, 6, 25, -15, -11],\n [11, -18, 9, -25, -9],\n [22, -36, 18, -50, -18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[18, -9, 18, -9, -18],\n [6, -3, 6, -3, -6],\n [24, -12, 24, -12, -24],\n [-24, 12, -24, 12, 24],\n [18, -9, 18, -9, -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 5x5 matrix:\n[[0, -5, -5, 25, 30],\n [0, 3, 3, -15, -18],\n [0, 4, 4, -20, -24],\n [0, 3, 3, -15, -18],\n [0, 6, 6, -30, -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[[6, -2, 5, -1, -3],\n [36, -12, 30, -6, -18],\n [-30, 10, -25, 5, 15],\n [18, -6, 15, -3, -9],\n [-24, 8, -20, 4, 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[[12, -24, 0, -24, -36],\n [-18, 6, 30, -14, 24],\n [-30, 24, 36, 0, 54],\n [12, -6, -18, 6, -18],\n [10, -14, -6, -10, -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 5x5 matrix:\n[[-18, 22, 59, 34, -2],\n [-12, -25, -31, -30, -31],\n [-1, -15, -30, 13, 9],\n [-22, 23, 10, 33, 14],\n [5, 11, 27, -9, -5]]\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, 10, 0, -2, 4],\n [-20, 20, 0, -4, 8],\n [-5, 5, 0, -1, 2],\n [-20, 20, 0, -4, 8],\n [20, -20, 0, 4, -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 5x5 matrix:\n[[6, 4, -6, -2, 3],\n [36, 24, -36, -12, 18],\n [-30, -20, 30, 10, -15],\n [0, 0, 0, 0, 0],\n [-6, -4, 6, 2, -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[[-23, 10, -12, 21, 21],\n [-23, 10, -12, 21, 21],\n [3, -30, -18, 9, 39],\n [9, -24, -9, 0, 21],\n [9, -24, -9, 0, 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 5x5 matrix:\n[[9, -6, 30, 51, -6],\n [12, -11, 29, 48, -10],\n [4, -22, 2, 0, -20],\n [28, 20, -18, -35, 26],\n [39, 10, -6, -17, 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[[-36, 6, 36, -24, -6],\n [-30, 5, 30, -20, -5],\n [18, -3, -18, 12, 3],\n [24, -4, -24, 16, 4],\n [12, -2, -12, 8, 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[[-12, 21, -16, 13, 8],\n [-31, 13, -34, 40, 28],\n [38, 16, 36, -54, -40],\n [-2, 11, -4, 1, 0],\n [-5, 5, -6, 6, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[38, -2, -50, -30, -18],\n [-15, -42, 54, -6, -9],\n [-46, -2, 56, 10, -16],\n [-27, 5, 24, -3, -64],\n [-17, -11, 38, 27, 30]]\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, 8, -25, -32, 25],\n [-2, 10, -25, -2, -1],\n [8, -22, 10, 26, -40],\n [14, -42, 62, 13, -21],\n [2, 2, -24, -3, -7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -32, 9, 15, -6],\n [-33, -18, 22, -7, 9],\n [3, -30, 6, -36, 39],\n [40, 0, -25, 11, -22],\n [25, -34, -1, 21, -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[[1, -5, 12, -2, 1],\n [-17, -17, 2, -23, 21],\n [5, -14, 38, -9, 4],\n [29, 22, 13, 50, -51],\n [-17, -20, 6, -24, 28]]\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, 0, 20, 5, 10],\n [7, 0, 10, -25, -6],\n [25, 0, -50, 25, -10],\n [-4, 0, 20, -20, 0],\n [-10, 0, 35, -30, 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[[21, -2, -17, -24, -12],\n [8, 18, -35, -13, 18],\n [-6, -28, 47, 23, -18],\n [14, -30, 34, -24, -60],\n [19, 2, -23, -8, 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[[14, -56, 2, -54, 20],\n [-6, 33, 3, 33, -9],\n [-9, 18, -9, 15, -12],\n [-3, 27, 6, 28, -5],\n [-22, 16, -34, 6, -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 5x5 matrix:\n[[4, -11, 4, -4, 28],\n [-4, 21, -18, 27, -15],\n [-12, 18, -10, 33, -8],\n [-20, 16, -6, 43, -15],\n [28, -32, 16, -60, 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[[-15, -3, 6, 3, -15],\n [15, 3, -6, -3, 15],\n [-30, -6, 12, 6, -30],\n [20, 4, -8, -4, 20],\n [10, 2, -4, -2, 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[[0, 0, 0, 0, 0],\n [-3, 3, 18, -6, 0],\n [4, -4, -24, 8, 0],\n [-3, 3, 18, -6, 0],\n [-3, 3, 18, -6, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[33, 25, 31, 20, -16],\n [-6, 48, -6, 21, 27],\n [25, 23, 19, 25, -9],\n [30, 16, 26, 19, -17],\n [-2, 14, -30, 56, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[18, -56, -12, -25, 6],\n [-19, 43, 12, 5, -9],\n [-23, 43, 0, -1, 3],\n [16, -34, 12, -9, -16],\n [1, 5, -42, 24, 47]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 4, 0, -10, -10],\n [-4, -4, 0, 10, 10],\n [-2, -2, 0, 5, 5],\n [12, 12, 0, -30, -30],\n [-10, -10, 0, 25, 25]]\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[[-16, -16, 0, 12, -20],\n [4, 4, 0, -3, 5],\n [-20, -20, 0, 15, -25],\n [-34, 6, -10, 18, -15],\n [0, -16, 4, 3, -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 5x5 matrix:\n[[11, 0, 4, 37, -21],\n [-34, 0, 18, 18, 8],\n [-3, 6, 6, 1, -9],\n [12, -6, -5, 27, -14],\n [-33, 9, 18, -36, 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[[-10, -8, -4, -4, 6],\n [30, 24, 12, 12, -18],\n [-20, -16, -8, -8, 12],\n [-25, -20, -10, -10, 15],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-35, -6, -19, 7, -62],\n [16, 30, 13, 25, 26],\n [-20, -40, -7, -36, -23],\n [10, 2, 38, -9, 49],\n [21, -26, -46, -23, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, -10, 6, -19, 14],\n [19, 26, 6, -1, 2],\n [-25, -20, -15, 25, -20],\n [7, -16, 15, -43, 32],\n [8, 28, -6, 28, -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[[-10, 31, -54, 62, -19],\n [-8, 46, -41, 21, 35],\n [23, -21, 34, -50, 20],\n [42, -56, 18, -26, -32],\n [-8, 24, -18, -22, 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[[15, 0, -5, -30, 25],\n [18, 0, -6, -36, 30],\n [12, 0, -4, -24, 20],\n [-6, 0, 2, 12, -10],\n [6, 0, -2, -12, 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[[-36, -29, 23, -44, 40],\n [0, -5, -23, 18, -42],\n [24, 42, -17, 29, -34],\n [-18, -23, -15, 3, -21],\n [2, 53, -34, 38, -49]]\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, 16, -10, -31, 10],\n [11, -8, 11, -1, -8],\n [-43, 2, 4, 32, 3],\n [28, -36, -32, -41, 6],\n [6, -3, -40, -18, 11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[22, 25, -2, -3, -10],\n [-39, -45, 3, 6, 24],\n [-7, -10, -1, 3, 22],\n [-19, -25, -1, 6, 40],\n [-42, -45, 6, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -10, 6, -10, -4],\n [-9, 15, -9, 15, 6],\n [-9, 15, -9, 15, 6],\n [3, -5, 3, -5, -2],\n [-15, 25, -15, 25, 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[[30, 18, 0, 30, -6],\n [20, 12, 0, 20, -4],\n [30, 18, 0, 30, -6],\n [-20, -12, 0, -20, 4],\n [20, 12, 0, 20, -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[[-49, 3, -18, -11, 51],\n [-50, 7, 36, -35, 32],\n [-8, 1, 24, 3, 7],\n [34, 21, 42, 27, -41],\n [42, -5, -24, 17, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-25, 15, 15, 15, 60],\n [25, -15, -15, -15, -60],\n [32, -16, -12, -24, -60],\n [13, -3, 3, -15, -6],\n [-4, -4, -12, 12, -24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-28, -27, -21, -32, -5],\n [28, 18, 24, 17, 23],\n [-44, -47, -33, -40, -25],\n [-20, 28, -26, 0, -16],\n [18, -5, 18, 18, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, 7, -23, 4, 17],\n [44, 22, -8, -22, -22],\n [40, -1, -25, 2, -4],\n [-18, 3, -15, 8, 23],\n [-28, 7, 13, -4, 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 5x5 matrix:\n[[8, -9, -22, 9, -7],\n [-8, 7, -30, -8, -6],\n [-12, -22, 20, 27, 30],\n [-20, -9, 26, 13, 30],\n [44, 2, -12, -7, -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[[2, 1, -4, 3, 1],\n [-8, -4, 16, -12, -4],\n [-10, -5, 20, -15, -5],\n [-10, -5, 20, -15, -5],\n [-10, -5, 20, -15, -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[[20, -6, -26, 4, -4],\n [-25, 17, 31, -25, -20],\n [-12, 19, -31, -28, 20],\n [-41, 27, 30, -52, -45],\n [-24, 2, 9, 1, 26]]\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, -7, 10, 10, -13],\n [-54, -9, 15, 24, -27],\n [30, 29, -35, -8, 23],\n [-30, -29, 35, 8, -23],\n [-24, -7, 10, 10, -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[[-26, 46, 5, 31, -40],\n [-9, 10, -5, 4, -9],\n [-4, -20, -30, -26, 16],\n [18, 24, 60, 42, -18],\n [12, -28, -10, -22, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-19, 14, 17, 3, 2],\n [1, 0, -19, -3, 24],\n [-15, -17, 17, 42, 21],\n [-39, 28, 53, 9, -20],\n [-16, 10, 24, 6, -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[[-14, 7, -17, 20, 8],\n [61, 38, -9, -13, 28],\n [-18, -4, -16, 20, 4],\n [0, -12, 11, 7, 33],\n [-12, -13, 23, -4, 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[[26, -26, 3, -44, 8],\n [-24, 39, -27, 14, 8],\n [-8, 6, -19, 19, 1],\n [2, 0, 25, -12, -36],\n [20, -24, 50, -33, -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[[10, 4, 12, -10, 10],\n [15, 6, 18, -15, 15],\n [20, 8, 24, -20, 20],\n [20, 8, 24, -20, 20],\n [-15, -6, -18, 15, -15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-13, 0, 2, 6, -12],\n [-3, -21, 1, -18, 1],\n [22, 24, -4, 12, 16],\n [6, -36, 0, -36, 12],\n [0, 39, -1, 36, -7]]\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, -25, -30, -30, -15],\n [24, 30, 36, 36, 18],\n [8, 10, 12, 12, 6],\n [24, 30, 36, 36, 18],\n [12, 15, 18, 18, 9]]\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, -18, -8, -15, -10],\n [52, -39, 37, -15, 29],\n [-51, 42, -40, 5, -27],\n [-37, 21, -31, 10, -25],\n [-9, 3, 13, -40, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-16, -25, -17, -9, -10],\n [12, 0, 18, -27, -6],\n [-23, -5, 3, -5, 44],\n [20, 15, 3, 28, -22],\n [-3, 45, 5, -17, 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[[30, 35, 10, 30, -25],\n [6, 5, 1, 12, 2],\n [10, 13, 4, 6, -13],\n [22, 21, 5, 36, -2],\n [-10, -9, -2, -18, -1]]\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 5x5 matrix:\n[[0, 0, 0, 0, 0],\n [12, 6, 6, -36, 36],\n [12, 6, 6, -36, 36],\n [-4, -2, -2, 12, -12],\n [2, 1, 1, -6, 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[[45, -24, -19, -25, -14],\n [27, 19, 18, 46, -17],\n [6, -12, 14, -10, -10],\n [-42, -40, -76, 0, 17],\n [-30, -14, -62, 12, 19]]\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, -6, 25, 10, -21],\n [-9, -20, 20, 8, -13],\n [-10, 3, -25, -10, 50],\n [-31, -23, 5, 2, 33],\n [-17, 16, -15, -6, 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 5x5 matrix:\n[[40, -2, 8, 30, -26],\n [22, -44, -12, -22, -38],\n [-35, -20, -46, -55, 41],\n [-5, -8, -39, -55, -23],\n [-4, 2, -32, -36, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[14, 11, -64, 14, 21],\n [28, -49, -12, -35, -30],\n [-2, 49, 20, 22, 47],\n [-24, 8, 65, -19, -12],\n [26, -12, -5, -18, 5]]\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[[30, 20, 33, -16, -13],\n [12, 10, -3, 12, -18],\n [-30, -8, -15, 40, -35],\n [12, 8, 42, -28, 2],\n [42, 18, 28, -40, 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[[-6, 18, 20, 4, 46],\n [-34, 6, -44, -14, 20],\n [27, 5, 56, 20, 5],\n [-38, 4, 2, 40, -24],\n [-41, 6, -41, -3, 11]]\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 5x5 matrix:\n[[-15, 25, 30, 0, 5],\n [23, 15, -6, 4, -21],\n [14, 30, 12, 4, -18],\n [16, 40, 18, 5, -22],\n [-9, 15, 18, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[22, -25, 19, -3, 10],\n [-32, 3, -23, 5, -28],\n [26, 7, 17, -3, 26],\n [24, 25, 4, 27, 18],\n [-28, -38, 1, -46, -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[[6, 18, -42, 8, 15],\n [9, -22, -2, -2, -7],\n [30, -10, -2, -64, 35],\n [21, -27, -28, -4, 0],\n [18, -40, 10, -20, -7]]?\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[[-39, -45, 33, 40, -23],\n [42, 14, -40, -37, 34],\n [48, 34, -32, -27, 21],\n [38, 10, 8, 15, 2],\n [14, 44, -30, -38, 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[[44, -57, 11, -28, -69],\n [25, -8, -25, -2, -8],\n [4, 9, 9, -1, 4],\n [25, -11, -4, -8, -17],\n [31, -13, 0, -11, -22]]\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 5x5 matrix:\n[[0, 20, 20, -12, 8],\n [0, -5, -5, 3, -2],\n [0, 0, 0, 0, 0],\n [0, 25, 25, -15, 10],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-24, -6, 9, 28, -27],\n [-32, -18, -13, -26, 9],\n [8, -18, -18, -31, 29],\n [-54, -51, -21, -17, 3],\n [-36, -30, 2, 32, -28]]?\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[[22, 81, -7, -56, 21],\n [-23, -20, 22, 38, 15],\n [-28, -50, -2, 27, 0],\n [21, 8, 4, -3, -17],\n [-6, -6, 6, -4, -4]]\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, -14, 27, -13, -34],\n [26, 28, 12, 2, 2],\n [-30, -36, -6, -6, -12],\n [-24, -32, 2, -8, -18],\n [10, 20, -15, 10, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-26, -20, -14, -8, 14],\n [-3, -6, 5, 4, 3],\n [-13, -34, 36, 28, 16],\n [-2, -20, 32, 24, 8],\n [-23, -38, 24, 20, 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[[9, 5, -18, 20, -23],\n [12, -24, 22, 19, -23],\n [-6, 34, -44, -4, 6],\n [-18, 14, 0, -34, 40],\n [-12, 20, -16, -20, 24]]\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, -12, -25, 32, -4],\n [20, -16, 32, -70, 30],\n [8, 6, -54, 83, 1],\n [-76, 9, 44, -28, -77],\n [-17, 22, 20, -10, -27]]\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, -4, 10, 6, 2],\n [1, -2, 5, 3, 1],\n [3, -6, 15, 9, 3],\n [0, 0, 0, 0, 0],\n [-1, 2, -5, -3, -1]]\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 5x5 matrix:\n[[-54, 7, -57, -14, -1],\n [4, -28, 13, 41, 5],\n [13, -8, -40, -2, 46],\n [-43, 6, -25, -11, -11],\n [17, 11, -3, -16, 7]]\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[[-2, -17, 17, -38, -38],\n [0, 18, -3, 21, 30],\n [0, -16, 6, -22, -30],\n [-10, -19, 40, -79, -46],\n [-6, 23, 6, 5, 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[[-30, -36, -30, -18, 18],\n [30, 36, 30, 18, -18],\n [30, 36, 30, 18, -18],\n [-10, -12, -10, -6, 6],\n [10, 12, 10, 6, -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[[59, -14, 51, -6, 27],\n [26, 4, 9, -34, 18],\n [-27, 5, -27, 6, -21],\n [10, -4, 21, 6, 18],\n [-8, 10, -27, -26, -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 5x5 matrix:\n[[21, -29, 9, -14, 15],\n [10, 7, -22, 24, -6],\n [-10, -26, 46, -52, 18],\n [13, -27, 17, -22, 15],\n [15, 20, -45, 50, -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 5x5 matrix:\n[[12, 2, -8, 22, -40],\n [-36, -22, -32, -32, 20],\n [54, 14, 34, 40, -16],\n [-29, -6, -35, -10, -4],\n [-6, -24, -18, -12, 0]]\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[[19, -35, -12, -6, -2],\n [-12, 15, -5, 27, -15],\n [-3, -28, 28, -10, -27],\n [24, -34, -2, -34, 18],\n [-11, -35, 29, 15, -56]]\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, 43, 7, -42, -32],\n [20, -6, 15, -12, 14],\n [20, -36, 3, 24, 26],\n [-8, -6, -6, 12, 4],\n [8, 50, 18, -60, -32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 8, 4, -4, 8],\n [4, -8, -4, 4, -8],\n [-6, 12, 6, -6, 12],\n [8, -16, -8, 8, -16],\n [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[[-1, -12, 5, 18, 5],\n [-10, -33, 5, 12, 5],\n [8, 30, -4, -18, -4],\n [7, 34, -20, -21, -20],\n [-1, -3, 5, -3, 5]]\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 5x5 matrix:\n[[-6, 3, 30, 12, -45],\n [29, -7, 3, -23, 45],\n [-7, 2, -31, -19, 34],\n [-34, 8, -37, 5, -6],\n [10, -2, 47, 21, -48]]\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, 0, -18, -15, -12],\n [5, 0, -6, -5, -4],\n [-5, 0, 6, 5, 4],\n [0, 0, 0, 0, 0],\n [30, 0, -36, -30, -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 5x5 matrix:\n[[5, 7, -17, 35, 9],\n [20, 10, -14, 32, 0],\n [10, 1, 5, -8, -8],\n [25, 12, -16, 37, -1],\n [-10, 2, -14, 26, 14]]\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, 0, 0, 0, 0],\n [-18, -12, 12, 6, -9],\n [-24, -16, 16, 8, -12],\n [18, 12, -12, -6, 9],\n [36, 24, -24, -12, 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, 9, -9, 0, 18],\n [16, -14, -1, 25, 7],\n [7, -5, -1, 10, 4],\n [-20, -14, 17, -5, -35],\n [10, -2, -4, 10, 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[[-8, -26, -2, -19, -8],\n [-50, -39, -49, 4, -42],\n [0, -6, 4, -9, 2],\n [-42, 29, -20, 11, 11],\n [-16, 32, -5, 13, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -8, 2, 4, -12],\n [-4, 8, -2, -4, 12],\n [-4, 8, -2, -4, 12],\n [-10, 20, -5, -10, 30],\n [-12, 24, -6, -12, 36]]?\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 5x5 matrix:\n[[-19, 56, -39, -21, -38],\n [-40, 18, 0, -49, -62],\n [6, 7, 9, 14, 3],\n [-8, 7, -33, -14, 5],\n [-17, 32, -39, 0, 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[[-18, 9, -3, -12, -9],\n [12, -6, 2, 8, 6],\n [-30, 15, -5, -20, -15],\n [-24, 12, -4, -16, -12],\n [-18, 9, -3, -12, -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[[20, -20, 24, 20, 24],\n [-15, 18, -21, -19, -17],\n [15, -21, 24, 23, 16],\n [-10, 4, -6, -2, -14],\n [-20, 17, -21, -16, -25]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-6, 6, 21, -12, 15],\n [24, -24, -20, 8, 4],\n [2, -2, -7, 4, -5],\n [-2, 2, -9, 6, -11],\n [-10, 10, 19, -10, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-13, -48, -42, 10, 8],\n [5, 24, 18, -14, -4],\n [-8, -12, -20, -26, 2],\n [-3, -6, -8, -7, 1],\n [-13, -48, -42, 10, 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 5x5 matrix:\n[[-29, -6, -7, -20, -15],\n [10, 24, 30, -12, -26],\n [-4, -24, -6, -12, 2],\n [19, 5, -3, 23, 19],\n [-41, -5, -14, -21, -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 5x5 matrix:\n[[26, 18, 2, 12, -2],\n [-11, -9, -14, -21, 23],\n [7, 3, -17, -18, 29],\n [19, 11, -19, -16, 33],\n [-10, -8, -11, -17, 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 5x5 matrix:\n[[12, -26, 18, 11, -11],\n [22, -48, 15, -19, -20],\n [-24, 27, -14, 5, 10],\n [30, -26, 23, 12, -9],\n [12, -20, 6, -10, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-1, -21, 25, -4, -8],\n [-16, -19, 9, -10, 3],\n [-25, 18, -38, -6, 6],\n [-11, -5, 3, -4, -13],\n [30, -5, 25, 10, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 29, 19, -27, -19],\n [-27, 14, 8, -6, -8],\n [-51, 0, -2, 12, 2],\n [-18, 66, 42, -54, -42],\n [39, -24, -14, 12, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, 35, 7, 20, 9],\n [-35, 11, 33, 14, -31],\n [12, 22, -2, 7, 17],\n [-1, -19, 1, -19, 0],\n [8, -14, -12, -8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-62, 1, -62, 16, -2],\n [35, 0, 46, -5, -1],\n [-64, 4, -84, 42, -1],\n [16, -26, -22, -29, 25],\n [-24, -26, -48, -6, 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[[9, 6, -33, 24, 36],\n [0, -18, -18, 27, 27],\n [5, 30, -7, -19, -20],\n [6, 44, 28, -49, -36],\n [-12, -30, 0, 12, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[24, -24, 12, -12, 36],\n [0, 0, 0, 0, 0],\n [-20, 20, -10, 10, -30],\n [24, -24, 12, -12, 36],\n [-8, 8, -4, 4, -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[[-19, -7, -21, 27, 6],\n [16, -3, -10, -12, 16],\n [-20, 8, 17, -3, -20],\n [31, -9, -8, 12, 14],\n [-8, 3, 17, 15, -20]]\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 5x5 matrix:\n[[3, 9, 18, 15, 0],\n [-2, -6, -12, -10, 0],\n [-4, -12, -24, -20, 0],\n [-1, -3, -6, -5, 0],\n [6, 18, 36, 30, 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 5x5 matrix:\n[[-24, -12, -20, -24, -12],\n [12, 6, 10, 12, 6],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [-12, -6, -10, -12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-27, -42, 5, 5, 34],\n [41, 11, -23, -2, -15],\n [9, -60, -17, 7, 32],\n [-18, 6, 12, 18, -18],\n [28, -56, -28, 8, 24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[28, -23, -6, -5, 9],\n [12, -11, 2, -9, 5],\n [28, -24, -2, -11, 10],\n [0, -5, 20, -30, 5],\n [-4, 3, 2, -1, -1]]\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 5x5 matrix:\n[[30, 22, -1, -7, 16],\n [39, 5, -10, -5, 23],\n [11, 33, 31, -6, 6],\n [55, -8, 32, 2, -26],\n [37, 22, 36, -4, -8]]\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 5x5 matrix:\n[[-1, 5, -6, 1, 2],\n [2, -10, 12, -2, -4],\n [2, -10, 12, -2, -4],\n [-4, 20, -24, 4, 8],\n [3, -15, 18, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[38, -13, 3, 11, 12],\n [16, -60, 11, -9, -30],\n [-14, 21, -4, 0, 6],\n [12, -10, 2, 2, 0],\n [-52, 6, -2, -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[[29, -42, -17, -30, 4],\n [42, -16, -57, 18, 39],\n [-104, 32, -22, -38, -18],\n [-4, 8, -8, 9, 19],\n [-50, 4, -22, -33, -23]]\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 5x5 matrix:\n[[-20, 8, -20, 20, 12],\n [-20, 8, -20, 20, 12],\n [20, -8, 20, -20, -12],\n [-15, 6, -15, 15, 9],\n [-20, 8, -20, 20, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, 2, 9, -11, 4],\n [-14, -4, 6, -34, -16],\n [-14, 4, 15, -15, 9],\n [7, -6, -12, -2, -17],\n [-12, 8, 18, -2, 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[[28, -42, -14, 14, -14],\n [0, 0, 14, -7, 21],\n [18, -29, 6, -1, 13],\n [10, -7, 15, 5, 27],\n [4, 4, -1, 14, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 15, 5, -30, 15],\n [4, -17, 21, -18, -17],\n [-3, 15, -15, 9, 15],\n [0, -15, -5, 30, -15],\n [3, -30, 10, 21, -30]]?\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 5x5 matrix:\n[[12, 36, 9, -3, 6],\n [-19, -11, 18, 22, -39],\n [-50, -26, 9, -11, -8],\n [-35, -22, -9, -31, 27],\n [16, 13, -9, -11, 22]]\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[[27, 21, 6, -54, -18],\n [-11, -10, 25, -30, 29],\n [-6, -5, 5, 0, 9],\n [-27, -22, 13, 18, 33],\n [11, 8, 13, -42, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-44, 10, 19, 9, 20],\n [111, 3, -21, -6, -15],\n [-61, 23, -7, -28, 25],\n [-69, -18, 23, 21, -2],\n [-16, -10, -3, -1, -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[[-32, 30, -15, -27, -21],\n [11, 3, 7, 2, 13],\n [6, 19, -2, 1, 8],\n [33, -2, 13, 19, 29],\n [-21, 5, -34, -43, -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[[-5, 1, 6, 6, 6],\n [-5, 1, 6, 6, 6],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [5, -1, -6, -6, -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 5x5 matrix:\n[[4, -2, 5, 1, 0],\n [-16, 8, -20, -4, 0],\n [-24, 12, -30, -6, 0],\n [8, -4, 10, 2, 0],\n [16, -8, 20, 4, 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[[-31, -11, -20, -20, -8],\n [27, -8, 7, -24, -21],\n [-29, 9, -15, -24, -22],\n [49, -61, 50, 14, 14],\n [-4, 17, -10, -4, -5]]\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[[-30, -34, -30, -20, -11],\n [-10, -1, -7, 0, 10],\n [-16, -3, -13, -4, 27],\n [-8, 10, -2, 8, 18],\n [-38, -25, -32, -12, 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[[-9, 15, 9, 6, 15],\n [-1, -19, 11, 12, -9],\n [53, -47, -23, -18, -67],\n [-18, -1, 8, 9, 14],\n [27, 17, -52, -48, -13]]\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, 19, 61, 13, 47],\n [-35, 21, -15, -53, -9],\n [-27, 19, -13, -15, -19],\n [8, 7, -45, -36, -53],\n [29, -29, -23, 34, -12]]\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, 12, 10, 46, -20],\n [26, 29, 13, -11, 11],\n [10, 22, 14, 29, -11],\n [22, 7, -3, -60, 32],\n [2, -1, -3, -18, 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[[21, 64, -24, 33, -40],\n [-15, -28, 34, -27, -4],\n [24, 60, -8, 24, -32],\n [-21, -5, -13, 3, -38],\n [-9, -39, 25, -25, 30]]\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, -24, 12, 21, -11],\n [12, 36, -20, -32, 20],\n [22, 24, -4, -19, -3],\n [16, 24, -8, -20, 4],\n [-13, 3, -11, -5, 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 5x5 matrix:\n[[22, 52, 11, 32, 8],\n [-62, -48, 21, -44, -4],\n [-24, -23, -3, -8, -4],\n [-2, 2, -10, 2, 0],\n [-35, -69, -26, -17, -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[[0, -6, -44, -6, 0],\n [13, -21, -20, 13, 45],\n [-8, -22, -60, 15, 10],\n [6, 31, -28, -2, -40],\n [1, -25, 102, 6, 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[[0, 0, 0, 0, 0],\n [12, 10, -4, 10, -12],\n [-12, -10, 4, -10, 12],\n [12, 10, -4, 10, -12],\n [24, 20, -8, 20, -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[[-21, -12, -9, -6, -33],\n [10, 5, 5, 5, 25],\n [13, 9, 4, -1, 0],\n [-2, 0, -2, -4, -18],\n [18, 11, 7, 3, 19]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[57, 25, -26, 34, 11],\n [21, -26, -15, 13, 23],\n [-7, 59, 8, -3, -37],\n [-3, -15, -2, -37, -3],\n [-8, 5, -41, 18, -27]]\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 5x5 matrix:\n[[3, 48, 45, -48, -39],\n [-39, -39, -45, 39, -3],\n [45, 6, -9, -6, 16],\n [-26, -29, -30, 29, 3],\n [0, -33, -36, 33, 24]]\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[[12, -63, 16, -40, -23],\n [-18, 27, 9, 33, -9],\n [-28, 41, 13, 36, 14],\n [30, 33, -12, 21, -24],\n [24, -14, -20, -8, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-8, 18, -12, 4, -18],\n [3, -12, 6, -6, 15],\n [-21, 0, -18, -30, 27],\n [9, -15, 12, 0, 12],\n [-29, 18, -30, -26, 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[[20, 30, -15, 10, 30],\n [16, 24, -12, 8, 24],\n [4, 6, -3, 2, 6],\n [0, 0, 0, 0, 0],\n [16, 24, -12, 8, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-16, -8, 51, 3, -10],\n [-25, -13, 75, -45, 62],\n [-8, 27, -29, 0, -34],\n [-45, 52, 15, -30, -18],\n [50, -58, -14, 42, 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[[6, -18, 18, -15, -33],\n [-2, 6, 13, 10, -3],\n [-48, -20, -29, -100, -36],\n [8, 3, -16, 5, 21],\n [-18, -6, 4, 2, -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[[30, 30, -5, -5, -20],\n [24, 24, -4, -4, -16],\n [-6, -6, 1, 1, 4],\n [24, 24, -4, -4, -16],\n [36, 36, -6, -6, -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[[-18, -18, -36, -36, 24],\n [12, 12, 24, 24, -16],\n [-12, -12, -24, -24, 16],\n [0, 0, 0, 0, 0],\n [9, 9, 18, 18, -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[[15, 5, 22, 26, 11],\n [-24, -35, 8, 34, 4],\n [-9, 5, -26, -38, -13],\n [0, -5, 8, 14, 4],\n [-27, -20, -22, -16, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, -41, -34, -42, 34],\n [17, -46, -47, -31, 38],\n [15, -7, -9, 1, 10],\n [-11, -7, -17, 27, -24],\n [21, 15, 5, 33, -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 5x5 matrix:\n[[36, -30, -18, 18, 6],\n [18, -15, -9, 9, 3],\n [24, -20, -12, 12, 4],\n [-36, 30, 18, -18, -6],\n [6, -5, -3, 3, 1]]\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 5x5 matrix:\n[[-16, -13, -6, -1, -37],\n [-11, -18, -41, 54, -17],\n [58, -51, -8, -6, 19],\n [-50, 27, 14, 18, 5],\n [-39, 50, -19, 8, -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 5x5 matrix:\n[[-6, 15, 12, -12, -9],\n [-8, 20, 16, -16, -12],\n [4, -10, -8, 8, 6],\n [4, -10, -8, 8, 6],\n [-8, 20, 16, -16, -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[[8, 8, -8, -8, -10],\n [-24, -24, 24, 24, 30],\n [20, 20, -20, -20, -25],\n [-8, -8, 8, 8, 10],\n [4, 4, -4, -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[[30, -9, -31, 23, -39],\n [-42, 20, -1, -10, -12],\n [-12, 10, -26, 10, -42],\n [18, -11, 15, -3, 27],\n [-36, 17, 0, -9, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[5, -4, -17, -9, 21],\n [-26, 14, -12, 22, -18],\n [-12, -29, -12, -22, 30],\n [-3, -19, 1, -15, 15],\n [-11, -35, 13, -23, 15]]?\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, 3, 15, -33, -24],\n [-1, -39, 2, -14, -30],\n [6, 11, 37, 15, 24],\n [2, 7, -11, 55, 48],\n [-2, 19, -9, -16, -6]]\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[[53, -3, 51, 5, 14],\n [-17, 3, -6, -41, 40],\n [-34, -6, -40, -36, 22],\n [5, -11, -2, -61, 62],\n [-13, -13, -31, -25, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[40, -7, 9, -31, -46],\n [63, 3, -13, -2, 0],\n [11, -2, 22, -27, -50],\n [-8, -3, -14, 11, 26],\n [21, 2, -13, 9, 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[[0, 0, 0, 0, 0],\n [4, 20, 24, -12, -12],\n [-4, -20, -24, 12, 12],\n [-5, -25, -30, 15, 15],\n [0, 0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[4, -65, -54, -8, -58],\n [-5, -18, -48, -12, -54],\n [-9, 48, 17, 1, 19],\n [-16, 18, -27, -2, -22],\n [3, -48, 7, -16, 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[[4, 9, 6, -30, -28],\n [16, 20, -16, -25, -31],\n [6, 12, -6, -15, -33],\n [-20, -15, 22, 15, -9],\n [0, -5, 14, -20, 22]]\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, 12, 0, 16, -4],\n [36, -18, 18, 12, -42],\n [-36, 21, -18, -8, 41],\n [-24, 18, -12, 0, 26],\n [6, -18, 3, -18, -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[[-17, 22, 22, -25, 9],\n [-37, 7, -19, 7, 20],\n [14, -11, -37, 6, -39],\n [27, -12, 12, 14, 7],\n [-23, -6, -30, -6, -29]]?\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[[-1, -5, 0, 4, 4],\n [-39, -51, 24, -18, 30],\n [2, 10, 0, -8, -8],\n [23, 19, -16, 24, -8],\n [-23, -19, 16, -24, 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 5x5 matrix:\n[[1, 0, -6, -6, -6],\n [4, 0, -24, -24, -24],\n [2, 0, -12, -12, -12],\n [-5, 0, 30, 30, 30],\n [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[[22, 26, -2, 34, 6],\n [24, 30, -12, 6, 0],\n [-6, -6, -6, -30, -6],\n [15, 18, -3, 18, 3],\n [-4, -5, 2, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-30, -48, -29, -34, 8],\n [27, 75, 1, 2, -10],\n [-32, 25, -40, 25, 64],\n [5, -33, 10, -28, -26],\n [45, 66, 38, 31, -26]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[7, -3, 29, 14, 13],\n [42, 0, 9, 51, 9],\n [-28, -4, 4, -30, 6],\n [-4, 2, -23, -9, -9],\n [-3, 5, 48, -1, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-20, 56, -23, -13, 31],\n [-12, 9, 24, 38, 6],\n [-8, -16, 7, -6, 7],\n [-4, 4, 20, 18, 2],\n [22, 21, -24, -11, -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[[-40, 52, -18, 36, 24],\n [47, -60, 31, -54, -20],\n [23, -38, 12, -52, 0],\n [5, -16, -37, 24, -28],\n [-9, -6, -36, -4, 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[[-9, -28, -39, -33, -22],\n [7, 20, 41, 35, 14],\n [1, 14, 29, 19, 4],\n [1, 12, -13, -14, 11],\n [14, 4, 46, 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[[-21, -38, 12, 40, 6],\n [-4, -12, -15, 32, -1],\n [-6, -7, 8, -5, -1],\n [-10, -8, 20, -36, -4],\n [17, 40, -13, -26, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-82, 1, 2, -12, 13],\n [-30, 23, 31, -62, -19],\n [-12, -4, 10, 25, 14],\n [-4, -12, 3, 7, 22],\n [74, -7, -12, -5, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-7, 42, -5, -33, -17],\n [43, -26, -39, -27, 21],\n [-21, 28, 13, -8, -16],\n [-29, 82, 21, 13, -35],\n [38, -22, -30, -5, 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[[28, -20, 2, 26, -36],\n [-37, 26, -27, 37, 18],\n [21, -10, 17, -26, 2],\n [31, -75, 8, -22, 4],\n [15, -38, 10, -31, 16]]\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[[-11, 22, 23, 26, 3],\n [6, 31, 68, 36, 20],\n [30, 6, 35, 21, 28],\n [-12, 11, -12, 6, -10],\n [-33, 28, 5, -6, -31]]\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 5x5 matrix:\n[[-36, -45, -19, -24, -26],\n [-44, -8, 30, -48, 22],\n [32, -13, -1, 26, 28],\n [48, 12, 2, 39, 28],\n [8, -28, 6, 3, 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[[0, 6, -9, -18, 3],\n [0, -10, 15, 30, -5],\n [0, -6, 9, 18, -3],\n [0, 4, -6, -12, 2],\n [0, 10, -15, -30, 5]]\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, 1, 4, 5, 5],\n [-24, -4, -16, -20, -20],\n [-18, -3, -12, -15, -15],\n [-24, -4, -16, -20, -20],\n [30, 5, 20, 25, 25]]?\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 5x5 matrix:\n[[15, -12, -9, 18, 0],\n [-20, 16, 12, -24, 0],\n [5, -4, -3, 6, 0],\n [-15, 12, 9, -18, 0],\n [-25, 20, 15, -30, 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[[12, 4, -16, 14, 20],\n [-4, -6, -4, -14, 5],\n [12, -2, -28, 2, 35],\n [-2, 6, 16, 11, -20],\n [2, -2, -8, -3, 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[[10, -44, -26, -20, -9],\n [2, 16, 2, -11, 3],\n [-4, 9, -34, -11, -66],\n [-8, -18, -4, -3, -1],\n [20, 10, -12, 19, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, 32, 24, -11, -7],\n [30, 32, 16, -26, -2],\n [7, 33, 20, -17, -2],\n [6, -18, 16, 42, -28],\n [40, 14, 8, -16, -6]]?\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[[-29, 27, -4, 53, -12],\n [34, -14, 46, -15, -46],\n [-15, 5, 6, 26, -7],\n [-20, 45, -5, 50, -20],\n [-19, -5, -8, 20, 7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[34, 34, -53, 26, -40],\n [-10, -2, 71, -54, -46],\n [24, -31, 3, 12, -3],\n [14, 11, -40, 34, 37],\n [-3, 68, -40, 17, 37]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[15, 8, 17, -20, -32],\n [3, -42, 10, 14, 12],\n [-52, 4, 21, -18, 3],\n [-2, -18, 41, -26, -34],\n [16, -34, 2, 16, 9]]\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[[-26, -46, -9, 6, -11],\n [0, -12, 5, 1, 9],\n [4, -4, 6, 0, 10],\n [-28, -44, -12, 6, -16],\n [44, 28, 36, -6, 56]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-8, -36, 52, -52, 30],\n [-8, -23, 42, -42, 35],\n [5, 26, -45, 45, -20],\n [-2, 0, 10, -10, 12],\n [-2, -8, 24, -24, 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[[-14, -14, 11, -4, 11],\n [32, 3, 37, -24, 8],\n [14, 0, 19, -12, 5],\n [0, 0, 0, 0, 0],\n [44, 12, 34, -24, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-14, 0, -14, -3, -13],\n [-32, 10, -32, 16, -4],\n [2, -12, 2, -27, -29],\n [26, -16, 26, -31, -17],\n [14, 0, 14, 3, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[20, 10, 20, 20, 15],\n [16, 8, 16, 16, 12],\n [12, 6, 12, 12, 9],\n [24, 12, 24, 24, 18],\n [16, 8, 16, 16, 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[[-28, 16, 8, -44, -14],\n [24, -24, -12, -24, 30],\n [-10, 12, 6, 22, -16],\n [-38, 32, 16, 2, -37],\n [-24, 24, 12, 24, -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[[0, 0, 0, 0, 0],\n [12, -8, -6, 8, -10],\n [-30, 20, 15, -20, 25],\n [0, 0, 0, 0, 0],\n [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[[14, 4, -12, 10, 16],\n [12, -6, -15, -3, 15],\n [6, 8, -2, 12, 6],\n [16, 14, -9, 23, 17],\n [-26, -20, 16, -34, -28]]\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, -20, -11, 1, 6],\n [22, -61, -55, 29, -6],\n [40, -31, -43, 29, -6],\n [-10, -27, -13, 7, -18],\n [1, -43, -31, 14, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 6, 4, 13, 6],\n [0, 25, 5, 20, 0],\n [20, 20, -10, -25, -30],\n [-4, -19, -1, -7, 6],\n [24, 4, -16, -46, -36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-67, 47, 9, 43, -21],\n [17, 7, -43, -1, 27],\n [8, -16, -43, 0, -6],\n [2, 34, -24, 36, 30],\n [26, 4, -37, 41, 18]]\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, 0, -2, 2, -2],\n [-36, 0, -12, 12, -12],\n [36, 0, 12, -12, 12],\n [18, 0, 6, -6, 6],\n [30, 0, 10, -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[[-34, -14, 39, -36, 19],\n [-16, 0, -23, -14, 3],\n [-19, 14, -11, -29, 10],\n [3, -2, -84, 21, 11],\n [-13, 16, 41, -33, 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[[16, 24, 8, 24, -8],\n [-16, -24, -8, -24, 8],\n [4, 6, 2, 6, -2],\n [-16, -24, -8, -24, 8],\n [8, 12, 4, 12, -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[[47, -31, 25, 9, 7],\n [-14, 44, -36, -24, 28],\n [35, 16, -24, -30, 40],\n [48, 3, 17, 11, 38],\n [-19, -32, 56, 59, -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[[25, 34, -14, -6, 12],\n [3, 8, 11, 0, -31],\n [-20, -32, 28, 0, -12],\n [-19, -17, -17, 13, -9],\n [26, 32, 17, -12, -15]]?\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, -40, 14, -14, -34],\n [10, 15, -3, 4, 13],\n [30, 25, -29, 20, 19],\n [15, -15, -42, 21, -18],\n [25, 25, -20, 15, 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[[-2, 32, 20, -6, 16],\n [-10, 22, 9, 7, 22],\n [72, 6, 41, -14, -7],\n [4, -54, -21, 1, 2],\n [12, 64, 40, -20, -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[[41, 54, 32, 40, 21],\n [16, -20, -36, 0, 28],\n [15, 12, -60, -43, 20],\n [-3, 25, -20, -32, -4],\n [-34, -21, -8, 16, 13]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, 20, -22, -7, -22],\n [1, -5, 6, 2, 7],\n [-20, 0, 10, 5, 30],\n [19, 5, -16, -7, -37],\n [16, 0, -8, -4, -24]]\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[[6, -2, 9, -26, 8],\n [-33, 18, -6, 0, -13],\n [-34, 3, -12, -7, 2],\n [2, 0, 9, -19, 7],\n [12, 20, 33, -10, -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 5x5 matrix:\n[[-18, 1, -7, 3, -9],\n [-50, 5, -5, -15, 5],\n [38, -5, -4, 24, -20],\n [-10, 1, -1, -3, 1],\n [-2, -1, -8, 12, -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 5x5 matrix:\n[[28, -25, 2, -7, 11],\n [24, -18, 19, -24, 16],\n [17, -19, -12, 11, 3],\n [38, -19, 14, -37, 5],\n [-18, 22, -25, 16, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, 1, 6, 4, -6],\n [9, 3, 18, 12, -18],\n [6, 2, 12, 8, -12],\n [-18, -6, -36, -24, 36],\n [-9, -3, -18, -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[[9, 18, -12, -6, 12],\n [0, -18, -4, 0, 2],\n [-6, -30, 4, 4, -6],\n [-18, -9, 30, 12, -27],\n [-27, -18, 44, 18, -40]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[46, -10, 2, 30, -10],\n [-29, 11, -1, -24, 10],\n [28, -6, -12, -6, 11],\n [14, -2, 24, 4, 12],\n [63, -29, -9, -2, 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[[-22, 56, -18, 50, 16],\n [-21, 8, 22, 10, -30],\n [-93, 14, 84, -10, -42],\n [-6, 35, -20, 22, 20],\n [31, -17, -26, -24, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-9, -12, 18, -9, -9],\n [-15, -20, 30, -15, -15],\n [-3, -4, 6, -3, -3],\n [-9, -12, 18, -9, -9],\n [-18, -24, 36, -18, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[47, -20, 28, 17, -35],\n [-40, 5, -22, -18, 65],\n [24, -45, 14, 1, -44],\n [39, -45, -24, -63, 2],\n [-3, -15, -21, -33, 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[[1, 25, -37, -22, 39],\n [6, 71, 30, 13, 6],\n [-2, 49, -29, -18, 2],\n [0, -27, 33, 34, 22],\n [9, -44, 21, -7, -3]]\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[[12, 2, 16, -35, 21],\n [14, -7, 28, -33, 4],\n [-11, 40, 6, -22, -20],\n [-1, 25, -14, -22, 35],\n [5, -8, -18, 3, 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[[-26, 14, -3, -5, -7],\n [0, 0, 30, -30, 5],\n [56, -40, 24, 8, 34],\n [-18, -2, -9, 21, 13],\n [24, -16, 6, 6, 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[[-24, -58, 27, -2, -39],\n [-48, -12, -6, -28, -34],\n [6, -22, 22, 7, 2],\n [-12, -40, 34, -2, -10],\n [-12, 12, -28, -6, -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[[16, -8, 12, 10, -38],\n [12, -3, 12, 15, -39],\n [28, -33, 2, -30, 0],\n [-24, 22, -8, 10, 22],\n [-36, 39, -6, 30, 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[[30, 0, 24, 24, 6],\n [-25, 0, -20, -20, -5],\n [-20, 0, -16, -16, -4],\n [30, 0, 24, 24, 6],\n [5, 0, 4, 4, 1]]\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, -16, 31, 11, 21],\n [-22, 8, -34, 30, -39],\n [-32, -42, 48, 6, -14],\n [-29, -42, 11, 9, 17],\n [18, -18, 16, -28, 48]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[36, 18, -6, 30, -24],\n [-18, -9, 3, -15, 12],\n [0, 0, 0, 0, 0],\n [-6, -3, 1, -5, 4],\n [-6, -3, 1, -5, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -6, 6, 6, 8],\n [15, 33, 39, 27, 40],\n [27, 36, 0, -6, -6],\n [-3, -9, -15, -11, -16],\n [6, -3, -33, -27, -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[[24, -33, 6, -20, -6],\n [-6, 55, -12, 24, -30],\n [-36, -21, 38, 4, 26],\n [-36, -21, 38, 4, 26],\n [48, 12, -2, -8, -68]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, -20, -4, -8, -24],\n [8, 20, 4, 8, 24],\n [4, 10, 2, 4, 12],\n [-8, -20, -4, -8, -24],\n [-2, -5, -1, -2, -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[[6, 7, -13, -2, 33],\n [2, 28, -18, 12, -10],\n [41, -26, -25, 2, 7],\n [19, -3, -18, 2, 14],\n [36, -32, -12, 8, -44]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-18, -18, 36, -30, -24],\n [-12, -12, 24, -20, -16],\n [-15, -15, 30, -25, -20],\n [12, 12, -24, 20, 16],\n [-15, -15, 30, -25, -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[[-19, -12, 5, -8, -1],\n [22, -34, 38, -24, 6],\n [19, -6, 10, 2, -2],\n [-17, 39, -38, 14, 4],\n [16, 32, -22, 12, 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[[36, -4, -13, -1, -8],\n [1, 53, -9, -22, -63],\n [-6, 1, 19, 15, 11],\n [21, 5, -25, -18, -23],\n [38, -33, -10, 10, 25]]\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, -16, -15, -21, 10],\n [-8, 6, 5, 9, -5],\n [-4, -4, -15, 15, -20],\n [12, -6, 0, -18, 15],\n [20, -12, -5, -27, 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[[6, 33, 3, -27, -30],\n [-20, 11, -1, 21, -2],\n [-19, 2, -7, 45, 16],\n [-3, -38, 3, 3, 21],\n [21, 3, -6, 0, 6]]?\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[[25, 14, 20, 7, -23],\n [14, -13, 7, 0, -22],\n [-23, -2, -9, 41, -1],\n [-36, -30, -24, 44, 0],\n [47, -11, -4, -31, 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[[56, 56, 9, -19, -6],\n [-17, -9, 8, 8, 33],\n [-39, -41, 22, -12, 24],\n [48, 38, -30, -16, -65],\n [-29, -40, 44, -27, 16]]?\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, -12, 0, -34, -21],\n [19, -21, 6, -20, -12],\n [41, 23, 7, -11, 5],\n [40, 36, -4, -2, 32],\n [38, -10, -14, -28, 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[[6, -24, -2, 9, 31],\n [4, -10, 0, 6, 14],\n [20, 13, 14, 30, 0],\n [8, -20, 0, 12, 28],\n [6, -15, 0, 9, 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[[-24, -4, 8, -8, 20],\n [18, 3, -6, 6, -15],\n [-24, -4, 8, -8, 20],\n [6, 1, -2, 2, -5],\n [6, 1, -2, 2, -5]]?\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[[-46, -6, -28, -44, -24],\n [-3, -1, -28, -13, 15],\n [8, -34, 10, 3, 9],\n [3, 28, -1, 7, -3],\n [-19, -49, 4, -21, -9]]?\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, -20, 38, -38, -38],\n [-30, -6, -12, 12, 30],\n [25, -18, 29, -29, -25],\n [13, 21, -10, 10, -13],\n [-8, 26, -26, 26, 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 5x5 matrix:\n[[1, -20, -22, -1, 22],\n [18, 0, -12, -34, -4],\n [-13, -25, 15, 11, 27],\n [14, 5, -28, -16, -6],\n [-2, 40, -1, 22, -39]]\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, 9, -6, 3],\n [0, -10, 15, -10, 5],\n [0, 2, -3, 2, -1],\n [0, 10, -15, 10, -5],\n [0, -12, 18, -12, 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 5x5 matrix:\n[[-11, 20, 0, -20, -6],\n [-21, 8, 3, -18, -6],\n [13, -37, 11, 5, -5],\n [23, 7, -15, 29, 13],\n [-24, -19, 3, 15, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[16, 12, -24, 8, 4],\n [24, 18, -36, 12, 6],\n [8, 6, -12, 4, 2],\n [12, 9, -18, 6, 3],\n [24, 18, -36, 12, 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[[40, -3, -4, -6, 35],\n [14, 38, -4, 32, 22],\n [15, -3, -6, 4, 9],\n [12, -57, -12, -26, -15],\n [-12, -26, 2, -20, -18]]\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, 0, 8, -24],\n [-10, -29, 9, -11, -21],\n [1, 11, -3, 5, 3],\n [18, 9, -5, -1, 33],\n [-9, -45, 13, -19, -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[[-1, -24, 27, 14, 12],\n [-6, -6, 12, -6, 48],\n [-2, 25, -29, -29, 22],\n [4, -4, -20, -44, 30],\n [11, 3, -48, -73, 15]]?\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, 66, 10, -46, -10],\n [-20, 42, 14, -39, -1],\n [-28, 36, -25, -28, -33],\n [-12, 37, -1, -33, -3],\n [21, -10, 30, 41, -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[[4, 11, 13, 7, -3],\n [0, 3, 4, 5, -1],\n [8, 28, 34, 24, -8],\n [-4, -2, -1, 8, 0],\n [-20, -22, -21, 20, 4]]\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, 16, -4, -32, -9],\n [-14, -12, 4, 20, 7],\n [44, 0, 8, -32, 2],\n [-8, -32, 16, 32, 20],\n [-24, -8, 0, 24, 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[[-10, -10, 4, 10, -8],\n [-20, -35, -6, -5, -13],\n [-12, -15, 2, 7, -9],\n [-15, -15, 6, 15, -12],\n [33, 45, -2, -13, 24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[30, -24, 12, -30, -36],\n [-5, 4, -2, 5, 6],\n [25, -20, 10, -25, -30],\n [30, -24, 12, -30, -36],\n [-15, 12, -6, 15, 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[[8, -22, 8, -42, -2],\n [0, -25, 15, -45, -10],\n [-28, -18, 29, -24, -31],\n [-36, -11, 30, -9, -35],\n [0, -30, 18, -54, -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[[26, -1, 31, -1, 4],\n [61, 17, 46, 14, -8],\n [-17, 11, -62, 52, 18],\n [2, -24, -6, 43, 1],\n [-30, 0, -34, 0, 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[[-2, 3, 2, 2, 1],\n [0, 0, 0, 0, 0],\n [-4, 6, 4, 4, 2],\n [6, -9, -6, -6, -3],\n [-2, 3, 2, 2, 1]]?\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, -3, 15, -39, -27],\n [-24, 6, -6, -66, -36],\n [-9, 2, 1, -28, -21],\n [3, -3, -3, -3, 27],\n [-3, 7, -16, 37, 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[[-2, 9, -30, -1, 50],\n [12, -32, -13, 8, -6],\n [-8, 8, 25, 0, -31],\n [-18, 1, 14, 1, -2],\n [12, 74, 16, -28, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[14, -21, -12, 22, 0],\n [28, 12, -30, -36, -68],\n [14, -33, -30, -8, -15],\n [60, 37, 5, -56, -80],\n [14, -26, 21, 42, 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 5x5 matrix:\n[[24, -44, -6, -71, -9],\n [-27, -36, 9, 51, 5],\n [14, 38, 28, -20, -24],\n [-1, 0, 7, 5, -5],\n [19, -22, 24, -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 5x5 matrix:\n[[-16, -20, 0, 0, 8],\n [-12, -1, 8, 12, -10],\n [-36, -24, 12, 18, -6],\n [-14, -7, 6, 9, -5],\n [-8, -31, -12, -18, 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 5x5 matrix:\n[[30, 20, 10, -25, -25],\n [-24, -16, -8, 20, 20],\n [30, 20, 10, -25, -25],\n [-30, -20, -10, 25, 25],\n [12, 8, 4, -10, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -8, -10, -12, -10],\n [0, -12, -15, -18, -15],\n [0, -16, -20, -24, -20],\n [0, -4, -5, -6, -5],\n [0, -16, -20, -24, -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[[-34, 9, -75, -13, 23],\n [53, -26, -29, -17, 6],\n [24, -34, 36, 46, 2],\n [-39, -5, -24, 27, 3],\n [1, -3, 80, 38, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-28, 2, 21, 8, -20],\n [-16, 4, 13, 6, -10],\n [8, 8, -3, 2, 10],\n [18, 23, -5, 7, 25],\n [-4, -34, -9, -16, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[35, -10, 10, 30, -20],\n [-60, 15, -51, 18, -51],\n [14, 22, 10, -12, 6],\n [39, -17, 29, 0, 23],\n [-4, -12, 12, -24, 36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-18, 14, 1, -24, -2],\n [13, 40, 29, -39, -58],\n [-6, 19, 11, -33, -31],\n [10, 30, 35, -20, -30],\n [-20, 1, -9, -29, -13]]\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, -1, 5, -2, -4],\n [0, 4, -20, 8, 16],\n [0, -2, 10, -4, -8],\n [0, 2, -10, 4, 8],\n [0, 4, -20, 8, 16]]?\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, 2, -4, -10, -6],\n [-12, -4, 8, 20, 12],\n [-15, -5, 10, 25, 15],\n [-9, -3, 6, 15, 9],\n [6, 2, -4, -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[[14, -42, -18, 52, -18],\n [-8, 13, 12, -52, 20],\n [-19, 34, 71, 12, -62],\n [10, -5, -10, 0, 0],\n [-3, 17, 11, 72, -44]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[20, 34, -24, 48, -20],\n [-12, -22, 24, -48, -4],\n [-14, -23, 12, -24, 22],\n [17, 30, -27, 54, -6],\n [-22, -38, 30, -60, 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 5x5 matrix:\n[[47, -44, 8, 14, 38],\n [39, -17, 17, -22, 26],\n [14, -19, -30, 23, -9],\n [32, -12, -10, -14, 2],\n [27, -39, 3, 30, 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 5x5 matrix:\n[[0, 0, 0, 0, 0],\n [2, 1, -1, 6, 3],\n [-8, -4, 4, -24, -12],\n [-10, -5, 5, -30, -15],\n [2, 1, -1, 6, 3]]\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[[-8, 65, -54, 61, 81],\n [-2, -4, -1, 0, -5],\n [-4, -11, 11, -15, -1],\n [-10, -11, -2, -3, -4],\n [0, 0, 7, -8, 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[[0, 0, 0, 0, 0],\n [9, 0, -18, 9, 9],\n [15, 0, -30, 15, 15],\n [-9, 0, 18, -9, -9],\n [12, 0, -24, 12, 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 5x5 matrix:\n[[-17, -12, -23, 1, 25],\n [11, 30, 5, -13, -10],\n [-12, 36, -36, -24, 30],\n [-11, -12, -13, 3, 15],\n [6, -18, 18, 12, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[18, 6, 27, -8, 3],\n [19, -45, -3, -18, 24],\n [36, -9, 16, -14, 16],\n [-1, 9, -12, 6, -3],\n [26, 18, 54, -12, 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[[9, -6, -18, 3, 15],\n [6, -4, -12, 2, 10],\n [9, -6, -18, 3, 15],\n [-3, 2, 6, -1, -5],\n [12, -8, -24, 4, 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 5x5 matrix:\n[[-11, -6, -7, 28, 24],\n [-7, 28, 23, -30, -6],\n [12, -34, -27, 28, -2],\n [-14, 40, 28, 0, 58],\n [-16, -36, -13, -22, 7]]\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 5x5 matrix:\n[[-14, 28, 12, 4, -1],\n [-7, 35, -6, -16, -17],\n [-21, -21, -4, 29, 40],\n [29, -29, 0, -11, -15],\n [-4, 6, -12, -6, -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 5x5 matrix:\n[[-6, 29, -28, 40, 9],\n [30, -10, 2, 22, -16],\n [-6, 12, -12, 21, -2],\n [6, -18, 18, -30, 0],\n [-21, 27, -21, 12, 20]]\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 5x5 matrix:\n[[-32, -39, -10, -7, -17],\n [43, 26, 28, 3, 31],\n [-9, -3, -12, 1, -11],\n [-15, -17, 4, -5, -1],\n [29, 32, 18, 4, 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[[-5, 3, -34, 10, 25],\n [-26, -14, 60, -22, 39],\n [28, 18, -54, 12, 5],\n [-9, 13, 14, -39, 34],\n [-50, -21, 51, -18, 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[[21, -28, 6, -4, 25],\n [-3, 19, -3, 7, -25],\n [6, 4, 0, 4, -10],\n [-48, 38, -10, -2, -20],\n [6, -24, 4, -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[[36, -6, 0, 12, -18],\n [6, -1, 0, 2, -3],\n [-12, 2, 0, -4, 6],\n [-24, 4, 0, -8, 12],\n [-36, 6, 0, -12, 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[[26, 28, -25, 4, -1],\n [36, 0, -30, 24, 9],\n [60, -6, -48, 48, 6],\n [2, 34, -7, -20, 2],\n [-22, -7, 18, -16, 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 5x5 matrix:\n[[3, -6, -15, 12, 3],\n [-2, -4, -22, 15, 4],\n [15, -6, 21, -9, -3],\n [-10, 12, 18, -17, -4],\n [-17, 18, 21, -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[[-16, 24, 16, -16, 22],\n [9, 21, 39, 12, 43],\n [-17, -12, -18, -66, -41],\n [11, 3, 12, -12, 9],\n [-35, 9, 1, -4, -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, 68, -66, -30, 2],\n [-10, 4, -20, 6, -12],\n [-12, 20, -26, -9, -3],\n [-1, -10, 6, 6, -3],\n [9, -30, 48, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-4, -2, 2, 0, -12],\n [-6, -3, 3, 0, -18],\n [-10, -5, 5, 0, -30],\n [-8, -4, 4, 0, -24],\n [4, 2, -2, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-5, 14, 2, -15, -6],\n [24, 12, 30, 6, 20],\n [24, 30, 39, -9, 18],\n [0, 36, 18, -30, -4],\n [-7, -38, -26, 27, -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[[-16, -18, 8, -18, -18],\n [7, 45, -44, 45, 45],\n [-1, 25, -28, 25, 25],\n [6, 37, -36, 37, 37],\n [-9, -6, 0, -6, -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 5x5 matrix:\n[[-13, 19, -19, -28, -10],\n [24, -3, -11, 28, -47],\n [25, -4, -14, 40, -23],\n [-3, -20, 48, -35, -63],\n [5, 21, -39, 5, -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[[-18, -11, -1, 6, 21],\n [-2, -5, 2, -1, 2],\n [-14, 1, -6, 25, 18],\n [-5, -35, 18, 46, 6],\n [-23, -16, 0, 33, 28]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, 1, 4, -3, -5],\n [12, -6, -24, 18, 30],\n [10, -5, -20, 15, 25],\n [6, -3, -12, 9, 15],\n [4, -2, -8, 6, 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[[-35, 22, 32, 7, -14],\n [-10, 7, 9, 3, -5],\n [5, -26, 0, -33, 34],\n [35, -32, -30, -21, 28],\n [-25, 20, 22, 11, -16]]\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, -10, -48, 24, 18],\n [13, -8, 38, -6, 15],\n [-15, -19, -23, 41, 4],\n [7, 5, 13, -27, -2],\n [8, -24, 4, 20, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-30, -30, 12, 30, 0],\n [-19, 10, 12, 3, 5],\n [35, -27, -40, -16, 4],\n [-40, 24, 54, 30, -15],\n [-11, 55, 36, 11, 19]]\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, 0, -5, -30, -5],\n [-18, 0, -6, -36, -6],\n [15, 0, 5, 30, 5],\n [-18, 0, -6, -36, -6],\n [15, 0, 5, 30, 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[[15, -9, -9, -12, -15],\n [-20, 12, 12, 16, 20],\n [-25, 15, 15, 20, 25],\n [-25, 15, 15, 20, 25],\n [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[[-18, 15, -9, 15, -15],\n [18, -15, 9, -15, 15],\n [30, -25, 15, -25, 25],\n [-12, 10, -6, 10, -10],\n [24, -20, 12, -20, 20]]\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[[-26, -10, -24, 0, 8],\n [9, 9, 12, -24, -36],\n [10, -4, 4, 34, 44],\n [-25, -5, -20, -20, -20],\n [5, 7, 8, -22, -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[[-1, 2, 6, 0, 17],\n [-12, -12, 0, -36, -30],\n [4, 6, 4, 14, 23],\n [-10, -4, 12, -24, 14],\n [1, -4, -10, -2, -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[[-8, -24, -12, 12, 0],\n [10, 30, 15, -15, 0],\n [8, 24, 12, -12, 0],\n [4, 12, 6, -6, 0],\n [-12, -36, -18, 18, 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[[1, 13, -6, 0, 9],\n [-14, -2, -56, 20, 14],\n [-5, 41, 32, 78, 35],\n [-4, 20, -25, -29, -23],\n [7, -49, -23, -53, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, 35, -45, 54, -9],\n [-4, 12, -10, 12, -21],\n [1, 11, -15, 18, 0],\n [-2, -38, 50, -60, 6],\n [-9, 5, 5, -6, -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[[0, -24, 8, -6, -12],\n [9, -18, 15, 9, 0],\n [11, -6, 13, 15, 8],\n [24, -36, 36, 27, 6],\n [16, -12, 20, 21, 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 5x5 matrix:\n[[4, 4, -1, -3, 0],\n [-20, -20, 5, 15, 0],\n [16, 16, -4, -12, 0],\n [-12, -12, 3, 9, 0],\n [-20, -20, 5, 15, 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 5x5 matrix:\n[[-54, 3, 21, 30, -21],\n [-70, 30, 36, 38, 18],\n [-3, 9, -3, -4, 19],\n [44, -36, -24, -20, -44],\n [57, -12, -18, -26, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[5, 2, -7, 13, 1],\n [60, -14, 21, 46, 10],\n [15, -21, -35, -3, -18],\n [68, -10, -12, 48, -13],\n [-40, -31, 2, 6, 50]]?\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 5x5 matrix:\n[[18, 20, -47, -40, 9],\n [-25, -50, 22, 7, -16],\n [49, 18, 24, -31, -38],\n [-13, -46, 8, -17, -22],\n [-11, -44, 3, -13, -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 5x5 matrix:\n[[-10, -5, 5, 19, 4],\n [-30, 43, 5, -61, 0],\n [13, 11, -17, -17, 1],\n [-4, -9, 21, -9, -10],\n [35, -5, -25, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[41, -10, -1, -56, 23],\n [-56, -36, 63, -4, -71],\n [-21, -14, 18, -40, 4],\n [15, 26, -33, 46, -7],\n [-73, -38, 72, 24, -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[[-30, 25, 32, -50, 29],\n [-10, 17, 23, -63, 8],\n [9, 8, 8, -58, -10],\n [-28, 9, 9, 31, 30],\n [34, -28, -25, 31, -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[[-2, -19, -14, -17, -4],\n [2, 31, 24, 27, 5],\n [8, -20, -24, -12, 8],\n [-20, 26, 40, 10, -22],\n [32, -20, -46, 2, 37]]\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, 24, -12, 12, 24],\n [0, -20, 10, -10, -20],\n [0, 12, -6, 6, 12],\n [0, -12, 6, -6, -12],\n [0, 20, -10, 10, 20]]\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[[-3, 9, 3, -9, -12],\n [4, -12, -4, 12, 16],\n [0, 0, 0, 0, 0],\n [5, -15, -5, 15, 20],\n [-4, 12, 4, -12, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-28, -56, 31, -46, 56],\n [6, 12, -15, 6, -12],\n [-7, -14, -2, -16, 14],\n [7, 14, 2, 16, -14],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-2, 26, 8, -12, 8],\n [26, 5, -47, 23, 34],\n [-1, 5, 19, 16, 46],\n [22, -29, -53, 19, -11],\n [-28, 19, 38, -1, -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[[-14, -2, 14, 14, -20],\n [-49, 10, 14, -36, 35],\n [-11, 1, 4, -35, 26],\n [-12, 11, -9, 49, -17],\n [-2, 8, -12, 20, 2]]\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, 0, 20, -16, -12],\n [0, 0, 0, 0, 0],\n [-5, 0, 5, -4, -3],\n [-15, 0, 15, -12, -9],\n [25, 0, -25, 20, 15]]\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, 32, 10, -57, 18],\n [38, -20, -52, 8, -22],\n [3, -19, -44, 0, 6],\n [-13, 7, 38, 11, 8],\n [14, 13, -40, -43, -19]]\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, -7, 5, -12, 38],\n [6, -9, 11, 26, -4],\n [-9, 30, 12, 20, 5],\n [-12, -42, 34, 6, 52],\n [-1, -11, 7, 23, -24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-42, -28, 30, 52, 6],\n [29, 32, -1, -48, 9],\n [35, 40, -5, -60, 5],\n [21, -6, -39, -6, -15],\n [-18, 6, 48, 6, 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 5x5 matrix:\n[[18, 33, 0, -30, -54],\n [-8, -19, -6, 22, 30],\n [20, 15, -30, 10, -30],\n [-22, -10, 42, -24, 24],\n [5, 7, -3, -4, -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[[-15, 30, 25, 25, 20],\n [-3, 6, 5, 5, 4],\n [-6, 12, 10, 10, 8],\n [-6, 12, 10, 10, 8],\n [6, -12, -10, -10, -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[[15, -23, 32, 35, 16],\n [-17, 11, -9, 7, -23],\n [33, -13, 4, -23, 35],\n [24, -18, 21, 36, 3],\n [-28, 22, -21, 8, -43]]\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, 18, 19, 12, 21],\n [5, 17, -29, 3, -3],\n [-11, 4, -33, -33, 15],\n [14, -52, 40, 21, -39],\n [-12, -16, 15, -48, 27]]?\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[[59, -31, -14, -17, 20],\n [13, -25, -38, -13, 12],\n [12, -4, 18, 3, 0],\n [-50, -9, -20, 8, -9],\n [-53, 30, 28, 20, -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[[9, -35, -69, -63, -8],\n [-5, 6, 15, 10, 21],\n [8, 18, 39, 37, -29],\n [-8, 26, 48, 46, 2],\n [0, 12, 27, 23, 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[[2, 14, -50, -8, 0],\n [5, -35, 5, 30, -50],\n [-7, 29, -5, -14, 30],\n [-9, 18, 16, 1, 15],\n [-10, 30, -6, -4, 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[[4, 64, 19, 13, -13],\n [5, -21, 23, 8, -6],\n [11, -15, -7, -48, -19],\n [10, -29, 0, 17, 22],\n [37, 12, 46, -40, -43]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[24, 24, -4, -24, 16],\n [36, 36, -6, -36, 24],\n [-6, -6, 1, 6, -4],\n [-12, -12, 2, 12, -8],\n [18, 18, -3, -18, 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[[24, 4, -28, 44, 8],\n [-18, -30, 36, -19, -38],\n [18, 66, -48, -24, 66],\n [29, 61, -58, -30, 79],\n [44, -26, -28, 9, 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 5x5 matrix:\n[[0, -2, -8, -6, 8],\n [0, 0, 0, 0, 0],\n [0, -4, -16, -12, 16],\n [0, 3, 12, 9, -12],\n [0, -4, -16, -12, 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 5x5 matrix:\n[[12, -30, -12, -24, -30],\n [-9, 30, 30, 21, 12],\n [9, -30, -30, -21, -12],\n [-3, 15, 24, 9, -3],\n [2, -5, -2, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[9, -14, -2, -7, 6],\n [-9, 18, 0, 9, -6],\n [15, -26, -2, -13, 10],\n [-15, 54, -12, 27, -10],\n [12, -36, 6, -18, 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[[4, -12, -24, 16, 8],\n [-5, 15, 30, -20, -10],\n [3, -9, -18, 12, 6],\n [-2, 6, 12, -8, -4],\n [-5, 15, 30, -20, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, 6, 24, 36, 30],\n [4, 2, 8, 12, 10],\n [8, 4, 16, 24, 20],\n [4, 2, 8, 12, 10],\n [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[[-37, -21, 34, 0, -10],\n [26, -24, -36, 12, -10],\n [-44, -6, 51, 18, -3],\n [33, -8, -18, -54, -32],\n [-24, 30, 12, 36, 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[[-19, 26, 17, 17, -20],\n [-10, 26, -28, 24, 36],\n [-6, 3, 21, -1, -26],\n [30, -51, 3, -39, -6],\n [20, -25, -25, -15, 30]]\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 5x5 matrix:\n[[46, 28, -21, 22, -30],\n [-46, -28, 21, -22, 30],\n [20, 10, 5, 15, 0],\n [-14, -6, -10, -13, -6],\n [-28, -18, 19, -11, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 34, -13, -9, -11],\n [0, 28, -23, 6, 1],\n [-3, -12, 25, -17, -4],\n [18, -16, -18, 18, -28],\n [18, -16, -18, 18, -28]]\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[[11, -2, 20, -22, 4],\n [-19, -16, -3, 20, -23],\n [3, -14, 10, 14, 2],\n [-7, -3, 7, -14, -15],\n [-14, -11, 9, -8, -25]]\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, -6, 6, -30, -24],\n [0, -4, 4, -20, -16],\n [0, -4, 4, -20, -16],\n [0, -1, 1, -5, -4],\n [0, -5, 5, -25, -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[[20, 6, -2, 16, 16],\n [-22, -3, 4, -11, -17],\n [-14, 3, 5, 2, -10],\n [-4, -30, -14, -56, -8],\n [-8, -24, -10, -46, -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[[-12, 0, 10, 6, -8],\n [-12, 0, 10, 6, -8],\n [-30, 0, 25, 15, -20],\n [30, 0, -25, -15, 20],\n [-30, 0, 25, 15, -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[[-30, -18, -12, 6, -36],\n [0, 0, 0, 0, 0],\n [-25, -15, -10, 5, -30],\n [10, 6, 4, -2, 12],\n [15, 9, 6, -3, 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[[18, -6, 2, 24, 20],\n [28, 24, 12, 4, 0],\n [-18, -9, -6, -9, -6],\n [-19, -12, -7, -7, -4],\n [-30, -15, -10, -15, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[48, 24, -2, 34, 24],\n [33, -12, -20, 32, 4],\n [-8, -12, -11, -3, -20],\n [-16, -9, 66, -29, 2],\n [-65, -27, 31, -49, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, -28, -41, 16, -50],\n [22, 9, 18, -10, -6],\n [-36, -15, -60, 24, 12],\n [9, -15, 41, -62, -21],\n [-6, 38, 15, -2, 60]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[30, 20, 20, 30, 5],\n [-12, -2, -2, 3, 13],\n [6, -10, -10, -29, -34],\n [-36, -24, -24, -36, -6],\n [-36, -14, -14, -11, 19]]\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, -60, -61, -17, 42],\n [24, 35, 44, 10, -5],\n [12, 12, 2, -12, 6],\n [24, -15, -15, -35, 41],\n [45, 8, 6, 5, 12]]\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[[21, 52, 15, 10, 2],\n [13, -16, 6, -19, 10],\n [19, -8, -27, -2, 20],\n [-14, -48, -60, 10, 12],\n [-15, -60, 0, -25, 0]]?\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, 3, -25, -20, -32],\n [24, 28, 22, 30, -38],\n [9, 41, 24, 110, -6],\n [-13, 25, 43, 55, -19],\n [-15, -5, 16, -15, -33]]\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[[-5, -43, -20, 19, -29],\n [25, -17, -16, -8, 0],\n [20, 20, 4, -19, 21],\n [-40, 16, 20, 17, -7],\n [40, -16, -20, -17, 7]]\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[[-6, -18, -24, -36, -6],\n [2, 6, 8, 12, 2],\n [4, 12, 16, 24, 4],\n [2, 6, 8, 12, 2],\n [6, 18, 24, 36, 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 5x5 matrix:\n[[-8, 17, -10, 0, 45],\n [-31, 22, -38, -33, 53],\n [-26, -22, -24, -24, -16],\n [-35, 2, -38, -33, 29],\n [9, 15, 4, -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[[-6, 7, 0, 7, -3],\n [28, -34, -12, -18, 2],\n [-20, 25, 15, 5, 5],\n [16, -20, -12, -4, -4],\n [8, -11, -15, 9, -11]]\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[[-31, 36, 13, -23, -40],\n [-24, 10, 26, -12, -46],\n [45, -45, 32, 7, 13],\n [2, 13, -5, -4, -3],\n [-9, -18, 11, 1, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 8, 10, 10, -4],\n [2, -4, -5, -5, 2],\n [10, -20, -25, -25, 10],\n [2, -4, -5, -5, 2],\n [2, -4, -5, -5, 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 5x5 matrix:\n[[9, -27, 2, 17, 12],\n [0, 36, -10, -4, -6],\n [-5, 11, 0, -9, -6],\n [-6, 24, -3, -12, -9],\n [-4, -20, 8, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[10, 1, 16, -7, 10],\n [22, -2, 38, 0, 36],\n [7, -2, 13, 5, 16],\n [-13, 2, -23, -3, -24],\n [11, 2, 17, -11, 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[[0, 4, -3, -5, -4],\n [0, -24, 18, 30, 24],\n [0, -8, 6, 10, 8],\n [0, 0, 0, 0, 0],\n [0, -16, 12, 20, 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 5x5 matrix:\n[[22, 2, 39, 16, 19],\n [-8, -25, -2, 51, 46],\n [15, 1, -10, -46, -34],\n [-33, -12, -51, 15, 6],\n [-48, 22, -32, -36, -49]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-30, -18, -12, -6, 6],\n [-14, -9, -10, -8, -2],\n [1, 0, -4, -5, -5],\n [30, 15, -10, -20, -30],\n [25, 12, -12, -21, -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[[9, 12, -9, 15, -15],\n [-3, -4, 3, -5, 5],\n [3, 4, -3, 5, -5],\n [0, 0, 0, 0, 0],\n [-18, -24, 18, -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[[-9, -2, -3, -8, -4],\n [-12, 16, -6, -8, -22],\n [-15, -22, -3, -16, 10],\n [9, 30, 0, 12, -21],\n [-13, -6, -4, -12, -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[[-70, 1, 28, -27, -6],\n [-15, -27, 19, 0, -7],\n [-60, 44, 24, 0, -22],\n [15, -29, -18, 39, 16],\n [-30, -10, 37, 5, -27]]\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, 4, 17, 9, 25],\n [-15, -20, 9, -16, 1],\n [91, 52, 14, 12, 14],\n [-11, -7, -45, 32, -23],\n [100, 55, 33, 3, 27]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-28, -11, 8, -50, 47],\n [45, -32, 52, -23, -17],\n [0, 46, 4, 43, -33],\n [19, 0, 46, 1, -23],\n [10, -44, -36, -29, 29]]\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[[-9, 0, 23, -3, 12],\n [8, 29, -22, 39, -10],\n [0, 40, 12, 24, 5],\n [-8, -42, -4, -6, 2],\n [-5, -25, -7, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-30, -36, 6, 30, -24],\n [-5, -6, 1, 5, -4],\n [0, 0, 0, 0, 0],\n [10, 12, -2, -10, 8],\n [10, 12, -2, -10, 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, 7, 3, -19, 7],\n [-34, -16, 2, 40, -30],\n [-17, -4, 3, 7, -16],\n [-1, -2, 3, 8, 1],\n [21, 6, 3, -9, 22]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-10, 10, 15, 5, 25],\n [8, -8, -12, -4, -20],\n [-8, 8, 12, 4, 20],\n [0, 0, 0, 0, 0],\n [-4, 4, 6, 2, 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[[22, -2, 10, 4, -4],\n [32, -37, 15, -25, 54],\n [63, -18, 30, 3, 15],\n [14, -22, 4, -22, 23],\n [34, -23, 17, -9, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, 5, -25, -4, 9],\n [-40, -32, 37, 21, -1],\n [-1, 5, 15, -30, -17],\n [-24, -9, 30, -13, 6],\n [26, 12, -45, -19, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, -5, -3, -6, 0],\n [-16, -20, -12, -24, 0],\n [-12, -15, -9, -18, 0],\n [-20, -25, -15, -30, 0],\n [16, 20, 12, 24, 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[[-5, -37, -12, 55, -70],\n [-3, -31, -16, 44, -53],\n [-4, -16, 4, 27, -39],\n [-1, -41, -12, 44, -59],\n [6, 6, 48, -45, 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 5x5 matrix:\n[[-18, -15, 9, 9, 0],\n [-6, -5, 3, 3, 0],\n [-18, -15, 9, 9, 0],\n [12, 10, -6, -6, 0],\n [6, 5, -3, -3, 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[[32, 18, -10, -16, -32],\n [6, 18, 12, -36, 9],\n [30, -3, 24, 21, -22],\n [18, 0, -36, 25, 26],\n [42, 12, 0, 1, -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[[16, 34, 4, -36, 19],\n [-4, -26, -6, 14, -11],\n [4, -16, -6, -2, -4],\n [28, 28, -2, -54, 22],\n [4, 40, 10, -18, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[21, 32, 30, 39, 16],\n [-12, 56, 23, 41, 31],\n [-24, 52, 13, 31, 29],\n [21, 2, 11, 14, -3],\n [-27, -34, -45, -42, -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[[0, -8, 16, -4, -20],\n [0, 10, -20, 5, 25],\n [0, -10, 20, -5, -25],\n [0, 10, -20, 5, 25],\n [0, -4, 8, -2, -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[[10, -14, -5, -15, 21],\n [-4, 20, 2, -6, 6],\n [2, 2, -1, -7, 9],\n [-4, 2, 2, 9, -12],\n [10, 16, -5, -40, 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[[51, 36, -49, -32, 1],\n [-8, 22, 22, -14, -63],\n [-59, -34, 47, 14, 6],\n [24, 4, -8, -40, -6],\n [-44, -26, 67, -26, -48]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[47, 9, -4, -26, -29],\n [48, 26, 0, -27, -28],\n [-48, -7, 2, 14, 21],\n [5, -34, 1, 27, 12],\n [16, 12, 4, 41, 30]]?\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[[8, -40, -70, 24, -1],\n [15, -6, -20, 24, 24],\n [-48, 4, 20, -66, -74],\n [1, -39, -75, 24, 9],\n [22, 29, 27, 20, 39]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-35, 14, -34, -12, -13],\n [21, -18, 34, 25, -5],\n [-4, 8, -20, -15, 0],\n [-35, 14, -34, -12, -13],\n [-45, 18, -42, -15, -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[[5, 9, 29, 0, 21],\n [-1, 12, 6, -15, -27],\n [-4, -21, -35, 15, 6],\n [1, -42, -22, 9, 9],\n [2, -18, 2, -12, -18]]\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, -3, 6, 15, -15],\n [-15, 3, -6, -15, 15],\n [0, 0, 0, 0, 0],\n [-10, 2, -4, -10, 10],\n [-10, 2, -4, -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[[15, -20, 20, 20, -30],\n [-15, 20, -20, -20, 30],\n [-9, 12, -12, -12, 18],\n [18, -24, 24, 24, -36],\n [15, -20, 20, 20, -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[[0, 0, 0, 0, 0],\n [-5, 20, -5, -10, 25],\n [0, 0, 0, 0, 0],\n [6, -24, 6, 12, -30],\n [-2, 8, -2, -4, 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[[-13, -4, -22, -14, 17],\n [-32, 36, -6, 29, 2],\n [-83, 38, -31, 30, 36],\n [-48, -2, 16, 8, 16],\n [-10, 28, -23, -5, 1]]\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[[5, 58, -25, 16, -38],\n [-3, 21, -24, -4, -9],\n [-8, 14, -31, -14, -6],\n [-4, 7, -31, -10, 11],\n [-14, 2, -24, -24, -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[[-6, -18, 0, -9, -6],\n [0, 0, 0, 0, 0],\n [8, 24, 0, 12, 8],\n [-12, -36, 0, -18, -12],\n [12, 36, 0, 18, 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[[3, -1, -3, 2, 0],\n [-12, 4, 12, -8, 0],\n [3, -1, -3, 2, 0],\n [-15, 5, 15, -10, 0],\n [-3, 1, 3, -2, 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[[-32, -26, -46, 6, 18],\n [26, 38, 61, -24, -9],\n [-20, -20, -34, 8, 10],\n [-28, -34, -56, 18, 12],\n [-18, 6, 3, -20, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-7, -31, 60, -7, -35],\n [-25, 7, -12, 31, 11],\n [-19, 24, -33, 23, 19],\n [-11, -32, 57, 1, -31],\n [-15, 17, 6, -5, -13]]?\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, 28, 2, -8, 30],\n [-38, -3, -34, -34, -45],\n [10, -27, 6, 14, -21],\n [28, -16, 36, 32, 18],\n [32, -13, 36, 34, 24]]?\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[[-8, 26, 80, -10, -18],\n [-28, 52, 84, -22, -14],\n [0, -22, -26, 36, 49],\n [2, 21, 60, -21, -35],\n [4, -7, 4, 21, 29]]\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 5x5 matrix:\n[[4, 14, 16, -2, -24],\n [-6, -36, -4, -22, 6],\n [2, -8, 28, -26, -42],\n [3, 33, -18, 36, 27],\n [-1, 10, -22, 23, 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 5x5 matrix:\n[[-4, -3, -1, 5, -1],\n [-4, -3, -1, 5, -1],\n [-16, -12, -4, 20, -4],\n [24, 18, 6, -30, 6],\n [-8, -6, -2, 10, -2]]\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[[-11, 71, 21, -25, -52],\n [-20, 4, -24, 4, -36],\n [-27, 39, 1, -33, -19],\n [-26, -8, -21, 0, -53],\n [-27, -13, 2, -29, -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 5x5 matrix:\n[[24, 24, 12, 15, 33],\n [-38, -36, -21, -25, -50],\n [16, 0, 24, 20, 4],\n [-8, 0, -12, -10, -2],\n [30, 28, 17, 20, 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 5x5 matrix:\n[[6, -18, 12, 30, -12],\n [-24, -8, -3, -50, -2],\n [4, 4, -1, 6, 2],\n [29, 9, 4, 61, 2],\n [10, 18, -7, 8, 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 5x5 matrix:\n[[-2, 10, 11, 26, -29],\n [-34, -28, 68, -4, -14],\n [6, -6, -22, -10, 4],\n [28, 12, -29, 12, -4],\n [4, -32, 11, -16, -2]]\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, -18, 36, -54, -48],\n [17, -18, 29, -19, -13],\n [-17, 15, -27, 30, 25],\n [-11, 12, -19, 11, 7],\n [-9, 6, -13, 23, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-5, -35, -5, -30, 15],\n [19, -51, -5, -6, 15],\n [-11, 14, 2, -6, 1],\n [11, -17, 1, 6, 11],\n [-8, 26, 14, 12, 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 5x5 matrix:\n[[6, 6, 4, 11, 0],\n [-2, -5, 1, -5, 3],\n [14, -19, 35, 11, 33],\n [-6, -6, -4, -11, 0],\n [-30, 6, -48, -39, -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[[-6, 12, -9, -14, 12],\n [-25, -11, -19, -23, -16],\n [-10, -14, -11, -22, -34],\n [12, 6, -3, -24, -24],\n [-3, -12, -4, -11, -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 5x5 matrix:\n[[6, 40, 4, -26, 33],\n [-13, -7, -17, 7, 0],\n [8, -4, 4, 4, 16],\n [-17, 25, -29, 37, -19],\n [-7, -18, -7, -25, 32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-27, -36, 23, -13, -11],\n [7, 3, 6, 28, 12],\n [1, 3, -4, -6, -2],\n [20, 15, 5, 55, 25],\n [19, 30, -25, -9, 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[[6, -12, -12, 30, 12],\n [5, -10, -10, 25, 10],\n [-3, 6, 6, -15, -6],\n [4, -8, -8, 20, 8],\n [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[[10, -4, -10, 10, -4],\n [-10, 4, 10, -10, 4],\n [-30, 12, 30, -30, 12],\n [30, -12, -30, 30, -12],\n [30, -12, -30, 30, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[10, -25, 39, -21, -21],\n [3, 4, 69, -32, -8],\n [29, -12, 3, -40, -32],\n [-13, -19, 18, 19, 5],\n [-5, 22, -69, 26, 18]]?\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[[29, -15, -27, 18, -8],\n [49, -25, -39, 22, -3],\n [-32, -12, 15, -9, 27],\n [8, -24, -15, 9, 15],\n [-12, -6, 12, -12, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 11, 15, -13, -8],\n [-54, 23, 51, -49, 22],\n [-26, 18, 16, 26, 40],\n [-6, 15, -5, 3, -24],\n [-20, 35, 21, -6, -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, -8, -23, -2, -9],\n [0, 13, 39, 11, 46],\n [0, -5, 5, 6, 31],\n [0, 2, 3, 4, 15],\n [0, 20, 22, 6, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, -17, 1, 6, 6],\n [-3, -8, 19, -21, 9],\n [-3, -1, -16, 21, -5],\n [-24, -38, 22, -12, 20],\n [6, 11, -13, 12, -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[[-32, -16, 18, -5, -14],\n [17, 19, -3, 2, -7],\n [-7, -5, 3, -1, -1],\n [-18, 10, 22, -4, -34],\n [18, -10, -22, 4, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -30, 24, 0, 36],\n [4, 10, -11, 2, -18],\n [20, 0, -5, 40, 30],\n [-16, 0, 4, -32, -24],\n [-3, -55, 27, 4, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-27, 18, -17, 41, 3],\n [33, 6, 13, -5, 15],\n [-6, -15, -53, 21, -45],\n [-2, 3, 25, 4, -17],\n [-26, -5, -43, 12, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[10, -2, -1, 6, 11],\n [30, -23, 49, 36, -30],\n [22, -10, 6, 24, 14],\n [4, -2, -12, 12, 18],\n [16, -13, 21, 24, -10]]\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, -21, -37, -24, -19],\n [13, 22, -7, 41, 11],\n [-26, -26, 23, -40, -10],\n [6, 18, 10, 22, 12],\n [8, -1, -1, -26, -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[[1, -3, -6, -4, -5],\n [4, -12, -24, -16, -20],\n [-4, 12, 24, 16, 20],\n [-5, 15, 30, 20, 25],\n [5, -15, -30, -20, -25]]\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[[-53, 71, -62, 40, 46],\n [10, -13, -2, -26, -17],\n [0, -9, 14, 2, -11],\n [-6, 5, -6, 0, -1],\n [-39, 19, -18, 3, -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 5x5 matrix:\n[[-7, -21, -14, 33, 20],\n [60, 12, 38, -43, -25],\n [-48, 42, -8, -14, -20],\n [25, 0, 10, 20, 0],\n [-16, 15, 2, -44, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-22, 14, -12, -2, 4],\n [12, -28, 60, 38, 22],\n [-15, 11, -12, -4, 1],\n [-15, 27, -54, -33, -18],\n [-7, 19, -42, -27, -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 5x5 matrix:\n[[27, -6, -24, 30, 22],\n [-3, 39, 6, -30, 12],\n [-1, -8, 0, 8, -3],\n [14, 7, -10, -22, 7],\n [36, 9, -30, 18, 33]]\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, 36, -54, 14, 18],\n [22, -36, 6, 2, 30],\n [-18, 24, 16, -8, -40],\n [3, -18, 51, -15, -33],\n [-12, 30, -43, 11, 13]]\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, 35, -34, 0, 34],\n [3, 20, -23, 1, 13],\n [3, 21, -22, 0, 15],\n [-2, -26, 28, 0, -16],\n [8, -24, 26, 2, -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[[-8, -4, -20, 8, -4],\n [10, 5, 25, -10, 5],\n [4, 2, 10, -4, 2],\n [6, 3, 15, -6, 3],\n [-6, -3, -15, 6, -3]]\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, 4, -12, -6, -22],\n [-21, 6, -17, 2, -24],\n [-12, -3, -13, 3, 22],\n [-24, 5, -17, 3, -18],\n [18, 12, -40, -10, -58]]\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, 0, -19, 2, -13],\n [21, -15, -39, 3, -36],\n [0, 10, 23, -16, 13],\n [-45, -55, 15, -9, -26],\n [0, -5, -18, 15, -7]]\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[[-7, 2, -6, 19, 9],\n [26, 4, -2, -42, -22],\n [9, 2, -2, -13, -7],\n [26, 20, -36, -2, -6],\n [5, -6, 14, -25, -11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-43, -18, 23, -67, -19],\n [7, 26, -14, 28, 6],\n [-12, 4, -19, -25, -41],\n [15, 27, -26, -17, -3],\n [75, 20, -74, 26, -32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[10, -7, -1, -22, 8],\n [-20, 1, 8, 26, -4],\n [-50, -30, 35, 20, 20],\n [20, 25, -20, 10, -20],\n [26, 0, -11, -32, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-34, -2, 13, 9, 11],\n [-5, 4, 25, 44, -26],\n [40, 1, -14, -34, 7],\n [9, 14, -7, -14, -46],\n [34, 12, -66, -62, -46]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[5, -21, 32, 28, 10],\n [9, 9, -23, -12, -21],\n [-25, -3, 26, 4, 40],\n [23, -21, 17, 28, -17],\n [14, 6, -22, -8, -26]]\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, -36, 39, 19, -3],\n [-1, 12, 22, 2, 11],\n [-8, -58, -6, 55, -16],\n [-8, -2, 25, -38, 6],\n [1, 10, 16, 1, 17]]?\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 5x5 matrix:\n[[2, -8, -28, -10, 6],\n [-27, -29, -7, 40, -19],\n [-7, -28, 8, 14, -17],\n [8, -5, 18, -20, -10],\n [14, -34, -36, 8, 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[[-24, 21, 2, 5, -40],\n [-27, 27, 3, 4, -35],\n [6, 9, 4, -12, 57],\n [12, -27, 2, -14, -5],\n [-15, 18, -7, 28, -44]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 24, -30, -30, 18],\n [-6, 24, -30, -30, 18],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [-2, 8, -10, -10, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[33, 9, 23, 19, -14],\n [57, -26, 59, 30, 0],\n [4, 75, -56, -3, -22],\n [-12, 26, 4, 6, -36],\n [-8, -76, 42, -4, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[20, -18, 2, -22, 4],\n [5, 3, 23, -8, -4],\n [25, -15, 25, -30, 0],\n [-5, 12, 22, 3, -6],\n [-40, 30, -22, 46, -4]]\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, 4, 6, 5, -23],\n [-16, 6, -6, 15, -27],\n [0, 0, 0, 0, 0],\n [16, -2, 18, -13, 1],\n [-6, -1, -12, 4, 11]]\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[[2, -20, 16, 0, -22],\n [10, -8, 12, 0, -10],\n [-5, 4, -6, 0, 5],\n [9, -44, 38, 0, -49],\n [41, 4, 22, 0, -1]]\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, 36, -18, -2, -8],\n [9, 33, 1, -5, -18],\n [-22, -9, -22, 4, 18],\n [-32, -9, -16, 0, 14],\n [-4, -48, 44, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-42, -16, -12, 4, 2],\n [19, 13, 2, -9, -21],\n [-6, 4, -6, -4, -14],\n [-22, -55, 30, 9, 44],\n [-1, 30, -22, -16, -55]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-44, 6, 2, -18, -42],\n [-50, 21, 15, -7, -51],\n [39, 0, 3, 21, 36],\n [-38, 30, 24, 8, -42],\n [-16, 27, 23, 17, -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 5x5 matrix:\n[[7, 7, -2, -18, 17],\n [25, -16, -16, -3, -12],\n [-12, -26, 18, 18, -4],\n [-24, 7, 20, 3, 15],\n [17, 24, -30, -3, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[7, 3, -16, -5, -38],\n [-9, 21, -8, -33, 2],\n [6, -15, -21, 30, 9],\n [-25, -11, 28, -3, 44],\n [5, 22, -5, -32, -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 5x5 matrix:\n[[30, 29, -14, 18, 27],\n [-1, -6, 0, -4, -4],\n [32, -2, -4, 4, 10],\n [-31, -16, 28, -3, -18],\n [-40, 35, 22, 24, 9]]\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[[46, 4, -20, -24, 0],\n [-2, 12, 0, -2, 10],\n [-17, 18, 6, 4, 16],\n [7, -14, -2, 0, -12],\n [31, 10, -14, -18, 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 5x5 matrix:\n[[3, 3, 4, 6, 2],\n [10, 10, 16, 32, 18],\n [20, 20, 16, -8, -32],\n [-1, -1, 0, 4, 5],\n [-20, -20, -20, -10, 15]]\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, 8, 0, 2, 2],\n [30, 20, 0, 5, 5],\n [-24, -16, 0, -4, -4],\n [6, 4, 0, 1, 1],\n [6, 4, 0, 1, 1]]?\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, -5, 10, 25, 14],\n [-9, 38, -33, 39, 3],\n [25, -36, 3, -6, 13],\n [3, -17, 13, -58, -6],\n [2, 4, -6, -46, 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[[-18, -12, 6, -6, -30],\n [0, 0, 0, 0, 0],\n [-15, -10, 5, -5, -25],\n [-15, -10, 5, -5, -25],\n [12, 8, -4, 4, 20]]\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, 3, 18, 6, 0],\n [12, -2, -12, -4, 0],\n [24, -4, -24, -8, 0],\n [-30, 5, 30, 10, 0],\n [30, -5, -30, -10, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[7, -30, 13, 27, 8],\n [-28, 25, -13, 35, 2],\n [24, -12, -3, 66, 36],\n [-33, 36, -12, -33, -24],\n [-15, 46, -27, 41, 16]]\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, -36, -3, -23, 23],\n [-18, -12, -9, -16, 11],\n [-6, -48, -3, -34, 29],\n [14, 30, -11, 21, -9],\n [14, 18, 3, 17, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-18, 66, 8, -33, 9],\n [8, -31, 27, 22, -33],\n [-12, -11, -25, 5, 19],\n [25, -33, -33, -13, 6],\n [11, -62, -14, 16, -18]]\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, -10, -2, -10, 10],\n [-5, 5, 1, 5, -5],\n [-30, 30, 6, 30, -30],\n [0, 0, 0, 0, 0],\n [-15, 15, 3, 15, -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[[1, 18, 11, 22, -32],\n [26, 72, -32, 8, 26],\n [-15, 0, -10, 0, -25],\n [13, 18, 19, 22, -12],\n [2, -6, -4, -9, 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[[43, 1, -19, 8, -2],\n [-2, -35, -25, -18, 22],\n [-60, 18, 20, -8, -15],\n [-2, -18, 1, 11, 16],\n [11, -26, -49, -39, 8]]\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, -31, 13, -42, -7],\n [-54, -24, -33, 42, 75],\n [-31, -6, -14, 30, 37],\n [-32, 23, -22, 44, 16],\n [-85, 30, -19, 56, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[20, 16, 41, -37, 24],\n [-16, 8, -34, 22, -28],\n [-20, -12, 25, 0, 5],\n [-15, -7, -20, 20, -15],\n [37, 45, 4, -36, 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[[28, 28, 39, 18, -25],\n [-20, -20, -15, 30, -15],\n [9, 9, 0, -36, 24],\n [17, 17, 24, 12, -16],\n [-11, -11, -15, -6, 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[[29, -4, 12, 33, 0],\n [17, -23, 32, 31, 11],\n [-3, 26, -43, -29, -7],\n [-35, 8, -8, -31, -8],\n [33, -1, 3, 29, 2]]\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 5x5 matrix:\n[[-16, 0, -12, -20, -16],\n [-20, 0, -15, -25, -20],\n [24, 0, 18, 30, 24],\n [-16, 0, -12, -20, -16],\n [12, 0, 9, 15, 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[[7, -11, 15, 21, 33],\n [12, 12, -28, 18, -30],\n [-22, 33, -23, -18, -50],\n [6, -28, 28, 24, 53],\n [18, -13, 3, 38, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[0, 36, -36, -6, 0],\n [0, 36, -36, -6, 0],\n [0, -24, 24, 4, 0],\n [0, -18, 18, 3, 0],\n [0, 12, -12, -2, 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[[4, -14, 21, 42, 17],\n [71, 26, 53, -32, -65],\n [-17, 31, -19, -26, -1],\n [-26, -35, -32, 2, 20],\n [59, 6, 49, -8, -45]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[25, -4, -5, 14, 3],\n [-30, 9, -19, -37, 7],\n [10, -16, 38, 62, -28],\n [46, -7, -47, 14, 12],\n [72, -18, -6, 63, -3]]\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[[8, 24, -20, 10, 48],\n [12, 48, -32, -1, 38],\n [-30, -21, 16, 23, 8],\n [0, 12, 0, -3, 12],\n [-6, -39, 28, -9, -50]]?\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, -4, -4, -2, 4],\n [-2, -8, -8, -4, 8],\n [6, 24, 24, 12, -24],\n [4, 16, 16, 8, -16],\n [6, 24, 24, 12, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-55, -16, -2, 5, 16],\n [18, -10, 16, 46, 3],\n [6, -6, -16, -6, -35],\n [-1, 10, 18, 3, 39],\n [-7, 6, -12, -29, -8]]\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[[-8, 0, 12, -2, -12],\n [4, 0, -6, 1, 6],\n [24, 0, -36, 6, 36],\n [-20, 0, 30, -5, -30],\n [4, 0, -6, 1, 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 5x5 matrix:\n[[13, 1, -7, 11, -22],\n [-19, -3, 30, -31, 31],\n [7, 7, 22, -13, -7],\n [30, 38, -46, 50, -24],\n [23, 47, -56, 55, -5]]\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 5x5 matrix:\n[[-30, -58, -15, -1, -7],\n [-6, -22, -6, -4, -13],\n [8, 18, 2, 11, 5],\n [26, 20, -11, 10, 26],\n [-6, -16, 5, -16, -36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-10, 4, -12, 10, 10],\n [30, -12, 36, -30, -30],\n [25, -10, 30, -25, -25],\n [-15, 6, -18, 15, 15],\n [10, -4, 12, -10, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-15, -30, -25, -10, -25],\n [12, 24, 20, 8, 20],\n [0, 0, 0, 0, 0],\n [12, 24, 20, 8, 20],\n [12, 24, 20, 8, 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[[-10, 10, 25, -20, 15],\n [4, -4, -10, 8, -6],\n [-6, 6, 15, -12, 9],\n [8, -8, -20, 16, -12],\n [12, -12, -30, 24, -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[[26, 21, 35, -36, -1],\n [38, -6, 40, 54, -6],\n [59, 25, 28, 10, -29],\n [18, 27, -29, -8, -19],\n [34, 28, -54, 0, -60]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-11, 10, -9, -8, 14],\n [1, -14, -9, 4, 2],\n [-26, 12, -30, -16, 36],\n [-18, 28, -6, -16, 20],\n [21, -38, 3, 20, -22]]\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[[12, -8, -24, -20, -8],\n [-12, 8, 24, 20, 8],\n [0, 0, 0, 0, 0],\n [-3, 2, 6, 5, 2],\n [-6, 4, 12, 10, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[14, 16, -4, 14, 40],\n [14, 4, -8, -28, -4],\n [26, 22, -10, -1, 46],\n [-4, 4, 4, 26, 20],\n [-7, 4, 6, 35, 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 5x5 matrix:\n[[2, 4, 0, 8, 6],\n [-4, -8, 0, -16, -12],\n [0, 0, 0, 0, 0],\n [-2, -4, 0, -8, -6],\n [6, 12, 0, 24, 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[[4, -10, 7, 6, -7],\n [6, -20, 13, 4, -23],\n [-2, 2, -2, -6, -4],\n [-4, 20, -12, 4, 32],\n [-6, 12, -9, -12, 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[[-2, -12, 8, 0, 18],\n [1, -19, -6, 8, 0],\n [-33, -3, 26, -16, 14],\n [43, 28, -8, 4, 15],\n [5, 25, 10, -10, 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[[24, 4, 4, -10, 24],\n [63, 12, -27, -6, 54],\n [-53, 2, 18, -4, -24],\n [-29, 6, -16, 8, -12],\n [7, 24, -25, -10, 42]]\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, -29, 18, 9, 30],\n [21, 26, -6, 11, 42],\n [25, 33, -11, 6, 18],\n [23, 32, -12, 3, 6],\n [12, 30, -12, 6, 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 5x5 matrix:\n[[-24, 20, -16, 4, -12],\n [30, -25, 20, -5, 15],\n [-12, 10, -8, 2, -6],\n [18, -15, 12, -3, 9],\n [18, -15, 12, -3, 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[[0, 0, 0, -1, 5],\n [0, 0, 0, 5, -25],\n [0, 0, 0, 3, -15],\n [0, 0, 0, -4, 20],\n [0, 0, 0, -2, 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[[-22, -32, -22, -17, -36],\n [28, 47, -14, 28, 52],\n [33, 11, -7, 33, 17],\n [-50, 31, 62, 25, 27],\n [2, 20, 20, 42, 23]]\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 5x5 matrix:\n[[28, 18, -28, 24, 30],\n [25, 15, -25, 25, 35],\n [-23, -15, 23, -19, -23],\n [-19, -15, 19, -7, 1],\n [-26, -18, 26, -18, -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[[12, 6, -24, 6, -18],\n [8, -20, -8, -12, -16],\n [0, 0, 0, 0, 0],\n [-4, -14, 12, -10, 4],\n [2, 7, -6, 5, -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[[-18, -43, -3, -19, -51],\n [-47, -5, 4, 5, 25],\n [26, 55, -34, 27, 20],\n [26, 4, -49, 28, -65],\n [-55, 34, -4, 28, 73]]?\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, -14, 13, 6, 3],\n [6, 23, -7, 9, -3],\n [10, -16, -11, -22, -3],\n [-6, 15, 4, 14, 1],\n [-2, -21, -8, -24, -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 5x5 matrix:\n[[3, 4, 24, -37, 25],\n [2, -22, 8, -12, 14],\n [-5, -16, 19, 6, -39],\n [5, 10, 10, -32, 77],\n [-2, 24, 9, -4, 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[[15, 0, 25, 20, -10],\n [18, 0, 30, 24, -12],\n [-12, 0, -20, -16, 8],\n [18, 0, 30, 24, -12],\n [-12, 0, -20, -16, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[22, 35, -41, 19, -39],\n [-26, -42, 55, -24, 52],\n [9, 14, -6, 1, -16],\n [25, 38, -33, 21, -26],\n [-16, -25, 28, -15, 23]]\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],\n [-30, -25, -5, 30, 10],\n [-24, -20, -4, 24, 8],\n [24, 20, 4, -24, -8],\n [18, 15, 3, -18, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 9, 9, 9, 6],\n [0, -6, -6, -6, -4],\n [0, 18, 18, 18, 12],\n [0, -6, -6, -6, -4],\n [0, -12, -12, -12, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[18, 15, 3, -3, 14],\n [22, -12, 34, -34, -32],\n [-32, -15, -17, 17, -6],\n [-15, -9, -6, 6, -6],\n [-18, 6, -24, 24, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[3, -24, -42, 45, -3],\n [6, 7, 4, 2, 5],\n [0, 15, 24, -24, 3],\n [0, 15, 24, -24, 3],\n [-15, 0, 18, -33, -9]]\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 5x5 matrix:\n[[16, -16, -24, -20, 8],\n [-20, 20, 30, 25, -10],\n [-8, 8, 12, 10, -4],\n [12, -12, -18, -15, 6],\n [16, -16, -24, -20, 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[[34, 12, 20, 28, -10],\n [-37, -10, -21, -19, -9],\n [-20, -4, -11, -5, -14],\n [13, 2, 7, 1, 13],\n [23, 10, 14, 26, -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[[32, -4, 44, -44, -12],\n [-3, -42, 35, 3, -33],\n [55, 10, 35, -37, -30],\n [21, -32, 57, -35, -11],\n [-15, 32, -5, -25, -32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-5, 0, 0, 1, -20],\n [33, 21, -9, 30, 9],\n [41, 14, 40, -1, -39],\n [41, 18, 26, 9, -23],\n [-17, 27, 28, -39, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-11, -16, -46, -28, -30],\n [-10, 23, -13, -26, 13],\n [-34, -24, 0, -48, 12],\n [4, 9, -31, -18, -15],\n [-2, 52, 44, -24, 64]]\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, 15, 4, -40, 11],\n [-6, -35, 1, -26, -9],\n [14, 43, -6, 28, 15],\n [-4, 0, 17, 30, -18],\n [2, 47, 17, -26, 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[[-8, -9, -14, -6, 24],\n [19, 0, 30, -10, -6],\n [35, 18, 16, -22, 0],\n [-7, 0, -28, -6, 24],\n [-18, 12, -60, 4, 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[[-36, -30, -24, 6, -30],\n [-30, -25, -20, 5, -25],\n [-6, -5, -4, 1, -5],\n [6, 5, 4, -1, 5],\n [-36, -30, -24, 6, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, 4, 48, -29, 35],\n [-27, 12, 27, -53, 44],\n [-9, 38, -46, -13, -2],\n [23, 8, 2, -3, 6],\n [-31, 10, 23, -59, 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[[0, -32, -34, 32, 26],\n [6, -18, -21, 12, 9],\n [18, 10, 5, -28, -25],\n [3, -1, -2, -2, -2],\n [-13, 31, 37, -18, -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[[2, -4, 1, -3, 4],\n [16, -16, -6, 2, -12],\n [13, -14, -4, 0, -7],\n [-40, 40, 15, -5, 30],\n [-5, 6, 1, 1, 1]]\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, 24, 30, 0, 36],\n [20, -4, -2, -12, 20],\n [0, -8, -10, 0, -12],\n [-5, 27, 33, 3, 34],\n [-15, 5, 4, 9, -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[[-6, -10, -8, 4, 8],\n [18, 30, 24, -12, -24],\n [-6, -10, -8, 4, 8],\n [18, 30, 24, -12, -24],\n [-18, -30, -24, 12, 24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[13, -16, 11, -15, -16],\n [-55, 32, -5, -1, 28],\n [-20, 44, -46, 12, 8],\n [2, 20, -30, -1, -10],\n [-28, 26, -13, 23, 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 5x5 matrix:\n[[8, -2, 4, -4, -8],\n [8, -2, 4, -4, -8],\n [-16, 4, -8, 8, 16],\n [0, 0, 0, 0, 0],\n [20, -5, 10, -10, -20]]\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[[2, 6, -3, -5, -4],\n [-4, -12, 6, 10, 8],\n [4, 12, -6, -10, -8],\n [0, 0, 0, 0, 0],\n [12, 36, -18, -30, -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[[2, 0, 6, -4, -4],\n [4, 0, 12, -8, -8],\n [-4, 0, -12, 8, 8],\n [-6, 0, -18, 12, 12],\n [12, 0, 36, -24, -24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, 5, -15, -25, 5],\n [-5, -5, 15, 25, -5],\n [2, 2, -6, -10, 2],\n [-1, -1, 3, 5, -1],\n [-2, -2, 6, 10, -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[[-12, -25, 8, -20, 18],\n [19, 23, 38, -20, 51],\n [12, -22, 16, 0, 4],\n [39, 11, 62, -20, 63],\n [15, -17, 34, -16, 33]]?\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[[-37, 27, 40, 29, -27],\n [12, 60, -15, 42, 24],\n [69, 21, -48, 3, 75],\n [-10, 12, 31, 14, 0],\n [-38, -16, 34, -4, -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[[-28, 6, -70, -35, 50],\n [-20, 38, -30, -67, 10],\n [11, 16, 9, -12, 9],\n [29, -4, 79, 34, -61],\n [7, -8, 5, 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[[-18, 36, 24, 24, 36],\n [6, -12, -8, -8, -12],\n [12, -24, -16, -16, -24],\n [-12, 24, 16, 16, 24],\n [-18, 36, 24, 24, 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[[-18, 6, 0, 12, -15],\n [6, -2, 0, -4, 5],\n [30, -10, 0, -20, 25],\n [-30, 10, 0, 20, -25],\n [-18, 6, 0, 12, -15]]\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, -47, 43, -15, -25],\n [5, 2, -7, 3, -2],\n [25, 26, -31, 11, 14],\n [5, -18, -3, -1, 10],\n [-35, -3, 39, -11, -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 5x5 matrix:\n[[12, -4, 0, -12, 24],\n [-3, 1, 0, 3, -6],\n [12, -4, 0, -12, 24],\n [18, -6, 0, -18, 36],\n [-12, 4, 0, 12, -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 5x5 matrix:\n[[-39, -35, 28, 20, -10],\n [16, 20, -12, 0, 0],\n [-5, -9, 4, -4, 2],\n [-18, -28, 14, -8, 4],\n [26, 27, -19, -8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-31, -5, -34, 14, -58],\n [-1, -14, -1, -1, 26],\n [5, 18, 12, 4, -25],\n [-9, -23, 1, 9, 27],\n [8, 17, 25, 9, -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 5x5 matrix:\n[[2, -15, -10, -17, 30],\n [10, 15, 20, 25, -30],\n [4, 42, 22, 38, -54],\n [40, 42, 24, 30, 6],\n [2, -33, -10, -23, 36]]\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, 3, -32, -17, 26],\n [14, 10, 18, 2, -16],\n [9, -3, 32, 17, -26],\n [12, 24, -18, -24, 12],\n [12, 12, 8, -4, -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 5x5 matrix:\n[[21, 50, -4, -29, -26],\n [-31, -13, 26, -14, 24],\n [-20, 13, 19, -43, 28],\n [18, 54, 0, -36, -24],\n [8, -46, -16, 70, -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[[9, 10, 20, 29, -6],\n [2, -36, 26, -70, -6],\n [3, -15, 5, -34, -27],\n [13, -7, 7, 4, 7],\n [15, -37, 38, -52, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 2, 27, -17, -3],\n [10, -27, -19, 28, 50],\n [-26, -6, -24, 26, -28],\n [17, 14, 4, -18, -11],\n [5, -20, -27, 9, -17]]\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, 18, -18, 0, 18],\n [-4, -3, 3, 0, -3],\n [4, 3, -3, 0, 3],\n [-16, -12, 12, 0, -12],\n [12, 9, -9, 0, 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[[-30, 11, -6, -7, 27],\n [7, 16, -26, 0, -4],\n [-15, 3, -27, 18, 9],\n [-20, 40, -36, -68, 32],\n [-3, -29, -5, 56, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, 25, -37, -18, -37],\n [26, 11, -2, 3, -2],\n [22, 13, -7, 0, -7],\n [-8, 20, -33, -17, -33],\n [-12, 6, -15, -9, -15]]?\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, -31, 6, -5, -10],\n [-11, -26, -9, -13, 10],\n [-1, 15, 0, 7, 0],\n [-36, 10, -30, 0, 34],\n [25, 15, 10, 5, -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[[25, -5, -15, -25, -15],\n [-20, 4, 12, 20, 12],\n [30, -6, -18, -30, -18],\n [-25, 5, 15, 25, 15],\n [10, -2, -6, -10, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, 4, 6, -10, -10],\n [6, -12, -18, 30, 30],\n [0, 0, 0, 0, 0],\n [6, -12, -18, 30, 30],\n [3, -6, -9, 15, 15]]\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, -29, 38, -16, 68],\n [2, -20, 52, 11, 54],\n [24, 22, 20, 14, -16],\n [-36, -44, 0, -10, 52],\n [-7, 12, -48, -12, -42]]\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, -33, 41, -13, 14],\n [-3, 27, -43, 5, 2],\n [7, 1, -1, 39, -20],\n [-8, 1, 11, 30, -29],\n [9, 12, -24, 27, -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[[-28, 2, 26, 35, 38],\n [-44, 6, 40, 55, 60],\n [-40, 10, 35, 50, 55],\n [-12, 8, 9, 15, 17],\n [4, -56, 13, -5, -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 5x5 matrix:\n[[20, -20, -8, 4, -19],\n [-20, 26, -4, -6, 27],\n [0, -24, 37, -14, -10],\n [-28, 1, 48, -31, 25],\n [28, -4, -41, 34, -31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 14, -6, -6, -3],\n [-30, 28, -22, 6, -11],\n [24, -28, 12, 12, 6],\n [42, -30, 40, -36, 20],\n [30, -30, 20, 0, 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[[1, 11, 0, 5, -10],\n [7, -1, 21, 11, -17],\n [-16, -8, -30, -20, 28],\n [-34, 20, -35, -10, -11],\n [25, -35, 20, -5, 35]]\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[[-10, 30, -5, 10, -5],\n [2, -6, 1, -2, 1],\n [-2, 6, -1, 2, -1],\n [-6, 18, -3, 6, -3],\n [0, 0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-6, -8, 4, 0, 10],\n [-6, -8, 4, 0, 10],\n [3, 4, -2, 0, -5],\n [6, 8, -4, 0, -10],\n [-6, -8, 4, 0, 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[[12, -12, -30, -30, -24],\n [-4, 4, 10, 10, 8],\n [6, -6, -15, -15, -12],\n [8, -8, -20, -20, -16],\n [-10, 10, 25, 25, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[30, -42, -12, 12, -24],\n [-10, 8, 4, 1, 6],\n [-5, 25, 2, -17, 10],\n [10, -20, -4, 9, -10],\n [20, -28, -8, 8, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, -23, 4, 24, 15],\n [-40, -35, -6, -9, -55],\n [12, 40, -4, -2, 24],\n [-11, -24, 5, 18, 21],\n [4, -17, 10, -27, -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[[-16, 0, -4, -12, -36],\n [3, 18, -24, -36, -27],\n [14, -4, 9, 19, 39],\n [-2, 12, -17, -27, -27],\n [15, 2, 1, 7, 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[[-21, -33, -30, -27, -15],\n [-37, -21, 14, -42, 7],\n [12, 16, 12, 15, 6],\n [-16, -28, -28, -21, -14],\n [25, 25, 10, 30, 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[[-5, 5, -4, -1, 1],\n [-20, 20, -16, -4, 4],\n [-25, 25, -20, -5, 5],\n [15, -15, 12, 3, -3],\n [20, -20, 16, 4, -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, 3, -9, 12, -9],\n [6, -1, 3, -4, 3],\n [24, -4, 12, -16, 12],\n [36, -6, 18, -24, 18],\n [24, -4, 12, -16, 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[[-8, -26, 13, 25, -7],\n [4, 24, -12, -24, 4],\n [21, 16, -8, -11, 16],\n [-11, 22, -11, -26, -7],\n [0, -22, 11, 23, -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[[24, 41, -28, 15, 20],\n [-7, 9, 9, -31, -23],\n [50, -36, 57, 34, 48],\n [-44, -9, 5, -45, 6],\n [38, -33, 39, 37, 30]]\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[[55, 11, 15, -7, -5],\n [-25, 15, -35, -5, 75],\n [-80, -50, -38, 20, 20],\n [-50, -44, -17, 17, -10],\n [45, -4, 37, 0, -65]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[32, 26, 5, 31, 5],\n [-6, -42, -3, 21, 63],\n [-29, -47, -24, -6, 41],\n [-24, -14, -64, -10, 4],\n [-2, -34, 10, 18, 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[[12, 0, 8, 0, -12],\n [-6, 0, -4, 0, 6],\n [15, 0, 10, 0, -15],\n [3, 0, 2, 0, -3],\n [-3, 0, -2, 0, 3]]\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, 0, 0, 0, 0],\n [30, 24, -30, 0, 0],\n [-15, -12, 15, 0, 0],\n [-5, -4, 5, 0, 0],\n [20, 16, -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 5x5 matrix:\n[[-30, 36, -6, 0, 6],\n [0, 0, 0, 0, 0],\n [15, -18, 3, 0, -3],\n [30, -36, 6, 0, -6],\n [25, -30, 5, 0, -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 5x5 matrix:\n[[-30, 38, -21, -13, 3],\n [-12, -12, -5, -12, -9],\n [12, -12, 8, 6, 0],\n [18, -18, 12, 9, 0],\n [18, 6, 9, 15, 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[[-4, 16, 8, -16, 0],\n [-5, 20, 10, -20, 0],\n [5, -20, -10, 20, 0],\n [6, -24, -12, 24, 0],\n [-4, 16, 8, -16, 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[[18, -4, -18, -1, -10],\n [-42, 16, 42, 4, 30],\n [-3, 4, 3, 1, 5],\n [39, -24, -39, -6, -37],\n [12, -8, -12, -2, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[20, -16, 16, 5, -2],\n [25, -19, -16, -8, -4],\n [-3, 15, 9, -17, -7],\n [3, -10, -3, 13, 8],\n [-11, -9, -50, 14, 16]]\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[[22, -26, -30, -25, -5],\n [-3, -12, -9, -3, 15],\n [14, -115, -79, 1, 33],\n [10, -39, -31, -15, 17],\n [-20, 89, 55, 7, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[0, -31, -12, -27, -39],\n [7, -3, 34, 29, 26],\n [22, -2, -25, -14, -7],\n [-16, 15, 15, 15, 16],\n [-9, -31, 16, -7, -24]]\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, -5, -1, -6, 0],\n [20, -20, -4, -24, 0],\n [5, -5, -1, -6, 0],\n [25, -25, -5, -30, 0],\n [5, -5, -1, -6, 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[[14, -21, 49, -26, 15],\n [-6, 15, -33, 18, -9],\n [-12, -12, 18, -12, 0],\n [-28, 14, -42, 20, -18],\n [-2, -9, 17, -10, 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, -2, -12, 8, 24],\n [-3, 3, 5, 15, 14],\n [78, -44, 14, -69, -20],\n [35, -3, -28, -23, 16],\n [50, -54, 2, -50, -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[[-19, -27, -52, -2, -17],\n [36, -7, -22, 26, -7],\n [-6, -68, 60, -28, 88],\n [4, -28, -44, 0, -8],\n [-32, 4, -34, 6, -30]]\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[[8, -22, 6, 38, -20],\n [-8, 19, -15, -17, 14],\n [6, -12, 18, -3, -6],\n [12, -30, 18, 36, -24],\n [18, -39, 45, 12, -24]]\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, 16, -12, -24, 0],\n [-30, -35, 0, 15, 6],\n [16, 13, 34, 43, -10],\n [-13, -9, -37, -49, 10],\n [33, 39, -3, -21, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0, 0],\n [-10, -8, -6, -2, -10],\n [20, 16, 12, 4, 20],\n [10, 8, 6, 2, 10],\n [20, 16, 12, 4, 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[[-8, 2, 31, -10, -7],\n [-16, -12, -11, -14, -6],\n [-18, 30, 32, -31, -1],\n [28, 8, 5, -7, -26],\n [56, 12, 9, 5, -36]]?\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[[-4, 1, -5, 2, -5],\n [32, 20, 12, -32, 36],\n [8, 12, -4, -12, 8],\n [-36, -12, -24, 30, -42],\n [0, -7, 7, 4, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0, 0],\n [4, 5, -6, 1, -6],\n [24, 30, -36, 6, -36],\n [20, 25, -30, 5, -30],\n [-24, -30, 36, -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[[-36, -12, 12, -30, -24],\n [-30, -10, 10, -25, -20],\n [0, 0, 0, 0, 0],\n [30, 10, -10, 25, 20],\n [-24, -8, 8, -20, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, 10, -4, -1, 15],\n [22, -25, -35, -4, 17],\n [25, -2, -45, -27, 27],\n [-22, -9, 41, 32, -27],\n [-9, 4, 14, 5, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-30, -32, -1, -2, -21],\n [25, 26, 28, 20, -8],\n [25, 29, -10, -19, 38],\n [-17, -1, -1, 5, 11],\n [-32, -21, 8, 51, -36]]?\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 5x5 matrix:\n[[8, 4, -12, 4, -2],\n [-22, -14, 39, -10, 7],\n [-18, -18, 45, -6, 9],\n [6, 6, -15, 2, -3],\n [4, 14, -30, -2, -7]]\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 5x5 matrix:\n[[49, 56, 13, 60, 3],\n [13, 50, -3, 18, -61],\n [-36, -36, -30, -64, -24],\n [-4, 4, 6, 0, -28],\n [-56, -34, -18, -50, 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 5x5 matrix:\n[[-34, 21, 7, 14, 22],\n [-51, 24, 15, 12, -9],\n [-13, -4, 31, -10, -25],\n [-8, -2, 5, -5, -35],\n [-38, 28, -16, 22, 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 5x5 matrix:\n[[24, 12, -28, 8, -8],\n [0, 0, 30, 30, -30],\n [20, 10, -15, 15, -15],\n [4, 2, -33, -27, 27],\n [-20, -10, -5, -35, 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[[0, -2, -2, 8, 8],\n [0, 4, 4, -16, -16],\n [0, 4, 4, -16, -16],\n [0, 0, 0, 0, 0],\n [0, -1, -1, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-26, -17, -11, -30, -28],\n [-31, -27, -66, -30, -68],\n [11, 60, 7, 52, 16],\n [16, 37, 9, 38, 20],\n [-18, 18, 20, -4, 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[[-20, -16, 5, 11, 20],\n [-20, -21, 20, 41, 49],\n [16, 17, -15, -34, -41],\n [-24, -13, -70, -24, 11],\n [20, 10, 20, 25, 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[[-29, 10, -13, 14, -39],\n [9, -8, 3, 2, 11],\n [14, 30, -23, -21, 8],\n [-27, 30, -30, 5, -43],\n [-16, 16, -38, 22, -36]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-18, -36, -12, 36, 0],\n [3, 6, 2, -6, 0],\n [-3, -6, -2, 6, 0],\n [-6, -12, -4, 12, 0],\n [9, 18, 6, -18, 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[[0, 0, 0, 0, 0],\n [-12, -6, -2, 8, 4],\n [0, 0, 0, 0, 0],\n [24, 12, 4, -16, -8],\n [12, 6, 2, -8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[13, 14, 23, 15, 10],\n [10, 17, 49, -8, -6],\n [46, 26, -27, -22, 59],\n [59, 38, -19, -31, 70],\n [-26, -13, 16, 16, -33]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-36, 10, -2, 0, -30],\n [-24, 16, 4, -8, -20],\n [-18, -2, -5, 6, -15],\n [-48, 18, 0, -4, -40],\n [-36, 24, 6, -12, -30]]\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 5x5 matrix:\n[[8, 22, -2, -2, 14],\n [-35, -33, 28, -27, 13],\n [-35, -10, 35, -40, 40],\n [3, 14, 1, -4, 12],\n [-36, -30, 30, -30, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-15, -5, 2, 0, -3],\n [-38, 12, -60, 4, 1],\n [-45, 3, -8, -4, 23],\n [-14, 12, -42, 4, 12],\n [-18, 10, -28, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[18, -12, -3, 9, -18],\n [-12, 4, 0, -5, 9],\n [0, 12, 6, -3, 9],\n [30, 12, 11, 7, -6],\n [42, 4, 9, 13, -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 5x5 matrix:\n[[-13, -39, 33, -13, 25],\n [8, 24, -12, -1, -5],\n [-2, -6, 6, -3, 5],\n [-2, -6, -6, 10, -10],\n [-10, -30, 6, 11, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[25, -21, 7, 13, 13],\n [0, 30, -8, 26, -12],\n [-28, 84, -28, 38, -34],\n [-18, 21, -14, -4, -3],\n [15, 33, 1, 47, -21]]\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, -6, -26, -3, 23],\n [22, 40, -12, -19, 15],\n [26, 27, 39, -1, -32],\n [0, 7, -33, -44, 19],\n [10, 14, 2, -13, -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[[18, -6, -9, -9, -9],\n [-36, 12, 18, 18, 18],\n [-18, 6, 9, 9, 9],\n [30, -10, -15, -15, -15],\n [24, -8, -12, -12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[10, -15, 0, -15, 25],\n [-2, 3, 0, 3, -5],\n [0, 0, 0, 0, 0],\n [-6, 9, 0, 9, -15],\n [-2, 3, 0, 3, -5]]\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[[10, -13, -5, -33, -58],\n [25, -7, 11, -19, 4],\n [-26, 14, -4, 38, 40],\n [21, -25, 7, -45, -48],\n [39, -15, 24, -27, 24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, -8, -4, 4, -4],\n [-15, -20, -10, 10, -10],\n [-12, -16, -8, 8, -8],\n [18, 24, 12, -12, 12],\n [-18, -24, -12, 12, -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 5x5 matrix:\n[[-23, -25, -27, 7, -8],\n [-33, -42, -33, -16, -8],\n [-6, -3, -2, -13, -16],\n [-3, -3, -20, 60, 22],\n [-13, -11, -24, 38, 2]]\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 5x5 matrix:\n[[-33, -33, -22, 18, -37],\n [-13, 20, -11, -3, 11],\n [-29, -21, -10, 18, -33],\n [21, 12, 14, -9, 17],\n [-21, 19, -28, -6, 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[[-18, 1, -2, 14, -23],\n [-12, -15, -24, -57, 18],\n [26, 10, 22, 32, 6],\n [18, 3, 18, 18, 3],\n [24, 21, 12, 42, 9]]\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, -2, -2, -8, -8],\n [0, 0, 0, 0, 0],\n [0, -2, -2, -8, -8],\n [0, 4, 4, 16, 16],\n [0, 4, 4, 16, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0, 0],\n [0, 22, -4, 16, -6],\n [-8, -6, 0, -4, 10],\n [-2, 15, -3, 11, -2],\n [-4, 30, -6, 22, -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[[-36, -31, -10, -11, -40],\n [20, -25, 56, -20, -10],\n [26, 3, 42, 7, -2],\n [-22, -9, -10, 7, -28],\n [-20, -21, -4, -10, -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 5x5 matrix:\n[[-8, 5, -5, -7, 3],\n [-15, 30, -19, 24, 29],\n [-3, -15, 6, -33, -18],\n [-12, 30, -18, 30, 30],\n [-3, 0, -1, -6, -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, 20, -20, -10, 0],\n [12, 12, -12, -6, 0],\n [16, 16, -16, -8, 0],\n [24, 24, -24, -12, 0],\n [16, 16, -16, -8, 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 5x5 matrix:\n[[22, -34, -6, 8, 32],\n [17, 20, -39, 42, -26],\n [-29, 7, 39, -27, -7],\n [10, -15, -4, 0, 16],\n [-30, 10, 42, -10, -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[[10, 14, 22, 4, 10],\n [13, 7, 23, 12, 10],\n [-32, -14, -6, -28, -8],\n [-26, 3, 23, -30, 4],\n [16, 10, 2, 12, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[5, -15, 20, 15, 30],\n [2, -6, 8, 6, 12],\n [-1, 3, -4, -3, -6],\n [1, -3, 4, 3, 6],\n [6, -18, 24, 18, 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[[-12, -24, 0, 6, -18],\n [2, 4, 0, -1, 3],\n [2, 4, 0, -1, 3],\n [6, 12, 0, -3, 9],\n [2, 4, 0, -1, 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[[-10, -5, -10, 0, -35],\n [-44, 36, -29, 22, -2],\n [15, 6, -2, -14, -20],\n [3, 2, -7, -8, -30],\n [33, -32, 16, -22, -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 5x5 matrix:\n[[-18, -12, -36, -6, 0],\n [-4, 3, 0, 3, -3],\n [-1, -12, -18, -9, 6],\n [5, 9, 18, 6, -3],\n [16, -12, 0, -12, 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[[-15, -2, 7, 14, 19],\n [-7, 2, 15, 40, 38],\n [-33, 13, -16, -14, -31],\n [11, 4, -21, -44, -52],\n [-48, 30, -18, 12, -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 5x5 matrix:\n[[-8, 20, -15, -40, -27],\n [-2, -13, -9, -28, 4],\n [26, 58, -27, -29, -19],\n [30, 31, -30, -40, 3],\n [-10, -52, 15, 15, 29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-5, -4, 1, 3, -5],\n [10, 8, -2, -6, 10],\n [15, 12, -3, -9, 15],\n [5, 4, -1, -3, 5],\n [-10, -8, 2, 6, -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 5x5 matrix:\n[[-1, 0, 1, 3, -1],\n [1, 0, -1, -3, 1],\n [-3, 0, 3, 9, -3],\n [1, 0, -1, -3, 1],\n [-5, 0, 5, 15, -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 5x5 matrix:\n[[6, -30, 12, 38, 8],\n [22, 51, -3, 2, -12],\n [13, 2, 13, 25, 2],\n [27, 25, -10, 35, -10],\n [16, 66, 18, -24, -8]]\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[[-12, -34, -3, -26, 6],\n [16, 12, 7, 17, -2],\n [-23, -4, 16, 13, -24],\n [-9, 22, 9, 23, -18],\n [40, 38, -26, -1, 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[[4, -8, 24, -32, 48],\n [3, 8, 6, -4, 0],\n [0, 0, 0, 0, 0],\n [6, 9, 18, -18, 18],\n [-12, -39, -18, 6, 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 5x5 matrix:\n[[-2, -3, 7, 17, 6],\n [-28, -12, -12, -42, 4],\n [-50, -30, 10, 5, 30],\n [36, 21, -5, 2, -20],\n [-40, -24, 8, 4, 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 5x5 matrix:\n[[-5, -5, 0, -10, -5],\n [-1, 2, -5, 12, 6],\n [-1, 2, -5, 12, 6],\n [18, 6, 20, -20, -10],\n [-38, -20, -30, 8, 4]]\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[[2, 6, 0, -2, 2],\n [-2, -6, 0, 2, -2],\n [4, 12, 0, -4, 4],\n [-4, -12, 0, 4, -4],\n [2, 6, 0, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[15, 21, 8, -8, 20],\n [9, 0, 2, 12, -2],\n [-3, -24, -6, 28, -26],\n [-9, 9, 0, -24, 12],\n [-6, 6, 0, -16, 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[[28, -55, 4, 29, -53],\n [-26, 26, 20, -6, 26],\n [-10, -24, -42, -18, 10],\n [0, -65, -30, 5, -25],\n [-7, 56, -1, -21, 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[[15, 0, -20, 10, 15],\n [-13, 1, 20, -8, -17],\n [15, 6, -4, 14, -9],\n [-7, 1, 12, -4, -11],\n [-6, 0, 8, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -20, 30, -25, 10],\n [0, 24, -36, 30, -12],\n [0, 12, -18, 15, -6],\n [0, 12, -18, 15, -6],\n [0, 12, -18, 15, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-62, -64, 42, 29, 3],\n [-67, -54, 61, 35, -26],\n [-37, -25, 35, 29, -10],\n [-17, -8, 13, 31, 16],\n [-18, -21, 16, -15, -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[[-19, 56, 32, -29, 25],\n [43, -54, -47, 6, -25],\n [12, 12, 6, 4, -30],\n [-45, -22, -27, 2, 24],\n [-40, -16, -24, 2, 14]]?\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 5x5 matrix:\n[[-25, 0, -5, -10, -15],\n [-8, -6, 17, 10, -9],\n [-22, 6, -23, -22, -9],\n [-27, -4, 7, -2, -19],\n [-5, 0, -1, -2, -3]]\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 5x5 matrix:\n[[13, -36, -1, -13, 45],\n [2, -37, 0, -51, 12],\n [-2, -13, -53, -24, -51],\n [26, 1, -6, 26, 27],\n [31, -13, -41, 32, 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[[4, -25, 10, 20, -10],\n [-7, 10, -13, -17, 4],\n [-7, -20, -9, -1, -8],\n [6, -45, 16, 34, -18],\n [5, 10, 7, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[7, 1, -4, -3, -3],\n [26, -6, 24, 1, -16],\n [6, -2, 8, 1, -4],\n [-3, -1, 4, 2, 1],\n [17, -5, 20, 2, -11]]\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, 44, -12, -28, 24],\n [-30, 3, -2, -16, 32],\n [-3, 52, -17, -27, 22],\n [21, -28, 31, -20, 4],\n [0, 42, 0, 33, 6]]\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 5x5 matrix:\n[[6, -3, 2, -16, -14],\n [-53, -39, -20, 39, 39],\n [11, -15, 6, 10, 15],\n [6, -9, -42, 24, -38],\n [-9, 23, 38, -64, -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[[-25, -66, -24, -29, -79],\n [19, 66, -24, 4, 20],\n [8, 6, 18, -6, 6],\n [6, 24, 0, 15, 29],\n [27, 12, 78, -16, 32]]?\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 5x5 matrix:\n[[-10, 4, 8, -8, 14],\n [-10, 4, 8, -8, 14],\n [22, -16, -8, 4, -22],\n [4, -16, 16, -24, 12],\n [-16, 10, 8, -6, 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[[0, 4, 6, -6, -6],\n [0, 8, 12, -12, -12],\n [0, 4, 6, -6, -6],\n [0, 12, 18, -18, -18],\n [0, -2, -3, 3, 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[[2, -1, 5, 6, -1],\n [-6, 3, -15, -18, 3],\n [-2, 1, -5, -6, 1],\n [10, -5, 25, 30, -5],\n [-10, 5, -25, -30, 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 5x5 matrix:\n[[18, -36, -36, -18, 14],\n [-23, 38, 30, 11, -13],\n [29, -26, 6, 19, 3],\n [33, -42, -18, 3, 11],\n [-24, 6, -36, -39, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-21, 22, -29, 8, 0],\n [19, 0, 21, -2, 11],\n [-18, 8, -22, 4, -6],\n [1, -30, 9, -8, -16],\n [-9, 4, -11, 2, -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[[-14, 17, 33, -1, 34],\n [6, 16, 12, 13, -17],\n [14, -20, -34, 6, -32],\n [4, 4, -6, 29, -17],\n [-25, -40, -35, -47, 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[[9, -43, -5, 2, -26],\n [31, -1, -32, 29, 4],\n [-5, 5, 2, -6, 0],\n [16, 24, -12, 24, 24],\n [-4, 0, -4, -10, -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[[0, 0, 0, 0, 0],\n [12, -10, -6, 6, -4],\n [6, -5, -3, 3, -2],\n [-24, 20, 12, -12, 8],\n [36, -30, -18, 18, -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[[3, -2, -6, -1, 5],\n [-9, 6, 18, 3, -15],\n [-6, 4, 12, 2, -10],\n [0, 0, 0, 0, 0],\n [6, -4, -12, -2, 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[[-6, 4, 8, 8, -8],\n [18, -12, -24, -24, 24],\n [-18, 12, 24, 24, -24],\n [15, -10, -20, -20, 20],\n [12, -8, -16, -16, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[31, 0, 33, -5, 0],\n [43, -20, 24, -22, 30],\n [-19, 25, 0, 16, -29],\n [14, -20, 3, -9, 18],\n [-24, 25, 21, 39, -61]]\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[[33, -15, -18, -36, -15],\n [11, 19, 14, -16, -14],\n [-12, -12, -8, 16, 12],\n [-1, 31, 26, -4, -11],\n [-16, -8, -4, 20, 13]]\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[[10, 5, 17, -29, 11],\n [-19, 5, -20, 2, 10],\n [2, -8, -8, 19, -22],\n [-18, -10, -36, 46, -28],\n [-10, -3, -17, 18, -9]]?\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, 17, 26, 40, 1],\n [-1, 31, 10, 35, 19],\n [8, -17, 4, 10, -13],\n [-45, 17, -22, -17, 33],\n [39, 16, 52, 2, -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[[-3, 3, -25, 12, -3],\n [-2, 2, -6, 4, 0],\n [-27, 27, -1, 24, 15],\n [-7, 7, -37, 20, -3],\n [5, -5, 31, -16, 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[[0, -6, -29, -5, -8],\n [4, 36, 13, -5, 20],\n [50, 40, -4, -8, 26],\n [-1, -6, 31, -8, -15],\n [34, -34, -33, -7, -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[[1, -7, 6, -6, -8],\n [-13, 5, -20, 2, 0],\n [-13, 37, -6, 24, 23],\n [20, -54, -6, -32, -26],\n [29, -17, 62, -12, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-23, -48, 0, -18, 41],\n [-16, 22, 30, 32, -6],\n [-8, -17, 11, -44, 4],\n [26, 15, -16, -10, -17],\n [14, 28, 4, -20, -36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-14, 26, 17, 6, -17],\n [-48, 0, 36, 2, -36],\n [12, 12, -6, 2, 6],\n [50, 10, -35, 0, 35],\n [2, 34, 7, 7, -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[[10, 0, -5, 10, 10],\n [37, 18, 22, 1, -44],\n [25, 10, 10, 5, -20],\n [12, 0, -6, 12, 12],\n [-34, -16, -19, -2, 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[[9, -28, -8, 0, -5],\n [20, 36, -8, -3, -10],\n [-21, -5, -25, -3, -16],\n [-2, 55, 3, -2, -1],\n [-9, 54, 2, -2, -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[[-32, -37, -4, 29, -11],\n [-6, 6, -24, 6, 36],\n [28, 36, 18, -18, -14],\n [2, 8, 38, 20, -6],\n [-28, -33, 32, 45, 17]]?\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, -4, 6, -4, 17],\n [-45, -3, 22, -17, 25],\n [-35, -11, -6, 7, 31],\n [0, 3, 8, -7, -4],\n [30, 9, 4, -5, -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 5x5 matrix:\n[[53, 21, -32, -39, 2],\n [0, -2, -16, -8, -14],\n [-34, 18, -11, 16, -40],\n [12, -2, 14, 0, 22],\n [52, -10, 15, -22, 54]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, -15, -6, 0, -9],\n [-3, 15, 6, 0, 9],\n [5, -25, -10, 0, -15],\n [-4, 20, 8, 0, 12],\n [-1, 5, 2, 0, 3]]\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, -7, -30, -2, -19],\n [-19, 6, 35, -4, 22],\n [15, -15, -3, -42, -3],\n [14, -6, -22, -4, -14],\n [24, -6, -48, 12, -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[[24, 32, -18, -6, 16],\n [-17, -34, 24, -1, -8],\n [4, -24, 32, 17, -9],\n [47, 42, -16, -25, 44],\n [-13, -10, 8, 32, -33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -4, -4, 20, -20],\n [0, 6, 6, -30, 30],\n [0, -6, -6, 30, -30],\n [0, -1, -1, 5, -5],\n [0, 6, 6, -30, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[10, 22, 2, 21, -1],\n [42, 32, -33, 31, 13],\n [-11, 3, -12, -42, -43],\n [-2, 0, -5, 14, -11],\n [-1, -43, -6, 0, 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 5x5 matrix:\n[[27, 61, 73, -29, -12],\n [-5, 19, 11, 38, 19],\n [1, 13, 18, 19, 5],\n [-1, -11, 11, -1, -34],\n [-7, -17, -36, -24, -10]]\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 5x5 matrix:\n[[-29, 1, -22, 21, 32],\n [5, -19, 28, -42, 22],\n [4, -20, 5, 0, 13],\n [-28, -26, -30, 49, -22],\n [28, -16, 47, -62, -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[[-2, -3, 6, -5, -3],\n [-6, -9, 18, -15, -9],\n [-8, -12, 24, -20, -12],\n [8, 12, -24, 20, 12],\n [6, 9, -18, 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[[-5, -70, -14, -44, -62],\n [24, -38, -39, -10, -59],\n [11, -34, -31, -38, -39],\n [-5, -60, -22, -29, -55],\n [42, 11, -32, 11, -25]]?\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, 4, -4, 10, -1],\n [25, 31, 24, 17, -27],\n [-26, -2, 12, -16, -3],\n [-4, 8, 12, -2, -9],\n [-56, -32, -8, -36, 22]]\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, 38, 14, 15, -33],\n [-52, -64, -25, -12, 57],\n [3, 10, 11, 9, -5],\n [7, -36, -31, -42, 20],\n [10, -6, -8, -15, 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[[4, -17, 12, -4, -30],\n [24, 2, -6, 2, -24],\n [0, 16, -12, 4, 24],\n [-4, 9, -6, 2, 18],\n [-4, 21, -15, 5, 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[[0, 0, 0, 0, 0],\n [-26, -31, 10, 27, 23],\n [12, 18, 36, -42, 30],\n [-10, -13, -8, 19, -3],\n [6, 5, -26, 11, -29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-24, -13, 5, 31, -24],\n [-21, -2, -1, 10, 5],\n [-6, -9, 1, -1, 12],\n [26, 33, -26, -26, -25],\n [-16, -28, 18, 32, -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[[20, -19, -2, -23, -5],\n [-13, -3, 7, 16, 9],\n [-1, -22, 29, -15, -4],\n [11, -6, -5, -11, -3],\n [-12, 16, -8, 20, 6]]\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[[-1, 1, 11, 3, -4],\n [15, 9, -13, -21, 12],\n [-6, 0, 28, 12, -12],\n [-32, -22, 10, 42, -20],\n [7, -1, -39, -15, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-45, 9, 30, 18, 15],\n [-34, 18, 43, -20, 7],\n [-49, -3, 15, 6, 38],\n [-34, 12, 26, 55, -9],\n [4, -12, -11, -80, 39]]\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, 43, -8, 28, 4],\n [42, 36, -6, 34, 15],\n [4, 11, 20, -7, -35],\n [-6, 29, -16, -48, -5],\n [46, 40, -8, 16, 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[[-25, 0, 13, -40, -12],\n [5, -17, 11, -9, -18],\n [-15, -9, 15, -33, -18],\n [-20, -22, 28, -54, -36],\n [25, 0, -13, 40, 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 5x5 matrix:\n[[-6, -5, -2, -2, 0],\n [-12, -10, -4, -4, 0],\n [-36, -30, -12, -12, 0],\n [-12, -10, -4, -4, 0],\n [-30, -25, -10, -10, 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 5x5 matrix:\n[[-4, -6, 2, 0, 12],\n [4, 6, -2, 0, -12],\n [-10, -15, 5, 0, 30],\n [10, 15, -5, 0, -30],\n [6, 9, -3, 0, -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[[50, -14, 46, -28, -12],\n [72, -6, 13, 4, 34],\n [-55, 34, -16, -24, -40],\n [-73, -44, 20, 0, -38],\n [-57, -10, -11, 2, -17]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[49, -40, 14, 16, 3],\n [-28, 30, 14, -20, 23],\n [3, -32, -4, 34, -16],\n [-52, 10, 10, 7, 12],\n [33, -10, 10, 4, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-36, -30, -27, 30, -21],\n [25, 28, 46, -2, 11],\n [-7, -17, -36, 11, -25],\n [15, 20, 38, 2, 9],\n [-22, -25, -35, 21, -25]]\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[[-5, -30, -5, 10, -40],\n [4, 42, -68, 33, 54],\n [53, -42, -10, -84, -18],\n [8, 24, -82, 40, 30],\n [-22, -24, 41, -20, -21]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[2, 4, -4, 8, 10],\n [5, 0, -25, 30, 25],\n [-1, 6, 14, -12, -5],\n [5, 16, -1, 14, 25],\n [0, -2, -3, 2, 0]]\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, -16, 0, -7, 34],\n [6, -16, 3, -1, -8],\n [2, -32, -14, 17, -2],\n [-26, 48, -7, 7, -4],\n [-27, 59, 0, 0, -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 5x5 matrix:\n[[18, -14, -9, -46, 56],\n [33, -3, 17, -4, 4],\n [-3, 13, 35, 68, -79],\n [-36, -16, -26, -20, 25],\n [-3, -27, -21, -27, 24]]\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[[8, -1, -19, -13, -19],\n [6, 9, 5, 14, 3],\n [-16, 29, 23, -7, -25],\n [13, -32, -14, 16, 40],\n [17, 27, 1, 20, -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[[-81, -60, -39, 47, 60],\n [-23, -8, -25, 0, 22],\n [68, 6, 81, -99, 3],\n [-40, -36, -14, 13, 32],\n [-65, -32, -47, 81, 8]]\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 5x5 matrix:\n[[-66, -30, 6, 12, 36],\n [38, 15, 2, -5, -20],\n [-24, 5, -36, -9, 8],\n [-5, 0, -5, -1, 2],\n [-12, -10, 12, 6, 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[[-18, -11, -10, 25, -3],\n [48, 76, 18, 24, 24],\n [-15, 25, 48, 56, -12],\n [-3, -16, -10, -15, -15],\n [-38, -71, -17, -39, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[57, 33, 29, 30, -19],\n [7, 23, -37, -14, 27],\n [-15, -30, 38, 12, -28],\n [-21, -23, 43, 24, 7],\n [3, 4, 23, 21, 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[[-5, 45, 7, -9, -7],\n [48, 0, 30, -54, -30],\n [-38, -10, -26, 46, 26],\n [25, 15, 19, -33, -19],\n [-11, 35, 1, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-28, -18, -52, 42, -12],\n [-12, 48, 12, 18, -18],\n [-8, -7, -16, 12, -3],\n [26, 0, 38, -39, 15],\n [-22, -16, -42, 33, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-51, 6, 27, 1, 12],\n [72, 27, -13, 16, 31],\n [-51, -54, -1, -7, -56],\n [12, -34, -34, -23, -51],\n [72, -3, -27, 12, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1, 4, -3, 3, 1],\n [-1, 4, -3, 3, 1],\n [0, 0, 0, 0, 0],\n [-1, 4, -3, 3, 1],\n [-3, 12, -9, 9, 3]]?\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, 33, 42, -40, 6],\n [-19, -1, -3, 11, 24],\n [-14, 34, 42, -34, 24],\n [2, 14, 18, -18, 0],\n [-50, 13, 12, 10, 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, 2, 25, 34, 24],\n [41, -28, 31, 4, 36],\n [21, -30, 21, -12, 24],\n [-10, 35, -60, -21, -34],\n [56, -22, 16, -2, 36]]\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, -47, -61, -14, -25],\n [28, -8, 17, 25, 5],\n [6, -33, -30, 3, -6],\n [10, 11, -2, -13, 22],\n [-16, -16, -11, 5, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, -6, 10, 4, -4],\n [3, -9, 15, 6, -6],\n [-5, 15, -25, -10, 10],\n [-4, 12, -20, -8, 8],\n [-3, 9, -15, -6, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, 10, 25, -31, -20],\n [-36, 37, -30, -13, -51],\n [14, -13, 18, 23, 20],\n [-31, -18, -31, -58, -18],\n [-8, 31, -2, 6, -27]]\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 5x5 matrix:\n[[6, -2, 8, 12, 4],\n [18, -6, 24, 36, 12],\n [15, -5, 20, 30, 10],\n [18, -6, 24, 36, 12],\n [-15, 5, -20, -30, -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[[-6, 2, 2, -4, -12],\n [15, -7, -19, -13, 12],\n [12, -4, -4, 8, 24],\n [-10, 2, -6, -22, -32],\n [18, -10, -34, -34, 0]]\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[[-8, 24, 4, -4, 16],\n [-12, 36, 6, -6, 24],\n [-2, 6, 1, -1, 4],\n [-12, 36, 6, -6, 24],\n [8, -24, -4, 4, -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[[11, 11, 9, -3, -1],\n [18, 4, 49, -21, 25],\n [-20, 0, 38, -6, 30],\n [27, -23, 28, -26, 18],\n [-17, 25, 18, 8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[15, -32, -20, 21, 6],\n [-8, 14, 12, -23, 4],\n [1, -12, -20, 17, 14],\n [-7, -8, -24, 3, 33],\n [7, -2, 20, -22, -13]]\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[[-42, 12, 22, 19, 13],\n [48, -14, -26, -22, -18],\n [-72, 18, 30, 30, -6],\n [18, -3, -3, -6, 18],\n [12, -8, -20, -10, -54]]?\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 5x5 matrix:\n[[28, 65, -64, 21, -6],\n [-28, -33, 12, -1, 14],\n [-76, -40, 14, 8, -12],\n [-10, 26, -52, 34, 18],\n [-48, -59, 31, -18, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, -4, 2, 3, -4],\n [-2, 0, -22, -31, 12],\n [10, -21, 5, 8, -18],\n [6, -16, -14, -19, -4],\n [6, -10, 16, 23, -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 5x5 matrix:\n[[-36, 14, -12, -10, -42],\n [-22, -8, -52, -10, 26],\n [-15, -10, -45, -1, 33],\n [-6, -4, -6, 30, 18],\n [-2, -1, 4, 23, 7]]\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 5x5 matrix:\n[[4, -20, 0, -4, 4],\n [2, -10, 0, -2, 2],\n [5, -25, 0, -5, 5],\n [3, -15, 0, -3, 3],\n [1, -5, 0, -1, 1]]\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[[-5, 26, 31, -3, 54],\n [-22, -28, -14, -4, 24],\n [16, 56, 58, -17, 40],\n [-7, 70, 59, 8, -22],\n [-15, 18, 21, -8, -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 5x5 matrix:\n[[-47, 0, -3, 37, 2],\n [27, 0, -8, 1, -8],\n [-41, -23, 3, 56, 22],\n [-9, -4, -6, 37, -4],\n [-24, 0, -9, 68, -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[[-6, -12, 2, -8, -12],\n [-18, -36, 6, -24, -36],\n [-9, -18, 3, -12, -18],\n [0, 0, 0, 0, 0],\n [-12, -24, 4, -16, -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[[33, -15, -3, -9, -18],\n [-11, 41, 61, 40, 14],\n [-41, 35, 31, 28, 26],\n [-43, 13, -7, 5, 22],\n [38, -14, 2, -7, -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[[-6, -29, -22, -21, 0],\n [21, -11, 43, 20, 126],\n [1, 27, 43, 25, 70],\n [-12, -23, -52, -49, -10],\n [-1, 46, 17, 10, 18]]\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, 0, 0, 0, 0],\n [6, -9, -12, 0, -15],\n [4, -6, -8, 0, -10],\n [0, 0, 0, 0, 0],\n [8, -12, -16, 0, -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 5x5 matrix:\n[[-8, -4, 2, 8, 12],\n [4, 2, -1, -4, -6],\n [16, 8, -4, -16, -24],\n [-12, -6, 3, 12, 18],\n [-20, -10, 5, 20, 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 5x5 matrix:\n[[15, 9, -3, -6, -12],\n [-15, -9, 3, 6, 12],\n [5, 3, -1, -2, -4],\n [-25, -15, 5, 10, 20],\n [-10, -6, 2, 4, 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[[10, 1, 4, -16, -7],\n [-2, 11, 16, -22, 7],\n [-2, 11, 16, -22, 7],\n [32, -8, -4, -26, -28],\n [-36, 6, 0, 36, 30]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[24, -16, 16, -12, -16],\n [6, -4, 4, -3, -4],\n [-6, 4, -4, 3, 4],\n [-24, 16, -16, 12, 16],\n [24, -16, 16, -12, -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[[12, -24, 6, -12, 36],\n [8, -16, 4, -8, 24],\n [6, -12, 3, -6, 18],\n [6, -12, 3, -6, 18],\n [8, -16, 4, -8, 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[[12, 6, -12, 18, 30],\n [23, 19, -3, -3, 40],\n [-4, -2, 4, -6, -10],\n [24, 18, -8, 6, 46],\n [10, 8, -2, 0, 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[[14, -39, 30, 15, 18],\n [-24, 49, -38, -43, -46],\n [-8, 36, -26, -7, -7],\n [21, -20, 20, 28, 37],\n [4, 10, -4, -2, 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[[-2, -6, 0, -2, -4],\n [-12, -36, 0, -12, -24],\n [-4, -12, 0, -4, -8],\n [6, 18, 0, 6, 12],\n [-4, -12, 0, -4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -4, -20, 16, 20],\n [1, 1, 5, -4, -5],\n [-3, -3, -15, 12, 15],\n [-4, -4, -20, 16, 20],\n [-1, -1, -5, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-25, 0, -10, 30, -20],\n [15, 0, 6, -18, 12],\n [20, 0, 8, -24, 16],\n [-20, 0, -8, 24, -16],\n [25, 0, 10, -30, 20]]\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, 21, 7, -9, 9],\n [5, -27, -9, 13, -3],\n [-1, 0, 0, 1, 6],\n [-3, 15, 5, -7, 3],\n [6, -27, -9, 12, -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[[-4, 2, -2, -10, -10],\n [-8, 4, -4, -20, -20],\n [0, 0, 0, 0, 0],\n [2, -1, 1, 5, 5],\n [2, -1, 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[[-30, -20, 10, -25, 10],\n [18, 12, -6, 15, -6],\n [-30, -20, 10, -25, 10],\n [-18, -12, 6, -15, 6],\n [18, 12, -6, 15, -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 5x5 matrix:\n[[-10, 26, 21, 5, -26],\n [-18, 12, 3, -2, -17],\n [-34, -34, -27, -17, 12],\n [-27, -21, 3, -8, 1],\n [18, -20, -39, -6, 29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-15, -15, -12, -15, -6],\n [15, 15, 12, 15, 6],\n [10, 10, 8, 10, 4],\n [-10, -10, -8, -10, -4],\n [10, 10, 8, 10, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 12, -24, 30, 9],\n [8, -16, 16, -24, -12],\n [-6, 12, -20, 26, 9],\n [4, -8, -24, 20, -6],\n [-6, 12, -16, 22, 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[[32, -19, 2, 19, 10],\n [15, 25, -23, 10, 22],\n [-18, 30, -6, -24, 12],\n [-45, 22, -17, 1, -32],\n [42, -30, 18, 6, 21]]\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[[-13, 6, 4, -9, -42],\n [-13, 3, 4, -10, -38],\n [12, 21, -6, 15, 12],\n [8, -17, 6, 9, 12],\n [14, -20, 3, 12, 36]]\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, -17, -8, -4, -4],\n [-8, 16, 24, -2, 26],\n [6, -10, -20, 3, -23],\n [-1, 9, -4, 5, -9],\n [-4, 20, 0, 8, -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[[-36, 36, 0, 36, -12],\n [12, -12, 0, -12, 4],\n [24, -24, 0, -24, 8],\n [-24, 24, 0, 24, -8],\n [-12, 12, 0, 12, -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[[26, -21, -36, 23, 6],\n [-26, 10, 6, -6, -1],\n [22, -22, -42, 26, 7],\n [-18, 12, 18, -12, -3],\n [36, -24, -36, 24, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[11, 0, 14, 4, 13],\n [10, 36, 52, 2, 2],\n [-6, 40, 36, -4, -18],\n [2, 16, 20, 0, -2],\n [-6, 40, 36, -4, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[31, -45, -3, 21, -11],\n [29, -27, 38, -39, 25],\n [2, -3, -4, 12, -6],\n [-36, -2, 4, 0, -40],\n [-44, 45, -5, -12, -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[[9, 25, 36, 29, 0],\n [19, 25, 42, 44, 10],\n [14, 26, 13, -16, -2],\n [12, 24, 31, 22, 2],\n [14, 16, 27, 29, 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[[-20, -12, -8, 46, 16],\n [-34, -41, -21, 10, -14],\n [-8, -13, -3, 2, -10],\n [-9, 7, -2, 52, 32],\n [-1, -12, -7, -44, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-14, 24, -5, 2, 21],\n [4, 1, -45, -36, -24],\n [0, -11, 42, 32, 13],\n [-22, 45, 10, 18, 49],\n [-6, 7, 5, 58, 28]]\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 5x5 matrix:\n[[8, 16, -20, 20, 0],\n [8, 14, -19, 15, 0],\n [-12, -22, 29, -25, 0],\n [10, 22, -26, 30, 0],\n [-12, -24, 30, -30, 0]]\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[[16, 0, -20, -16, -4],\n [-4, 0, 5, 4, 1],\n [-12, 0, 15, 12, 3],\n [-12, 0, 15, 12, 3],\n [20, 0, -25, -20, -5]]\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, -18, 30, 0, 18],\n [2, -6, 10, 0, 6],\n [35, 12, 4, -54, -12],\n [31, -2, 22, -42, 2],\n [-12, 36, -60, 0, -36]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[14, 5, 0, 42, -35],\n [-22, 31, -36, -16, -3],\n [-3, -21, 43, 22, -10],\n [14, 1, 12, 56, -45],\n [-29, 20, 13, 47, -52]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -6, 3, -15, 12],\n [0, 12, -6, 30, -24],\n [0, 12, -6, 30, -24],\n [0, -6, 3, -15, 12],\n [0, 10, -5, 25, -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 5x5 matrix:\n[[12, 27, -30, -21, -39],\n [-16, 34, -2, 14, -32],\n [-8, 32, -10, 4, -34],\n [12, -8, -9, -14, 3],\n [16, 21, -31, -25, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[24, -76, 6, 14, -6],\n [-33, 64, -18, -12, 4],\n [43, -42, 32, 36, 22],\n [-10, -60, -44, -3, -31],\n [-7, -58, -28, 15, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 1, 8, 10, 4],\n [-30, 14, -5, -4, -25],\n [-6, -1, 18, 22, 14],\n [30, -18, 25, 28, 45],\n [-30, 17, -20, -22, -40]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 1, -4, 1, 4],\n [-4, -1, 4, -1, -4],\n [-12, -3, 12, -3, -12],\n [0, 0, 0, 0, 0],\n [12, 3, -12, 3, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[13, -14, 28, -28, 24],\n [6, 2, 16, -6, -2],\n [-4, 17, -4, 19, -27],\n [-11, -11, -32, 5, 15],\n [-2, 25, 4, 23, -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[[-3, 0, 3, -3, 12],\n [1, 0, -1, 1, -4],\n [-1, 0, 1, -1, 4],\n [-4, 0, 4, -4, 16],\n [-4, 0, 4, -4, 16]]\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[[49, 35, 57, -20, -27],\n [26, -25, -31, -17, -25],\n [37, 31, 56, -14, -21],\n [23, -2, 19, -9, -43],\n [23, -14, -12, -19, 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[[-12, 2, -16, -14, 8],\n [-14, -5, -15, -9, 13],\n [14, 1, 17, 13, -11],\n [8, 0, 10, 8, -6],\n [-14, -9, -13, -5, 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[[-15, -9, 12, -3, 12],\n [15, 9, -12, 3, -12],\n [10, 6, -8, 2, -8],\n [20, 12, -16, 4, -16],\n [-20, -12, 16, -4, 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[[40, 0, -25, -45, 30],\n [-36, -4, 19, 37, -26],\n [-24, -8, 8, 20, -16],\n [-10, -6, 1, 6, -6],\n [18, -2, -13, -22, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[37, 30, 31, 8, -8],\n [-18, -28, -26, -36, -70],\n [-44, -37, -5, 8, -2],\n [-5, -2, -15, -4, 14],\n [43, 34, 27, 2, -13]]\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[[-9, 18, 3, -15, -9],\n [3, -6, -1, 5, 3],\n [-3, 6, 1, -5, -3],\n [9, -18, -3, 15, 9],\n [3, -6, -1, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[56, -16, -12, 30, 18],\n [2, 18, -36, 0, -30],\n [20, 4, -16, -20, 24],\n [-12, 12, -20, 20, -48],\n [31, -9, -6, 15, 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[[-24, -45, -1, -7, -12],\n [-75, -54, -23, 7, 36],\n [-42, -42, -31, -46, 11],\n [-18, 0, -47, -23, 4],\n [-46, -13, 3, 24, 49]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -6, -8, 10, 4],\n [4, -15, -4, 17, -10],\n [5, -24, -8, 28, -14],\n [-26, 24, -16, -16, 44],\n [-14, 0, -16, 8, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-24, -8, 4, -8, -8],\n [-52, 4, 18, -12, -32],\n [14, -22, -14, -2, 23],\n [-12, -4, 2, -4, -4],\n [-6, 14, 8, 2, -13]]\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 5x5 matrix:\n[[4, -8, 1, -12, 3],\n [-1, -38, -2, 7, -15],\n [54, 13, 35, 11, 7],\n [-1, 13, 4, 10, -25],\n [-11, 39, 1, -14, -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 5x5 matrix:\n[[0, 36, -6, 51, -24],\n [18, -6, 19, -31, 22],\n [-16, -36, -10, -31, 8],\n [18, 6, 17, -14, 14],\n [12, 12, 10, 2, 4]]\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[[16, 20, -12, -12, 8],\n [24, 30, -18, -18, 12],\n [20, 25, -15, -15, 10],\n [20, 25, -15, -15, 10],\n [16, 20, -12, -12, 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[[0, -12, 18, -12, -6],\n [0, 4, -6, 4, 2],\n [0, 0, 0, 0, 0],\n [0, 4, -6, 4, 2],\n [0, -4, 6, -4, -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 5x5 matrix:\n[[25, 25, -26, 14, -56],\n [21, 35, 8, -10, -24],\n [-5, -3, 3, 1, -2],\n [-13, -6, 18, -7, 14],\n [17, -6, -44, 21, -18]]\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[[12, -6, 6, 6, 6],\n [-18, 9, -9, -9, -9],\n [-6, 3, -3, -3, -3],\n [-24, 12, -12, -12, -12],\n [18, -9, 9, 9, 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[[-15, -11, -49, -10, 14],\n [17, -11, -64, 24, 16],\n [3, 11, -13, 28, -38],\n [-13, -9, 6, -6, 64],\n [-25, -12, -27, -37, 12]]?\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 5x5 matrix:\n[[-27, 17, 17, 15, -18],\n [33, 15, -53, -26, -20],\n [54, 9, 0, 39, -15],\n [13, -13, -21, -30, 24],\n [-30, -5, 48, 35, -1]]\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, -54, 5, 29, -25],\n [30, 5, -61, 42, 23],\n [2, 4, -15, 38, -21],\n [20, 15, -18, -4, 44],\n [-22, 1, 51, -52, -25]]\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[[3, -13, 24, 4, 64],\n [24, -43, -10, 6, -38],\n [33, -32, 4, -24, 11],\n [-22, 22, 23, -15, 18],\n [20, -17, -22, 6, -27]]\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, 9, -9, 18, 0],\n [0, 0, 0, 0, 0],\n [9, 9, -9, 18, 0],\n [-3, -3, 3, -6, 0],\n [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[[4, 1, -3, 8, -2],\n [10, 15, -14, -26, -16],\n [-30, 1, -1, 2, -37],\n [-14, -4, 5, 2, -6],\n [-34, -2, 7, -18, -24]]?\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, -16, 16, 18, -3],\n [-2, -24, -10, -24, -13],\n [14, 24, -2, 6, 10],\n [21, -12, -27, -45, -12],\n [1, 20, 9, 21, 11]]\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[[-4, 30, 13, 14, -19],\n [6, 18, 3, 18, -9],\n [20, -24, -20, 8, 20],\n [12, -6, -9, 10, 7],\n [-7, 42, 19, 18, -27]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-6, 3, -6, -6, 0],\n [30, -15, 30, 30, 0],\n [-18, 9, -18, -18, 0],\n [30, -15, 30, 30, 0],\n [30, -15, 30, 30, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 6, 12, -8, 2],\n [-7, -21, -30, 21, -8],\n [15, 12, 36, -23, 3],\n [28, -21, 30, -14, -13],\n [26, -3, 42, -24, -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[[41, 62, 15, -10, -7],\n [-48, -57, 1, -10, 18],\n [-17, -32, -9, 20, 31],\n [29, 51, 45, 16, 15],\n [-19, -34, -2, 28, 53]]?\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, -14, -22, 26, 7],\n [-9, 11, 13, -29, -13],\n [36, 6, 18, 6, 12],\n [33, 8, 20, 0, 9],\n [-21, -1, -7, -9, -9]]?\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 5x5 matrix:\n[[6, 20, -50, 33, 57],\n [5, -28, 12, -41, -36],\n [-16, -15, 50, -23, -12],\n [5, 21, -34, 32, 32],\n [-10, -19, 36, -28, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, 18, -3, -3, -3],\n [1, -6, 1, 1, 1],\n [-3, 14, 2, 3, -1],\n [1, -26, 26, 31, 11],\n [9, -34, -16, -21, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-20, -19, 21, -8, -47],\n [-25, -3, 29, -10, -11],\n [-10, -52, -10, -26, 12],\n [-29, -26, 36, -28, 26],\n [26, 29, 26, 23, -29]]\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, 2, -22, -46, 16],\n [-20, 12, 8, -16, -4],\n [-10, 14, 28, 16, -18],\n [30, -22, -24, 12, 14],\n [30, -22, -24, 12, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-45, 12, 8, 26, -17],\n [50, -22, 8, -42, 8],\n [-65, 26, -3, 48, -15],\n [30, -20, -6, -8, 10],\n [-25, 8, 18, -2, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-24, 70, -59, 33, 15],\n [-15, 34, -6, -7, 47],\n [5, 14, -21, 11, -14],\n [4, -41, 40, -25, 9],\n [-16, -17, -14, 18, -27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, -1, -8, 8, -4],\n [9, -9, 0, -12, -24],\n [1, -1, -8, 8, -4],\n [2, -2, 14, -19, -3],\n [9, -9, 6, -19, -23]]\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 5x5 matrix:\n[[-12, 10, 12, -6, 2],\n [36, -30, -36, 18, -6],\n [30, -25, -30, 15, -5],\n [-36, 30, 36, -18, 6],\n [24, -20, -24, 12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-10, -10, 7, 1, -4],\n [21, -2, -14, 7, 15],\n [24, -44, 14, 22, -14],\n [19, -17, 4, 11, -5],\n [16, -9, 27, 7, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-21, -24, 33, 3, -39],\n [8, 10, -17, -3, 20],\n [32, 28, -6, 14, 8],\n [11, 16, -35, -9, 41],\n [-4, -2, -7, -5, 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[[2, -2, -8, -8, -6],\n [1, -1, -4, -4, -3],\n [-3, 3, 12, 12, 9],\n [-4, 4, 16, 16, 12],\n [-2, 2, 8, 8, 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 5x5 matrix:\n[[-28, -10, -3, 14, -7],\n [-1, -12, -10, 76, 38],\n [-21, 12, -6, -36, -30],\n [8, 42, -37, 22, 11],\n [32, -12, 14, 16, 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[[-24, 33, 47, -47, -12],\n [0, -20, -4, 12, 20],\n [-15, -2, 19, -14, 23],\n [6, -33, 21, 15, -23],\n [3, 10, -31, 6, 25]]\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, -29, -24, -4, -35],\n [67, 35, 9, 20, 31],\n [47, 10, -26, 1, 7],\n [2, 1, 1, 0, 6],\n [-43, -45, 1, 1, -49]]?\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 5x5 matrix:\n[[15, -12, -3, -12, 36],\n [-25, 20, 5, 20, -60],\n [15, -14, 3, -7, 30],\n [5, -4, -1, -4, 12],\n [20, -28, 32, 14, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, 12, -1, 20, -24],\n [2, -8, 57, -35, 49],\n [20, 27, -10, -44, 32],\n [-23, 28, 20, -16, 8],\n [10, -34, 18, 49, -31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 20, 0, -4, -12],\n [-10, -25, 0, 5, 15],\n [-6, -15, 0, 3, 9],\n [0, 0, 0, 0, 0],\n [6, 15, 0, -3, -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[[-65, 38, 2, -59, 5],\n [-23, 20, -1, -26, -4],\n [38, 6, -12, 6, 14],\n [11, 13, 7, -14, -22],\n [-15, -5, -6, 9, -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 5x5 matrix:\n[[6, -3, 33, 10, 29],\n [2, 50, -63, 36, -18],\n [-26, -13, -4, -28, -23],\n [2, -19, 38, 25, 21],\n [26, -9, 37, -22, 35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[15, 9, 15, 18, -15],\n [-15, -9, -15, -18, 15],\n [30, 18, 30, 36, -30],\n [10, 6, 10, 12, -10],\n [-25, -15, -25, -30, 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[[-12, 20, -40, -56, -12],\n [-24, -26, 34, 26, 12],\n [18, 25, -35, -31, -12],\n [32, 20, -20, -4, -8],\n [-30, 6, -24, -48, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, -10, 40, -2, 39],\n [-1, -10, 40, -2, 39],\n [38, -12, -1, 27, -12],\n [-29, 6, 13, -21, 21],\n [1, 10, -40, 2, -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 5x5 matrix:\n[[-42, -30, -36, -12, 0],\n [-9, -11, -6, -4, 2],\n [-42, -30, -36, -12, 0],\n [-3, 7, -6, 2, -4],\n [-18, -22, -12, -8, 4]]\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, 20, 40, -28, -34],\n [10, -10, -5, 11, 12],\n [34, -49, -5, 50, 56],\n [0, -3, 20, -1, -4],\n [-16, 43, -40, -35, -36]]\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[[43, 33, -42, 58, -11],\n [-40, -52, 19, -58, 35],\n [25, 1, -21, -15, -8],\n [32, -3, -40, 9, -1],\n [-23, -12, 29, -28, -5]]\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, 0, -10, 24, -10],\n [33, -11, -19, 6, 10],\n [33, -23, -26, -40, -1],\n [-32, 9, 16, -10, -15],\n [-12, 6, 13, -2, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, 20, 10, 8, 19],\n [17, 4, -9, 20, 17],\n [54, 24, -44, 56, 38],\n [-17, -12, 17, -16, -9],\n [24, 40, -10, 28, 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[[11, -3, -7, -21, -2],\n [-1, 9, 1, 3, -2],\n [-3, 27, 3, 9, -6],\n [-1, 9, 1, 3, -2],\n [9, -33, -7, -21, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, -6, -38, 25, -6],\n [-2, 30, 18, 2, -2],\n [-18, 54, 34, -4, -14],\n [14, 24, 36, -11, 8],\n [17, 21, -5, 25, 13]]\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[[-8, 24, 52, 20, -44],\n [-34, 5, 14, 25, 1],\n [0, 7, 7, -22, -18],\n [-51, -2, 17, 19, -1],\n [27, 36, -10, -14, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[29, -10, 16, -58, 16],\n [2, -16, 23, -4, 34],\n [7, -50, -15, -14, -34],\n [-19, -26, 24, 38, 40],\n [0, -14, -34, 0, -57]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[28, -18, 22, -6, 22],\n [24, -17, 59, -3, 33],\n [12, -7, 45, -17, 40],\n [-7, 3, -21, 17, -29],\n [-38, 27, -33, -11, -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 5x5 matrix:\n[[9, 3, 9, 10, -29],\n [-19, -2, 13, 28, 16],\n [-12, 36, -20, -10, 15],\n [38, -8, 0, -4, -4],\n [-53, 23, 3, 22, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-27, 49, -66, 13, -40],\n [67, -57, 42, -31, 26],\n [-3, 1, 24, -2, 37],\n [20, 18, -12, -9, 25],\n [-13, -1, -6, 19, -40]]\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, -12, -9, 6, -12],\n [10, -20, -15, 10, -20],\n [-2, 4, 3, -2, 4],\n [8, -16, -12, 8, -16],\n [2, -4, -3, 2, -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[[-3, -2, -18, 2, 4],\n [38, 15, 2, 26, -4],\n [-13, 0, 53, -17, -14],\n [4, 14, 43, 9, -26],\n [29, -7, -40, 4, 32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[5, -21, 4, 40, 47],\n [-65, -15, 11, -22, -20],\n [-3, 23, -13, -14, -54],\n [13, -9, -1, 25, 40],\n [-17, -29, 12, 34, 27]]\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, 18, -6, -12, 18],\n [-6, -6, 2, 4, -6],\n [-6, -6, 2, 4, -6],\n [6, 6, -2, -4, 6],\n [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[[20, -28, -36, -30, 24],\n [13, 1, -13, -22, 28],\n [12, 15, 5, 1, -16],\n [10, 8, -12, -36, 68],\n [-18, -34, 16, 2, 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[[-6, 8, 2, 2, -6],\n [3, -4, -1, -1, 3],\n [-9, 12, 3, 3, -9],\n [15, -20, -5, -5, 15],\n [12, -16, -4, -4, 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, -13, 6, -39, -4],\n [-28, -11, -21, 12, 7],\n [23, 2, 17, -45, -16],\n [-24, -8, -17, 27, 13],\n [50, -6, 52, 6, 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 5x5 matrix:\n[[-4, 9, 24, 0, 11],\n [8, -11, -20, 28, 27],\n [4, -9, -24, 0, -11],\n [-10, 14, 26, -34, -32],\n [-7, 8, 11, -31, -35]]\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 5x5 matrix:\n[[-2, -12, 8, -4, -48],\n [-9, -24, 6, 12, -6],\n [11, 34, -12, -10, 40],\n [-8, -26, 10, 6, -38],\n [15, 42, -12, -18, 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 5x5 matrix:\n[[3, -5, -11, -3, 30],\n [55, -32, 4, -98, 48],\n [-59, 58, -41, 16, 34],\n [-28, 23, -16, 20, 10],\n [26, -25, 38, -7, -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[[38, 5, -10, -38, -19],\n [20, -10, 8, -20, -22],\n [-26, 5, -2, 26, 21],\n [-40, -20, 26, 40, 6],\n [-2, 25, -26, 2, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, 3, 1, -6, -6],\n [4, -6, -2, 12, 12],\n [-4, 6, 2, -12, -12],\n [10, -15, -5, 30, 30],\n [-8, 12, 4, -24, -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[[21, 11, 13, 50, -23],\n [10, -2, -39, -14, 8],\n [-5, -1, 23, 5, 39],\n [-4, 18, -23, 5, -16],\n [10, -14, 37, 17, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[12, -4, 2, -6, 6],\n [24, -8, 4, -12, 12],\n [36, -12, 6, -18, 18],\n [-36, 12, -6, 18, -18],\n [6, -2, 1, -3, 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[[14, -8, -11, -15, 9],\n [40, -32, 4, -2, 42],\n [-28, -16, -10, -12, 30],\n [-6, -14, 16, 8, 9],\n [-38, 46, -14, 45, 18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, 36, 12, -21, -23],\n [8, 26, 9, 1, -9],\n [21, 9, -15, 6, -6],\n [-3, 21, 12, -38, -23],\n [-6, -6, -41, 26, -31]]\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[[9, -13, 23, -19, 12],\n [-39, -49, 14, -19, 3],\n [-19, -32, 13, -20, 11],\n [-23, -22, -4, -10, 8],\n [-20, -29, -29, -59, 86]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[24, -4, 20, -24, -20],\n [22, -23, -9, 6, -35],\n [-23, -1, -26, 30, 15],\n [41, -31, 0, -6, -55],\n [12, -31, -31, 30, -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[[6, 24, -18, 12, 24],\n [3, 12, -9, 6, 12],\n [4, 16, -12, 8, 16],\n [1, 4, -3, 2, 4],\n [4, 16, -12, 8, 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[[-12, -12, -27, -18, 9],\n [32, 16, 12, 8, -36],\n [-10, -12, -30, -20, 6],\n [28, 16, 18, 12, -30],\n [-10, 0, 15, 10, 15]]\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, -15, 12, 25, -9],\n [-29, -9, 45, -15, -2],\n [25, 22, -75, 4, 15],\n [15, 4, -3, 4, -13],\n [4, 28, -6, -30, -24]]?\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, 0, 20, -20, -15],\n [20, 0, -20, 20, 15],\n [16, 0, -16, 16, 12],\n [-8, 0, 8, -8, -6],\n [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[[-1, -4, 20, -14, 12],\n [-6, -29, 61, -56, 33],\n [-4, -6, -17, 14, -22],\n [-11, -10, -18, 30, -43],\n [11, 19, 6, -12, 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[[-5, 19, -26, 24, 9],\n [16, 5, 6, 45, 15],\n [5, -6, 4, 9, -6],\n [0, -7, 9, -14, -4],\n [4, 11, 22, -13, 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[[32, -18, -36, 44, -6],\n [19, 9, -16, 71, 0],\n [-12, -20, 23, -65, -33],\n [-11, -9, 16, 1, 18],\n [-8, 52, -11, -23, 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[[11, 3, 21, -49, -26],\n [49, -55, -10, 13, 49],\n [-22, 34, -4, -6, -38],\n [-6, -3, 22, -29, -30],\n [-36, 34, 18, -16, -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[[-2, 20, 6, -14, 4],\n [-12, 8, 12, -12, 16],\n [8, 4, -6, 2, -10],\n [-11, 40, 18, -32, 17],\n [-9, 6, 9, -9, 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[[6, -22, 48, -22, 4],\n [5, -16, 25, -12, 0],\n [-10, -20, 2, -4, 0],\n [-16, -37, 1, -2, 3],\n [-5, 9, -4, -10, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[10, -10, 10, -26, 6],\n [-6, 2, -4, 8, -2],\n [16, 22, 6, 34, 6],\n [8, -9, 10, -10, 15],\n [-8, -17, -7, -27, -7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[38, 44, -17, 31, -39],\n [30, 21, -26, 12, -14],\n [-27, 3, 9, -41, 0],\n [29, 8, -7, 10, 4],\n [-7, -4, -14, -42, 15]]\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, -10, 33, 23, 17],\n [-6, -18, 16, 26, 4],\n [-13, -31, 0, 35, -10],\n [-9, -21, -2, 23, -8],\n [-4, -13, 15, 20, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-34, 29, 54, -7, -36],\n [-29, -34, -70, 61, 1],\n [32, 49, 64, -82, -18],\n [20, 29, 16, -56, 1],\n [0, 37, 10, -53, -14]]\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 5x5 matrix:\n[[33, -24, 2, -15, -24],\n [8, -17, -29, 9, 6],\n [-31, 20, 17, 6, 16],\n [-6, 9, 27, -9, -6],\n [31, -11, -3, -12, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, -3, 15, -15, -21],\n [26, 17, 14, -22, -2],\n [42, 51, -14, -8, 18],\n [-22, -41, 12, 4, -44],\n [42, 52, -9, -13, 27]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, -46, 31, -8, -10],\n [30, 30, -39, 24, 42],\n [1, 22, -16, 5, 7],\n [7, 34, -28, 11, 17],\n [-39, -18, 36, -27, -49]]\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, 12, -12, -19, -13],\n [-7, -9, 9, 37, 29],\n [20, -24, 24, -27, -29],\n [15, -15, 15, -25, -25],\n [10, -18, 18, -4, -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 5x5 matrix:\n[[6, 4, 7, -34, 24],\n [-12, 3, 30, 24, 18],\n [0, 2, 8, -8, 12],\n [4, 3, 6, -24, 18],\n [-10, -5, -5, 50, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-34, 4, 4, -34, -20],\n [-19, -17, -8, 4, -7],\n [-1, 22, 18, -43, -10],\n [28, -72, -20, 42, 12],\n [0, -61, -48, 35, 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 5x5 matrix:\n[[-32, -13, 4, -42, -51],\n [-8, -11, -49, 23, 12],\n [57, 19, -16, 72, 32],\n [28, 15, 19, 5, 6],\n [-27, -18, -59, -21, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[24, -49, -74, 19, 27],\n [12, -34, -11, 16, 36],\n [-8, 4, -11, -26, -38],\n [26, 1, 45, -75, -55],\n [39, -11, -37, -22, -18]]?\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[[-1, 12, 4, 19, -36],\n [0, 9, 3, 9, -18],\n [-8, -39, -13, 17, -18],\n [-3, -3, -1, 18, -30],\n [-11, -48, -16, 29, -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[[-20, 20, 30, 15, 10],\n [-8, 8, 12, 6, 4],\n [-16, 16, 24, 12, 8],\n [8, -8, -12, -6, -4],\n [-12, 12, 18, 9, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[15, -4, -11, 9, 3],\n [31, 43, -49, -41, 5],\n [-6, -10, 20, 8, -4],\n [-33, -18, -2, 8, -16],\n [-8, 25, -9, -15, 31]]?\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[[-2, 2, 0, -2, 0],\n [-25, 30, 10, 5, 25],\n [-5, 4, -2, -11, -5],\n [-20, 26, 12, 16, 30],\n [5, -4, 2, 11, 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[[-16, 16, 20, -24, -4],\n [-30, 42, 39, -18, 9],\n [-14, -2, 0, -14, -16],\n [-7, -11, -9, -8, -17],\n [11, -35, -40, 27, -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 5x5 matrix:\n[[10, 20, 0, 0, 30],\n [-6, -12, 0, 0, -18],\n [12, 24, 0, 0, 36],\n [4, 8, 0, 0, 12],\n [8, 16, 0, 0, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-37, 14, -30, 7, 22],\n [15, -32, 16, 4, -16],\n [-1, 15, -26, 33, 11],\n [-3, -21, 18, -21, -9],\n [-28, 24, -38, 23, 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[[24, -6, -20, -2, 26],\n [-52, 0, -28, -29, 48],\n [40, -2, 21, 39, -39],\n [12, -4, 26, 60, -34],\n [-76, 1, -51, 19, 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[[21, 3, -12, 25, 18],\n [11, 21, 20, -1, 14],\n [13, -31, -54, 42, 6],\n [25, -22, -51, 51, 18],\n [12, -34, -70, 59, 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[[-18, -29, -6, -20, -31],\n [-24, 9, -30, 21, -12],\n [-10, -32, 4, -27, -27],\n [30, 5, 30, -10, 25],\n [-18, -3, -18, 6, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-14, -26, -32, 2, 34],\n [8, 39, 35, 34, -30],\n [-16, -6, -2, -40, 18],\n [-12, 31, 23, 22, -2],\n [5, 13, 4, 47, -8]]?\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, 0, -30, 20, -10],\n [-6, 0, -12, 8, -4],\n [-6, 0, -12, 8, -4],\n [15, 0, 30, -20, 10],\n [-6, 0, -12, 8, -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[[32, -24, -5, -22, 25],\n [-30, 13, -36, 33, -6],\n [-2, 1, -2, 1, -8],\n [23, -12, 19, -22, 13],\n [20, -21, -30, -13, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-17, 12, -11, 5, 2],\n [10, -36, -1, 25, -13],\n [36, 11, 32, -39, 1],\n [22, -28, 12, -4, 6],\n [-30, 36, -18, 18, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-6, 15, 68, 20, -6],\n [-53, -43, 22, -5, 23],\n [-41, 12, 44, 57, 51],\n [-10, 33, 11, 58, 42],\n [3, -24, -16, -37, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-16, -14, 16, -26, 40],\n [28, 2, -30, 27, -28],\n [16, -31, -31, 11, -22],\n [-12, -18, -4, 5, -48],\n [16, -11, -27, 23, -46]]\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 5x5 matrix:\n[[-12, 12, -24, 24, -18],\n [-6, 6, -12, 12, -9],\n [-6, 6, -12, 12, -9],\n [-10, 10, -20, 20, -15],\n [4, -4, 8, -8, 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 5x5 matrix:\n[[-14, 33, 49, 15, -18],\n [12, 12, -27, 7, -4],\n [29, -1, -13, 25, -20],\n [-22, 26, -23, -17, 16],\n [-13, 16, -36, -26, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-18, 30, -3, -6, 3],\n [-24, 45, -3, -4, 10],\n [6, -43, 2, -14, -31],\n [-12, -13, -1, -20, -28],\n [6, -27, 9, 4, -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[[0, -18, 30, 60, 0],\n [1, -8, 19, 34, 0],\n [-4, -16, 4, 24, 0],\n [4, 4, 16, 16, 0],\n [10, 22, 20, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-34, 34, 2, 10, -6],\n [31, -38, 43, 49, -4],\n [-6, -3, 9, 18, -3],\n [7, 10, -22, -39, 6],\n [15, -12, 12, 9, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[6, 0, 1, 5, -1],\n [6, 0, 1, 5, -1],\n [36, 0, 6, 30, -6],\n [-30, 0, -5, -25, 5],\n [30, 0, 5, 25, -5]]\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[[-31, -27, 35, 15, 0],\n [-1, 16, -27, -1, 7],\n [-6, -3, 1, -33, 16],\n [2, 21, -33, 21, -2],\n [51, 17, -10, 10, -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 5x5 matrix:\n[[12, 30, -36, 24, 60],\n [14, 31, -7, 27, 4],\n [8, 14, -6, 10, 4],\n [0, 10, 16, 16, -24],\n [-10, -30, 22, -28, -38]]\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[[53, 15, 60, 3, 7],\n [-3, -48, -66, 0, -27],\n [40, 3, 46, -8, -2],\n [-34, -13, -6, -41, -28],\n [-6, -29, -38, 16, 24]]\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, -62, -36, 51, 52],\n [-34, -1, -5, -1, 22],\n [21, 8, 31, 0, -54],\n [34, 30, 4, -27, -20],\n [2, 4, 38, 5, -56]]\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[[11, 16, 13, -9, 23],\n [8, 18, 9, -7, 24],\n [5, -22, 8, -2, -23],\n [15, -24, 21, -9, -21],\n [-17, -12, -21, 13, -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[[4, -12, -16, 4, -8],\n [5, -15, -20, 5, -10],\n [0, 0, 0, 0, 0],\n [-2, 6, 8, -2, 4],\n [-3, 9, 12, -3, 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[[61, 29, -17, -10, 17],\n [-55, -7, 24, 12, -74],\n [46, 12, -16, -2, 65],\n [9, 17, 6, 16, 20],\n [-19, -57, -25, -54, -65]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[7, -6, 1, -9, 3],\n [-7, 2, 7, 21, 1],\n [9, -18, 15, 1, 11],\n [-20, -3, 10, 13, -1],\n [16, 26, -36, -30, -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[[0, 25, -6, -16, 31],\n [28, -26, 30, 14, -6],\n [33, -38, 18, -8, -11],\n [-25, 15, -13, 11, -8],\n [-5, 21, 18, 29, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[13, 12, -6, 6, -21],\n [25, 36, -18, 18, -21],\n [-33, -36, 18, -18, 45],\n [-26, -36, 18, -18, 24],\n [12, 12, -6, 6, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-22, 20, -4, -12, -17],\n [-6, -4, 10, 11, -4],\n [-51, 39, 3, 36, -48],\n [16, -18, 4, -29, 20],\n [-34, 30, -4, -1, -29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 28, 12, 17, 34],\n [-12, 53, -66, -39, 23],\n [13, -3, 56, 22, -6],\n [-16, 22, -18, -18, -32],\n [13, -58, 58, 41, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 12, -12, -12, -18],\n [18, 18, 9, 12, -9],\n [-12, -14, -4, -6, 9],\n [0, 2, -2, -2, -3],\n [12, 4, 14, 16, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-14, 62, 16, -44, 10],\n [-67, -41, -9, 25, 51],\n [-9, 36, 21, -3, 13],\n [5, 7, -26, -24, -7],\n [-9, -51, 10, 32, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-55, 9, 86, -35, 15],\n [-22, 5, 31, -16, 45],\n [46, 15, -55, 15, 24],\n [-15, -2, 19, -7, 6],\n [22, 30, -4, -6, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[5, 1, -6, -4, 1],\n [25, 5, -30, -20, 5],\n [-15, -3, 18, 12, -3],\n [-30, -6, 36, 24, -6],\n [10, 2, -12, -8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 24, -16, 12, 12],\n [-4, 24, -16, 12, 12],\n [-1, 6, -4, 3, 3],\n [6, -36, 24, -18, -18],\n [-3, 18, -12, 9, 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[[-5, -24, 11, -11, 12],\n [-1, -17, 20, -16, 26],\n [12, -32, -25, 24, 60],\n [11, -13, -45, -2, -18],\n [1, 45, -30, 26, -58]]?\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, 39, 30, -29, 7],\n [-6, -4, 15, -7, 16],\n [-13, -8, 20, -16, 22],\n [-6, 30, -5, -21, -22],\n [9, -6, -25, 15, -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[[6, 2, 2, 10, -4],\n [-15, -5, -5, -25, 10],\n [12, 4, 4, 20, -8],\n [15, 5, 5, 25, -10],\n [-3, -1, -1, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-9, 15, -18, -30, -12],\n [9, -15, 0, 3, -6],\n [-21, 35, 4, -1, 18],\n [-6, 10, -10, -17, -6],\n [0, 0, -36, -54, -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[[8, 10, -7, -8, 30],\n [3, 25, -26, 14, 24],\n [-4, 40, -46, 40, 12],\n [2, -20, 23, -20, -6],\n [4, -10, 13, -16, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[45, 20, 15, 1, 23],\n [23, 0, -28, -34, -41],\n [-27, 22, -1, 41, -7],\n [-23, -24, 17, 11, -13],\n [25, -4, 18, -8, 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[[0, 0, 0, 0, 0],\n [0, -36, 20, -8, -12],\n [12, 30, -18, -6, 18],\n [-2, 22, -12, 7, 6],\n [2, 14, -8, 1, 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 5x5 matrix:\n[[1, -12, 13, 12, 6],\n [5, -4, 9, -24, 30],\n [0, -8, 8, 12, 0],\n [-9, 8, -17, 42, -54],\n [5, -2, 7, -27, 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[[0, 0, 0, 0, 0],\n [24, 16, 24, 20, 20],\n [-36, -24, -36, -30, -30],\n [36, 24, 36, 30, 30],\n [12, 8, 12, 10, 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 5x5 matrix:\n[[20, 40, 33, -3, 16],\n [-12, 58, 23, 27, 38],\n [16, -44, 1, -21, -44],\n [24, -66, -21, -39, -46],\n [48, 8, 10, -42, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-24, -20, 2, 28, 20],\n [38, 46, -33, -9, -26],\n [20, -4, 9, -27, 10],\n [-38, -30, 26, 10, 4],\n [8, 0, 12, -24, -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[[-4, -5, -3, -2, 4],\n [-20, -25, -15, -10, 20],\n [0, 0, 0, 0, 0],\n [-24, -30, -18, -12, 24],\n [-16, -20, -12, -8, 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[[-18, 18, -12, -3, 0],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [18, -18, 12, 3, 0],\n [-24, 24, -16, -4, 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[[30, 11, 16, 1, 21],\n [68, -27, -25, -41, -19],\n [4, 49, 12, 23, 27],\n [-27, 81, 18, -7, -32],\n [32, 7, 11, -35, -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 5x5 matrix:\n[[-30, 16, 44, 30, -24],\n [-12, -31, 21, -5, -13],\n [-9, 29, 11, 20, -5],\n [-6, 23, 7, 15, -3],\n [-30, 5, 45, 25, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[40, -9, 3, -51, -41],\n [41, -15, 6, 0, -4],\n [-21, 0, 5, 5, 13],\n [-48, 41, 6, -1, -30],\n [-43, 28, -8, -11, -18]]\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, -8, 1, -12, -23],\n [0, -4, 2, -8, -14],\n [13, -13, -16, 13, 10],\n [22, 14, -22, -6, -34],\n [-3, 3, 0, 13, 26]]\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[[-25, -30, 0, 15, -30],\n [-1, 12, 6, -3, -4],\n [-20, -24, 0, 12, -24],\n [-13, -42, -12, 15, -10],\n [15, 18, 0, -9, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, -12, 6, 4, 8],\n [-7, 12, 12, -10, -20],\n [9, 6, -9, 0, 0],\n [-1, 26, 9, -16, -32],\n [-10, 20, 18, -16, -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 5x5 matrix:\n[[27, -29, -30, 22, 36],\n [36, -28, -24, 8, 0],\n [30, -18, -12, -4, -24],\n [-18, 10, 6, 4, 18],\n [-27, 21, 18, -6, 0]]\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, -21, 22, -1, 4],\n [-16, -11, -5, -28, -22],\n [6, -20, 27, -35, 13],\n [22, 2, 9, -3, 30],\n [-4, -13, 17, -16, -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[[27, 34, -17, -59, 20],\n [-9, 9, -8, -42, 43],\n [-16, -12, -24, -32, 8],\n [51, 24, 9, -25, 6],\n [10, 1, 4, 12, -15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[50, -41, -16, 19, 17],\n [72, -56, -17, 10, 6],\n [-6, 23, 11, -25, 33],\n [-2, -7, -11, 32, 22],\n [-2, 5, 11, -31, -41]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-17, -7, 7, 31, 3],\n [-4, -7, 7, 4, 4],\n [-10, -24, 24, 6, 14],\n [-6, 9, -9, 18, -6],\n [-22, 7, -7, 50, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[20, -6, -5, 26, -19],\n [-12, -10, 44, 86, -24],\n [22, 14, 1, 44, -28],\n [24, -24, -21, -26, 5],\n [0, 42, -21, -58, 19]]?\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[[-44, 36, 5, -45, 35],\n [32, -36, -20, 36, -32],\n [36, -18, 15, 33, -21],\n [-8, -24, -50, 2, -14],\n [16, -12, 0, 16, -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[[28, 21, 12, -15, 0],\n [26, -14, -18, 6, 40],\n [-1, -14, -13, 7, 15],\n [45, 26, 23, -12, 32],\n [37, 35, 42, -6, 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[[-5, 0, 0, -5, 5],\n [-25, -5, -10, -10, -10],\n [-19, -5, -10, -4, -16],\n [24, 5, 10, 9, 11],\n [18, 3, 6, 9, 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[[-14, -32, 3, 17, -16],\n [-14, 53, -26, -46, 35],\n [26, 21, 52, -6, -17],\n [-2, 22, 6, -19, 8],\n [-14, 27, 2, -33, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[15, 20, 20, -25, 0],\n [8, -16, 8, 20, -20],\n [-12, -16, -16, 20, 0],\n [15, 0, 18, 0, -15],\n [-21, -8, -26, 10, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-31, 35, -6, 19, -5],\n [-24, 9, -54, -33, -45],\n [-34, 21, -54, -25, -45],\n [-28, 27, -18, 5, -15],\n [-27, 28, -12, 10, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[49, 11, -37, 4, -6],\n [31, 9, -23, 4, -2],\n [38, -18, -34, -16, -28],\n [0, -50, -10, -36, -44],\n [-38, 18, 34, 16, 28]]?\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[[44, -64, 18, -41, -4],\n [-17, 20, 17, 8, 31],\n [35, -6, 9, -1, 11],\n [-47, 27, -16, 15, -11],\n [-35, -5, 4, -9, 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[[12, -25, 5, 30, 5],\n [-27, 43, 25, -16, -16],\n [-17, 65, 5, -44, -19],\n [16, -33, -15, 12, 12],\n [-22, -8, 22, 10, 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[[36, -12, 6, 18, -12],\n [6, -2, 1, 3, -2],\n [18, -6, 3, 9, -6],\n [36, -12, 6, 18, -12],\n [-24, 8, -4, -12, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[29, 15, -3, 30, 1],\n [54, -4, 10, 6, 16],\n [26, 35, 22, 9, 5],\n [28, -36, -41, 42, -1],\n [12, 9, 15, -9, 6]]\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[[-47, 28, -29, -5, 39],\n [-8, 22, -9, -2, 1],\n [1, -18, -18, -35, 4],\n [-5, 10, -25, -17, 39],\n [6, -10, -12, -18, 16]]\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[[48, 32, -48, -60, 26],\n [-24, -8, -12, 13, 12],\n [22, 0, 0, -32, 2],\n [38, 20, -24, -52, 20],\n [-42, -38, 60, 48, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, -6, 3, 3, 3],\n [6, -6, 3, 3, 3],\n [-18, 18, -9, -9, -9],\n [18, -18, 9, 9, 9],\n [-12, 12, -6, -6, -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 5x5 matrix:\n[[5, 26, -23, 20, -14],\n [25, 40, 8, 14, 26],\n [0, 6, 6, 1, 22],\n [-15, 18, -27, 20, 10],\n [-5, 10, -16, 11, -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[[29, -29, 20, -41, -30],\n [-30, 21, -24, 45, 27],\n [-3, -12, -5, 2, -5],\n [2, -23, 4, -23, -17],\n [57, -51, 26, -43, -48]]\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, -33, 26, 43, -22],\n [34, -39, 22, 22, 3],\n [-46, 69, -40, -24, -5],\n [19, -48, 23, -17, 3],\n [2, -6, -3, -28, 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[[-19, 23, 31, 5, 33],\n [-15, 30, 10, -25, 30],\n [-7, 17, 1, -19, 15],\n [8, -22, 2, 28, -18],\n [2, -1, -5, -4, -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[[-12, -6, 2, 4, -2],\n [-18, -9, 3, 6, -3],\n [18, 9, -3, -6, 3],\n [24, 12, -4, -8, 4],\n [6, 3, -1, -2, 1]]\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[[7, 28, -25, 25, -19],\n [8, -6, -27, 19, -46],\n [30, 42, 21, -41, -24],\n [-13, 12, 18, 30, 5],\n [3, -8, -4, 19, -44]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[10, -25, -7, 33, -52],\n [-22, -3, -6, 25, 13],\n [5, -33, -7, 22, -57],\n [-30, -21, 0, 3, -9],\n [-78, -32, -16, 38, 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[[-15, 20, -25, 30, 10],\n [-9, 12, -15, 18, 6],\n [-15, 20, -25, 30, 10],\n [-18, 24, -30, 36, 12],\n [18, -24, 30, -36, -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 5x5 matrix:\n[[19, -3, 7, -3, -15],\n [17, -21, 29, 3, 3],\n [-23, -11, 15, 15, 40],\n [-27, -3, 1, 9, 31],\n [-17, -3, 9, 15, 32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-24, -4, 8, -17, -9],\n [54, 16, -11, 40, 29],\n [24, 16, 4, 20, 24],\n [42, 16, -5, 32, 27],\n [42, 4, -17, 29, 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[[-34, -8, -20, -18, -16],\n [-1, -8, 1, 3, 5],\n [-25, -24, -11, -5, 1],\n [-26, 12, -19, -22, -25],\n [8, -24, 10, 16, 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[[14, 18, -1, -5, 15],\n [18, 14, -3, 1, -3],\n [-39, -33, 6, 0, 0],\n [-24, -8, 6, -10, 30],\n [7, 1, -2, 4, -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[[8, 25, -11, 17, -4],\n [-4, -26, -8, -22, -16],\n [2, 10, 1, 8, 4],\n [6, 9, -18, 3, -16],\n [-4, 4, 22, 8, 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[[9, 0, -18, -6, -15],\n [6, 0, -12, -4, -10],\n [18, 0, -36, -12, -30],\n [3, 0, -6, -2, -5],\n [12, 0, -24, -8, -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[[33, -15, -13, -14, 15],\n [39, -12, -6, -32, 28],\n [21, -16, 6, -12, 12],\n [3, -7, 21, -12, 9],\n [15, -9, -4, -5, 6]]\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, 19, -33, 44, -19],\n [16, 20, -24, 0, -41],\n [0, -47, 29, -38, -9],\n [-20, 22, -36, 32, -34],\n [-31, -12, 7, 9, 19]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-13, 5, 8, 3, 2],\n [33, -11, -31, 24, -3],\n [39, -17, -55, 70, -23],\n [-30, 12, 39, -47, 13],\n [3, 5, 16, -37, 26]]?\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, -28, 1, -4, 5],\n [-3, -10, -15, -13, -15],\n [3, 17, 19, 24, 27],\n [21, 33, 17, 5, -3],\n [0, 4, 4, 7, 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[[-24, 12, 23, -29, 4],\n [-12, 6, 8, -32, -12],\n [-12, 6, 14, -2, 12],\n [6, -3, -7, 1, -6],\n [-6, 3, 3, -21, -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[[-5, 3, -3, -5, -2],\n [3, 5, -3, -5, 2],\n [-18, -30, 18, 30, -12],\n [9, -19, 15, 25, 2],\n [2, -8, 6, 10, 0]]\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[[-36, 24, -12, -12, -36],\n [-24, 16, -8, -8, -24],\n [-36, 24, -12, -12, -36],\n [24, -16, 8, 8, 24],\n [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[[12, 6, 20, 10, 7],\n [0, 0, -6, 24, -12],\n [-16, -8, -23, -28, -2],\n [-24, -12, -30, -60, 6],\n [4, 2, 0, 30, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[36, -24, 24, -12, 36],\n [0, 0, 0, 0, 0],\n [12, -8, 8, -4, 12],\n [6, -4, 4, -2, 6],\n [30, -20, 20, -10, 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[[-27, -14, -10, 41, 53],\n [18, -1, -43, -11, 3],\n [9, 10, 72, -61, -75],\n [26, 9, -22, -16, -21],\n [-19, 7, 49, -14, -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[[30, 25, -15, -20, 30],\n [0, 0, 0, 0, 0],\n [12, 10, -6, -8, 12],\n [-12, -10, 6, 8, -12],\n [6, 5, -3, -4, 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[[45, -3, 33, 33, -48],\n [3, 19, -17, -5, -8],\n [-6, -6, 2, -2, 8],\n [-24, -8, -8, -14, 28],\n [9, -15, 21, 12, -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[[37, 19, 10, 25, 13],\n [-4, -36, -18, -46, -12],\n [-82, -10, 38, 31, -34],\n [34, 24, -23, -2, 33],\n [24, 18, 0, 23, 33]]\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, -6, -12, 0, -8],\n [-6, 18, 36, 0, 24],\n [1, -3, -6, 0, -4],\n [6, -18, -36, 0, -24],\n [2, -6, -12, 0, -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[[-15, -30, -5, 0, -25],\n [-9, -18, -3, 0, -15],\n [6, 12, 2, 0, 10],\n [-6, -12, -2, 0, -10],\n [15, 30, 5, 0, 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[[12, 0, -16, 8, 16],\n [9, 0, -12, 6, 12],\n [6, 0, -8, 4, 8],\n [-6, 0, 8, -4, -8],\n [-18, 0, 24, -12, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-24, -12, -12, 30, 36],\n [42, 21, 24, -21, -21],\n [16, 8, 12, 22, 32],\n [-44, -22, -26, 13, 10],\n [-46, -23, -28, 5, -1]]\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[[6, 4, -10, -8, 6],\n [-15, -10, 25, 20, -15],\n [-6, -4, 10, 8, -6],\n [6, 4, -10, -8, 6],\n [-6, -4, 10, 8, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 0, -1, -6, 5],\n [36, 0, -6, -36, 30],\n [30, 0, -5, -30, 25],\n [30, 0, -5, -30, 25],\n [24, 0, -4, -24, 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[[22, -18, -27, -43, -64],\n [-45, 14, -34, -4, 9],\n [-14, 17, -44, -29, -32],\n [-19, -35, -21, -22, -27],\n [43, -19, 13, -4, -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[[-9, -28, -30, 29, -11],\n [12, 30, 36, -30, 6],\n [-20, -28, -48, 24, 16],\n [-3, -24, -18, 27, -21],\n [9, 6, 18, -3, -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 5x5 matrix:\n[[12, -36, -24, 18, -12],\n [-5, 14, 7, -1, 7],\n [-17, 46, 19, 7, 27],\n [12, -34, -18, 5, -16],\n [0, -6, -18, 39, 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[[-58, 16, 24, -31, 14],\n [40, 12, -3, 27, 40],\n [-24, -35, -30, 4, 2],\n [-26, -7, 4, -33, -28],\n [30, 23, 9, 22, 42]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[71, -18, 15, -36, -2],\n [-22, -63, 16, 22, 17],\n [-16, 44, -15, 0, 0],\n [-29, 35, -29, 13, -3],\n [17, 29, -14, -14, 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[[-5, -26, 32, -5, 3],\n [0, 36, -29, 62, 37],\n [26, 31, -26, 38, 33],\n [-14, -15, 10, -29, -24],\n [-53, 9, -22, 6, -35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-10, 12, -1, -1, -4],\n [23, -20, -30, -11, 32],\n [-2, 0, 10, 4, -8],\n [8, -8, -6, -2, 8],\n [-19, 20, 10, 3, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-9, 57, -41, 9, -29],\n [5, 25, 2, -4, -14],\n [-29, 21, 7, -23, 3],\n [1, -35, -20, 34, 4],\n [24, 18, -28, 22, -20]]\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, 25, 18, 19, -20],\n [-20, 22, 18, 16, -14],\n [20, -13, -12, -9, 6],\n [0, 9, 6, 7, -8],\n [-20, -14, -6, -12, 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 5x5 matrix:\n[[-8, -24, -20, -16, 12],\n [-8, -24, -20, -16, 12],\n [-8, -24, -20, -16, 12],\n [2, 6, 5, 4, -3],\n [2, 6, 5, 4, -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[[-6, 45, -9, 49, 15],\n [2, -19, 7, -23, -1],\n [3, -6, -12, 3, -24],\n [-1, 23, -17, 34, -13],\n [5, -16, -14, -5, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, -3, -24, -16, 6],\n [4, 10, 14, 2, -20],\n [-1, 4, 29, 19, -8],\n [5, 15, 30, 10, -30],\n [6, 17, 31, 9, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[25, -20, -30, 25, -15],\n [-25, 20, 30, -25, 15],\n [10, -8, -12, 10, -6],\n [15, -12, -18, 15, -9],\n [5, -4, -6, 5, -3]]\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[[-44, -45, 7, 0, 18],\n [1, -10, 9, 22, -13],\n [10, 72, 32, 35, 7],\n [26, 40, -32, -61, 23],\n [12, 37, 11, 19, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-11, -9, -5, 0, -4],\n [-24, -13, 12, -22, -11],\n [36, -6, -12, -12, 22],\n [-20, -33, -2, -8, -5],\n [-8, -39, -38, 12, 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[[5, 29, -40, 18, -6],\n [-23, 53, -1, 24, -15],\n [7, 49, -38, 18, -12],\n [-28, 5, 17, 18, 3],\n [-49, 10, -2, 42, 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[[37, 52, 18, -70, -57],\n [29, -44, -54, -14, -46],\n [27, -24, -24, -3, -63],\n [43, 2, -23, -26, -21],\n [-19, -28, -22, 8, 22]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-20, 10, 25, -25, -30],\n [12, -6, -15, 15, 18],\n [-4, 2, 5, -5, -6],\n [16, -8, -20, 20, 24],\n [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[[8, 6, -6, 0, 10],\n [-6, 36, 0, 0, 42],\n [-6, 27, 1, 0, 31],\n [-4, 33, -1, 0, 39],\n [-4, -12, 4, 0, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, 22, -3, 32, 26],\n [4, 23, 9, 0, 47],\n [-36, -23, 39, 16, -23],\n [34, 20, -45, 0, 8],\n [-16, -13, 15, 8, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-48, 38, -24, 6, -32],\n [32, -47, 42, -22, 10],\n [7, -14, -8, -36, -20],\n [-17, -2, -8, 16, -4],\n [-20, 15, -16, -13, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[42, 13, -59, 19, 37],\n [48, 6, -57, 18, 36],\n [-14, -44, 9, 32, 28],\n [-15, -20, 2, 46, -4],\n [15, 18, 7, -36, -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[[18, -27, 18, -19, 7],\n [-20, -4, -20, -28, -38],\n [16, -4, 16, 12, 24],\n [22, -10, 22, 10, 29],\n [12, -21, 12, -17, 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[[-2, -16, 2, -13, 11],\n [3, -12, 7, -12, -29],\n [4, 8, 12, -16, 0],\n [5, 8, 9, -7, -22],\n [-8, 10, -30, 52, 13]]?\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[[36, 0, 0, 30, -18],\n [-24, 0, 0, -20, 12],\n [24, 0, 0, 20, -12],\n [6, 0, 0, 5, -3],\n [12, 0, 0, 10, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-21, -14, 20, 23, -4],\n [-3, -36, -23, 13, -8],\n [12, 4, -8, -12, 4],\n [12, 4, -3, -12, 6],\n [6, 44, 40, -18, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0, 0],\n [-30, -30, -30, 18, -36],\n [-15, -15, -15, 9, -18],\n [-15, -15, -15, 9, -18],\n [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[[6, 3, 5, -6, 6],\n [-12, -6, -10, 12, -12],\n [-6, -3, -5, 6, -6],\n [-12, -6, -10, 12, -12],\n [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[[-16, 12, -28, 20, -1],\n [-16, 18, -16, 16, 11],\n [18, -12, 27, -16, 1],\n [8, -39, 14, -54, -38],\n [32, -3, 50, -6, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-35, 40, 1, 24, -19],\n [1, 14, 4, -28, 30],\n [14, -25, 6, 12, -19],\n [-13, 6, -10, 20, -16],\n [-16, 34, 20, -8, 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 5x5 matrix:\n[[2, -25, -32, -18, -3],\n [-32, 4, 6, 24, -18],\n [-18, -9, -11, 6, -12],\n [0, 36, 46, 24, 6],\n [-48, 6, 9, 36, -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[[0, 0, 0, 0, 0],\n [0, -12, 4, 12, 0],\n [0, 6, -2, -6, 0],\n [0, 9, -3, -9, 0],\n [0, 18, -6, -18, 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[[-18, 22, 1, 25, -18],\n [64, -57, -57, -57, 100],\n [18, -5, -26, 7, -9],\n [-44, 23, 15, 27, -58],\n [-24, 4, 22, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[30, -34, 5, 8, 22],\n [-20, 8, -40, 24, 0],\n [20, -24, 0, 8, 16],\n [-25, 20, -25, 10, -10],\n [30, -24, 30, -12, 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 5x5 matrix:\n[[13, 15, -26, 4, 1],\n [-11, -2, 4, 17, -20],\n [8, 45, -22, 3, 1],\n [45, 43, -74, 4, -23],\n [-23, -41, 42, -4, 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 5x5 matrix:\n[[8, -29, 13, -18, 4],\n [12, 28, -8, 28, 6],\n [-4, 22, 28, 18, 16],\n [0, -5, -23, -6, -12],\n [-28, -10, -40, -26, -32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-17, -14, 33, -30, 19],\n [25, -30, -9, 32, 23],\n [34, -11, -11, 34, -20],\n [-22, 5, 10, -12, 16],\n [2, 18, -34, 23, -3]]?\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, 0, 0, 0, 0],\n [30, -36, -18, 0, 12],\n [0, 0, 0, 0, 0],\n [10, -12, -6, 0, 4],\n [-20, 24, 12, 0, -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 5x5 matrix:\n[[9, -3, -15, 9, -3],\n [-18, 6, 30, -18, 6],\n [-3, 1, 5, -3, 1],\n [15, -5, -25, 15, -5],\n [9, -3, -15, 9, -3]]\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, -4, 6, 0, 0],\n [-20, -16, 24, 0, 0],\n [20, 16, -24, 0, 0],\n [25, 20, -30, 0, 0],\n [-15, -12, 18, 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 5x5 matrix:\n[[-4, -4, 20, 8, 4],\n [3, 3, -15, -6, -3],\n [-5, -5, 25, 10, 5],\n [6, 6, -30, -12, -6],\n [1, 1, -5, -2, -1]]\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 5x5 matrix:\n[[1, 12, -11, 30, 15],\n [-22, 24, 26, 24, -42],\n [4, 8, -14, 25, 20],\n [7, -4, -11, 1, 17],\n [3, 12, -15, 33, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, -6, 13, -7, -4],\n [-14, -18, -2, 2, 0],\n [-13, -12, -7, -7, -16],\n [-26, -5, -16, 4, -8],\n [-14, 0, 22, -26, -32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-20, -30, 25, -10, 20],\n [8, -10, 4, -2, 10],\n [-4, 60, -37, 16, -50],\n [-12, -7, 8, -3, 3],\n [8, -54, 32, -14, 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, -6, -2, -8, 6],\n [32, 22, 8, 14, -24],\n [34, 20, 7, 19, -21],\n [6, 21, 9, -18, -27],\n [14, 22, 9, -9, -27]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-1, -11, -38, 31, -32],\n [35, -42, 14, -23, -3],\n [-2, -17, -43, 37, -33],\n [-18, 4, -41, 41, -24],\n [24, 10, 7, -25, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-18, -26, -17, -5, -21],\n [-30, -30, -10, 10, 22],\n [24, 60, 25, 45, 25],\n [-13, 14, 9, 40, 22],\n [0, 16, -22, 50, 42]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, 1, -1, 0, -4],\n [-4, 2, -2, 0, -8],\n [-6, 3, -3, 0, -12],\n [-8, 4, -4, 0, -16],\n [6, -3, 3, 0, 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[[-19, 24, 5, 20, -20],\n [21, 0, -15, 0, 12],\n [-18, -6, 15, -5, -8],\n [-17, 6, 10, 5, -12],\n [-13, 12, 5, 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 5x5 matrix:\n[[10, -25, 10, 25, -25],\n [-8, 20, -8, -20, 20],\n [8, -20, 8, 20, -20],\n [-4, 10, -4, -10, 10],\n [-12, 30, -12, -30, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[54, 19, -34, -54, -61],\n [26, -9, -6, -26, -19],\n [-16, -16, 16, 16, 24],\n [48, 20, -32, -48, -56],\n [-12, 16, -4, 12, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, 24, 30, 24, 30],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [-2, -4, -5, -4, -5],\n [-8, -16, -20, -16, -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[[60, -31, 22, 36, 0],\n [14, 9, -16, -5, 76],\n [-45, 23, 19, 2, -62],\n [-21, 14, 1, 0, -14],\n [53, -50, 7, 8, -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 5x5 matrix:\n[[-30, 5, -30, -15, -30],\n [-12, 2, -12, -6, -12],\n [-30, 5, -30, -15, -30],\n [36, -6, 36, 18, 36],\n [-24, 4, -24, -12, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-11, 12, -9, 15, -33],\n [-16, -24, 52, -28, -32],\n [-4, -66, 12, -18, 18],\n [-1, 28, 11, -1, -15],\n [-5, -1, -11, 10, -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[[-48, 34, 6, 18, 16],\n [-74, 62, 18, 49, -17],\n [-74, 60, 28, 39, -1],\n [66, -56, -30, -39, 10],\n [-60, 46, -10, 40, -8]]\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[[5, 6, 2, 6, 1],\n [15, 18, 6, 18, 3],\n [10, 12, 4, 12, 2],\n [-25, -30, -10, -30, -5],\n [-15, -18, -6, -18, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[12, -10, -4, 10, 6],\n [-30, 25, 10, -25, -15],\n [-30, 25, 10, -25, -15],\n [36, -30, -12, 30, 18],\n [12, -10, -4, 10, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, -12, 12, -18, 18],\n [6, 24, -24, 36, -36],\n [2, 8, -8, 12, -12],\n [-3, -12, 12, -18, 18],\n [-2, -8, 8, -12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -4, -2, 1, 1],\n [0, 16, 0, -10, -26],\n [-44, -28, -22, 1, -15],\n [-32, -16, -16, -2, -18],\n [20, 20, 10, -5, -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[[12, 8, -24, -24, -16],\n [3, 2, -6, -6, -4],\n [-12, -8, 24, 24, 16],\n [-12, -8, 24, 24, 16],\n [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[[24, 36, 36, -36, -12],\n [-4, -6, -6, 6, 2],\n [16, 24, 24, -24, -8],\n [-16, -24, -24, 24, 8],\n [24, 36, 36, -36, -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[[-32, -24, 22, 18, 26],\n [32, 20, -13, -11, -23],\n [-32, -16, 4, 4, 20],\n [4, 12, -23, -18, -10],\n [44, 20, -1, -2, -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[[-40, 46, -18, 6, -14],\n [-3, 12, -13, -23, -8],\n [-46, 29, -7, 4, -7],\n [0, 13, -1, 19, -3],\n [-30, 18, -11, -34, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[11, 9, 11, 5, 39],\n [17, 12, -7, -25, -16],\n [-16, -9, -7, 5, -18],\n [-12, -26, 20, 28, -14],\n [17, 12, 11, -1, 36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, 8, 12, -6, -10],\n [-16, -6, -26, -3, 5],\n [-2, -7, -2, 9, 10],\n [12, -8, 22, 21, 15],\n [16, -14, 30, 33, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[3, -27, -2, 1, -24],\n [10, -15, 35, -5, -30],\n [-3, -36, -33, 6, -18],\n [3, -18, 3, 0, -18],\n [-6, 0, -26, 4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -15, 25, 14, -15],\n [-8, -50, 0, 18, -20],\n [-15, 41, -32, -34, 31],\n [2, -14, 31, 11, -15],\n [23, -17, 26, 28, -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[[-36, 0, 50, -21, 15],\n [-34, 32, 16, -3, 19],\n [4, -7, 9, -2, 6],\n [48, 3, -39, 27, 15],\n [43, -18, -23, 14, 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[[-12, 4, 18, 16, 28],\n [16, -7, -16, -1, -12],\n [6, -35, -31, 1, 12],\n [-16, 43, 39, -11, -19],\n [16, -12, -25, -12, -23]]\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, 34, 0, -32, -3],\n [-18, -19, -26, -20, -12],\n [15, 29, -10, -36, -9],\n [44, 28, -12, -8, -16],\n [19, 17, -27, -34, -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[[-1, 23, 6, 23, -27],\n [15, -15, 15, -15, 15],\n [-13, -7, -15, -3, 11],\n [-5, -11, -21, -21, 13],\n [-26, -20, -33, -13, 29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[20, -15, 15, 20, -20],\n [8, 24, -4, 23, -33],\n [16, 12, 4, 28, -36],\n [24, 12, 8, 39, -49],\n [24, 18, 6, 42, -54]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[36, -8, 44, -32, 0],\n [27, 24, 12, -12, 18],\n [21, 12, 14, -12, 10],\n [42, 4, 42, -32, 8],\n [33, 6, 31, -24, 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 5x5 matrix:\n[[-2, -1, 6, 2, 1],\n [-2, -1, 6, 2, 1],\n [10, 5, -30, -10, -5],\n [-10, -5, 30, 10, 5],\n [-4, -2, 12, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[32, -21, 17, 14, -5],\n [12, -21, -19, -14, -29],\n [6, -18, -24, -18, -30],\n [-16, 18, 6, 4, 18],\n [35, -15, 34, 27, 11]]\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[[36, -24, 4, 12, -16],\n [3, 22, 19, -31, -12],\n [-12, -7, -13, 16, 12],\n [3, -23, -16, 29, 8],\n [-9, 6, -1, -3, 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[[43, 20, 12, -24, 18],\n [-41, -19, 16, -5, -31],\n [0, -6, 17, 29, -26],\n [45, 20, -13, -7, 34],\n [7, 7, -36, 33, 24]]?\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[[-31, 60, 29, 22, 15],\n [-28, 4, -7, -39, -53],\n [18, -36, -18, -20, -18],\n [-5, -4, -8, -23, -28],\n [29, -50, -31, -38, -35]]\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, -2, 28, 8, -24],\n [39, -3, 33, 3, -30],\n [16, 2, -1, 19, 6],\n [-3, 3, -15, 15, 18],\n [27, 3, 0, 30, 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[[0, -6, 4, -3, -1],\n [0, -18, 12, -9, -3],\n [0, -12, 8, -6, -2],\n [0, 6, -4, 3, 1],\n [0, -30, 20, -15, -5]]?\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[[29, 12, 0, 3, 3],\n [5, -39, -34, -21, 29],\n [-12, 11, 27, 24, -36],\n [-23, -40, -10, 10, -12],\n [26, 11, -2, -31, 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[[12, -1, -13, 2, -7],\n [0, 7, -15, -12, 3],\n [0, 4, 15, 3, -3],\n [-12, -2, -12, -10, 12],\n [24, -3, -16, 9, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, 0, -5, -3, -2],\n [1, 0, -5, -3, -2],\n [1, 0, -5, -3, -2],\n [5, 0, -25, -15, -10],\n [-1, 0, 5, 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 5x5 matrix:\n[[39, 28, -1, 16, -15],\n [-4, 0, 8, 12, 36],\n [29, 20, -3, 8, -21],\n [-25, -20, -5, -20, -15],\n [61, 44, -1, 26, -21]]\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, -10, -8, 8, 4],\n [0, 0, 0, 0, 0],\n [16, 20, 16, -16, -8],\n [-4, -5, -4, 4, 2],\n [16, 20, 16, -16, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[10, -10, 12, 6, -4],\n [10, -10, 12, 6, -4],\n [-10, 10, -12, -6, 4],\n [20, -20, 24, 12, -8],\n [-15, 15, -18, -9, 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[[4, 43, 3, -27, 20],\n [-29, 10, -60, 5, 60],\n [-20, 12, -9, -51, 4],\n [-51, -23, -23, -28, 10],\n [15, 16, 43, -16, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-2, 18, -10, -8, 8],\n [10, 9, -4, 10, 2],\n [-34, -24, 10, -36, -4],\n [-4, 36, -20, -16, 16],\n [-12, 9, -6, -18, 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 5x5 matrix:\n[[-48, -24, 26, 27, 22],\n [-3, 4, 19, -11, -15],\n [-3, -12, -67, 20, 9],\n [-48, -24, -34, 17, -18],\n [-24, -16, 8, 24, 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 5x5 matrix:\n[[-25, 35, -28, -25, 42],\n [0, 36, -39, 2, 6],\n [-5, -41, 43, -27, -12],\n [-46, -5, 24, -70, 74],\n [18, 4, -13, 33, -38]]\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[[-17, -10, 15, -32, -14],\n [-1, -32, 18, -4, -32],\n [-15, -2, -3, -19, -2],\n [1, 46, -24, -25, 54],\n [-13, 4, -10, -36, 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[[-14, 0, 17, 9, 0],\n [-36, 4, 61, -3, 24],\n [-13, 38, 35, 21, -4],\n [36, 10, -43, -12, -8],\n [-13, -4, -4, 39, -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 5x5 matrix:\n[[-21, -36, 11, -1, 32],\n [-3, -4, -14, -16, -1],\n [3, 10, 25, 25, 14],\n [30, 48, -11, -9, -7],\n [22, 28, 8, 8, 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[[22, 31, 23, -2, 18],\n [-18, -10, -23, 7, -19],\n [34, 16, 14, -18, -16],\n [-12, -4, 1, 17, -3],\n [36, -20, 25, -24, -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[[10, -11, 41, -20, -45],\n [16, 14, -14, -30, -2],\n [8, 39, 1, -5, -1],\n [-4, -31, 31, 2, -27],\n [-6, -39, -11, 0, 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[[0, -4, -15, -15, 1],\n [0, 3, -40, -41, 5],\n [-37, 0, -23, -6, -28],\n [-10, -13, -43, -4, -14],\n [-30, 7, -16, 35, -31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-36, -18, -30, 12, 30],\n [30, 42, 28, 20, -34],\n [42, 39, 37, 6, -41],\n [27, 36, 25, 16, -30],\n [6, 30, 8, 28, -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, 2, -4, 8, -8],\n [-18, 3, -6, 12, -12],\n [-6, 1, -2, 4, -4],\n [36, -6, 12, -24, 24],\n [36, -6, 12, -24, 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[[-3, -18, -15, -12, 3],\n [-28, -3, -30, 18, -27],\n [15, 24, 31, 8, 7],\n [-18, 24, -2, 32, -26],\n [-23, -6, -27, 12, -21]]?\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, 20, -20, 40, -12],\n [-18, 5, -20, 0, 21],\n [-18, 11, -17, 18, 3],\n [6, 7, 11, 26, -33],\n [-24, 0, -30, -20, 48]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-36, -8, -4, 22, 54],\n [10, 10, 38, 20, -14],\n [-14, 4, 26, 18, 18],\n [6, 13, 20, 40, -21],\n [0, 5, -10, -36, -18]]?\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[[-3, -13, -6, 17, -27],\n [0, 9, 8, -24, 27],\n [15, 20, 1, 2, 18],\n [-24, 21, -9, 19, 41],\n [3, 6, -10, 31, -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[[-13, -6, 9, 19, -6],\n [-32, 30, 45, -22, 14],\n [-23, 18, 27, 2, 16],\n [18, 12, -18, -6, 28],\n [27, 18, -21, -30, 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[[-14, 1, -22, 4, 16],\n [-2, 1, 27, 17, 19],\n [38, -8, -27, -13, -19],\n [-18, 4, 3, -7, -9],\n [4, 2, 40, -4, -20]]?\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 5x5 matrix:\n[[30, -30, 12, -36, 6],\n [10, -10, 4, -12, 2],\n [-5, 5, -2, 6, -1],\n [-20, 20, -8, 24, -4],\n [30, -30, 12, -36, 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[[-6, 0, -2, 2, -2],\n [9, -9, 2, -17, 17],\n [3, 0, 1, -1, 1],\n [0, -18, -2, -28, 28],\n [-10, -24, -6, -34, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[24, -12, 0, -8, -20],\n [-18, 9, 0, 6, 15],\n [18, -9, 0, -6, -15],\n [-12, 6, 0, 4, 10],\n [-18, 9, 0, 6, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[50, 15, -25, -8, 12],\n [-50, 28, 24, 15, 32],\n [-9, -9, -51, -32, -17],\n [-4, -73, -49, -40, -18],\n [1, -55, -45, -34, 5]]\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, 12, 9, -5, -3],\n [42, 45, 0, -21, -9],\n [6, 15, -15, -8, -2],\n [-50, -45, -15, 20, 10],\n [2, 21, -33, -12, -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[[-28, 10, 49, -27, 25],\n [4, 22, -3, -23, 5],\n [-37, -6, 9, 5, -32],\n [33, -28, 32, -23, -48],\n [40, -20, 29, -27, -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[[-15, 30, -25, 15, -5],\n [12, -24, 20, -12, 4],\n [-3, 6, -5, 3, -1],\n [3, -6, 5, -3, 1],\n [15, -30, 25, -15, 5]]\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, 16, -12, -4, 16],\n [12, 24, -18, -6, 24],\n [-8, -16, 12, 4, -16],\n [-4, -8, 6, 2, -8],\n [10, 20, -15, -5, 20]]?\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[[-12, -12, -4, -16, 8],\n [15, 15, 5, 20, -10],\n [-18, -18, -6, -24, 12],\n [18, 18, 6, 24, -12],\n [9, 9, 3, 12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, -36, -26, -34, -20],\n [51, 40, 23, -19, 20],\n [20, 45, 73, 29, -23],\n [19, -9, -53, -55, 1],\n [-6, -24, -61, -37, 2]]\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, 7, -26, 40, 4],\n [30, -14, -22, 36, -26],\n [-3, -13, -7, 4, -35],\n [-28, -24, 16, -21, -29],\n [-21, -23, 14, -15, -23]]\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[[3, -18, 3, -18, -15],\n [-6, 36, -6, 36, 30],\n [3, -18, 3, -18, -15],\n [5, -30, 5, -30, -25],\n [-4, 24, -4, 24, 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[[-11, 5, -17, 26, 12],\n [-10, 9, -7, 2, -8],\n [-9, 9, 10, -34, -20],\n [-43, 29, -31, 18, -4],\n [-14, 11, -7, -2, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, 1, -6, 11, 13],\n [-16, -23, -6, -26, 10],\n [-7, -12, -6, -3, -14],\n [-12, -19, -18, 2, 24],\n [11, 22, 24, -21, 23]]\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, -24, -18, 18, 6],\n [-24, -8, 0, -24, -4],\n [10, 0, -3, 15, 3],\n [30, 20, 9, 15, 1],\n [-40, -20, -6, -30, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[5, -10, 10, 0, -5],\n [-6, 12, -12, 0, 6],\n [0, 0, 0, 0, 0],\n [-6, 12, -12, 0, 6],\n [2, -4, 4, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0, 0],\n [8, -16, -4, -20, 24],\n [-4, 8, 2, 10, -12],\n [10, -20, -5, -25, 30],\n [-8, 16, 4, 20, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-20, 5, -25, 25, -10],\n [8, -2, 10, -10, 4],\n [8, -2, 10, -10, 4],\n [12, -3, 15, -15, 6],\n [8, -2, 10, -10, 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[[6, -15, -9, 18, 3],\n [12, -30, -18, 36, 6],\n [2, -5, -3, 6, 1],\n [4, -10, -6, 12, 2],\n [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[[-24, -15, -42, 13, 2],\n [-18, -15, -47, 10, 0],\n [12, 11, 56, -3, 6],\n [-30, -16, -3, 23, 14],\n [-6, 13, 25, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-23, -14, -14, -2, 10],\n [-19, -2, 18, -10, 6],\n [16, -7, -12, -5, -9],\n [20, 38, 18, 31, 0],\n [1, 3, -2, 5, 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[[-5, -12, -6, -42, -34],\n [10, -3, -24, -33, -31],\n [5, -6, -18, -36, -32],\n [13, 6, -18, 0, -4],\n [27, 18, -30, 24, 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[[30, 25, -10, -10, 10],\n [18, 15, -6, -6, 6],\n [-30, -25, 10, 10, -10],\n [12, 10, -4, -4, 4],\n [36, 30, -12, -12, 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 5x5 matrix:\n[[-21, -32, -6, -2, 21],\n [40, 65, 22, -9, -14],\n [64, -24, 64, -20, 88],\n [-7, -43, -8, 0, 16],\n [1, -33, 12, 0, 32]]\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, 0, -6, 2, -4],\n [21, -12, -6, 10, -32],\n [34, 12, -60, 12, -12],\n [13, -6, -6, 6, -18],\n [-21, -18, 54, -6, -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 5x5 matrix:\n[[3, 5, -23, -30, 10],\n [-22, -10, 22, -20, -20],\n [8, 2, 1, 22, 4],\n [15, 9, -27, -6, 18],\n [-18, -10, 28, 0, -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[[-12, 36, -27, -21, -21],\n [-24, -54, 4, 0, -12],\n [-27, -12, -32, -7, 35],\n [19, 6, 31, 24, 18],\n [-1, -9, 21, 4, -32]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 19, -13, 11, -1],\n [12, -6, 6, -62, 6],\n [4, -5, -17, -16, 4],\n [26, -34, -8, -22, 13],\n [9, -6, 23, 41, 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[[23, -17, 14, -18, 20],\n [-10, -18, -9, 35, 25],\n [8, -30, -24, 50, 31],\n [28, 18, 7, -31, 34],\n [-22, -20, 6, 16, -17]]\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 5x5 matrix:\n[[-30, -8, -34, 10, 6],\n [-29, -28, 19, -50, -25],\n [3, 0, 0, 13, 6],\n [-14, -8, 0, 9, 0],\n [13, -12, 36, -69, -25]]\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, 4, 33, 16, 31],\n [2, -5, -32, -5, -28],\n [17, -1, -10, -6, -19],\n [-6, 2, -14, -42, -14],\n [0, -5, -16, 21, -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 5x5 matrix:\n[[-24, 10, -22, -12, 0],\n [3, -2, -52, -37, 2],\n [-12, 23, 15, 22, 8],\n [-3, 23, -25, -5, 12],\n [-18, 6, -34, -22, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 10, -5, 22, 12],\n [20, 6, 30, 16, -21],\n [-8, 4, 0, -8, -6],\n [24, -24, -10, -8, 15],\n [-40, 8, -30, -16, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[10, -3, -1, -3, 3],\n [-22, 8, 5, 36, -1],\n [4, -2, -2, -18, -2],\n [16, -6, -4, -30, 0],\n [-38, 12, 5, 24, -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[[-21, 42, 0, -42, 24],\n [-1, -34, 9, 16, -31],\n [-13, 34, -2, -30, 22],\n [-18, 32, 1, -34, 17],\n [-27, 6, 12, -30, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-15, 20, -9, -14, 13],\n [-6, -24, -22, 34, 16],\n [2, 24, 16, -31, -13],\n [-22, 32, -15, -23, 4],\n [7, 36, 36, -51, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-28, -37, -37, -13, -13],\n [35, 9, 2, -53, -86],\n [-6, -47, -38, 5, 6],\n [-29, -45, -30, 29, 50],\n [23, 0, -7, -50, -79]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0, 0],\n [3, 15, 15, -15, -15],\n [0, 0, 0, 0, 0],\n [5, 25, 25, -25, -25],\n [-4, -20, -20, 20, 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[[24, -2, 22, 25, -14],\n [-35, 15, 76, 18, 9],\n [-3, -25, 27, 16, 17],\n [11, 5, -30, -28, -45],\n [12, 42, -21, 15, 18]]\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, 31, -7, 30, -42],\n [78, -18, 61, 40, 30],\n [28, -1, 29, 22, 12],\n [35, 14, 22, 40, -33],\n [-25, 34, -23, 20, -45]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[5, -3, -4, 0, -1],\n [10, -6, -8, 0, -2],\n [-25, 15, 20, 0, 5],\n [25, -15, -20, 0, -5],\n [30, -18, -24, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -14, 1, 1, -10],\n [-12, 10, 1, -2, 2],\n [-12, 2, 5, -4, -14],\n [20, -18, -1, 3, -6],\n [36, -38, 1, 4, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, 17, 4, 33, -30],\n [12, -6, 33, 39, -2],\n [42, 31, -22, -3, 23],\n [15, -18, 8, 30, -3],\n [13, -20, -20, -16, 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[[-12, 0, 18, 18, 12],\n [4, 0, -6, -6, -4],\n [-10, 0, 15, 15, 10],\n [10, 0, -15, -15, -10],\n [8, 0, -12, -12, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-24, -2, -10, -4, 24],\n [-6, 5, -8, -23, 6],\n [-42, -6, -15, 3, 42],\n [6, 6, -3, -21, -6],\n [42, 1, 20, 17, -42]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[15, 3, -3, 0, 3],\n [25, 5, -5, 0, 5],\n [25, 5, -5, 0, 5],\n [20, 4, -4, 0, 4],\n [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[[23, 38, 4, -38, 21],\n [23, 24, -12, -24, 6],\n [18, 20, -8, -20, 6],\n [-22, -26, 8, 26, -9],\n [-1, 2, 4, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-22, 10, -6, -20, 24],\n [-13, 11, -15, -8, 18],\n [-21, 11, -9, -18, 24],\n [1, 5, -12, 5, 3],\n [6, -2, 0, 6, -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 5x5 matrix:\n[[34, -26, -20, 0, -20],\n [4, -6, 10, 0, -10],\n [-18, 22, -24, 0, 32],\n [-20, 15, 13, 0, 11],\n [-36, 24, 36, 0, 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[[-7, 39, 39, -22, -3],\n [-22, 34, 32, 22, -23],\n [4, -61, -35, -12, 23],\n [11, 22, 8, -25, 2],\n [-37, 30, 30, 59, -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[[0, 16, 12, -16, -8],\n [0, 16, 12, -16, -8],\n [0, 20, 15, -20, -10],\n [0, -4, -3, 4, 2],\n [0, -4, -3, 4, 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[[13, -32, 18, -38, 37],\n [4, 4, 4, 6, -4],\n [44, 8, 48, 20, -4],\n [-54, 0, -60, -12, -6],\n [-39, -12, -42, -24, 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[[14, -4, 28, 11, 22],\n [-6, -20, 4, -9, 6],\n [21, 30, -14, 12, 10],\n [15, 33, -8, 15, -2],\n [-28, -33, 10, -16, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -24, 6, -6, -30],\n [6, 24, -6, 6, 30],\n [6, 24, -6, 6, 30],\n [-6, -24, 6, -6, -30],\n [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[[-3, 12, -15, -12, 6],\n [15, 45, -15, -45, 10],\n [27, 18, 27, -18, -6],\n [-2, -34, 26, 34, -12],\n [15, 24, 3, -24, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[7, -1, 32, -42, -13],\n [-40, 41, 51, -16, -25],\n [-9, 5, 4, -14, -4],\n [18, -9, 3, 12, 3],\n [9, -6, 15, -30, -6]]\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, -15, 48, -21],\n [-21, 25, 3, 3, 0],\n [-26, 30, 2, 8, -2],\n [4, 0, 8, -22, 10],\n [24, -30, -6, 3, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[23, -17, -10, 5, 34],\n [-11, 11, 19, -44, -42],\n [21, -6, -11, -9, 6],\n [-22, 1, 35, -40, -20],\n [-29, -1, 48, -53, -22]]\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, 6, 9, 9, -27],\n [32, 15, 34, 16, -25],\n [-52, -3, -10, 2, 35],\n [-4, 6, 1, 19, 11],\n [16, 0, -19, 17, 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[[-23, -25, -31, -22, 5],\n [-9, 36, 30, 24, 18],\n [31, -7, 27, 10, -37],\n [-32, -16, -18, -14, 8],\n [18, 51, 25, 28, 27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[28, -6, -50, 34, 4],\n [-4, 18, 34, 0, 6],\n [10, -3, 39, -6, -17],\n [24, 12, 8, 38, 6],\n [30, 36, -18, -5, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-34, -3, -26, 40, -22],\n [12, 13, 8, 18, -21],\n [0, 18, 39, 30, -21],\n [10, 0, 3, -12, 6],\n [-8, -9, 6, -18, 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[[10, 0, -2, 12, 6],\n [-51, 24, -27, -36, 3],\n [11, -24, 35, -12, -27],\n [49, -16, 15, 42, 7],\n [20, 0, -4, 24, 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[[-13, 26, -19, 32, 9],\n [13, 2, -6, -5, -9],\n [43, 18, -28, -25, -11],\n [72, 24, -42, -42, -24],\n [-21, -18, 24, -17, 25]]\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, -6, -15, 5, -12],\n [-27, 12, -40, -3, -18],\n [-41, 66, -5, -38, 30],\n [-24, 24, -20, -12, 0],\n [-19, 24, -10, -13, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, -2, -3, 10, -21],\n [-24, 8, -23, -15, 14],\n [-28, 2, -33, 1, 38],\n [22, 7, 29, 35, -33],\n [20, 4, 24, 43, -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[[15, 32, -51, 27, 16],\n [20, 17, -45, 11, -4],\n [-10, 32, -8, 24, 16],\n [-13, -8, 5, 4, -26],\n [27, 7, -37, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[30, -15, 20, 30, -15],\n [-24, 12, -16, -24, 12],\n [6, -3, 4, 6, -3],\n [30, -15, 20, 30, -15],\n [36, -18, 24, 36, -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[[-4, 26, 2, 28, -40],\n [13, -23, -20, -39, 24],\n [6, -21, 12, -15, 30],\n [12, -9, 33, 8, 4],\n [3, 12, -3, 9, -24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-26, -6, -9, -18, 10],\n [35, 3, 53, 26, 15],\n [-18, -18, 72, 24, 54],\n [-21, 15, -12, 8, -19],\n [19, -57, 45, 22, 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 5x5 matrix:\n[[29, -10, -21, -11, 16],\n [-37, -43, 0, 8, 17],\n [-18, -33, -9, 0, 15],\n [13, 0, -3, -1, 6],\n [31, 3, -18, -12, 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[[-4, 1, 3, -6, 3],\n [2, -14, 3, -18, -15],\n [-2, 5, 0, 4, 6],\n [26, -20, -15, 18, -33],\n [16, -13, -9, 10, -21]]\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, 42, 12, 2],\n [-20, 14, 24, -18, -22],\n [2, 27, 0, -21, -9],\n [-24, 26, 42, -30, -34],\n [4, -16, 21, 12, 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[[-5, -35, -18, -19, -18],\n [-12, -7, 15, -3, -11],\n [16, -34, -18, -22, 24],\n [-2, 9, -61, -11, -22],\n [27, -55, -12, -9, 11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-36, 18, 24, 36, 12],\n [-18, 9, 12, 18, 6],\n [6, -3, -4, -6, -2],\n [18, -9, -12, -18, -6],\n [-36, 18, 24, 36, 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[[-6, 42, -6, -2, -30],\n [-15, -23, 33, 11, 37],\n [-9, 39, 0, 0, -24],\n [-18, 22, 21, 7, 1],\n [-12, -4, 21, 7, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[36, -12, -24, -30, 12],\n [30, -10, -20, -25, 10],\n [18, -6, -12, -15, 6],\n [36, -12, -24, -30, 12],\n [-6, 2, 4, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-28, -2, 44, -8, 0],\n [-8, -1, 10, -4, 0],\n [26, 4, -28, 16, 0],\n [-2, -1, -2, -4, 0],\n [-4, 1, 14, 4, 0]]\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[[13, -4, 26, -17, -7],\n [-15, 19, -8, -21, -19],\n [18, 52, -8, 8, 0],\n [9, -28, 26, -9, 1],\n [32, 11, 26, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-11, -10, 3, -19, -54],\n [21, -2, 21, 3, -48],\n [21, -2, -6, -6, -9],\n [-5, -6, -21, -19, 0],\n [-8, -8, -9, -19, -27]]\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, -15, 10, 41, -16],\n [-6, 20, -7, -6, 2],\n [-25, 36, -1, -31, 29],\n [-26, 4, 11, -6, -22],\n [-13, -7, -11, -35, 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[[32, 36, -18, 21, -22],\n [18, -20, 10, 0, -22],\n [26, 24, -5, 21, -17],\n [-44, 12, 27, 15, 55],\n [-24, 0, 33, 18, 33]]\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 5x5 matrix:\n[[-18, -36, -3, 50, 35],\n [-8, 20, -38, -44, -22],\n [-5, 15, -42, -24, -13],\n [-6, -4, -14, -3, 2],\n [-23, -19, -26, 7, 14]]\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[[-11, -18, -43, -41, -30],\n [1, -18, 1, -7, 2],\n [37, -11, -8, -3, -23],\n [16, 28, 53, 15, 47],\n [36, 37, 46, 41, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-6, -18, -17, 8, 23],\n [-6, -14, -4, 33, 5],\n [-20, 38, 12, -5, -31],\n [-50, 58, 17, 0, -43],\n [9, -6, 20, 33, -18]]\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, -8, -12, 8, 12],\n [15, -10, -15, 10, 15],\n [-6, 4, 6, -4, -6],\n [9, -6, -9, 6, 9],\n [9, -6, -9, 6, 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 5x5 matrix:\n[[-30, -30, 36, -12, 6],\n [-30, -30, 36, -12, 6],\n [0, 0, 0, 0, 0],\n [5, 5, -6, 2, -1],\n [10, 10, -12, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[25, -10, -25, -25, -10],\n [-18, 2, 26, 40, 16],\n [-61, 40, 37, -5, -2],\n [-43, 25, 31, 10, 4],\n [6, 8, -22, -50, -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[[5, 27, 22, 13, 16],\n [2, -42, -33, -19, -20],\n [14, -30, -22, -12, -8],\n [-12, 12, 8, 4, 0],\n [3, -27, -21, -12, -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[[13, -6, 57, 43, -16],\n [18, 85, -34, 42, -30],\n [-33, -46, 18, -33, 16],\n [-4, 15, -63, 4, -30],\n [-26, 4, -55, -22, -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[[-25, -25, 0, 5, 25],\n [15, 15, 0, -3, -15],\n [-20, -20, 0, 4, 20],\n [-30, -30, 0, 6, 30],\n [-15, -15, 0, 3, 15]]\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, -61, -3, -37, -58],\n [43, 4, -1, 7, 12],\n [6, -2, 12, 9, 0],\n [-70, -38, 17, -15, -34],\n [-14, -11, 19, 6, 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[[-18, -18, -32, -13, 19],\n [-28, -25, -43, -21, 24],\n [-32, -17, -6, -26, -10],\n [-16, -31, 0, -4, -14],\n [-42, -9, -36, -41, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, -23, -30, -16, -9],\n [9, -16, -9, 20, -44],\n [-15, -20, -20, -20, 7],\n [-33, -31, 4, -4, 0],\n [-3, 2, 23, 20, -10]]\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[[-17, 20, 30, 4, 0],\n [-18, 21, 39, 3, 0],\n [45, -55, 5, -25, 0],\n [10, -12, -8, -4, 0],\n [0, 1, -41, 7, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [6, -1, -6, 0, 3],\n [-36, 6, 36, 0, -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[[-1, -1, 12, -18, -3],\n [-24, 4, -6, -12, 12],\n [16, -6, 39, -42, -18],\n [-2, 2, -18, 24, 6],\n [6, 2, -30, 48, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, 29, -40, 63, -4],\n [-21, 20, -7, 66, 18],\n [10, 0, 1, 27, 14],\n [-48, 11, 76, 57, 42],\n [-33, 12, 33, 45, 24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[34, -17, 34, 38, 30],\n [-2, 6, 8, 8, -6],\n [28, -27, 2, 8, 36],\n [-7, 9, 4, 25, -9],\n [5, -4, 2, -29, 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[[-23, -5, 22, 40, -29],\n [-10, -22, -21, 14, 29],\n [1, 9, 19, 18, -4],\n [-29, -23, -7, 22, -20],\n [20, 3, -11, -6, 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[[61, -10, -18, -43, -28],\n [-12, 26, 24, -4, 14],\n [-5, -10, -15, -25, -7],\n [8, -48, -17, -60, -47],\n [31, -8, 16, 4, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-10, 4, -18, 8, 10],\n [-6, -6, 20, -26, -8],\n [30, 0, 10, 20, -10],\n [30, -3, 21, 9, -15],\n [8, -5, 21, -13, -11]]?\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, -51, 23, 7, 13],\n [40, -30, -15, -33, -2],\n [17, -11, -17, -23, 10],\n [-44, -34, -4, 31, 38],\n [-61, 13, -27, 49, 11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[25, -8, -37, -34, 42],\n [12, -42, -25, -22, 39],\n [25, -22, -25, -37, -3],\n [-41, 46, 45, 33, 3],\n [38, 6, -40, -15, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[13, -10, 1, -9, 13],\n [-4, -50, 68, 32, 28],\n [15, -25, 39, 9, 12],\n [24, -55, 84, 24, 27],\n [2, 5, -10, -6, -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[[10, 10, -10, -2, -4],\n [-25, -25, 25, 5, 10],\n [-5, -5, 5, 1, 2],\n [-20, -20, 20, 4, 8],\n [25, 25, -25, -5, -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[[30, 3, 13, 31, 15],\n [-24, 16, -23, -19, -12],\n [6, -13, 17, 7, 3],\n [-36, -6, -9, -33, -18],\n [18, -9, 24, 24, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[40, 26, -35, 0, 25],\n [42, 24, -36, 0, 30],\n [-31, -24, 28, 0, -15],\n [-29, -26, 27, 0, -10],\n [-2, 2, 1, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-24, 0, 6, 18, -12],\n [-24, 0, 6, 18, -12],\n [-8, 0, 2, 6, -4],\n [-8, 0, 2, 6, -4],\n [20, 0, -5, -15, 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 5x5 matrix:\n[[-6, -15, -52, 24, 23],\n [-1, -38, -46, 57, 8],\n [40, -16, -38, 6, 34],\n [-44, -23, -5, 42, -5],\n [-13, -1, 33, 6, -24]]\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, 5, 19, 24, -28],\n [-29, 7, -34, -28, -76],\n [-9, 28, -21, -28, -20],\n [54, -2, -37, 51, 0],\n [16, 44, -24, -18, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[7, -35, 15, 7, -31],\n [22, 18, -26, -10, -6],\n [11, 37, -29, -12, 17],\n [0, 0, 0, 0, 0],\n [-1, -11, 7, 3, -7]]\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[[26, 37, -15, -6, 31],\n [-11, -43, 9, -9, -28],\n [-39, -13, 30, 16, 15],\n [14, -48, -9, -13, -65],\n [30, 55, -16, 10, 27]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-42, -52, 32, 22, 30],\n [10, 6, -24, 12, -26],\n [-20, -30, -18, 45, 25],\n [6, 6, 8, -16, -30],\n [22, 23, -18, -10, -41]]\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 5x5 matrix:\n[[0, 18, -6, -30, 0],\n [0, 12, -4, -20, 0],\n [0, 3, -1, -5, 0],\n [0, 15, -5, -25, 0],\n [0, 18, -6, -30, 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[[-30, -10, 10, 20, -5],\n [-14, 6, -8, -6, -1],\n [30, 10, -10, -20, 5],\n [-34, -6, 5, 15, -5],\n [-22, -18, 20, 30, -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[[12, 2, -10, 4, -2],\n [-12, -2, 10, -4, 2],\n [-24, -4, 20, -8, 4],\n [36, 6, -30, 12, -6],\n [36, 6, -30, 12, -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 5x5 matrix:\n[[2, 0, 10, 4, 12],\n [0, 0, 0, 0, 0],\n [2, 0, 10, 4, 12],\n [1, 0, 5, 2, 6],\n [2, 0, 10, 4, 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[[27, -6, -25, -4, 44],\n [19, -13, -17, -24, 34],\n [-2, 1, -10, 4, 6],\n [23, -9, -5, -16, 26],\n [-2, 16, -5, 39, -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[[6, 30, -6, -36, 12],\n [4, 20, -4, -24, 8],\n [6, 30, -6, -36, 12],\n [-2, -10, 2, 12, -4],\n [-2, -10, 2, 12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 6, 36, 30, -18],\n [-6, -3, -18, -15, 9],\n [10, 5, 30, 25, -15],\n [0, 0, 0, 0, 0],\n [10, 5, 30, 25, -15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[48, 16, 4, 11, -15],\n [-12, -4, 20, -8, -54],\n [-12, -4, 16, -7, -43],\n [-48, -16, -8, -10, 26],\n [-6, -2, 22, -7, -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[[4, 12, 10, -12, -8],\n [-12, -36, -30, 36, 24],\n [4, 12, 10, -12, -8],\n [6, 18, 15, -18, -12],\n [-8, -24, -20, 24, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0, 0],\n [5, 1, 4, -1, -6],\n [-15, -3, -12, 3, 18],\n [-15, -3, -12, 3, 18],\n [-10, -2, -8, 2, 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[[-8, 20, 16, 16, -36],\n [-22, -40, -36, -11, 1],\n [20, 27, 23, 7, 7],\n [-24, 12, 26, -4, -38],\n [-36, 8, 14, 10, -64]]\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 5x5 matrix:\n[[-5, -63, -32, 59, 26],\n [44, 18, 29, -26, -41],\n [1, 48, 49, -8, -42],\n [16, -25, 20, 31, -26],\n [-14, -19, -25, 27, 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[[-47, -26, 48, -49, 25],\n [14, 11, -30, 8, 13],\n [4, -31, 6, -18, -3],\n [-1, -28, 15, -16, -8],\n [-22, -23, 21, -33, 18]]\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[[-2, 8, 10, -10, 8],\n [-6, 24, 30, -30, 24],\n [-4, 16, 20, -20, 16],\n [4, -16, -20, 20, -16],\n [1, -4, -5, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-34, -24, 15, -13, -2],\n [22, -8, 3, -9, 6],\n [-5, -55, 30, -40, 10],\n [26, -14, 6, -14, 8],\n [-12, -32, 18, -22, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-18, 6, 12, 0, -30],\n [-3, 1, 2, 0, -5],\n [15, -5, -10, 0, 25],\n [3, -1, -2, 0, 5],\n [18, -6, -12, 0, 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[[-47, 30, -11, -2, -7],\n [-47, 18, -26, 4, -37],\n [-28, 16, -6, -12, 13],\n [-30, 26, 12, 24, -37],\n [17, 8, -6, -4, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, -11, -39, 12, -7],\n [-30, -18, -69, 4, 11],\n [6, 27, -14, 22, 21],\n [-33, -30, 37, -38, 27],\n [-14, -5, -41, 16, 11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, -12, 10, 4, -10],\n [3, 18, -15, -6, 15],\n [1, 6, -5, -2, 5],\n [-6, -36, 30, 12, -30],\n [1, 6, -5, -2, 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[[-51, 13, 33, -13, 12],\n [-27, 4, 29, -38, 21],\n [-12, 7, -8, -31, -14],\n [39, -13, -13, 7, 5],\n [-42, 6, 46, 0, 31]]\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[[-9, -6, 6, -16, 6],\n [-4, 30, -9, 10, -16],\n [5, 36, -15, 26, -22],\n [-23, 36, -3, -14, -14],\n [-20, 24, 0, -16, -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[[-12, -10, 13, 0, -18],\n [0, 10, 5, 0, -30],\n [38, 50, -32, 0, 2],\n [-34, -40, 31, 0, -16],\n [40, 50, -35, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-7, -17, -24, -18, -8],\n [8, 2, -36, -2, 2],\n [-15, -8, 44, -13, 17],\n [11, 10, -10, 25, -31],\n [-11, -14, 12, -7, -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[[-1, 30, -14, 29, 0],\n [16, 11, -16, 5, 4],\n [12, -19, 0, -17, -8],\n [-3, 10, -6, 23, -26],\n [-19, 29, -2, 36, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, 12, 4, 24, 8],\n [16, -12, -4, -24, -8],\n [-20, 15, 5, 30, 10],\n [-12, 9, 3, 18, 6],\n [-4, 3, 1, 6, 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 5x5 matrix:\n[[11, -8, -19, -12, -5],\n [-46, -27, -36, -28, -35],\n [21, 35, 25, 28, 34],\n [14, 0, 15, 37, 41],\n [50, 19, 17, -15, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, 18, 4, 16, 10],\n [12, 31, 0, 13, 15],\n [-16, 1, 9, 5, -5],\n [-48, 48, 51, -54, -66],\n [8, 2, -11, 44, 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 5x5 matrix:\n[[30, -4, 5, -7, 57],\n [-11, -25, 23, -22, -9],\n [-14, 15, -4, 19, -6],\n [28, 28, 29, 9, 33],\n [6, -13, -31, -16, -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[[-8, -14, 5, 6, 5],\n [3, 16, 36, 5, -6],\n [10, 34, 29, -4, -4],\n [-14, -22, -7, 4, 17],\n [9, 2, -15, -3, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[0, 14, 22, -10, -21],\n [-39, 33, 6, 6, -13],\n [38, -27, -38, -6, -23],\n [-51, 57, 5, -8, -5],\n [-41, 17, 33, 26, -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[[-13, 31, 8, 61, -15],\n [-17, 7, 4, 37, 13],\n [19, -6, -8, -42, -22],\n [-26, -17, -10, 13, 31],\n [2, 33, 22, 51, -11]]\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 5x5 matrix:\n[[22, 6, -42, -9, 31],\n [10, -30, -4, 30, -9],\n [30, -18, -50, 3, 19],\n [-41, 24, 62, -20, -33],\n [17, -42, -14, 34, -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[[4, -36, 31, 20, 32],\n [7, 2, 45, 14, 20],\n [7, 42, -7, -32, -22],\n [2, 32, -4, -15, -17],\n [24, 24, 35, -41, 9]]\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, 10, 12, -10, 10],\n [15, 15, 18, -15, 15],\n [0, 0, 0, 0, 0],\n [-20, -20, -24, 20, -20],\n [10, 10, 12, -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[[2, 13, -28, -25, 11],\n [-9, 42, -26, -31, -3],\n [11, 16, -2, 3, 11],\n [-1, 46, -26, -27, 5],\n [16, 14, 16, 22, 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[[-11, -19, -16, -9, 19],\n [18, 54, 60, -12, -54],\n [-7, -12, -31, 35, 17],\n [-24, -17, -3, -40, 18],\n [-28, -33, -39, 0, 38]]\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[[-17, -25, 66, -6, 30],\n [-18, 22, -5, 6, 11],\n [27, 19, -1, -47, 3],\n [17, -28, 50, -32, -6],\n [59, -70, 37, -36, -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 5x5 matrix:\n[[-2, -8, 6, 6, -6],\n [6, 24, -18, -18, 18],\n [1, 4, -3, -3, 3],\n [-6, -24, 18, 18, -18],\n [1, 4, -3, -3, 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[[8, -2, -10, -12, 0],\n [-4, 1, 5, 6, 0],\n [-4, 1, 5, 6, 0],\n [12, -3, -15, -18, 0],\n [20, -5, -25, -30, 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[[-8, 16, 16, -4, -24],\n [0, 0, 0, 0, 0],\n [-4, 8, 8, -2, -12],\n [0, 0, 0, 0, 0],\n [4, -8, -8, 2, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[24, -39, 12, -28, 9],\n [-50, 46, 19, 4, 35],\n [26, 11, -12, 38, -21],\n [20, 11, -23, 30, -34],\n [-2, -15, 11, -22, 14]]\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, -30, -36, -6, -24],\n [-12, -10, -12, -2, -8],\n [12, 10, 12, 2, 8],\n [36, 30, 36, 6, 24],\n [-12, -10, -12, -2, -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[[-21, 5, -38, 22, 17],\n [7, 31, 1, 16, -6],\n [5, 13, -22, 26, 17],\n [5, 31, -16, 38, 17],\n [42, 12, 55, -10, -15]]?\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, 68, 17, -31, 49],\n [22, -9, -22, 0, -23],\n [17, -1, -27, -14, -14],\n [-23, -17, -19, -8, 2],\n [30, 32, -34, -38, 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[[58, -7, 69, -19, -5],\n [2, -4, -28, 72, -64],\n [-22, 15, -41, -44, 46],\n [-22, -3, 51, -33, 35],\n [30, -14, -62, -30, 30]]\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, 44, 30, -7, 7],\n [-4, 25, 24, -8, -4],\n [6, 40, 24, -23, -8],\n [-12, 5, 42, 6, -15],\n [-8, 46, 12, -12, 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[[6, -14, 23, 12, 7],\n [23, 60, -7, -43, 47],\n [34, 8, 4, -14, 8],\n [-18, 36, -12, -18, 24],\n [-21, 68, -50, -45, 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[[67, 25, 4, -25, -19],\n [-21, 6, -9, 17, 32],\n [-6, 35, -12, 23, 11],\n [-30, 5, 3, 23, 23],\n [50, 55, -7, 5, 29]]\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[[-9, -12, 12, -6, -13],\n [-36, -42, 24, 6, -23],\n [-66, -72, 24, 36, -18],\n [1, 0, 4, -6, -5],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 0, -38, 18, 8],\n [-20, 24, 10, 5, 36],\n [-5, -19, -5, 2, 25],\n [30, -30, -6, -7, -22],\n [7, -39, 43, -24, 13]]?\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 5x5 matrix:\n[[-24, -16, 4, 12, 24],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [36, 24, -6, -18, -36],\n [-12, -8, 2, 6, 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, 45, -8, -31, -2],\n [-12, -42, 30, -16, -2],\n [8, -27, 8, 9, -2],\n [-12, -3, 10, -15, 0],\n [-8, 27, -8, -9, 2]]\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 5x5 matrix:\n[[21, 23, 14, 13, -15],\n [-3, -33, 24, 39, 30],\n [-8, -8, -6, -6, 5],\n [-30, -42, -12, -6, 30],\n [-13, 1, -22, -29, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-10, 2, 6, 10, -8],\n [4, -20, 4, -24, 24],\n [7, 13, -9, 8, -10],\n [23, 5, -17, -13, 8],\n [-6, -18, 10, -14, 16]]\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[[31, -22, -29, 28, 27],\n [8, -12, -12, 6, -6],\n [-30, 33, 42, -30, -24],\n [5, 17, 17, 2, 19],\n [6, -5, -8, 7, 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[[3, 18, 18, 15, 6],\n [-5, -30, -30, -25, -10],\n [-3, -18, -18, -15, -6],\n [0, 0, 0, 0, 0],\n [-3, -18, -18, -15, -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 5x5 matrix:\n[[-27, -4, -10, 6, 9],\n [-34, -39, -1, -14, 32],\n [-20, -12, -14, -4, 22],\n [-46, 14, -33, 20, 9],\n [-30, 12, -20, 20, 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[[0, 0, 0, 0, 0],\n [-36, 36, -12, 6, -6],\n [-24, 24, -8, 4, -4],\n [6, -6, 2, -1, 1],\n [30, -30, 10, -5, 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[[23, 5, 29, 9, -8],\n [14, 3, 14, 2, -4],\n [-26, 7, -20, -3, 11],\n [10, -7, 12, 7, -7],\n [8, -21, -10, -7, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, 2, 0, 3, -5],\n [-18, 7, -19, -25, -15],\n [-14, 10, -8, -26, -14],\n [-3, 10, -10, 5, -27],\n [-22, -24, -44, -14, 26]]?\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, 24, 0, -18, 24],\n [0, -24, 0, 18, -24],\n [0, -16, 0, 12, -16],\n [0, 12, 0, -9, 12],\n [0, -16, 0, 12, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[13, -16, 37, -4, 3],\n [-22, 17, -61, 2, -9],\n [-8, 29, -6, 11, 10],\n [11, 8, -17, 8, 1],\n [-2, 15, 13, 6, 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[[-5, -10, 18, 12, -64],\n [7, 42, 15, -30, -9],\n [13, -54, 20, -10, 27],\n [-3, 26, -8, -2, -1],\n [9, -14, 4, -14, 37]]\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, -5, 54, -34, -10],\n [22, 1, -22, 18, 2],\n [8, -4, 24, -8, -8],\n [24, 3, -38, 26, 6],\n [16, 4, -40, 24, 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[[51, -30, -17, -16, -49],\n [-44, 26, 7, 10, 26],\n [-20, -28, -22, 8, 8],\n [-18, 18, -2, 0, -11],\n [-40, -44, -57, -33, 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[[18, 4, 14, 16, 16],\n [-20, 24, 4, 0, 0],\n [30, -36, -6, 0, 0],\n [35, -10, 15, 20, 20],\n [-18, 60, 30, 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[[57, -21, -47, 15, -29],\n [0, -11, -3, -4, -7],\n [5, -27, -37, -31, -13],\n [25, 30, -13, 20, 20],\n [49, 18, -36, 23, 6]]\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 5x5 matrix:\n[[-12, 50, -44, 36, 30],\n [-22, 25, -33, 15, -1],\n [-19, 6, -5, 39, 8],\n [-36, 13, -25, 31, -9],\n [7, 8, -3, 1, 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[[30, -26, 14, -24, 9],\n [-24, -5, -13, 12, -6],\n [66, -61, 27, -30, -3],\n [6, -50, -2, -6, -7],\n [12, 7, 11, -33, 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 5x5 matrix:\n[[-10, -20, -34, -4, -1],\n [14, 3, -3, 7, 9],\n [22, -23, -44, -7, 15],\n [-4, 18, 67, -34, -20],\n [5, 28, 28, -20, -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 5x5 matrix:\n[[24, 12, 8, 24, -12],\n [-30, -15, -10, -30, 15],\n [-12, -6, -4, -12, 6],\n [-6, -3, -2, -6, 3],\n [-12, -6, -4, -12, 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 5x5 matrix:\n[[26, 22, -6, 22, 30],\n [-43, -2, -9, -11, -45],\n [21, 23, -14, 23, 19],\n [14, -44, 12, -26, -6],\n [23, 44, -7, 35, 41]]\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[[-9, -1, 8, 3, -12],\n [9, 1, -8, -3, 12],\n [3, -13, -16, 23, 12],\n [-15, -5, 10, 11, -18],\n [-3, -2, 1, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, -20, -4, 12, -8],\n [10, 26, 1, -16, 10],\n [-21, 15, 24, -7, 8],\n [21, -39, -33, 21, -18],\n [-3, -15, -3, 9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, -3, 0, -18, -27],\n [9, 12, 3, -18, -18],\n [16, 20, 4, 0, 12],\n [2, 2, 0, 12, 18],\n [19, 24, 5, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, 30, 15, -15, 18],\n [5, 14, -4, -11, 31],\n [22, 20, -15, -10, 19],\n [42, 26, -38, -12, 25],\n [-16, -6, 7, -2, 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[[50, -40, 6, 32, -4],\n [-15, 12, 7, -8, -6],\n [-10, 8, -54, -16, 44],\n [0, 0, 22, 4, -18],\n [-25, 20, 19, -12, -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[[10, 17, 32, 34, -21],\n [0, 3, 21, 25, -23],\n [10, -23, -10, 18, 15],\n [-22, -6, 10, 1, -36],\n [14, 1, -23, -20, 41]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-33, 42, -27, 15, 39],\n [-6, 14, -12, -8, 23],\n [-27, 14, -23, 31, -5],\n [-3, -20, -13, 17, -34],\n [8, -20, 4, 4, -26]]\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 5x5 matrix:\n[[-18, 7, 0, 2, -20],\n [-16, -9, 36, 6, -14],\n [-2, 22, -18, 2, 6],\n [-5, 33, -6, 8, 15],\n [23, -38, 12, -8, 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 5x5 matrix:\n[[8, -16, -4, 16, 12],\n [-10, 20, 5, -20, -15],\n [-12, 24, 6, -24, -18],\n [12, -24, -6, 24, 18],\n [10, -20, -5, 20, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-16, 10, -6, -4, 26],\n [0, 2, 2, 28, 2],\n [9, -4, 5, 25, -13],\n [-9, 3, -6, -39, 12],\n [1, 0, 1, 9, -1]]\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 5x5 matrix:\n[[-20, 36, 16, 24, 38],\n [-17, 24, 6, 3, 55],\n [12, -37, -21, -35, -19],\n [-4, -8, -12, -28, 42],\n [19, -27, -19, -42, 33]]\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 5x5 matrix:\n[[46, 6, -44, 28, 20],\n [48, -27, -12, 12, 33],\n [-68, 12, 44, -32, -40],\n [12, -13, 4, -4, 3],\n [-8, -13, 19, -6, 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[[0, 0, 0, 0, 0],\n [30, -25, 30, 15, -25],\n [18, -15, 18, 9, -15],\n [-36, 30, -36, -18, 30],\n [-36, 30, -36, -18, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 24, 0, 24, -24],\n [-4, -16, 0, -16, 16],\n [-1, -4, 0, -4, 4],\n [-4, -16, 0, -16, 16],\n [2, 8, 0, 8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 24, 16, -24, 8],\n [12, -24, -16, 24, -8],\n [-12, 24, 16, -24, 8],\n [18, -36, -24, 36, -12],\n [15, -30, -20, 30, -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[[1, 4, 6, 1, -1],\n [11, 8, -6, 11, 10],\n [18, 12, -12, 18, 17],\n [-9, 24, 66, -9, -26],\n [7, 16, 18, 7, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-64, 4, 2, -6, -20],\n [-40, 6, 19, -13, -6],\n [-7, -4, 12, -12, -3],\n [-77, 6, -11, 4, -24],\n [-6, 2, -51, 30, -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[[0, -54, 6, 0, 0],\n [-1, 4, -3, -2, -6],\n [-11, -10, -27, -22, -66],\n [-5, -34, -9, -10, -30],\n [-4, -11, -9, -8, -24]]?\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[[-49, -18, -13, -20, 19],\n [-18, -16, 18, -51, -13],\n [31, 22, 12, -35, 19],\n [-11, -10, -1, 9, -12],\n [37, 26, 11, -30, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [2, -5, 2, 1, -2],\n [0, 0, 0, 0, 0],\n [-6, 15, -6, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -12, 12, 12, -24],\n [2, -6, 6, 6, -12],\n [1, -3, 3, 3, -6],\n [1, -3, 3, 3, -6],\n [-2, 6, -6, -6, 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[[20, 32, -14, -30, 56],\n [14, 22, -12, -36, 20],\n [-14, 16, -7, 21, 6],\n [18, -23, 19, 12, 57],\n [19, -11, 8, -54, 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 5x5 matrix:\n[[-10, -24, 16, -15, 30],\n [-43, 24, -4, -9, -5],\n [30, 19, -53, -42, 21],\n [28, -10, 43, 17, 5],\n [15, 10, 62, 3, 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[[-41, 42, -16, -23, 6],\n [7, -12, 14, 5, -30],\n [-8, 15, -19, -6, 42],\n [-5, 15, -25, -5, 60],\n [-34, 30, -2, -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[[12, -25, -7, 22, -22],\n [0, 11, 8, -20, 38],\n [-5, -3, -9, 17, -41],\n [16, -30, 19, 2, 28],\n [-39, 43, 23, -25, -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[[29, 11, -21, 29, -17],\n [40, 2, -12, 14, -43],\n [13, 58, 53, 0, -28],\n [48, -8, -53, 20, -27],\n [62, -6, -54, 30, -44]]?\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, -6, 13, 8, -14],\n [4, -36, 5, -11, -8],\n [-18, 51, -1, 13, 0],\n [-33, 45, -69, -21, 78],\n [3, 9, 7, 2, -2]]\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, -4, 32, 9, -35],\n [-36, -4, 7, -24, -25],\n [57, 6, 21, 45, 12],\n [-19, 1, -22, 33, 48],\n [24, 20, -15, -42, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, 37, 4, 29, 20],\n [27, 39, -26, 43, 31],\n [59, -1, -42, 3, 15],\n [-21, 3, 8, 15, -3],\n [1, -17, -8, 3, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-13, -2, -13, -14, -2],\n [-11, 2, -3, -2, -6],\n [-7, -2, -9, -10, 0],\n [-2, 8, 16, 20, -10],\n [-17, 2, -7, -6, -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[[-8, 16, 24, 12, 16],\n [2, -4, -6, -3, -4],\n [2, -4, -6, -3, -4],\n [2, -4, -6, -3, -4],\n [-4, 8, 12, 6, 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[[0, -6, 2, -4, -6],\n [0, -36, 12, -24, -36],\n [0, -24, 8, -16, -24],\n [0, 18, -6, 12, 18],\n [0, -30, 10, -20, -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[[40, 20, -16, 22, -20],\n [-8, -55, -26, -31, -4],\n [-10, 25, -42, 47, -64],\n [32, 10, -36, 26, -40],\n [28, 20, 12, 7, 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[[12, -9, -12, -15, 15],\n [8, -6, -8, -10, 10],\n [16, -12, -16, -20, 20],\n [-12, 9, 12, 15, -15],\n [4, -3, -4, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[20, -10, -13, -9, -10],\n [28, -25, -12, -3, 26],\n [-38, 23, 15, -17, -70],\n [-62, 69, 26, 24, -36],\n [-18, -2, 8, -23, -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[[-23, 22, -4, -7, 33],\n [7, -8, -4, 3, -17],\n [-4, 5, 4, -2, 12],\n [8, -4, 16, 0, 8],\n [10, -11, -4, 4, -22]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[11, 19, 28, 35, -10],\n [-24, -57, -30, -33, 45],\n [14, -9, -51, -67, 38],\n [-22, -3, -11, -14, -35],\n [62, 61, -13, -26, 23]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-24, -36, 36, 0, -6],\n [20, 30, -30, 0, 5],\n [20, 30, -30, 0, 5],\n [-16, -24, 24, 0, -4],\n [-12, -18, 18, 0, -3]]\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[[1, -10, -8, -5, -6],\n [5, -18, -22, -5, -8],\n [-11, 14, 34, -5, 0],\n [6, -12, -21, 0, -3],\n [-8, 0, 19, -10, -7]]\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 5x5 matrix:\n[[-7, -6, -23, -38, 19],\n [-14, 4, 25, 41, -26],\n [-33, -16, -7, -1, 2],\n [28, 18, -9, -33, 12],\n [-24, -15, 8, 38, -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[[2, 35, 33, -13, -24],\n [38, -52, -30, 11, 12],\n [8, -34, -34, 16, 0],\n [16, -38, -22, 6, 30],\n [10, 23, 29, -13, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-20, -18, -12, -6, 3],\n [12, 10, 4, 0, 0],\n [-6, -5, -2, 0, 0],\n [-2, 5, 26, 30, -15],\n [0, -8, -32, -36, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[13, -16, -21, 9, 34],\n [17, -17, -27, 15, 38],\n [-24, 6, 36, -36, -24],\n [-5, -20, 5, -25, 30],\n [22, -14, -34, 26, 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[[-23, 3, 18, 28, 42],\n [32, 4, -18, -29, -36],\n [5, 9, 18, 23, 0],\n [-14, -16, -24, -31, -6],\n [-13, 13, 18, 16, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -20, -8, 16, -4],\n [6, -30, -12, 24, -6],\n [0, 0, 0, 0, 0],\n [-1, 5, 2, -4, 1],\n [3, -15, -6, 12, -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[[-35, 12, -5, 23, -12],\n [24, 4, -22, 36, 16],\n [-14, 10, -6, 38, 13],\n [-11, -1, -16, 11, -10],\n [18, -30, -6, -42, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-52, -56, -13, -35, -12],\n [19, 0, -40, -5, 2],\n [-35, -34, 9, -45, 11],\n [65, 60, 2, 17, 26],\n [-41, -28, 35, -38, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-10, -3, 11, 18, -7],\n [11, -25, 19, -8, -23],\n [36, 11, 19, -26, -29],\n [-72, -9, 21, 82, -11],\n [-13, -19, 1, 20, 14]]?\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 5x5 matrix:\n[[34, 32, 31, 12, 30],\n [-44, 0, -26, 24, -20],\n [25, -14, 10, -27, 5],\n [41, 14, 29, -9, 25],\n [-9, 42, 9, 45, 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[[9, 15, 6, 18, 18],\n [12, 20, 8, 24, 24],\n [3, 5, 2, 6, 6],\n [0, 0, 0, 0, 0],\n [-15, -25, -10, -30, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[73, 58, 36, 46, -17],\n [2, -21, -22, -14, 77],\n [-7, 18, 22, 10, -39],\n [-7, 32, -17, 20, -20],\n [-4, 16, -17, 9, 29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-16, 20, -1, 3, -8],\n [-4, -12, -23, -37, -4],\n [28, -52, -9, -13, -6],\n [4, -8, 6, 17, -13],\n [-12, 36, 19, 28, 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 5x5 matrix:\n[[30, 0, 0, -24, -6],\n [10, 0, 0, -8, -2],\n [-30, 0, 0, 24, 6],\n [25, 0, 0, -20, -5],\n [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[[4, 2, -4, 46, 17],\n [-1, -6, -25, -1, 4],\n [31, -34, -16, -11, -31],\n [6, -11, 4, -59, -30],\n [72, -50, -31, -16, -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[[4, -27, 40, 34, 4],\n [4, 33, -50, -46, -6],\n [-4, 3, -4, -2, 0],\n [4, -27, 40, 34, 4],\n [-28, -15, 26, 34, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[11, -10, -15, -9, 48],\n [20, -30, -6, -14, -12],\n [-27, 40, 9, 19, 12],\n [0, 0, 0, 0, 0],\n [-14, 15, 15, 11, -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[[0, 0, 0, 0, 0],\n [-24, -16, -4, -24, 8],\n [-18, -12, -3, -18, 6],\n [-30, -20, -5, -30, 10],\n [-6, -4, -1, -6, 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 5x5 matrix:\n[[10, -5, -20, -10, 25],\n [-8, 4, 16, 8, -20],\n [4, -2, -8, -4, 10],\n [-6, 3, 12, 6, -15],\n [-2, 1, 4, 2, -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[[12, 40, -12, 7, -26],\n [24, 27, -4, 7, -16],\n [40, -7, 11, 7, 24],\n [4, 37, -6, -1, -38],\n [-8, 41, -32, 17, -24]]\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[[13, -3, 28, 18, -23],\n [-40, -40, 19, 13, 23],\n [-6, -2, -32, -20, 10],\n [40, 24, 10, 6, -38],\n [-1, -9, -73, -45, 2]]\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, 10, -12, -6, -6],\n [9, -19, -30, -26, -15],\n [-1, 3, 6, 5, 3],\n [3, -9, -18, -15, -9],\n [-10, 14, 12, 12, 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[[6, 6, -10, 10, -12],\n [-18, -18, 30, -30, 36],\n [-18, -18, 30, -30, 36],\n [15, 15, -25, 25, -30],\n [12, 12, -20, 20, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, -2, -2, -8, -8],\n [8, -2, -2, -8, -8],\n [-8, 2, 2, 8, 8],\n [8, -2, -2, -8, -8],\n [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[[9, 12, 15, -1, -26],\n [-3, 29, 45, -5, -60],\n [-42, -1, 24, -38, -18],\n [-25, 7, 17, 4, -6],\n [-20, 10, 10, 35, 10]]\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, -28, 25, -12, 8],\n [1, -9, 19, 14, 49],\n [5, -23, -1, 22, 56],\n [-5, 5, -13, -2, -15],\n [-12, 8, -10, -8, -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[[4, -14, 12, -12, -12],\n [36, -18, -36, 36, -12],\n [22, -5, -30, 30, -2],\n [14, -22, 6, -6, -18],\n [0, -9, 12, -12, -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[[0, 0, 0, 0, 0],\n [10, -8, 0, 0, -12],\n [15, -12, 0, 0, -18],\n [-20, 16, 0, 0, 24],\n [-25, 20, 0, 0, 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[[24, -43, 12, 38, 12],\n [62, 28, 27, 9, -8],\n [4, 3, -30, -27, 17],\n [-18, -47, -34, 8, 17],\n [-30, -39, 24, 31, 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[[5, -35, 21, 4, 4],\n [34, 11, -9, 38, -85],\n [-13, 49, -27, -14, 19],\n [-29, 0, -16, -16, -26],\n [-44, 6, -10, -40, 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[[-9, 9, -6, 0, 12],\n [18, -18, 12, 0, -24],\n [-18, 18, -12, 0, 24],\n [18, -18, 12, 0, -24],\n [9, -9, 6, 0, -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[[-35, -15, 0, -38, -10],\n [5, -19, 16, -9, 3],\n [6, -11, 22, 13, 9],\n [9, -14, 18, -39, 1],\n [25, 34, -51, 34, -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[[-17, 9, 24, -18, 14],\n [-15, -9, 24, -6, 18],\n [14, 6, -22, 7, -16],\n [18, -18, -24, 24, -12],\n [5, 3, -8, 2, -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[[-30, 6, 0, 6, -18],\n [10, -2, 0, -2, 6],\n [-10, 2, 0, 2, -6],\n [-20, 4, 0, 4, -12],\n [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[[30, 39, -23, 47, 56],\n [-6, 21, -7, 10, 1],\n [-25, -10, 39, -5, -9],\n [-17, 25, 0, 9, -6],\n [-46, 2, 46, -7, -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 5x5 matrix:\n[[0, 12, -30, 18, 0],\n [0, 8, -20, 12, 0],\n [0, -6, 15, -9, 0],\n [0, 2, -5, 3, 0],\n [0, 10, -25, 15, 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 5x5 matrix:\n[[12, 21, -18, -8, -10],\n [-6, 24, 4, -5, -33],\n [-24, 26, -19, 6, -42],\n [-24, 8, 11, 6, -30],\n [-24, -16, 16, 12, -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[[-38, -32, 32, -18, -18],\n [15, 20, -9, 0, -17],\n [16, 14, -7, 5, 25],\n [-30, -22, -30, 40, -43],\n [3, -12, 6, -17, -14]]\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 5x5 matrix:\n[[-27, 22, -28, -15, 30],\n [-28, 24, -16, -12, 24],\n [-11, 8, -22, -9, 18],\n [15, -12, 18, 9, -18],\n [18, -12, 48, 18, -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[[26, 7, 14, -24, 4],\n [22, 2, -30, -2, -28],\n [-32, -10, -32, 36, -16],\n [-30, -9, -26, 32, -12],\n [24, 6, 8, -20, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, 43, -21, -38, 4],\n [-17, 52, 21, -11, 26],\n [-32, 22, 6, -64, 22],\n [-4, 23, -4, -27, 15],\n [21, -12, 0, 40, 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[[-26, 59, -7, 38, -24],\n [14, 45, -54, -12, 29],\n [5, -9, 1, -16, 7],\n [7, 5, 14, 21, 4],\n [-13, -12, 4, 9, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[36, 30, -12, 6, -42],\n [-30, -18, -8, 20, 36],\n [-24, -6, -22, 12, 18],\n [39, 14, 32, -45, -43],\n [0, -2, -6, 56, 22]]\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[[-29, -45, 12, 21, 17],\n [-2, -2, -2, 18, 6],\n [12, 75, -3, 12, -12],\n [-57, -9, 33, 33, 15],\n [15, 28, -5, -15, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[16, -10, 4, 14, -20],\n [31, -18, 5, 23, -14],\n [27, -16, 5, 21, -18],\n [-13, 9, -5, -14, 32],\n [29, -17, 5, 22, -16]]\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, -16, 14, -28, 8],\n [11, 6, 23, 7, 5],\n [-1, 22, 23, 3, -7],\n [13, -14, -3, 9, 11],\n [5, -18, 31, -27, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-37, 23, -21, -4, 4],\n [7, -2, -9, 7, -21],\n [37, -5, -10, -7, -41],\n [-36, -7, -28, -7, -15],\n [24, 6, 48, 30, 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[[0, 0, 0, 0, 0],\n [-5, 4, -4, 1, 0],\n [20, -16, 16, -4, 0],\n [10, -8, 8, -2, 0],\n [25, -20, 20, -5, 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[[20, -30, -24, 6, -4],\n [-40, -10, -32, 18, 8],\n [-35, -14, -34, 18, 7],\n [-50, -2, -28, 18, 10],\n [25, -20, -10, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[30, 0, 19, -29, -2],\n [-24, -1, -10, 11, 17],\n [-1, -15, -50, -4, -20],\n [32, -4, 43, -10, -29],\n [23, 6, 64, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 8, -8, 10, 8],\n [6, -12, 12, -15, -12],\n [8, -16, 16, -20, -16],\n [-4, 8, -8, 10, 8],\n [-2, 4, -4, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0, 0],\n [-18, -30, -12, 0, -30],\n [-12, -20, -8, 0, -20],\n [6, 10, 4, 0, 10],\n [-15, -25, -10, 0, -25]]?\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 5x5 matrix:\n[[-6, -6, -18, 0, -27],\n [5, 12, 12, -10, 2],\n [11, 10, 18, -8, 19],\n [-30, 14, 12, 11, -2],\n [-8, 14, 18, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, -6, -15, -15, 6],\n [5, -10, -25, -25, 10],\n [0, 0, 0, 0, 0],\n [1, -2, -5, -5, 2],\n [-1, 2, 5, 5, -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[[40, -26, 44, 9, -26],\n [-3, -4, -28, 22, -8],\n [20, -29, 20, 12, -28],\n [32, -26, 30, 5, -24],\n [15, -15, 10, 25, -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[[15, 5, -20, 30, -10],\n [0, 0, 0, 0, 0],\n [6, 2, -8, 12, -4],\n [12, 4, -16, 24, -8],\n [-15, -5, 20, -30, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[20, -15, -30, -10, -20],\n [-16, 12, 24, 8, 16],\n [-12, 9, 18, 6, 12],\n [-16, 12, 24, 8, 16],\n [16, -12, -24, -8, -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 5x5 matrix:\n[[4, -5, 0, 3, -4],\n [12, -15, 0, 9, -12],\n [24, -30, 0, 18, -24],\n [-4, 5, 0, -3, 4],\n [-12, 15, 0, -9, 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[[15, 9, -7, -27, 7],\n [-10, 24, 18, -22, -8],\n [-8, 15, 10, -38, 13],\n [45, 13, -23, -19, -9],\n [-15, -18, 3, 39, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[23, -7, -35, -19, 27],\n [25, -26, 6, -21, 0],\n [47, -1, -29, -34, -9],\n [19, 10, -36, -3, -12],\n [-52, 0, 30, 25, 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[[12, -18, 0, 0, -15],\n [8, -12, 0, 0, -10],\n [16, -24, 0, 0, -20],\n [12, -18, 0, 0, -15],\n [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[[-60, -2, -1, 12, -3],\n [14, -35, 7, 17, 60],\n [-19, 29, -17, -17, -42],\n [43, 6, -30, -16, 18],\n [-9, -22, 3, 46, 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[[0, 6, -9, -12, -6],\n [0, -4, 6, 8, 4],\n [0, 0, 0, 0, 0],\n [0, 10, -15, -20, -10],\n [0, -4, 6, 8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, 19, -24, 25, 38],\n [18, 13, -6, 12, 20],\n [-12, -1, -14, 10, 16],\n [6, 1, -2, 4, 8],\n [15, 21, -18, 23, 36]]?\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[[72, -34, -38, -56, -22],\n [6, -16, -14, -17, 9],\n [-30, 14, 10, 41, -9],\n [30, -56, -55, -36, -5],\n [30, 5, 10, -21, -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[[5, 18, 0, -19, -10],\n [2, 6, 1, -5, -5],\n [-15, -30, -20, 5, 50],\n [-5, -6, -10, -7, 20],\n [10, 36, 0, -38, -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[[-67, 32, -2, -40, -30],\n [31, -14, 4, 18, 16],\n [-45, 12, -4, -22, -32],\n [-13, 8, 40, -10, 12],\n [-56, 42, -5, -41, -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 5x5 matrix:\n[[12, -32, -27, 12, -17],\n [6, -34, -24, 12, -14],\n [30, -11, -54, -6, -38],\n [24, 13, -18, -6, -16],\n [-80, 29, 16, -46, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[18, 54, -6, -54, 66],\n [5, 2, 37, 30, -34],\n [-14, -30, 26, 54, -66],\n [-29, 28, -33, -30, 26],\n [30, 30, -24, -63, 81]]\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, -36, -24, -9, 3],\n [-23, 9, -10, 33, 25],\n [-37, 33, 22, 27, 11],\n [2, 10, 12, -14, -14],\n [-22, 35, 24, 2, -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[[16, 16, -8, -16, 16],\n [4, 14, 23, 21, -6],\n [0, -12, -30, -30, 12],\n [-16, -24, -12, -4, -8],\n [-24, -14, 37, 49, -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 5x5 matrix:\n[[-2, -36, -21, -10, -23],\n [-39, 79, 54, 32, 65],\n [-25, 25, -2, 50, 25],\n [-9, 46, 36, -5, 36],\n [14, 0, 16, -26, -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[[0, 2, -6, 6, 0],\n [0, -3, 9, -9, 0],\n [0, 6, -18, 18, 0],\n [0, -3, 9, -9, 0],\n [0, -4, 12, -12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[36, -12, -30, -6, -34],\n [-8, -2, 23, -29, -1],\n [-38, 10, 41, -11, 31],\n [42, -12, -42, 6, -36],\n [18, -6, -15, -3, -17]]?\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 5x5 matrix:\n[[-42, 20, -38, -32, 18],\n [28, 44, -1, 47, 32],\n [43, -9, 28, 37, -10],\n [3, -68, 24, -29, -53],\n [14, 0, -7, 11, -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[[-15, -24, 6, 18, 2],\n [25, 39, -11, -30, -5],\n [-30, -21, 39, 36, 49],\n [15, 15, -15, -18, -17],\n [10, 18, -2, -12, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-34, -33, -26, -16, 30],\n [7, 41, 17, -67, -21],\n [35, 2, 36, 22, -28],\n [-3, -11, 10, -2, 2],\n [-59, 8, -18, -47, 40]]\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[[-3, -3, -27, -12, 9],\n [27, 21, 35, 19, -32],\n [-16, -32, -2, 47, -23],\n [-11, -3, 1, -14, 19],\n [33, 27, 13, 5, -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[[0, -12, -7, 11, 10],\n [22, 43, 42, 3, -3],\n [16, -8, -3, 3, 6],\n [23, -22, -8, 22, 23],\n [-36, -6, -17, -17, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[21, 19, 2, -30, -11],\n [-21, -10, -32, 39, -13],\n [-27, -21, -14, 42, 5],\n [30, 28, 0, -42, -18],\n [-3, -1, -6, 6, -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[[-16, 12, 4, 8, -12],\n [-24, 18, 6, 12, -18],\n [24, -18, -6, -12, 18],\n [20, -15, -5, -10, 15],\n [12, -9, -3, -6, 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[[22, 16, -12, 14, -30],\n [-30, -18, 0, -24, 30],\n [-3, 1, -12, -6, -5],\n [-1, -2, 6, 1, 5],\n [4, -6, 36, 14, 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[[30, -9, -10, 18, 27],\n [42, 0, -8, 36, 45],\n [0, 21, 10, 18, 12],\n [-18, 60, 32, 36, 15],\n [42, -21, -18, 18, 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 5x5 matrix:\n[[-18, 21, -51, 30, 27],\n [-30, -37, -13, 14, -15],\n [-18, 15, -45, 27, 22],\n [6, 5, 5, -4, 1],\n [-6, -35, 25, -11, -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 5x5 matrix:\n[[10, -42, -58, 2, 5],\n [19, -2, -8, -4, 20],\n [-11, 12, 38, -10, -19],\n [34, 18, 22, -14, 35],\n [24, -74, -51, -29, -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 5x5 matrix:\n[[-12, -20, -20, 8, -20],\n [-18, -30, -30, 12, -30],\n [-12, -20, -20, 8, -20],\n [-18, -30, -30, 12, -30],\n [18, 30, 30, -12, 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[[-15, 42, -78, -40, 4],\n [21, -2, 2, 0, 12],\n [21, -22, -14, 13, 17],\n [-21, 28, -22, -22, -10],\n [48, -56, 56, 45, 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[[3, 14, 19, -19, 9],\n [-13, 7, 40, -3, 31],\n [2, 21, 23, -23, 15],\n [5, 5, 3, 5, -2],\n [5, 29, -9, -48, 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 5x5 matrix:\n[[10, -4, -10, -6, -12],\n [-10, 4, 10, 6, 12],\n [15, -6, -15, -9, -18],\n [30, -12, -30, -18, -36],\n [30, -12, -30, -18, -36]]\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 5x5 matrix:\n[[35, -50, -14, -28, -64],\n [27, 27, -24, -10, 15],\n [13, -3, -9, -8, -14],\n [-18, 0, 9, 66, -1],\n [-4, 5, -1, 44, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 24, 10, -12, 44],\n [-4, 30, -4, -13, 6],\n [-4, 10, -3, 3, 5],\n [-1, -16, 1, 12, 18],\n [12, -66, 18, 15, 72]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-2, 4, -4, 5, 6],\n [8, -16, 16, -20, -24],\n [10, -20, 20, -25, -30],\n [12, -24, 24, -30, -36],\n [-12, 24, -24, 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[[2, 0, -1, 0, 3],\n [-8, 0, 4, 0, -12],\n [-8, 0, 4, 0, -12],\n [-8, 0, 4, 0, -12],\n [2, 0, -1, 0, 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[[-6, -3, -2, -4, -1],\n [12, 6, 4, 8, 2],\n [12, 6, 4, 8, 2],\n [-30, -15, -10, -20, -5],\n [36, 18, 12, 24, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-5, 27, 2, 8, 17],\n [3, -8, 22, -24, -30],\n [-7, -10, -4, 12, -22],\n [-21, 82, 24, 12, 10],\n [6, -38, -16, 6, -4]]?\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[[-18, 15, 0, -6, 33],\n [-18, 16, -27, -4, 16],\n [-9, -4, 36, 41, -16],\n [-11, -1, 32, 23, 13],\n [-5, 20, -29, 5, -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 5x5 matrix:\n[[7, 27, -42, 24, 13],\n [-28, -27, 42, -27, -40],\n [58, -6, 30, -48, 54],\n [21, -18, 21, 5, 31],\n [1, 3, -6, 6, 3]]\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, 8, -16, 32, -16],\n [19, 38, 6, 6, 27],\n [-13, -16, 18, -16, 7],\n [14, -11, 2, 30, -19],\n [23, -9, 0, 46, -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[[18, -6, 12, -12, -15],\n [-12, 4, -8, 8, 10],\n [36, -12, 24, -24, -30],\n [36, -12, 24, -24, -30],\n [-24, 8, -16, 16, 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[[-44, 40, -26, -86, 24],\n [-36, 14, 19, 17, -44],\n [11, -8, 28, 40, 30],\n [62, -40, -7, 21, 14],\n [-5, 15, -24, -58, 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 5x5 matrix:\n[[42, -13, 88, -51, 22],\n [-11, 32, -75, 54, 14],\n [50, 2, 64, -29, 36],\n [-8, -15, -10, 16, -34],\n [-23, 22, -58, 26, 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, -9, 6, -6, 9],\n [0, 0, 0, 0, 0],\n [10, 6, -4, 4, -6],\n [-10, -6, 4, -4, 6],\n [30, 18, -12, 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[[8, 22, 12, 32, -12],\n [9, -28, -19, 24, -1],\n [-19, 40, 37, 38, -15],\n [-37, -12, 5, 55, -4],\n [-14, -16, -5, 39, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -4, 10, -14, 13],\n [26, 21, 14, 2, 18],\n [-10, 0, -32, 23, -43],\n [-28, -18, -42, 34, -45],\n [-17, -19, -21, 14, -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[[20, -25, 10, -10, -5],\n [8, -10, 4, -4, -2],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [12, -15, 6, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 13, 12, 3, 21],\n [-5, -5, 18, -6, 0],\n [-18, 18, 36, 0, 36],\n [-13, -7, 42, -12, 6],\n [15, -30, -18, -9, -45]]\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 5x5 matrix:\n[[-8, -5, -27, 15, -5],\n [-24, -25, -31, -5, 15],\n [8, 5, 27, -15, 5],\n [-8, -12, 8, -20, 16],\n [-16, -11, -49, 25, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-14, -20, 24, 54, 4],\n [-16, -22, 30, 60, 5],\n [-12, -12, 36, 36, 6],\n [-3, -4, 6, 11, 1],\n [-10, -12, 24, 34, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[29, 21, 33, 60, 27],\n [-31, -6, -17, -58, -21],\n [10, 6, -10, 64, -6],\n [-6, 17, 30, -26, 12],\n [-7, 25, -46, 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[[20, 28, -60, -12, -6],\n [-6, -18, 18, 42, -11],\n [-10, -20, 30, 30, -5],\n [6, -3, -18, 42, -17],\n [-2, -19, 6, 66, -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[[3, -9, 6, -18, 9],\n [-6, 18, -12, 36, -18],\n [-4, 12, -8, 24, -12],\n [-6, 18, -12, 36, -18],\n [-3, 9, -6, 18, -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 5x5 matrix:\n[[1, 6, -4, 2, -5],\n [-1, -6, 4, -2, 5],\n [-5, -30, 20, -10, 25],\n [0, 0, 0, 0, 0],\n [-6, -36, 24, -12, 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[[8, -1, -4, -30, -18],\n [-6, 11, -38, 0, -6],\n [-41, 9, 5, 28, 39],\n [-26, 10, -14, 58, 36],\n [-13, 9, -23, 32, 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[[20, 15, -23, 7, -44],\n [-18, -12, 18, 5, 21],\n [8, 6, -30, 21, -67],\n [6, 6, 8, -2, 10],\n [-8, 0, 16, 27, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[19, -11, 14, 6, 27],\n [-6, 4, -1, 1, -3],\n [31, -21, 3, -7, 12],\n [7, -5, -1, -3, 0],\n [-13, 9, 0, 4, -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[[-12, -24, 4, -4, 16],\n [-7, -18, 6, 4, 13],\n [15, 42, -16, -14, -31],\n [-2, -12, 8, 12, 10],\n [-9, -42, 25, 35, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0, 0],\n [20, -5, 30, -20, 10],\n [16, -4, 24, -16, 8],\n [-20, 5, -30, 20, -10],\n [20, -5, 30, -20, 10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-18, -18, -67, -13, 5],\n [-15, 12, -9, 6, -9],\n [-22, 28, 6, -19, -10],\n [15, -54, -60, -34, -2],\n [44, -38, 22, 9, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[14, 5, -3, 40, 32],\n [-53, 8, 3, -2, -50],\n [-37, 17, -2, 58, -6],\n [-35, 8, 9, 70, -8],\n [-40, 10, 6, 56, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[48, 7, -43, -12, 26],\n [23, -26, -7, -6, 24],\n [16, -10, -20, 24, 36],\n [-8, 14, 1, 0, -12],\n [40, -14, -34, 8, 44]]\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 5x5 matrix:\n[[25, 15, 35, 15, -10],\n [25, 9, 32, 12, -10],\n [20, -48, -2, -18, -8],\n [30, 6, 36, 12, -12],\n [30, 12, 39, 15, -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[[14, -13, 26, 9, -24],\n [-10, 19, -2, 28, 3],\n [8, -15, -21, -15, 4],\n [10, -9, -48, 27, 2],\n [-2, 7, -26, 26, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-16, -24, -6, 24, -4],\n [13, 21, 4, -21, 5],\n [9, 21, -1, -21, 11],\n [5, 9, 1, -9, 3],\n [4, 12, -2, -12, 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 5x5 matrix:\n[[-20, 6, -28, 38, 52],\n [-38, -24, -54, -22, -43],\n [17, -12, 25, -20, 5],\n [-39, -6, -48, -15, -57],\n [40, 25, 58, -3, -15]]\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, -10, 25, 15, 0],\n [-25, 10, -25, -15, 0],\n [-5, 2, -5, -3, 0],\n [30, -12, 30, 18, 0],\n [15, -6, 15, 9, 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[[30, -21, -32, -25, 2],\n [28, -17, -18, -115, -36],\n [-64, -19, -52, -10, 10],\n [14, -34, 4, 20, 4],\n [-22, -40, -27, 10, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, -5, -2, 2, -22],\n [4, -4, 2, 7, -17],\n [2, 9, 12, 9, 41],\n [6, -1, 8, 13, -3],\n [14, 1, 22, 32, 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[[-27, -1, -34, 17, 11],\n [6, 24, -7, 3, 7],\n [-21, -5, -32, 8, 10],\n [8, 52, -28, 18, -6],\n [-6, -66, 24, -27, -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 5x5 matrix:\n[[-2, 0, 12, -24, -8],\n [-6, 6, -6, 10, 2],\n [-19, -17, -33, 25, 23],\n [-32, -4, -27, 12, 15],\n [-13, 12, -6, 8, 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[[8, -28, 22, 42, -4],\n [9, 6, -9, 36, 3],\n [8, 12, -14, 30, 4],\n [-8, 8, -4, -36, 0],\n [0, 50, -45, -15, 10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-23, 7, -27, -6, 29],\n [-7, -1, 45, 42, -35],\n [2, -2, 26, 20, -22],\n [0, 0, 0, 0, 0],\n [-39, 9, 3, 30, 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[[-25, 3, -23, -5, 21],\n [10, -14, 6, 2, -2],\n [35, 3, 34, 7, -33],\n [-10, -6, -11, -2, 12],\n [-25, 19, -19, -5, 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[[-36, 15, -6, 20, -9],\n [42, -37, 3, -6, -18],\n [-36, 52, 33, -24, -3],\n [32, -60, -39, 36, -7],\n [-54, 48, 0, 6, 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[[6, 8, 4, 0, 2],\n [6, 8, 4, 0, 2],\n [-9, -12, -6, 0, -3],\n [18, 24, 12, 0, 6],\n [18, 24, 12, 0, 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[[-13, 1, 32, 32, -29],\n [-13, 15, -43, 3, 14],\n [-33, 7, -23, 35, -2],\n [16, -2, -14, -28, 18],\n [33, 57, 18, -12, -45]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-15, -15, 3, 0, -18],\n [-25, -25, 5, 0, -30],\n [-25, -25, 5, 0, -30],\n [-30, -30, 6, 0, -36],\n [-5, -5, 1, 0, -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, 30, 18, 30, -18],\n [-6, -26, -14, -38, 22],\n [21, -13, -3, -49, 27],\n [-33, -7, -9, 29, -15],\n [0, 8, 4, 14, -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[[26, 17, -12, -26, 1],\n [-2, 3, 4, 10, -5],\n [-30, -25, 10, 20, 5],\n [18, 8, -11, -25, 5],\n [14, 7, -8, -18, 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[[-5, 6, -6, 2, -1],\n [-5, 6, -6, 2, -1],\n [-20, 24, -24, 8, -4],\n [-15, 18, -18, 6, -3],\n [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[[-6, -4, -6, 4, 16],\n [-16, -6, -21, 8, 45],\n [-9, -6, -9, 6, 24],\n [11, 12, 6, -10, -27],\n [-4, -54, 51, 32, -15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, -8, -8, 16, 0],\n [12, -8, -8, 16, 0],\n [15, -10, -10, 20, 0],\n [12, -8, -8, 16, 0],\n [-18, 12, 12, -24, 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[[-13, -37, -11, -25, 16],\n [-24, 17, -45, -12, 42],\n [42, -19, 27, 30, -30],\n [-27, 11, -25, -19, 26],\n [-51, 11, -32, -41, 37]]\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, 4, -60, -7, -12],\n [26, -24, -54, -7, 17],\n [-20, 1, 7, 2, -1],\n [22, -22, 14, -9, 0],\n [17, -12, -20, -4, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, -30, -25, 5],\n [0, 0, -30, -25, 5],\n [0, 0, -18, -15, 3],\n [0, 0, 36, 30, -6],\n [0, 0, -18, -15, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[32, 16, 26, -3, -6],\n [-50, -7, -7, -22, -1],\n [34, 15, 19, 8, -3],\n [4, -18, -6, -18, -2],\n [24, 2, 19, -18, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[28, 23, -23, 20, 5],\n [-7, 14, -4, -3, -19],\n [-8, -17, 25, -8, -3],\n [-12, 5, -9, -6, -6],\n [-16, -25, -31, -8, 49]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-25, 22, 33, -35, 17],\n [7, 19, 3, 3, 17],\n [-6, -11, 0, -4, -10],\n [-9, -35, -9, -1, -31],\n [3, -13, -9, 7, -11]]\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[[35, -46, -4, 1, 20],\n [41, 1, -28, -14, 24],\n [-21, -13, 16, 26, -2],\n [-21, 42, -12, 21, 12],\n [-49, 37, 0, 24, 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[[10, -2, -12, -6, -2],\n [10, -2, -12, -6, -2],\n [0, 0, 0, 0, 0],\n [-15, 3, 18, 9, 3],\n [-25, 5, 30, 15, 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 5x5 matrix:\n[[-16, -20, -20, 11, -9],\n [-16, -24, -24, 26, 2],\n [-18, -24, -24, 18, -6],\n [-22, -24, -24, 2, -22],\n [17, 20, 20, -7, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, 6, -22, -4, -16],\n [-35, -39, -11, -18, 16],\n [20, 21, 14, 12, -4],\n [3, 3, 3, 2, 0],\n [6, 9, -12, 0, -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[[7, -10, -32, -21, -17],\n [-3, 15, -22, -16, -7],\n [-8, 23, -2, -3, 4],\n [-3, -6, 48, 33, 21],\n [11, -26, -16, -9, -13]]\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[[-9, -9, 6, -15, -6],\n [-9, -9, 6, -15, -6],\n [3, 3, -2, 5, 2],\n [-9, -9, 6, -15, -6],\n [-3, -3, 2, -5, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[10, -10, 4, -4, -6],\n [-25, 25, -10, 10, 15],\n [-15, 15, -6, 6, 9],\n [-10, 10, -4, 4, 6],\n [25, -25, 10, -10, -15]]\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[[5, -23, -3, 6, -7],\n [25, 17, 29, -14, 31],\n [-25, 7, -21, 6, -19],\n [-20, 2, -18, 6, -17],\n [5, -11, 1, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-11, 7, -4, 9, -11],\n [-2, 7, 19, -6, -9],\n [40, -23, 23, -36, 37],\n [26, -19, 1, -18, 29],\n [-40, 23, -23, 36, -37]]\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[[-6, 2, 10, -6, -6],\n [-6, 2, 10, -6, -6],\n [-3, 1, 5, -3, -3],\n [18, -6, -30, 18, 18],\n [-18, 6, 30, -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 5x5 matrix:\n[[-6, -38, -45, -42, 20],\n [14, 32, 23, 12, -36],\n [-2, -37, -44, -30, 15],\n [-48, -29, -9, -18, 77],\n [36, -23, -33, -36, -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[[12, 3, 0, 9, 9],\n [12, 3, 0, 9, 9],\n [-4, -1, 0, -3, -3],\n [0, 0, 0, 0, 0],\n [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[[9, 27, -18, -3, 15],\n [-1, 19, -6, -5, 7],\n [1, -19, 6, 5, -7],\n [13, -16, -6, 9, 0],\n [-4, -23, 12, 4, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, 19, 11, 10, 27],\n [15, -3, -7, 10, 11],\n [30, 0, -10, 22, 29],\n [0, 12, 8, 4, 14],\n [-45, 27, 33, -24, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-25, -10, 30, -25, 0],\n [-15, -6, 18, -15, 0],\n [10, 4, -12, 10, 0],\n [-5, -2, 6, -5, 0],\n [10, 4, -12, 10, 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 5x5 matrix:\n[[0, 0, 0, 0, 0],\n [20, 24, -4, -12, 16],\n [-15, -18, 3, 9, -12],\n [0, 0, 0, 0, 0],\n [5, 6, -1, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 10, -10, 0, -4],\n [-2, 28, -45, 34, 16],\n [-2, 10, -15, 10, 4],\n [10, -20, 25, -10, 0],\n [-16, 14, -10, -8, -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[[-8, -10, -5, -41, 10],\n [54, 36, -52, 2, 20],\n [-45, -22, 39, 2, -10],\n [6, -22, 7, -15, -18],\n [17, 4, -5, 16, -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[[18, 9, -15, 0, 9],\n [-41, -16, 36, 6, -13],\n [24, 12, -20, 0, 12],\n [-26, 5, 29, 24, 17],\n [31, -7, -35, -30, -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[[20, -14, -32, -10, -72],\n [-19, -2, 25, -24, 6],\n [-17, -4, 27, -20, 18],\n [-1, 7, 1, 11, 18],\n [1, 5, -3, 8, 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[[-36, -16, -12, 12, -11],\n [-22, -62, 16, -66, -12],\n [-20, -32, -4, -6, 4],\n [27, -3, 18, -36, 3],\n [37, 17, 8, -1, 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[[-6, 6, -6, -14, 53],\n [-24, -4, 3, 9, 33],\n [-24, -44, 28, 34, 8],\n [-48, 48, -21, 23, -35],\n [-30, 30, -12, 20, -41]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -2, 1, 5, -6],\n [0, 10, -5, -25, 30],\n [0, 6, -3, -15, 18],\n [0, 12, -6, -30, 36],\n [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[[12, -4, 15, 6, 11],\n [-24, -8, -6, 20, -14],\n [12, 4, 3, -10, 7],\n [30, 3, 18, -11, 21],\n [-30, -11, -6, 27, -17]]\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[[-2, -52, -62, -30, 56],\n [7, -37, -36, -30, 26],\n [-2, -32, -22, -30, -4],\n [28, -41, -41, -39, 44],\n [22, -48, -40, -48, 26]]\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 5x5 matrix:\n[[-18, 15, -21, 6, -33],\n [-6, -11, 17, -10, 9],\n [0, -12, 18, -9, 15],\n [18, 21, -33, 21, -12],\n [-30, -3, 7, -11, -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[[0, 0, 0, 0, 0],\n [-24, 24, -18, 30, -30],\n [-8, 8, -6, 10, -10],\n [16, -16, 12, -20, 20],\n [-4, 4, -3, 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[[-40, -42, -34, 34, 21],\n [37, 12, 32, 30, -24],\n [-1, -6, -16, 16, 9],\n [-1, -30, 51, -1, -13],\n [6, 0, -16, 104, -28]]\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 5x5 matrix:\n[[4, 37, 16, -11, -12],\n [-40, -2, 12, 10, -58],\n [-2, 9, 38, 3, -8],\n [-1, -26, 11, -9, 14],\n [-12, -61, -12, 7, 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[[12, 12, 6, -6, -15],\n [12, 12, 6, -6, -15],\n [-16, -16, -8, 8, 20],\n [12, 12, 6, -6, -15],\n [20, 20, 10, -10, -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, 10, -12, -81, -45],\n [-4, 10, -14, -37, -23],\n [-22, 6, -12, 41, 29],\n [-10, -10, 14, 32, 24],\n [48, 27, -42, 3, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-19, 8, 4, 3, 2],\n [-44, -8, 10, 4, 12],\n [14, 32, -4, 2, -12],\n [-27, 0, 6, 3, 6],\n [-25, 20, 5, 5, 0]]\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, 6, -29, 7, 7],\n [20, 12, 12, -16, 24],\n [10, -24, 11, 17, -43],\n [40, -6, 29, -7, -7],\n [-5, 21, -7, -16, 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[[28, 23, 8, -3, 2],\n [38, 34, -4, -18, -14],\n [7, 8, -10, -12, -13],\n [23, 19, 6, -3, 1],\n [-4, -5, 8, 9, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, 4, -4, -9, -2],\n [7, 8, -7, -24, -5],\n [-1, -25, 13, 27, 17],\n [27, -18, 11, -39, 7],\n [-2, -9, -6, 9, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[18, -3, 0, -31, -2],\n [-7, 2, 0, 14, 8],\n [-1, -4, 0, -8, -36],\n [5, 5, 0, 5, 50],\n [-10, 2, 0, 18, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -16, -33, 19, 11],\n [27, 23, 5, -13, -1],\n [29, 47, 36, -42, -38],\n [6, 30, 27, -33, -45],\n [29, 33, 28, -26, -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[[-13, -4, -12, 8, -1],\n [-43, -16, -10, -1, -26],\n [-48, -63, -21, 22, -82],\n [-13, -66, -16, 41, -39],\n [17, 47, 15, -31, 23]]\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, 20, -2, 20, -38],\n [-48, -7, 8, 0, 24],\n [57, 55, 34, -18, -39],\n [-34, -16, -14, 4, 22],\n [-39, -7, 26, 18, 1]]\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, 2, -10, -24, -8],\n [4, -10, 34, -62, 22],\n [12, -6, 36, -42, 24],\n [4, -22, 12, 20, 10],\n [0, 24, -31, 46, -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[[33, -13, 37, 26, 39],\n [-6, 10, -6, -4, -12],\n [27, 33, -33, -30, 27],\n [-9, -28, 15, 13, 0],\n [11, -4, 3, 1, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[55, -14, 0, -18, 48],\n [-16, -10, 36, 22, -6],\n [54, -9, -27, -16, 33],\n [-45, 12, 10, 50, -36],\n [22, -20, 0, -28, 6]]\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, 18, 24, -13, -16],\n [-28, 12, -16, -14, 0],\n [29, -15, 11, 16, 3],\n [-25, 3, -31, -8, 9],\n [-27, 9, -21, -12, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 6, -4, 5, -1],\n [6, -6, 4, -5, 1],\n [12, -12, 8, -10, 2],\n [-30, 30, -20, 25, -5],\n [-30, 30, -20, 25, -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[[3, -15, -18, -15, 12],\n [-43, -1, -14, -9, 12],\n [51, -3, -27, -18, 21],\n [20, -7, -54, -36, 43],\n [-22, -31, -20, -20, 11]]\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 5x5 matrix:\n[[2, 33, 62, -55, -15],\n [20, -20, -23, 42, 50],\n [14, 4, 17, -4, 20],\n [14, -20, -27, 28, 20],\n [4, 11, 23, -21, -5]]\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[[5, -5, -30, 10, 0],\n [-3, 3, 18, -6, 0],\n [3, -3, -18, 6, 0],\n [-4, 4, 24, -8, 0],\n [4, -4, -24, 8, 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[[-26, 18, 6, 10, -16],\n [-54, 36, 11, 22, -37],\n [-15, 12, 9, 12, -18],\n [1, 10, -3, -38, 78],\n [-3, -6, -4, 16, -37]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[43, 46, -17, 8, -12],\n [30, 43, 0, -1, -17],\n [8, 19, 18, 15, -5],\n [-21, -49, -31, -9, 21],\n [-62, -55, 38, -16, 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[[-54, -13, 5, -19, -2],\n [-30, -9, 1, -9, 0],\n [6, -27, -29, 27, 18],\n [24, -12, -20, 24, 12],\n [-18, 9, 15, -18, -9]]\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 5x5 matrix:\n[[4, -28, 0, 4, 26],\n [8, 36, -12, -4, -36],\n [10, 22, -12, -2, -23],\n [-36, -1, 33, -3, 8],\n [-50, 5, 45, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0, 0],\n [-24, 18, 30, -6, 0],\n [-24, 18, 30, -6, 0],\n [0, 0, 0, 0, 0],\n [12, -9, -15, 3, 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 5x5 matrix:\n[[-20, -12, 1, 0, -34],\n [38, 19, 3, -29, 32],\n [-23, 19, 15, 10, -8],\n [-1, -39, -6, -6, -18],\n [13, -26, 10, -53, -36]]\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[[-29, 22, 64, 8, 2],\n [-18, -42, -14, -82, -22],\n [21, -1, -24, -4, 6],\n [19, -45, -54, -28, 9],\n [-9, -21, -28, -40, -30]]\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, -16, 64, -26, 14],\n [-16, 23, -42, 32, -57],\n [16, -16, 0, -18, 22],\n [-14, -15, 34, -21, 12],\n [39, 0, 4, -2, 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 5x5 matrix:\n[[-42, 26, 44, -6, -34],\n [15, 1, 6, -5, -3],\n [-27, 3, 30, 3, -15],\n [0, 12, 10, -7, -11],\n [-3, -37, -38, 23, 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 5x5 matrix:\n[[35, 5, 29, -6, -12],\n [13, -29, -17, 24, 21],\n [-48, 24, -12, -18, -9],\n [-60, 20, -24, -14, -3],\n [-28, 4, -16, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-21, -42, 13, -2, 10],\n [-31, -58, 3, -12, 16],\n [-15, -3, -5, -2, 7],\n [51, 21, -43, -28, -19],\n [-7, 4, 31, 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[[1, 4, 0, -12, 16],\n [-22, 3, -13, 30, -1],\n [-9, 6, -6, 0, 18],\n [-17, 9, -11, 6, 25],\n [15, 4, 8, -36, 24]]\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[[6, 3, -9, 9, -18],\n [0, 0, 0, 0, 0],\n [-2, -1, 3, -3, 6],\n [-6, -3, 9, -9, 18],\n [10, 5, -15, 15, -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[[-5, -1, -1, 0, 5],\n [3, 28, 50, 6, -7],\n [4, 26, 42, -22, 30],\n [15, -3, -13, -35, 32],\n [-26, -16, -20, 28, -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 5x5 matrix:\n[[-44, -16, -12, 0, -24],\n [7, 24, -29, -20, -6],\n [33, 39, -30, -25, 6],\n [-12, -23, 31, 5, -24],\n [1, -17, 26, 15, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, -24, -23, -44, 31],\n [-16, 8, -4, 0, -27],\n [36, -24, 0, 24, 51],\n [-36, 50, 29, -13, -65],\n [40, -48, -24, 20, 67]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[23, 29, 5, -26, 14],\n [-7, -11, -5, 9, -6],\n [-5, 5, 17, 0, 6],\n [13, 9, -9, -11, 2],\n [-9, 3, 21, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[24, 4, 4, -24, 16],\n [12, 2, 2, -12, 8],\n [-36, -6, -6, 36, -24],\n [-18, -3, -3, 18, -12],\n [36, 6, 6, -36, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, -36, 24, 5, -16],\n [22, 23, -60, -20, -31],\n [6, 36, 10, 8, 14],\n [-50, -32, -30, -24, 30],\n [2, -28, 38, 43, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-6, -2, -6, 0, -8],\n [12, 4, 12, 0, 16],\n [15, 5, 15, 0, 20],\n [-18, -6, -18, 0, -24],\n [-6, -2, -6, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[14, 43, 25, 45, 47],\n [-8, -5, 9, 17, 35],\n [10, 25, 3, 2, -13],\n [-1, 4, 0, -18, -31],\n [-16, -25, -3, -13, -1]]\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, -20, 16, 20, 20],\n [18, 15, -12, -15, -15],\n [-6, -5, 4, 5, 5],\n [24, 20, -16, -20, -20],\n [12, 10, -8, -10, -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[[-13, -13, 15, -1, 5],\n [3, 9, -15, -3, 15],\n [-15, -6, 0, -6, 30],\n [-28, -19, 15, -7, 35],\n [7, 8, -10, 0, 0]]\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[[16, -16, 16, -8, 0],\n [12, -12, 12, -6, 0],\n [20, -20, 20, -10, 0],\n [-20, 20, -20, 10, 0],\n [-16, 16, -16, 8, 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[[8, 3, -11, -20, -33],\n [-33, -24, -3, -36, 30],\n [16, 33, -9, 28, 13],\n [19, -3, 4, 0, -49],\n [-20, -41, 1, -56, -33]]\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, 2, 74, 48, -23],\n [-3, 34, -30, -31, 18],\n [49, -25, 29, 12, 4],\n [-1, 22, -24, 12, 7],\n [-37, 14, -16, -32, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[10, -5, 20, 15, -20],\n [-10, 5, -20, -15, 20],\n [-8, 4, -16, -12, 16],\n [10, -5, 20, 15, -20],\n [2, -1, 4, 3, -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[[24, 25, -30, -13, -4],\n [24, -18, 63, -36, 9],\n [70, -6, 6, -52, -30],\n [76, 5, 0, -57, -26],\n [-18, 14, 21, 2, 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[[1, 6, 43, -23, 38],\n [-60, -30, 18, 20, 0],\n [20, 0, 2, -4, 8],\n [-29, 6, -23, 11, -30],\n [-16, 54, -34, -16, -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[[-13, 0, -21, -18, -11],\n [24, 60, 18, 24, -12],\n [-6, -28, 0, -4, 10],\n [1, -4, 3, 2, 3],\n [-16, -40, -12, -16, 8]]\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, -18, -6, -3, 15],\n [-6, -36, -12, -6, 30],\n [4, 24, 8, 4, -20],\n [0, 0, 0, 0, 0],\n [-4, -24, -8, -4, 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[[30, 20, -18, 30, -24],\n [-15, -15, 7, -20, 21],\n [45, 30, -27, 45, -36],\n [-18, -14, 10, -20, 18],\n [-48, -39, 26, -55, 51]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[34, -35, 33, -15, 6],\n [19, -19, 11, 24, 32],\n [-4, 13, -29, -20, -23],\n [-37, 33, 25, 6, -10],\n [-11, 16, -67, 13, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-15, 10, -59, 14, -19],\n [21, -4, 39, -22, -21],\n [-10, -36, 61, 39, -45],\n [-39, -14, 4, 17, -10],\n [-8, -6, 0, 10, -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[[-6, 6, -1, 50, -45],\n [33, 6, 40, -19, -31],\n [-15, 15, -5, 3, -19],\n [15, 8, 21, -27, -10],\n [18, -15, 9, -48, 48]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-35, 6, 16, -6, -33],\n [-15, -6, 8, -6, -25],\n [14, 48, 42, 34, -28],\n [12, 15, -12, 8, 41],\n [13, -51, -27, -23, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[12, 4, -20, 0, -8],\n [6, 2, -10, 0, -4],\n [-12, -4, 20, 0, 8],\n [6, 2, -10, 0, -4],\n [-6, -2, 10, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -48, -36, 0, 42],\n [-2, -39, -17, 38, 3],\n [-7, -23, -10, 19, 5],\n [13, 32, 25, 11, -38],\n [22, -42, -20, 50, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, -18, -9, -15, 15],\n [6, -36, -18, -30, 30],\n [1, -6, -3, -5, 5],\n [1, -6, -3, -5, 5],\n [1, -6, -3, -5, 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 5x5 matrix:\n[[-7, 18, 3, -12, 6],\n [-4, -14, 6, -20, 11],\n [18, 23, -17, 24, -21],\n [-21, 9, 24, 36, -1],\n [-32, 1, -15, -8, 15]]\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, -8, 27, -33, -31],\n [15, 18, -46, 7, 70],\n [-23, 27, -28, -18, 26],\n [8, 4, -10, -29, 29],\n [6, 10, -29, 6, 37]]?\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[[26, -30, -44, -44, 12],\n [0, -10, -8, -28, 22],\n [9, 1, -2, 10, -14],\n [-39, 30, 44, 18, 20],\n [60, 2, -8, -20, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-24, -39, -3, 30, -9],\n [-16, -17, -17, -10, 21],\n [-10, -8, -15, -15, 21],\n [14, 13, 18, 15, -24],\n [24, 39, 3, -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[[-10, -2, -26, -10, 6],\n [23, -1, 13, 25, -35],\n [-22, 6, 29, 15, -10],\n [38, -8, -46, -18, 4],\n [12, -16, 13, -13, 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[[-5, -30, 5, -5, 20],\n [3, 3, 1, -1, -2],\n [13, 18, 3, -3, -12],\n [-13, -3, -7, 7, 2],\n [-13, -3, -7, 7, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-9, -10, -52, 35, -14],\n [14, -35, -16, -4, -4],\n [-30, 39, 16, -59, 5],\n [0, -35, 56, -25, 41],\n [4, -16, -24, -33, -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[[-9, 13, 14, 16, -18],\n [-5, 15, 28, 26, -10],\n [13, -1, 26, 16, 26],\n [-19, 13, -8, 2, -38],\n [-19, 23, 18, 24, -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[[36, 51, 3, -24, -42],\n [-2, 90, -22, 16, -22],\n [-16, 5, -11, 8, 14],\n [8, 71, -17, -4, -22],\n [32, -11, 25, -10, -30]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[16, 4, -40, -11, -48],\n [-11, -47, -1, -11, -3],\n [-12, 2, 14, 0, 15],\n [24, -23, -32, 12, -24],\n [9, 41, -25, 16, -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[[-23, -2, 3, -10, 8],\n [17, 8, -7, 15, -12],\n [-4, -16, 12, -20, 16],\n [-18, -12, 10, -20, 16],\n [-20, 10, -6, 5, -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[[9, -15, -3, -9, 9],\n [0, 0, 0, 0, 0],\n [-9, 15, 3, 9, -9],\n [-3, 5, 1, 3, -3],\n [-3, 5, 1, 3, -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[[0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [16, 4, 4, 12, -20],\n [12, 3, 3, 9, -15],\n [4, 1, 1, 3, -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 5x5 matrix:\n[[-3, -9, -4, -2, -17],\n [18, 18, 12, -30, 6],\n [-17, -19, -12, 26, -11],\n [-7, -11, -6, 7, -13],\n [21, 27, 16, -28, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 12, -9, 18, -12],\n [-4, 4, -3, 6, -4],\n [-8, 8, -6, 12, -8],\n [-20, 20, -15, 30, -20],\n [20, -20, 15, -30, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-36, 29, -29, 4, -23],\n [6, -13, 13, -10, 12],\n [-12, 33, -33, 28, -31],\n [-6, 20, -20, 18, -19],\n [-6, -36, 36, -46, 37]]\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, -4, -8, 16, -20],\n [-5, -2, 5, -13, 16],\n [-9, 2, 13, -29, 36],\n [-1, -6, -3, 3, -4],\n [-19, -30, 3, -27, 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 5x5 matrix:\n[[39, 0, 23, 20, -36],\n [-4, 6, -4, -5, 2],\n [-7, -12, -1, 4, 8],\n [-5, -6, -1, -3, 10],\n [-2, -14, 4, -9, 22]]\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, 2, -2, -12, -10],\n [30, 5, -5, -30, -25],\n [18, 3, -3, -18, -15],\n [24, 4, -4, -24, -20],\n [36, 6, -6, -36, -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 5x5 matrix:\n[[-20, 16, 24, -24, -24],\n [-20, 16, 24, -24, -24],\n [10, -8, -12, 12, 12],\n [-25, 20, 30, -30, -30],\n [-15, 12, 18, -18, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, 20, 18, 0, -9],\n [6, 12, 2, -11, -23],\n [0, 12, 10, -1, -7],\n [9, -24, -32, -13, -10],\n [3, 0, -4, -5, -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[[4, -1, 2, -3, 0],\n [12, -3, 6, -9, 0],\n [-16, 4, -8, 12, 0],\n [-16, 4, -8, 12, 0],\n [-12, 3, -6, 9, 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[[-4, -12, -20, 0, 16],\n [-3, -9, -15, 0, 12],\n [-3, -9, -15, 0, 12],\n [-5, -15, -25, 0, 20],\n [-6, -18, -30, 0, 24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-30, -20, 0, 5, -10],\n [10, 40, 0, 19, 18],\n [-41, -19, 0, 12, -10],\n [-16, -44, 0, -18, -20],\n [-8, 28, 0, 22, 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[[-30, 24, -54, -18, -12],\n [-8, -20, -76, 48, 10],\n [-15, -20, 5, 23, 10],\n [6, -6, 48, -6, 3],\n [5, 30, -5, -37, -15]]\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, 19, 8, 16, -2],\n [20, 8, 10, -1, 8],\n [-36, -20, -22, -1, -16],\n [22, 13, 14, 1, 10],\n [24, 4, 8, -4, 8]]\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[[2, 1, 1, -5, -4],\n [2, 1, 1, -5, -4],\n [-4, -2, -2, 10, 8],\n [-2, -1, -1, 5, 4],\n [2, 1, 1, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, 12, -15, -5, 10],\n [-4, 0, -18, -17, -11],\n [-8, 12, -45, -43, -2],\n [-18, -4, -12, -25, -19],\n [27, 28, -36, -2, 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[[-34, -18, -46, 52, -42],\n [-2, 10, -21, 35, -7],\n [22, -19, 14, -34, 23],\n [-22, -18, -13, 7, -23],\n [-9, 4, -4, 9, -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 5x5 matrix:\n[[25, -6, 35, -23, 37],\n [-40, -5, -9, 16, -45],\n [-2, 1, 45, -22, 1],\n [-19, 11, -31, 34, -20],\n [12, -10, 5, -1, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[27, -1, 31, 35, 29],\n [-4, 19, -3, 11, 2],\n [-17, -19, -21, -39, -25],\n [6, -48, -12, -24, 6],\n [-12, -19, -11, -35, -24]]\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[[27, 14, 20, -35, -1],\n [18, -10, -4, 7, 8],\n [6, -21, -17, 30, 10],\n [9, -6, -6, 6, 15],\n [-9, -11, -17, 23, 19]]\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[[-36, -36, 0, 42, 3],\n [-6, -6, 2, 9, 0],\n [12, 12, -4, -18, 0],\n [-12, -12, 20, 34, -4],\n [-6, -6, -2, 5, 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[[10, -23, 16, 12, -10],\n [15, -35, 15, -2, -12],\n [25, 9, -8, 55, 8],\n [-17, 19, 7, 15, -19],\n [14, -22, -1, -13, -8]]\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, -6, -6, -36, -12],\n [-18, 3, 3, 18, 6],\n [6, -1, -1, -6, -2],\n [12, -2, -2, -12, -4],\n [36, -6, -6, -36, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 36, -24, -18, 30],\n [-6, -36, 24, 45, -9],\n [-5, 9, -6, 18, 25],\n [4, 6, -4, -21, -9],\n [-6, -36, 24, 45, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[14, 36, 11, -4, -2],\n [12, 0, 3, 12, -12],\n [-14, -36, -11, 4, 2],\n [15, -18, 0, 24, -21],\n [42, 36, 18, 24, -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[[0, 0, 3, 6, -12],\n [0, 0, 6, 12, -24],\n [0, 0, 6, 12, -24],\n [0, 0, -4, -8, 16],\n [0, 0, 5, 10, -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[[-4, 4, 8, 2, -8],\n [-2, 2, 4, 1, -4],\n [-4, 4, 8, 2, -8],\n [-8, 8, 16, 4, -16],\n [0, 0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-15, -17, -7, -37, 35],\n [-4, 12, 20, 20, -44],\n [29, 7, -25, 17, 21],\n [70, 26, -53, 49, 27],\n [34, 27, -21, 24, -16]]\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, -78, -47, 22, 81],\n [-4, -28, -14, 12, 28],\n [-8, 63, 26, -22, -60],\n [-11, -15, -9, 24, 17],\n [-25, 43, 13, 8, -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 5x5 matrix:\n[[1, 0, -2, 5, 14],\n [3, 4, 14, -17, -58],\n [34, 11, -4, -35, -33],\n [-10, -7, -15, 6, 35],\n [-28, -13, -13, 16, 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[[36, 30, 24, -18, -6],\n [-30, -25, -20, 15, 5],\n [36, 30, 24, -18, -6],\n [-12, -10, -8, 6, 2],\n [18, 15, 12, -9, -3]]\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, 30, 24, 14, 12],\n [-58, 3, 16, -3, -22],\n [-4, 3, 16, 15, 8],\n [-8, 15, 20, 9, 0],\n [-12, 36, 12, -18, -24]]\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[[51, -18, -39, 51, -36],\n [18, 21, 23, 15, 24],\n [-27, -39, 6, -10, -29],\n [13, -36, -27, 1, 15],\n [-7, 0, -26, -26, 27]]?\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 5x5 matrix:\n[[7, 0, -26, 8, 2],\n [16, -6, -2, 2, 8],\n [19, -20, -30, 20, -6],\n [-42, -22, -20, 27, -58],\n [-49, -30, -40, 40, -74]]\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 5x5 matrix:\n[[0, 24, 18, 24, 6],\n [-12, -4, -21, -24, -15],\n [-3, -14, -15, -19, -7],\n [-18, 24, -9, -6, -15],\n [-6, 12, 0, 2, -4]]\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, 8, -17, -3, 13],\n [18, -21, 0, -15, -30],\n [-37, -18, -14, -11, 1],\n [35, -9, 10, -6, -27],\n [-16, 14, 22, 22, 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[[6, 31, 45, -28, 50],\n [-46, -24, -34, 22, -18],\n [14, -47, -17, 62, -43],\n [2, 26, 55, 7, 49],\n [-60, 0, 30, 16, 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[[12, -16, -16, 20, 0],\n [-9, 12, 12, -15, 0],\n [15, -20, -20, 25, 0],\n [15, -20, -20, 25, 0],\n [-12, 16, 16, -20, 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[[15, 21, -10, -15, 8],\n [-36, -18, 30, 0, -6],\n [31, 20, -25, -5, 7],\n [-14, -16, 10, 10, -6],\n [-20, 8, 20, -20, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[19, 21, -15, -25, -16],\n [3, 18, -34, 8, -14],\n [29, 27, -28, -21, -7],\n [9, 30, -54, 13, -12],\n [49, 22, 5, -63, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, -14, 21, 33, -10],\n [-4, -21, 28, 41, -19],\n [20, -3, -5, -16, -13],\n [24, -6, -3, -15, -18],\n [40, -6, -10, -32, -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 5x5 matrix:\n[[16, -4, 16, -4, -8],\n [24, -6, 24, -6, -12],\n [4, -1, 4, -1, -2],\n [-16, 4, -16, 4, 8],\n [-4, 1, -4, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-20, 86, -36, 6, -14],\n [39, 35, -14, 16, -10],\n [-8, -6, -48, 70, 14],\n [47, 34, -20, -22, 8],\n [13, -8, -1, -57, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[18, -10, 17, 6, -22],\n [5, 5, -4, 0, 16],\n [23, -9, 18, 12, -22],\n [11, 7, 0, 44, -15],\n [9, -15, 19, -2, -33]]\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 5x5 matrix:\n[[-9, -3, -12, 3, 15],\n [-1, 3, -18, 22, -5],\n [-16, -8, -8, -12, 32],\n [-16, -8, -8, -12, 32],\n [-12, 0, -36, 30, 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 5x5 matrix:\n[[-14, -34, -18, -34, -13],\n [-28, 28, 10, -18, -4],\n [-26, 50, 18, -6, 3],\n [17, 49, -3, 27, 30],\n [-29, 32, 9, -9, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, -2, -8, 12, 4],\n [-9, 3, 12, -18, -6],\n [0, 0, 0, 0, 0],\n [18, -6, -24, 36, 12],\n [18, -6, -24, 36, 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, -8, 4, 8, -16],\n [3, 6, -3, -6, 12],\n [1, 2, -1, -2, 4],\n [5, 10, -5, -10, 20],\n [-1, -2, 1, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-36, -60, 20, -36, -24],\n [-64, -13, 70, 17, 4],\n [-8, -23, 2, -14, -12],\n [-12, -27, 14, 3, -28],\n [-16, -31, 26, 20, -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[[-20, -24, -24, -16, 4],\n [0, 0, 0, 0, 0],\n [20, 24, 24, 16, -4],\n [5, 6, 6, 4, -1],\n [15, 18, 18, 12, -3]]\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[[-12, -4, 8, 10, -6],\n [0, 0, 0, 0, 0],\n [-18, -6, 12, 15, -9],\n [30, 10, -20, -25, 15],\n [30, 10, -20, -25, 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[[-32, -14, 5, 62, -31],\n [-42, 28, 20, 10, 60],\n [-12, -14, 12, -16, -30],\n [-61, 0, 30, 29, 8],\n [23, -46, 0, -21, -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[[22, -17, 13, 7, 12],\n [-2, -13, 37, 3, 28],\n [12, -10, 9, 4, 8],\n [-22, 9, 8, -5, 4],\n [22, 7, -50, 1, -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[[4, 24, 4, -12, -16],\n [-4, -24, -4, 12, 16],\n [-3, -18, -3, 9, 12],\n [1, 6, 1, -3, -4],\n [1, 6, 1, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-36, -16, -24, -25, -7],\n [23, 18, 9, 0, 9],\n [42, 30, 8, -20, 10],\n [32, 0, 24, 30, -6],\n [19, 17, 20, 30, 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[[0, 0, 0, 0, 0],\n [0, 24, 36, -30, 12],\n [0, 24, 36, -30, 12],\n [0, -16, -24, 20, -8],\n [0, 4, 6, -5, 2]]\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[[15, 32, 53, 32, 37],\n [27, 12, -6, -21, 30],\n [6, -19, -40, -30, -10],\n [-60, -86, -2, -4, -66],\n [9, 19, -37, -63, 15]]\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, -15, -3, 15, 9],\n [10, -6, 6, -12, 18],\n [1, -6, 0, 3, 6],\n [8, -30, 2, 10, 34],\n [10, -15, 5, -5, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-22, 17, -1, 24, 1],\n [9, -6, 0, -8, 3],\n [8, -10, 6, -4, 10],\n [16, 1, -11, -10, 11],\n [29, -31, 15, -18, 28]]?\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],\n [0, 0, -2, 4, -6],\n [0, 0, 12, -24, 36],\n [0, 0, 0, 0, 0],\n [0, 0, 2, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[7, 19, 0, -17, -33],\n [-33, 4, 15, 63, 2],\n [-41, 4, 41, 90, -12],\n [36, 7, -40, -85, -1],\n [33, -30, -15, -18, -18]]?\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[[-19, 26, -38, -21, -40],\n [4, 0, -36, 16, 16],\n [-47, 44, 7, -43, -44],\n [-19, 22, -16, -21, -32],\n [65, -54, -30, 45, 24]]?\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[[-12, -2, 8, -2, 12],\n [12, 2, -8, 2, -12],\n [-36, -6, 24, -6, 36],\n [18, 3, -12, 3, -18],\n [-18, -3, 12, -3, 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[[3, 7, 13, -12, -5],\n [3, 6, 6, -4, -5],\n [-9, -12, 24, -36, 15],\n [-24, -42, -6, -16, 40],\n [-12, -19, 11, -24, 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[[43, -18, -34, 42, 2],\n [-46, 12, 52, -48, 1],\n [9, -30, 24, 0, 6],\n [-30, 36, 2, -22, -5],\n [-31, 2, 60, -36, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, 1, -28, -10, -3],\n [22, 7, -5, -18, -18],\n [5, -23, -8, -49, -47],\n [43, -10, -45, -74, -65],\n [35, -49, -2, -19, -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 5x5 matrix:\n[[-3, -18, -9, 18, -15],\n [66, -36, 18, -36, 42],\n [39, -18, 12, -24, 27],\n [3, -18, -6, 12, -9],\n [27, -18, 6, -12, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 1, -6, -3, 2],\n [0, 6, -36, -18, 12],\n [0, -2, 12, 6, -4],\n [0, -4, 24, 12, -8],\n [0, -3, 18, 9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-24, -3, 0, -24, 24],\n [3, 5, -50, 18, -37],\n [5, -3, -44, -16, -3],\n [18, -1, 22, 6, 2],\n [-11, -4, 24, -20, 29]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-18, 0, 15, -6, 3],\n [0, 24, -10, 4, 10],\n [-6, 24, -5, 2, 11],\n [32, 8, -30, 12, -2],\n [-18, -12, 20, -8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[16, -9, -4, -25, -17],\n [18, 19, 22, -22, -13],\n [-12, 12, -15, 12, 6],\n [-10, 0, -30, 5, 0],\n [18, 15, 15, -24, -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[[10, 4, -25, 5, -32],\n [59, -40, 45, -36, 47],\n [50, 10, 21, -29, 37],\n [-2, -50, 35, -19, 13],\n [-17, -2, 6, 13, 14]]\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 5x5 matrix:\n[[-2, -34, -56, -36, -6],\n [-74, 2, 2, -30, -72],\n [6, -45, 67, 48, 0],\n [8, 52, -59, -39, 13],\n [11, -23, -61, -27, 14]]\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 5x5 matrix:\n[[22, 19, 0, 5, 27],\n [-34, -28, 0, 10, -24],\n [4, 3, 0, -5, -1],\n [-32, -26, 0, 14, -18],\n [-2, -3, 0, -17, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, 56, -4, 32, -16],\n [1, -24, 15, -16, 0],\n [-44, -38, -49, 31, 14],\n [0, -5, 20, -10, 0],\n [9, 5, 11, -12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 0, -12, -8, -16],\n [-40, -18, 21, -10, -2],\n [-18, -24, -2, 4, -24],\n [15, -8, -13, 18, -12],\n [50, -18, -59, 30, -62]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 16, 20, -8, 16],\n [3, -4, -5, 2, -4],\n [6, -8, -10, 4, -8],\n [6, -8, -10, 4, -8],\n [3, -4, -5, 2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, -15, -60, 0, -21],\n [-5, 5, 44, -6, 20],\n [39, -42, 18, 3, 15],\n [-2, 8, 12, 2, 2],\n [-4, -20, -32, -12, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 4, -4, -12, 20],\n [2, 2, -2, -6, 10],\n [-1, -1, 1, 3, -5],\n [-5, -5, 5, 15, -25],\n [2, 2, -2, -6, 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[[-28, -34, -100, -56, -82],\n [7, -25, -24, -29, -16],\n [-40, 47, -24, -21, -24],\n [34, -18, 53, 48, 45],\n [16, 23, 65, 40, 48]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-28, -13, -31, -6, 21],\n [16, -17, 4, 26, -22],\n [15, 6, 42, -42, -3],\n [8, 23, -4, 26, -6],\n [-4, 38, 17, -36, 19]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-20, -28, -28, -17, -28],\n [19, 21, 26, 13, 22],\n [-26, -34, -32, -16, -28],\n [-12, -17, 7, 17, 20],\n [12, -30, 18, -9, -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[[8, -24, 34, -4, -44],\n [-36, -9, -36, -12, 0],\n [22, 11, 34, 10, -16],\n [-21, -22, -28, -13, 6],\n [-52, 30, -35, -2, -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[[16, 2, 0, 0, 16],\n [-42, -3, -9, 6, -36],\n [-14, -4, 9, -6, -20],\n [16, 5, -12, 8, 24],\n [2, 1, -3, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-6, 0, 8, -2, 12],\n [-3, 0, 4, -1, 6],\n [-3, 0, 4, -1, 6],\n [-6, 0, 8, -2, 12],\n [9, 0, -12, 3, -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[[5, 50, -30, 35, 0],\n [12, 57, -48, 27, -24],\n [-8, 32, -26, 6, 11],\n [3, -29, 0, -38, -27],\n [-28, -9, 20, -7, 58]]\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 5x5 matrix:\n[[28, 5, -12, -19, 4],\n [-20, 1, 20, 17, -12],\n [-12, 3, 18, 12, -12],\n [12, 21, 42, 6, -36],\n [-32, -12, -2, 17, 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[[22, -36, -12, 26, -68],\n [-27, 36, 0, -23, 56],\n [8, -30, -6, 6, -18],\n [0, -27, -27, 13, -43],\n [15, -29, 3, 8, -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 5x5 matrix:\n[[8, 19, -4, -24, 23],\n [29, 43, 20, 5, 23],\n [1, 8, -8, -23, 16],\n [33, 48, 24, 9, 24],\n [5, 4, 8, 13, -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[[-3, -5, 2, 1, 0],\n [6, 10, -4, -2, 0],\n [-15, -25, 10, 5, 0],\n [0, 0, 0, 0, 0],\n [-15, -25, 10, 5, 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[[15, 32, -17, 4, 16],\n [30, 14, 16, -2, -8],\n [10, -12, 22, -4, -16],\n [15, 17, -2, 1, 4],\n [15, 22, -7, 2, 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[[57, 33, 9, 9, -9],\n [-38, -29, 36, 21, -32],\n [24, 21, -4, -11, 10],\n [-20, -21, 36, 15, -34],\n [-33, -13, -23, -15, 24]]\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[[-25, -11, 29, 23, 0],\n [-10, -38, 34, -2, 28],\n [15, 3, -15, -15, 3],\n [-15, -15, 23, 11, 7],\n [-15, -15, 23, 11, 7]]\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 5x5 matrix:\n[[18, -4, -28, 16, -14],\n [21, -2, -29, 20, -10],\n [-6, 4, 13, -4, 11],\n [5, 14, 13, 12, 32],\n [4, -8, -16, 0, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[1, 6, -8, 10, 1],\n [3, 18, -24, 30, 3],\n [-21, -36, 33, -45, -6],\n [-14, 6, -23, 25, 1],\n [7, 12, -11, 15, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-16, -40, -44, -34, 10],\n [10, 6, 18, 26, -11],\n [0, -20, -10, 5, -5],\n [-2, -14, -10, -2, -1],\n [-4, -8, -10, -9, 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[[59, 5, -28, 5, 49],\n [43, 5, -28, 7, 37],\n [7, 5, -46, 37, 31],\n [61, 5, -31, 9, 54],\n [-33, 1, -20, 27, -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[[26, -27, -34, -36, 15],\n [-2, 30, 28, 18, -24],\n [4, 28, 24, 12, -24],\n [14, 10, 4, -6, -12],\n [12, 7, 2, -6, -9]]\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 5x5 matrix:\n[[3, 4, 5, -2, -2],\n [9, 12, 15, -6, -6],\n [-3, -4, -5, 2, 2],\n [0, 0, 0, 0, 0],\n [-15, -20, -25, 10, 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[[-18, 6, 34, -23, -19],\n [-13, 3, 14, -39, 14],\n [8, 2, -8, 14, -14],\n [-8, -2, 18, 11, -11],\n [-1, 5, -8, -40, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-18, -30, -36, -6, 6],\n [3, 5, 6, 1, -1],\n [3, 5, 6, 1, -1],\n [18, 30, 36, 6, -6],\n [-12, -20, -24, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, -4, 8, -2, -8],\n [-1, 2, -4, 1, 4],\n [3, -6, 12, -3, -12],\n [3, -6, 12, -3, -12],\n [6, -12, 24, -6, -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 5x5 matrix:\n[[1, 3, 1, -1, -8],\n [4, 12, 22, -22, 13],\n [0, 0, -6, 6, -15],\n [1, 3, 7, -7, 7],\n [-6, -18, -18, 18, 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 5x5 matrix:\n[[-21, -28, -46, 17, 11],\n [18, 27, 41, -3, -10],\n [24, -7, 24, 15, -10],\n [-21, -28, -27, 4, 4],\n [18, -42, 27, 12, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[21, 77, 31, -28, 4],\n [1, -22, -13, 7, -17],\n [2, 23, 15, -13, 13],\n [-11, -26, 12, -13, 32],\n [16, 20, -13, 32, -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[[-20, 69, -9, 55, 13],\n [-69, 28, 3, 61, 78],\n [-16, 38, -3, 49, 20],\n [-23, -2, 2, 18, 23],\n [-20, -19, 1, -5, 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 5x5 matrix:\n[[0, 0, 0, 0, 0],\n [15, 6, 0, 6, -15],\n [-20, -8, 0, -8, 20],\n [-10, -4, 0, -4, 10],\n [-10, -4, 0, -4, 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[[-48, 6, -60, -24, 66],\n [-6, -13, 10, -3, -3],\n [6, 2, 4, 3, -6],\n [12, -18, 36, 6, -30],\n [12, 15, -6, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 6, -1, 1, 0],\n [4, -12, 2, -2, 0],\n [0, 0, 0, 0, 0],\n [-4, 12, -2, 2, 0],\n [12, -36, 6, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[30, -25, -10, 15, 15],\n [-30, 25, 10, -15, -15],\n [36, -30, -12, 18, 18],\n [6, -5, -2, 3, 3],\n [-24, 20, 8, -12, -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[[-20, -3, -4, 3, -5],\n [14, 17, 24, 21, 36],\n [-7, -32, -27, -34, -35],\n [4, -40, -12, -32, -4],\n [-17, -16, -5, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, -31, 6, -76, -66],\n [5, 25, 0, 67, 38],\n [-15, -8, 11, 6, 18],\n [7, -44, 56, -6, 12],\n [-23, -25, 48, 35, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[10, -30, -10, 0, 15],\n [-16, 0, 10, -12, -15],\n [-26, -18, 14, -24, -21],\n [10, 2, -6, 8, 9],\n [-28, 20, 20, -16, -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[[6, -20, 22, -24, -6],\n [21, 7, 0, 4, 23],\n [-3, 3, -4, 4, -1],\n [-9, -19, 16, -20, -19],\n [0, 14, -14, 16, 8]]?\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, -12, 20, 6, -22],\n [-14, 15, -28, -9, 27],\n [3, -9, 6, 0, -18],\n [24, -18, 48, 18, -30],\n [-15, 0, -30, -15, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-36, 18, 36, 0, -48],\n [8, 40, 34, -16, -30],\n [14, 31, 16, -41, 17],\n [20, -2, -8, 16, -4],\n [16, -4, -10, 8, 6]]\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, 34, -22, 58, 13],\n [4, 25, -11, 11, -12],\n [7, 31, -21, 25, -9],\n [3, -21, -4, -25, -6],\n [-4, -19, 6, 17, 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[[47, -24, -27, 27, 24],\n [1, -57, -6, 26, -23],\n [-12, -26, 25, -3, -31],\n [-45, 38, 2, -20, -3],\n [-32, 37, 19, -27, -7]]\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, 10, -4, -6, 6],\n [4, -10, 4, 6, -6],\n [-10, 25, -10, -15, 15],\n [2, -5, 2, 3, -3],\n [-6, 15, -6, -9, 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 5x5 matrix:\n[[14, 8, 5, 8, 1],\n [-32, -62, 25, 16, 39],\n [4, 41, -7, 9, -21],\n [16, 21, 3, 8, 2],\n [66, -24, -3, -24, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[14, 7, 31, -3, -10],\n [-4, 2, 14, 6, 12],\n [0, -7, -10, -9, -16],\n [-10, -16, -46, -12, -18],\n [-12, 6, 21, 18, 36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[15, -18, 3, -2, 14],\n [-3, -3, 6, -5, -4],\n [11, -29, 28, -10, 13],\n [12, -14, 14, 4, 18],\n [-4, 17, -21, 7, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[50, 28, -14, 33, 8],\n [46, 4, -43, 54, -33],\n [44, 24, -23, 33, -17],\n [18, 12, -6, 11, -2],\n [36, 40, 9, 5, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[30, 4, 20, 2, -6],\n [-24, 6, -18, 0, 6],\n [-13, 16, 14, 22, -9],\n [2, -25, -25, -28, 13],\n [7, -3, -21, -20, 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[[-28, 6, -5, -46, 19],\n [-9, 1, -3, -12, 14],\n [-18, 2, -6, -24, 28],\n [-18, 4, -3, -30, 11],\n [-12, 4, 0, -24, -4]]\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, 38, -1, -53, 5],\n [17, 20, -9, -23, 13],\n [11, 25, -2, -24, 14],\n [-21, 9, 15, -20, 45],\n [-9, -29, -4, 40, -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[[10, -13, 7, -5, -6],\n [18, -21, 15, -9, -6],\n [8, -12, 4, -4, -8],\n [16, -20, 12, -8, -8],\n [-14, 18, -10, 7, 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[[6, -17, -30, 4, 7],\n [37, -27, -6, 3, 21],\n [-25, -4, 12, 35, -4],\n [-25, 8, 0, 11, -10],\n [-3, 6, 6, -3, -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[[0, 6, 0, 3, -12],\n [0, 6, 0, 3, -12],\n [0, 6, 0, 3, -12],\n [0, -10, 0, -5, 20],\n [0, -12, 0, -6, 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, 34, 23, -2, 19],\n [12, 54, 35, 4, -3],\n [19, -35, -26, -1, -23],\n [-13, 32, 17, -8, 11],\n [-22, -12, -4, 0, 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[[-10, -15, 2, -22, -22],\n [0, 0, 0, 0, 0],\n [-28, -3, -10, 6, 6],\n [24, 9, 6, 6, 6],\n [-5, 0, -2, 2, 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[[-20, 8, -8, -16, -16],\n [15, -6, 6, 12, 12],\n [30, -12, 12, 24, 24],\n [-5, 2, -2, -4, -4],\n [20, -8, 8, 16, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-20, 30, -15, 5, 30],\n [4, -6, 3, -1, -6],\n [20, -30, 15, -5, -30],\n [-20, 30, -15, 5, 30],\n [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[[-25, -27, 12, -24, 36],\n [5, -10, -9, -15, 6],\n [-10, -15, 3, -15, 18],\n [-15, 9, 18, 18, 0],\n [25, 13, -18, 6, -24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0, 0],\n [3, -3, 4, -4, -4],\n [15, -15, 20, -20, -20],\n [3, -3, 4, -4, -4],\n [-9, 9, -12, 12, 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 5x5 matrix:\n[[22, -42, 7, -14, -10],\n [10, -6, -11, -50, 2],\n [33, -49, 42, 28, -1],\n [-18, 10, -26, -3, -11],\n [-9, 5, 17, 60, -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[[-3, -34, -16, 20, -38],\n [9, -15, 12, -15, -12],\n [-12, -6, -24, 30, -12],\n [-2, -27, -12, 15, -30],\n [-1, -20, -8, 10, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-20, -12, -8, -16, 12],\n [26, -6, 20, 28, -30],\n [13, -30, 22, 23, -33],\n [-10, 21, -16, -17, 24],\n [6, 36, -12, -6, 18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-14, -3, -7, -4, -5],\n [-10, 23, -27, -28, -13],\n [24, 12, 6, 0, 6],\n [-12, 34, -38, -40, -18],\n [-42, -9, -21, -12, -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[[16, 18, 34, -14, -6],\n [-12, -17, -39, 9, 11],\n [20, 12, 2, -22, 12],\n [34, 26, 25, -35, 10],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[35, -3, 20, 2, -8],\n [-5, -15, -8, -2, 8],\n [20, 6, 14, 2, -8],\n [0, 45, 15, 5, -20],\n [0, -9, -3, -1, 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[[-14, -10, -2, -1, 22],\n [-9, 10, -13, 11, 10],\n [47, 35, 2, 21, -4],\n [-11, 5, -8, -4, -38],\n [8, -15, 13, -1, 48]]?\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[[-2, 24, -48, -4, 36],\n [-44, -54, 56, 4, -72],\n [-61, -21, 12, 10, -19],\n [9, 17, -2, 4, -1],\n [26, 16, -20, -4, 50]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, -9, 20, 9, 10],\n [-30, 14, 11, -13, 36],\n [2, 30, 3, -17, 22],\n [27, 10, 1, 16, 32],\n [-36, -23, 20, -2, -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 5x5 matrix:\n[[19, -40, 41, 24, 9],\n [13, 0, 33, 26, 5],\n [37, 2, 50, 4, 46],\n [2, 48, 12, 18, 0],\n [31, -4, 35, -8, 43]]\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 5x5 matrix:\n[[0, 18, -30, -36, 30],\n [0, -3, 5, 6, -5],\n [0, 15, -25, -30, 25],\n [0, -15, 25, 30, -25],\n [0, 12, -20, -24, 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 5x5 matrix:\n[[4, -2, -6, 27, -9],\n [-14, 2, -8, 28, 7],\n [-24, -2, -2, 19, 7],\n [-28, 32, -12, -36, 72],\n [-24, -12, -12, 84, -18]]\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 5x5 matrix:\n[[-5, -6, 5, 4, -5],\n [50, 18, -26, -4, 20],\n [40, 27, -28, -14, 25],\n [50, 18, -26, -4, 20],\n [0, 35, -20, -30, 25]]\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, -29, 4, -12, 11],\n [24, -9, -6, -24, 15],\n [-35, 20, 5, 30, -20],\n [-32, 23, 2, 24, -17],\n [-33, 33, -3, 18, -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[[39, 24, -3, 33, 30],\n [-4, 29, -43, -52, -17],\n [-34, -27, 41, -4, -33],\n [39, 37, -70, -11, 41],\n [-63, -27, 45, -14, -45]]\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[[-3, -31, -17, -42, -4],\n [50, 9, -33, 4, -17],\n [-4, 47, 9, 40, 1],\n [13, 2, 22, -13, -6],\n [30, -9, -47, -3, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-18, 20, -42, -14, 21],\n [-6, -28, 41, 2, -41],\n [-36, -8, -17, -24, -14],\n [24, -12, 40, 20, -16],\n [30, 24, -4, 22, 25]]\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, 4, 6, -3, -28],\n [-40, 4, -5, -3, 27],\n [-12, 0, -2, 0, 10],\n [6, 0, 1, 0, -5],\n [-36, 24, 4, -18, -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 5x5 matrix:\n[[22, -48, -50, 7, 15],\n [22, -36, -52, -1, 7],\n [-4, 3, 26, 5, 6],\n [6, -21, -46, 2, -1],\n [22, -24, -2, -1, 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[[-2, 6, 9, -15, -8],\n [14, 6, 1, 9, 24],\n [12, -18, 8, 16, 24],\n [-25, 18, -11, -26, -47],\n [12, 30, -4, -4, 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 5x5 matrix:\n[[-8, -17, 34, -16, -15],\n [-18, -47, 10, -29, -18],\n [-5, -15, 33, -20, -6],\n [12, 38, 24, 20, 2],\n [-8, -17, -56, 11, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-24, 20, 24, -12, -4],\n [-21, -14, -14, 11, 12],\n [-39, 45, 44, -42, -19],\n [-36, 11, 6, -19, -3],\n [27, -24, -22, 25, 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[[-13, 35, 38, 38, 26],\n [-40, 25, 3, -7, 4],\n [-27, 10, -1, -16, -5],\n [-69, 49, 38, -7, 7],\n [-52, 26, -4, -19, -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 5x5 matrix:\n[[31, 4, -20, 27, 42],\n [4, 2, -1, 10, 14],\n [62, -22, -45, 44, 34],\n [14, -27, -22, 2, -20],\n [-36, 26, 34, -2, 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[[14, 16, 26, -28, -56],\n [0, 29, 23, 19, -6],\n [-6, -29, -27, -6, 28],\n [57, 26, -33, 1, -10],\n [-47, -30, 29, -30, 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 5x5 matrix:\n[[-9, 5, -3, 6, 7],\n [14, -5, 8, -2, 8],\n [-58, 41, -44, 2, -36],\n [-48, 54, -48, -6, -36],\n [21, -8, 11, -5, 7]]\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, -19, 0, 3, -24],\n [18, 15, -18, 15, 8],\n [-27, 42, -19, -57, 51],\n [17, 6, 20, -26, 10],\n [7, -65, 58, 20, -58]]\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, 0, 0, 0, 0],\n [0, 4, -8, 2, 12],\n [0, 0, 0, 0, 0],\n [0, 12, -24, 6, 36],\n [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[[-6, -3, 2, 5, -6],\n [-36, -18, 12, 30, -36],\n [-36, -18, 12, 30, -36],\n [-12, -6, 4, 10, -12],\n [18, 9, -6, -15, 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[[-33, 16, -11, -10, 25],\n [-5, -17, -12, 37, -18],\n [-18, 16, -2, -28, 10],\n [-18, 25, 3, -59, 1],\n [-31, 19, -8, -31, 8]]\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[[-37, 27, 1, 1, -31],\n [-18, 17, 0, 8, 16],\n [-20, 25, 14, 6, -2],\n [19, 1, 17, 9, 45],\n [-22, 44, 40, 12, 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[[14, -48, -30, 6, -12],\n [30, -4, 38, -38, -4],\n [-13, -7, -16, 10, -4],\n [-2, -14, -7, -2, -7],\n [-28, 2, -4, -2, -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[[4, -35, -39, -29, -16],\n [2, 15, 12, 0, 14],\n [-3, 2, 11, 5, -13],\n [3, -16, -16, -19, -6],\n [3, -1, 1, -22, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [8, 12, 0, -12, -8],\n [-8, -12, 0, 12, 8],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-3, 0, -2, 2, 2],\n [18, 0, 12, -12, -12],\n [-18, 0, -12, 12, 12],\n [15, 0, 10, -10, -10],\n [-18, 0, -12, 12, 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 5x5 matrix:\n[[-22, 2, -34, 0, -4],\n [-35, -5, -28, -9, -51],\n [40, 14, 19, -14, 57],\n [-16, 66, -53, -11, 26],\n [-11, 17, 11, 41, -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[[23, 15, 13, -32, -26],\n [-14, 24, -45, -8, -22],\n [-20, -31, 2, 44, 35],\n [-15, 4, -32, 11, -6],\n [-6, -18, 10, 20, -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[[24, -30, 17, 14, 30],\n [23, -41, 32, 30, 39],\n [12, 42, 3, -42, -51],\n [-7, -59, -18, 46, 75],\n [-23, 23, -53, -24, -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[[39, 9, 14, -4, -16],\n [28, 21, 17, -18, -5],\n [28, 50, 7, -29, -37],\n [37, 14, 39, -24, -1],\n [30, 51, 20, -37, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[14, 21, -13, 19, -20],\n [-12, 6, -6, 10, 0],\n [-22, -3, -1, 3, 10],\n [10, -33, 25, -39, 20],\n [-6, -18, 12, -18, 15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, -2, -8, -2, 2],\n [-9, 3, 12, 3, -3],\n [12, -4, -16, -4, 4],\n [3, -1, -4, -1, 1],\n [12, -4, -16, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 4, 24, -4, -24],\n [6, 3, 18, -3, -18],\n [-8, -4, -24, 4, 24],\n [6, 3, 18, -3, -18],\n [12, 6, 36, -6, -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[[6, 8, 26, -14, 26],\n [-13, -8, -54, -2, -29],\n [28, -3, 37, 58, -18],\n [-18, -9, -11, 4, -16],\n [-24, -3, -72, -39, -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[[-22, -13, 0, 12, -3],\n [-52, -22, -12, 18, -12],\n [10, 35, -40, -40, -15],\n [-6, 27, -42, -33, -18],\n [20, -10, 30, 15, 15]]?\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, 24, 24, 18, -6],\n [0, -4, -4, -3, 1],\n [0, -20, -20, -15, 5],\n [0, 0, 0, 0, 0],\n [0, -24, -24, -18, 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[[-12, 6, -6, 36, -30],\n [30, -3, 3, -48, 36],\n [-24, -4, 4, 16, -8],\n [-42, -3, 3, 42, -27],\n [-20, -2, 2, 18, -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 5x5 matrix:\n[[-11, 45, 17, 9, -2],\n [-16, 0, -24, -12, -12],\n [30, 7, 36, 84, 24],\n [6, 7, 34, -3, 5],\n [-25, -13, -24, -6, -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[[-8, 20, 8, -12, 0],\n [0, 0, 0, 0, 0],\n [-10, 25, 10, -15, 0],\n [10, -25, -10, 15, 0],\n [10, -25, -10, 15, 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[[5, 10, -20, -15, -10],\n [5, 8, -4, -3, -7],\n [-15, -20, -20, -15, 15],\n [-12, -14, -32, -24, 9],\n [17, 26, -4, -3, -22]]?\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 5x5 matrix:\n[[-20, -24, 20, 4, 4],\n [-15, -18, 15, 3, 3],\n [-15, -18, 15, 3, 3],\n [20, 24, -20, -4, -4],\n [10, 12, -10, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [0, -20, -15, 10, 10],\n [0, -8, -6, 4, 4],\n [0, -12, -9, 6, 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 5x5 matrix:\n[[-8, 24, 8, 0, -24],\n [12, -36, -12, 0, 36],\n [4, -12, -4, 0, 12],\n [2, -6, -2, 0, 6],\n [4, -12, -4, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[15, 11, 30, -8, -17],\n [60, -7, 30, 46, 19],\n [-23, -1, -18, -12, -1],\n [-12, -2, -12, -4, 2],\n [-5, 2, 0, -6, -4]]\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, 32, -22, -30, 10],\n [2, 10, -17, -6, 2],\n [2, -2, -2, 3, -1],\n [-12, 28, -8, -30, 10],\n [-6, 10, 1, -12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, -15, 13, 60, 98],\n [3, -38, -61, 71, -31],\n [24, -21, -57, 24, -58],\n [-26, -12, -10, 90, 58],\n [8, 6, -38, 30, -48]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 12, 2, 12, 2],\n [12, -36, -6, -36, -6],\n [-12, 36, 6, 36, 6],\n [10, -30, -5, -30, -5],\n [8, -24, -4, -24, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 3, 4, -5, 6],\n [8, 6, 8, -10, 12],\n [-4, -3, -4, 5, -6],\n [20, 15, 20, -25, 30],\n [-24, -18, -24, 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[[-24, -26, 14, 0, -30],\n [-27, 12, -18, -15, -15],\n [-6, -12, 8, 2, -10],\n [-18, -3, -3, -6, -15],\n [-18, 19, -21, -14, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[8, -15, 3, -1, -31],\n [12, -27, 21, 0, -36],\n [13, 24, -28, 29, 11],\n [-19, -2, -8, -30, -6],\n [0, -21, 9, -15, -33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, -16, 56, -17, -44],\n [9, -20, 6, 26, 0],\n [16, -15, -1, 29, 10],\n [29, 21, 17, -19, 4],\n [-5, -24, -2, 26, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 63, 25, -10, -32],\n [10, 39, 24, -2, -11],\n [24, 6, 30, 3, 2],\n [-58, 29, 14, 34, -37],\n [18, 2, 46, -19, -35]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-12, 15, 6, 21, -3],\n [33, -12, -21, -15, -12],\n [6, -14, -2, -20, 6],\n [-6, 1, 4, 1, 3],\n [-6, 14, 2, 20, -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[[-25, 26, 65, -30, -12],\n [-22, 9, 14, -5, -6],\n [21, -9, -21, 6, 5],\n [42, -4, 6, -10, 6],\n [-4, 4, -28, -1, -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[[-25, -24, -23, -7, 19],\n [-27, -36, -29, -5, 22],\n [17, 35, 24, 4, -16],\n [-5, -29, -38, -34, 39],\n [11, 51, 18, 50, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[14, 26, 25, -14, 18],\n [-31, 26, 19, -4, 26],\n [24, -41, -25, 12, -34],\n [19, -23, 19, -2, -25],\n [-3, 26, 25, -16, 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[[-15, 35, 30, -8, -15],\n [-6, -54, -29, -18, 16],\n [-3, -7, -17, -26, -47],\n [-18, -51, -12, -18, 39],\n [12, 10, -22, -16, -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[[0, 0, 0, 0, 0],\n [18, 0, -36, 0, 12],\n [15, 0, -30, 0, 10],\n [-12, 0, 24, 0, -8],\n [3, 0, -6, 0, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, -1, 5, 4, -10],\n [17, 15, -11, -12, 10],\n [-14, -7, 19, 16, -35],\n [-2, 4, 12, 8, -30],\n [9, 3, -15, -12, 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[[10, 5, 4, 2, -4],\n [-22, -35, -5, -20, 28],\n [-18, -5, 27, -20, 4],\n [-46, -25, 14, -28, 20],\n [32, -30, -34, 6, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-2, 19, 67, -14, -14],\n [-14, -66, 32, -4, -2],\n [21, 1, -18, -54, -22],\n [0, -36, 20, 17, 10],\n [-68, -52, 16, -38, -30]]\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[[-39, 10, -30, -7, -5],\n [41, 41, -32, 60, -42],\n [-18, 2, 44, -52, 42],\n [4, -52, 28, -42, 26],\n [14, 54, -22, 56, -31]]\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, 36, 0, 39, 30],\n [31, 50, -9, 54, 24],\n [24, 2, 14, 1, -11],\n [-23, -4, -11, -6, 1],\n [-26, -51, 4, -54, -33]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-18, 16, -8, 5, -8],\n [8, -5, 12, -13, 8],\n [-22, 6, -6, -1, -20],\n [32, -32, 23, -21, 14],\n [-24, 29, -10, 7, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-30, 12, -18, -12, 21],\n [2, -4, 6, -8, 13],\n [36, -24, 36, -12, 18],\n [10, -8, 12, -7, 11],\n [34, -16, 24, 7, -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[[1, -2, -18, -9, 3],\n [16, -1, -43, 24, -10],\n [8, -17, 41, 15, -18],\n [46, -42, -66, 19, -18],\n [35, -15, -58, 54, -37]]\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[[12, -3, -15, -18, -15],\n [8, -2, -10, -12, -10],\n [20, -5, -25, -30, -25],\n [12, -3, -15, -18, -15],\n [24, -6, -30, -36, -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[[6, 16, 7, 11, -13],\n [4, -16, 6, -2, 6],\n [-5, -10, -6, -8, 9],\n [-5, 10, -7, -1, -2],\n [-14, 36, -20, 0, -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[[19, 34, -2, 26, -39],\n [-8, -34, -10, -10, 34],\n [-5, -2, -14, 11, 23],\n [55, 17, 30, -20, -59],\n [42, -29, 28, -54, 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[[-16, 6, 11, -52, 47],\n [52, 18, 0, -20, 16],\n [-6, 25, -15, -34, 37],\n [-21, 16, -26, 34, -28],\n [9, -10, 15, 24, -33]]\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 5x5 matrix:\n[[-30, -4, 10, -7, 15],\n [12, 10, 2, -32, 15],\n [-6, 6, -6, 54, -15],\n [-31, -34, 10, -20, -2],\n [48, 48, -12, 6, 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[[-6, -9, 15, -3, 12],\n [0, 0, 0, 0, 0],\n [4, 6, -10, 2, -8],\n [0, 0, 0, 0, 0],\n [-6, -9, 15, -3, 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[[-50, 31, 24, -25, -39],\n [-5, 22, -3, 11, 6],\n [-16, 6, 24, -18, -6],\n [-6, 11, -3, 4, -3],\n [12, 12, 18, 6, 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 5x5 matrix:\n[[30, 0, 10, -2, 5],\n [17, 19, 15, -14, 4],\n [-11, 23, 11, -14, 0],\n [23, -14, -23, 2, 0],\n [-31, 13, 7, -4, -3]]\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, -18, 36, 30, -12],\n [-9, 9, -18, -15, 6],\n [3, -3, 6, 5, -2],\n [0, 0, 0, 0, 0],\n [-3, 3, -6, -5, 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 5x5 matrix:\n[[13, 2, -26, 10, -4],\n [21, -32, -12, -18, 20],\n [1, -27, -22, -13, 25],\n [3, 17, 12, 9, -17],\n [-35, -11, 22, -17, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[18, -18, -15, 15, 6],\n [3, -24, -11, -10, 2],\n [-27, 48, 31, -10, -10],\n [25, -60, -35, 0, 10],\n [40, -12, -22, 50, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 20, -16, 20, 12],\n [-6, 30, -24, 30, 18],\n [2, -10, 8, -10, -6],\n [1, -5, 4, -5, -3],\n [5, -25, 20, -25, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-48, -10, -12, 5, 24],\n [11, 10, 3, 37, -10],\n [-9, 26, -4, 45, -10],\n [8, -9, 0, -3, -13],\n [-29, -8, -16, -37, -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[[-1, -3, 5, 1, 5],\n [-5, -15, 25, 5, 25],\n [5, 15, -25, -5, -25],\n [5, 15, -25, -5, -25],\n [1, 3, -5, -1, -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 5x5 matrix:\n[[-12, 8, 16, -8, -24],\n [-18, 12, 24, -12, -36],\n [-9, 6, 12, -6, -18],\n [18, -12, -24, 12, 36],\n [3, -2, -4, 2, 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[[-25, 10, -25, 10, -5],\n [0, 2, 7, 3, 6],\n [20, -14, -1, -17, -14],\n [5, -12, -30, -17, -29],\n [40, -24, 12, -28, -16]]\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[[-6, 20, 29, 20, -20],\n [0, -24, -36, -24, 24],\n [42, -4, 1, -4, 4],\n [-18, 0, -3, 0, 0],\n [30, -12, -13, -12, 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[[-30, 24, -18, -36, -30],\n [20, -16, 12, 24, 20],\n [15, -12, 9, 18, 15],\n [5, -4, 3, 6, 5],\n [-10, 8, -6, -12, -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[[43, 2, -7, -4, -10],\n [0, 6, -3, -34, -13],\n [-61, 4, 10, -44, -7],\n [32, 24, -46, 0, 14],\n [-6, 64, -43, -34, 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[[-75, 9, 24, -34, -15],\n [-52, 25, 20, 10, -3],\n [6, 54, -33, -21, -11],\n [30, -74, 17, -10, 0],\n [10, 3, 12, 22, -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[[-12, 31, -41, -23, -16],\n [7, -21, -60, 26, -66],\n [5, 11, 62, -12, 58],\n [3, 25, 26, -18, 34],\n [31, 7, 8, 14, -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[[20, -30, 8, -48, 2],\n [25, -9, 29, -3, -26],\n [0, 12, 8, 24, -12],\n [15, -24, 5, -39, 3],\n [25, -18, 23, -21, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[27, -35, -47, 16, -4],\n [13, -25, 17, 49, 12],\n [-8, 0, -24, -32, -18],\n [-13, 5, -4, -22, -12],\n [65, 15, -4, 46, 54]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[22, -37, -30, -18, -28],\n [4, -9, -6, -2, -8],\n [13, -23, -18, -10, -18],\n [-19, 24, 24, 20, 14],\n [1, 4, 0, -4, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-16, 7, 18, -4, 14],\n [10, -9, -32, 27, -16],\n [29, -17, 20, -1, 41],\n [7, -20, 16, 7, 28],\n [-38, 15, -14, 18, -22]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[65, 7, 38, 16, 50],\n [-20, 42, 1, -23, -24],\n [-24, 6, -3, -3, -32],\n [62, 24, 53, 17, 28],\n [13, -25, 16, 26, -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[[-2, 0, 5, -6, 1],\n [-10, 0, 25, -30, 5],\n [4, 0, -10, 12, -2],\n [8, 0, -20, 24, -4],\n [4, 0, -10, 12, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[22, 37, 21, 32, -1],\n [-24, -34, 10, -8, 1],\n [-29, -42, 3, -13, 0],\n [-2, 7, 27, 44, -7],\n [-22, -35, -39, -20, -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[[27, 56, 31, 28, 24],\n [9, 51, 40, 16, 0],\n [-9, 38, -3, 10, -16],\n [-16, -25, -38, 16, 14],\n [19, 8, 14, -6, 6]]\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[[-21, 21, 0, -30, -45],\n [25, -20, 10, 20, 45],\n [0, 34, 18, -24, -39],\n [-15, 36, -18, 12, -45],\n [-12, 6, 18, -48, -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 5x5 matrix:\n[[15, 26, 8, -22, 4],\n [21, 12, 24, -38, -14],\n [13, -13, -8, 24, -17],\n [-28, -3, -24, -14, 36],\n [9, -32, -24, -14, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, 9, -6, -3, 3],\n [0, 0, 0, 0, 0],\n [-16, 12, -8, -4, 4],\n [-12, 9, -6, -3, 3],\n [-12, 9, -6, -3, 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[[0, -2, 0, -29, -3],\n [13, 4, 17, 65, -25],\n [11, -26, 26, 5, -23],\n [-1, 40, -18, 41, -4],\n [15, 52, -4, -15, -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[[22, 28, 10, 49, 44],\n [48, -55, -19, -17, -41],\n [-31, -34, -24, -7, 0],\n [-47, 28, 8, -15, 4],\n [36, -10, -4, -2, -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 5x5 matrix:\n[[3, -19, 15, 2, -1],\n [18, 16, 18, 28, 1],\n [16, -20, 40, 24, 6],\n [15, 34, -16, 13, -25],\n [-21, -43, -5, -34, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[30, -13, -12, 3, -1],\n [19, -21, -6, -35, 39],\n [-18, -3, -7, -63, 46],\n [-51, 14, 36, -24, -28],\n [63, -36, -1, 18, -7]]\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 5x5 matrix:\n[[-6, -6, 6, -12, -36],\n [-4, -4, 4, -8, -24],\n [-5, -5, 5, -10, -30],\n [5, 5, -5, 10, 30],\n [4, 4, -4, 8, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[35, -10, 0, -10, -40],\n [15, -21, 36, -30, -12],\n [-39, 13, -4, 14, 44],\n [-13, 0, 8, -2, 16],\n [1, -17, 36, -26, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-30, -34, 2, 11, 1],\n [39, 23, -22, 2, 1],\n [35, 12, -26, -19, 9],\n [32, 24, 4, 17, 11],\n [21, 4, -34, -11, -7]]\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 5x5 matrix:\n[[17, 21, 1, 16, -28],\n [-33, 87, -26, -4, -71],\n [23, -48, 13, 4, 74],\n [-51, 43, -25, -40, -56],\n [34, -73, 21, 0, 63]]\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[[-8, -14, -20, 11, -15],\n [11, -23, -5, 6, -20],\n [26, 26, 50, -26, 30],\n [-18, -12, -30, 15, -15],\n [26, -26, 10, 0, -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[[29, -21, 12, 42, 18],\n [36, 8, -4, 13, 21],\n [14, 39, -55, 18, -39],\n [33, 20, 14, 31, 18],\n [-38, -38, 3, -56, 4]]\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[[-8, -25, 0, -10, 0],\n [12, 24, -41, -4, -23],\n [18, 17, -50, -15, -32],\n [14, 11, -29, -31, -17],\n [12, 24, -16, 31, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, -10, 2, -10, 0],\n [24, 20, -4, 20, 0],\n [6, 5, -1, 5, 0],\n [0, 0, 0, 0, 0],\n [-30, -25, 5, -25, 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 5x5 matrix:\n[[0, 0, 0, 0, 0],\n [-3, 2, -2, -3, 1],\n [-3, 2, -2, -3, 1],\n [9, -6, 6, 9, -3],\n [-12, 8, -8, -12, 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[[-4, -55, 27, 2, -6],\n [-3, 18, -12, 3, -12],\n [8, 15, -1, -14, 62],\n [-15, 42, -30, -9, 60],\n [25, 32, -1, -9, 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[[-8, 24, 24, -8, -16],\n [14, -27, -18, 13, 16],\n [9, 45, 0, -12, -18],\n [19, -18, -24, 11, 14],\n [-5, -6, 50, 9, -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[[-10, 8, 4, -11, 9],\n [10, -8, -4, 11, -9],\n [-26, 22, 7, -28, 23],\n [-28, 26, 1, -29, 24],\n [2, 2, -11, 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[[9, 6, 18, 18, -18],\n [3, -10, -6, 6, 0],\n [15, 10, 30, 30, -30],\n [9, -6, 6, 18, -12],\n [-15, -10, -30, -30, 30]]\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 5x5 matrix:\n[[-2, -14, 4, -14, 6],\n [-3, -9, 6, -18, 15],\n [-5, -27, 10, -33, 19],\n [-2, -30, 4, -18, -2],\n [1, 3, -2, 6, -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[[0, 22, -34, -45, 33],\n [17, -2, 21, -1, -18],\n [57, 18, 11, -38, 8],\n [-16, -8, -8, 36, 26],\n [30, 12, 2, -16, 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 5x5 matrix:\n[[-6, 24, -30, -30, -36],\n [0, 0, 0, 0, 0],\n [-2, 8, -10, -10, -12],\n [0, 0, 0, 0, 0],\n [-3, 12, -15, -15, -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[[3, 6, 6, 6, -18],\n [-2, -4, -4, -4, 12],\n [-2, -4, -4, -4, 12],\n [0, 0, 0, 0, 0],\n [4, 8, 8, 8, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [-12, 12, -36, 30, 36],\n [4, -4, 12, -10, -12],\n [-8, 8, -24, 20, 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 5x5 matrix:\n[[-4, -16, -8, 8, -24],\n [-6, -24, -12, 12, -36],\n [-5, -20, -10, 10, -30],\n [4, 16, 8, -8, 24],\n [-1, -4, -2, 2, -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[[51, -12, -36, 27, 3],\n [29, -10, -24, 21, 3],\n [0, 27, 30, -48, -11],\n [-46, 14, 36, -30, -4],\n [45, -9, -30, 21, 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[[-4, 0, -1, -2, -5],\n [8, 0, 2, 4, 10],\n [0, 0, 0, 0, 0],\n [16, 0, 4, 8, 20],\n [-24, 0, -6, -12, -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[[-13, 24, 14, -13, -10],\n [14, -30, -28, 19, -5],\n [18, -36, -30, 22, 1],\n [1, -12, -8, 5, -9],\n [25, -36, -38, 27, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-6, -18, -12, 0, -6],\n [-5, -21, 2, -24, -35],\n [6, 18, 12, 0, 6],\n [2, 0, 16, -24, -28],\n [-2, -5, -6, 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[[-26, -14, -15, -29, -13],\n [-30, -3, 23, -25, 26],\n [-12, -9, -8, -59, 20],\n [7, -8, 18, -68, 61],\n [31, 22, -35, 47, -46]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-13, 45, -2, -32, 11],\n [-5, -6, -28, -37, 4],\n [-27, 44, 12, -9, 6],\n [-26, -1, 17, 17, 10],\n [-31, -5, 35, 50, 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[[12, 18, 0, 24, 24],\n [-12, -18, 0, -24, -24],\n [-6, -9, 0, -12, -12],\n [-8, -12, 0, -16, -16],\n [-12, -18, 0, -24, -24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-19, -39, -15, -17, 2],\n [-51, -24, -18, -24, -18],\n [-8, -7, 4, -3, 7],\n [43, -50, -2, 0, 44],\n [-50, 27, -26, -15, -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 5x5 matrix:\n[[-14, -8, -2, -7, -1],\n [12, 70, 27, -25, -52],\n [-30, 13, -4, -3, -11],\n [13, 16, 9, 34, -18],\n [34, -18, 4, 4, 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[[69, 10, -15, 50, -20],\n [-41, -12, -13, -49, 23],\n [-12, 44, -30, 10, 44],\n [13, 24, -4, 27, 6],\n [-17, -35, 23, -35, -27]]\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[[3, -2, -2, 10, 7],\n [21, -14, 18, 22, 1],\n [-21, 14, -18, -22, -1],\n [-3, 2, -4, -1, 2],\n [-9, 6, -4, -15, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0, 0],\n [9, 6, 9, 0, -9],\n [3, 2, 3, 0, -3],\n [-18, -12, -18, 0, 18],\n [-12, -8, -12, 0, 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[[17, 2, -16, 9, 21],\n [24, -14, -31, -11, 9],\n [8, 10, -3, 17, 21],\n [3, 12, 3, 18, 18],\n [-10, 4, 12, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[27, 45, -36, 21, -24],\n [0, 0, -18, -48, 60],\n [-3, -5, 21, 43, -54],\n [18, 30, -24, 14, -16],\n [0, 0, 0, 0, 0]]\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[[-6, -2, -4, 0, -6],\n [0, 0, 0, 0, 0],\n [-12, -4, -8, 0, -12],\n [-12, -4, -8, 0, -12],\n [9, 3, 6, 0, 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[[8, -12, -4, -12, -12],\n [24, -9, -6, -27, 0],\n [-12, 18, 6, 18, 18],\n [-20, 39, 12, 33, 42],\n [0, -9, -2, -3, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[7, -8, 2, 12, -3],\n [12, -28, -18, 42, 12],\n [23, -32, -2, 48, -3],\n [-5, 20, 20, -30, -15],\n [11, -4, 16, 6, -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[[6, -3, 12, 15, -3],\n [8, -4, 16, 20, -4],\n [2, -1, 4, 5, -1],\n [-8, 4, -16, -20, 4],\n [12, -6, 24, 30, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[18, 3, -14, 25, 1],\n [-14, -1, 6, -15, 1],\n [-18, -6, 25, -35, -5],\n [-34, -5, 24, -45, -1],\n [12, 3, -13, 20, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[13, 9, 34, -28, 3],\n [3, -6, 9, -3, 3],\n [8, 12, 20, -20, 0],\n [6, 16, 14, -18, -2],\n [2, -11, 7, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-9, -1, 18, -40, 31],\n [-12, -10, -15, 3, -2],\n [-12, -10, -15, 3, -2],\n [39, 31, 42, 0, -1],\n [-18, -16, -27, 11, -8]]\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, -23, -44, -2, 44],\n [22, 66, 3, -35, -7],\n [-28, -46, 0, 23, -16],\n [-7, -3, -7, -2, -5],\n [2, 24, -21, -22, 1]]\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, -10, 2, -2, -4],\n [6, -15, 3, -3, -6],\n [-10, 25, -5, 5, 10],\n [-10, 25, -5, 5, 10],\n [4, -10, 2, -2, -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[[27, -57, 10, 19, -7],\n [-30, 33, -51, -18, -6],\n [11, -4, 19, -3, 1],\n [2, -6, -20, -14, -10],\n [2, 29, 22, -21, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[40, -41, -52, -5, -19],\n [19, -17, -22, -2, -10],\n [-33, 32, 42, -5, -3],\n [-11, 21, 26, -6, -18],\n [-27, 7, 18, -44, -76]]?\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[[17, -11, 6, -5, -9],\n [-41, -49, -34, 62, -7],\n [-4, 0, 42, -28, 4],\n [39, 34, 47, -62, 15],\n [28, 39, -49, 4, -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[[0, 2, -12, -8, 4],\n [0, 3, -18, -12, 6],\n [0, 2, -12, -8, 4],\n [0, 5, -30, -20, 10],\n [0, -3, 18, 12, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, -24, 12, 16, -16],\n [6, 12, -6, -8, 8],\n [-6, -12, 6, 8, -8],\n [-15, -30, 15, 20, -20],\n [-18, -36, 18, 24, -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 5x5 matrix:\n[[24, 32, 0, -12, -36],\n [0, 6, -54, 45, 0],\n [0, -2, 18, -15, 0],\n [-12, -14, -18, 21, 18],\n [14, 20, -12, 3, -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[[-32, -5, 9, 2, -2],\n [41, 37, 23, -26, 51],\n [-50, -49, -7, 54, -47],\n [-55, -19, -1, -8, -21],\n [-8, -15, -5, 10, -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[[65, -9, -42, 11, -54],\n [-37, -4, 31, -20, 50],\n [-8, -8, 20, -22, 53],\n [-11, 14, 7, -26, -82],\n [-44, 1, 23, -17, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, -6, -2, -12, -2],\n [24, -12, -4, -24, -4],\n [-12, 6, 2, 12, 2],\n [6, -3, -1, -6, -1],\n [24, -12, -4, -24, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[12, 36, -36, 24, -12],\n [10, 30, -30, 20, -10],\n [0, 0, 0, 0, 0],\n [6, 18, -18, 12, -6],\n [10, 30, -30, 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[[18, 36, -30, 12, 36],\n [-3, -6, 5, -2, -6],\n [-9, -18, 15, -6, -18],\n [-3, -6, 5, -2, -6],\n [18, 36, -30, 12, 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[[24, -36, -39, -42, -21],\n [-11, 14, 14, 27, 17],\n [8, 9, 17, 28, 5],\n [11, -30, -37, -53, -22],\n [20, -7, 0, 26, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-30, -6, 0, 31, 26],\n [-39, -14, -27, 22, 41],\n [-1, 16, 22, -8, 15],\n [-27, 0, 6, 46, 53],\n [-6, -7, 12, 51, 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[[-12, 10, -8, 0, 12],\n [-30, 29, -1, -18, 12],\n [0, -4, -19, 18, 18],\n [20, -14, 26, -12, -32],\n [-32, 24, -34, 12, 44]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[25, 20, 10, -10, 15],\n [22, 28, 10, 1, -3],\n [29, 49, 8, 4, -12],\n [30, -6, 48, 12, 0],\n [35, -11, 38, -13, 35]]?\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[[-7, 16, 9, 1, 0],\n [9, -20, -35, -33, 4],\n [-14, 19, 11, 8, -10],\n [8, -27, -33, -21, -4],\n [-8, -25, -35, -8, -30]]?\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[[5, -17, -15, 3, 16],\n [36, 24, 24, 56, -20],\n [9, 18, 33, 13, -43],\n [5, -15, -49, -11, 34],\n [-25, -7, -20, -13, 61]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-21, 22, 18, -2, 20],\n [-27, 24, 18, -12, 30],\n [-22, 24, 20, 0, 20],\n [6, -12, -12, -12, 0],\n [24, -18, -12, 18, -30]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 22, -36, -10, 15],\n [32, 24, -16, -40, 44],\n [-14, -7, 2, 15, -16],\n [-4, 4, -8, 0, 1],\n [40, 16, 0, -40, 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[[12, -24, -8, 16, -4],\n [2, 7, -2, -4, 6],\n [-3, -27, 4, 16, -19],\n [10, 2, -8, 0, 10],\n [-28, 34, 20, -24, -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[[36, 6, 16, -52, 38],\n [3, -26, -12, 19, -18],\n [35, 4, 40, -75, 62],\n [19, -24, 4, -13, 8],\n [42, -31, 12, -40, 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[[9, -13, 35, 35, -36],\n [34, 18, -8, -8, 11],\n [12, 14, -14, -14, 19],\n [11, 8, -15, -15, 11],\n [-20, 5, -20, -20, 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 5x5 matrix:\n[[25, 10, 20, -13, 18],\n [35, -20, 15, 5, 0],\n [-12, 2, -19, 0, 4],\n [19, -8, 11, 1, 1],\n [-18, 18, 9, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[4, -1, 1, -2, -6],\n [32, 17, 19, 6, -42],\n [40, 15, 21, 2, -54],\n [6, -14, -4, -14, -12],\n [-8, -23, -13, -18, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -12, 8, 24, 4],\n [0, 15, -10, -30, -5],\n [0, 0, 0, 0, 0],\n [0, -6, 4, 12, 2],\n [0, 15, -10, -30, -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 5x5 matrix:\n[[13, 15, -18, 9, -4],\n [22, -10, -12, 46, 24],\n [-9, 2, 6, -17, -8],\n [2, -3, 0, 6, 4],\n [-36, -15, 36, -48, -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 5x5 matrix:\n[[54, -96, 6, -66, 0],\n [-22, 24, 2, 26, 6],\n [11, -30, 18, -35, 20],\n [7, -10, -3, -5, -2],\n [-23, 18, -6, 47, -12]]\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, 1, 11, -10, 14],\n [-8, -28, 0, -6, 4],\n [4, -6, -10, 8, -12],\n [-8, -20, 4, -8, 8],\n [0, 4, 2, -1, 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[[12, -30, 24, 3, -45],\n [-15, 22, 2, -2, 45],\n [-7, -31, 6, -15, -39],\n [30, 33, 24, 39, 36],\n [-40, -33, -28, -47, -30]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, -60, 33, 9, -7],\n [7, 40, -10, -16, 19],\n [31, 37, -11, -9, -1],\n [46, 46, -32, -4, 32],\n [-7, -7, -41, 23, 41]]\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[[-30, 18, 6, 6, -30],\n [25, -15, -5, -5, 25],\n [-20, 12, 4, 4, -20],\n [15, -9, -3, -3, 15],\n [25, -15, -5, -5, 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[[8, 22, 26, 59, 36],\n [-10, -15, 25, 36, -4],\n [-6, 5, -29, -40, -6],\n [-29, -29, 20, 41, -23],\n [-5, 5, 2, -45, 29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 16, -4, -8, 16],\n [-12, 16, -4, -8, 16],\n [0, 0, 0, 0, 0],\n [9, -12, 3, 6, -12],\n [15, -20, 5, 10, -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 5x5 matrix:\n[[36, -36, 36, 12, -6],\n [-30, 30, -30, -10, 5],\n [-12, 12, -12, -4, 2],\n [-30, 30, -30, -10, 5],\n [18, -18, 18, 6, -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, -42, 50, -36, -53],\n [5, -19, 41, -19, -16],\n [28, -7, 15, -32, -26],\n [14, -4, 8, -1, 2],\n [-20, 2, -14, 14, 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[[8, 14, 1, 20, 18],\n [-4, 4, -6, 45, 35],\n [-12, -10, 15, -32, -18],\n [12, 18, 3, 15, 15],\n [-20, 0, 2, 68, 60]]\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, 6, 18, -6, -12],\n [-6, -1, -3, 1, 2],\n [24, 4, 12, -4, -8],\n [30, 5, 15, -5, -10],\n [6, 1, 3, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 28, 25, 27, 39],\n [-3, -24, -21, -21, -33],\n [-5, -4, -2, 4, -4],\n [15, 0, -5, -25, -5],\n [8, 28, 23, 17, 37]]\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 5x5 matrix:\n[[-4, 36, 8, -8, 16],\n [28, -12, 22, 20, -16],\n [42, -18, 33, 30, -24],\n [-15, 15, -9, -12, 12],\n [17, 7, 18, 10, -4]]\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[[12, -15, -18, 12, 9],\n [-8, 10, 12, -8, -6],\n [8, -10, -12, 8, 6],\n [20, -25, -30, 20, 15],\n [-24, 30, 36, -24, -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[[15, -25, 0, -15, 0],\n [-12, 20, 0, 12, 0],\n [12, -20, 0, -12, 0],\n [-18, 30, 0, 18, 0],\n [-6, 10, 0, 6, 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 5x5 matrix:\n[[-18, 13, -13, -17, 15],\n [2, -4, -19, 7, -17],\n [-8, 4, -20, -4, -4],\n [10, -9, -7, 13, -19],\n [0, -2, -16, 4, -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 5x5 matrix:\n[[-6, -9, 6, 6, 15],\n [6, 9, -6, -6, -15],\n [8, 12, -8, -8, -20],\n [-8, -12, 8, 8, 20],\n [-8, -12, 8, 8, 20]]\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[[12, 4, -2, -6, -12],\n [24, 8, -4, -12, -24],\n [6, 2, -1, -3, -6],\n [-18, -6, 3, 9, 18],\n [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[[-2, 11, -4, -8, -2],\n [6, -1, 0, -2, -4],\n [-34, 27, -8, -6, 16],\n [-10, -25, 10, 25, 15],\n [-52, 30, -8, 0, 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 5x5 matrix:\n[[-1, -10, 6, 21, 20],\n [19, -12, 2, 23, 36],\n [53, -22, 30, -9, -28],\n [3, 18, -18, -27, -12],\n [-11, 40, -50, -35, 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[[9, -27, 24, 0, 6],\n [32, -26, 20, -42, -30],\n [20, -20, 16, -24, -16],\n [-23, 29, -24, 24, 14],\n [0, 0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, -4, -6, -2, -1],\n [-4, -8, -12, -4, -2],\n [0, 0, 0, 0, 0],\n [8, 16, 24, 8, 4],\n [-8, -16, -24, -8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, -2, 4, 1, -6],\n [6, -12, 24, 6, -36],\n [-3, 6, -12, -3, 18],\n [-5, 10, -20, -5, 30],\n [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[[-2, -6, 5, 5, -21],\n [14, 21, 13, -2, 6],\n [-25, 7, 0, 13, 6],\n [6, 18, -15, -15, 63],\n [-45, -50, -25, 15, -30]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, 2, -3, 5, 4],\n [18, 6, -9, 15, 12],\n [-12, -4, 6, -10, -8],\n [36, 12, -18, 30, 24],\n [12, 4, -6, 10, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, 5, -1, 1, -2],\n [9, 15, -3, 3, -6],\n [0, 0, 0, 0, 0],\n [-6, -10, 2, -2, 4],\n [18, 30, -6, 6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[14, -8, -14, -4, -22],\n [-65, 62, 73, -14, 17],\n [-9, 3, 5, -20, -37],\n [-9, -3, 4, -5, 0],\n [-20, 26, 28, 12, 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[[0, 0, 0, 0, 0],\n [-16, -24, -16, -24, 24],\n [-16, -24, -16, -24, 24],\n [16, 24, 16, 24, -24],\n [-16, -24, -16, -24, 24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, 0, 6, 4, -8],\n [13, -15, 6, -21, -28],\n [25, -15, 15, -15, -40],\n [-6, -6, -6, -14, 0],\n [24, -12, 15, -10, -36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-18, -33, 42, -15, 30],\n [36, -6, -4, -42, -12],\n [-36, -39, 54, -3, 42],\n [-6, -5, -3, -26, 22],\n [30, -14, 17, -17, -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[[4, -12, 11, -17, -22],\n [-20, -14, 29, 6, -5],\n [-44, 20, 20, -25, -6],\n [0, -10, 15, -35, -35],\n [12, -12, -3, 33, 18]]?\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[[32, 24, 36, -6, -28],\n [50, 30, 54, 3, -46],\n [-32, -24, -36, 6, 28],\n [-40, -20, -42, -9, 38],\n [26, 2, 24, 24, -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[[-21, 33, -31, 35, -6],\n [-14, -14, 21, -66, -52],\n [-42, -25, 29, -28, -47],\n [9, 3, 10, -11, 6],\n [-27, 36, -47, 51, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-10, 10, 16, -10, -33],\n [14, -8, -8, -2, -7],\n [-5, -13, -22, -34, -23],\n [-45, 16, 10, -12, 13],\n [-73, 17, 2, -38, 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[[-18, -12, -24, -18, -12],\n [-6, -4, -8, -6, -4],\n [15, 10, 20, 15, 10],\n [18, 12, 24, 18, 12],\n [15, 10, 20, 15, 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[[24, 2, -12, -12, 22],\n [0, 20, 24, 0, 4],\n [4, -23, -30, -2, -1],\n [-12, -16, -12, 6, -14],\n [8, -11, -18, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-27, -26, 31, 7, 2],\n [0, -3, 40, 7, -14],\n [-18, -18, -7, -21, 6],\n [-16, -14, -24, -18, 4],\n [17, 14, 25, 15, 14]]\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[[20, -5, 0, -15, -15],\n [-16, 4, 0, 12, 12],\n [20, -5, 0, -15, -15],\n [-16, 4, 0, 12, 12],\n [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[[13, 14, -24, 15, -22],\n [-36, -21, 39, 15, 27],\n [-3, 12, -18, 45, -24],\n [-7, 6, -8, 35, -14],\n [-33, -22, 40, 5, 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[[17, 18, 1, -23, 13],\n [18, -10, 21, -22, 5],\n [-15, 6, -11, 13, -3],\n [-30, -6, -19, 38, -15],\n [-6, 8, -20, 18, -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[[5, 10, -25, 30, -20],\n [6, 12, -30, 36, -24],\n [1, 2, -5, 6, -4],\n [4, 8, -20, 24, -16],\n [-3, -6, 15, -18, 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[[14, 42, -4, 8, -18],\n [5, -29, -14, 6, 3],\n [12, -36, -24, 12, 0],\n [11, 37, -2, 6, -15],\n [-26, -6, 28, -20, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-27, 14, -23, -1, -35],\n [-39, -72, -25, 33, 5],\n [-21, -50, -15, 33, 34],\n [-6, 7, -32, 14, 28],\n [63, 20, 40, -22, 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 5x5 matrix:\n[[-10, 2, 4, 7, -18],\n [-10, -9, -3, -9, -24],\n [4, -3, -3, -6, 6],\n [-26, -8, 2, -1, -54],\n [-10, 35, 25, 55, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-15, 25, -42, -35, 32],\n [22, -3, 42, 2, -16],\n [1, 18, -18, -25, 38],\n [23, 1, 9, -1, -12],\n [-21, -24, -3, 37, 42]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[27, 58, 21, 41, 9],\n [23, 40, 1, 31, -53],\n [52, 41, 13, 51, -6],\n [-15, 38, 22, 7, 36],\n [-9, -19, -24, -30, 8]]\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[[17, 21, -11, -13, 11],\n [12, 14, -2, -10, -26],\n [25, 30, -10, -20, -20],\n [37, 45, -19, -29, -5],\n [-10, -13, 11, 7, -33]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-36, 54, -14, 21, -20],\n [9, -12, -3, -18, -3],\n [60, -72, 30, -6, -18],\n [8, 4, 0, -38, 44],\n [-9, 6, 7, 21, 25]]\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, 4, 4, -10, 12],\n [-3, -30, 11, 18, -26],\n [-26, 27, 10, -36, 23],\n [-2, -26, 12, 14, -26],\n [-2, -9, 15, -3, -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[[-19, -4, -18, -46, -6],\n [15, -8, -6, -31, 16],\n [-33, 3, -30, -22, -29],\n [13, -1, 30, -3, 17],\n [-12, 8, 0, 35, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-54, 49, -38, 0, -41],\n [-8, 8, -6, 0, -12],\n [-56, 50, -39, 0, -36],\n [-20, 14, -12, 0, 18],\n [28, -26, 20, 0, 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[[23, 4, 8, 9, 1],\n [-42, -48, 12, -18, 6],\n [-1, 10, -7, 0, -2],\n [-40, -42, 9, -17, 5],\n [-18, -2, -7, -7, -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[[-8, 4, 20, 8, 20],\n [2, -1, -5, -2, -5],\n [-10, 5, 25, 10, 25],\n [12, -6, -30, -12, -30],\n [8, -4, -20, -8, -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[[-12, -4, 8, 8, 16],\n [6, 2, -4, -4, -8],\n [-18, -6, 12, 12, 24],\n [-6, -2, 4, 4, 8],\n [18, 6, -12, -12, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-28, 2, 54, 27, -43],\n [-22, 11, -49, -7, -2],\n [-46, 18, 33, -31, 34],\n [-22, -46, 8, -19, 10],\n [-22, 46, 53, -9, 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[[26, -13, -6, 41, 47],\n [-26, -47, 7, -33, -33],\n [-47, -18, -30, 11, -18],\n [-27, 34, -58, 45, 28],\n [0, 24, 18, -9, -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 5x5 matrix:\n[[3, 1, 0, 4, 5],\n [-6, -2, 0, -8, -10],\n [-9, -3, 0, -12, -15],\n [-15, -5, 0, -20, -25],\n [9, 3, 0, 12, 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[[-2, -10, -12, -4, 2],\n [-5, -25, -30, -10, 5],\n [3, 15, 18, 6, -3],\n [-2, -10, -12, -4, 2],\n [1, 5, 6, 2, -1]]\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 5x5 matrix:\n[[4, 1, -6, 1, 2],\n [-14, 40, 12, -14, -4],\n [1, -36, 6, 9, -2],\n [-5, 6, 6, -3, -2],\n [0, 0, 0, 0, 0]]\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[[-27, -23, -35, -25, -10],\n [-29, -14, 29, -12, 24],\n [5, 32, -20, -18, 19],\n [-5, -1, 3, 11, -8],\n [-20, -34, -12, -22, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[20, -15, 7, -21, 24],\n [-42, 19, -34, 32, 28],\n [-15, 11, -14, 10, 26],\n [-30, 14, -21, 25, 4],\n [-11, -34, -23, 1, 18]]?\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, -26, 35, -21, 24],\n [-40, 40, -75, 23, -46],\n [-9, 1, -22, -48, 11],\n [-41, 11, -17, 57, -41],\n [-13, 10, -18, -19, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[19, 10, 38, -21, 4],\n [9, -3, 18, 28, 38],\n [30, -43, 27, 40, 26],\n [26, -26, 32, 29, 29],\n [34, -44, 28, 4, -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[[14, -34, -24, -25, -71],\n [37, 40, 47, 10, 1],\n [-20, -14, 3, 19, 36],\n [-8, 10, 1, -4, 23],\n [7, 16, 11, -27, 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[[10, 0, -30, -46, 32],\n [-13, 28, 39, 15, -8],\n [12, -32, -36, -4, 0],\n [9, 6, -27, -51, 36],\n [-11, 6, 33, 41, -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[[-20, 0, -20, -20, 4],\n [-6, 18, 0, -3, 12],\n [21, 12, 25, 23, 3],\n [9, 48, 25, 17, 27],\n [-7, -24, -15, -11, -13]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-5, -1, 16, -8, 43],\n [30, 13, 3, -19, 26],\n [-8, 1, 23, -7, 48],\n [9, -36, -14, -34, 55],\n [-36, -13, -18, 18, 16]]\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[[39, -1, 1, 72, 25],\n [-21, 5, 7, -8, -25],\n [10, -2, 3, -10, 40],\n [-25, 5, 6, -14, -31],\n [15, -1, -5, 36, -11]]\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 5x5 matrix:\n[[27, -2, -3, -19, -15],\n [9, 13, -3, -16, -15],\n [36, 11, -6, -35, -30],\n [13, -4, -1, -7, -5],\n [35, -36, 1, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-4, -10, -15, -5, -2],\n [17, 12, -18, -16, 8],\n [-29, -20, 32, 28, -14],\n [-8, -16, -18, 0, -18],\n [-22, -12, 34, 30, -24]]\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, 3, -6, 18, 0],\n [-10, -2, 4, -12, 0],\n [30, 6, -12, 36, 0],\n [-20, -4, 8, -24, 0],\n [-5, -1, 2, -6, 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 5x5 matrix:\n[[-5, -20, -25, -15, 30],\n [18, 24, 6, 12, 0],\n [4, -8, -22, -9, 30],\n [-1, 4, 9, 4, -12],\n [-3, 12, 27, 12, -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[[-9, -5, -3, -3, 14],\n [-12, 4, -20, 12, -8],\n [-24, -24, 1, 3, -19],\n [4, -6, 9, 7, -41],\n [-3, 23, -31, 9, 26]]?\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],\n [-3, 3, 18, 3, -6],\n [5, -5, -30, -5, 10],\n [2, -2, -12, -2, 4],\n [-6, 6, 36, 6, -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 5x5 matrix:\n[[1, 12, 26, 39, -32],\n [-20, 44, -32, 2, 14],\n [-1, -34, -12, -49, 48],\n [-17, -9, 53, -9, -53],\n [55, -25, -45, 23, 31]]\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 5x5 matrix:\n[[12, 24, 20, -8, 16],\n [12, 24, 20, -8, 16],\n [15, 30, 25, -10, 20],\n [18, 36, 30, -12, 24],\n [-3, -6, -5, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[10, 16, 12, 25, 16],\n [5, 35, -3, 35, 8],\n [-25, 14, 8, 0, 44],\n [25, 22, -4, 35, -20],\n [-25, -45, 9, -55, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[13, -18, 54, -42, 34],\n [-32, 34, 4, -32, 29],\n [36, -32, 24, 24, -4],\n [33, -38, -26, -4, -37],\n [-52, 27, -2, -11, -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[[-6, -36, 30, -18, 18],\n [0, 0, 0, 0, 0],\n [-3, -18, 15, -9, 9],\n [0, 0, 0, 0, 0],\n [6, 36, -30, 18, -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[[-30, 6, 24, -24, 6],\n [20, -4, -16, 16, -4],\n [-15, 3, 12, -12, 3],\n [-15, 3, 12, -12, 3],\n [-20, 4, 16, -16, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[24, -30, -30, 30, -30],\n [12, -15, -15, 15, -15],\n [-16, 20, 20, -20, 20],\n [-8, 10, 10, -10, 10],\n [-24, 30, 30, -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[[12, -6, 18, 0, -6],\n [-4, 2, -6, 0, 2],\n [-8, 4, -12, 0, 4],\n [-4, 2, -6, 0, 2],\n [-8, 4, -12, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, -4, -15, 0, -33],\n [0, 0, -3, 2, -5],\n [18, 6, -3, 17, 7],\n [-18, -6, -15, -5, -37],\n [-18, -6, 9, -21, 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[[30, -28, -4, -4, 9],\n [49, -33, 7, -3, -10],\n [-11, 45, 20, 21, -33],\n [19, -3, -18, -43, 28],\n [45, 42, 1, -39, -2]]\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, 17, -32, -58, 2],\n [55, -45, -5, 32, -7],\n [-44, 35, 15, -6, 3],\n [-18, -12, 12, -3, 6],\n [70, -42, -12, 21, -18]]\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[[-17, 13, -35, -10, 42],\n [-5, 25, -25, -20, 30],\n [29, 35, 20, -29, -24],\n [41, 11, 55, -10, -66],\n [20, 44, 0, -36, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -16, 12, -24, 16],\n [24, 28, 18, -6, -40],\n [27, -6, 24, -33, 0],\n [-36, 8, -32, 44, 0],\n [-30, 20, -28, 46, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, 0, 3, -2, -5],\n [-18, 0, 18, -12, -30],\n [-3, 0, 3, -2, -5],\n [6, 0, -6, 4, 10],\n [9, 0, -9, 6, 15]]\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[[5, 0, 20, 30, 35],\n [11, -78, 38, 6, -25],\n [-4, 54, -16, 30, -1],\n [6, -9, 19, 42, -15],\n [9, -39, 33, 24, 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 5x5 matrix:\n[[39, 6, -59, -62, -46],\n [24, -17, -30, -69, -16],\n [54, 17, 12, -22, -57],\n [-45, -47, -9, -2, 57],\n [52, 75, 34, -9, -59]]\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, -26, -61, -32, -71],\n [47, 35, 21, 30, 40],\n [-25, -19, -21, 18, 16],\n [-8, -11, -7, -14, -14],\n [0, -1, -2, 20, 29]]\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 5x5 matrix:\n[[-22, 12, 8, -14, 14],\n [-12, 12, 12, -2, 4],\n [-3, 18, 24, 15, -9],\n [1, 24, 34, 26, -17],\n [6, -6, -6, 1, -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[[20, -7, -17, 16, -27],\n [24, -12, -18, 24, -30],\n [12, 9, -19, -8, -25],\n [24, 6, -30, 0, -42],\n [-4, -4, 7, 4, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-18, 6, -24, -24, 30],\n [18, -6, 24, 24, -30],\n [6, -2, 8, 8, -10],\n [6, -2, 8, 8, -10],\n [-12, 4, -16, -16, 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[[17, 14, 7, 9, -6],\n [-11, -10, -13, 13, 18],\n [-24, -18, 6, -48, -18],\n [13, 12, 17, -19, -24],\n [19, 14, -7, 43, 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 5x5 matrix:\n[[37, -2, -23, -14, -40],\n [18, 18, -29, 8, -15],\n [-12, -16, 24, -8, 20],\n [-4, 24, -24, 18, -40],\n [2, 28, -28, 21, 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[[-12, 0, 18, 15, 6],\n [-12, 0, 18, 15, 6],\n [-8, 0, 12, 10, 4],\n [-16, 0, 24, 20, 8],\n [8, 0, -12, -10, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -43, 44, -3, -47],\n [3, 44, -40, 51, 64],\n [-29, -22, -11, 36, -1],\n [15, 10, 13, 8, 7],\n [21, 28, -11, -44, 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[[8, 10, -6, 2, -4],\n [32, 6, -22, -14, -4],\n [-4, 12, 2, 10, -4],\n [-24, 21, 15, 27, -6],\n [-10, -4, 7, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[10, -4, -8, 0, 12],\n [10, -4, -8, 0, 12],\n [25, -10, -20, 0, 30],\n [-10, 4, 8, 0, -12],\n [15, -6, -12, 0, 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 5x5 matrix:\n[[-12, 6, 30, -36, -30],\n [-4, 2, 10, -12, -10],\n [6, -3, -15, 18, 15],\n [4, -2, -10, 12, 10],\n [-6, 3, 15, -18, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[10, -2, 10, -4, -8],\n [20, -4, 20, -8, -16],\n [25, -5, 25, -10, -20],\n [25, -5, 25, -10, -20],\n [30, -6, 30, -12, -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[[9, -4, -1, -2, -14],\n [21, -24, 27, -30, -6],\n [5, -12, 19, -18, 10],\n [-10, -9, 28, -21, 40],\n [-9, -7, 23, -17, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[30, -20, 0, -15, -10],\n [-12, 8, 0, 6, 4],\n [24, -16, 0, -12, -8],\n [-6, 4, 0, 3, 2],\n [36, -24, 0, -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 5x5 matrix:\n[[8, 14, -8, -5, 20],\n [-18, 7, 16, -17, -2],\n [18, 31, -8, -30, 22],\n [-44, -32, 32, 13, -38],\n [-34, -25, 28, 4, -37]]\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[[9, 4, -10, -7, -3],\n [27, 14, -32, -17, -6],\n [-42, -18, 46, 34, 15],\n [30, 8, -28, -34, -18],\n [36, 14, -38, -32, -15]]?\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, 36, 30, 0, -12],\n [4, -6, -5, 0, 2],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [20, -30, -25, 0, 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[[18, -28, 16, -26, -24],\n [26, -12, 0, 14, -24],\n [37, -22, 4, 11, -36],\n [-37, 22, -4, -11, 36],\n [24, -32, 17, -25, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-5, 5, 6, 1, 4],\n [5, -5, -6, -1, -4],\n [0, 0, 0, 0, 0],\n [-5, 5, 6, 1, 4],\n [-30, 30, 36, 6, 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[[20, -32, -16, 8, -24],\n [52, -40, -42, 51, -19],\n [7, -27, 26, 25, 3],\n [-2, -36, 40, 12, -4],\n [-1, 4, -8, -8, -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[[22, 25, -16, -31, -4],\n [11, -11, 8, -29, -9],\n [58, 40, 11, -19, -26],\n [18, -22, 7, -69, -14],\n [-27, 0, -24, 6, 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 5x5 matrix:\n[[-19, -33, 20, 4, -6],\n [-19, -19, 11, -6, -23],\n [-3, -52, 37, -28, -41],\n [-20, -1, -18, 20, -29],\n [-2, 23, 7, -12, 43]]\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[[-5, -10, 30, 25, -5],\n [-1, -2, 6, 5, -1],\n [-5, -10, 30, 25, -5],\n [4, 8, -24, -20, 4],\n [4, 8, -24, -20, 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[[14, -44, 26, 12, 8],\n [6, -16, 12, 6, 6],\n [8, -28, 14, 6, 2],\n [2, -12, 2, 0, -4],\n [11, -36, 20, 9, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-24, 18, -24, -30, -12],\n [-4, 3, -4, -5, -2],\n [0, 0, 0, 0, 0],\n [4, -3, 4, 5, 2],\n [20, -15, 20, 25, 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[[-13, -17, 9, 29, 29],\n [2, -22, 0, 12, 6],\n [-30, -12, 4, 26, 22],\n [-28, -5, 8, 27, 28],\n [0, -22, -14, -8, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[12, -5, -19, 2, -16],\n [-29, 26, -53, 16, 48],\n [29, 13, -10, 38, -54],\n [-8, 1, 12, 30, -18],\n [-10, -6, -32, 28, -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[[3, 42, -24, 47, -20],\n [14, 20, 35, -2, -30],\n [-8, -32, 10, -40, 12],\n [-1, -31, -24, 18, 58],\n [-11, -11, -52, 32, 42]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[10, 39, -17, 15, -21],\n [4, -39, -2, -2, 3],\n [-10, 55, 5, 5, -5],\n [-26, 62, 19, 3, 2],\n [-18, -7, 3, 19, -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 5x5 matrix:\n[[4, -3, 2, 0, -5],\n [-24, 18, -12, 0, 30],\n [-20, 15, -10, 0, 25],\n [-24, 18, -12, 0, 30],\n [-20, 15, -10, 0, 25]]\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[[-33, -16, -37, -25, -19],\n [-1, -5, -16, -4, 19],\n [5, 16, -1, 33, 35],\n [10, -19, 14, -12, -2],\n [-11, 39, -60, -6, 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[[-18, 18, -24, 6, -12],\n [42, 9, 47, -17, 31],\n [9, -33, -12, -11, -6],\n [33, 24, 41, -12, 28],\n [-18, 21, -9, 11, -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 5x5 matrix:\n[[36, 18, 9, -19, -33],\n [-5, -15, -16, 14, -4],\n [41, 21, 4, -15, -38],\n [-10, -18, -11, 10, 1],\n [0, 20, 35, -30, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -4, 12, 8, 0],\n [-9, -1, 15, 14, -12],\n [-6, -4, 15, 11, -3],\n [-6, -6, 18, 12, 0],\n [1, -5, 6, 1, 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[[12, -12, 20, 38, 20],\n [-30, 3, 3, -39, -19],\n [-9, -9, 4, -11, 1],\n [12, 51, -29, -2, -31],\n [49, -28, -7, 54, 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[[0, -10, -4, -12, -10],\n [0, 10, 4, 12, 10],\n [0, -25, -10, -30, -25],\n [0, -30, -12, -36, -30],\n [0, 20, 8, 24, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-24, -4, 17, 22, 19],\n [3, -2, 1, 6, 2],\n [-39, 2, 17, 6, 16],\n [-36, 0, 18, 12, 18],\n [-12, 8, -4, -24, -8]]\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, 72, 0, 48, 102],\n [-42, 57, -71, -31, 10],\n [5, -14, 38, 51, 22],\n [6, 20, -10, -10, 1],\n [20, 4, -6, -20, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 0, 0, 10, -4],\n [12, 0, 0, -30, 12],\n [10, 0, 0, -25, 10],\n [-6, 0, 0, 15, -6],\n [-2, 0, 0, 5, -2]]\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[[-10, 6, -2, -12, 10],\n [-30, 18, -6, -36, 30],\n [5, -3, 1, 6, -5],\n [5, -3, 1, 6, -5],\n [-5, 3, -1, -6, 5]]\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[[5, 0, -1, -5, -2],\n [-31, 18, -1, 25, -2],\n [-22, 36, -10, 10, -20],\n [-32, 6, 4, 30, 8],\n [-7, -24, 11, 15, 22]]?\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 5x5 matrix:\n[[-12, -10, -12, 12, 4],\n [6, 5, 6, -6, -2],\n [12, 10, 12, -12, -4],\n [-18, -15, -18, 18, 6],\n [30, 25, 30, -30, -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[[-3, -39, -21, -24, 51],\n [12, -34, -36, 2, 10],\n [-45, -1, 3, -19, 58],\n [58, -30, -42, 20, -46],\n [-3, 13, 3, 10, -15]]?\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, -27, 16, -10, 6],\n [26, 9, -1, -2, 18],\n [-6, -24, 22, 30, -28],\n [33, 2, -2, -53, 74],\n [-3, -39, 32, 15, -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[[18, 10, -5, -5, 12],\n [-43, -36, 50, 15, 23],\n [-32, 10, -30, 38, -18],\n [8, -13, -34, -22, -23],\n [30, 38, -45, -7, -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[[-20, 30, 0, 27, -41],\n [-21, -12, 9, -2, 15],\n [-15, 0, 3, 3, 2],\n [64, 0, -8, -37, 15],\n [9, -18, -17, -2, 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[[26, 66, -12, 40, 46],\n [32, -32, 16, 16, -6],\n [54, 22, -52, 56, 60],\n [15, 39, 22, 20, 13],\n [-14, 17, 26, -10, -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[[-14, 15, -59, 66, 45],\n [-29, -8, -8, -9, -33],\n [0, -5, -29, 31, 0],\n [15, 18, 35, -25, 35],\n [-41, 19, -73, 67, 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[[-11, 7, -7, -12, -12],\n [34, 32, 22, -14, 8],\n [-14, -16, -39, -24, -5],\n [-80, -15, -50, 15, -30],\n [1, -19, -11, 10, 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[[18, 33, -54, -6, -21],\n [0, 15, -19, 11, -25],\n [15, 39, -57, -15, 3],\n [-7, -5, 9, 23, -37],\n [36, -29, 5, -29, 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[[18, 4, -17, -7, -24],\n [44, 11, -41, 18, -57],\n [-19, -2, -1, 16, 13],\n [-22, 0, -30, -16, -10],\n [35, 5, -16, 22, -18]]\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, 0, 0, 0, 0],\n [0, 30, 18, 30, -24],\n [0, -25, -15, -25, 20],\n [0, 0, 0, 0, 0],\n [0, 5, 3, 5, -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[[-40, -50, 30, -20, -10],\n [9, 18, -3, 3, 3],\n [21, 24, -17, 11, 5],\n [-4, -14, -2, 0, -2],\n [16, 2, -22, 12, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, -24, 16, 24, 24],\n [2, 6, -4, -6, -6],\n [6, 18, -12, -18, -18],\n [2, 6, -4, -6, -6],\n [4, 12, -8, -12, -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[[23, 4, -60, -37, 3],\n [-3, 2, 26, 13, 11],\n [-23, 52, 8, 23, 23],\n [-22, 36, 34, 30, 16],\n [21, -21, -51, -33, -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 5x5 matrix:\n[[-16, -12, -8, -4, 27],\n [-22, 11, -26, 22, -31],\n [-50, 0, -40, 16, 9],\n [-35, -24, -36, 22, -2],\n [-7, -2, -8, 6, -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[[11, 21, 18, 14, -20],\n [-3, 34, -30, -8, -5],\n [-14, 13, -48, -22, 15],\n [0, 38, -24, -4, -10],\n [10, -12, 36, 16, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[24, 24, 30, 12, 12],\n [-12, -12, -15, -6, -6],\n [-4, -4, -5, -2, -2],\n [-4, -4, -5, -2, -2],\n [-16, -16, -20, -8, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, -6, -6, -8, 34],\n [-4, -28, 44, -12, 0],\n [11, 13, -38, 6, 0],\n [-12, 14, 2, 16, -62],\n [-3, 33, -39, 21, -42]]\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 5x5 matrix:\n[[-49, 61, -56, 70, -17],\n [-25, 41, -48, 38, -16],\n [0, 13, 0, 19, 19],\n [-10, 15, -42, 0, -33],\n [26, 1, 54, 10, 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[[12, 6, 9, 6, 6],\n [-4, -2, -3, -2, -2],\n [20, 10, 15, 10, 10],\n [16, 8, 12, 8, 8],\n [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[[-6, 12, -18, 3, 6],\n [-10, 20, -30, 5, 10],\n [-6, 12, -18, 3, 6],\n [2, -4, 6, -1, -2],\n [-8, 16, -24, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, -2, -10, 2, 4],\n [-5, -5, -25, 5, 10],\n [6, 6, 30, -6, -12],\n [5, 5, 25, -5, -10],\n [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[[-23, 8, 4, -1, -11],\n [8, -30, -22, 11, 3],\n [5, -55, -10, 27, -11],\n [-46, -16, -40, 6, -14],\n [19, -15, -26, 1, 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[[9, -6, -36, 0, -27],\n [21, 10, -3, 18, 0],\n [-27, -6, 27, -18, 18],\n [-32, -16, 2, -28, -2],\n [-13, -2, 16, -8, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[21, -5, 2, 10, 50],\n [12, 4, 14, 50, 32],\n [7, 5, 5, 11, 20],\n [2, -22, -9, -3, -6],\n [-2, -10, -13, -39, -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[[-16, -57, -4, 29, -36],\n [-42, -21, -7, 23, 25],\n [-28, 2, -19, 2, 51],\n [-18, -52, -16, 26, -9],\n [2, 72, 12, -30, 47]]\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, 32, 34, -9, 22],\n [-31, -18, -17, -9, -7],\n [-42, 54, -41, -19, 29],\n [-7, 6, 55, -15, 17],\n [24, -8, 20, 8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-37, -12, -29, -10, 10],\n [-7, -30, -6, 13, 6],\n [-23, -6, -18, -7, 6],\n [3, -18, 2, 11, 2],\n [39, -18, 30, 27, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-32, -19, 4, -19, 11],\n [-28, 28, 50, 25, 10],\n [-38, 8, 34, -11, -4],\n [30, 11, -1, 11, -5],\n [-20, -19, -31, -4, 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 5x5 matrix:\n[[18, -12, 6, -3, -3],\n [-36, 24, -12, 6, 6],\n [30, -20, 10, -5, -5],\n [24, -16, 8, -4, -4],\n [30, -20, 10, -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[[-12, -15, 7, 7, 6],\n [1, -29, 48, 11, 21],\n [13, -33, 78, 7, 9],\n [7, -10, -49, 34, -1],\n [-25, 37, -12, -43, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 6, -12, 8, 10],\n [4, 6, -12, 8, 10],\n [-2, -3, 6, -4, -5],\n [-12, -18, 36, -24, -30],\n [6, 9, -18, 12, 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[[-50, 13, -20, -11, -6],\n [-15, 27, 64, 3, -13],\n [12, -4, 2, -1, 4],\n [-21, 3, -16, -9, 1],\n [15, 12, 54, 3, -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[[-4, 8, -8, 9, 3],\n [-34, 15, -24, -32, -31],\n [-26, 39, -10, -6, -37],\n [-28, 2, -14, -18, -20],\n [-36, 56, -14, -16, -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[[-12, 0, 0, -12, -10],\n [-36, 0, 0, -36, -30],\n [-24, 0, 0, -24, -20],\n [0, 0, 0, 0, 0],\n [30, 0, 0, 30, 25]]\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, -42, -33, -10, -20],\n [-28, 33, 19, 17, 9],\n [-28, 13, -25, 29, 29],\n [-3, 17, 26, -5, -18],\n [-29, 12, 17, -6, 13]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-5, 1, 3, 5, 4],\n [-5, 1, 3, 5, 4],\n [-5, 1, 3, 5, 4],\n [5, -1, -3, -5, -4],\n [25, -5, -15, -25, -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 5x5 matrix:\n[[-16, 4, -14, 4, -2],\n [-13, 5, -12, 0, -7],\n [7, -7, 8, 8, 17],\n [-5, 3, -5, -2, -6],\n [-33, 3, -27, 18, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, 8, 15, -13, 19],\n [7, 11, 5, -14, 13],\n [7, 20, 25, -28, 37],\n [15, 35, 25, -45, 49],\n [0, -21, 20, 16, 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[[6, -41, -31, 22, 15],\n [28, -17, -43, 50, -17],\n [-12, 13, -5, -4, -1],\n [-6, -21, 19, -34, 25],\n [35, -59, -10, 4, 18]]\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, 16, 11, 34, 19],\n [16, 15, 11, 36, 2],\n [-8, -5, -3, -8, -16],\n [16, 16, 12, 40, -4],\n [-8, -5, -3, -8, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 29, 40, 28, -5],\n [13, -6, -2, -4, 10],\n [35, -5, 10, 0, 25],\n [7, -1, 2, 0, 5],\n [-20, 7, 0, 4, -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 5x5 matrix:\n[[14, 25, 20, -29, -19],\n [14, -8, -40, 10, 32],\n [8, 21, 28, -27, -23],\n [6, 3, -6, -3, 4],\n [13, -19, -32, 8, 37]]\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, 4, -2, -2, -5],\n [-4, -4, 2, 2, 5],\n [12, 12, -6, -6, -15],\n [20, 20, -10, -10, -25],\n [-16, -16, 8, 8, 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[[36, 18, -18, 18, -30],\n [36, 18, -18, 18, -30],\n [36, 18, -18, 18, -30],\n [30, 15, -15, 15, -25],\n [-18, -9, 9, -9, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-57, 24, 0, -35, -38],\n [24, -12, 12, -20, 4],\n [39, -9, 21, -16, 13],\n [-6, 36, 26, -6, -2],\n [69, -39, -5, 36, 43]]\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 5x5 matrix:\n[[0, 0, 0, 0, 0],\n [5, 1, -6, 4, -6],\n [-22, 11, -17, 30, 18],\n [-16, 10, -18, 28, 12],\n [-28, 12, -16, 32, 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[[-8, 4, -10, 2, -4],\n [24, -5, 2, 15, -16],\n [-16, 5, -8, -5, 4],\n [-16, -3, 24, -29, 36],\n [-20, -2, 23, -31, 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[[-6, -9, 9, -6, -15],\n [-10, -15, 15, -10, -25],\n [4, 6, -6, 4, 10],\n [-12, -18, 18, -12, -30],\n [-8, -12, 12, -8, -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 5x5 matrix:\n[[-14, -12, -34, -2, 24],\n [11, 13, 14, 9, -4],\n [-6, -12, -12, -10, 5],\n [-12, -31, -28, 15, 11],\n [27, 4, -18, 34, 35]]\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, 0, -30, -24, 6],\n [-3, 0, 15, 12, -3],\n [-2, 0, 10, 8, -2],\n [-5, 0, 25, 20, -5],\n [-2, 0, 10, 8, -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 5x5 matrix:\n[[-9, -4, -4, -14, -9],\n [-31, -20, 8, -28, -31],\n [19, 12, -4, 18, 19],\n [0, 0, 0, 0, 0],\n [-35, -24, 14, -27, -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[[5, 0, 0, -20, 30],\n [-1, 0, 0, 4, -6],\n [3, 0, 0, -12, 18],\n [-2, 0, 0, 8, -12],\n [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[[-18, 24, 39, -22, 41],\n [-9, 75, -11, -14, -15],\n [-40, -12, -6, -4, -11],\n [24, 30, -11, -25, 43],\n [-10, 38, -6, 6, -36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-31, -8, -3, 31, -27],\n [31, 7, -37, 1, 22],\n [5, 23, -5, -27, 40],\n [-62, 2, 4, 37, -29],\n [26, -15, -28, -14, 33]]\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 5x5 matrix:\n[[-12, 18, -15, -3, -6],\n [12, -18, 15, 3, 6],\n [0, 0, 0, 0, 0],\n [-16, 24, -20, -4, -8],\n [-16, 24, -20, -4, -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[[30, 12, -12, -30, -36],\n [10, 4, -4, -10, -12],\n [-25, -10, 10, 25, 30],\n [-5, -2, 2, 5, 6],\n [15, 6, -6, -15, -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[[-4, 4, -16, -8, 16],\n [12, 18, -12, -15, -15],\n [23, 37, -28, -32, -26],\n [8, 12, -8, -10, -10],\n [27, 33, -12, -24, -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[[41, -34, -50, -1, 4],\n [-24, 32, 34, 31, 20],\n [-36, 33, 33, 12, 18],\n [-32, 18, 18, -16, 4],\n [-34, 20, 24, -16, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[0, 8, -20, 12, -16],\n [0, -6, 15, -9, 12],\n [0, -6, 15, -9, 12],\n [0, 8, -20, 12, -16],\n [0, -10, 25, -15, 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 5x5 matrix:\n[[3, -15, -18, 12, -6],\n [3, -15, -18, 12, -6],\n [4, -20, -24, 16, -8],\n [-5, 25, 30, -20, 10],\n [4, -20, -24, 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[[18, 59, -26, -28, -1],\n [-9, 27, -3, 9, 18],\n [-14, -43, 6, 44, -7],\n [6, 2, -30, 4, -22],\n [19, -13, -7, -19, -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[[-12, -41, -34, 8, 26],\n [-11, 12, 15, 3, -3],\n [-28, -29, -13, 23, 20],\n [10, 14, 7, -11, -8],\n [-34, -42, -24, 24, 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 5x5 matrix:\n[[-12, -15, 9, 0, 6],\n [24, 30, -18, 0, -12],\n [16, 20, -12, 0, -8],\n [-8, -10, 6, 0, 4],\n [24, 30, -18, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-24, 0, 0, 24, 12],\n [16, 20, -16, -16, 10],\n [-2, 10, -8, 2, 10],\n [30, 30, -24, -30, 12],\n [-25, -5, 4, 25, 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[[6, 6, -12, -6, 18],\n [-2, -2, 4, 2, -6],\n [-6, -6, 12, 6, -18],\n [-3, -3, 6, 3, -9],\n [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[[4, -7, -46, -31, 0],\n [16, 16, -8, 8, 0],\n [-48, -48, 24, -24, 0],\n [32, 36, 0, 28, 0],\n [-32, -28, 32, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -20, 20, -50, 15],\n [0, -20, 12, -34, -1],\n [0, 20, 2, 6, 29],\n [0, 24, 0, 12, 30],\n [0, 0, -12, 24, -24]]\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[[22, 21, 21, 26, -11],\n [-21, 45, 2, -2, -20],\n [9, -12, -7, 16, -23],\n [-15, -54, -33, -24, 9],\n [-20, -12, -12, -28, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, -4, 22, 10, -7],\n [16, -30, -15, 16, 10],\n [26, 7, 11, -3, -31],\n [16, -32, 3, 31, 16],\n [12, -6, 1, -3, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[55, -51, 38, -12, 24],\n [10, -11, 3, -21, -9],\n [31, -11, -6, -8, 35],\n [-32, 44, -26, 40, 8],\n [-6, 3, -38, -41, 25]]\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, -4, 4, -8, 10],\n [-5, 6, 4, -3, 0],\n [-50, 40, 10, 5, -25],\n [-45, 30, 0, 15, -30],\n [15, -6, 6, -12, 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 5x5 matrix:\n[[-3, 13, 17, -6, -24],\n [-11, -43, 9, -2, 12],\n [-28, -60, 20, 30, -66],\n [16, 56, 0, -20, 12],\n [6, -16, -38, 24, 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[[-3, -18, 43, -81, -21],\n [32, 14, -3, 12, -12],\n [26, -10, -9, 30, 30],\n [-16, -4, -8, 12, 12],\n [-20, -32, 8, -12, 36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[24, 14, 10, -4, 22],\n [0, 7, -9, 11, -6],\n [27, 18, 3, -6, 21],\n [27, 12, 25, -2, 31],\n [-22, -22, -20, -32, -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[[6, 5, 2, -4, 3],\n [36, 30, 4, -24, 15],\n [-66, -55, 26, 44, -15],\n [36, 30, -20, -24, 6],\n [30, 25, -38, -20, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, 12, -36, 18, 36],\n [-8, 8, -24, 12, 24],\n [-12, 12, -36, 18, 36],\n [6, -6, 18, -9, -18],\n [2, -2, 6, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-15, 32, 13, 35, -13],\n [-8, 34, 21, 23, -20],\n [-15, -14, -26, 22, 7],\n [26, 5, 16, 14, -22],\n [-5, 37, 26, 20, -23]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[24, -8, -16, -30, -42],\n [20, 8, -4, -5, -43],\n [-30, -5, 15, 25, 55],\n [4, -8, 4, 5, -17],\n [-18, -24, 12, 15, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[12, 15, -15, 15, 0],\n [12, 15, -15, 15, 0],\n [0, 0, 0, 0, 0],\n [12, 15, -15, 15, 0],\n [-12, -15, 15, -15, 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[[-5, 8, 2, 28, -21],\n [-40, -15, 20, 12, 2],\n [-15, 14, 12, 44, -31],\n [15, -1, 5, 6, 8],\n [0, -5, 34, 12, 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[[8, -9, 3, -5, 10],\n [-5, 31, -8, 11, -36],\n [-12, -30, 6, -6, 36],\n [0, -29, 7, -9, 34],\n [1, -12, 3, -4, 14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, -21, -19, 10, 13],\n [-2, -10, -10, -6, 12],\n [25, -17, 1, 0, -25],\n [18, -14, 0, -14, -14],\n [-38, -16, -43, 57, 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 5x5 matrix:\n[[-12, -24, -4, 20, -16],\n [12, 16, 8, -10, 10],\n [-9, 6, -15, -15, 6],\n [-15, 10, -25, -25, 10],\n [-30, -4, -38, -20, 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[[5, 5, 2, -1, 0],\n [10, -2, 1, -8, -12],\n [20, 0, 3, -14, -20],\n [5, -7, -1, -7, -12],\n [-15, -23, -8, -1, -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[[-8, -55, 37, 53, 15],\n [26, 5, -65, -34, -25],\n [7, 30, -30, -28, -5],\n [10, -35, -1, 2, -25],\n [1, -45, 15, 31, 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[[28, 10, -14, -7, -2],\n [-41, 2, -28, -1, 16],\n [-3, -24, 6, 6, 10],\n [-3, 42, -24, -13, 16],\n [-21, 5, -16, -1, -7]]\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, 18, 18, 18, -6],\n [-1, 5, -2, 5, 2],\n [-16, 11, -17, 11, 11],\n [-24, 28, -28, 28, 20],\n [5, 21, 0, 21, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, -7, 2, 0, 0],\n [-11, 20, 19, -17, -39],\n [27, -22, -33, 47, 75],\n [1, 7, -2, 0, 0],\n [-15, -13, 36, -10, -43]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[21, -12, 7, -11, 13],\n [-3, 3, 1, 4, 1],\n [10, -4, 6, -2, 10],\n [-28, 4, -28, -8, -44],\n [-1, 4, 5, 7, 7]]\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[[2, 26, -8, 14, 24],\n [6, -18, 0, -6, -48],\n [24, -3, -21, 3, -62],\n [13, 33, -18, 23, -14],\n [-4, -21, 9, -11, -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[[-26, 0, 24, -1, 22],\n [-12, 4, 8, 2, 8],\n [-18, 6, 12, 3, 12],\n [-12, -9, 18, -6, 15],\n [-28, 18, 12, 10, 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 5x5 matrix:\n[[41, 32, -28, -19, 18],\n [21, -4, -1, -30, 10],\n [13, -24, -28, -51, 4],\n [6, 34, 25, 38, 6],\n [-1, 38, -4, 44, 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[[-44, -4, -35, -11, 16],\n [-9, 39, 7, 2, -27],\n [-14, 34, 43, -21, -14],\n [58, -31, -19, 51, -14],\n [7, -19, 9, -4, 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[[-16, 18, -28, 16, 16],\n [-4, -6, 21, -3, -24],\n [12, -30, 22, -16, -6],\n [-28, -30, -57, 15, 64],\n [28, 12, 19, -13, -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[[-10, -25, 5, 25, 20],\n [0, 40, 0, -50, -40],\n [24, 12, -12, 0, 0],\n [8, 4, -4, 0, 0],\n [-10, -17, 5, 15, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-24, -6, -36, 6, 36],\n [-20, -5, -30, 5, 30],\n [20, 5, 30, -5, -30],\n [-12, -3, -18, 3, 18],\n [12, 3, 18, -3, -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 5x5 matrix:\n[[37, -17, 41, -24, -2],\n [27, -21, 11, -19, 13],\n [-12, -12, -24, 21, 51],\n [1, 10, 17, -3, -23],\n [-2, -5, -26, -6, 2]]\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 5x5 matrix:\n[[-1, 0, 8, 13, 15],\n [13, -32, -40, 23, 29],\n [-6, 17, 14, -24, -29],\n [-8, 19, 26, -10, -13],\n [-14, 32, 48, -10, -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[[22, -28, 30, -36, 14],\n [-3, 18, -10, -1, -9],\n [8, -20, 15, -9, 10],\n [-7, 10, -10, 11, -5],\n [5, -2, 5, -10, 1]]?\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 5x5 matrix:\n[[-20, 5, 25, 20, -5],\n [0, 0, 0, 0, 0],\n [-12, 3, 15, 12, -3],\n [24, -6, -30, -24, 6],\n [-16, 4, 20, 16, -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[[45, -13, 36, -10, 30],\n [-31, 41, 0, 48, -56],\n [-50, -33, -10, -28, 8],\n [-3, -19, 51, 0, 16],\n [-7, -29, 62, -4, 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[[34, 13, 22, -38, -9],\n [7, 2, 14, -20, -12],\n [-10, -5, 10, -10, -15],\n [13, 6, -6, 4, 12],\n [13, 4, 22, -32, -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 5x5 matrix:\n[[24, 16, -1, 19, -41],\n [36, 10, -12, 32, -44],\n [30, -9, -23, 31, -15],\n [30, -5, -20, 30, -20],\n [0, 16, 12, -4, -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[[24, -46, 2, 42, -18],\n [-16, 14, -18, -18, 2],\n [12, -28, -4, 24, -12],\n [-20, 30, -10, -30, 10],\n [-16, 9, -23, -15, -1]]?\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, -24, -12, -27, -3],\n [6, 12, 2, 19, -1],\n [-12, 24, 20, 16, 8],\n [6, -12, -10, -8, -4],\n [-33, 26, 35, -1, 17]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[45, 4, 27, 20, 26],\n [40, 5, 23, 21, 8],\n [-15, -16, 9, -8, -20],\n [-30, -11, -8, -15, -19],\n [30, -1, 24, 19, -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[[1, -36, 20, -3, -13],\n [9, 1, -1, 20, -1],\n [-3, -31, 3, -38, 13],\n [27, -6, 54, -15, 33],\n [-25, 30, 14, -23, -14]]\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 5x5 matrix:\n[[-12, -16, 4, 16, -24],\n [-6, -8, 2, 8, -12],\n [15, 20, -5, -20, 30],\n [12, 16, -4, -16, 24],\n [-12, -16, 4, 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 5x5 matrix:\n[[38, 25, 4, -20, -26],\n [10, 28, -10, -7, -10],\n [6, 10, 8, -15, -32],\n [22, 12, -6, -1, 10],\n [-16, 27, -17, 1, -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[[0, -8, -8, -8, -36],\n [0, -4, 10, -4, 24],\n [0, -8, 10, -8, 18],\n [0, 4, -2, 4, 0],\n [0, 10, -7, 10, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[41, 22, 5, 15, 6],\n [-39, 4, 6, 4, -39],\n [-10, -6, 17, 13, 5],\n [-2, 8, 61, 59, 5],\n [25, 6, -2, 2, 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[[-15, 20, -30, 30, -15],\n [-6, 8, -12, 12, -6],\n [9, -12, 18, -18, 9],\n [18, -24, 36, -36, 18],\n [6, -8, 12, -12, 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[[36, 9, 36, -15, -12],\n [-28, 12, -38, 28, 2],\n [32, 24, 24, -8, -12],\n [24, 3, 24, 19, -25],\n [6, -3, 7, 21, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, -18, -5, -33, -22],\n [6, -26, -17, 25, -3],\n [-12, 12, -37, -26, -29],\n [29, 7, 16, 60, 39],\n [4, -20, -14, -32, -18]]\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[[-82, -35, -24, 5, -4],\n [1, 10, 20, -15, -3],\n [-32, -26, -52, 15, 7],\n [25, -13, -18, 85, -17],\n [1, 20, 6, -83, 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[[-18, -16, -8, -39, 18],\n [36, 34, -46, -6, 0],\n [26, 26, -29, 3, -4],\n [12, 8, -10, 2, 0],\n [-34, -19, 29, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 16, 8, 20, 20],\n [-22, -14, -7, 2, 8],\n [8, -14, -7, -37, -43],\n [12, 24, 12, 30, 30],\n [38, 26, 13, 0, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[18, -28, 38, -26, 22],\n [1, -22, 11, -25, 3],\n [-10, 38, -40, 36, -13],\n [35, 6, 5, -1, 43],\n [-14, -28, -14, -40, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, 12, -19, 10, 17],\n [-4, 4, -7, 4, 6],\n [8, -16, 24, -12, -22],\n [12, 16, -14, 2, 17],\n [-24, 4, -17, 14, 11]]\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, -39, 15, 34, -33],\n [-3, -9, 30, -7, -15],\n [5, 1, -12, -13, 13],\n [-12, 30, -42, 24, 18],\n [15, -18, -7, 29, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 32, 29, 33, -23],\n [20, 0, 21, -33, -57],\n [-2, -5, 40, -18, -37],\n [-14, 0, -17, 31, 50],\n [49, 32, 5, 0, -62]]?\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 5x5 matrix:\n[[-12, -24, -24, 16, 8],\n [-6, -12, -12, 8, 4],\n [9, 18, 18, -12, -6],\n [-9, -18, -18, 12, 6],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-16, -13, -10, 10, 8],\n [-34, -34, -22, 1, 23],\n [-18, -8, -8, 57, 11],\n [30, 30, 18, -15, -25],\n [30, 19, 16, -57, -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 5x5 matrix:\n[[-8, 12, -11, 10, -2],\n [-5, -6, 16, 10, 10],\n [-35, -15, -5, 15, -19],\n [3, 36, -12, 20, 16],\n [-12, -9, 18, 15, 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 5x5 matrix:\n[[27, 2, 26, 17, 3],\n [2, 1, -27, 21, 38],\n [38, 9, 18, -9, -17],\n [-17, 13, -27, -42, -33],\n [-34, -8, -9, -24, -19]]\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, -21, -21, -10, -14],\n [15, -40, -10, 25, 0],\n [0, 12, 32, 10, 1],\n [-32, 4, 9, -20, -12],\n [45, -23, -28, 10, -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[[15, 10, 30, -25, -30],\n [6, 4, 12, -10, -12],\n [18, 12, 36, -30, -36],\n [-12, -8, -24, 20, 24],\n [12, 8, 24, -20, -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[[12, -10, -7, 6, -23],\n [30, 2, -31, 24, 1],\n [-18, 12, 12, -10, 28],\n [0, 0, 0, 0, 0],\n [15, -14, -8, 7, -32]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -3, -3, -6, -6],\n [-16, -12, -12, -24, -24],\n [-12, -9, -9, -18, -18],\n [16, 12, 12, 24, 24],\n [-12, -9, -9, -18, -18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, 40, -52, 31, 35],\n [-33, 0, -9, -8, 14],\n [-37, -2, -13, -13, 23],\n [27, 15, -30, 10, 31],\n [1, 2, 7, 6, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, -2, 28, -24, -9],\n [22, 38, 1, 80, 31],\n [2, 2, -12, 11, 7],\n [-6, 2, -27, 6, 5],\n [-13, 18, 14, -18, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-19, 19, -8, -17, 11],\n [-14, 14, -22, -22, -8],\n [-20, 20, 22, 0, 42],\n [-9, 9, 15, 3, 24],\n [-15, 15, 8, -5, 23]]\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 5x5 matrix:\n[[-35, 30, 0, 3, -30],\n [36, -24, 0, 0, 24],\n [-29, 26, 0, 3, -26],\n [36, -24, 0, 0, 24],\n [-20, 40, 0, 12, -40]]\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, -3, 30, -30, -22],\n [7, 26, -100, -24, 1],\n [0, 12, -82, -47, -23],\n [15, 4, -38, -30, -33],\n [22, 16, 34, -18, 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[[-6, 16, -31, -28, 31],\n [-54, 2, -38, 2, -11],\n [-13, 31, -24, -37, 35],\n [46, -16, 4, 7, 9],\n [2, 26, -12, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, -6, -6, 9, 10],\n [3, 14, 10, -29, -42],\n [-24, -28, -38, 22, 0],\n [-12, -18, -21, 21, 16],\n [-27, -30, -42, 21, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -5, -1, 3, 5],\n [0, -30, -6, 18, 30],\n [0, -25, -5, 15, 25],\n [0, 5, 1, -3, -5],\n [0, 15, 3, -9, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 6, 12, -6, -36],\n [-2, 1, 2, -1, -6],\n [-6, 3, 6, -3, -18],\n [8, -4, -8, 4, 24],\n [-8, 4, 8, -4, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -12, -54, 42, -21],\n [38, -42, -32, -18, -30],\n [29, -39, -28, -13, -30],\n [-26, -32, -1, 36, -50],\n [14, -10, 20, -58, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-15, 60, 25, 0, 50],\n [18, -6, 25, 55, -16],\n [-6, 12, 0, -10, 12],\n [-18, 72, 30, 0, 60],\n [-3, 0, -5, -10, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -15, 36, 56, 29],\n [-56, 41, -28, -44, -7],\n [-6, 30, -12, 42, 60],\n [-28, -31, 52, 14, -25],\n [2, -14, 28, 40, 18]]\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 5x5 matrix:\n[[55, 2, 7, -27, 26],\n [36, -33, -30, -42, 32],\n [0, -39, -32, -12, 21],\n [-26, 10, 18, 30, -19],\n [7, -9, -29, -51, -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, 0, 0, -6, -9],\n [8, 0, -26, -4, 14],\n [-15, -14, 28, -2, -17],\n [17, -6, 25, -8, -28],\n [-30, -32, -14, -10, 13]]?\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[[7, -11, -15, -3, -9],\n [35, -33, 55, -18, 51],\n [2, -22, 26, -12, 2],\n [-8, -12, 4, -6, -16],\n [-18, -16, 12, -9, -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[[9, 57, 71, -34, -50],\n [7, 24, 21, -8, -24],\n [25, 52, 47, -8, -48],\n [-2, -35, -7, 4, 24],\n [19, 2, -14, 22, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, -4, 16, 20, 12],\n [-6, 3, -12, -15, -9],\n [12, -6, 24, 30, 18],\n [4, -2, 8, 10, 6],\n [-2, 1, -4, -5, -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[[26, -20, 65, -45, -9],\n [-13, 5, -34, 6, 31],\n [-3, -27, 26, -12, -45],\n [-8, -10, 2, -9, 26],\n [30, 1, 39, -33, 0]]\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, -1, 5, 3, -5],\n [-36, 6, -30, -18, 30],\n [12, -2, 10, 6, -10],\n [-30, 5, -25, -15, 25],\n [18, -3, 15, 9, -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[[-8, 8, 31, 9, -2],\n [-10, -5, 20, 15, 5],\n [8, -12, -36, -8, 4],\n [-10, -9, 15, 16, 7],\n [-10, 15, 45, 10, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, 3, 11, 14, -2],\n [24, 12, 8, 2, 28],\n [-9, -3, 1, 4, -10],\n [-18, -12, -14, -11, -22],\n [16, 18, 32, 33, 22]]\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 5x5 matrix:\n[[3, 6, 1, -1, 4],\n [-6, -12, -2, 2, -8],\n [12, 24, 4, -4, 16],\n [6, 12, 2, -2, 8],\n [12, 24, 4, -4, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[18, 24, -33, -24, 15],\n [8, 27, -11, -24, 42],\n [17, -7, -20, 31, -3],\n [-23, 20, 8, 7, 12],\n [8, 21, -22, 15, 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[[0, -12, -12, 18, 30],\n [0, 10, 10, -15, -25],\n [0, 2, 2, -3, -5],\n [0, 4, 4, -6, -10],\n [0, -2, -2, 3, 5]]\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, -24, 24, -32, -30],\n [0, -8, 16, -16, -36],\n [3, -3, -12, 6, 45],\n [0, 12, -24, 24, 54],\n [6, -22, 8, -20, 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 5x5 matrix:\n[[-6, 8, -8, -24, 6],\n [-15, 4, -2, -25, -3],\n [1, -1, 1, 3, 0],\n [30, 1, -21, 17, 25],\n [19, 42, 24, -5, 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[[27, 30, 16, -2, -23],\n [-12, -25, -18, -3, 18],\n [12, 10, 4, -2, -8],\n [0, 30, 28, 10, -20],\n [48, 10, -12, -18, -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[[15, 3, 0, 12, 6],\n [-25, -17, -9, -20, 2],\n [-25, 7, 9, -20, -22],\n [15, 27, 18, 12, -18],\n [-20, 20, 18, -16, -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[[6, 10, -43, -29, -18],\n [7, -14, 43, 10, -10],\n [31, -24, -2, -19, 36],\n [-51, 13, 6, 14, -19],\n [-54, 2, -44, -52, -38]]\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[[50, -17, 28, 2, 26],\n [8, -7, 47, 47, 36],\n [-46, 1, 0, 35, 22],\n [38, -15, 32, 14, 30],\n [-26, 16, 7, 16, -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[[9, -12, -15, 18, 9],\n [14, -4, -16, 22, 8],\n [15, -42, -36, 39, 24],\n [-8, -26, -5, -1, 7],\n [-4, 20, 14, -14, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[36, 54, 15, 46, 3],\n [-30, 6, 3, -7, -49],\n [-3, -12, -16, -10, -9],\n [12, 30, 19, 24, 3],\n [-6, -6, 5, -5, 5]]?\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 5x5 matrix:\n[[-18, 9, 0, -6, -3],\n [12, -6, 0, 4, 2],\n [6, -3, 0, 2, 1],\n [6, -3, 0, 2, 1],\n [-12, 6, 0, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-25, 43, -40, 0, 3],\n [6, 38, 6, -14, -40],\n [-19, -24, -1, 23, -24],\n [9, -44, 27, 11, -8],\n [-17, 46, -29, -5, -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 5x5 matrix:\n[[12, 15, 9, -14, 4],\n [-32, -19, 15, 0, 7],\n [10, -22, -1, 14, 24],\n [-8, 29, 25, -24, 5],\n [-18, -21, -18, -10, -53]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[16, -2, -14, -16, 28],\n [3, 6, 3, -5, 2],\n [-6, 30, -24, 18, 24],\n [3, 15, -12, 1, 18],\n [12, 12, -33, -3, 45]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-7, 23, -25, 4, 35],\n [8, -25, 17, 7, 5],\n [-5, 12, 2, 8, 5],\n [-9, 14, 32, 36, 13],\n [-3, 11, -17, 3, 28]]\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, -21, 12, -15, -9],\n [44, -35, -4, -2, 3],\n [-16, 8, -8, 9, 6],\n [20, -1, 28, -27, -21],\n [-28, 23, 4, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-5, 15, -30, -15, -20],\n [4, -12, 24, 12, 16],\n [3, -9, 18, 9, 12],\n [-1, 3, -6, -3, -4],\n [-2, 6, -12, -6, -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 5x5 matrix:\n[[44, -56, 0, -10, -43],\n [22, 12, -70, -22, 0],\n [-26, 30, -14, -35, -23],\n [24, -12, 28, -54, -71],\n [-8, -14, 36, -42, -68]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[36, 42, -11, 7, -30],\n [-11, -40, -6, 22, -22],\n [-7, 50, 2, 3, 2],\n [-28, -48, 7, -8, 0],\n [9, 18, 5, -28, -9]]\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 5x5 matrix:\n[[-3, 4, 2, 0, 2],\n [6, -8, -4, 0, -4],\n [-18, 24, 12, 0, 12],\n [3, -4, -2, 0, -2],\n [-18, 24, 12, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-30, 5, -5, -30, 10],\n [0, 0, 0, 0, 0],\n [-6, 1, -1, -6, 2],\n [0, 0, 0, 0, 0],\n [18, -3, 3, 18, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-23, -4, 19, 41, -15],\n [-75, 26, 33, -17, 45],\n [33, 40, -14, 3, -9],\n [-21, -46, 9, 13, -9],\n [-41, 6, 18, 23, -3]]?\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[[-12, 12, -9, 15, 0],\n [16, -16, 12, -20, 0],\n [-24, 24, -18, 30, 0],\n [16, -16, 12, -20, 0],\n [12, -12, 9, -15, 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[[-6, -30, 6, 12, 30],\n [-1, -5, 1, 2, 5],\n [-1, -5, 1, 2, 5],\n [-2, -10, 2, 4, 10],\n [6, 30, -6, -12, -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[[8, -26, -6, -21, 8],\n [-13, -8, 3, -8, 6],\n [46, -35, -27, -20, 13],\n [-12, 25, -21, -5, -1],\n [9, 18, -9, 18, 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[[-3, 15, -13, -13, 5],\n [6, 24, 2, 2, 20],\n [21, 30, 31, 31, 40],\n [-9, -9, -15, -15, -15],\n [3, 12, 1, 1, 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[[-14, 15, 9, -10, -15],\n [0, -8, 12, 10, 8],\n [0, 20, -30, -25, -20],\n [-14, 27, -9, -25, -27],\n [6, -7, -3, 5, 7]]\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, -8, 3, -30, -15],\n [22, 36, 32, 62, 22],\n [-30, -16, 5, 12, 17],\n [-35, -54, -40, -58, 7],\n [17, 2, -3, -3, 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[[-28, -8, -18, 12, -34],\n [-43, -24, -8, 22, -25],\n [48, 19, 14, -32, 31],\n [-32, -12, -13, 18, -27],\n [20, 27, -35, -30, -48]]\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[[-8, 32, 20, -44, -4],\n [-12, 24, 6, -18, -22],\n [10, -16, -1, 7, 21],\n [10, -19, -4, 13, 19],\n [2, 10, 13, -25, 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[[19, 10, 6, -32, 5],\n [-5, -18, 0, 28, -21],\n [-20, -40, 18, -20, 32],\n [-9, 2, -9, 30, -13],\n [-14, -34, 15, -14, 21]]\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, -41, -3, 6, -19],\n [30, 9, 17, -54, 19],\n [-28, 10, -16, 42, -5],\n [-10, -33, -9, 18, -17],\n [31, -4, 15, -60, 18]]\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, 20, 9, -18, 27],\n [-33, -30, -27, 1, -12],\n [4, -4, -13, -24, 15],\n [-26, -27, -5, -28, 1],\n [11, 20, 29, -35, 43]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-30, -20, -10, 30, 15],\n [24, 16, 8, -24, -12],\n [36, 24, 12, -36, -18],\n [0, 0, 0, 0, 0],\n [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[[12, 12, 0, -30, -18],\n [-8, -16, 12, 25, 19],\n [-5, -33, 42, 30, 32],\n [7, 3, 6, -15, -7],\n [-10, -10, 0, 25, 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[[23, 28, -5, -49, 23],\n [-24, 60, -30, -6, 50],\n [-40, 3, 40, 5, -33],\n [0, -32, 45, -9, -49],\n [-4, 40, -5, -31, 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 5x5 matrix:\n[[0, 18, -24, 21, 24],\n [-10, 8, -34, 16, -6],\n [8, 8, 8, 4, 24],\n [-5, -8, -1, -6, -19],\n [-4, -22, 20, -23, -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[[29, 25, -40, 14, -5],\n [-23, -15, 30, -18, -5],\n [21, 21, -30, 6, -9],\n [-19, -27, 30, 6, 23],\n [22, 32, -35, -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[[25, -9, 13, -21, -2],\n [40, 44, -8, -28, 32],\n [-11, -18, 3, 14, -16],\n [-27, -8, -5, 20, -8],\n [5, -22, -1, 38, -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 5x5 matrix:\n[[25, -38, 11, -11, 27],\n [-38, 10, -22, 2, 2],\n [-41, 17, -39, 7, -17],\n [-10, -15, 20, -10, 40],\n [0, 19, 34, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[20, 4, 8, -20, -24],\n [-5, -1, -2, 5, 6],\n [-20, -4, -8, 20, 24],\n [-25, -5, -10, 25, 30],\n [15, 3, 6, -15, -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[[-12, 20, -6, -14, -22],\n [3, 28, 18, -2, -33],\n [-12, 2, -15, -11, -1],\n [-9, 6, -9, -9, -6],\n [-6, -32, -24, 0, 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[[1, 18, -17, -10, -32],\n [-19, -2, -1, -16, 19],\n [-30, 14, 9, -28, 6],\n [43, 12, -12, 11, -11],\n [34, -16, 4, 40, -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[[17, 11, -5, -5, -24],\n [1, 13, -5, 5, -22],\n [26, 2, -2, -14, -12],\n [3, -24, 9, -12, 39],\n [-11, 4, -1, 8, -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[[0, -12, -4, -6, 6],\n [0, 6, 2, 3, -3],\n [0, -30, -10, -15, 15],\n [0, 6, 2, 3, -3],\n [0, -30, -10, -15, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-15, 24, -3, 6, -30],\n [-7, 18, -5, 10, -18],\n [10, 35, -25, 50, -10],\n [12, 42, -30, 60, -12],\n [-20, -2, 14, -28, -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[[-14, 6, 75, -40, 48],\n [-17, 52, 34, -76, -23],\n [30, -30, -30, 15, -15],\n [-3, 9, 0, -42, -15],\n [18, 16, 46, -51, -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 5x5 matrix:\n[[-8, 52, -6, -40, 0],\n [-18, 78, -18, -57, -9],\n [-9, 30, -27, -33, -9],\n [0, 28, 0, -26, 6],\n [10, 38, 42, -21, 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[[0, 25, 0, 30, -10],\n [0, -5, 0, -6, 2],\n [0, -5, 0, -6, 2],\n [0, 10, 0, 12, -4],\n [0, -20, 0, -24, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 2, 2, 12, -6],\n [24, -4, -4, -24, 12],\n [36, -6, -6, -36, 18],\n [6, -1, -1, -6, 3],\n [-36, 6, 6, 36, -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[[-1, -4, -23, 44, 1],\n [12, -10, 20, -7, -8],\n [2, 14, -2, -19, 10],\n [-13, -20, 45, -50, -23],\n [-8, 32, -36, -1, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1, 5, 20, 17, -21],\n [-18, 21, -8, -16, -10],\n [1, -5, -20, -17, 21],\n [-29, 40, 20, 3, -49],\n [-19, 23, -4, -13, -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 5x5 matrix:\n[[4, -12, -16, 4, 24],\n [-3, 9, 12, -3, -18],\n [-6, 18, 24, -6, -36],\n [-4, 12, 16, -4, -24],\n [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[[-43, 62, 19, -35, -59],\n [-16, 2, -30, -7, -7],\n [-50, 70, 23, -35, -61],\n [28, -38, -11, 19, 33],\n [10, -32, -40, 8, 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[[33, -39, 7, 18, -38],\n [-22, 42, -16, -16, 24],\n [-21, 3, 11, -6, 26],\n [3, 3, -4, 0, -4],\n [8, -24, 12, 8, -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[[-30, -18, 12, -18, -18],\n [-5, -3, 2, -3, -3],\n [25, 15, -10, 15, 15],\n [-15, -9, 6, -9, -9],\n [-10, -6, 4, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[25, 20, 10, 0, 25],\n [10, 8, 4, 0, 10],\n [0, 0, 0, 0, 0],\n [20, 16, 8, 0, 20],\n [20, 16, 8, 0, 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[[-15, 15, -30, -14, -3],\n [-8, -18, 0, -61, 11],\n [0, -22, 4, -17, -17],\n [-3, 33, -12, 22, 21],\n [-11, 7, -16, -29, 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[[12, 1, -2, -17, 8],\n [8, -14, -22, 58, -18],\n [8, -14, -22, 58, -18],\n [-24, 14, 2, -34, -2],\n [35, -10, 45, -10, 35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[2, -19, -13, -15, -15],\n [12, -30, -18, -24, -24],\n [-30, 33, 15, 27, 27],\n [30, -19, -5, -16, -16],\n [-44, 26, 6, 22, 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[[20, -21, 10, -20, 20],\n [55, -49, 10, -55, 20],\n [-35, 33, -10, 35, -20],\n [5, -7, 6, -5, 12],\n [-5, 3, 2, 5, 4]]\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[[6, -30, -36, 0, -6],\n [0, 0, 0, 0, 0],\n [6, -30, -36, 0, -6],\n [2, -10, -12, 0, -2],\n [1, -5, -6, 0, -1]]\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 5x5 matrix:\n[[-40, 13, 7, -42, 4],\n [6, 27, 43, 22, 34],\n [-14, 17, 11, 0, 12],\n [-33, 18, -5, -14, 3],\n [61, -46, -35, 38, -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[[32, 12, -54, 66, -30],\n [16, -8, -20, 12, -36],\n [16, 4, -26, 30, -18],\n [-18, 6, 24, -18, 36],\n [-16, 0, 24, -24, 24]]\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, 2, 10, 4, 10],\n [8, -4, -20, -8, -20],\n [6, -3, -15, -6, -15],\n [-6, 3, 15, 6, 15],\n [8, -4, -20, -8, -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, 4, 24, 20],\n [0, 0, 3, 18, 15],\n [0, 0, 6, 36, 30],\n [0, 0, -1, -6, -5],\n [0, 0, -2, -12, -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[[-2, -21, 23, -1, 1],\n [-27, 27, -31, 16, 22],\n [6, 17, -49, 34, 16],\n [18, -14, 20, -8, -8],\n [-17, 9, -28, 19, 11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-26, 3, -46, -32, -23],\n [-23, -7, -52, -18, -67],\n [-30, 12, -72, -30, -66],\n [7, -5, 0, 12, -7],\n [-7, -17, 6, -13, 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[[-15, 15, -10, 30, 30],\n [-17, 1, 6, 14, -30],\n [35, -20, 24, -39, -10],\n [-17, 11, -29, 9, 10],\n [14, -4, -16, -26, 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 5x5 matrix:\n[[20, 60, 46, -38, -22],\n [10, 6, 3, -7, 9],\n [-15, 18, 18, -3, -36],\n [5, 12, 9, -8, -3],\n [15, -18, -18, 3, 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[[19, 30, 25, -12, 26],\n [-2, -14, -24, -2, -26],\n [-6, -1, -21, -15, -8],\n [-31, -4, -20, -31, 58],\n [10, 19, 5, -13, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[22, -18, -17, 6, -8],\n [-3, 16, 35, -22, -34],\n [20, 14, 3, -20, -36],\n [13, 16, 11, -22, -34],\n [7, 34, 4, -28, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-36, 16, -32, 26, 28],\n [-21, 14, 8, -39, 21],\n [-24, -12, 22, -22, -16],\n [24, -38, 13, -34, -56],\n [50, 4, 38, -15, -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[[19, -16, -4, 12, -12],\n [19, 18, 14, 34, -15],\n [19, -16, -4, 12, -12],\n [-24, 22, 6, -14, 15],\n [54, -24, 0, 48, -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[[-30, 33, -12, 42, -15],\n [-25, 14, -21, 31, -10],\n [-9, 18, 3, 15, -6],\n [15, 24, 39, -9, 0],\n [-2, -41, -36, -10, 7]]\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, 0, -12, -18, -9],\n [4, 0, -16, -24, -12],\n [2, 0, -8, -12, -6],\n [-6, 0, 24, 36, 18],\n [6, 0, -24, -36, -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[[-21, -12, 12, 27, -3],\n [-9, -8, 4, 16, -3],\n [25, -20, -28, 21, -17],\n [3, 16, 4, -26, 9],\n [32, -16, -32, 12, -16]]?\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[[-31, 39, -16, 48, -49],\n [12, -18, 9, -9, 12],\n [-5, -9, 9, -9, 13],\n [-26, 14, 0, 4, -2],\n [-6, 10, -4, 32, -30]]\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, 6, 0, 0, 6],\n [18, 6, 0, 0, 6],\n [-6, -2, 0, 0, -2],\n [-15, -5, 0, 0, -5],\n [12, 4, 0, 0, 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[[-28, 31, -8, 24, -21],\n [-7, 4, 6, 7, 41],\n [-2, 7, -4, 14, 20],\n [16, -9, -8, -4, -24],\n [-6, 14, -12, 14, -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[[6, -18, 12, 15, 0],\n [12, -36, 24, 30, 0],\n [-4, 12, -8, -10, 0],\n [4, -12, 8, 10, 0],\n [8, -24, 16, 20, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, 13, -35, 45, -6],\n [2, 15, -58, 31, 19],\n [2, -32, -12, 19, -29],\n [12, 17, -70, 47, 12],\n [10, 29, -54, 17, 35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-8, -11, 12, 13, -8],\n [-30, 42, 0, -12, 60],\n [-35, 12, 20, 13, 30],\n [19, 3, -16, -14, -6],\n [-7, 32, -12, -19, 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[[-25, -12, 52, 28, 2],\n [12, 0, -26, -28, -8],\n [8, -4, -4, -19, -20],\n [-26, 25, 40, 22, 44],\n [-31, -14, 44, 42, 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 5x5 matrix:\n[[-10, 6, -16, 0, -8],\n [0, 42, -42, -45, -6],\n [-4, 36, -40, -36, -8],\n [10, -6, 16, 0, 8],\n [-10, -8, -2, 15, -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 5x5 matrix:\n[[24, 17, -23, 1, 26],\n [12, 29, -27, 5, -2],\n [2, 17, 16, 34, -24],\n [8, -4, -41, -27, 8],\n [-17, -63, -45, -94, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 6, -2, -4, 6],\n [15, -33, -12, 24, -24],\n [-15, 30, 13, -22, 21],\n [30, -48, -30, 36, -30],\n [10, -22, -8, 16, -16]]\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, 16, -8, -24],\n [-39, -12, -37, -34, 42],\n [-26, -10, -26, 8, 48],\n [-1, -4, 5, 20, -3],\n [15, 7, 15, -20, -36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-34, -2, 23, 28, 7],\n [-2, -32, 22, -29, 18],\n [31, -14, -47, -38, -12],\n [36, 40, 0, -24, 2],\n [1, 16, 34, -19, 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[[-22, 21, 26, -54, -15],\n [-8, -47, -43, -12, -20],\n [12, -4, 34, -12, -18],\n [-14, -11, -20, -18, -7],\n [10, -56, -31, 6, -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[[-31, 13, 13, -13, 8],\n [11, -9, -9, 1, 8],\n [-16, -7, -7, -18, 38],\n [6, -8, -8, -2, 12],\n [16, -10, -10, 4, 4]]\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, -12, 12, 16, -24],\n [-12, 9, -9, -12, 18],\n [0, 0, 0, 0, 0],\n [-12, 9, -9, -12, 18],\n [4, -3, 3, 4, -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[[-24, -12, 40, -6, -28],\n [6, 38, -38, 39, 34],\n [26, -22, 8, -21, -10],\n [33, -6, -28, -12, 16],\n [30, 10, -30, 9, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, -2, 11, 27, 23],\n [5, -1, 7, -1, 3],\n [-27, 6, -39, -1, -13],\n [-25, 6, -32, 1, 17],\n [-15, 3, -15, 11, 23]]?\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[[9, -18, 11, -11, -8],\n [2, -4, -30, -13, -19],\n [-38, 28, -11, 30, 15],\n [27, -14, 9, -13, -4],\n [-5, -16, 25, -4, -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[[-17, -32, -47, -17, -16],\n [-15, 20, -9, 27, -25],\n [31, -40, -15, -49, 24],\n [8, -29, -22, -28, 6],\n [6, -38, -10, -38, 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[[-22, -9, 44, -16, 47],\n [15, -43, 33, -29, 50],\n [-12, 12, 16, 15, 4],\n [-37, 17, 61, -16, 22],\n [-41, 40, 51, 9, -5]]\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[[-30, 0, 24, 0, 0],\n [-15, 0, 12, 0, 0],\n [-30, 0, 24, 0, 0],\n [5, 0, -4, 0, 0],\n [-20, 0, 16, 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, 0, 0, 0, 0],\n [3, 6, 6, -3, -3],\n [2, 4, 4, -2, -2],\n [6, 12, 12, -6, -6],\n [4, 8, 8, -4, -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[[-15, 7, -28, -32, -15],\n [9, 18, 36, 54, 6],\n [-27, 28, 14, 4, 22],\n [-9, -4, -32, -38, -16],\n [-18, 16, -10, -14, -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[[-44, -34, 8, -44, -12],\n [6, 18, 4, 20, -20],\n [-1, 4, 2, 4, -8],\n [-17, -16, 2, -20, 0],\n [16, -1, -8, 2, 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[[0, 0, 0, 0, 0],\n [8, 24, -20, 4, 8],\n [-4, -12, 10, -2, -4],\n [0, 0, 0, 0, 0],\n [-10, -30, 25, -5, -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[[18, 12, 12, -12, 12],\n [6, 4, 4, -4, 4],\n [15, 10, 10, -10, 10],\n [18, 12, 12, -12, 12],\n [-6, -4, -4, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[29, -33, -9, 4, 1],\n [-7, -19, -22, -66, -11],\n [4, -10, -33, -46, -30],\n [-17, 59, 6, 50, -21],\n [8, 0, 0, 16, -2]]?\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 5x5 matrix:\n[[8, -25, -34, 51, 22],\n [28, 11, 6, -17, -14],\n [-33, 0, 16, -10, -1],\n [-7, -16, -39, 44, 33],\n [-4, 31, 14, -45, -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 5x5 matrix:\n[[-28, -15, 32, 24, -18],\n [-18, 21, 15, 21, -45],\n [-2, -27, 7, -3, 27],\n [-20, 5, 20, 20, -30],\n [4, -23, 0, -8, 30]]\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 5x5 matrix:\n[[-9, 32, -14, 24, -37],\n [-19, 22, 16, -4, -28],\n [-12, 16, 8, 0, -20],\n [6, 2, -14, 12, -1],\n [-18, 4, 32, -24, -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 5x5 matrix:\n[[-26, -59, -26, -46, -6],\n [18, 41, 19, 31, 2],\n [-3, -7, -4, -9, -7],\n [3, 15, 54, 3, -33],\n [12, 26, 4, 28, 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[[-42, 12, -27, -16, -19],\n [52, -16, 34, 18, 24],\n [-26, 8, -17, -9, -12],\n [6, 24, -9, 43, -8],\n [-34, 4, -19, -22, -13]]?\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[[-9, 12, 9, -12, 12],\n [-9, 12, 9, -12, 12],\n [18, -24, -18, 24, -24],\n [9, -12, -9, 12, -12],\n [-18, 24, 18, -24, 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[[47, -19, -7, 53, -51],\n [-10, 3, -14, 16, 0],\n [-3, -16, -8, 34, -18],\n [8, -10, 2, -16, 6],\n [24, -16, 13, -20, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-36, -18, -24, 18, 0],\n [-6, -3, -4, 3, 0],\n [18, 9, 12, -9, 0],\n [-6, -3, -4, 3, 0],\n [36, 18, 24, -18, 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[[4, -20, 22, 9, -11],\n [-4, 2, 0, -4, 3],\n [-37, 11, -51, -46, 45],\n [3, 17, -11, 0, 2],\n [-28, -16, -14, -29, 25]]\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[[-9, -6, -12, -15, 0],\n [9, 6, 12, 15, 0],\n [15, 10, 20, 25, 0],\n [-12, -8, -16, -20, 0],\n [6, 4, 8, 10, 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 5x5 matrix:\n[[-44, 42, 7, -27, 3],\n [-14, -18, -26, -11, 4],\n [27, -56, -40, 21, -4],\n [24, -46, -32, 19, -4],\n [-14, 34, 11, -5, -1]]\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[[8, 4, -10, 6, 6],\n [-16, -8, 20, -12, -12],\n [-24, -12, 30, -18, -18],\n [20, 10, -25, 15, 15],\n [20, 10, -25, 15, 15]]\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, -14, 7, 41, -25],\n [-44, 7, -8, -24, 8],\n [-52, -16, -16, -30, -8],\n [10, 18, 10, 21, 6],\n [22, -8, 11, 52, -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 5x5 matrix:\n[[-7, -6, -24, 15, -15],\n [-14, 8, 18, -6, -8],\n [-30, 10, 15, 0, -25],\n [20, 0, 12, -12, 24],\n [11, -12, -33, 15, 0]]\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, -36, 24, 6, 36],\n [-12, -36, 24, 6, 36],\n [-6, -18, 12, 3, 18],\n [12, 36, -24, -6, -36],\n [12, 36, -24, -6, -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[[-2, -14, -12, -1, 2],\n [21, 43, 32, 7, -20],\n [9, 2, -6, 3, -2],\n [-16, -20, -12, -5, 14],\n [-16, 3, -2, -3, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[24, -12, -24, 8, -12],\n [-6, 3, 6, -2, 3],\n [-30, 15, 30, -10, 15],\n [-30, 15, 30, -10, 15],\n [18, -9, -18, 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[[20, -5, 25, -25, 15],\n [-4, 1, -5, 5, -3],\n [20, -5, 25, -25, 15],\n [8, -2, 10, -10, 6],\n [4, -1, 5, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[10, -10, -15, -25, 25],\n [8, -8, -12, -20, 20],\n [10, -10, -15, -25, 25],\n [6, -6, -9, -15, 15],\n [10, -10, -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[[-24, -22, 33, 4, -7],\n [34, 27, -3, 11, -13],\n [26, 21, -6, 7, -8],\n [-28, -22, 0, -10, 12],\n [14, 13, -21, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-28, 4, -22, 37, 15],\n [4, -4, -2, -1, 3],\n [8, -4, 2, -7, 0],\n [-12, -12, -30, 33, 27],\n [28, -24, -8, -12, 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[[-8, -9, -8, -9, -17],\n [13, -18, -11, 24, 22],\n [23, -27, -19, 33, 23],\n [42, -32, -34, 24, -20],\n [26, 3, -4, 9, -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[[1, -1, 66, 14, -40],\n [33, -69, 8, -14, -18],\n [0, -14, -36, 10, 48],\n [-15, 39, -1, -2, 7],\n [-30, 51, -19, 25, 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[[44, 32, -18, -28, 38],\n [-34, -46, -5, 0, 23],\n [-36, -35, 24, 20, -24],\n [12, 4, -6, 6, 2],\n [6, 15, 21, -6, -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 5x5 matrix:\n[[-5, 10, -8, 5, 24],\n [44, 0, -20, -32, -22],\n [-28, -14, 20, 29, 8],\n [-46, -34, 50, 46, -12],\n [-23, 37, 7, 5, 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[[28, 39, -21, 8, 13],\n [-4, -6, -2, 14, 22],\n [20, 30, -30, -10, 34],\n [6, -73, -1, -43, 15],\n [4, -26, 16, 71, 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[[12, 4, -12, -24, 12],\n [-5, -11, 13, -6, -21],\n [1, 5, -5, 6, 9],\n [-11, -13, 19, 6, -27],\n [5, 11, -13, 6, 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 5x5 matrix:\n[[-28, -8, -23, 4, -13],\n [-35, -9, -39, 26, -25],\n [-30, -15, -44, 42, -23],\n [-23, 3, -29, 26, -27],\n [-4, 18, 15, -32, -5]]\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 5x5 matrix:\n[[4, -20, -19, 27, 4],\n [4, -8, -9, 13, 0],\n [4, -32, -29, 41, 8],\n [4, -8, -9, 13, 0],\n [0, -36, -30, 42, 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[[0, -6, 36, 0, 30],\n [0, 2, -12, 0, -10],\n [0, -3, 18, 0, 15],\n [0, -4, 24, 0, 20],\n [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[[16, 38, -14, 33, 36],\n [29, 14, -60, -7, -22],\n [68, -20, -56, 39, -36],\n [-37, -17, 81, 9, 51],\n [-50, 4, 32, -40, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -8, -16, -16, 16],\n [0, -6, -12, -12, 12],\n [0, 6, 12, 12, -12],\n [0, 2, 4, 4, -4],\n [0, 10, 20, 20, -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[[4, 23, -41, 9, -12],\n [5, 36, -25, 2, -14],\n [1, 31, -20, 15, -22],\n [-5, -8, 37, 2, -2],\n [3, -7, -18, -7, 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[[-13, 3, 9, 11, 11],\n [-24, -29, 0, -36, 21],\n [23, -14, 9, 8, -10],\n [16, 27, -6, 22, -14],\n [36, -51, 14, -10, -36]]\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, -6, 23, 7, -26],\n [3, -14, -6, 6, 4],\n [15, -12, -1, 1, -38],\n [9, -12, -3, 3, -18],\n [13, -7, -3, -2, -36]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[24, 12, 0, 16, 4],\n [42, 24, 8, 18, 12],\n [30, 21, 16, 0, 15],\n [21, 6, -12, 29, -4],\n [21, 9, -4, 19, 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[[-10, 24, 17, -17, 13],\n [-23, -26, -16, -13, -31],\n [-22, 8, 7, -23, -5],\n [27, -6, -6, 27, 9],\n [-5, -2, -1, -4, -4]]\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, -10, -16, 22, 26],\n [4, 0, -5, -18, -61],\n [-30, -33, -28, 18, -16],\n [54, 42, 37, -26, -32],\n [-42, -38, 19, 62, 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[[18, 36, 6, 0, 18],\n [-6, -12, -2, 0, -6],\n [-3, -6, -1, 0, -3],\n [0, 0, 0, 0, 0],\n [-15, -30, -5, 0, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-11, 14, 4, -20, 9],\n [6, -15, -3, 33, -18],\n [-23, 8, 6, 22, -19],\n [-17, 2, 4, 28, -21],\n [-12, 3, 3, 15, -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[[24, 18, -12, 18, -24],\n [-16, -12, 8, -12, 16],\n [-8, -6, 4, -6, 8],\n [-24, -18, 12, -18, 24],\n [4, 3, -2, 3, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 4, -4, 24, 16],\n [8, -4, 4, -24, -16],\n [-10, 5, -5, 30, 20],\n [10, -5, 5, -30, -20],\n [-12, 6, -6, 36, 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[[-13, -3, -16, 31, 10],\n [-10, 18, 34, -18, -44],\n [16, -51, -47, -7, 14],\n [-25, 6, 7, 20, -32],\n [12, 51, 60, -37, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[34, -3, -86, -63, -48],\n [37, 23, 12, 66, 16],\n [23, -8, -4, 15, 6],\n [-16, -1, -9, 54, -38],\n [44, 0, -22, 18, 0]]\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[[8, 12, -16, 16, 4],\n [12, 18, -24, 24, 6],\n [-2, -3, 4, -4, -1],\n [6, 9, -12, 12, 3],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-22, 16, 30, -16, 36],\n [-7, 13, 12, -7, 21],\n [25, -5, -30, 15, -25],\n [-1, 6, 3, -2, 8],\n [4, 34, 6, -6, 38]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-6, 0, 6, -4, 6],\n [0, 0, 0, 0, 0],\n [3, 0, -3, 2, -3],\n [15, 0, -15, 10, -15],\n [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[[25, -3, 51, 14, 42],\n [26, 66, -30, 22, -42],\n [-38, -4, -90, -2, -68],\n [8, 20, 18, -1, 3],\n [35, 57, -3, -4, -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[[16, -24, 24, 8, 12],\n [16, -24, 24, 8, 12],\n [16, -24, 24, 8, 12],\n [20, -30, 30, 10, 15],\n [16, -24, 24, 8, 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[[12, 28, 0, -5, -58],\n [-4, -30, -22, -49, -15],\n [4, -12, -18, 8, -49],\n [46, 12, -16, -31, -42],\n [-16, -24, -2, 14, 31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-18, -3, -6, -15, -6],\n [-30, -5, -10, -25, -10],\n [12, 2, 4, 10, 4],\n [-24, -4, -8, -20, -8],\n [-12, -2, -4, -10, -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[[22, -17, 9, -5, 4],\n [20, -20, 15, 0, 5],\n [2, -17, 24, 15, 5],\n [-20, 30, -30, -10, -8],\n [-10, 15, -15, -5, -4]]\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, -46, -14, -14, 40],\n [25, -28, -4, 45, -15],\n [11, 17, 10, 28, -22],\n [57, -99, -12, 48, 36],\n [10, -44, -40, 2, -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[[-42, -16, 24, 18, 2],\n [24, 22, 2, -16, 16],\n [-12, -2, 10, 4, 4],\n [18, 30, 18, -18, 30],\n [3, -13, -19, 5, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-30, 8, 33, 9, 34],\n [19, 43, 7, -32, 9],\n [-29, -16, 21, 46, 34],\n [-15, 13, 20, -15, 13],\n [15, 13, -5, 0, 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[[-4, 12, 10, 10, -12],\n [12, -36, -30, -30, 36],\n [-2, 6, 5, 5, -6],\n [4, -12, -10, -10, 12],\n [4, -12, -10, -10, 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 5x5 matrix:\n[[6, -18, 24, -6, -18],\n [-5, 15, -20, 5, 15],\n [-6, 18, -24, 6, 18],\n [6, -18, 24, -6, -18],\n [4, -12, 16, -4, -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[[-12, 0, 16, -20, -8],\n [15, 0, -20, 25, 10],\n [-15, 0, 20, -25, -10],\n [6, 0, -8, 10, 4],\n [9, 0, -12, 15, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 0, 42, 0, 36],\n [4, -20, -18, -64, -30],\n [-15, 39, 25, 22, 0],\n [23, -34, 8, -1, 8],\n [2, -34, -6, -30, 17]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[23, 9, 50, 27, -19],\n [30, 30, 18, 22, -31],\n [-2, -36, -42, -6, 10],\n [36, -18, -22, 24, -24],\n [35, 30, 15, 25, -35]]?\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[[-27, -9, 0, 9, 0],\n [22, 3, -3, -8, 3],\n [-15, -18, -9, 3, 9],\n [8, -6, -6, -4, 6],\n [-9, -3, 0, 3, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0, 0],\n [-24, 12, 6, 30, 0],\n [16, -8, -4, -20, 0],\n [20, -10, -5, -25, 0],\n [-8, 4, 2, 10, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, -6, -6, -18, -6],\n [-10, -5, -5, -15, -5],\n [-4, -2, -2, -6, -2],\n [6, 3, 3, 9, 3],\n [2, 1, 1, 3, 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[[4, 30, -16, 27, -36],\n [24, -6, 2, 16, -37],\n [2, 0, 6, -2, -10],\n [-42, 72, -42, 24, 12],\n [-22, 36, -24, 13, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0, 0],\n [18, 15, -3, 0, 3],\n [6, 5, -1, 0, 1],\n [-6, -5, 1, 0, -1],\n [-18, -15, 3, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -9, -12, 22, -48],\n [-27, 1, -3, 10, -18],\n [-24, 14, 14, 2, -60],\n [39, -27, -31, 36, -42],\n [15, -4, -3, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-42, -27, -30, 21, -18],\n [8, 19, 10, 1, -10],\n [24, 33, -6, 26, 13],\n [28, 17, 19, -19, 12],\n [17, 25, -44, 47, 31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-38, -26, -36, -14, -26],\n [-26, -26, -12, 19, -20],\n [-27, -20, -24, 2, -21],\n [22, 8, 32, 30, 14],\n [-22, -20, -8, -36, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-32, 60, 32, 28, 18],\n [-14, 0, 14, 16, -14],\n [-6, 48, 6, 0, 34],\n [31, -24, -31, -32, 11],\n [25, -60, -25, -20, -25]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[24, -14, -12, 6, -12],\n [-12, -18, 16, -18, 26],\n [12, 18, -16, 18, -26],\n [12, -17, -2, -3, 2],\n [-36, 31, 14, -3, 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 5x5 matrix:\n[[5, -1, 0, 3, 6],\n [5, -1, 0, 3, 6],\n [20, -4, 0, 12, 24],\n [25, -5, 0, 15, 30],\n [25, -5, 0, 15, 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[[20, 16, 20, -28, -14],\n [-28, -4, 22, 2, 24],\n [36, -7, -9, -19, 27],\n [2, -7, 10, -10, 33],\n [-16, -20, -5, 13, 45]]\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[[19, -8, 1, 22, 14],\n [20, 4, -20, 30, -5],\n [-21, -4, 23, -31, 10],\n [-19, 12, 3, -18, 3],\n [1, 0, 9, 3, 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[[-3, -15, 0, 6, 3],\n [-1, -5, 0, 2, 1],\n [-4, -20, 0, 8, 4],\n [-6, -30, 0, 12, 6],\n [-3, -15, 0, 6, 3]]\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, 0, -9, 6, -18],\n [9, -4, 5, -10, 14],\n [26, -10, 23, -32, 56],\n [-23, 10, -14, 26, -38],\n [13, -8, -5, -10, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[24, 4, -4, 0, 8],\n [-36, -6, 6, 0, -12],\n [-24, -4, 4, 0, -8],\n [36, 6, -6, 0, 12],\n [18, 3, -3, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-30, -10, -10, 0, 5],\n [-24, -8, -8, 0, 4],\n [6, 2, 2, 0, -1],\n [-24, -8, -8, 0, 4],\n [36, 12, 12, 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 5x5 matrix:\n[[33, 31, -18, 18, 22],\n [-18, 20, 6, 38, 34],\n [-43, -31, 42, -22, 6],\n [14, -14, -54, 6, -54],\n [-4, 13, 33, -4, 32]]\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[[37, 8, -13, -26, 23],\n [-19, -11, 31, 17, -11],\n [9, 7, -21, -9, 5],\n [8, -7, 28, -1, 6],\n [7, -4, 17, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[7, -6, -4, -5, -11],\n [-64, -6, 4, 30, 32],\n [20, -15, -14, -15, -25],\n [5, -24, -32, -15, -10],\n [-8, 18, 44, 20, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 12, 9, -3, -15],\n [-10, 20, 15, -5, -25],\n [0, 0, 0, 0, 0],\n [8, -16, -12, 4, 20],\n [2, -4, -3, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[34, 12, 12, 38, -15],\n [-28, -24, 6, -26, 0],\n [-20, -24, 12, -16, -6],\n [-14, -4, -6, -16, 7],\n [20, 24, -12, 16, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[14, -39, -26, 15, 16],\n [8, -7, -11, 2, 7],\n [-10, -4, 12, 2, -8],\n [6, -2, -26, -18, -10],\n [56, -53, -1, 10, 37]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[20, 21, -2, -4, -19],\n [14, -9, 16, 3, 0],\n [36, -51, -6, -8, 10],\n [-58, -24, 22, 17, 38],\n [-34, -21, 4, 7, 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 5x5 matrix:\n[[-18, 12, -42, -54, 42],\n [-6, 9, -16, -23, 16],\n [-9, 1, -19, -22, 19],\n [-9, 21, -27, -42, 27],\n [-6, -11, -8, -3, 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[[-4, 3, 1, 9, -7],\n [20, -1, 9, -10, -7],\n [-16, -4, -12, -4, 20],\n [-20, -3, -13, 0, 19],\n [16, -6, 2, -21, 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[[4, -37, -20, 42, -15],\n [11, 9, 12, 10, -10],\n [21, -2, -15, 13, 11],\n [11, -33, -23, 45, -17],\n [3, 28, -4, -22, -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[[8, 8, 4, 12, 12],\n [12, 12, 6, 18, 18],\n [-12, -12, -6, -18, -18],\n [-12, -12, -6, -18, -18],\n [-4, -4, -2, -6, -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[[-16, -24, 16, -8, 12],\n [4, 6, -4, 2, -3],\n [8, 12, -8, 4, -6],\n [-12, -18, 12, -6, 9],\n [-4, -6, 4, -2, 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[[-48, -8, 1, -8, -28],\n [-26, 11, 56, 20, -54],\n [-17, -25, -22, 16, 8],\n [-14, -18, 67, 16, -60],\n [-24, 10, -8, 38, 0]]?\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, 12, 2, 4, 4],\n [-18, 36, 6, 12, 12],\n [15, -30, -5, -10, -10],\n [9, -18, -3, -6, -6],\n [-18, 36, 6, 12, 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 5x5 matrix:\n[[-8, -12, -6, 11, 44],\n [-9, -2, 20, 27, 63],\n [5, -40, -17, 30, 14],\n [0, 24, -4, -34, -46],\n [4, 18, 1, -21, -87]]\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[[-30, 29, 26, 29, 28],\n [18, 5, 18, 5, -28],\n [24, -8, 2, -8, -30],\n [6, -29, -40, -29, 6],\n [36, -26, -18, -26, -38]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-9, -4, 2, -15, 12],\n [12, 13, 3, -3, -17],\n [1, 8, 6, 1, -2],\n [-3, -29, -23, -33, 6],\n [11, 35, 23, 38, -17]]\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[[5, -20, -5, -5, 0],\n [0, 0, 0, 0, 0],\n [5, -20, -5, -5, 0],\n [-4, 16, 4, 4, 0],\n [1, -4, -1, -1, 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[[-18, 2, -31, 23, 11],\n [14, -19, 44, -7, -25],\n [-7, 7, -56, 5, 43],\n [26, -35, -12, -3, 17],\n [-4, 6, 39, -9, -18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, -2, 6, -2, 0],\n [13, -20, 13, -26, 44],\n [-13, -4, -11, 2, 16],\n [0, 1, -11, 7, 1],\n [15, 29, 46, -43, -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[[-4, -12, -10, 2, -2],\n [-4, -12, -10, 2, -2],\n [-4, -12, -10, 2, -2],\n [8, 24, 20, -4, 4],\n [2, 6, 5, -1, 1]]?\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[[0, -4, 10, -4, 6],\n [0, 6, -15, 6, -9],\n [0, 4, -10, 4, -6],\n [0, -10, 25, -10, 15],\n [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[[-31, -25, 20, -11, 18],\n [-9, -45, 0, 65, -26],\n [-12, -15, 5, -7, -2],\n [-36, -20, 17, -2, 22],\n [-24, -25, 7, 23, 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 5x5 matrix:\n[[-2, -12, -12, -16, -14],\n [21, 24, -51, 9, 24],\n [-10, -4, 22, 2, -6],\n [25, 0, 1, 5, 20],\n [-9, 4, -9, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[10, -15, -5, 5, -30],\n [6, -9, -3, 3, -18],\n [-10, 15, 5, -5, 30],\n [-2, 3, 1, -1, 6],\n [-4, 6, 2, -2, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[30, 40, 27, -26, -13],\n [30, 42, 16, -22, -15],\n [36, 10, -44, 0, -48],\n [-30, 50, 15, -61, -38],\n [-48, -12, -13, 13, 27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, -8, 12, -4, 6],\n [-9, 12, 54, 18, 9],\n [6, -16, -36, -18, -3],\n [2, 32, -12, 22, -15],\n [5, 4, -30, -2, -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[[26, 24, 18, 19, 15],\n [24, 27, 27, 30, 18],\n [20, 26, 30, 34, 18],\n [36, 30, 18, 18, 18],\n [24, 20, 12, 12, 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 5x5 matrix:\n[[-2, 2, -12, -4, 23],\n [22, 5, 30, 5, -43],\n [-34, -22, -8, 0, -21],\n [70, 54, 41, 35, 24],\n [-10, -9, 4, 1, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[15, 43, 10, -3, -49],\n [1, -13, 9, -12, -12],\n [-3, -13, 0, -19, -3],\n [19, 2, -13, 44, 9],\n [39, -45, -20, 43, 0]]\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, 36, 18, -5, -4],\n [0, 0, 0, -20, -16],\n [0, -36, -18, 10, 8],\n [0, 36, 18, 15, 12],\n [0, -12, -6, 30, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[58, 30, 4, -7, -6],\n [-16, -6, -6, 9, -10],\n [-14, 18, 6, -26, -46],\n [-48, -11, 12, -25, -6],\n [-3, -19, -29, 9, 5]]?\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, -2, 12, 12, 3],\n [3, -7, 17, 10, -7],\n [-2, -9, 4, -8, -4],\n [-5, 7, -11, -2, 14],\n [8, -2, -12, -20, -25]]\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[[12, 30, -24, -36, 0],\n [-12, -30, 24, 36, 0],\n [-2, -5, 4, 6, 0],\n [-12, -30, 24, 36, 0],\n [8, 20, -16, -24, 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[[-5, 16, 29, 26, 2],\n [9, -20, -28, -16, -8],\n [2, 4, 17, 26, -6],\n [2, 0, 6, 12, -4],\n [6, -20, -37, -34, -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[[-30, 0, -5, -20, 10],\n [-22, 12, -15, 0, -6],\n [-4, 12, -12, 12, -12],\n [-16, 12, -14, 4, -8],\n [19, 15, -11, 31, -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[[36, -6, -20, 26, -22],\n [-18, -42, -24, 6, 12],\n [-2, -16, -16, -24, 30],\n [-20, 14, 19, -20, 13],\n [23, 38, 19, 0, -16]]\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, -26, 4, -22, -40],\n [-12, -30, 24, -26, -40],\n [-31, -23, 15, 1, -35],\n [6, 3, -18, -3, 0],\n [8, 18, -28, 14, 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[[-26, 1, 10, 5, -7],\n [-91, 5, 27, -1, -1],\n [96, 0, -30, 0, 6],\n [-33, 4, 7, -6, 8],\n [5, -3, -18, -41, 48]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-24, -18, 24, 36, 30],\n [-20, -15, 20, 30, 25],\n [24, 18, -24, -36, -30],\n [4, 3, -4, -6, -5],\n [20, 15, -20, -30, -25]]\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, -26, -3, 6, 26],\n [-8, 27, 3, -8, -25],\n [24, -18, 27, -62, 26],\n [6, 14, 18, -40, -10],\n [16, -32, 3, -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[[1, 6, -5, 5, 3],\n [1, 6, -5, 5, 3],\n [-1, -6, 5, -5, -3],\n [-1, -6, 5, -5, -3],\n [3, 18, -15, 15, 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[[31, 3, 4, 39, -47],\n [-20, -27, 16, -60, 31],\n [-15, 53, -54, 61, 17],\n [-13, 31, -33, 16, -7],\n [19, -50, 61, -54, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-20, 24, 16, -24, -20],\n [-5, 6, 4, -6, -5],\n [-25, 30, 20, -30, -25],\n [-25, 30, 20, -30, -25],\n [30, -36, -24, 36, 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[[-18, 33, 12, -18, -21],\n [-34, -52, 14, 23, -7],\n [24, -28, 16, 28, 8],\n [-23, 29, -54, -42, 2],\n [-22, 31, -6, -33, 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[[4, 12, 20, 0, 12],\n [-4, -12, -20, 0, -12],\n [2, 6, 10, 0, 6],\n [-1, -3, -5, 0, -3],\n [-1, -3, -5, 0, -3]]?\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[[1, -4, 6, 0, 6],\n [0, 0, 0, 0, 0],\n [-5, 20, -30, 0, -30],\n [-6, 24, -36, 0, -36],\n [-3, 12, -18, 0, -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[[-28, 30, -2, -15, 10],\n [2, 50, 24, -34, 24],\n [48, -16, 15, 16, -14],\n [7, -17, -22, 11, -52],\n [2, -12, -29, 6, -66]]\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, 5, -25, 24, -21],\n [-19, -15, -31, -6, -41],\n [0, -8, 8, -17, 4],\n [33, 7, -9, 27, 9],\n [29, -16, -21, -4, -24]]?\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[[27, -18, 33, 9, -27],\n [44, -16, 46, 20, -24],\n [29, -32, 23, 59, 3],\n [-31, -2, -27, -13, 3],\n [-8, -8, -2, -8, -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[[17, 50, -17, 10, 11],\n [4, 27, -4, 4, 3],\n [22, 19, -22, 8, 13],\n [-18, -66, 18, -12, -12],\n [7, 1, -7, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, 1, 2, -4, -1],\n [-11, -1, -10, 2, -9],\n [-6, 16, -4, -21, 7],\n [-26, -11, 12, -19, -40],\n [-7, -4, -10, 9, -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[[-12, -22, 35, 14, 7],\n [32, -14, -5, 18, 15],\n [34, 10, 15, -4, -5],\n [-26, -10, 50, 0, -6],\n [-18, 5, -5, -7, -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[[-4, 26, -21, 4, -35],\n [24, -6, 36, -24, 30],\n [0, -25, 15, 0, 30],\n [24, 9, 27, -24, 12],\n [-8, 2, -12, 8, -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 5x5 matrix:\n[[18, -38, -53, 25, 27],\n [-16, -27, 20, 16, -24],\n [14, -12, -34, -18, 42],\n [20, -9, -17, 29, -25],\n [-15, -48, 13, -45, 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[[10, -8, -8, 2, -4],\n [0, 0, 0, 0, 0],\n [-15, 12, 12, -3, 6],\n [-30, 24, 24, -6, 12],\n [10, -8, -8, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-21, -3, -18, -42, -10],\n [-17, 8, -9, 35, 18],\n [23, -53, 0, 15, -34],\n [62, -37, -12, 64, -16],\n [-1, 60, 30, 12, 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 5x5 matrix:\n[[-29, -7, -33, 36, 6],\n [22, 11, 39, -10, -6],\n [-4, -22, -43, 28, -31],\n [22, -31, -5, -42, 12],\n [-34, 26, -12, 86, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-10, 5, -25, 10, 0],\n [4, -2, 10, -4, 0],\n [-2, 1, -5, 2, 0],\n [2, -1, 5, -2, 0],\n [-4, 2, -10, 4, 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[[-38, 36, 54, -30, 26],\n [21, -22, -28, 10, -17],\n [5, -6, -6, 0, -5],\n [36, -40, -46, 10, -32],\n [20, -24, -24, 0, -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[[3, -1, 3, -4, 10],\n [-10, 6, -10, 32, -12],\n [7, -1, 7, 0, 34],\n [9, -3, 9, -12, 30],\n [1, -3, 1, -20, -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 5x5 matrix:\n[[6, -12, 15, 3, 3],\n [-4, 8, -10, -2, -2],\n [10, -20, 25, 5, 5],\n [0, 0, 0, 0, 0],\n [10, -20, 25, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, -7, 2, 4, -7],\n [-27, -23, 4, -10, -27],\n [-48, -12, 24, 30, -34],\n [-43, -40, 20, -2, -44],\n [14, -36, 12, -42, 6]]\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, -2, 0, -1, -6],\n [-6, 12, 0, 6, 36],\n [5, -10, 0, -5, -30],\n [4, -8, 0, -4, -24],\n [-1, 2, 0, 1, 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[[8, 8, -10, 10, -6],\n [4, 4, -5, 5, -3],\n [-12, -12, 15, -15, 9],\n [20, 20, -25, 25, -15],\n [20, 20, -25, 25, -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[[30, -6, -6, -30, -36],\n [10, -2, -2, -10, -12],\n [10, -2, -2, -10, -12],\n [15, -3, -3, -15, -18],\n [-30, 6, 6, 30, 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[[22, -28, -40, -29, -10],\n [16, 1, -23, 14, -1],\n [-24, 8, 36, -6, 20],\n [-33, 47, 28, 14, 19],\n [-10, 29, 18, 34, 0]]\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[[12, -6, -4, -10, 10],\n [-16, 16, 0, 20, 0],\n [-20, 26, -4, 30, 10],\n [32, -50, 12, -55, -30],\n [-2, -1, 2, 0, -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[[19, 23, 2, -24, 23],\n [23, 29, 36, -36, 7],\n [-14, -16, 26, 12, -34],\n [-9, -12, -33, 18, 9],\n [-3, -3, 18, 0, -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 5x5 matrix:\n[[0, 0, 0, 0, 0],\n [-12, -8, 10, 0, 10],\n [-6, -4, 5, 0, 5],\n [36, 24, -30, 0, -30],\n [-24, -16, 20, 0, 20]]\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[[12, 6, 0, 15, -12],\n [-4, -2, 0, -5, 4],\n [0, 0, 0, 0, 0],\n [-24, -12, 0, -30, 24],\n [-24, -12, 0, -30, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, -6, 10, -8, 8],\n [-6, 18, -30, 24, -24],\n [3, -9, 15, -12, 12],\n [-1, 3, -5, 4, -4],\n [3, -9, 15, -12, 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 5x5 matrix:\n[[-32, -4, -16, 36, 16],\n [-28, -2, -2, 33, 17],\n [-20, 0, 10, 25, 15],\n [-44, -5, -18, 50, 23],\n [32, 4, 16, -36, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-21, 25, -6, -4, 27],\n [41, -17, 11, 6, -21],\n [-42, 8, -28, -18, 25],\n [16, 7, 43, 33, -20],\n [-26, -15, 3, 9, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-18, -36, -24, 30, 36],\n [9, 18, 12, -15, -18],\n [-12, -24, -16, 20, 24],\n [9, 18, 12, -15, -18],\n [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[[-24, 24, -12, -24, -12],\n [-12, 12, -6, -12, -6],\n [-36, 36, -18, -36, -18],\n [36, -36, 18, 36, 18],\n [-12, 12, -6, -12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-9, -24, 8, 10, -4],\n [23, 15, -12, 17, -7],\n [1, -14, 24, 8, -2],\n [24, 35, -62, 13, -8],\n [26, 29, -54, 19, -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 5x5 matrix:\n[[20, -16, 16, -16, 0],\n [-10, 8, -8, 8, 0],\n [25, -20, 20, -20, 0],\n [-15, 12, -12, 12, 0],\n [25, -20, 20, -20, 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[[30, -15, -30, -30, -20],\n [-18, 9, 18, 18, 12],\n [-6, 3, 6, 6, 4],\n [-30, 15, 30, 30, 20],\n [-18, 9, 18, 18, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -4, -2, -5, 1],\n [-1, 1, 20, 17, -4],\n [6, -6, 10, 3, -1],\n [-70, 16, 14, 20, -4],\n [-36, 54, -14, 36, -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 5x5 matrix:\n[[-38, -62, -29, 27, 13],\n [28, 14, -17, 9, -11],\n [7, 13, 7, -6, -2],\n [-13, -2, 23, -24, -7],\n [-22, 13, 32, -12, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[17, -20, -8, 17, 24],\n [-8, 16, 6, -7, -31],\n [-19, 20, 54, -27, -58],\n [-34, 24, 14, -37, -3],\n [5, -12, -28, 8, 45]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-26, -12, 22, 36, 30],\n [-25, -4, 19, 33, 24],\n [5, 12, -7, -9, -12],\n [-16, -16, 16, 24, 24],\n [-8, -36, 16, 18, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 6, 18, -30, -18],\n [-2, 1, 3, -5, -3],\n [4, -2, -6, 10, 6],\n [6, -3, -9, 15, 9],\n [6, -3, -9, 15, 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[[47, 1, -22, -39, -33],\n [47, 7, -7, -39, -36],\n [24, 5, 2, -22, -22],\n [20, -15, 1, 1, -37],\n [17, -10, 21, 11, -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[[7, 18, 9, 41, -1],\n [8, 15, 14, 32, -3],\n [5, 0, 15, -5, -5],\n [-9, -15, -17, -31, 4],\n [0, -9, 6, -24, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 15, -49, -54, 2],\n [-8, -18, 46, 52, 4],\n [4, 18, -50, -56, -2],\n [12, -6, 30, 32, -6],\n [-8, -12, 28, 32, 4]]?\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, 4, 16, -24, -16],\n [5, -5, -20, 30, 20],\n [0, 0, 0, 0, 0],\n [-5, 5, 20, -30, -20],\n [-6, 6, 24, -36, -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[[-6, 5, -4, 6, -1],\n [36, -30, 24, -36, 6],\n [36, -30, 24, -36, 6],\n [24, -20, 16, -24, 4],\n [-30, 25, -20, 30, -5]]\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[[-10, 10, 6, 14, 14],\n [3, 6, -20, -26, -29],\n [1, -10, 18, 19, 19],\n [8, -12, 2, 3, 14],\n [-19, 24, 4, 5, -17]]?\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],\n [-8, -20, -12, 16, -8],\n [-12, -30, -18, 24, -12],\n [12, 30, 18, -24, 12],\n [2, 5, 3, -4, 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[[0, 10, 0, -4, 12],\n [0, -20, 0, 8, -24],\n [0, -10, 0, 4, -12],\n [0, 10, 0, -4, 12],\n [0, 10, 0, -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 5x5 matrix:\n[[2, 42, 32, -12, 32],\n [-11, -23, -8, 18, 0],\n [25, 31, 1, -36, -18],\n [-8, -12, -2, 12, 4],\n [11, 23, 8, -18, 0]]\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, 54, -10, -29, -8],\n [44, -32, -10, 31, 11],\n [32, 8, -18, 11, -5],\n [-2, -29, 21, 1, 23],\n [-11, 15, 1, -10, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[20, 24, -16, 20, 20],\n [10, 12, -8, 10, 10],\n [-5, -6, 4, -5, -5],\n [-30, -36, 24, -30, -30],\n [-30, -36, 24, -30, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 40, -22, -36, -4],\n [-18, -26, 29, 21, 2],\n [12, 60, -54, -48, 6],\n [-22, 58, 14, -25, -12],\n [8, -56, 32, 44, 0]]\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 5x5 matrix:\n[[33, 20, -20, 36, 15],\n [27, 5, -20, 24, 15],\n [27, 30, -12, 36, 9],\n [36, 15, -24, 36, 18],\n [-27, -30, 12, -36, -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[[0, 13, -4, 17, -29],\n [-15, 12, -6, -12, 9],\n [0, 13, -4, 17, -29],\n [8, 4, 0, 20, -28],\n [14, -6, 4, 18, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[6, -18, -22, -16, -6],\n [16, 20, 32, 14, -16],\n [12, 12, 20, 8, -12],\n [-5, 11, 13, 10, 5],\n [-6, 6, 6, 6, 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 5x5 matrix:\n[[2, -45, -13, 9, -16],\n [-14, 11, -23, 13, -2],\n [-6, 23, -3, 1, 6],\n [-22, 15, -37, 21, -4],\n [6, -31, 0, 1, -9]]\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 5x5 matrix:\n[[18, -19, -4, 7, -22],\n [36, -38, -8, 14, -44],\n [-14, 12, 22, -26, 16],\n [45, -50, 7, -1, -56],\n [33, -34, -13, 19, -40]]\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, -9, -42, -33, 48],\n [-21, -5, -9, -15, 17],\n [-45, -6, 10, -13, 5],\n [-24, -5, 15, -6, -28],\n [45, 4, -12, 9, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-24, 17, 10, -9, 36],\n [-42, -7, -17, 42, 81],\n [-23, -22, -19, 70, 71],\n [-19, 21, -12, -2, 31],\n [-3, 67, -52, -30, 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[[-32, -4, -20, -36, 32],\n [1, 18, 9, 17, 1],\n [-9, 24, 13, 7, 3],\n [-12, 13, 13, -11, -4],\n [3, -29, -30, -9, 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[[14, 8, -26, 14, -14],\n [-1, -2, -1, 39, 11],\n [-2, 0, 6, -34, -6],\n [18, 12, -30, -30, -30],\n [22, 14, -38, -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[[-8, -20, -5, 9, -5],\n [5, 12, 3, -5, 3],\n [1, 4, 1, -3, 1],\n [-1, -8, -2, 8, -2],\n [7, 24, 6, -16, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[45, -64, 31, 35, 38],\n [-22, 10, -35, -42, 6],\n [38, -40, 36, 40, 4],\n [-15, 4, -37, -47, -6],\n [5, 0, 23, 29, 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 5x5 matrix:\n[[-15, 25, -25, 25, -30],\n [0, 0, 0, 0, 0],\n [-18, 30, -30, 30, -36],\n [-6, 10, -10, 10, -12],\n [9, -15, 15, -15, 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[[-68, 22, 16, 68, -46],\n [12, 36, 25, -73, -21],\n [-44, 28, 59, -5, -61],\n [-14, -3, -20, 48, 6],\n [-4, 14, 16, -2, -15]]\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[[-3, 3, 0, 9, -9],\n [0, 0, 0, 0, 0],\n [-6, 6, 0, 18, -18],\n [-5, 5, 0, 15, -15],\n [4, -4, 0, -12, 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 5x5 matrix:\n[[-20, -5, -10, -10, -25],\n [-12, -3, -6, -6, -15],\n [-4, -1, -2, -2, -5],\n [16, 4, 8, 8, 20],\n [-20, -5, -10, -10, -25]]\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[[38, 7, -52, -22, 11],\n [78, -48, 14, -17, -34],\n [2, 8, -10, -3, 14],\n [-34, 35, -16, 6, 29],\n [-6, 3, 14, 6, -2]]?\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, -21, 18, 9, 24],\n [9, -25, 18, 11, -5],\n [24, 26, -32, -20, -16],\n [-3, -12, 54, 36, 15],\n [-42, -35, 26, 17, 10]]\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 5x5 matrix:\n[[2, -1, 2, 17, -14],\n [-9, -5, -5, 17, -5],\n [0, 5, -1, 2, -4],\n [-48, 17, -37, 34, -4],\n [25, -35, 25, -5, 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[[15, 61, 13, 7, 81],\n [-30, 14, 24, -31, 37],\n [14, 0, 12, -25, 22],\n [-32, -38, 28, -52, -12],\n [14, -20, 14, -54, 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[[-4, -24, -62, 12, -24],\n [17, 16, 34, -29, -17],\n [12, 22, 52, -18, 16],\n [7, -22, -64, 11, -7],\n [10, 13, 31, -31, -38]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[5, -25, 25, 0, 20],\n [4, -20, 20, 0, 16],\n [1, -5, 5, 0, 4],\n [-1, 5, -5, 0, -4],\n [-5, 25, -25, 0, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[34, -13, 26, 23, 37],\n [32, 47, -28, 10, -21],\n [25, 32, -21, 12, -30],\n [21, 43, -29, 12, -35],\n [-5, -28, 41, 47, 40]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-19, -29, -13, -17, -7],\n [-9, -20, -23, 18, 4],\n [-1, 17, 11, 4, -19],\n [-17, -3, 21, -30, -32],\n [-8, -15, -12, -9, 1]]\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, -2, -18, -9, -3],\n [-9, 16, 2, -24, 15],\n [7, 26, -40, 0, 14],\n [20, -51, 11, 20, -40],\n [18, -33, -3, -3, -6]]\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, 43, -15, -4, 17],\n [13, -12, -14, 7, -1],\n [38, -15, -43, 17, 4],\n [-23, -10, 28, -7, -9],\n [-30, 21, 33, -15, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[0, 0, 20, -4, -24],\n [0, 0, 20, -4, -24],\n [0, 0, -20, 4, 24],\n [0, 0, 30, -6, -36],\n [0, 0, 20, -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 5x5 matrix:\n[[-24, -8, -20, -12, -24],\n [6, 2, 5, 3, 6],\n [-6, -2, -5, -3, -6],\n [-12, -4, -10, -6, -12],\n [-12, -4, -10, -6, -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[[-8, 26, 13, 3, 39],\n [10, 12, -4, -53, -18],\n [10, 42, 14, -31, -20],\n [-10, -4, 6, 43, 24],\n [6, 4, -2, -21, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[28, 6, 32, -50, -8],\n [18, 15, -11, 5, 6],\n [30, 9, 27, -45, -6],\n [-6, -3, -2, 5, 0],\n [20, 6, 18, -30, -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[[6, 0, 0, -5, 2],\n [-12, -6, -24, 31, -22],\n [-27, 6, -4, 26, 9],\n [51, -7, 20, -60, -4],\n [-21, 5, 4, 14, 8]]?\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, 4, 11, -6, 9],\n [24, 16, 14, -12, 12],\n [-12, 24, -19, -2, -14],\n [9, -12, 12, 0, 9],\n [-12, 24, -19, -2, -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 5x5 matrix:\n[[-25, -52, 15, 30, 34],\n [13, 42, -38, 20, -16],\n [-16, 33, -30, 4, 17],\n [-49, -4, -10, 4, 58],\n [2, 13, -6, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, 6, -4, -2, 3],\n [-6, -18, 12, 6, -9],\n [12, 36, -24, -12, 18],\n [-8, -24, 16, 8, -12],\n [10, 30, -20, -10, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[21, -12, -42, -60, -6],\n [-40, 14, 48, 45, 12],\n [12, 4, -20, -24, 16],\n [54, -14, -62, -54, -8],\n [34, -18, -52, -63, -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 5x5 matrix:\n[[0, 10, 8, 16, 2],\n [15, 3, 15, 15, -6],\n [-5, 4, -1, 3, 3],\n [5, -14, -7, -19, -5],\n [30, 1, 26, 22, -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[[-20, 4, -4, 0, 16],\n [-15, 3, -3, 0, 12],\n [25, -5, 5, 0, -20],\n [-5, 1, -1, 0, 4],\n [-20, 4, -4, 0, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 18, -24, 0, -6],\n [0, -6, 8, 0, 2],\n [0, 6, -8, 0, -2],\n [0, 0, 0, 0, 0],\n [0, -9, 12, 0, 3]]\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, 0, 0, 0, 0],\n [6, -4, -5, -3, 5],\n [-6, 4, 5, 3, -5],\n [24, -16, -20, -12, 20],\n [30, -20, -25, -15, 25]]\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 5x5 matrix:\n[[-8, 2, -4, -4, -12],\n [24, -6, 12, 12, 36],\n [20, -5, 10, 10, 30],\n [-20, 5, -10, -10, -30],\n [-24, 6, -12, -12, -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[[18, 12, 24, 30, 12],\n [-27, -22, -32, -13, -8],\n [24, 20, 28, 8, 6],\n [15, 20, 10, -55, -15],\n [15, 18, 12, -39, -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[[-24, 0, -8, -4, -4],\n [24, -6, 1, -10, 11],\n [6, -6, -5, -13, 8],\n [4, -2, -1, -4, 3],\n [-26, 4, -4, 5, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-25, 10, -15, 5, -10],\n [-20, 8, -12, 4, -8],\n [5, -2, 3, -1, 2],\n [-15, 6, -9, 3, -6],\n [15, -6, 9, -3, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, -14, -11, -14, -27],\n [-15, 35, -24, -15, -10],\n [-5, 13, 32, 35, -46],\n [-17, 38, 18, 25, 42],\n [33, -21, 8, -9, -28]]?\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, -4, -38, 27, 9],\n [43, 5, -74, -44, 57],\n [7, -34, 12, 25, -3],\n [43, 1, -46, -32, 41],\n [-52, -2, 0, 43, -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[[-48, -12, -18, 30, 6],\n [31, -2, 20, -9, 1],\n [0, -16, 36, 20, 4],\n [-1, -31, 1, 30, 20],\n [-40, -10, -15, 25, 5]]\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, -20, -26, 26, 26],\n [0, 13, -38, 65, 47],\n [-4, -4, 24, -36, -28],\n [35, -37, -41, 32, 38],\n [-13, 13, 9, 0, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[26, -3, -29, -20, 42],\n [-3, 4, 2, 0, -6],\n [-26, 3, 29, 20, -42],\n [-6, 8, 4, 0, -12],\n [6, -27, 3, 12, 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[[5, -30, 25, -15, -15],\n [7, 27, -10, 30, 18],\n [-13, 32, -35, 5, 13],\n [10, 32, -10, 38, 22],\n [-28, 30, -50, -18, 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[[28, -31, -14, 5, -33],\n [25, -30, -20, 30, -30],\n [18, -19, -6, -7, -21],\n [18, -48, -22, 42, -50],\n [23, -44, -17, 19, -47]]\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 5x5 matrix:\n[[2, 13, -19, -27, 5],\n [36, 7, -29, -5, -10],\n [16, 20, 32, -20, 12],\n [-26, 4, -31, -26, 6],\n [-42, -14, 26, 14, 7]]\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, 21, -3, -8, -10],\n [-4, -7, 3, -7, 0],\n [28, 3, -12, 58, 20],\n [-20, -7, -3, -27, 3],\n [28, 8, 6, 44, -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[[-4, -56, 12, -12, 52],\n [-13, 13, 4, -38, 11],\n [-4, -25, 3, -13, 24],\n [-16, -27, -15, 1, 8],\n [2, 48, -26, 34, -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 5x5 matrix:\n[[-21, 39, 29, -3, -44],\n [52, -2, 24, -15, 36],\n [37, 25, 42, 18, -18],\n [-40, -20, -31, 2, 28],\n [-2, -16, -16, 40, -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[[-30, 22, 42, 12, -50],\n [-11, -11, 26, -16, -16],\n [49, -7, 30, -10, 52],\n [9, -43, 18, -38, 2],\n [-12, 26, 50, -4, 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[[-9, -11, 16, -28, 19],\n [36, -1, -28, -5, 14],\n [-9, -6, 12, -15, 9],\n [-39, 4, 28, 13, -21],\n [0, 15, -12, 39, -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[[0, 0, 0, 0, 0],\n [-12, -6, -18, -24, 0],\n [-4, -2, -6, -8, 0],\n [8, 4, 12, 16, 0],\n [12, 6, 18, 24, 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[[-12, -12, 4, -48, 42],\n [8, -8, 6, -22, 37],\n [29, -3, 12, -1, 43],\n [1, -27, -22, -14, -13],\n [-67, 37, 18, -25, -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[[-27, -7, -17, -7, 32],\n [2, 51, -42, -31, 29],\n [45, -3, 39, 15, -30],\n [30, 32, -6, -20, 50],\n [34, 8, 22, 9, -39]]\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[[-37, -27, 18, -9, -16],\n [5, -8, -39, 55, -7],\n [-16, -7, 24, 11, -7],\n [-39, 10, -47, 17, -16],\n [-64, 41, 46, -47, -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[[5, -45, 23, 46, -23],\n [-21, 6, -39, -75, -6],\n [1, -9, 25, 63, 28],\n [10, 2, 0, -14, -22],\n [21, 30, -12, -33, -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[[29, 32, 36, -35, -35],\n [75, -7, -45, 13, 16],\n [-50, -2, -1, 8, -11],\n [22, 0, 45, -28, -9],\n [2, 49, -12, -6, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[15, 25, -15, 15, 15],\n [-15, -25, 15, -15, -15],\n [-6, -10, 6, -6, -6],\n [15, 25, -15, 15, 15],\n [6, 10, -6, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 39, -8, 29, 17],\n [24, 39, 12, -28, -39],\n [14, 0, 17, -50, -47],\n [30, -6, -31, 40, 53],\n [-64, 24, -4, 61, 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[[-4, -8, -16, -14, -10],\n [-4, -25, 6, -2, -23],\n [0, 53, 17, -6, 53],\n [1, -12, 14, 2, -9],\n [7, 4, -13, -10, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[19, -22, -21, -34, -27],\n [-41, 11, 5, 4, -8],\n [42, 18, 2, 30, 28],\n [8, 19, 2, 22, 13],\n [-28, -23, 18, -14, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[12, -18, -12, 12, -30],\n [16, 2, -12, 24, -30],\n [-3, -2, 2, -5, 5],\n [-21, -1, 16, -31, 40],\n [-3, 11, 4, -1, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 0, -8, -12, 24],\n [-1, 0, -2, -3, 6],\n [-3, 0, -6, -9, 18],\n [-4, 0, -8, -12, 24],\n [5, 0, 10, 15, -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[[-17, 8, 17, -30, -36],\n [-26, 14, 11, -24, 27],\n [31, -18, -23, 40, 6],\n [19, 28, 38, 4, 9],\n [-35, 0, 0, -36, -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[[-9, -11, -43, 57, -44],\n [10, -13, 23, -5, 38],\n [22, -32, -6, 46, 22],\n [40, -15, 15, -1, 40],\n [23, -21, -36, 58, -19]]\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[[25, 10, 20, 20, 30],\n [-20, -8, -16, -16, -24],\n [-20, -8, -16, -16, -24],\n [-10, -4, -8, -8, -12],\n [-15, -6, -12, -12, -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 5x5 matrix:\n[[-16, 12, 16, 24, 16],\n [-16, 12, 16, 24, 16],\n [24, -18, -24, -36, -24],\n [-8, 6, 8, 12, 8],\n [-24, 18, 24, 36, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[30, 10, -30, 25, 10],\n [-24, -8, 24, -20, -8],\n [6, 2, -6, 5, 2],\n [-6, -2, 6, -5, -2],\n [-6, -2, 6, -5, -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 5x5 matrix:\n[[-39, -7, 21, 15, 28],\n [-25, -25, 32, 2, 58],\n [33, 26, -21, -18, -14],\n [-9, -21, 18, 0, 30],\n [-3, -40, 18, 3, 16]]\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, 20, -22, -4, 39],\n [18, 11, -17, -3, 45],\n [15, 20, -9, 9, 33],\n [-24, 2, 16, 10, -45],\n [18, -19, 1, -9, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-17, 22, 28, 34, -36],\n [15, -38, 50, 38, 21],\n [-9, -40, 4, 7, 51],\n [-36, 52, -2, 16, -55],\n [16, 20, -12, -18, -24]]?\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, 0, 4, -2, -1],\n [-12, 0, -24, 12, 6],\n [8, 0, 16, -8, -4],\n [-6, 0, -12, 6, 3],\n [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[[-19, -14, 26, -3, 4],\n [12, 15, -42, -9, -12],\n [-40, -20, -16, -30, -17],\n [-36, -37, 30, -1, 2],\n [36, 42, 12, 6, 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[[10, 19, 10, 40, -4],\n [14, 11, 2, -4, 4],\n [15, 22, 10, 35, -2],\n [-15, -9, 0, 15, -6],\n [-16, -7, 2, 26, -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[[2, -6, 0, -3, 4],\n [-10, 30, 0, 15, -20],\n [-12, 36, 0, 18, -24],\n [-6, 18, 0, 9, -12],\n [6, -18, 0, -9, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-13, 21, -10, -29, 17],\n [37, -45, -6, 11, -33],\n [35, -37, -8, -3, -34],\n [-23, 17, 8, -50, 30],\n [-40, 33, 52, 4, 16]]\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, -4, 26, 12, 40],\n [-21, 9, -50, 7, -22],\n [-23, 7, -40, 1, -26],\n [-34, 2, -16, -18, -44],\n [-27, 9, -51, 3, -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[[0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [30, 6, -36, -6, -12],\n [-20, -4, 24, 4, 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[[5, 3, -1, -6, 2],\n [15, 9, -3, -18, 6],\n [20, 12, -4, -24, 8],\n [-20, -12, 4, 24, -8],\n [-25, -15, 5, 30, -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[[-15, 20, -15, -15, -25],\n [18, -24, 18, 18, 30],\n [3, -4, 3, 3, 5],\n [3, -4, 3, 3, 5],\n [-6, 8, -6, -6, -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[[10, 14, -6, 48, 8],\n [-12, -10, 26, -38, 24],\n [-11, -10, 19, -38, 14],\n [30, -9, -30, 36, -30],\n [-18, 30, -1, 23, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-45, 34, 30, -25, 42],\n [25, -25, -6, 2, -32],\n [13, 17, -26, -10, 28],\n [-30, -8, 21, -50, 8],\n [34, -13, -23, 13, -18]]\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, 15, 12, 32, -14],\n [-22, 15, 14, 19, -13],\n [18, 3, 6, -17, -1],\n [38, -24, -22, -33, 21],\n [-12, -30, -36, 14, 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[[18, -20, 26, 2, 16],\n [30, -25, 45, 10, 20],\n [12, 10, 22, 20, -8],\n [9, -25, 10, -11, 20],\n [0, 0, 0, 0, 0]]\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, -6, -6, -10, 2],\n [-12, 6, 6, 10, -2],\n [30, -15, -15, -25, 5],\n [0, 0, 0, 0, 0],\n [-12, 6, 6, 10, -2]]\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, -21, 36, 14, -47],\n [29, -9, 2, 8, 18],\n [-11, 22, -41, -14, 59],\n [35, -6, 25, 30, 13],\n [-21, -9, -24, -36, -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[[3, -19, -13, -20, -6],\n [0, 15, 12, 12, 3],\n [-3, 29, 21, 28, 8],\n [15, 25, 31, -4, -6],\n [15, 10, 19, -16, -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[[0, 2, -3, 1, 1],\n [0, 8, -12, 4, 4],\n [0, 10, -15, 5, 5],\n [0, 8, -12, 4, 4],\n [0, 6, -9, 3, 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[[16, -15, 15, 27, 19],\n [28, -8, 29, 41, 49],\n [3, 23, -9, 20, 25],\n [27, -34, 32, -9, 8],\n [6, -2, 6, -53, -13]]\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, 6, 0, -3, 6],\n [0, 0, 0, 0, 0],\n [4, -4, 0, 2, -4],\n [10, -10, 0, 5, -10],\n [4, -4, 0, 2, -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[[-38, -68, 16, -28, -2],\n [24, 47, -17, 18, -1],\n [-3, 9, -10, 3, -5],\n [2, -34, -16, -26, 2],\n [16, -27, -7, -22, 9]]\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, -2, 19, 0, 8],\n [11, -7, -12, 28, -21],\n [-18, -5, 28, -38, 26],\n [16, -27, 23, 18, -11],\n [-36, -37, -28, -48, -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[[21, -1, -17, 5, -37],\n [-23, 21, 33, -27, 23],\n [-18, 31, -14, -1, 15],\n [-12, -42, 27, -10, 23],\n [-11, 34, -31, 8, 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[[-30, -19, 29, -6, -24],\n [-2, 20, -9, -3, 4],\n [-16, 2, 0, -10, -8],\n [50, -15, -3, 28, 24],\n [-12, 3, -10, -13, -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[[0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [-36, 36, 6, 30, 12],\n [-24, 24, 4, 20, 8],\n [6, -6, -1, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-11, -30, -7, 21, -1],\n [7, 4, -5, 1, -7],\n [36, 51, -15, 3, 30],\n [7, -3, -7, 0, -25],\n [40, 25, -32, 19, -10]]\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, 0, -4, 16, -16],\n [-18, 0, 6, -24, 24],\n [12, 0, -4, 16, -16],\n [6, 0, -2, 8, -8],\n [-15, 0, 5, -20, 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[[-20, 13, -4, 9, 14],\n [-40, 19, -1, 27, 30],\n [-36, 29, -10, 25, 6],\n [16, 13, -17, -19, -38],\n [24, -32, 18, -8, 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[[8, -12, -6, -2, -8],\n [-12, 18, 9, 3, 12],\n [-20, 30, 15, 5, 20],\n [4, -6, -3, -1, -4],\n [12, -18, -9, -3, -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[[1, 4, -5, 2, -6],\n [5, 20, -25, 10, -30],\n [4, 16, -20, 8, -24],\n [3, 12, -15, 6, -18],\n [-5, -20, 25, -10, 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[[-28, -6, -19, 6, 22],\n [12, 18, 9, 1, 13],\n [-51, -39, 1, 42, -41],\n [44, -56, -12, -33, -3],\n [3, 25, 16, 13, 6]]?\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[[15, -13, 18, 18, 33],\n [-41, 2, 10, 54, -33],\n [57, -13, -18, -8, 43],\n [-14, -28, 36, 17, 32],\n [-27, 48, 22, 11, -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 5x5 matrix:\n[[10, 30, 20, -25, 0],\n [-10, -18, 28, 7, 20],\n [8, 24, 16, -20, 0],\n [-21, -48, 18, 30, 25],\n [14, 24, -44, -8, -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[[-10, 26, -7, 21, -1],\n [54, -24, 6, -12, -18],\n [15, -29, 5, -22, 3],\n [-39, -16, 14, -23, 8],\n [-29, 9, -16, 7, 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 5x5 matrix:\n[[-16, 18, -32, -30, -22],\n [-10, -8, -13, -10, -19],\n [-4, 32, -18, -20, 2],\n [-8, 9, -16, -15, -11],\n [2, 17, -3, -5, 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[[32, -33, -41, 13, -42],\n [18, -33, -29, -19, -30],\n [-24, 21, 29, -17, 30],\n [25, -25, -31, 13, -33],\n [19, -22, -24, 6, -27]]?\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, -1, -26, 1, 17],\n [25, -8, -46, -26, 41],\n [-9, 15, -8, -17, -10],\n [-10, 33, 10, -1, 13],\n [-6, 44, 28, 4, 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[[24, -24, 5, -12, 8],\n [-20, 22, 35, 40, 20],\n [-32, 32, -15, 12, -16],\n [52, -46, 20, 12, 28],\n [29, -28, -15, -19, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-29, 30, -24, 13, 2],\n [-18, 8, -42, 16, 14],\n [9, 4, 32, -13, -2],\n [-36, 47, -16, 10, 8],\n [24, -26, 18, -10, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[10, -12, -12, -30, 34],\n [10, -3, -12, -12, 19],\n [-30, -9, 36, 0, -27],\n [15, 6, -18, 3, 11],\n [15, 24, -18, 39, -19]]?\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[[6, -1, -4, -3, 13],\n [-3, -25, -19, -21, 28],\n [16, 3, -6, -3, 27],\n [19, 45, 27, 33, -24],\n [18, -3, -12, -9, 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[[24, -16, 20, 10, 17],\n [-27, 33, -33, -19, -10],\n [9, 15, 17, -23, 35],\n [3, -13, 31, -95, 31],\n [-18, 59, -30, 7, 15]]\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[[12, 5, 13, -11, 3],\n [18, -6, -18, 18, 6],\n [6, 5, 29, -7, 11],\n [16, -12, -6, 42, 24],\n [7, 0, -7, -1, -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[[-2, 12, -4, -4, -12],\n [4, -24, 8, 8, 24],\n [-5, 30, -10, -10, -30],\n [1, -6, 2, 2, 6],\n [6, -36, 12, 12, 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[[25, 5, 20, -30, -5],\n [-5, -1, -4, 6, 1],\n [15, 3, 12, -18, -3],\n [10, 2, 8, -12, -2],\n [-30, -6, -24, 36, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[26, -22, 16, 6, 28],\n [-2, 1, -4, 12, 11],\n [-2, 2, 0, -6, -8],\n [-8, 6, -8, 12, 6],\n [-18, 14, -16, 18, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-33, -6, 3, -6, -18],\n [-7, 11, -3, -14, 18],\n [-6, -6, 2, 4, -12],\n [5, -31, 9, 34, -54],\n [22, 4, -2, 4, 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[[30, 12, -18, 24, 30],\n [20, 8, -12, 16, 20],\n [-20, -8, 12, -16, -20],\n [-10, -4, 6, -8, -10],\n [-20, -8, 12, -16, -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 5x5 matrix:\n[[-15, -48, -15, -37, 21],\n [-54, 4, -10, -22, 15],\n [-21, -24, -13, -15, 17],\n [-15, -20, -3, -37, 7],\n [39, 8, 15, 5, -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[[-18, 15, -21, 42, -15],\n [-3, -7, -1, -1, -5],\n [12, -10, 14, -28, 10],\n [3, -12, 6, -15, 0],\n [7, -9, 9, -19, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[23, -9, 22, 50, 54],\n [-24, 16, 38, 40, 30],\n [21, 37, 6, 3, -32],\n [24, 6, -18, -21, -36],\n [28, -18, -1, 10, -9]]\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 5x5 matrix:\n[[-3, 9, 9, 0, -15],\n [-6, 18, 18, 0, -30],\n [-3, 9, 9, 0, -15],\n [3, -9, -9, 0, 15],\n [5, -15, -15, 0, 25]]\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, -32, 37, 19, -44],\n [-17, -6, 2, -22, 8],\n [42, -26, 29, 17, -4],\n [-21, 6, -11, -26, 16],\n [37, -12, 19, 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[[15, 2, 22, -6, 18],\n [4, -44, -24, -24, 24],\n [-50, 11, -8, -8, 8],\n [15, 11, -6, 22, -34],\n [0, 15, 21, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -5, 4, -3, 0],\n [-30, -25, 20, -15, 0],\n [0, 0, 0, 0, 0],\n [-24, -20, 16, -12, 0],\n [6, 5, -4, 3, 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 5x5 matrix:\n[[-5, 20, -11, 48, 12],\n [14, 20, 3, 9, -24],\n [14, -13, 3, -57, -3],\n [-45, -52, 2, -15, 60],\n [17, -7, 1, -36, -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[[-55, 21, 25, 29, -35],\n [14, 37, -37, 22, -26],\n [0, 29, 0, 36, -27],\n [9, -23, 19, -9, 13],\n [1, 20, -31, -1, -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[[2, 17, -7, -26, 4],\n [8, 11, 29, -9, -22],\n [10, 37, 13, -50, -12],\n [0, -6, 6, 10, -4],\n [-8, -14, -26, 14, 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[[-36, 30, -18, -18, 30],\n [-30, 25, -15, -15, 25],\n [-36, 30, -18, -18, 30],\n [18, -15, 9, 9, -15],\n [24, -20, 12, 12, -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[[-3, -9, 9, -11, -27],\n [-8, 4, 10, -20, -16],\n [8, -22, -1, 14, -20],\n [5, -25, 5, 5, -35],\n [-6, 0, 9, -16, -18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[30, -25, -10, -17, 5],\n [12, -36, 0, -12, -24],\n [8, 18, -7, -1, 26],\n [12, 18, -4, 10, 30],\n [38, -27, -12, -17, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-28, -27, -40, -18, -18],\n [10, 0, 2, 40, 20],\n [-9, 24, 11, -36, -6],\n [44, 54, 65, 19, 10],\n [-43, -18, -50, -29, -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[[3, -7, -1, 5, 8],\n [-9, 25, -8, -11, -17],\n [2, -10, 14, -2, -4],\n [-2, 18, -36, 10, 18],\n [-13, 37, -14, -15, -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[[12, -6, 24, -30, 12],\n [-10, 5, -20, 25, -10],\n [12, -6, 24, -30, 12],\n [-2, 1, -4, 5, -2],\n [-10, 5, -20, 25, -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 5x5 matrix:\n[[48, 33, 30, -49, -43],\n [-47, 60, -20, -39, -45],\n [23, -15, -49, -41, -48],\n [-32, 3, -65, -24, -38],\n [-13, 15, 5, -11, -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[[46, 15, 18, 16, -21],\n [-23, -4, -15, 19, 43],\n [7, -9, 5, 9, 28],\n [-44, -25, -12, -26, 25],\n [-8, 0, -9, 25, 39]]?\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 5x5 matrix:\n[[24, 49, -23, 21, -48],\n [-28, -33, 11, -17, 36],\n [-3, -17, 10, -6, 15],\n [-19, -40, 19, -17, 39],\n [-25, -16, 1, -11, 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[[-21, -12, 46, 27, 17],\n [20, -6, -14, -21, 0],\n [15, -13, -20, -33, 5],\n [-19, -26, 14, -15, 23],\n [-24, -25, 56, 21, 28]]\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, 51, -3, 45, -50],\n [10, -10, -8, -10, 16],\n [-23, 19, 20, 13, -6],\n [-7, 7, 0, 5, -2],\n [55, -62, 19, -51, 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[[2, -14, 40, -28, 18],\n [40, -28, 24, 10, -36],\n [48, -26, 4, 25, -30],\n [31, -9, -21, 35, -39],\n [-13, 1, 19, -16, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[24, 1, -4, 11, -49],\n [32, -1, -26, 22, -26],\n [-1, -32, -76, 41, -25],\n [-12, 38, 72, -48, 38],\n [-44, 16, 28, -34, -30]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[24, -9, 6, -13, -13],\n [0, 0, 0, 0, 0],\n [0, 25, 10, 5, 5],\n [-30, 0, -12, 14, 14],\n [-24, 29, 2, 17, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-39, 57, -9, 9, 16],\n [18, -31, -5, 5, -2],\n [-23, -8, -38, 38, 10],\n [-47, 48, -7, 7, 0],\n [-6, -30, 0, 0, -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[[-3, 19, -18, 28, 1],\n [-18, -30, -12, 24, 6],\n [-15, -19, -14, 26, 5],\n [9, 9, 10, -18, -3],\n [6, 46, -20, 28, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-5, 3, 6, 6, 6],\n [5, -3, -6, -6, -6],\n [10, -6, -12, -12, -12],\n [15, -9, -18, -18, -18],\n [10, -6, -12, -12, -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[[-2, 10, 8, -2, 10],\n [3, -15, -12, 3, -15],\n [0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0],\n [-5, 25, 20, -5, 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[[-3, -7, 10, 10, -28],\n [-18, 0, 10, -10, 24],\n [-33, -62, 10, 45, -38],\n [-42, -29, 25, 9, 4],\n [-18, -51, 5, 43, -48]]\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[[36, 7, -13, 8, 36],\n [-6, -12, 13, -10, -6],\n [-30, 15, -10, 10, -30],\n [-6, -17, 18, -14, -6],\n [18, 21, -24, 18, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, 0, -6, -2, -4],\n [6, 0, -36, -12, -24],\n [1, 0, -6, -2, -4],\n [-2, 0, 12, 4, 8],\n [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[[21, 21, 6, 30, 12],\n [0, 0, 0, 0, 0],\n [-17, -18, -6, -26, -12],\n [0, -14, -16, -24, -32],\n [-12, -23, -16, -36, -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[[33, 15, 35, -25, -18],\n [11, 16, -3, -13, -3],\n [14, 1, 22, -16, -23],\n [-18, -9, -18, -4, -23],\n [20, 46, -28, 0, 55]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[22, -1, 30, 0, -39],\n [-22, 1, -30, 0, 39],\n [2, -3, -6, 0, -21],\n [4, 2, 12, 0, 6],\n [18, -1, 24, 0, -33]]\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, 10, 0, -24, 13],\n [27, 17, -30, -32, 46],\n [-13, -7, 3, 30, -23],\n [14, -10, 31, -44, -16],\n [-8, -16, 40, -18, -49]]\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[[5, -2, 5, 4, 4],\n [-30, 12, -30, -24, -24],\n [25, -10, 25, 20, 20],\n [5, -2, 5, 4, 4],\n [-5, 2, -5, -4, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}