{"messages": [{"content": "Find the rank of the matrix:\n[[-9, 4, 16, -2, -7],\n [21, -22, -12, 11, -9],\n [9, -14, 4, 7, -13],\n [-21, 24, 8, -12, 13],\n [0, 4, -8, -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[[16, -8, -32, -28, -10],\n [8, 22, 44, 29, -2],\n [3, -10, -24, -18, -9],\n [-43, -14, 30, 33, 9],\n [-39, -18, 4, 14, 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[[16, -11, -67, 7, -19],\n [10, 1, -7, 2, -7],\n [-18, -23, -3, 1, 9],\n [-29, -36, -5, -7, 22],\n [24, 34, 12, 6, -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[[-9, -4, -4, 9, -4],\n [29, 24, 8, -31, 14],\n [-8, 6, 12, 12, 0],\n [-7, -40, -34, 0, -13],\n [-1, -27, -26, -5, -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, 9, 8, 10, 1],\n [9, 19, 15, -15, -24],\n [-2, 46, 30, 20, -24],\n [-21, 7, 10, 10, 5],\n [46, 12, -11, 15, -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[[18, 24, 0, 6, -3],\n [32, 17, 5, 6, 20],\n [-33, -34, -3, -10, 20],\n [-11, -13, -20, 11, 11],\n [1, -6, 55, -41, -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[[30, -6, -25, -6, -10],\n [0, 12, 19, 21, -17],\n [-8, 26, 13, -22, -12],\n [-9, -3, -2, -4, 6],\n [6, 18, -5, -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[[28, -25, -10, -33, 15],\n [-24, 20, 28, 18, -27],\n [-4, -10, -4, 2, 6],\n [0, 0, 0, 0, 0],\n [-32, 15, 10, 33, -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[[-3, -1, -33, -33, -5],\n [-15, -25, -5, -25, 20],\n [6, -23, 22, 11, -21],\n [10, 2, -13, -9, -20],\n [-7, 22, 0, 17, 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, -20, -25, 25],\n [-17, 21, -27, 20, -16],\n [15, -15, 5, 1, -1],\n [-35, 30, 38, 0, -5],\n [20, -15, -11, 39, -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[[-20, 10, 5, -15, 0],\n [-22, 0, 10, -16, -2],\n [-28, -8, 16, -20, -4],\n [23, -6, -8, 17, 1],\n [4, -2, -1, 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[[2, 1, 2, 2, -4],\n [6, 11, 8, 2, -12],\n [-8, 16, -3, -18, 16],\n [6, 3, 6, 6, -12],\n [-10, 11, -6, -18, 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[[5, -6, -5, 12, 13],\n [32, 15, 0, -4, 7],\n [12, 14, 30, -37, -30],\n [10, 14, 26, -34, -28],\n [25, 20, 13, -23, -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, 28, -17, 4, 18],\n [22, 35, -21, -21, -22],\n [-26, 10, -12, 32, 38],\n [22, 6, 3, -16, -16],\n [-32, -21, -3, 13, 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, 29, -42, -42, 15],\n [-7, 19, 20, 24, -25],\n [26, -24, 13, 2, 35],\n [8, -24, 2, -6, 25],\n [28, -5, 9, 2, 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[[12, -13, -15, 0, 1],\n [0, -10, -15, 0, -5],\n [-32, 16, 12, 0, -12],\n [20, -13, -12, 0, 6],\n [-16, 8, 6, 0, -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[[2, 0, -5, 3, 1],\n [-2, 0, 5, -3, -1],\n [-14, -10, 7, -11, -11],\n [-24, -25, -10, -11, -22],\n [10, 0, -25, 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[[6, 29, -12, 22, -25],\n [-27, -28, 24, -9, 30],\n [12, -2, -6, 2, -8],\n [-7, -12, 8, 3, 6],\n [4, 18, -8, 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[[20, -13, -17, 36, 24],\n [16, -5, -19, 36, 21],\n [12, -18, 0, 8, 11],\n [-4, 14, -8, 8, -1],\n [-4, 11, -5, 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[[28, 1, -5, 1, -8],\n [-25, 20, 25, 6, -5],\n [44, -1, -35, 35, -11],\n [2, -18, 0, -42, 21],\n [7, 15, 0, 25, -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, 8, 8, 22, -10],\n [28, 20, 6, 20, -11],\n [3, 0, 6, 15, -6],\n [26, 20, 2, 10, -7],\n [-5, -4, 0, -1, 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[[-10, -6, 16, -10, 6],\n [11, 0, -20, 20, -12],\n [0, 0, 0, 0, 0],\n [13, 21, -16, -5, 3],\n [9, 23, -8, -15, 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[[12, -19, -11, -7, 3],\n [-16, 28, 20, 8, -8],\n [-4, -3, -15, 7, 13],\n [4, -3, 3, -4, -4],\n [-16, 26, 16, 9, -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, -5, 16, 19, 17],\n [4, 4, 38, 15, -30],\n [-13, -14, 0, -14, -9],\n [-10, 2, 16, -16, 2],\n [-13, -37, -8, -3, -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, 6, 2, -18, -14],\n [4, 19, -3, -13, -35],\n [4, 7, -7, -17, -7],\n [12, -21, 13, -17, 29],\n [-6, -4, 6, 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, -9, 3, 27, -12],\n [-18, 3, 3, -25, 0],\n [3, 0, -1, 4, 1],\n [3, -12, 11, 8, -23],\n [-9, 6, -3, -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[[0, -15, -2, -6, -13],\n [2, 10, -1, 3, 8],\n [-2, 5, 3, 3, 5],\n [2, 40, 3, 15, 34],\n [-22, -5, 25, 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[[11, 17, 6, 9, -12],\n [-4, 2, -6, 0, 0],\n [23, 26, 17, 15, -20],\n [-23, -26, -17, -15, 20],\n [-35, -20, -35, -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[[-12, 2, 26, 0, 6],\n [-12, 15, 0, 47, -9],\n [-25, 7, 25, 0, 2],\n [-15, 7, 16, 13, 0],\n [3, -8, 34, -16, 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, -6, -2, -17, -10],\n [5, 5, 42, -13, -31],\n [-10, 27, 63, 23, -40],\n [-2, 5, 9, 21, 8],\n [-7, -24, -10, -39, -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[[-36, -9, 19, -15, 3],\n [-23, 13, 11, 21, -43],\n [-9, -3, -32, -14, 25],\n [-31, -7, -1, -9, 2],\n [-9, -12, -8, -22, 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[[-25, -6, 19, -4, 4],\n [40, -4, -10, 20, -20],\n [30, 0, -12, 12, -12],\n [30, 4, -18, 8, -8],\n [15, 2, -9, 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[[-25, -16, -26, -23, -8],\n [-4, -39, 29, 31, -16],\n [5, 7, -18, -15, 5],\n [42, 34, 7, 12, 34],\n [33, 8, -1, 9, 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[[-15, 30, -3, -27, -9],\n [11, -20, 1, 19, 11],\n [17, -30, 1, 29, 19],\n [-9, 15, 0, -15, -12],\n [-9, 20, -3, -17, -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, 14, 3, 9, 7],\n [5, -13, 4, -3, -9],\n [-17, 5, -22, -15, 11],\n [-18, 2, -24, -18, 10],\n [12, -20, 12, 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[[-8, -17, -6, 18, -10],\n [11, -17, 21, 5, 1],\n [-9, -12, -9, 15, -9],\n [9, 31, 3, -29, 15],\n [17, 10, 21, -19, 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[[-36, -3, 17, 23, 1],\n [35, 7, -1, -15, 30],\n [-14, 15, 33, 3, 20],\n [-1, 12, 19, -5, -8],\n [3, 10, 21, 1, 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[[-6, -46, -25, -7, -1],\n [-16, -42, -3, 17, -30],\n [-4, 0, -7, 20, -21],\n [9, 16, 28, -19, 15],\n [1, 24, -4, 5, 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[[17, 8, 6, -6, -4],\n [6, 9, -7, -8, -7],\n [1, 15, -39, -10, -29],\n [-5, -3, -12, 5, -8],\n [-5, -5, -18, 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[[-20, 5, 15, 8, -4],\n [15, -3, -12, -6, 3],\n [25, -19, -6, -10, 5],\n [10, 11, -21, -4, 2],\n [15, 0, -15, -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[[-9, 43, 10, 37, 10],\n [9, -16, -4, -2, -8],\n [-15, 17, 2, -5, 8],\n [6, -2, 4, 2, 4],\n [-3, -6, -6, -6, -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[[-20, 8, 16, 20, 20],\n [-9, 6, 15, 12, 3],\n [2, 0, 1, -1, -4],\n [15, -10, -25, -20, -5],\n [1, -2, -6, -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[[-6, -3, -17, -8, -23],\n [-2, -6, -2, -21, -11],\n [-31, 22, -7, -23, -18],\n [-30, 30, 2, -7, -1],\n [-1, -3, 4, -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[[-46, -29, 45, 27, 18],\n [2, 0, -8, -23, 16],\n [-30, -10, 19, 31, 25],\n [-3, 12, 3, -5, -15],\n [-23, 11, 0, 35, 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, 11, -30, 4, -7],\n [13, 14, 38, 5, 5],\n [24, 30, 16, 14, 0],\n [25, 27, 14, 38, -41],\n [-2, 3, -36, -17, 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[[-17, 4, 12, -24, -8],\n [10, -3, 2, 7, -5],\n [5, 0, -20, 20, 20],\n [-19, 5, 6, -21, -1],\n [-20, 5, 10, -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[[-14, -27, -14, 16, -3],\n [16, 13, 21, -9, 17],\n [6, 13, 21, -9, 10],\n [-26, 7, -9, -3, -28],\n [-8, -19, 4, 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[[12, 12, -53, -23, -3],\n [21, 12, 22, 1, -5],\n [9, 6, -29, -11, -6],\n [6, 9, -46, -19, -6],\n [4, 25, 44, -4, -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[[11, -8, -36, -27, 23],\n [-33, 4, 4, 11, 7],\n [3, -5, 1, -17, 14],\n [-11, -11, 14, -13, 23],\n [-35, 42, -26, 9, -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[[-17, 25, -1, 12, -18],\n [-21, 33, -1, 17, -23],\n [-17, 21, 3, -1, 19],\n [18, -2, 2, 16, -4],\n [4, -8, -4, 3, -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, 0, -10, -25, -20],\n [-6, -9, -9, -15, -15],\n [-2, -9, -1, 5, 1],\n [-8, 0, -9, -23, -15],\n [25, 3, 7, 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[[12, 20, -22, -10, -17],\n [-14, -35, 26, 3, 18],\n [-12, -16, 21, -5, 10],\n [9, -23, -7, 15, 20],\n [-12, -30, 25, 5, 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[[6, 14, 14, -4, 5],\n [-3, 38, 12, 12, -2],\n [3, -1, -9, 12, -11],\n [9, 2, -8, 16, -15],\n [9, 9, 9, 0, 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, 5, -15, -3, -15],\n [4, 20, 16, -12, 16],\n [-22, 15, -13, -9, -13],\n [-2, 25, 13, -15, 13],\n [-6, -15, -15, 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[[5, 18, -7, 6, 2],\n [25, -12, 31, -3, -13],\n [4, 2, 63, 12, 25],\n [-23, 57, 16, 39, 48],\n [-22, 21, -7, 27, 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, 40, 20, -30, -5],\n [5, 35, 21, -28, -1],\n [-2, 14, -14, 0, -22],\n [-3, -24, -12, 18, 3],\n [-5, -10, -26, 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[[17, 4, -11, 23, -10],\n [45, -1, 18, 22, -1],\n [-3, -4, -27, -1, 21],\n [26, -6, 16, 0, 16],\n [-5, 0, 35, -15, -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[[-5, 7, -20, -17, 13],\n [-12, -12, 0, -12, -4],\n [-3, -12, 15, 6, -12],\n [11, 8, 5, 14, 0],\n [9, 9, 0, 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[[30, 10, 49, -28, 28],\n [-5, -9, 9, 5, 23],\n [20, 21, 42, -21, 10],\n [0, -15, 27, 1, 48],\n [55, -5, 10, -45, -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[[3, -5, 6, 6, 8],\n [1, -5, 1, 4, 4],\n [6, 0, 15, 6, 12],\n [2, 10, 8, -4, 0],\n [3, -15, 3, 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[[34, -34, 14, -20, -8],\n [-35, 30, -16, 17, 15],\n [-30, 30, -24, 9, 19],\n [20, -8, -8, -16, 0],\n [-9, -3, 15, 12, -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[[-12, 21, 8, 13, 4],\n [-13, 19, 12, 17, 6],\n [-9, 9, 12, 15, 6],\n [2, -5, 0, -1, 0],\n [-5, 17, -4, -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[[-6, -55, 23, 9, 5],\n [13, -2, 2, -12, 15],\n [-49, 16, 23, 37, -26],\n [-15, -36, 35, -2, 2],\n [-4, 24, -3, -16, -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, 23, -12, 4, -8],\n [0, 28, -2, 8, -22],\n [-37, -9, -8, -36, 12],\n [-28, -9, -10, -27, 15],\n [-4, -26, -4, -10, 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, -20, 8, 6],\n [-20, -31, -29, 29, 9],\n [-6, -27, 7, 49, 42],\n [15, 45, 20, -40, -15],\n [-29, -6, -51, -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[[36, -25, -10, -5, 16],\n [16, 5, -27, -28, -9],\n [0, 0, 0, 0, 0],\n [20, -5, -18, -17, 0],\n [12, -5, -8, -7, 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, -6, 10, 2, -30],\n [-15, 22, 3, 2, 5],\n [10, -18, -4, -2, 0],\n [-15, -3, -12, -3, 30],\n [-20, 1, -13, -3, 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[[-2, 11, -9, 11, -1],\n [0, 0, -43, 39, -9],\n [12, -9, -2, 6, 4],\n [-12, -9, -12, 0, -10],\n [-7, 34, 8, 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[[2, -10, -6, -8, 0],\n [5, 19, 11, 13, 3],\n [26, -7, -22, -34, -1],\n [0, -2, -18, -24, -14],\n [19, -14, -24, -35, 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[[10, 4, -18, -16, 18],\n [-10, 22, 6, -18, -16],\n [-10, 34, -7, -36, -7],\n [12, -26, 15, 28, -5],\n [-2, -19, 12, 27, -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[[-16, -18, 6, -24, -16],\n [2, -3, 1, -11, -19],\n [-24, -21, 7, -20, 0],\n [-6, -6, 2, -7, -3],\n [12, 6, -2, -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[[3, 12, 17, 4, 20],\n [0, -15, -20, 0, -25],\n [16, -32, -24, 8, -40],\n [8, -1, -2, 14, -5],\n [23, -37, -25, 14, -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[[-19, 11, 2, 2, 12],\n [0, 12, 25, -7, -9],\n [-16, 8, -20, 8, 22],\n [-11, -11, -33, 7, 19],\n [0, -1, 53, -33, -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, 12, -35, -16],\n [4, 0, 12, -22, -8],\n [6, -6, 12, -9, 0],\n [4, 0, 12, -22, -8],\n [8, -10, 14, -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[[42, -25, 39, -10, 56],\n [-30, 6, -14, -10, -42],\n [47, -37, 45, -25, 63],\n [13, 2, -8, 5, 29],\n [18, -2, 18, 10, 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, 9, 28, 14, -6],\n [24, 12, -8, 8, 0],\n [20, 14, 2, 12, -2],\n [-16, -4, 14, 0, -2],\n [0, -12, -26, -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[[-10, -13, -17, -8, -7],\n [6, 9, -5, -12, -11],\n [16, 17, 13, -22, -25],\n [0, 6, -8, 12, 16],\n [18, 18, 14, -30, -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, -6, 24, 2, -1],\n [0, 3, -12, -1, -2],\n [40, -38, 40, -34, 15],\n [30, -24, 24, -22, 4],\n [-11, 6, 12, 13, -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, 4, -13, 8, 8],\n [11, -7, 8, 13, -17],\n [10, -9, 11, 18, -22],\n [-15, -2, 3, 14, -6],\n [1, -3, 20, -24, -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[[-19, 34, 26, -8, 8],\n [-10, -20, -35, -2, 20],\n [8, -14, -24, 10, 6],\n [-26, -4, -1, -22, 12],\n [-33, 39, 24, -15, 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[[-5, 1, -23, 17, -19],\n [23, -13, 3, 6, 27],\n [-5, 0, -25, 26, -18],\n [-29, 15, -17, 6, -41],\n [37, -19, 23, -9, 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[[-4, 4, 4, 0, 10],\n [-2, -7, 2, -6, 20],\n [10, -16, -10, -4, -15],\n [0, -12, 0, -8, 20],\n [2, 4, -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[[-10, -1, 8, 19, -17],\n [6, -2, -2, -10, 6],\n [9, 10, -17, -22, 30],\n [-9, 16, -11, 8, 12],\n [17, -10, -1, -26, 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, 0, 11, 11, -26],\n [20, 15, -14, 1, 25],\n [29, 30, -19, 11, 4],\n [17, 10, -3, 7, 12],\n [-6, 0, 3, 3, -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[[-4, 13, 10, 14, 14],\n [-6, 23, 18, 24, 24],\n [-1, -9, -8, -7, -7],\n [7, -7, -4, -11, -11],\n [-2, -11, -10, -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[[18, 9, -3, -20, 0],\n [-21, -33, 6, -14, 15],\n [2, 11, -9, -2, -18],\n [-7, -16, 3, -12, 9],\n [26, 28, 6, 22, 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, 10, -5, -15, 15],\n [-23, 7, -8, 0, 0],\n [0, 0, 0, 0, 0],\n [-3, 3, 0, -8, 8],\n [-17, 1, -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[[-11, -8, -25, -7, 8],\n [-23, 2, -21, 2, 2],\n [18, 8, -10, 14, 0],\n [-9, 4, -11, 5, 0],\n [-1, 16, 33, 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[[2, 14, 10, 2, -10],\n [-5, 5, -3, 3, -1],\n [20, -20, 12, -12, 4],\n [6, 2, 8, -2, -4],\n [15, -15, 9, -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[[-15, 3, 24, 0, 13],\n [10, -33, 16, -7, -5],\n [-2, -1, 16, -3, 3],\n [1, 17, -41, 9, -5],\n [-10, 31, -37, 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[[-6, -9, 1, 19, -17],\n [-5, 3, -5, 3, -6],\n [1, 3, -1, -5, 4],\n [3, -9, 7, 7, -2],\n [-3, 9, -7, -7, 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[[-18, 7, -10, 20, 33],\n [-18, -23, 29, 23, 15],\n [10, -5, 7, -11, -19],\n [-2, -17, 22, 4, -7],\n [-2, -27, 35, 5, -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[[8, -14, 20, 16, 8],\n [41, -33, -6, -11, 10],\n [-28, 24, 0, 4, -8],\n [19, -17, 2, -1, 6],\n [-25, 25, -10, -5, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-23, -13, -12, 8, 14],\n [17, -8, -12, 13, -11],\n [7, 11, 12, -10, -4],\n [10, -19, -24, 23, -7],\n [6, -6, -8, 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, 29, 10, -1, -15],\n [5, 3, 20, -13, -11],\n [-25, 17, 13, 44, 39],\n [-21, 4, -17, -11, 6],\n [21, 15, 14, -25, -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[[16, 24, -9, -16, -33],\n [-2, 28, -34, -23, -11],\n [10, 26, -17, -20, -27],\n [-15, -11, -1, 2, 22],\n [14, -6, 9, 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, -2, -7, -7, -24],\n [-4, 29, 29, -25, -9],\n [-20, -5, 36, -4, 31],\n [-3, 22, -2, -6, -8],\n [22, 5, -1, -18, -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[[-2, -1, 1, -10, 5],\n [-14, 9, -25, 3, -3],\n [-10, -3, 1, -12, 1],\n [-14, 10, -27, -11, 7],\n [6, -1, 5, -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, 8, -6, 0, -16],\n [13, 36, -1, -26, -7],\n [-15, -40, 0, 30, 5],\n [11, 28, 1, -22, -1],\n [-13, -36, 1, 26, 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[[-4, 0, 12, 4, 12],\n [-5, -11, 6, 4, 10],\n [-14, -10, -20, 8, -12],\n [-10, -6, -22, 5, -16],\n [8, -3, -13, -7, -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, 0, -32, 29, -7],\n [-12, -15, 16, 10, -15],\n [21, 38, -9, 0, 15],\n [15, 17, -39, 30, 0],\n [2, 18, 29, 3, -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[[-13, 2, -7, -10, 12],\n [18, -13, -7, -7, 12],\n [8, -11, 16, -19, -23],\n [-17, 14, -3, 21, 0],\n [5, -3, 4, 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[[7, -16, -6, -5, 3],\n [26, -22, 2, 0, 12],\n [-32, -1, 11, 0, 1],\n [32, -28, 12, 4, 20],\n [36, 21, -31, -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[[3, -5, -1, -10, -2],\n [14, 4, -21, -24, -17],\n [-5, 8, -10, -5, -29],\n [31, -5, 11, -42, -6],\n [-4, -17, -15, -21, -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[[13, 1, -17, 5, 14],\n [-11, 13, -11, 5, 2],\n [0, -6, 11, -4, -6],\n [3, 3, -9, 3, 6],\n [-6, 0, 7, -2, -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[[-37, 7, 46, 18, -37],\n [8, 17, 4, 27, -15],\n [17, 11, 9, 38, -14],\n [20, -6, -10, 17, 22],\n [-39, 9, 12, -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[[-29, -11, 30, -25, -12],\n [-16, -20, 6, 30, 10],\n [20, -2, -33, 15, 1],\n [31, 12, -35, 6, 1],\n [16, 21, -6, -38, -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[[10, -11, 1, -8, -7],\n [-8, -7, -24, 30, -35],\n [2, 9, 14, -14, 37],\n [-5, -10, -25, 30, -30],\n [29, -32, -4, -12, 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[[-23, -12, -12, -17, 5],\n [1, 20, 20, 23, -3],\n [0, -28, -28, -32, 4],\n [5, 16, 16, 19, -3],\n [35, 0, 0, 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[[14, 25, 19, -9, 3],\n [18, 21, 12, 3, -3],\n [6, 22, 29, -14, 4],\n [-14, -2, 5, -22, 12],\n [-6, -22, -29, 14, -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[[-33, 2, 33, 4, 11],\n [31, -26, -40, 27, -41],\n [-18, -8, 17, 6, 7],\n [3, 14, 0, -11, 5],\n [-2, -32, -9, 38, -35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, 12, -27, -19, 28],\n [14, 7, 23, 25, -7],\n [11, 2, -24, -22, 39],\n [2, 18, -26, -19, 31],\n [-7, 28, -22, -5, -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[[0, 8, -4, 3, -2],\n [-14, 7, 16, -10, 16],\n [17, -12, -29, 13, -28],\n [-14, 17, 2, -4, 6],\n [24, -14, -20, -9, -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[[3, -4, 4, -1, -4],\n [9, -12, 12, -3, -12],\n [15, -20, 20, -5, -20],\n [20, -20, 15, 20, 20],\n [27, -32, 29, 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[[14, 7, 12, -22, -24],\n [9, -1, 14, -22, -28],\n [20, 25, 0, -10, 0],\n [5, 8, -2, 0, 4],\n [7, 14, -6, 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[[11, -19, 16, -9, -1],\n [6, 22, -4, 27, -4],\n [2, 7, 8, -5, -37],\n [17, -6, -20, 1, 6],\n [8, -36, 28, -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[[-11, -1, -11, -12, -21],\n [-3, 10, -11, -14, 7],\n [9, 10, 8, -11, 10],\n [-2, 15, 6, -21, -2],\n [-13, 14, 21, 13, 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, -3, -15, -27, -19],\n [10, -23, -10, -26, -8],\n [-24, -7, 25, 17, 7],\n [-11, 3, -5, 15, 19],\n [-29, 16, 20, 40, 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[[-15, -1, 0, -1, -1],\n [41, -25, 25, -12, 2],\n [24, 4, 12, 5, -4],\n [3, 3, -24, -10, -25],\n [23, -45, -10, -40, -15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-9, 14, 35, -12, -34],\n [8, 6, 12, 26, 0],\n [45, -2, -17, 0, 52],\n [23, 21, 9, -19, 10],\n [-20, -41, -2, 22, -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, 17, 4, 25, -19],\n [6, 27, 5, 14, 5],\n [-2, 13, 2, -1, 13],\n [-4, 14, 2, -4, 18],\n [-8, -26, -5, -17, 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, -7, 20, 25, 15],\n [32, -41, 22, 24, -5],\n [32, -44, 16, 16, -12],\n [16, -13, 8, 8, -21],\n [18, -21, 6, 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[[20, 35, -20, -41, -8],\n [-11, -15, 11, 19, 6],\n [9, 16, -9, -2, 14],\n [11, 11, -11, 1, 10],\n [12, -5, -12, 11, 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[[9, -18, 3, -6, 3],\n [8, 16, 0, 0, -4],\n [-6, -12, 0, 0, 3],\n [18, 12, 2, -4, -4],\n [-16, 16, -4, 8, -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, 0, 18, 0, 6],\n [6, -5, 7, 25, -16],\n [28, 0, -24, 0, -8],\n [2, -4, 8, 20, -12],\n [24, 1, -23, -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[[0, -25, -22, -21, -4],\n [27, -27, 37, -40, -11],\n [-8, -29, 25, -31, -6],\n [13, -3, -17, -3, -10],\n [-7, 13, 7, 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[[-15, 24, -11, 8, -2],\n [0, -11, -21, -22, -12],\n [-13, -4, -55, -28, -22],\n [-2, 6, 2, -8, -4],\n [15, -25, -28, -6, -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[[-15, -12, 0, -3, -13],\n [11, -18, -2, -1, -25],\n [21, -4, -5, 6, -7],\n [23, -11, -15, 17, -12],\n [-16, 1, 3, -4, 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, -23, -29, 6, 2],\n [-13, 4, 7, -13, 14],\n [-36, -13, 0, 3, -1],\n [-28, -9, -5, 1, 5],\n [12, -4, -2, -17, 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, 16, 12, -28, 16],\n [0, -3, 3, -9, 9],\n [0, 4, -4, 12, -12],\n [0, -20, -8, 16, -4],\n [0, 5, 2, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-29, 17, 9, -12, 14],\n [24, -33, -26, 25, -10],\n [26, 12, 22, -14, 5],\n [15, 3, 9, -22, 7],\n [-1, 14, 13, 5, -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, 23, 23, 11, 12],\n [12, -24, -5, -28, 4],\n [-2, 5, 2, 5, 0],\n [10, -19, -3, -23, 4],\n [-6, 21, 13, 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[[11, -7, 21, -12, -8],\n [-3, 2, 19, 33, 36],\n [17, 3, 18, -47, -31],\n [-9, -9, -33, 9, -12],\n [-5, -5, 0, 28, 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[[-1, -17, -17, -21, 9],\n [-2, -28, -25, -34, 11],\n [0, -12, -8, -16, -1],\n [3, 15, -1, 15, 12],\n [5, 25, 25, 25, -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[[-6, -10, -12, 0, 0],\n [12, 0, 12, -4, -4],\n [12, 15, 21, -1, -1],\n [3, 0, 3, -1, -1],\n [-9, 10, -3, 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[[-15, 2, -8, 14, -19],\n [-10, -12, 6, 7, -5],\n [-30, -12, 12, 26, -4],\n [-35, 0, 6, 33, -6],\n [15, 13, 2, -11, 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, -4, -6, -14, 8],\n [-1, -1, 9, 7, 23],\n [15, -3, 25, 17, 17],\n [-14, -27, 30, -33, -21],\n [7, 18, -27, 15, 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[[15, 35, 0, -30, -25],\n [-16, -20, -8, 4, 16],\n [0, 13, -6, -21, -8],\n [8, 10, 4, -2, -8],\n [-8, 3, -10, -19, 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, -27, -18, 19, 14],\n [-10, 6, 43, 21, -33],\n [-9, -1, 6, 29, 2],\n [-16, -32, 2, -18, -16],\n [10, -10, 0, -50, -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[[-2, -24, -2, 30, 2],\n [-12, 37, -5, 19, -1],\n [18, -8, -10, -4, -28],\n [-20, -2, 15, -8, 36],\n [-16, 2, 6, 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[[-12, 17, -5, -23, 12],\n [4, 1, -5, -9, 6],\n [-8, 2, 6, 8, -6],\n [8, -6, -2, 2, 0],\n [4, 5, -9, -19, 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[[-25, -7, -16, -11, 27],\n [34, 34, 22, 2, -30],\n [7, 9, 13, -9, 0],\n [-12, -8, 6, -16, 18],\n [-14, 2, -7, -12, 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, -12, 8, 4],\n [6, -6, 12, 14, -26],\n [-17, -3, -4, -23, 27],\n [12, 0, 6, 18, -24],\n [29, 27, -26, 21, 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, 11, -10, 10, 17],\n [10, -3, 1, 0, 24],\n [34, 17, -7, 32, 56],\n [-29, -24, 9, -31, -34],\n [9, 5, 5, 1, 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[[-17, -30, -8, 32, -10],\n [-26, 7, -5, 7, 14],\n [-26, 11, -5, 1, 6],\n [2, 4, 2, 1, 20],\n [6, -14, 0, 11, 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[[11, -10, -5, -14, 12],\n [-3, 42, -16, -12, 16],\n [6, 0, -14, -8, 8],\n [5, 17, -12, -15, 16],\n [-27, 21, 8, 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[[16, -20, -8, 12, 0],\n [-17, 22, -5, -24, -12],\n [-5, 7, -11, -15, -12],\n [-7, 8, 17, 6, 12],\n [15, -20, 15, 30, 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[[-23, 2, -34, 13, 16],\n [-11, 28, -4, 2, -13],\n [-10, 41, -21, -7, 4],\n [8, 14, -15, -13, 19],\n [4, -14, -6, -5, 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, 3, 14, -12, -10],\n [-10, 5, 7, -6, -33],\n [14, 25, -14, 2, 17],\n [-11, -12, 9, -2, -27],\n [-9, 26, 11, -18, 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[[-33, 31, 30, 2, -8],\n [18, -20, -21, 11, 1],\n [21, -25, -22, 7, -3],\n [-16, 24, 15, -2, 12],\n [13, 5, -16, 6, 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[[-36, 23, -16, 4, 21],\n [2, 3, 6, -4, 3],\n [2, 14, 26, -36, 4],\n [22, -2, 22, -6, 2],\n [-28, 20, -4, -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[[1, 12, 4, -4, 12],\n [17, -16, 18, 22, 14],\n [3, -31, -11, 6, -28],\n [-8, 34, 1, -17, 19],\n [0, 28, 15, -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, 7, 27, -1, 8],\n [44, -29, -5, 27, -32],\n [-10, 1, 15, -21, -4],\n [-21, 6, -20, -3, 8],\n [40, -35, -15, 25, -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[[0, 16, 36, -22, 26],\n [-27, 15, 0, 3, -6],\n [29, -9, 16, -13, 18],\n [-1, -3, -8, 5, -6],\n [-9, -11, -36, 23, -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[[7, -20, 11, 8, -18],\n [-2, -20, -4, 26, -28],\n [7, -20, 5, -10, 14],\n [-7, 0, -12, 13, -6],\n [-3, 5, -5, 0, 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[[32, -4, 6, -5, 0],\n [-8, 22, 24, 26, -45],\n [-16, 16, 2, -5, -15],\n [-40, 26, -6, -17, -15],\n [16, -8, 14, 27, -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, 14, 7, 24, 1],\n [-4, -10, 26, 2, 20],\n [-10, -1, -10, -20, 20],\n [-15, -19, 6, -23, 9],\n [14, 31, -40, 10, -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, 10, -15, -5, 30],\n [-5, 25, -15, 0, 20],\n [10, 3, 9, -1, -1],\n [0, 4, 9, 7, -29],\n [-3, 25, -12, 3, 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[[0, -6, -21, -20, -28],\n [7, -13, 4, -1, 24],\n [11, -9, -28, -13, -8],\n [7, -3, 4, 9, 24],\n [-3, 1, -12, -11, -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, -4, 8, 7, 9],\n [-46, -6, 5, 6, 13],\n [22, -41, -52, -37, -2],\n [15, 17, 6, 4, -9],\n [11, -8, -13, -22, 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[[-8, -35, 19, -14, -28],\n [-21, 1, -6, -14, -2],\n [-9, 15, 13, -20, 1],\n [-15, 14, -5, -12, 6],\n [27, 5, 31, 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[[-3, -19, -10, -41, -15],\n [-14, 20, 7, 5, -7],\n [17, -27, -11, -9, 8],\n [-4, -22, -15, -43, -15],\n [-12, -10, -19, -25, -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[[7, -6, 23, 7, -6],\n [20, -24, 2, 41, 5],\n [43, 2, 22, 12, -20],\n [-7, 16, -17, 14, -1],\n [-3, -8, -25, 21, 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[[-18, 10, 14, 22, -9],\n [28, 14, 1, -14, -13],\n [-16, 1, 5, 2, 16],\n [22, 2, -22, -26, -7],\n [24, -10, -12, -16, -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, -18, -20, 10, 5],\n [15, -15, -20, 10, 5],\n [7, -8, -12, 6, 3],\n [-8, 7, 8, -4, -2],\n [25, -23, -28, 14, 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[[-8, -6, 5, 9, 19],\n [2, 4, -2, 0, -5],\n [10, -1, 42, -23, -8],\n [-16, -21, 5, 5, 30],\n [0, 0, 0, 0, 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[[41, 16, -4, -1, 3],\n [13, -1, -17, 4, 27],\n [1, 0, 0, -1, -6],\n [-36, -20, -8, -20, -5],\n [1, 10, 14, -39, 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, -26, -5, -59, -8],\n [42, 1, -8, 30, -7],\n [-13, -14, -7, -33, -7],\n [1, -13, -12, -12, 2],\n [-13, -6, -10, 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[[-30, -15, 0, -35, 40],\n [4, 34, -39, -12, -8],\n [-1, 14, -10, -27, 17],\n [-16, -2, -12, -5, 1],\n [-19, -29, 16, 20, -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[[20, -18, -16, 24, 8],\n [15, -15, -15, 15, 9],\n [-15, 7, -1, -31, 7],\n [20, -30, -40, 0, 32],\n [10, -16, -22, -2, 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[[50, -5, 3, -4, 15],\n [-34, -17, -43, 8, -12],\n [8, 13, 43, -16, -42],\n [31, 1, 19, -8, -12],\n [-13, -1, 25, 32, 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[[5, -7, -3, 11, -5],\n [-15, 0, -19, -5, -20],\n [-10, 8, -2, -14, 0],\n [15, -9, 7, 17, 5],\n [20, -10, 12, 20, 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, 10, -12, -6, 16],\n [4, 2, 5, 7, -16],\n [20, 28, -15, -9, 4],\n [-21, -30, 19, 36, -15],\n [-2, 8, -9, 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[[-3, -11, 14, 1, -7],\n [-1, 8, -3, 4, 0],\n [-4, -24, 15, -17, 21],\n [-10, -4, 14, -4, 20],\n [22, -15, -23, -11, -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, -30, -25, -7, 16],\n [-16, 9, 27, -28, 5],\n [13, -52, -21, -21, 25],\n [25, -30, 21, -8, 36],\n [-3, 3, -36, -18, -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[[-15, 9, -21, -14, 17],\n [7, -35, 10, -1, -6],\n [-22, 25, -34, -1, 23],\n [-7, 19, -15, 30, 5],\n [0, 13, -24, 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[[1, 18, 7, 21, 42],\n [-11, -7, 5, -14, 7],\n [-16, -6, -46, 0, -10],\n [-11, 5, -15, 2, 11],\n [-12, 9, 7, 10, 57]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-5, 2, 30, 26, 9],\n [13, -11, 9, -1, 9],\n [27, -6, -10, -14, 25],\n [1, 16, -28, -12, 7],\n [-15, 19, -1, 13, 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[[-9, -12, -12, -12, 9],\n [5, -6, 0, 14, -5],\n [-12, -16, -16, -16, 12],\n [-16, -15, -18, -25, 16],\n [-11, 17, 2, -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[[-6, 24, 6, 18, -14],\n [-15, -12, -21, -9, 22],\n [-16, 8, -12, 6, 7],\n [20, -40, 0, -30, 15],\n [0, 24, 12, 18, -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, -21, 4, -3, -35],\n [13, 5, -16, -12, 2],\n [34, 22, -16, -29, 12],\n [-9, -4, 8, 3, -31],\n [5, 34, -6, -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[[26, -4, 30, -31, -5],\n [-18, -2, -30, 28, 4],\n [27, -20, 6, -8, -14],\n [-21, 14, -4, 10, 4],\n [-6, -5, -19, 15, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 13, -15, -7, 1],\n [3, 11, 12, -26, -1],\n [-20, -27, 26, -33, -4],\n [36, -3, 22, -25, -20],\n [22, -15, 6, -31, -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, -29, 13, 9, -8],\n [-1, -4, 2, -15, 9],\n [-1, 8, -9, 3, -23],\n [-16, 13, -16, -32, -5],\n [5, -12, 7, 8, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[13, -18, -27, 13, 53],\n [18, 3, -1, -5, 17],\n [-21, 16, 20, -25, -39],\n [22, -3, -13, 25, 55],\n [40, -5, -7, -31, 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[[25, 13, -17, 0, 4],\n [-14, -3, 14, -3, -6],\n [13, 27, -13, -18, -24],\n [0, -11, 17, 12, 19],\n [12, 21, -17, -14, -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[[0, -4, 4, 16, -16],\n [-10, -3, 18, 2, 3],\n [0, -1, 1, 4, -4],\n [2, 3, -6, -10, 9],\n [10, 10, -25, -30, 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[[25, -5, 0, 25, 30],\n [-34, 22, 19, -15, -37],\n [-13, 9, 8, -5, -14],\n [9, 3, 6, 15, 12],\n [14, -22, -24, -10, 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, 26, 15, 11, 21],\n [-2, 1, -7, -9, 0],\n [8, -18, -1, -7, -6],\n [14, -9, 33, 39, 0],\n [-10, -10, 11, 25, -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[[26, 9, 21, -15, -5],\n [-1, 12, 31, -27, -10],\n [19, -2, 33, -17, -12],\n [-10, -4, 2, 8, 5],\n [-5, 19, 1, -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[[3, 24, 1, -2, -5],\n [6, -8, 2, -4, 18],\n [6, -8, 2, -4, 18],\n [12, 16, 4, -8, 20],\n [-3, -4, -1, 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[[-8, -1, 15, -12, -2],\n [7, 5, 33, 1, -2],\n [-9, -7, -37, -3, 4],\n [-7, -10, -44, -1, 10],\n [7, -4, -18, 9, 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[[0, -15, 10, 5, 25],\n [8, -13, 14, 19, 15],\n [-6, 0, -4, -11, 5],\n [-6, 6, -8, -13, -5],\n [-2, 7, -6, -6, -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, -54, -8, 35, 15],\n [25, -5, -5, 9, 8],\n [-15, 27, 17, -8, -15],\n [13, -14, 25, 0, -12],\n [44, -12, 4, -7, 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, -19, 23, -10, 10],\n [-34, 4, 36, -41, 18],\n [18, 2, -24, 20, -15],\n [7, 15, -21, 10, -3],\n [42, -20, -30, 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[[-21, -27, 16, 22, 4],\n [-41, -23, 18, 18, 27],\n [-10, 14, -12, -18, 24],\n [-50, -60, 26, 9, 8],\n [24, 38, -10, -1, 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[[2, -8, -1, 3, 2],\n [-14, -10, -5, -9, 22],\n [2, 25, 5, -3, -16],\n [2, 3, 1, 1, -4],\n [2, 14, 3, -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[[1, 7, 6, -8, 4],\n [8, 0, -15, 6, -17],\n [7, 1, -12, 4, -14],\n [-11, -13, 6, 8, 12],\n [-19, -13, 21, 2, 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[[1, -35, -4, 8, 21],\n [-7, 17, 27, -17, 9],\n [2, -13, 9, -32, -10],\n [-9, 0, 25, 0, 31],\n [5, -10, -10, -8, -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[[15, -24, 0, 0, 3],\n [-10, 22, -6, 10, 0],\n [8, 7, -18, 27, 5],\n [-2, 14, 0, -18, -16],\n [-13, 28, 0, -12, -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[[10, 26, -17, -1, -28],\n [-11, -13, -1, -5, 0],\n [-5, 17, 6, 18, 4],\n [-1, 33, -12, 12, -24],\n [-12, 0, 4, 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[[-13, -14, -20, 5, 16],\n [13, 16, 21, -2, 4],\n [-7, -10, -12, -1, -16],\n [22, 26, 35, -5, -4],\n [8, 10, 13, -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[[6, 3, 29, -13, -33],\n [8, 12, 20, -20, -20],\n [-1, 0, -6, 2, 7],\n [1, 6, -8, -4, 11],\n [6, 15, 1, -17, 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, 1, 10, 20, 6],\n [-3, 7, 4, 16, -4],\n [-8, 8, 5, 6, 17],\n [-7, 0, 1, -18, 33],\n [-4, -2, 0, -16, 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, 1, -9, -9, -11],\n [0, 5, 15, -15, 5],\n [8, 3, 1, -13, -5],\n [-4, -1, 1, 5, 3],\n [-4, -3, -5, 11, 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[[-2, -1, 16, 8, -11],\n [11, -16, 24, -5, -28],\n [11, -10, 7, 7, -20],\n [-8, -2, 21, 24, 6],\n [10, 9, -41, -36, -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[[-18, 14, -11, 3, -31],\n [30, -29, -15, -24, 27],\n [24, -13, 22, -15, 8],\n [-12, -7, 5, -11, 14],\n [-28, 8, 8, 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[[-5, 16, -8, -17, 15],\n [25, -40, 30, 35, -35],\n [10, 12, 5, -21, 14],\n [25, -12, 23, 0, -7],\n [-5, -12, -1, 18, -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[[20, 18, 29, 8, -12],\n [31, -2, 7, 17, 9],\n [-11, 13, -20, 19, -14],\n [-10, -18, -7, -18, 14],\n [-20, -13, 1, -28, 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, 19, 29, 6, 16],\n [21, 5, 7, 0, 9],\n [14, -11, -17, -5, -5],\n [-15, -17, -15, -10, -12],\n [-4, -27, -37, -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[[-9, 31, -32, -13, 22],\n [19, -5, -8, 35, 14],\n [-13, 11, -4, -23, -2],\n [11, -29, 28, 17, -18],\n [15, -25, 20, 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[[20, 12, -20, -17, 9],\n [-30, 16, 18, 28, 20],\n [5, -28, 1, 12, -32],\n [-15, -6, 23, -26, 4],\n [-20, 16, 20, 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[[1, -10, -11, 13, 16],\n [-5, 6, -11, 23, 30],\n [2, -6, -1, -2, -3],\n [5, -14, -1, -7, -10],\n [5, -8, 8, -19, -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[[25, -12, -6, -32, 29],\n [25, -25, -29, 5, 20],\n [6, -17, -32, 17, 3],\n [6, 8, 20, -32, 12],\n [12, -15, -30, -9, 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, 18, -16, 8, -6],\n [0, -18, 16, -8, 6],\n [0, 9, -8, 4, -3],\n [14, -15, 4, -2, -9],\n [12, 0, -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[[14, 2, 1, -8, -6],\n [0, -16, 20, -8, -8],\n [0, -5, 22, -10, 1],\n [4, -16, 3, -2, -14],\n [7, -12, 1, -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[[12, -10, 4, -4, 9],\n [6, 2, 1, -7, 6],\n [16, -10, 12, -8, -1],\n [8, 0, -9, -7, 28],\n [4, 2, -3, -5, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[10, 6, 8, 2, -4],\n [15, 9, 12, 3, -6],\n [30, 31, -12, 27, -9],\n [19, 14, 8, 8, -7],\n [-12, -2, -24, 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[[20, 14, -22, -7, 16],\n [-25, -14, -3, 17, 16],\n [-15, -25, 31, 27, -12],\n [25, 27, -19, -32, -4],\n [-5, -14, 25, 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[[33, 30, -3, -26, -28],\n [-15, -12, -3, 18, 6],\n [31, 25, 1, -22, -31],\n [16, 1, 16, -6, -29],\n [-9, 4, -20, 17, 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[[-10, 0, -13, 1, -10],\n [-20, -4, -23, 7, -16],\n [5, -18, 20, 22, 23],\n [-25, -10, -25, 15, -15],\n [-5, -22, 10, 28, 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[[11, -20, -14, 13, 21],\n [4, -20, -16, 16, 16],\n [-12, 11, 30, 21, 5],\n [-6, -15, -6, 25, 13],\n [-12, 8, 24, 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[[-19, 31, 19, 19, -12],\n [-17, 15, 17, -5, 2],\n [9, -6, -9, 6, -3],\n [8, -9, -8, -1, 1],\n [-8, 9, 8, 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[[-2, -7, -1, 1, -3],\n [1, -22, -4, 7, -15],\n [0, -17, -3, 5, -11],\n [-28, 4, 4, -16, 24],\n [-5, -9, -1, 0, -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[[23, -41, -12, -39, -10],\n [-8, 34, -18, 12, -35],\n [0, 15, 0, 10, -25],\n [8, 4, 0, 10, 1],\n [-16, -7, 2, -20, -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[[25, 2, 3, -25, 15],\n [-10, -12, -12, -20, -18],\n [-15, -15, -14, -20, -23],\n [7, -8, 1, -15, 1],\n [-34, -27, -10, 0, -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[[16, 12, 4, 0, 12],\n [6, -3, 3, -4, 3],\n [-17, -9, -5, 2, -12],\n [7, -6, 4, -6, 3],\n [28, 6, 10, -8, 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, -16, 25, -8, -10],\n [-32, -14, 10, -7, -23],\n [-20, 4, -15, 2, -8],\n [-16, 2, -10, 1, -7],\n [-8, 16, -30, 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[[20, -20, -16, 16, -8],\n [25, -20, -13, 18, -8],\n [15, -20, -19, 14, -8],\n [5, -10, -11, 6, -4],\n [-5, 0, -3, -2, 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, 14, 0, 19, 6],\n [0, -8, -8, -5, 0],\n [-6, 16, 16, 1, 6],\n [-9, -16, 12, -14, -23],\n [17, -28, -28, 8, -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[[15, 9, 4, 2, 15],\n [22, 16, -1, 10, -16],\n [-27, -36, 10, 0, 6],\n [-32, -7, -22, -2, 1],\n [6, 12, 10, -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[[-25, 41, 32, 27, 17],\n [31, -5, -5, -12, 46],\n [2, -2, -1, -6, 19],\n [-12, -28, 5, -17, 29],\n [10, 11, 1, 9, -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[[-4, 17, 21, -11, -33],\n [15, -5, -28, 18, 20],\n [-6, -22, 4, 0, 4],\n [8, 26, -11, 2, -10],\n [-4, 9, -2, -5, 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[[-21, 29, 36, -27, 15],\n [-1, 9, 20, -15, 3],\n [-17, 13, 4, -3, 9],\n [6, -14, -24, 18, -6],\n [24, -16, 0, 0, -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, -15, -50, -15, 15],\n [-5, -1, 20, 13, -11],\n [-3, 30, -5, -33, 24],\n [-1, 16, -5, -19, 14],\n [-6, 6, 20, 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, 19, 36, -32, 9],\n [-11, -38, -18, 11, 12],\n [2, 9, -17, 18, 5],\n [8, -4, -3, 6, 6],\n [5, 19, 7, 0, -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, 23, 7, -26, 8],\n [-6, 29, 10, -33, 9],\n [-9, 19, -13, -18, 24],\n [4, -3, 12, 1, -13],\n [-8, 13, -16, -11, 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[[33, -9, -15, 18, -8],\n [36, 0, -9, 18, -3],\n [-10, 14, 13, -18, -15],\n [19, 25, 14, 4, 10],\n [-20, -8, -1, -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[[-5, -3, 12, -8, 2],\n [-20, -6, 36, -17, 8],\n [0, -8, 16, -20, 0],\n [-10, 6, 0, 14, 4],\n [10, 2, -16, 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[[13, -1, -6, 10, 2],\n [-17, -7, 12, -8, 2],\n [9, 9, -9, 1, -4],\n [40, -10, -15, 35, 10],\n [-4, 10, -3, -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[[-7, -1, -20, 5, 12],\n [9, 5, 28, 5, -6],\n [-10, -19, 3, -27, 12],\n [-8, 7, -25, -1, 4],\n [7, 8, 25, 2, -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[[-19, -5, -18, -3, -11],\n [-5, 1, -5, 0, -2],\n [1, -7, 3, 12, 8],\n [-2, 11, -3, 6, 5],\n [9, 7, 8, 3, 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[[5, -3, -1, 2, 5],\n [0, 8, -12, 16, -4],\n [25, -13, -8, 14, 24],\n [25, -5, -20, 30, 20],\n [-15, 9, 3, -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[[0, 15, 10, 0, -25],\n [-8, -6, -4, 4, -14],\n [10, 24, 16, -5, -10],\n [-4, 9, 6, 2, -27],\n [4, 21, 14, -2, -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[[-14, -6, -2, -7, -5],\n [22, 3, 11, 1, 15],\n [14, 24, -20, 35, -15],\n [6, -9, 15, -15, 15],\n [18, 18, -10, 25, -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, 23, 43, 19, 2],\n [-1, -50, -16, -15, -49],\n [29, 25, 6, 4, 15],\n [22, -2, -1, -5, -9],\n [-3, -42, 5, -8, -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[[6, -5, 8, 13, 3],\n [-6, -17, -8, -4, 16],\n [-24, -15, -28, 19, 28],\n [22, -5, 26, -16, -12],\n [-6, 48, -9, 13, -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[[0, 0, 6, -12, -15],\n [15, 20, -11, 34, 46],\n [-12, 1, 13, -22, -15],\n [9, 13, 0, 8, 13],\n [-9, -13, -6, 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[[18, -1, 26, -9, 20],\n [-5, 8, 3, -25, 16],\n [-20, 4, 8, -51, 39],\n [-25, -6, -25, -6, -7],\n [5, 12, -31, 41, -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[[27, -26, 7, 16, -26],\n [8, 12, -28, 12, 12],\n [-16, -5, 27, -17, -5],\n [17, -22, 13, 8, -22],\n [3, 14, -25, 8, 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[[12, 16, -2, -15, 3],\n [24, 24, 0, -32, -12],\n [-3, 17, -3, 2, 29],\n [-12, -16, -6, 23, 17],\n [-3, 9, -5, 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[[0, -7, -8, 25, 6],\n [1, -30, -5, -28, -44],\n [7, -14, -24, -11, -34],\n [3, -6, 23, -26, -10],\n [18, -12, 9, 3, -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[[-16, 24, 10, 39, 4],\n [-4, -17, -11, 23, -2],\n [12, 6, 4, -27, -8],\n [-13, 5, 3, 19, 12],\n [-1, 1, -1, 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[[45, -8, 27, -22, -4],\n [37, 11, 30, -17, -13],\n [-40, 20, -24, 10, 6],\n [-2, -29, -11, 5, 11],\n [10, 0, 26, 30, -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, -20, -6, 25, -23],\n [0, 2, 2, -3, 3],\n [-12, -16, 12, 14, -10],\n [-15, -19, 16, 16, -11],\n [6, 2, -12, 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[[35, 0, 4, 15, -33],\n [-27, 3, -5, -11, 27],\n [-19, 14, 0, -6, 16],\n [-3, -2, 8, -2, -4],\n [0, -11, 5, -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[[6, -5, 28, -33, -2],\n [16, 6, 23, -28, 1],\n [6, -7, 41, -40, -4],\n [13, 18, 34, 12, -4],\n [23, 4, 3, -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[[2, -5, -5, -3, 0],\n [-2, -31, -31, 3, -4],\n [18, 0, 0, -27, 5],\n [8, -2, -2, -12, 2],\n [6, -15, -15, -9, 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[[-2, -28, -14, -1, -2],\n [21, -7, 22, 36, 20],\n [13, 22, 27, 34, 2],\n [-8, 12, -5, 10, -12],\n [13, 10, 20, 26, 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[[4, 15, -5, -2, -6],\n [0, 10, -6, -12, 4],\n [2, 0, 0, -5, -5],\n [-19, -30, 9, 25, 40],\n [19, 40, -13, -24, -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[[39, 52, -5, 20, 13],\n [15, 23, -7, 10, 4],\n [-2, -5, 20, 43, 30],\n [13, 10, 41, -3, 14],\n [-20, -27, 7, 36, 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[[-6, -33, -26, 16, -13],\n [23, -27, -6, 0, -7],\n [22, -36, -8, 7, 12],\n [0, 25, 18, -10, 9],\n [-21, 12, -16, 5, 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[[2, 5, -20, 4, 14],\n [14, -1, -15, 14, 2],\n [-7, 39, -24, 7, -4],\n [-19, -15, 32, 2, -16],\n [-4, -17, 11, 7, -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[[31, 3, -7, 6, -21],\n [-20, -4, -2, 0, 12],\n [10, -13, 16, 15, -12],\n [-17, 9, -16, -12, 15],\n [-33, 1, -9, -8, 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[[-23, -16, -32, -3, -5],\n [-11, -10, -2, -3, 25],\n [4, 2, 10, 0, 10],\n [4, 5, -7, 2, -25],\n [6, 6, -2, 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[[12, 5, 5, -15, -21],\n [10, 5, 4, -12, -16],\n [-12, -25, -1, 3, -15],\n [-18, -20, -5, 15, 9],\n [-2, 5, -2, 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[[-3, -23, 18, -2, -10],\n [7, 9, -18, -4, 12],\n [-11, -24, 24, 5, -15],\n [10, 17, 4, -7, -3],\n [-16, -22, -6, 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[[-9, 4, 12, 2, -12],\n [10, -4, -10, 9, -1],\n [28, -6, -24, 20, 8],\n [33, -4, -24, 28, 6],\n [35, 3, -20, 22, 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, -1, -17, -5, -17],\n [20, -13, 12, -2, 19],\n [9, -13, 2, -9, 5],\n [-14, -42, -33, -37, -25],\n [18, 55, 43, 49, 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[[-11, 11, -14, -2, -10],\n [-2, -2, 26, 10, 8],\n [-11, 31, -17, 20, -9],\n [27, -19, 11, 2, 17],\n [14, -16, 8, -5, 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[[13, 2, -6, 12, 2],\n [-10, -8, 12, -12, 4],\n [-1, 2, -2, 0, -2],\n [-14, -7, 12, -15, 2],\n [5, 4, -6, 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[[-16, 26, 1, -29, 10],\n [-6, -8, 7, 13, 23],\n [8, -14, 18, 12, 23],\n [24, -16, 2, 10, -22],\n [43, -12, 28, -11, -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, 3, 0, 7, -5],\n [-3, -3, 6, 9, -12],\n [18, -31, 20, -19, -5],\n [1, 8, -10, -8, 15],\n [5, -16, 14, 0, -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[[-37, 0, -4, 16, 16],\n [31, 13, -6, -26, 11],\n [4, -18, 20, 11, 3],\n [-28, -22, 27, 43, 2],\n [-9, -7, -5, -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[[3, -12, 17, 9, -28],\n [7, 5, -29, -11, 20],\n [-10, -2, -15, 12, 22],\n [-8, 23, -3, 2, 18],\n [24, 10, -2, -8, -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[[-14, -17, -25, -12, 25],\n [11, -7, -14, 30, -10],\n [0, 17, 11, -1, -5],\n [3, -17, -4, 0, 0],\n [-8, -23, -5, -23, 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, 2, 5, 3, 4],\n [3, 2, 7, 10, 11],\n [23, -14, -27, 7, 0],\n [-20, 0, -10, -35, -35],\n [-18, 12, 24, -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[[8, 11, -8, -7, -12],\n [1, -10, -1, 0, 9],\n [-12, 16, 12, 8, -12],\n [13, 0, -13, -10, -3],\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, 7, -13, -1, 19],\n [0, 12, -16, -4, 32],\n [-6, 12, -5, -8, 31],\n [6, -9, 1, 7, -23],\n [-12, 9, 10, -11, 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[[6, 9, 6, 21, 9],\n [-8, -12, -6, -32, -14],\n [-8, -12, -8, -28, -12],\n [6, 9, 14, 5, 1],\n [8, 12, 10, 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[[14, -28, 20, 4, 17],\n [-4, 8, -8, 0, -10],\n [-4, 8, -20, 6, -37],\n [-4, 8, -20, 6, -37],\n [18, -36, 16, 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[[-10, 2, 9, -3, 0],\n [-20, -20, -5, 20, -54],\n [14, 11, 6, -3, -21],\n [4, -29, -6, 1, -14],\n [44, 0, 0, -11, -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, -30, 20, -6, 4],\n [-12, -15, 12, 3, 6],\n [2, 5, -2, 5, 2],\n [-13, -20, 13, -5, 2],\n [-27, -40, 27, -7, 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[[17, -27, -5, -22, -5],\n [3, -9, 1, 3, 2],\n [29, -51, 2, -7, -6],\n [-17, 11, 1, 18, 17],\n [-21, 35, -4, -1, 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, 29, -5, -4, -18],\n [-11, 44, 0, 5, -19],\n [38, 4, -26, 4, -10],\n [-2, -4, -11, 17, 6],\n [-3, 24, -2, 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[[-9, -8, 25, 12, -16],\n [4, 17, -5, 2, 1],\n [7, 5, -20, -10, 13],\n [-3, -32, -5, -12, 8],\n [-1, -18, -5, -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[[1, 18, 16, 0, 20],\n [-11, -22, -8, 8, -28],\n [-18, 6, 27, 15, 0],\n [15, 28, 9, -11, 36],\n [16, 2, -17, -13, 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[[-2, 20, -49, 14, 7],\n [-4, -4, -18, -5, 17],\n [18, 24, -3, 27, -16],\n [-10, -36, 41, -32, 12],\n [-8, 0, -2, -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[[3, -45, 4, 15, 6],\n [5, 11, 30, 7, -8],\n [5, 11, 30, 7, -8],\n [-11, 12, 29, -2, -10],\n [-47, -5, -6, -25, -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[[-4, 4, 0, 12, 20],\n [-14, 4, -8, 14, 26],\n [10, -5, 4, -16, -28],\n [-11, -4, -12, -9, -11],\n [-18, -2, -16, -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[[-5, 2, -5, -39, -6],\n [6, 19, -10, -7, 15],\n [15, -11, -25, -24, 5],\n [8, 12, 0, 36, 16],\n [4, -2, -10, -18, 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[[15, 0, 20, -15, -30],\n [-21, -27, 29, 30, -3],\n [12, 9, -3, -15, -9],\n [7, 3, 3, -8, -9],\n [1, 3, -5, -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[[21, 17, 4, 10, -18],\n [4, -5, -5, 13, 7],\n [5, 1, 12, 24, 26],\n [-6, -15, -8, 9, 21],\n [17, 14, 14, 23, 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[[25, -15, 4, -19, -10],\n [-10, 0, -6, -4, -10],\n [17, 12, 19, 30, 45],\n [-5, 15, 8, 27, 30],\n [-5, 15, 8, 27, 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[[6, 4, -16, -6, 6],\n [5, 5, -25, -15, 0],\n [-2, -3, 17, 12, 3],\n [3, 4, -22, -15, -3],\n [-1, 4, -30, -27, -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[[54, -25, -38, -7, -33],\n [28, -13, -24, 9, 9],\n [37, -47, -13, -13, -34],\n [-1, 2, 0, -7, 2],\n [-20, -6, 22, 4, -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[[17, 14, 2, -9, 7],\n [-27, -20, -11, 2, 9],\n [-28, -22, -7, 9, -2],\n [20, 14, 11, 3, -14],\n [15, 10, 10, 5, -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[[10, -25, -36, 49, 23],\n [-2, -11, -22, 26, 12],\n [0, -16, -18, 19, 11],\n [16, -8, -14, 29, 11],\n [8, -12, -18, 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[[5, -20, -19, 2, 11],\n [0, -5, -11, -2, 9],\n [7, -20, -9, 6, 1],\n [-5, 20, 19, -2, -11],\n [-7, 20, 9, -6, -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[[-40, -20, -40, -25, 20],\n [11, -8, 7, 2, 7],\n [-7, -2, -14, 4, -15],\n [-12, -8, 0, -12, 36],\n [53, 40, 74, 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[[12, 11, 0, -28, -1],\n [-14, 16, -39, 10, -39],\n [20, 13, -17, 8, -28],\n [-20, -24, 13, 40, 17],\n [-9, 17, -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[[-3, -6, 3, -1, -1],\n [-35, -10, -35, -25, 25],\n [-6, -12, 6, -2, -2],\n [16, 20, -2, 8, -2],\n [22, 14, 13, 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[[11, 22, -12, -17, 5],\n [-29, 24, -1, -14, 34],\n [27, -10, 1, 10, -30],\n [7, -8, 8, 13, -17],\n [-23, 0, 26, 25, -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[[11, -2, -5, 2, -10],\n [19, -1, -11, 4, -19],\n [-9, 0, 5, -6, -5],\n [31, 9, -27, 16, -13],\n [10, 10, -16, 4, -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[[-14, -8, -23, -1, -13],\n [2, 2, -18, 1, -29],\n [12, -4, 18, 12, 28],\n [29, 12, 7, 10, -21],\n [-4, 2, -2, -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[[10, -19, 18, 12, 23],\n [-6, 7, -13, -5, -16],\n [-10, 31, -12, -18, -17],\n [-6, 25, -4, -14, -7],\n [2, -1, 5, 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[[9, 5, 2, 27, -37],\n [-8, -3, -14, 38, -4],\n [-17, 20, 26, -15, 1],\n [15, -11, -15, 2, -1],\n [34, -25, -4, -34, -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[[-32, 25, 12, -11, 36],\n [15, -34, -27, 30, -31],\n [28, 19, 12, -5, 24],\n [-27, 23, 6, -3, 44],\n [-26, 17, 20, -24, -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[[26, 8, -22, -16, -4],\n [25, 10, -5, 0, -10],\n [6, 0, -18, -16, 4],\n [-20, -8, 4, 0, 8],\n [-27, -9, 18, 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[[32, 30, 4, -24, 42],\n [3, 16, 30, -1, 11],\n [-34, -25, -8, 26, -35],\n [18, 19, -6, -14, 29],\n [11, 22, 21, -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[[40, -20, 5, 15, 35],\n [-17, 16, -7, -15, -13],\n [11, 12, -10, -16, 14],\n [-4, -8, 6, 10, -6],\n [5, -20, 12, 22, 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[[-28, -2, 0, -10, 12],\n [16, 5, -6, 1, -12],\n [-13, 1, -3, -7, 3],\n [-13, -8, 11, 4, 15],\n [-41, -1, -3, -17, 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[[-7, -40, 28, -37, 5],\n [2, 9, -6, 8, -2],\n [-8, -19, 10, -14, 12],\n [3, 22, -16, 21, -1],\n [-2, -26, 20, -26, -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, 14, 25, 15, 30],\n [-31, 27, -8, -15, 23],\n [41, -2, -5, 31, -9],\n [5, -8, 21, 21, 5],\n [5, 12, 47, -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[[24, 30, -17, 21, -1],\n [-18, -15, 25, 6, 4],\n [21, 15, -37, -3, -17],\n [-31, -40, 16, -19, -11],\n [2, 5, 2, 11, -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[[32, 15, 10, -33, -18],\n [16, 5, -1, -39, -21],\n [-19, 15, 13, -1, 5],\n [24, -25, -27, -29, -23],\n [41, 0, -11, -13, -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, -3, -5, -26, 19],\n [8, -2, 3, 8, 0],\n [-2, 4, 1, 12, -14],\n [-11, 3, -4, -10, -1],\n [-6, 2, -2, -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[[11, -7, 10, 2, -19],\n [27, -27, 4, 30, -19],\n [-15, 12, -8, -11, 15],\n [41, -51, 23, 33, -34],\n [30, -18, 19, 27, -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[[-10, -4, 4, 29, -20],\n [3, -13, -16, 9, -7],\n [24, -13, -19, 10, -1],\n [-38, -5, -1, 0, -13],\n [26, -14, -24, -2, 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, -19, -17, 21, -7],\n [7, -35, -11, 16, -36],\n [4, -22, -14, 6, -34],\n [2, 1, 19, 9, 29],\n [4, 4, -5, -11, -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[[-8, 10, -4, 10, -8],\n [-33, 20, -19, 15, -8],\n [8, -10, 4, -10, 8],\n [-33, 20, -19, 15, -8],\n [-37, 25, -21, 20, -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, -39, -20, -22, -17],\n [-6, 8, -2, 4, 4],\n [-12, 33, 13, 20, 21],\n [-21, -1, -7, -15, 6],\n [-35, 23, -11, 1, 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[[17, -21, -8, -33, 23],\n [-4, 15, 4, 4, 37],\n [-13, 36, 13, 43, -2],\n [-38, 11, -3, 14, 3],\n [-25, 10, 0, 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[[-12, -4, -9, 11, -17],\n [-12, 11, -18, -1, -14],\n [0, 15, -9, -12, 3],\n [-20, -5, -16, 17, -28],\n [0, 20, -12, -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[[30, 6, 9, -7, -20],\n [-16, -4, -2, 6, 12],\n [-7, -4, 7, 9, 9],\n [0, -6, 21, 17, 10],\n [-17, -2, -10, 0, 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[[7, -13, -15, 35, 13],\n [-12, 12, 16, -40, -16],\n [-12, -6, -1, -5, -5],\n [26, 16, 5, 5, 9],\n [13, -1, -6, 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[[-2, -17, 35, 6, 6],\n [4, -4, 18, 25, 10],\n [5, -10, 11, -1, -5],\n [-15, 30, -4, 16, -16],\n [-21, 10, -15, -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[[15, -20, -24, 3, -13],\n [11, -4, -12, 27, -21],\n [30, 5, 9, -10, -4],\n [-16, -21, -17, -22, 40],\n [-25, 8, 8, -1, -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, 0, 0, 1, 3],\n [20, 0, 0, 4, 12],\n [-10, 0, 0, -2, -6],\n [-21, -20, -20, -5, -11],\n [3, -15, -15, 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[[-2, 5, -14, -3, 5],\n [10, -11, 0, -13, 17],\n [4, -9, 23, 4, -7],\n [-2, 1, 6, 5, -7],\n [-8, 9, -1, 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[[-13, -31, -39, -42, -32],\n [-7, -33, -33, -43, -20],\n [5, 18, 16, 18, 9],\n [-13, 5, 5, 32, -4],\n [13, 13, 17, 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[[-20, -2, -16, 34, 4],\n [-20, 4, -28, -8, 22],\n [4, -22, -24, 18, 10],\n [14, 7, 36, 3, -25],\n [-18, 8, 2, 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[[26, -16, -8, -22, 25],\n [12, -3, -1, -7, 15],\n [-25, 29, 8, 30, -14],\n [-22, 9, 1, 15, -25],\n [-2, 6, -6, 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[[-6, 28, -40, 28, 37],\n [-34, -15, 8, -19, -5],\n [4, -13, 12, -29, -29],\n [-22, -22, 4, -4, -6],\n [-3, 0, 2, -16, -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[[-18, -20, 10, -14, -20],\n [-35, 15, -5, 25, 27],\n [11, 8, -11, 1, -23],\n [-10, -27, 14, -22, -26],\n [17, 15, -19, 2, -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, 0, 0, 0, 0],\n [11, 4, 1, -12, 19],\n [-12, -12, -3, 1, -8],\n [17, 16, 4, -3, 13],\n [0, -12, -3, -19, 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, 38, 7, -16, -6],\n [0, -14, -11, 8, 0],\n [-26, 18, -1, -4, 5],\n [7, -63, -14, 29, 11],\n [-24, 0, -12, 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[[-9, -11, 12, -1, 15],\n [-2, 4, 34, -16, -14],\n [-12, -20, 4, 8, 32],\n [1, -7, -3, 10, 14],\n [12, -7, 11, 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[[4, 3, -4, -2, 6],\n [16, 12, -10, -14, 12],\n [-16, -12, 13, 11, -18],\n [-20, -15, 19, 11, -28],\n [4, 3, -6, 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[[-2, 7, 9, -3, 12],\n [-9, 23, 32, -5, 20],\n [-4, 11, 15, -3, 12],\n [-1, 4, 5, -2, 8],\n [-1, 5, 6, -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[[-25, 34, 31, -45, 17],\n [-10, 35, 5, -44, 39],\n [-11, 10, -20, 2, 6],\n [-4, 3, 12, -7, -2],\n [22, -23, -27, 30, -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[[-13, 19, 38, 29, -2],\n [7, -14, -2, -1, 41],\n [41, 27, -16, -15, -8],\n [-44, -27, 15, 15, -3],\n [7, 9, -15, -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[[-24, -40, 32, 0, -5],\n [-56, -17, 42, 21, -4],\n [45, 42, -46, 3, 13],\n [-23, 17, 4, 36, 40],\n [23, -22, -2, -35, -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, 15, -25, 0, -30],\n [13, -3, -25, 24, 0],\n [-10, 12, -5, -12, -21],\n [-21, 15, 15, -32, -22],\n [3, 3, -15, 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[[-4, 38, -2, 10, 2],\n [39, 21, 38, 41, -25],\n [17, -25, 30, -3, -29],\n [-23, 14, -33, -10, 32],\n [29, 3, 13, 33, 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, 0, -2, -21, -12],\n [5, 36, 2, 0, 12],\n [4, -16, 16, -16, -24],\n [4, 20, 1, -6, 3],\n [5, -4, 26, -5, -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[[-6, -32, 4, -14, -10],\n [-9, -7, 14, 0, 6],\n [-18, -24, 3, -5, 2],\n [24, 9, -30, -5, -19],\n [-6, 13, 22, 9, 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[[6, -8, -12, -3, -1],\n [13, 35, -5, 11, 38],\n [36, 13, -9, 15, -13],\n [24, 1, -13, 4, 6],\n [16, 39, -11, 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[[-23, -14, -4, 8, -4],\n [22, 18, -8, -4, 2],\n [9, 6, 4, 2, -1],\n [4, 9, -16, 4, -2],\n [-9, -13, 20, 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[[22, -39, -49, -13, -5],\n [-17, -14, 1, 19, 29],\n [-19, -23, -24, 22, 6],\n [-8, 7, 27, 11, 23],\n [-23, 4, -15, -1, 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[[-1, 3, 0, -3, 4],\n [-20, -11, 45, 25, -21],\n [16, -4, 0, 8, -8],\n [28, -8, -35, -1, -7],\n [22, 4, -25, -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[[40, -6, 18, 3, 29],\n [-6, -4, -2, 9, 3],\n [-4, -12, 0, 24, 16],\n [-6, -4, -2, 9, 3],\n [-1, -3, 0, 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[[0, 2, -7, 3, -2],\n [-4, 4, 8, 0, 10],\n [14, -20, -7, -9, -29],\n [-12, 18, 3, 9, 24],\n [-6, 14, -16, 12, 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, -6, -22, -20, -3],\n [1, 5, -2, 1, -3],\n [5, 2, 16, -15, -20],\n [11, 41, 6, -4, -43],\n [-8, -24, -2, 9, 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[[-1, -9, -8, -3, -6],\n [-24, 9, 6, -18, 0],\n [14, -24, -20, 6, -12],\n [14, -24, -20, 6, -12],\n [-35, 10, 6, -27, -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[[37, 7, 9, 31, -4],\n [14, 8, 5, 22, 3],\n [6, 1, -12, 2, -9],\n [14, -12, -5, 17, -22],\n [-26, -9, -17, -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[[-8, 35, -13, -34, 13],\n [-29, -65, 16, 2, 6],\n [-8, -35, 1, 8, 6],\n [-18, -35, -1, -6, 13],\n [1, -5, 10, 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[[-3, 7, 1, 2, 16],\n [1, 8, 1, 23, 12],\n [14, -6, -14, -8, -20],\n [3, -32, 1, 19, 18],\n [9, -1, -13, -28, -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[[7, -13, -16, -7, -13],\n [15, -20, -30, -15, -20],\n [-2, 21, 14, 2, 21],\n [-13, 21, 28, 13, 21],\n [-6, -25, -6, 6, -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[[-23, 11, 15, -11, 17],\n [-9, 4, 5, -5, 6],\n [17, -13, -25, -3, -23],\n [12, -10, -20, -4, -18],\n [6, 2, 10, 14, 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[[-7, -5, -6, -1, 19],\n [28, 25, -6, 24, 10],\n [-13, -11, 2, -11, -3],\n [-31, -18, 0, -29, -3],\n [-13, -1, -8, -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[[20, -4, 8, -8, -8],\n [-9, -15, -30, 10, -6],\n [-26, 22, 16, 4, 20],\n [-24, 9, -3, 8, 12],\n [-15, 3, -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[[-7, -15, -25, -14, -5],\n [-8, -12, -23, -13, -7],\n [-6, 6, -1, -1, -9],\n [20, 0, 25, 15, 25],\n [2, -6, -4, -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[[-25, -3, -20, 15, 20],\n [-13, -7, -12, 24, 22],\n [-6, -16, -16, 12, 11],\n [0, -25, -40, 13, 10],\n [-6, -32, -56, 11, 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[[13, -6, -6, -5, 9],\n [-27, 4, 14, 15, -26],\n [5, 18, -6, -13, 21],\n [29, -10, -14, -13, 23],\n [3, -20, 2, 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[[1, -20, -3, 31, -1],\n [-5, -17, 2, 14, -8],\n [-7, -31, 2, 30, -12],\n [-7, -4, 5, -9, -9],\n [-8, -11, 5, -1, -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[[22, 21, -16, 21, -20],\n [-2, -9, -4, -9, 16],\n [-16, -7, 18, -7, -2],\n [24, 17, -22, 17, -10],\n [-11, -17, 3, -17, 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[[0, -20, 8, -8, 8],\n [-18, 13, 45, -31, 26],\n [-4, -10, 37, -25, 15],\n [-2, 19, -23, 21, -9],\n [-21, 20, 51, -32, 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[[-5, 4, -31, -4, 32],\n [17, 14, -15, 6, 12],\n [-8, -29, 17, -57, -11],\n [14, 10, -33, -5, 40],\n [-28, -36, 49, -29, -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[[-1, -30, -15, -3, -1],\n [23, -11, 11, 3, -11],\n [6, -30, -25, -17, -9],\n [27, -23, -3, -10, -20],\n [-9, 27, 23, 10, -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[[20, -11, 3, -13, 14],\n [-25, 8, 10, -1, 16],\n [3, 13, -19, 20, -30],\n [40, 43, -43, 17, 10],\n [-7, 4, -4, 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[[-5, 8, -14, -10, -15],\n [-17, 5, 4, -5, -3],\n [1, -4, 40, -20, -21],\n [-27, 12, -21, 1, 3],\n [-33, 5, 18, -3, 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, -32, -29, 29, -10],\n [-26, 1, 26, -21, -3],\n [-32, 9, -1, 10, 3],\n [-30, 10, 22, -15, 1],\n [-24, 27, 4, 4, 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[[9, 3, 6, 5, 11],\n [-12, -14, 2, 8, 7],\n [-3, -10, -4, 8, 7],\n [15, -15, -10, 8, 25],\n [10, 27, 4, -18, -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[[6, -6, -8, -12, -12],\n [-7, 11, 13, 22, 23],\n [-14, -2, 4, -4, -8],\n [-4, -4, -2, -8, -10],\n [11, 5, 0, 10, 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, 18, 15, 27, -3],\n [5, -1, 9, 31, -20],\n [-6, 15, 22, 36, -19],\n [17, 8, -5, -17, 47],\n [26, -9, -26, -12, 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[[0, 10, 10, 36, 7],\n [-16, 8, 8, -32, -20],\n [9, -14, 22, 9, 1],\n [8, -2, -8, 19, 12],\n [1, 2, 32, 32, 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[[-10, -2, 8, -8, -6],\n [-20, 15, 40, -25, 0],\n [-11, 13, 28, -16, 3],\n [-25, -24, -4, -11, -27],\n [-8, -13, -8, -1, -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[[26, 2, 11, 8, 3],\n [-13, -19, 1, 7, 18],\n [40, -1, -10, -8, -9],\n [-20, 7, 35, 26, 18],\n [24, -2, -23, -18, -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, -18, -39, -8, 21],\n [-19, 33, 4, -9, -22],\n [-4, -18, 1, 0, 5],\n [34, -10, 16, 18, 12],\n [-12, -26, -5, -4, 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[[13, 41, -30, 3, 7],\n [-2, 11, 38, -23, 60],\n [1, 11, 4, -3, 34],\n [2, -30, -15, 19, -50],\n [-13, -7, -21, 16, 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[[11, 7, 20, -8, 5],\n [-36, 8, -20, 8, -20],\n [-22, 3, -15, 6, -12],\n [-16, -4, -20, 8, -8],\n [-14, 5, -5, 2, -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[[-5, 25, -7, 4, -16],\n [35, -9, 23, 5, 33],\n [-20, -25, -11, 15, 0],\n [-5, 5, -7, 29, -1],\n [-5, -23, 1, -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[[7, 29, 18, 2, -12],\n [-6, -21, -11, 5, 16],\n [-13, -25, 4, 10, 21],\n [-9, -26, -9, 7, 20],\n [-5, -10, 3, -13, -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, 1, 3, -5, -2],\n [33, -16, -15, 29, 21],\n [-9, 15, 3, -22, -28],\n [-33, -8, 45, -7, 30],\n [6, -4, 24, 3, 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, -3, -10, -17, 26],\n [3, 9, 10, 7, -10],\n [1, -1, -4, 3, -4],\n [18, -16, -6, -3, 2],\n [-8, -14, -34, 3, -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[[7, 15, 1, 6, -5],\n [-20, -40, 0, -4, 8],\n [14, 30, 2, 12, -10],\n [-17, -35, -1, -8, 9],\n [-18, -35, 1, 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[[-18, 1, -33, -10, -24],\n [16, -2, -18, -30, 12],\n [19, -29, 2, -3, 8],\n [-10, -16, -29, 3, 1],\n [-12, -23, -3, 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[[15, 4, -16, 8, -8],\n [-3, -6, -2, 14, -14],\n [3, 4, 0, -8, 8],\n [0, -4, -4, 12, -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": "What is the rank of the matrix:\n[[-8, -17, -29, 19, 20],\n [26, -57, -16, -25, -1],\n [-2, 12, 1, 1, -5],\n [-28, 11, -17, 31, 0],\n [11, 12, 27, -8, 26]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[7, -39, -39, -55, -12],\n [-31, -3, -20, -21, 10],\n [32, -21, -11, -21, -26],\n [-12, -10, -13, -16, 10],\n [1, -45, -47, -65, -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[[-15, 10, 23, 5, -12],\n [2, 5, 15, -23, 14],\n [3, 10, 5, 8, -9],\n [-4, 6, 2, 18, -16],\n [1, -28, -31, -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[[16, -16, -22, -8, 26],\n [0, 4, 3, -2, 6],\n [15, -15, -24, -6, 27],\n [-11, 31, 56, -16, -8],\n [-12, 0, -6, 18, -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[[-3, -4, 6, 14, -11],\n [2, -8, 8, 16, -6],\n [-11, 20, -17, -31, 3],\n [0, 0, 0, 0, 0],\n [-1, -4, 5, 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[[-6, -6, -2, -4, 2],\n [-16, 0, -6, -8, -22],\n [0, 30, -11, -1, -37],\n [12, 10, 3, 7, 1],\n [-5, 27, -16, -6, -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[[0, -19, 14, -10, 9],\n [-3, -9, 9, -3, 6],\n [-15, 31, -11, 25, -6],\n [29, -8, -17, -21, -13],\n [10, 11, -16, 0, -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, -42, 21, 3, 14],\n [-24, -8, 16, -23, -13],\n [-18, 24, -6, 3, -3],\n [-12, -22, 23, -10, 1],\n [1, -18, 8, -19, -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, -1, -6, 4, 1],\n [-12, -9, 21, 11, 6],\n [-11, -2, -19, 5, -17],\n [-22, -3, -11, 11, -8],\n [-7, 10, -6, -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[[12, 2, -8, 13, -17],\n [21, 20, 27, -4, 13],\n [9, 29, 9, 2, 19],\n [-23, 28, 6, 15, -6],\n [-55, -3, -17, 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[[-3, -11, -28, 30, -2],\n [9, -7, 20, 2, 26],\n [-3, -30, 12, 0, -9],\n [2, -5, -16, 24, 11],\n [7, 18, 4, -1, 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[[167, -8, 6, 14, 150, 167],\n [119, -18, -53, -64, 17, 32],\n [82, -40, -100, -110, 3, -56],\n [20, -124, -7, 14, -71, -141],\n [141, -64, -41, -38, 5, 4],\n [4, 1, 24, 69, -76, -33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-107, -34, 134, 9, 134, -59],\n [22, 79, -8, 74, 73, 16],\n [15, -30, -30, -33, -66, 3],\n [-74, -63, 84, -41, 36, -39],\n [106, 72, -108, -8, -90, 88],\n [-104, -48, 132, -23, 105, -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[[-59, 40, -96, 76, -115, 27],\n [-21, -58, 24, -2, 75, -13],\n [-21, 24, -36, 24, 3, 9],\n [-81, -54, -54, 72, -81, 9],\n [-61, -84, -12, 44, -53, -3],\n [-5, -48, 27, -7, 11, -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[[-88, -44, -155, -118, -84, 121],\n [36, 68, 14, 43, -49, -43],\n [60, 22, 100, 68, 55, -74],\n [-12, -22, -9, -18, 11, 17],\n [-32, 24, -60, -12, -56, 24],\n [20, 58, -61, -26, -117, 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[[10, -40, 10, 5, -15, 65],\n [2, -18, 82, -24, -88, -2],\n [7, -33, 47, -9, -53, 38],\n [7, -21, -49, 21, 49, 56],\n [-3, 5, 53, -19, -55, -30],\n [-12, 48, -12, -6, 18, -78]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-65, 48, 51, 72, -61, 83],\n [39, -19, 81, -64, -13, 58],\n [-23, -52, 9, -44, 17, -39],\n [39, 57, -15, -32, -41, -10],\n [-135, -103, 3, 136, 81, 16],\n [4, -60, -120, -6, 89, -142]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-45, 16, 100, -64, -120, -86],\n [-5, -71, 107, -48, -47, -187],\n [50, 97, -151, 116, -50, 53],\n [-59, 36, 60, -72, -70, 22],\n [28, 69, -140, 88, 37, 151],\n [28, 136, -169, 132, -68, 146]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[72, -24, 54, 28, -34, -62],\n [144, -22, 55, 37, -20, -102],\n [36, 58, 2, -48, -104, 16],\n [32, 90, 18, -50, -130, 44],\n [72, -14, 94, 56, -36, -50],\n [120, -45, 108, 47, -86, -109]]\n\nPresent the 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, 78, -17, 85, 49, 70],\n [17, -35, 63, 115, -88, 68],\n [-14, 51, -13, 42, 33, 34],\n [22, 11, 12, 86, -5, 70],\n [-47, -81, 53, -101, -110, -120],\n [-17, -47, 4, -107, -28, -92]]?\n\nPresent the answer 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, -72, 64, -8, 16, 80],\n [83, -58, 96, -47, -31, 110],\n [12, -42, -16, 44, 62, -8],\n [40, -80, 0, 56, 88, 16],\n [-5, 10, 0, -7, -11, -2],\n [95, -55, 120, -71, -58, 134]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-125, 152, 28, -17, -54, -62],\n [102, 13, -5, -19, -43, 21],\n [122, 19, 41, 29, 45, -25],\n [67, -151, -26, 26, 86, 33],\n [80, 137, 90, 68, 91, -122],\n [-3, -107, -8, 93, 151, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[18, 0, -8, 10, 10, 16],\n [24, -30, -18, 6, 0, 21],\n [-122, 40, 64, -58, -50, -108],\n [49, 40, -12, 37, 45, 44],\n [-130, 50, 70, -60, -50, -115],\n [25, -20, -16, 9, 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[[-67, 48, -104, -39, 9, -15],\n [9, 8, -25, 34, -82, -57],\n [73, 38, 113, 42, 46, -15],\n [-16, 37, 70, -11, 129, 82],\n [66, -10, 115, 61, -7, 2],\n [48, 16, 146, 46, 78, 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[[65, 88, -75, -63, 14, -84],\n [69, 37, 32, 1, 22, 82],\n [37, -18, 142, -19, -18, 60],\n [26, 53, -102, -48, -27, -59],\n [-79, -38, 35, -23, -46, -61],\n [-80, -109, -156, 60, -100, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[36, 63, 77, -103, 57, -8],\n [-38, 100, 74, -104, 6, 118],\n [-7, -19, -115, -33, -53, -175],\n [32, 47, 96, 25, 80, 110],\n [-28, 140, 69, -92, 33, 114],\n [33, -111, -86, 133, -12, -109]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-101, -19, -65, -73, 17, 134],\n [-46, 16, -34, -70, 98, -22],\n [24, -6, 66, 48, -34, -64],\n [32, -35, 145, 113, -127, -72],\n [138, 6, 29, 15, -3, -95],\n [95, -20, -28, -44, -18, 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 6x6 matrix:\n[[-132, -107, -66, 44, 93, 42],\n [160, 72, 24, -72, -72, 56],\n [74, 47, 80, 53, -10, 36],\n [72, 37, -14, -74, -53, -2],\n [-48, 16, 41, 51, 2, -79],\n [122, 56, 34, -33, -47, 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[[-1, -55, -33, 39, -31, -36],\n [-16, 80, -48, -36, 44, 84],\n [-11, 67, -27, -33, 37, 66],\n [-15, 55, -55, -20, 30, 65],\n [-12, 92, -20, -49, 51, 85],\n [0, 32, 16, -22, 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 6x6 matrix:\n[[-54, 51, 66, -9, 28, -4],\n [-64, -33, -12, 57, 16, 6],\n [-64, -33, -12, 57, 16, 6],\n [81, -33, -57, -18, -34, 1],\n [32, 60, 48, -60, 0, -8],\n [-21, -72, -63, 63, -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[[-21, -46, -8, 87, -72, 117],\n [-9, 15, 109, 1, -131, 84],\n [7, -35, -4, 50, 17, 85],\n [-49, -3, -57, 18, -105, -6],\n [72, -45, -138, 41, 19, 2],\n [8, -31, -120, 45, -107, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[22, 21, -12, 23, -12, -10],\n [125, 104, -88, -114, -53, -166],\n [-12, -26, 82, -145, -107, -27],\n [20, 24, -50, 15, 43, -25],\n [45, 5, 2, 14, -50, -8],\n [14, 26, 28, 42, -62, 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 6x6 matrix:\n[[-40, 77, -30, -72, -51, -3],\n [-44, -31, -46, 56, -47, -67],\n [65, 18, 69, 31, 33, 46],\n [0, -71, -5, 141, -22, -66],\n [23, 84, 40, 54, -58, -3],\n [8, -15, 12, 130, -45, -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[[0, 21, 7, -84, 42, 84],\n [0, -12, 80, -6, -42, -12],\n [0, 12, -38, -21, 33, 30],\n [0, -11, -13, 50, -20, -48],\n [0, 26, -10, -92, 56, 96],\n [0, 9, 17, -45, 15, 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[[5, -22, 11, -22, -17, -12],\n [52, 27, 12, 66, 48, 54],\n [19, -14, -59, 6, -78, -87],\n [36, -36, 72, -66, -179, -44],\n [-32, 64, -44, 42, -15, -6],\n [50, 12, 6, 92, 229, 123]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[16, 26, 78, -167, -70, 46],\n [19, 27, -74, 76, 63, -34],\n [17, -88, -82, -40, -78, 46],\n [76, -53, -102, 28, -61, -32],\n [39, 86, 76, 48, 38, -90],\n [-194, -69, 77, 37, 66, 112]]\n\nPresent the 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, 67, 70, -19, -108],\n [9, 14, -105, -61, -21, 101],\n [13, 54, -20, 65, 4, 145],\n [40, 97, -26, 27, 34, 164],\n [37, 110, 56, 147, 3, 56],\n [7, 34, 37, 58, 19, 40]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-7, 59, 12, 10, 0, 14],\n [52, -89, 72, 8, -27, 82],\n [-33, 85, -22, -2, 36, -23],\n [-50, 24, -104, -20, 18, -120],\n [-22, 105, 2, 12, 9, 3],\n [22, -76, 8, -4, -18, 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[[-45, -84, 57, 91, -20, -3],\n [8, 20, -60, -132, 28, -12],\n [-3, -73, -16, -81, 17, -39],\n [-57, -91, 20, 0, -1, -12],\n [36, 89, -49, -68, 15, 12],\n [-6, 59, -25, -24, 5, 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, 138, 90, 224, -164, -23],\n [-69, 72, -72, 53, -34, -47],\n [-177, 81, 9, -16, 45, -197],\n [36, 6, 144, 3, 33, -33],\n [27, -56, -174, -14, -51, 120],\n [-18, -10, -24, -99, 129, -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[[-101, -26, 28, -132, 103, -142],\n [-113, -81, 130, -157, 86, -142],\n [79, 25, -35, 91, -34, 63],\n [-21, -16, -73, 11, 54, -59],\n [-137, -160, 57, -70, 33, -95],\n [33, 74, 4, -35, 46, -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 6x6 matrix:\n[[-112, 80, -78, 134, -8, -40],\n [-22, -34, 23, -12, 15, -12],\n [52, 28, -14, -12, -18, 24],\n [86, -46, 48, -91, 1, 32],\n [-38, -50, 33, -14, 23, -20],\n [6, -78, 61, -64, 25, -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[[14, -53, -26, 50, -64, 77],\n [-6, -37, 22, -16, 22, 43],\n [14, -9, -34, 46, -60, 21],\n [-18, 54, 36, -63, 81, -81],\n [-6, -15, 18, -18, 24, 15],\n [-12, -19, 34, -37, 49, 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[[-32, 14, -46, -72, -12, 2],\n [-26, -73, 101, 9, 24, -22],\n [30, 40, -44, 25, -10, 13],\n [-12, -26, 34, -2, 8, -8],\n [32, 11, 5, 52, 2, 5],\n [68, 14, 26, 118, 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[[-119, -81, 14, 73, 37, -20],\n [19, 94, -82, -79, 54, 95],\n [99, -230, 104, 175, -59, -25],\n [89, 109, 18, 52, 219, -49],\n [-132, -29, -33, 1, -13, 28],\n [-98, 47, 26, -24, -85, -93]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[5, 6, -45, -20, 58, -50],\n [-15, -70, 67, -10, -135, 82],\n [25, -7, 27, 30, -26, 2],\n [-34, -43, -6, -52, -39, 28],\n [51, -10, 29, 48, -20, -22],\n [86, -63, 54, 58, -74, -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 6x6 matrix:\n[[-92, 38, 62, -44, -113, 40],\n [24, 36, -20, 44, 18, -20],\n [32, -32, -20, 2, 44, -10],\n [52, 38, -40, 67, 49, -35],\n [-96, 24, 66, -57, -114, 45],\n [-20, -118, 24, -99, 7, 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 6x6 matrix:\n[[-50, -9, 2, 42, -19, 32],\n [140, 72, -10, -160, 168, -148],\n [-46, 89, 82, 33, 100, -150],\n [78, -103, -154, -157, -42, 86],\n [-52, -49, 21, 96, -105, 94],\n [-92, -101, -42, 35, -122, 58]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-10, 13, 1, 46, 48, -17],\n [6, -7, 5, -6, -8, -1],\n [-60, 67, -71, -21, 2, 52],\n [54, -59, 73, 54, 32, -65],\n [76, -86, 82, -4, -32, -50],\n [22, -26, 16, -31, -38, 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[[40, 81, 88, -35, -64, -65],\n [-73, -55, 96, -41, -14, -2],\n [59, 197, -22, -37, 1, -9],\n [99, 100, -42, 36, 27, -120],\n [-15, -92, 16, 22, -7, -14],\n [-44, 7, 35, -24, 65, -59]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[31, -40, -5, 45, 26, -99],\n [-140, -100, -164, -6, 50, 144],\n [49, -125, 13, 33, 6, -156],\n [-115, -40, -151, 201, -132, -105],\n [-56, -108, -48, -70, 22, 90],\n [-25, 87, -53, 180, -67, -94]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[29, 80, 32, -44, -17, 40],\n [-56, -65, -96, -82, 97, 85],\n [61, -123, 18, 9, 28, 10],\n [56, -134, 32, 68, -2, -50],\n [-14, 117, -12, -96, 13, 85],\n [-20, -22, -48, -68, 58, 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[[-42, 36, -7, 53, 3, 20],\n [73, -3, -67, -24, -40, 73],\n [16, 48, -50, -136, -28, -6],\n [113, -25, -54, 19, -103, 81],\n [-146, 140, -7, -85, 27, -63],\n [-36, -92, 112, 74, 92, -83]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[55, 64, -63, 50, -5, -49],\n [70, -7, -198, 38, 30, 89],\n [101, -124, -69, 85, 155, 208],\n [19, -17, -129, -100, -95, -22],\n [-54, 67, -66, -56, -98, -39],\n [-13, -22, -101, -54, -36, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-116, 41, -58, 77, -6, 79],\n [-71, 56, -22, 68, -24, 28],\n [171, 51, 72, -45, -90, -159],\n [122, -56, 34, -92, 6, -64],\n [12, -60, 15, -42, 51, 12],\n [71, 49, -5, -5, -75, -61]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-38, -1, -51, -64, 46, 45],\n [2, 4, -21, 31, -34, 45],\n [-4, -2, 6, -20, 20, -18],\n [60, 0, 90, 90, -60, -90],\n [74, 10, 51, 181, -154, 9],\n [12, 9, -36, 81, -84, 90]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[-190, 20, -40, 39, -117, 162],\n [-30, 18, -36, 21, -63, 33],\n [-50, 20, -40, 25, -75, 50],\n [50, 4, -8, -1, 3, -38],\n [110, -4, 8, -15, 45, -90],\n [180, -20, 40, -38, 114, -154]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[114, 71, 31, 79, 38, -56],\n [3, -61, -71, -35, 56, 16],\n [-158, -58, -29, -178, 42, 2],\n [-49, 31, -30, -23, 20, 100],\n [-153, -26, -10, -172, 46, -4],\n [-44, -3, -50, -23, 18, 100]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-95, 46, -38, 62, -55, -30],\n [3, 0, -87, 62, -27, -66],\n [-150, 3, -54, 56, -105, -25],\n [51, 39, 75, -38, 66, 41],\n [170, -28, 116, -116, 130, 76],\n [17, 122, -25, 82, 37, -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[[-48, -15, -111, 19, 58, -55],\n [1, 8, 51, -32, -20, 2],\n [-43, -11, -84, 7, 46, -49],\n [-7, -11, -72, 39, 30, -9],\n [-72, -9, -81, -27, 54, -81],\n [36, 9, 69, -5, -38, 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[[38, 14, 13, -14, 8, 0],\n [-1, 17, -18, 5, -28, 11],\n [-26, -38, 20, 2, 40, -18],\n [149, 107, -2, -41, -52, 33],\n [49, 7, 28, -21, 28, -7],\n [53, 59, -22, -9, -52, 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[[-84, 86, 68, -58, -88, -106],\n [108, 104, -133, 64, 60, 214],\n [-80, -31, 106, -29, -59, -136],\n [-25, -132, 4, -28, 42, -65],\n [-28, 93, -8, -247, -142, -219],\n [-7, 164, 45, 12, -90, 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[[39, 98, 74, -31, 56, 122],\n [-90, -6, 26, -146, 44, -3],\n [-78, -34, -27, -8, 123, -37],\n [-13, -9, 49, -137, -131, -10],\n [-18, 41, 44, -42, 84, 55],\n [-60, 28, 53, -154, 25, 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, -20, -21, -52, -4, -44],\n [23, 5, 49, 63, -24, 36],\n [70, -50, 35, -30, -60, -60],\n [38, -30, 14, -26, -32, -40],\n [52, -20, 56, 36, -48, 0],\n [12, -40, -49, -112, -4, -92]]\n\nPresent 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, -5, 49, -39, -90],\n [26, 118, 145, -47, 96, -111],\n [-88, -89, -51, 66, -42, -114],\n [-23, -50, -47, 26, -73, -13],\n [99, 76, 50, -71, -34, 85],\n [-50, -165, -151, 58, -53, 67]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[-89, 97, -39, 51, -128, -58],\n [120, 44, -2, -17, 31, 107],\n [31, -16, 52, -70, 94, 116],\n [-82, -28, 88, -68, 52, -74],\n [-33, -12, 86, -95, 97, 85],\n [14, -177, 15, -1, 90, -108]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[33, -39, 185, 12, -101, 17],\n [-20, 95, -74, -129, -12, -22],\n [-57, 11, -81, -154, -19, -59],\n [1, -107, 77, 122, 7, 19],\n [-23, 55, -131, 38, 91, 17],\n [-14, -96, 238, -11, -142, 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[[40, -86, -86, 123, 64, -73],\n [105, -94, -46, -36, 69, -71],\n [156, -38, 179, 22, -58, -26],\n [-35, -58, 23, 158, 11, 107],\n [101, -23, 121, -36, -43, -7],\n [55, -23, 35, -42, -32, -46]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[116, -76, -49, -33, -9, -77],\n [130, -117, -5, -86, -12, 25],\n [-36, -45, 152, -13, -11, 126],\n [48, -22, -38, 24, 0, -102],\n [84, -47, 69, -70, -72, -5],\n [-16, -50, 107, 86, 7, -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[[-37, -6, 83, -13, 113, 4],\n [106, 19, -239, 77, 87, 27],\n [56, -3, -81, 29, -36, 59],\n [22, 59, -69, 21, -62, 69],\n [-98, 112, 98, -38, -62, 12],\n [94, -49, -139, 45, 3, 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[[118, 36, 29, 44, -31, -5],\n [85, -20, -54, 47, -60, -89],\n [-81, -15, -38, -57, 78, -14],\n [137, 17, -40, 76, -84, -83],\n [-6, 96, 27, 57, -77, 62],\n [15, -191, 99, -117, 143, 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[[-24, 13, 128, -5, 108, 10],\n [35, -99, 104, 131, 7, -149],\n [-26, -32, 2, -48, 108, -4],\n [39, -66, 62, 78, 12, -95],\n [48, -55, 138, 99, 37, -98],\n [94, 20, 15, 8, -20, 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 6x6 matrix:\n[[20, -20, -20, 25, 40, -30],\n [-10, 42, 8, -16, -58, 34],\n [-44, -84, 52, -41, 64, -10],\n [21, 91, -28, 14, -91, 35],\n [-7, 55, 4, -14, -71, 39],\n [-2, -30, 4, 1, 34, -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[[-75, 24, 62, -66, 16, -49],\n [27, -60, -24, 1, 106, -63],\n [39, 120, 60, -38, 173, -45],\n [88, -46, -31, -20, 181, 5],\n [-97, 13, 0, 23, -200, -12],\n [-3, 40, 0, 19, -46, 11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-54, -142, -74, -132, 73, -128],\n [127, -152, 11, -74, 45, 61],\n [59, -54, 93, -124, -88, 73],\n [45, 8, 69, -49, -59, -15],\n [121, -156, -74, -11, 10, 47],\n [49, -10, -12, 54, 39, 45]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[45, -19, 26, -34, -24, -11],\n [77, 2, 42, -41, -41, 3],\n [57, 122, -22, -27, 50, -69],\n [107, 156, 22, -13, -11, 17],\n [-14, 48, -28, 10, 38, -26],\n [-135, -19, -46, 98, 24, 73]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-33, -2, 63, 57, 74, -49],\n [-62, 11, -10, -34, 94, -7],\n [-94, 5, 104, 150, 92, 16],\n [-28, -40, -34, -4, 82, -49],\n [18, 37, 103, 148, -88, 133],\n [-62, 72, 20, 2, -66, 136]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-32, -80, -112, -112, -16, 0],\n [-18, 50, 62, 62, -4, 50],\n [-58, -12, -28, -28, -22, 70],\n [-32, 34, 38, 38, -10, 60],\n [-14, 22, 26, 26, -4, 30],\n [-18, -26, -38, -38, -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 6x6 matrix:\n[[279, 67, 128, 24, -121, -26],\n [278, 151, 23, 8, -142, -74],\n [-41, -52, -48, 72, 114, -18],\n [134, 68, 68, -64, -84, 4],\n [-9, -48, 91, -16, 33, 86],\n [-146, -62, -24, -28, 12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[87, -126, -125, -51, -43, 47],\n [37, -44, -35, 3, -11, 19],\n [-23, 55, 60, 51, 23, -7],\n [-6, 66, -27, -36, -3, 69],\n [9, -57, -18, -17, -11, -33],\n [21, -54, -7, 15, -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[[-78, -77, 57, 6, 137, 11],\n [107, 59, 54, -81, 29, 54],\n [-28, -134, 172, -16, -22, 4],\n [-7, -60, 37, 32, -113, 89],\n [-182, -120, -13, 67, 157, -161],\n [-73, 35, -111, 42, 97, -59]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[108, -12, -143, 49, -69, 66],\n [31, -92, -6, 36, 68, 39],\n [51, 59, -123, 110, -29, 21],\n [34, -47, -117, 241, 39, 84],\n [-26, -5, -3, -11, 37, -52],\n [76, 100, 80, -139, 48, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[146, -56, -8, -30, -8, 156],\n [54, -5, -7, 38, -40, 32],\n [-56, 50, 6, 104, -64, -104],\n [-4, 17, 11, 54, -36, -26],\n [80, -33, 53, -5, 2, 103],\n [-75, 24, 168, 54, 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 6x6 matrix:\n[[0, 63, -3, 21, 39, -42],\n [-10, 109, -49, -7, 17, -36],\n [-16, 40, -72, -56, -56, 32],\n [-9, 96, -44, -7, 14, -31],\n [21, 21, 91, 98, 119, -91],\n [-6, 36, -28, -14, -8, -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[[72, 39, 155, 17, -78, 7],\n [58, 14, -20, 74, 102, 102],\n [56, -34, 60, 4, -42, 78],\n [78, -73, 35, 11, -22, 143],\n [85, 64, 105, 44, 9, -36],\n [106, -106, 66, -37, -77, 62]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[7, -105, 134, -78, 16, -61],\n [-134, -136, -21, 60, -65, -76],\n [-70, -88, -17, 12, 5, -8],\n [-137, 0, -84, 146, -71, 58],\n [-121, -20, -13, 120, -80, 30],\n [-174, -100, -46, 106, -58, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[99, 82, 40, -103, -60, -112],\n [-52, 25, 41, 46, -48, 17],\n [-90, 2, -122, 79, 35, 31],\n [-53, -3, -125, -22, 66, 6],\n [-205, 56, 22, 28, -52, 61],\n [-82, 30, 42, -42, -27, 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[[45, -10, 64, 36, 9, -22],\n [-20, 6, -56, -35, -11, 21],\n [103, 26, 76, 33, 19, -13],\n [-1, -53, -55, 5, -5, 27],\n [-25, 91, 173, 36, 23, -86],\n [-20, 194, 290, 111, 90, -113]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-87, 128, -17, -55, 62, 1],\n [82, -111, -5, 9, -22, -37],\n [59, 8, 129, -103, 138, 89],\n [10, 39, 41, -97, 110, 13],\n [-90, 50, -84, 96, -112, -28],\n [-95, 74, -135, 7, -38, -109]]\n\nPresent the 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, 39, 15, -48, -34, -56],\n [-111, -179, -11, 190, -152, 26],\n [50, 64, -68, -78, 188, 32],\n [-30, -15, -60, 162, -80, -121],\n [-2, 33, 33, 25, 38, 48],\n [24, 95, 56, 2, 46, 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[[26, -167, -130, 65, -83, -280],\n [-6, -4, 48, -27, 82, 71],\n [-39, -84, 51, -66, 30, -123],\n [1, 20, 1, 45, 32, 64],\n [-29, 48, 37, -64, -70, -39],\n [39, 3, -57, 2, -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[[56, -24, -45, 66, -83, 63],\n [-8, 2, 7, -6, 9, -9],\n [-40, -30, 51, 66, -35, -45],\n [-48, -8, 50, 12, 14, -54],\n [-32, -22, 40, 48, -24, -36],\n [64, -11, -58, 36, -62, 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[[-110, -46, -35, 5, 88, 89],\n [-20, 23, -169, 97, -118, -108],\n [58, -209, 23, -133, 24, -14],\n [120, -19, 155, -143, 90, -25],\n [-123, 26, -306, 145, -71, -125],\n [-3, 76, 139, -72, 171, 71]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[68, 93, -105, 151, 6, -38],\n [104, 65, -97, 143, 23, -21],\n [20, -24, -12, 100, -15, -127],\n [35, -131, 76, -42, 16, -37],\n [-81, -19, 32, 10, -43, -104],\n [-163, -74, 121, -153, -50, -29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[-140, -79, 90, -74, -20, 140],\n [-54, -55, 154, 148, -3, 59],\n [146, 51, -10, 76, -10, -60],\n [-42, 37, -44, -134, -16, 58],\n [-57, -2, -68, 59, 63, -156],\n [-60, -52, -14, -146, -14, 50]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[52, 60, 4, -134, -125, 50],\n [-83, -12, -15, 115, 91, -44],\n [-22, 55, -10, -38, -51, 13],\n [96, 82, -8, -124, -80, -14],\n [115, 21, 11, -119, -74, 15],\n [-119, -62, 21, 33, -46, 112]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-21, -9, 16, 9, -7, -13],\n [54, -54, 6, -18, 48, -6],\n [82, 18, -52, -34, 34, 42],\n [-28, -72, 58, 16, 14, -48],\n [85, -135, 40, -25, 95, -35],\n [82, 18, -52, -34, 34, 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[[38, -1, 4, -86, -57, -134],\n [-108, 89, 79, 1, -116, -44],\n [105, -87, -40, -7, 92, -92],\n [112, -63, -74, -66, 69, 37],\n [-65, 63, 12, -13, -64, 110],\n [-39, 0, 1, 80, 36, 81]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[117, -102, 18, 64, -65, -64],\n [101, -111, -99, 13, -150, -33],\n [-13, -39, -67, -19, -26, 79],\n [-174, 179, 33, -145, 97, 125],\n [-28, -35, 77, 9, 19, 5],\n [-56, 131, 63, -5, 139, 11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[80, -26, 45, 55, 109, 7],\n [-55, 66, 47, 95, 98, -19],\n [-166, -123, 173, 42, -96, 45],\n [-100, -21, 132, 75, 46, -17],\n [-209, -66, 139, 3, -96, -15],\n [3, -112, 26, 24, -133, 138]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[60, -55, 20, -20, 10, 110],\n [-38, 72, -24, 16, -26, -54],\n [-75, -10, 35, -50, 85, 20],\n [55, -69, 24, -20, 19, 93],\n [96, -65, -11, 38, -52, -5],\n [29, 13, -12, 12, -31, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[107, -78, -71, -32, 240, -146],\n [-15, 64, 18, 125, -237, 196],\n [-30, 70, 50, 28, -116, 68],\n [-3, 14, 42, -41, -79, 51],\n [-52, 8, -19, -65, -15, 8],\n [-12, 5, 132, -76, 35, -98]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[117, 10, -82, 39, -44, -17],\n [101, 58, 186, 11, 87, 19],\n [-68, 6, 32, -8, -26, -78],\n [6, 117, -24, -109, 113, 62],\n [-153, -35, -142, 76, -82, -115],\n [-114, -48, -256, -8, -94, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[104, -4, 16, -8, -76, -76],\n [66, -13, 103, -60, -94, -77],\n [88, 4, -52, 32, -32, -44],\n [54, -15, 123, -72, -96, -75],\n [54, 9, -90, 54, 9, -9],\n [-44, 14, -116, 68, 86, 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[[60, -6, -107, -5, -100, -24],\n [38, -114, -79, 27, -14, -123],\n [42, 4, -76, 8, -106, 13],\n [19, 126, -16, -71, -8, 63],\n [-35, 184, 83, -62, 14, 166],\n [-20, -38, 29, 31, 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[[10, 72, -8, -4, -81, -39],\n [-9, 126, 186, 34, -100, 59],\n [120, 67, 60, 11, 3, 40],\n [-83, -99, -86, -15, 47, -31],\n [-46, 79, 68, 11, -98, -7],\n [-85, 9, -10, -3, -59, -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[[2, -7, -3, 6, 21, 14],\n [2, -25, -7, 21, 70, 49],\n [16, 34, -4, -27, -77, -63],\n [-58, -13, 39, 6, -21, 14],\n [42, -21, -35, 21, 98, 49],\n [-12, -12, 6, 9, 21, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[28, 58, 20, -212, 38, -18],\n [10, 37, -50, 8, -50, -12],\n [9, 28, 51, -34, -27, 46],\n [-119, -14, 35, -32, -80, -117],\n [-106, 5, 34, -82, -73, -117],\n [28, -24, -44, 144, -2, 44]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[118, -46, -28, -51, 21, -1],\n [8, -40, -10, -20, -48, -130],\n [55, -19, -34, -27, 15, -23],\n [7, -115, -82, -132, -36, -19],\n [0, -32, -39, -32, -22, -83],\n [59, -87, -22, -94, -10, 61]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[18, -55, -10, 91, -52, 21],\n [-84, -58, -28, -14, -88, 78],\n [-84, 1, -14, -91, -26, 45],\n [-19, 22, 2, -49, 17, -2],\n [-53, 21, -4, -84, 5, 17],\n [-5, 12, 2, -21, 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[[117, 81, 12, -27, -59, 89],\n [-24, 18, 36, 44, -2, -8],\n [-105, -90, -30, 5, 60, -85],\n [-15, -90, -90, -85, 40, -35],\n [-15, -36, -30, -25, 18, -19],\n [-78, 18, 72, 98, 10, -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[[42, -21, 16, 49, -111, 18],\n [-87, 3, 42, -57, 78, -66],\n [-83, -3, 53, -40, 46, -66],\n [119, -18, -58, 36, -85, 56],\n [68, 42, -109, 21, 86, 86],\n [58, 19, -53, 80, -19, 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[[54, -73, -78, -135, -93, 3],\n [-32, -116, -86, 20, -148, 10],\n [14, 52, -28, -20, 64, -106],\n [-48, -49, -94, 65, -65, -99],\n [35, -68, -49, -92, -86, 32],\n [1, -19, -38, -13, -25, -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[[60, 25, -75, 20, 35, -30],\n [-33, 11, 21, 52, -35, -6],\n [-81, 2, 72, 64, -70, 8],\n [63, 18, -72, 0, 42, -24],\n [102, 48, -132, 48, 56, -56],\n [-39, 25, 15, 92, -49, -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[[92, 88, -22, -50, -4, -30],\n [-8, 36, 36, -78, 42, 26],\n [1, -22, 20, 113, 98, 107],\n [36, 72, 34, -66, 76, 50],\n [-139, -94, 62, -1, 38, 61],\n [105, 72, -21, 45, 51, 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 6x6 matrix:\n[[106, -50, 99, -3, 10, 44],\n [-88, 67, -18, -75, 38, -54],\n [-98, -58, -63, 3, 46, -60],\n [10, -96, 3, 34, 23, -3],\n [-2, -51, 75, -68, 80, -30],\n [-6, 21, -27, 18, -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[[-40, -6, 42, -12, 38, 40],\n [-30, -17, 29, -4, 21, 5],\n [20, -17, -25, 14, -31, -60],\n [30, 12, -30, 6, -24, -15],\n [40, -34, -50, 28, -62, -120],\n [60, 59, -53, -2, -27, 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 6x6 matrix:\n[[-155, -17, 90, 4, 101, -127],\n [130, 47, -90, 16, -56, 92],\n [47, 76, -137, -17, 70, 41],\n [4, -10, 76, 48, -48, -24],\n [-4, -2, 34, 22, -14, -16],\n [0, 48, -15, 33, 39, -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 6x6 matrix:\n[[30, 70, -160, -10, 40, -10],\n [3, -29, 20, -25, 28, 5],\n [24, 38, -110, -20, 44, -5],\n [21, -29, -34, -59, 80, 6],\n [-30, -40, 130, 30, -60, 5],\n [24, 68, -140, 0, 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[[112, -145, -166, 131, 141, 15],\n [202, -120, -84, 104, -20, 66],\n [-84, 148, 188, -94, -160, 88],\n [-33, 13, 42, -86, -36, -31],\n [30, -29, -52, 14, 44, -86],\n [65, 13, -34, 91, 26, -37]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-17, -20, -6, -18, -29, 28],\n [-80, -34, -62, -88, -92, 84],\n [-1, 16, -10, -2, 11, -12],\n [4, -64, 40, 8, -44, 48],\n [-50, -3, -49, -56, -44, 38],\n [-8, 55, -39, -12, 34, -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[[26, -155, 76, -101, 63, 29],\n [-94, -82, 107, -185, -20, -94],\n [75, -23, -56, 81, 73, 96],\n [65, -113, 10, 67, -111, 44],\n [-56, 213, -54, 23, 53, -57],\n [-124, 32, -94, -38, 40, -136]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-14, 23, 47, 25, -44, 31],\n [-88, 28, 52, 44, -64, 116],\n [-80, 44, 86, 58, -92, 118],\n [6, 29, 61, 27, -52, 13],\n [-84, 36, 69, 51, -78, 117],\n [-70, 47, 93, 59, -96, 109]]\n\nPresent the answer 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, 57, -102, -26, -57, 8],\n [12, 59, -14, -6, -55, -68],\n [35, -26, 26, 3, 16, -4],\n [28, 62, 28, 8, -46, -88],\n [-137, -46, -26, 14, 80, 158],\n [107, 2, 70, 8, -16, -94]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-106, -4, 59, -138, -6, 84],\n [44, 21, 32, -54, 8, 30],\n [-180, 21, -79, -13, 70, 117],\n [69, -74, -117, 78, -16, -24],\n [-56, 15, 87, -16, -79, 37],\n [17, 55, -97, 190, 72, -68]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[31, -25, 26, -7, 9, -16],\n [54, -18, 48, -54, 18, -60],\n [-110, 110, -90, -10, -30, 30],\n [5, -53, -1, 79, -3, 59],\n [-33, -33, -34, 105, -15, 92],\n [-84, 72, -70, 12, -24, 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 6x6 matrix:\n[[5, -78, -22, 19, -143, 68],\n [155, 21, 29, -155, 172, 60],\n [-78, -82, -130, 68, -183, -30],\n [5, -32, 48, 11, -50, 64],\n [-83, 62, 66, 67, 59, -72],\n [84, -66, 72, -104, 101, 70]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-36, 54, -24, -24, 42, 18],\n [4, 10, -20, 2, -6, -8],\n [28, -98, 98, 21, -28, 7],\n [-16, 80, -90, -13, 14, -13],\n [-42, 135, -130, -31, 43, -6],\n [26, -55, 40, 18, -29, -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[[24, 29, 24, 34, -25, 47],\n [-104, -3, 80, 6, 47, -81],\n [-40, -3, 28, 0, 19, -33],\n [56, 33, 4, 36, -41, 75],\n [-104, -7, 74, 1, 49, -85],\n [112, 10, -76, 2, -54, 94]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-63, 26, 48, 69, 15, 137],\n [111, 34, -54, 168, 108, -77],\n [-57, 28, 23, 59, -110, -43],\n [43, -4, 25, 56, 108, 70],\n [-193, 41, 81, -13, -175, 8],\n [8, -5, 31, 14, 31, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-28, -35, 17, 38, 127, 110],\n [104, -20, 4, 239, -36, -31],\n [28, -161, 17, 26, 17, 1],\n [25, -78, 82, 154, 43, 24],\n [-56, 100, 65, 23, 102, 79],\n [35, 87, 14, 3, -98, -103]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[77, 10, 17, -2, -106, 126],\n [-77, -37, -44, -43, 10, -63],\n [-39, -16, -25, -31, 9, -33],\n [78, 54, -24, -144, -42, 108],\n [-10, -2, 56, 148, 74, -72],\n [22, 26, 28, 38, 52, -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[[-64, 57, -65, 10, -66, 39],\n [-17, -53, 62, -78, 52, 34],\n [-20, 76, -88, 72, -80, -8],\n [-21, 70, -81, 64, -74, -5],\n [29, 27, -32, 58, -24, -36],\n [30, -65, 75, -50, 70, -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 6x6 matrix:\n[[-58, -44, 38, 60, -4, -12],\n [21, 78, -99, -30, -78, -66],\n [-17, 44, -67, 10, -74, -68],\n [-67, -56, 51, 70, 2, -8],\n [-65, 5, -32, 60, -74, -75],\n [2, -14, 20, 0, 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[[49, 0, 29, -29, 21, 41],\n [42, -42, 36, -78, -42, 90],\n [-42, -56, -10, -46, -98, 38],\n [0, 0, 0, 0, 0, 0],\n [35, -35, 30, -65, -35, 75],\n [15, -57, 24, -81, -75, 87]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[34, -93, -101, 190, 146, -93],\n [-113, 37, -59, -129, 23, -42],\n [143, -28, 129, 29, -155, 60],\n [-116, 8, -120, -62, 10, -101],\n [180, -37, 139, 60, -90, 111],\n [23, -78, -156, 85, 142, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-58, 8, 54, 72, -14, 56],\n [-77, 22, -9, 18, -31, 34],\n [84, -26, 24, -6, 36, -30],\n [-66, 11, 48, 69, -18, 57],\n [-88, 22, 12, 42, -32, 50],\n [-72, 5, 102, 123, -12, 87]]\n\nPresent 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, -43, 1, 23, -140, 122],\n [41, -21, 72, 71, 73, -85],\n [2, -30, 47, 60, 56, -113],\n [15, 4, 40, 19, 99, -76],\n [-92, 104, -117, -180, 86, 37],\n [-61, 53, -83, -65, -59, 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 6x6 matrix:\n[[-4, 44, -5, -68, -4, -41],\n [-89, 68, 126, -55, 33, -84],\n [-84, 5, 145, 31, 36, -49],\n [105, -67, -135, 59, -46, 67],\n [27, 38, -136, -87, 7, 102],\n [157, -82, -112, 96, -100, -52]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[102, -1, 21, -86, -41, 50],\n [-32, 128, 28, -90, -92, -72],\n [-12, 14, 0, 37, 4, -28],\n [-58, 56, 5, -61, -38, -29],\n [-70, -65, -25, -102, 23, 84],\n [84, -12, 12, 9, -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[[-59, -89, -48, -70, -29, -75],\n [-71, -61, 67, 110, -153, -68],\n [-32, -11, -51, 38, -17, -48],\n [-49, -53, 91, 41, -117, -26],\n [-32, 132, 119, 227, -100, 61],\n [19, -83, 7, 73, -71, -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[[26, 64, -48, 6, -29, 31],\n [-105, 81, 76, -141, 38, -60],\n [-213, -115, 31, -5, -153, 115],\n [165, 97, -77, 15, 113, -73],\n [118, 22, -107, 149, 11, 2],\n [-35, 41, 137, -86, -15, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[35, 9, 89, -41, -113, -105],\n [18, -82, -111, -148, 87, 75],\n [-35, -53, -89, -67, 130, 97],\n [22, 86, -33, 103, 167, 103],\n [-46, 30, 66, 97, -33, -14],\n [6, 10, -155, 140, 19, 100]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[176, 58, 57, -70, 55, -7],\n [14, -199, -82, 9, -88, 142],\n [-29, -51, -100, 89, 21, 105],\n [-10, 41, -25, 25, 35, -9],\n [-190, -27, -100, 85, -30, -12],\n [125, -37, -72, -21, 26, 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[[38, 95, -67, -118, 27, -107],\n [-17, 29, 27, -55, 73, -52],\n [-20, 22, -28, -45, 84, -121],\n [-7, -104, -74, 65, 72, -83],\n [-62, 69, 78, 28, -74, 45],\n [10, 36, 3, -77, 85, -51]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-21, -93, 39, -33, -102, 72],\n [-49, 19, -4, 24, -42, -27],\n [-1, -7, -26, -2, 14, -3],\n [60, 11, 46, -16, 40, 21],\n [22, 65, -127, 23, 152, -78],\n [84, -19, 116, -38, 0, 69]]\n\nPresent the 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, -10, -82, 92, 67, -37],\n [17, -40, -58, 152, 25, -67],\n [22, -20, -44, 88, 26, -38],\n [6, 15, 8, -46, 3, 21],\n [104, 20, -96, 24, 100, -4],\n [7, -35, -42, 126, 14, -56]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-37, -85, 55, -4, 116, 60],\n [-180, -130, -22, -36, 89, 131],\n [-46, -64, -271, 58, -114, 242],\n [-131, -96, -28, -69, 39, 88],\n [43, -24, 9, 83, -16, -3],\n [147, 97, 46, 112, -15, -87]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[15, -40, -5, -19, -67, 15],\n [6, 36, -2, 21, 46, -33],\n [18, 8, -6, 8, -2, -24],\n [21, 36, -7, 24, 35, -48],\n [-6, 4, 2, 1, 10, 3],\n [6, -104, -2, -56, -150, 72]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[-8, -12, 4, 16, 40, 4],\n [18, -1, 7, 8, -54, 27],\n [-2, 60, -35, -95, -71, -80],\n [6, 51, -27, -78, -84, -57],\n [-2, 4, -3, -7, 1, -8],\n [-16, 32, -24, -56, 8, -64]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[38, -22, 8, -48, -54, 7],\n [76, -27, -26, 0, 2, 61],\n [-84, 53, 6, 0, 2, -67],\n [116, -102, 20, 0, -8, 92],\n [110, -67, -6, -16, -20, 80],\n [62, -98, 46, 28, 19, 62]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-7, 8, 12, -9, -32, 37],\n [-7, 8, 4, -5, -8, 5],\n [23, -52, -50, -32, -86, 59],\n [19, 4, 52, 49, 56, 15],\n [-13, 32, 28, 25, 72, -57],\n [-15, 30, 34, 10, 18, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[84, 37, -22, 33, 47, -54],\n [118, 54, -60, -94, 32, 32],\n [154, 39, -45, 2, 85, -81],\n [-80, -112, 55, 41, 6, -73],\n [-76, 36, 24, 76, -48, 32],\n [70, 143, -56, -19, -21, 92]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[26, -157, 87, 81, 17, -63],\n [-77, -73, 4, 0, -100, -36],\n [16, -141, 19, 25, 11, -62],\n [-10, -52, -106, -72, -8, -61],\n [-89, -29, 13, 30, -129, -79],\n [40, -41, 42, -3, 18, 128]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-45, 32, 67, 18, 35, -113],\n [-143, 64, -21, -57, 88, 3],\n [141, -101, 31, 67, -130, 25],\n [-18, 35, -26, -123, -8, 55],\n [-116, 23, -37, -51, 58, 47],\n [-31, 50, 26, 4, 49, -75]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-43, -28, -35, -5, -27, -18],\n [-18, -16, 3, -16, 1, 16],\n [16, 8, 23, -6, 17, 20],\n [-3, 12, -60, 45, -42, -78],\n [-20, -32, 62, -64, 42, 96],\n [22, 24, -22, 34, -14, -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[[-26, -34, -22, -114, 186, -113],\n [-17, 39, -39, -146, 149, -66],\n [-124, -27, -142, -69, -88, 97],\n [-3, -33, -57, -32, 109, 26],\n [42, 62, 154, 172, 26, 10],\n [-28, -94, -96, -160, 136, -101]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[32, 36, 44, 8, -28, 12],\n [-116, 37, -41, -88, 23, 65],\n [68, 64, -4, -18, 138, 178],\n [170, -20, 71, 111, -21, -49],\n [-62, -31, -80, -39, 84, 42],\n [-48, -54, -66, -12, 42, -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[[-68, -42, 84, 48, 32, -26],\n [16, 56, -80, 0, -32, -8],\n [47, 42, -75, -30, -29, 14],\n [41, 70, -109, -18, -43, 2],\n [-21, -49, 73, 6, 29, 3],\n [-26, 56, -62, 36, -26, -32]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[26, 18, 21, 4, -12, 4],\n [-30, -24, -49, -38, 2, -45],\n [-48, -54, -18, -86, 18, 5],\n [22, 30, 41, 88, 8, 52],\n [90, 84, 14, 68, -52, -55],\n [-104, -90, 3, -32, 72, 99]]\n\nPresent 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, -68, -35, 39, 35, -84],\n [-14, -20, -122, -64, 83, 63],\n [19, 96, 181, 34, -129, 19],\n [11, 68, 50, -29, -50, 69],\n [60, 56, -31, -75, -86, 57],\n [-54, -84, 17, 91, 87, -100]]\n\nPresent the answer 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, 92, 34, 62, -108, 86],\n [40, 104, 34, 42, -168, 14],\n [75, 89, 49, 17, -123, 59],\n [-122, -8, -82, -41, 90, 56],\n [83, 59, 79, 80, -123, 19],\n [33, 38, 49, 73, -75, 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[[88, -88, -104, -32, 104, 128],\n [59, -41, -43, -28, 37, 64],\n [89, -68, -74, -40, 67, 104],\n [-38, 32, 36, 16, -34, -48],\n [-16, 10, 10, 8, -8, -16],\n [37, 14, 32, -32, -49, -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[[28, 95, 25, -59, -71, -121],\n [22, -40, -90, 4, 36, -84],\n [-1, -98, -11, 96, 68, 120],\n [-8, -70, -20, 54, 51, 76],\n [-4, -26, 40, 50, 13, 92],\n [13, 89, 24, -67, -65, -101]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-134, -29, -39, -62, -56, -50],\n [18, 110, 55, 81, -23, 28],\n [116, 9, 50, 34, 27, 45],\n [82, -54, -68, 13, 126, -1],\n [70, 17, -10, 45, 63, 20],\n [40, -17, -18, 8, 45, 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[[-14, -4, -14, -4, 10, -8],\n [-43, -2, 101, 86, -39, 44],\n [27, 9, 45, 20, -28, 24],\n [45, 9, -9, -24, -6, 0],\n [-24, 6, 156, 116, -70, 72],\n [-1, 1, 17, 12, -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[[-24, 195, 111, -33, 62, 90],\n [-14, 15, 85, -29, 66, 102],\n [-12, 35, 11, -37, 26, 62],\n [-21, 105, 168, -21, 98, 126],\n [19, -90, -143, 22, -86, -114],\n [12, -85, -133, -1, -66, -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[[-2, -19, 30, -23, -20, -7],\n [86, 127, 40, 129, -60, 11],\n [54, 169, -132, 140, -56, 131],\n [-68, -124, 6, -104, 88, -64],\n [8, 20, -8, 8, -32, 28],\n [70, 55, 120, 65, -60, -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[[-138, -2, 140, -71, 67, 39],\n [-136, 6, 52, 15, 95, 90],\n [74, -84, 144, -43, 2, 6],\n [65, -62, 218, -141, -19, -67],\n [89, -56, 14, 3, -56, -14],\n [-80, 52, 36, -75, 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[[-83, 86, -227, 159, -27, -86],\n [-148, 76, -243, 62, -30, 0],\n [32, 59, 109, 38, -40, 100],\n [-44, 58, -190, 88, -16, -20],\n [-52, 159, -31, 188, -93, 57],\n [4, -76, -72, -80, 48, -54]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-93, -38, -55, -11, -57, 49],\n [7, -73, -66, 37, -71, 102],\n [-90, 58, 68, -10, 122, -148],\n [24, -164, 35, 23, -50, 37],\n [-54, 99, 78, -16, 138, -161],\n [-181, 74, -103, 43, 55, -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[[8, 74, -20, -101, -118, -19],\n [44, -28, -23, 10, -40, -61],\n [8, -6, -4, 3, -6, -11],\n [8, 4, -6, -10, -20, -12],\n [0, 90, -18, -117, -126, -9],\n [-36, 32, 17, -20, 20, 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[[-44, 24, -113, -1, 6, 33],\n [-5, -96, 62, -36, -7, 1],\n [-28, 94, -26, -95, 134, -101],\n [70, 106, -108, -37, -28, 67],\n [5, 16, -36, -24, 3, 15],\n [133, 146, -44, 19, -67, 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 6x6 matrix:\n[[127, 175, -34, 92, 71, -70],\n [-39, -57, 52, -63, -31, 7],\n [25, 39, -30, -52, -25, 40],\n [-93, -68, 110, -160, -24, 89],\n [55, 51, -43, -42, -36, 16],\n [-19, -71, 4, -144, -121, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[11, -38, 99, -17, -9, 27],\n [3, 118, -135, -82, 70, 45],\n [-73, 26, 74, -144, -81, -19],\n [-26, -155, 101, 12, 30, -85],\n [-24, -21, 34, -52, 3, -17],\n [-95, -27, -2, -107, 32, 28]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[-143, -17, -140, -93, -57, -108],\n [-147, 81, -97, -86, -46, 46],\n [-101, -24, 7, -106, -90, 150],\n [-125, 82, -58, -84, -34, 104],\n [25, -76, 27, 8, 16, -56],\n [-121, -141, -11, -93, -139, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[49, 28, 0, 86, 30, -24],\n [8, 72, 93, 26, -111, 31],\n [-104, -118, -24, -187, -92, -49],\n [-101, -84, 59, -40, 113, -83],\n [-24, -70, -29, 45, 213, -62],\n [-1, -54, -9, 25, 23, 59]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[23, 159, 202, -118, 161, 40],\n [141, 11, -27, 3, -43, -39],\n [106, 16, 34, -40, 70, 1],\n [144, 6, 40, 17, -11, 13],\n [-70, 24, 31, -23, 36, 13],\n [-103, 39, 48, -11, 12, 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 6x6 matrix:\n[[-39, -161, -26, 34, 36, -93],\n [-117, -59, -87, 139, -63, -66],\n [-206, -183, 54, 25, 68, -5],\n [-11, -64, 73, -6, -7, 30],\n [148, 54, -115, -122, -19, -42],\n [-82, -107, 145, 21, 97, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[90, 79, -93, 26, -117, 61],\n [100, 52, -88, -12, -84, 78],\n [50, -65, -5, -110, 75, 65],\n [50, 19, -41, -14, -33, 41],\n [-30, 46, 0, 74, -54, -41],\n [-90, 19, 51, 86, -9, -89]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[71, -88, 115, 7, 3, 91],\n [-121, -120, -85, 59, -97, 29],\n [4, -32, -21, -29, 3, 80],\n [196, 51, 65, -31, 100, 14],\n [-143, -30, -66, 50, -80, -59],\n [144, 91, 103, -57, 98, 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[[-40, -25, 40, 20, 30, 25],\n [34, 15, -104, -47, -58, -10],\n [54, 40, 16, 3, -8, -45],\n [14, 10, 0, -1, -4, -11],\n [114, 80, -16, -15, -40, -87],\n [-34, -30, -64, -25, -20, 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[[82, 12, 140, -96, -18, 16],\n [57, 67, 43, 12, -86, 16],\n [56, 72, 50, -54, -16, 15],\n [-141, -91, -82, -37, 135, 36],\n [44, -33, 41, -2, 1, -43],\n [-86, -34, -60, 10, 38, 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 6x6 matrix:\n[[20, 80, 95, 65, -45, -5],\n [-68, -110, 1, 49, 99, -91],\n [48, 66, -24, -54, -66, 72],\n [-8, 4, 34, 34, 6, -22],\n [-64, -106, -4, 42, 94, -84],\n [-8, -56, -86, -66, 26, 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[[-179, -6, 1, -91, 2, 28],\n [69, 1, -84, -9, -181, 37],\n [-23, 8, 7, 68, 30, -51],\n [95, 16, -107, -9, -196, 70],\n [47, -31, -47, -1, -177, -31],\n [-182, -22, 32, -132, 34, 32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, -84, 90, -18, -40, 6],\n [-25, -35, -56, -62, -33, -6],\n [20, 12, -79, -81, -2, -37],\n [42, 54, 24, 36, 42, -12],\n [44, 109, 22, 106, 76, 6],\n [-3, -4, 106, 92, 13, 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 6x6 matrix:\n[[10, 29, -87, 50, 8, -54],\n [17, 36, 32, -70, 72, 121],\n [-50, -95, -51, 180, -49, -200],\n [-88, -24, 26, 35, -57, 31],\n [50, 36, -100, 20, -72, -134],\n [111, -26, 24, -25, 123, -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[[18, -50, -48, 32, -18, 44],\n [56, -82, 151, -28, 6, -66],\n [-90, 144, 43, -12, -68, -50],\n [6, 10, 122, -40, 8, -74],\n [-92, 142, -25, 4, -60, -12],\n [-26, 4, 2, 40, -93, 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[[29, 28, 68, 10, -7, 42],\n [104, 60, -88, 126, 30, -28],\n [121, 130, 22, 23, -70, -4],\n [100, 76, -62, 84, -4, -28],\n [-170, -184, 52, -32, 106, 60],\n [-55, -84, 32, 38, 81, 50]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[24, -32, 160, -195, 127, 138],\n [-39, -133, -36, -217, 158, 239],\n [42, 42, -21, -54, 30, -39],\n [-89, 41, 111, 31, 94, -2],\n [7, 7, 210, 68, -89, -74],\n [60, -43, 46, -129, 20, 76]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-46, -54, 82, -34, 8, 64],\n [62, -58, -58, 78, -72, -16],\n [-64, -35, 80, -63, 33, 59],\n [15, -69, 13, 34, -44, 28],\n [-2, -70, 58, 24, -36, 52],\n [-14, -21, 46, -3, -3, 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[[119, 184, 71, 29, 108, 147],\n [152, -34, -6, 86, -26, 10],\n [-122, 101, 76, 12, 26, 39],\n [4, 106, 112, 76, 89, 36],\n [-216, 25, -55, -238, 36, 11],\n [-37, 32, 44, -99, 164, -27]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[68, 37, -12, -16, 33, 6],\n [-14, 20, 40, -24, -26, 18],\n [18, -51, -136, -2, 83, -41],\n [16, 98, 152, 152, -40, 118],\n [-16, 106, 45, -215, -68, -30],\n [-15, 28, 0, -26, 4, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[-69, 31, -65, -86, 106, 26],\n [-66, 26, 38, -22, 44, 52],\n [-17, 14, -115, -55, 68, -6],\n [49, -21, -103, -70, 34, -82],\n [-20, -2, 72, -42, 20, -8],\n [-7, 10, -77, -11, 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[[-30, 85, -28, 8, 12, 65],\n [38, 61, -78, 88, -6, 71],\n [76, -43, -45, 80, -21, -8],\n [26, 7, -30, 40, -6, 17],\n [12, 54, -48, 48, 0, 54],\n [40, 70, -86, 96, -6, 80]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-71, -30, 3, 11, 2, -24],\n [-4, 52, 18, 64, 126, 107],\n [22, -22, -22, -52, -107, -30],\n [31, -40, -13, -61, -107, -111],\n [6, 12, 32, 42, 112, -49],\n [-52, -4, -4, 16, 6, 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[[11, 96, 89, -17, 15, -35],\n [-6, -54, -54, 12, -12, 24],\n [-9, -75, -61, 8, -4, 18],\n [3, 48, 97, -41, 55, -75],\n [7, 69, 83, -24, 28, -46],\n [-12, -84, -28, -16, 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 6x6 matrix:\n[[26, 59, 101, 65, -93, 42],\n [-106, 15, -16, -79, -71, -32],\n [-105, -13, -67, -84, -39, -40],\n [3, 11, 26, 0, -9, 2],\n [-41, 62, -5, 47, -50, 40],\n [6, -44, 13, -4, -117, -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, -70, 4, -128, 82, -26],\n [48, -4, 136, 54, 3, -38],\n [-61, -25, -112, -78, 66, -7],\n [-30, 16, 50, 90, 51, -64],\n [-25, -70, 35, -80, 145, -85],\n [-41, 5, -90, -24, 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[[33, 38, 93, 4, -50, -48],\n [-29, -72, -77, 12, 24, -12],\n [144, 78, 90, 147, 111, -42],\n [-73, -23, -26, 4, -149, -61],\n [56, -73, 73, 48, -3, -143],\n [67, 5, 42, -57, 156, 71]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[13, 40, 25, -31, 41, -15],\n [13, 125, -9, -57, 13, 110],\n [-67, 39, -20, -55, 35, 54],\n [6, 8, -85, -74, -3, -9],\n [56, 50, -4, 167, -236, 175],\n [-32, -129, 26, 104, -48, -67]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[51, -62, -54, 22, -10, 31],\n [-66, 16, 11, -82, -62, -99],\n [87, -62, -52, 74, 34, 93],\n [-54, 48, 41, -38, -10, -49],\n [6, -44, -40, -28, -44, -30],\n [-105, 38, 29, -120, -84, -146]]\n\nPresent the answer 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, 44, 33, -100, 132, 107],\n [-44, 5, -116, -26, -4, 121],\n [51, 22, 80, -44, 123, 9],\n [62, -73, 13, 60, -119, -85],\n [27, 47, 32, 22, 65, 8],\n [98, 13, 132, -18, 78, -41]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-52, -8, -74, 44, 99, 162],\n [-56, 54, -14, 36, 66, 111],\n [120, -76, -8, 56, -42, 14],\n [-92, 66, 22, -58, 15, -47],\n [-112, 62, 0, -54, 42, -11],\n [0, -140, -112, -36, 36, 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[[-87, 87, -86, -36, 4, 105],\n [52, 21, 76, -12, -74, -33],\n [28, 94, -28, -162, -41, 53],\n [17, -56, 18, 106, 26, -76],\n [-56, -104, 128, 80, -38, 50],\n [-37, -44, 112, -85, -66, 116]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[5, 77, 14, -82, -19, -97],\n [-49, 50, 96, -52, 41, -113],\n [16, -21, 14, 74, -9, 14],\n [10, -12, 18, -60, 58, 14],\n [-55, 48, 24, 24, -49, -83],\n [60, -62, -87, -30, 23, 134]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[103, -121, -93, 8, -156, -36],\n [-9, 79, 65, -19, 86, 67],\n [108, -49, 53, -30, -15, 178],\n [-50, 57, 27, 0, 61, -12],\n [19, -26, 26, -7, 3, 67],\n [-35, 57, 1, 2, 36, -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 6x6 matrix:\n[[0, -77, 56, 49, 21, -7],\n [-14, 10, -20, -49, -46, -22],\n [0, 77, -56, -49, -21, 7],\n [18, 39, -12, 30, 45, 33],\n [6, -20, 20, 31, 24, 8],\n [8, -23, 24, 39, 31, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[27, 44, -30, -23, -134, -40],\n [104, -44, 95, 169, 88, -137],\n [-19, 17, -113, -74, -138, 48],\n [37, 9, 112, 82, 10, -127],\n [-94, 37, -26, -106, -116, 29],\n [194, 13, -79, 88, -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[[-1, -24, 1, 24, 18, -12],\n [20, 24, -36, -40, -24, -16],\n [-22, -129, 36, 143, 102, -40],\n [27, -36, -51, 12, 18, -60],\n [-7, -54, 11, 58, 42, -20],\n [-27, -135, 45, 153, 108, -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, -55, -15, 33, -35, 131],\n [28, 101, 27, 17, 1, -109],\n [-72, -16, -83, -23, 4, 101],\n [237, 181, 217, 104, -39, 50],\n [-12, 74, -32, 32, -22, -36],\n [182, 38, 188, 46, -10, 66]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-54, 32, 14, 82, -104, 18],\n [-12, -4, 2, 136, -62, -36],\n [-32, 16, 8, 80, -72, 0],\n [63, -54, -18, 81, 63, -81],\n [-19, 2, 4, 127, -69, -27],\n [-56, 38, 15, 34, -91, 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 6x6 matrix:\n[[-103, 77, -3, 76, 39, 22],\n [-52, 70, -10, 57, 27, 65],\n [4, 200, 55, 131, -164, 98],\n [-87, 58, -24, 82, 20, -65],\n [-36, -197, -19, -147, 155, -101],\n [30, -136, -68, -130, 134, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[27, -88, -38, 68, 12, 24],\n [19, 67, 68, 103, -122, -53],\n [59, -36, -73, -17, 43, -67],\n [56, -81, -91, -8, 67, -34],\n [36, 94, 55, 71, -115, -99],\n [11, -44, -13, 43, -1, 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[[2, -18, -108, 97, 140, 138],\n [-12, -1, -42, 130, 110, 144],\n [-14, -15, 72, 16, -72, 32],\n [3, 6, -110, 116, 161, 123],\n [-81, 125, 127, 72, -169, -46],\n [28, -66, -221, -42, 272, 71]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[61, -79, 57, 88, 10, 84],\n [51, -85, 67, 88, 2, 74],\n [-111, -49, 0, -29, -54, -18],\n [3, -103, -8, 61, 2, 140],\n [68, -66, 75, 87, 8, 54],\n [10, 156, -1, -87, 8, -188]]\n\nPresent the 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, -100, 40, 32, -52, -85],\n [100, -111, 11, 146, 7, -159],\n [0, 18, 16, -38, 13, 21],\n [6, -51, -80, -56, -49, 15],\n [129, 17, -76, 8, 99, -42],\n [-4, -140, -42, 14, -113, -59]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[-10, -13, -45, 14, -40, -57],\n [-6, 29, -50, -10, -24, -48],\n [-12, -54, -30, 36, -48, -54],\n [-8, -84, 10, 48, -32, -18],\n [-10, -21, -40, 18, -40, -54],\n [14, 135, -10, -78, 56, 36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-52, 93, -52, -111, -35, 90],\n [-87, 71, 35, 0, -80, -33],\n [-31, -21, 135, 180, -100, -197],\n [123, -21, 7, 66, -50, -41],\n [-52, 80, -13, -54, -60, 31],\n [74, -75, 56, 123, -5, -102]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, -3, 8, -31, -32, -47],\n [68, 65, 31, 109, 120, 25],\n [41, 62, 47, 62, 29, 45],\n [20, 20, 32, -28, -28, -96],\n [-13, 22, 25, 6, -55, 97],\n [8, 51, 57, 7, -67, 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[[-9, 28, 56, -95, 20, -46],\n [-21, 27, -3, -9, 18, -30],\n [-5, 5, 67, -76, 47, -34],\n [-5, 29, 3, -43, -24, -22],\n [31, -43, -5, 29, -28, 50],\n [1, 24, -28, -9, -52, -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[[-86, 39, 59, -20, 119, -35],\n [-78, -40, 100, -19, 70, -97],\n [46, -13, -27, 15, -79, 16],\n [25, -68, -83, 14, -37, -8],\n [66, -81, -69, 17, -94, 3],\n [-4, -75, 19, -20, 45, -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[[134, 78, 44, 61, 56, 23],\n [-78, -1, -76, -66, -57, -40],\n [-128, -211, 298, -102, 184, 100],\n [-50, -35, 72, -51, 53, -23],\n [-93, -95, 144, -86, 78, 14],\n [3, -21, 158, -29, 110, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, 0, 6, -24, -12, 0],\n [41, 49, 1, -25, 26, -28],\n [62, 70, -2, -22, 44, -40],\n [19, 14, -7, 22, 22, -8],\n [-39, -42, 3, 6, -30, 24],\n [2, 0, -2, 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[[0, -1, -9, 16, -12, -27],\n [21, 13, -9, 37, -26, -76],\n [-24, -16, 0, -24, 16, 56],\n [-15, -14, -36, 49, -38, -73],\n [30, 23, 27, -18, 16, 11],\n [-39, -32, -54, 57, -46, -71]]\n\nPresent 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, 28, -33, 36, 50, 13],\n [27, 20, -51, 60, 22, -25],\n [41, 36, -31, 32, 70, 31],\n [-28, -24, 26, -28, -44, -14],\n [25, 16, -68, 82, 4, -54],\n [20, 12, -61, 74, -2, -53]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[137, 153, -131, 24, -14, -100],\n [41, 29, -4, 2, -4, -21],\n [-38, -16, -129, -33, 22, -11],\n [-195, -175, 108, -18, 12, 119],\n [77, 141, -68, 5, 72, 3],\n [127, 47, -104, -116, 76, -47]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[6, 44, -114, -57, -36, -30],\n [-110, -59, -154, -77, -127, -76],\n [-11, 1, 35, 17, 57, -14],\n [10, 10, 114, 0, 54, 64],\n [-177, -118, -90, -98, -155, -46],\n [-55, -7, -31, -76, -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[[-6, -44, -14, 34, -16, 34],\n [18, -33, 9, 30, 48, 63],\n [3, 17, 6, -13, 8, -12],\n [21, -1, 18, 5, 56, 36],\n [6, -16, 2, 14, 16, 26],\n [-6, -44, -14, 34, -16, 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[[-32, 14, 42, -3, 38, 0],\n [96, -36, -44, 10, -84, -16],\n [-100, 28, -84, -12, 40, 42],\n [-92, 38, 90, -9, 98, 6],\n [-128, 44, 4, -14, 92, 32],\n [-118, 40, -4, -13, 82, 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 6x6 matrix:\n[[-27, 75, 7, 45, 15, -7],\n [75, 25, 120, -4, 105, -82],\n [10, -90, -150, 30, -130, 110],\n [-56, 70, -59, 65, -40, 39],\n [35, 98, 53, 82, 61, -36],\n [-85, 16, -99, 20, -83, 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[[3, 22, 59, -94, 11, 60],\n [-48, 96, 93, 27, 87, -48],\n [-31, -45, 9, 40, -43, 20],\n [-9, 23, -36, 117, -36, -52],\n [-17, -5, -109, -69, 64, 64],\n [-55, 95, 112, 42, 77, -52]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[130, 36, -56, -12, -36, -58],\n [77, 130, 42, -66, 50, -77],\n [10, 0, -31, -58, -34, -11],\n [35, -74, -24, 144, -6, 32],\n [54, 100, 11, -61, 10, -64],\n [-45, 18, 74, -95, 78, 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[[-13, -88, 27, -26, -144, -41],\n [22, -42, 61, -29, -9, 75],\n [-40, 64, -104, 48, 0, -136],\n [-15, -44, -1, -8, -90, -49],\n [-2, 44, -28, 18, 54, -8],\n [-20, 66, -71, 37, 45, -69]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[31, 83, -108, -127, 52, 38],\n [125, 44, 22, -54, 13, -43],\n [31, 8, -86, 6, 75, -14],\n [-89, -15, -56, -9, 22, 144],\n [17, 10, 142, -23, -112, -57],\n [68, 48, 28, -57, -25, -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[[-109, 26, -84, -84, 125, 103],\n [4, -52, -10, -95, -137, 27],\n [-45, 22, 69, 29, 94, -16],\n [-21, 6, -69, -39, 14, 48],\n [9, 34, 120, 35, -90, -34],\n [10, 20, -160, 40, 160, 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[[85, 30, 25, 5, 75, 105],\n [100, 90, 2, -38, -20, -8],\n [-98, -121, 19, 71, 90, 92],\n [-64, -78, 31, 77, 80, 80],\n [56, 43, 2, -20, 0, 10],\n [-51, -57, -26, -22, -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[[74, 11, 42, 35, -31, 34],\n [-73, 82, 80, -74, -44, 2],\n [-1, 72, -2, 79, 5, 15],\n [-13, 4, 112, -61, -117, 93],\n [-104, 67, -93, 21, 104, -97],\n [1, -66, -141, 54, 111, -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[[-45, -38, 47, -35, -96, 37],\n [45, -7, 54, 80, 49, 38],\n [23, 63, -8, 48, 83, -100],\n [-30, -12, 38, -19, -78, 42],\n [-17, -56, 72, 11, -88, 32],\n [-12, 15, -110, -90, -64, 63]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-22, 15, -48, 16, 26, -27],\n [117, -135, -20, -60, -13, -77],\n [-109, 149, -62, 36, 71, 15],\n [-22, -106, 30, 116, -9, 116],\n [-49, 78, -130, 12, 147, 2],\n [120, -38, 0, -128, 44, -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[[-24, -85, -15, 93, -39, 48],\n [-51, -22, 39, 66, -93, 102],\n [-64, 24, 72, 40, -120, 128],\n [34, -48, -54, 8, 66, -68],\n [15, -82, -51, 54, 33, -30],\n [-46, 29, 57, 19, -87, 92]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[-172, -162, 104, -100, -94, -212],\n [-24, 48, 133, 4, -114, -20],\n [98, 174, 31, 64, -7, 132],\n [34, 79, 30, 30, 83, 70],\n [-54, -120, -119, -68, -15, -104],\n [17, -12, -38, 2, -69, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[40, -14, -2, 20, 70, -46],\n [-14, 28, 37, -40, -41, 15],\n [-46, -28, -67, 40, -49, 55],\n [-18, 0, -9, 0, -27, 21],\n [18, -21, -24, 30, 42, -20],\n [18, 21, 42, -30, 12, -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[[-44, 42, -13, 1, -14, -53],\n [-21, 36, -24, -3, -3, -48],\n [-33, 12, 12, 5, -15, -12],\n [105, -24, -54, -19, 51, 18],\n [-38, 54, -31, -3, -8, -71],\n [-16, 72, -68, -12, 8, -100]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[-6, 6, 0, 18, 4, -12],\n [6, 42, 24, -54, 24, 72],\n [-6, 66, 30, -27, 39, 63],\n [-12, 60, 24, 0, 36, 36],\n [-20, 88, 34, 9, 53, 45],\n [-26, 70, 22, 45, 43, 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, 71, -61, -60, 81, 66],\n [-118, 95, -7, 10, -56, 41],\n [84, -33, -2, -33, 6, -43],\n [75, -45, 56, -61, 37, 6],\n [-90, 18, 43, 33, -18, 50],\n [-39, 11, 55, -24, 19, 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 6x6 matrix:\n[[38, 139, 92, 8, 35, 40],\n [-43, 51, 22, 13, 72, -95],\n [-109, -7, -95, 17, 133, 58],\n [21, 64, 17, 38, 64, 58],\n [21, -68, -47, -86, 2, -35],\n [56, -87, 9, -85, -90, -149]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[55, -112, 23, 42, 98, 67],\n [115, -32, -76, 33, 72, 64],\n [-29, 156, -41, -34, 0, -25],\n [-60, 102, -6, -87, -84, -81],\n [-45, -77, 33, -12, -58, 5],\n [124, 5, -29, -80, 31, -90]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-226, 138, 174, 128, 44, 209],\n [-8, -114, -47, 36, -15, 3],\n [114, 0, -51, -123, -78, -105],\n [-7, 63, 28, -42, 105, 14],\n [-78, 26, 42, 60, 156, 78],\n [-126, 20, 67, 135, 54, 115]]\n\nPresent the 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, -34, -29, 102, -46, 30],\n [22, -36, -9, 90, -14, 3],\n [-25, 14, 18, 12, -14, 17],\n [103, -52, -87, 66, -48, 23],\n [6, -48, 25, -18, 118, -113],\n [-80, 36, 72, -72, 64, -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, -71, 41, -117, -22, 18],\n [-25, 51, -17, 80, 39, -32],\n [29, -66, -89, -82, 108, -2],\n [-23, 32, -12, 49, 63, -42],\n [16, -12, -40, -8, -4, 24],\n [-18, 50, 37, 69, -63, 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[[-38, 25, 72, -85, -154, 133],\n [-59, 117, 61, -28, -97, 77],\n [-30, 10, 70, -98, -76, 16],\n [-13, -17, 22, -74, -50, -15],\n [53, -77, -72, 73, 99, -46],\n [21, -27, -24, 24, 78, -75]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[127, -118, -38, 97, -46, 84],\n [-50, 44, 9, -90, 155, -108],\n [110, -78, -10, 22, 110, -46],\n [32, -140, 3, 8, 35, 57],\n [-25, 82, -13, -46, 106, -173],\n [71, -21, 19, 1, 67, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[-115, -80, -131, 54, 57, -92],\n [55, 57, 81, -57, -16, 42],\n [23, -46, 24, 149, -8, 63],\n [-110, -44, -70, -64, 78, -64],\n [-102, -26, -21, 49, 117, -57],\n [-7, 66, -92, -55, -30, -143]]\n\nPresent the 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, 98, 41, 13, 74, 109],\n [-42, -68, 17, 17, 41, 41],\n [88, 72, 34, 174, 22, 78],\n [-66, -54, -1, -71, 22, 1],\n [-76, -42, 27, -25, 70, 71],\n [-19, 82, 16, -37, 34, 47]]\n\nPresent the answer 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, 64, 73, 46, -86, -17],\n [90, -23, 47, 93, -96, -12],\n [121, -4, -43, 158, 86, 20],\n [97, 49, 17, 141, 24, 3],\n [97, -77, 9, 59, -28, -7],\n [36, 85, 38, 87, -6, -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, 40, -62, -16, 62, -86],\n [-36, 42, 27, 99, -90, 24],\n [-96, 40, 78, 92, -50, -54],\n [-27, -45, 36, -81, 90, -63],\n [15, 5, -30, -37, 58, -53],\n [0, -44, 32, -22, -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[[79, 43, -151, -55, 50, 52],\n [-66, -53, 166, 26, 27, 32],\n [70, -69, -89, -31, 12, 86],\n [20, -175, 2, -6, -23, 100],\n [-71, 88, -42, -20, 2, -90],\n [-30, 40, 42, -6, 42, 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[[-54, -22, 102, -18, 20, -44],\n [-57, 75, 33, -51, -54, -66],\n [53, 60, -65, 23, -43, 54],\n [-56, 31, 80, -32, -19, -52],\n [-10, 80, -28, -26, -59, -20],\n [-121, 11, 143, -71, -5, -122]]?\n\nPresent the 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, -61, -57, 48, 119, -78],\n [30, 56, -51, -50, -134, 104],\n [47, -96, 18, 32, 126, -49],\n [-77, 102, -47, -60, -92, -40],\n [-7, -20, -39, -64, 68, -113],\n [32, 57, -78, -65, -103, -28]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[-32, 17, 52, -39, 95, 57],\n [16, -5, -20, 24, -8, -54],\n [100, 56, -28, -56, 5, 9],\n [-154, -4, 44, 75, -14, -26],\n [196, 22, -76, -71, -26, -6],\n [-127, -20, 40, 68, 17, -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[[-92, -72, -7, 3, -5, 62],\n [160, 93, -7, -19, 56, 3],\n [68, -28, -24, -39, 32, 0],\n [-28, 9, -149, -136, 130, -13],\n [-62, 89, -5, 25, 23, 54],\n [-82, 76, -187, -151, 168, -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[[-69, -52, 81, 2, 36, 16],\n [58, 1, 31, 15, 96, -41],\n [-15, -11, 38, 19, 20, 5],\n [59, 7, -111, -64, -47, -106],\n [-35, 15, 85, 74, 27, 100],\n [-44, -22, 34, -2, 3, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[72, -14, 25, -84, -76, 22],\n [152, -78, 77, -32, -112, 107],\n [-120, 70, -65, 0, 80, -95],\n [-24, -14, 1, 84, 44, 16],\n [-48, 4, -14, 72, 56, -8],\n [-8, 10, -7, -16, 0, -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 6x6 matrix:\n[[-19, -37, -56, 47, -17, 45],\n [-29, -72, -42, 53, -20, 66],\n [-39, -42, -60, 51, -39, 69],\n [36, -7, 6, 0, 43, -37],\n [79, 12, 6, -7, 88, -90],\n [30, 0, 46, -26, 37, -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 6x6 matrix:\n[[-7, 0, 7, 42, -7, -63],\n [-17, -10, 2, 46, -2, -75],\n [-15, -10, 0, 34, 0, -57],\n [-93, -110, -72, -58, 72, 21],\n [134, 160, 106, 92, -106, -42],\n [58, 70, 47, 44, -47, -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[[-50, 1, -14, -25, -47, 5],\n [-90, 33, -46, -71, -69, -17],\n [0, 24, -16, -20, 12, -20],\n [-40, -22, 4, -1, -49, 23],\n [-60, 84, -72, -99, -15, -63],\n [100, -80, 80, 115, 55, 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[[87, -39, 48, 24, 75, -51],\n [-85, 59, -38, -22, -89, 61],\n [-23, -116, -5, 63, 9, -79],\n [24, 25, -33, -69, 60, 30],\n [-106, 29, -51, -11, -94, 46],\n [121, 53, 74, -8, 65, 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[[95, 41, -116, 72, -68, 65],\n [-66, 78, 48, -20, -70, -28],\n [45, 101, -10, 102, -66, 69],\n [-27, 79, -80, -20, -112, -25],\n [9, -101, -44, -58, 65, -32],\n [-84, -10, 137, -117, -44, -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[[-11, 85, -25, 20, 19, -25],\n [3, 54, -16, 57, -81, -27],\n [86, 1, -29, -27, 170, -68],\n [-74, 56, 28, -68, 4, 80],\n [121, -26, 3, -11, 16, -46],\n [78, -86, 16, 44, -120, -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, 10, 11, 33, 42, -49],\n [3, 5, -54, -53, -30, 41],\n [27, 23, 128, 175, 151, -48],\n [-26, -18, 1, -5, -33, -52],\n [-53, 9, 9, -6, 37, -75],\n [9, 9, 11, 32, 31, 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 6x6 matrix:\n[[-9, 8, -92, 21, 16, -35],\n [-135, -40, 93, -91, -180, -130],\n [23, 47, 48, 71, -1, -21],\n [-106, -100, -19, -143, -110, -56],\n [-36, -34, -14, -78, -14, 16],\n [-51, 44, -1, 13, -40, -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[[57, 65, 1, 160, -55, -25],\n [-45, -92, -107, 120, -19, -5],\n [29, 94, 30, 75, 13, -35],\n [-31, 18, 43, 70, 33, -45],\n [40, 69, 171, -125, 2, 0],\n [85, 46, 109, -50, -77, 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[[77, 3, 11, -33, -37, 12],\n [-93, -33, -17, 25, 69, -2],\n [84, 27, 15, -24, -60, 3],\n [20, -6, 2, -12, -4, 6],\n [-30, 96, 8, 62, -66, -46],\n [-96, 81, -3, 84, -24, -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[[-19, -2, 40, -30, -59, 61],\n [-52, -46, 80, -60, 8, 38],\n [-8, 9, 24, -18, -66, 57],\n [-53, -49, 80, -60, 17, 32],\n [21, 19, -32, 24, -5, -14],\n [-10, 3, 24, -18, -48, 45]]\n\nPresent the 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, 17, 17, 1, 26, 2],\n [44, 8, 8, -8, -28, 56],\n [64, 23, 23, -13, -33, 96],\n [16, -38, -38, 2, -38, -32],\n [9, 13, 13, -3, 2, 26],\n [24, -32, -32, 0, -40, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[12, -33, -21, -28, -50, 18],\n [-1, 54, -70, -25, -30, 60],\n [26, -114, 14, -38, -80, -12],\n [-9, 36, 0, 15, 30, 0],\n [9, 9, -63, -39, -60, 54],\n [6, 66, -126, -58, -80, 108]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[59, 44, 59, 50, 51, 17],\n [33, -41, 83, 16, 25, 44],\n [70, 40, 106, 5, 139, 101],\n [-122, 51, -82, -97, -2, 46],\n [97, -23, 55, 5, 100, 29],\n [-34, -71, 14, -87, 38, 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 6x6 matrix:\n[[-55, -52, -27, -48, 103, 56],\n [59, 36, -42, 21, -107, 55],\n [-164, -109, 142, 79, 17, -113],\n [-141, -102, 49, 139, -50, -51],\n [116, 85, -97, -88, 79, 38],\n [-23, -6, 2, 137, -95, -73]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[-9, -9, -3, -14, 20, -27],\n [135, 135, 135, 90, -36, 0],\n [63, 63, 51, 58, -52, 54],\n [36, 36, 12, 56, -80, 108],\n [15, 15, 15, 10, -4, 0],\n [-93, -93, -81, -78, 60, -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[[41, 95, 25, -96, -28, 46],\n [102, 25, 109, 11, -9, 99],\n [8, 120, 35, -121, 8, 10],\n [-5, -20, -143, -26, -109, 11],\n [64, -60, 90, 98, 20, 56],\n [-27, 90, -35, -112, -13, -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[[-65, 50, -15, -20, -35, 30],\n [33, -10, -25, -16, 19, -26],\n [-117, 90, -27, -36, -63, 54],\n [70, -100, 114, 100, 34, 0],\n [-46, 70, -84, -73, -22, -3],\n [42, -40, 26, 26, 22, -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[[-16, -130, -38, 112, -52, 4],\n [106, -43, 31, 36, 99, 23],\n [60, -22, 46, 8, 82, 18],\n [-40, -63, -51, 62, -77, -8],\n [8, -5, -19, 12, -12, -2],\n [-76, -3, -27, 2, -77, -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, -21, 77, -120, 11, -75],\n [37, -112, -27, 20, -7, -42],\n [-41, -11, 24, -131, 30, -60],\n [23, -5, -79, 36, 63, 97],\n [23, 52, 218, -73, -6, -19],\n [60, -98, 44, -140, 160, 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[[-24, 33, -69, -77, -133, 6],\n [-47, -12, 36, 74, 12, -149],\n [-59, -47, 77, 112, 116, -89],\n [33, 58, -34, 64, 42, -89],\n [55, -69, 111, 24, 68, 1],\n [-4, 50, -80, -59, -97, 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[[122, 77, -139, 274, 88, 7],\n [116, -105, 23, -28, -87, -86],\n [4, -25, 89, -46, 45, -65],\n [-16, 56, -54, 74, 31, 37],\n [-47, 23, -2, -24, 52, 83],\n [14, -56, 46, -68, -102, -100]]?\n\nPresent the 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, 82, -35, -70, 60, 0],\n [-9, 13, 19, 149, -29, 48],\n [63, 83, -28, 19, 22, 20],\n [7, -36, 15, -112, 11, -13],\n [-21, -120, 14, 85, -57, -55],\n [26, 22, 36, -45, -13, 64]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-15, -9, -66, 3, 85, 80],\n [186, 155, -70, 11, 157, 29],\n [-78, -91, 49, 13, -63, -3],\n [49, 103, -19, -49, -29, -70],\n [98, 56, 9, 105, 12, -15],\n [-3, -43, 54, 0, -19, -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, 15, 0, -9, 3, -6],\n [1, 12, -70, -45, -69, 40],\n [45, -32, -30, 3, -37, 32],\n [-20, 24, -40, -36, -36, 16],\n [-10, 1, 40, 21, 41, -26],\n [-35, 31, -10, -24, -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[[-33, 72, 30, 30, 15, -18],\n [-19, -48, -22, 50, 13, -6],\n [-37, 36, 14, 50, 19, -18],\n [-22, -34, -16, 50, 14, -8],\n [74, 10, 8, -130, -42, 32],\n [40, -132, -56, -20, -16, 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[[-111, 18, 71, 49, -20, 25],\n [-116, -16, 93, 155, 2, 34],\n [11, -26, 18, -112, -6, 3],\n [-44, 20, 26, -91, -26, 7],\n [-1, 10, -10, 51, 4, -2],\n [95, -110, 9, -40, 42, 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[[-36, -61, -6, 18, 46, -62],\n [94, 90, 69, -113, 52, -34],\n [-17, -26, 48, 53, 149, -9],\n [76, 116, 117, -130, 103, -30],\n [151, 185, 99, -83, 110, -85],\n [-33, -88, 54, -22, 132, 33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[-53, 20, 93, -17, -31, 102],\n [12, 40, -42, 38, 24, -38],\n [30, -57, -63, -42, -15, -72],\n [-4, -2, -72, -46, -42, -66],\n [0, 58, -57, 29, 8, -47],\n [-26, -7, -42, -71, -67, -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[[-21, 12, -47, -12, 8, 14],\n [38, 20, -45, -75, -8, -61],\n [-18, 0, 13, 24, 2, 20],\n [-25, -60, -14, 33, -17, 58],\n [12, -40, 116, 52, -42, -2],\n [53, 4, -89, -87, 17, -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[[1, -143, 43, 4, 35, 79],\n [-145, 7, -116, 18, -77, 44],\n [-69, -79, 6, -29, 1, -17],\n [35, 195, -78, 37, -53, -13],\n [23, 38, -37, -20, -32, 46],\n [26, -8, -36, 9, -24, 109]]\n\nPresent the 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, 90, -66, -10, -26, 2],\n [-120, 49, -44, -76, 107, -128],\n [7, -106, -84, 11, 66, -150],\n [-74, 70, -25, 25, 143, -113],\n [36, -49, -86, -44, -46, -17],\n [-99, 53, 118, 85, 48, -33]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[62, -108, 36, 8, 36, 64],\n [-30, -56, -43, 14, -103, -100],\n [-55, 2, 47, -253, 17, 73],\n [-37, -58, -130, 17, -88, -43],\n [-79, 58, 14, -11, -40, 89],\n [18, 18, 29, -29, 71, 99]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[139, -100, -24, -79, -48, -53],\n [-97, 90, 3, 48, 53, 3],\n [40, 40, -13, -51, 64, -124],\n [82, -20, 47, -69, 34, -82],\n [-17, 40, 74, -9, 58, -25],\n [22, -20, -52, -6, -26, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[-26, 30, -73, -41, 70, 32],\n [36, 66, -66, 51, 56, 3],\n [-10, -37, 70, 116, 174, -139],\n [49, 50, -47, -77, -82, 69],\n [-25, -39, -78, -94, 48, 1],\n [12, 18, 8, -57, -42, 36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[-14, -28, 168, 21, 7, 7],\n [11, 52, -77, 55, 0, -2],\n [9, 34, -127, -44, -47, -21],\n [-7, -67, 86, 25, 87, 35],\n [-14, -32, 154, 2, 0, 4],\n [-7, 79, 122, 44, -104, -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[[55, 117, 9, -32, 94, -175],\n [-31, -11, -89, 131, 6, 223],\n [29, 17, -77, 107, 3, 109],\n [-8, -84, -29, -12, -32, 41],\n [-14, -86, 61, -104, -61, -79],\n [33, -155, -42, -7, -112, 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[[-20, 105, 28, -122, -2, -18],\n [17, 94, 58, -117, -30, -23],\n [-47, -116, -30, 151, 70, -43],\n [-70, 61, -50, -58, 44, 14],\n [-106, 10, -62, 12, 90, -20],\n [-96, 0, 39, 23, 101, -131]]\n\nPresent the 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, -26, 26, -44],\n [-105, -29, 52, -23, -15, -17],\n [52, 4, -40, -32, 56, -68],\n [92, 28, -42, 31, 1, 34],\n [-80, -16, 48, 8, -40, 32],\n [41, -3, -40, -51, 73, -99]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-97, -92, 10, 30, 17, -9],\n [146, 19, 22, -112, -107, 24],\n [-10, 28, 6, 88, 30, 4],\n [74, -11, -108, -52, -119, 64],\n [-32, 74, 0, 72, 88, -22],\n [-44, -133, 12, 0, -65, 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[[7, 21, 7, -14, 7, 35],\n [17, 11, -55, -42, -39, 21],\n [-6, 7, 39, 17, 29, 10],\n [-13, 11, 77, 36, 57, 15],\n [14, 17, -31, -33, -21, 30],\n [10, 5, -35, -25, -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[[49, -28, -46, -10, -45, -27],\n [-82, 90, 45, 49, -35, -49],\n [-92, -28, 66, -22, -70, -34],\n [-60, 36, 86, 6, 190, 130],\n [120, -40, -122, -6, -130, -90],\n [-18, 120, -8, 72, -10, -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[[18, 55, -52, -84, 17, -42],\n [33, 33, 46, -72, 36, -27],\n [56, -48, 38, -10, 40, -34],\n [-27, 115, 41, -93, 2, 12],\n [36, -76, 2, 42, 16, -18],\n [-21, -78, -38, 108, -33, 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, -24, 13, -78, -7, 63],\n [9, -25, 25, -64, 25, 0],\n [47, -103, 1, 32, 106, -29],\n [-8, 9, 26, -66, -2, -7],\n [19, -28, -13, 2, 0, 50],\n [-40, 80, 18, -64, -73, 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[[110, -19, -96, 46, -56, -27],\n [140, 28, -97, 65, 18, 21],\n [-29, 59, 82, 21, -80, -80],\n [52, 165, -30, 83, 6, -45],\n [91, -9, -50, 59, -172, -120],\n [-152, 21, 109, -29, 38, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-81, 54, -20, -8, -12, -14],\n [42, 36, 33, -42, 64, 40],\n [-12, -44, 28, 40, 34, 36],\n [68, -58, 36, 44, 99, 35],\n [-58, -23, 50, 30, 37, 80],\n [-17, 55, 28, -70, -13, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[-14, 10, 28, 16, 24, -2],\n [-16, -3, 16, 8, 3, 3],\n [-39, -73, -63, -4, -134, 69],\n [-132, -44, 126, 40, 8, 12],\n [-20, -20, 25, -20, 0, -20],\n [-13, -62, -73, -20, -119, 50]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[9, 15, 9, -7, 8, 0],\n [-77, -70, -27, 71, -74, -25],\n [-76, 25, 54, 88, -82, -65],\n [-36, -60, -36, 28, -32, 0],\n [12, 90, 72, 4, 4, -30],\n [-63, 0, 27, 69, -66, -45]]\n\nPresent the 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, 37, 4, 28, -75, -19],\n [79, 96, -30, 72, -107, -54],\n [27, -88, 56, -94, 122, -2],\n [23, 146, -41, 120, -182, -31],\n [-67, 116, -10, 80, -101, 10],\n [83, 46, -67, 78, -135, -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[[32, -48, 14, -14, 3, -18],\n [10, -107, 21, 20, -54, 59],\n [42, -165, 15, 17, -60, 62],\n [-38, 3, 31, 40, -36, -61],\n [-14, 110, -26, -19, 52, -40],\n [12, -15, 17, -34, 10, 78]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[19, 45, 112, -35, -103, -16],\n [-149, 31, -75, 10, 16, 30],\n [-34, 56, 16, 128, 62, -42],\n [-75, 47, 6, 41, -55, -52],\n [0, 36, 81, -53, 17, 96],\n [-40, 20, 40, -100, -16, 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[[-30, 52, -74, 19, -73, -68],\n [-66, 26, -10, 5, -17, -34],\n [154, 27, -34, 52, -46, -44],\n [52, 46, -58, 6, -8, -180],\n [70, -30, -41, -25, -7, 35],\n [-16, 37, -48, 17, -51, -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[[-46, 72, -110, 26, 112, -2],\n [-27, 15, -99, -45, 60, -27],\n [-96, -112, -154, -76, 28, 10],\n [43, 110, 42, 53, 38, -14],\n [72, 157, 106, 106, 32, -4],\n [-22, 27, -62, -4, 52, -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[[1, -38, -24, 16, 56, 160],\n [231, -133, 25, -30, -119, -6],\n [-84, 93, -57, 70, 5, -44],\n [-47, 103, 0, -34, -55, -46],\n [-123, 40, -46, 100, 94, -56],\n [36, -74, -22, 56, 42, 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[[32, 40, -125, -86, 27, -20],\n [-120, -175, -48, 19, 78, 24],\n [28, 53, -56, -64, 56, -62],\n [158, 233, 96, 10, -55, -28],\n [36, 93, 151, -46, -122, -142],\n [12, -17, -28, 29, 33, 72]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[113, -77, -13, -2, 44, -45],\n [60, -28, 4, -8, -20, 30],\n [-34, 56, 15, 33, -144, 192],\n [113, -81, -11, -16, 64, -75],\n [-49, 29, 17, -42, 14, -36],\n [30, -28, 9, -53, 60, -90]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-28, -2, 23, 27, -33, 42],\n [-12, 42, 57, 63, -117, 108],\n [56, 24, -24, -30, 18, -42],\n [36, 44, 16, 15, -57, 33],\n [12, 48, 42, 45, -99, 81],\n [24, 56, 40, 42, -102, 78]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[44, -70, 8, 44, -14, 16],\n [-82, -36, -94, 30, 54, 80],\n [22, -31, 76, 22, -27, -24],\n [19, 55, 79, -37, -30, -64],\n [35, -64, 65, 43, -27, -8],\n [60, 8, 102, -8, -48, -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[[-50, 53, -18, 100, -81, -110],\n [8, -2, 9, -7, 9, 5],\n [-4, -26, -30, -34, 12, 50],\n [-38, 5, -47, 27, -40, -15],\n [4, -10, -4, -16, 10, 20],\n [-28, 16, -23, 37, -37, -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[[-50, -78, -22, 42, -79, 59],\n [32, 75, -49, -31, 76, -49],\n [-4, 99, -45, -113, 115, -159],\n [26, -6, -6, 46, -15, 61],\n [8, 45, -27, -35, 49, -51],\n [-18, -57, 31, 35, -60, 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[[86, 62, 51, 121, -32, -17],\n [-46, 27, 70, 33, 12, 128],\n [-74, -91, -22, -114, -70, 4],\n [24, -59, 13, -22, -4, -53],\n [6, 38, 58, 59, 76, 70],\n [-54, -45, -27, -81, 88, 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[[-92, -52, 48, -52, 100, -24],\n [42, 51, -53, 18, -60, 54],\n [-18, 27, -33, -18, 0, 54],\n [1, 8, -9, -1, -5, 12],\n [16, -43, 51, 20, 10, -78],\n [71, 55, -54, 37, -85, 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 6x6 matrix:\n[[-6, -2, -18, -10, 5, 71],\n [31, 43, -44, 115, 112, -68],\n [-74, 22, -128, -20, 16, -56],\n [54, -43, 126, -23, -65, 103],\n [40, -11, 128, -77, -22, 92],\n [-16, -41, -84, 106, -62, -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[[7, 3, -61, 50, 58, 49],\n [-44, -27, 55, -32, -66, -42],\n [135, 87, -1, -46, 50, -7],\n [106, 69, 27, -60, 14, -28],\n [-45, -27, 81, -54, -90, -63],\n [14, 12, 120, -108, -104, -98]]\n\nPresent 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, 97, 3, -61, 1, -86],\n [-56, -77, 7, 63, -7, 70],\n [56, 48, -28, -76, 20, -48],\n [52, -30, -80, -104, 52, 12],\n [-24, -91, -39, 1, 23, 74],\n [-52, 1, 59, 91, -39, 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[[42, 62, 80, 28, -17, 22],\n [11, -115, 172, -129, 23, 30],\n [20, -26, -3, -67, -21, 65],\n [-12, -88, 118, -56, 38, 6],\n [4, 70, 25, 61, -4, -105],\n [27, 33, -134, 9, -40, 178]]\n\nPresent the 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, -44, 19, -14, 16, 2],\n [92, -2, -42, -75, 7, -69],\n [-64, -52, 26, 26, -46, -2],\n [32, -88, 60, 1, 45, 42],\n [-8, 70, -41, -2, -14, -19],\n [60, 14, -18, -34, 28, -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[[24, -32, 48, -16, -40, -64],\n [53, 44, -78, 26, 61, 128],\n [81, -22, 24, -8, -23, -14],\n [-40, -4, 12, -4, -8, -28],\n [-91, 21, -21, 7, 21, 7],\n [-66, 2, 6, -2, -2, -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[[46, 32, -26, 50, 40, 70],\n [-43, -24, 9, -69, -52, -95],\n [-26, -24, 30, -6, -8, -10],\n [73, 70, -91, 7, 16, 15],\n [48, 26, -8, 80, 60, 110],\n [74, 67, -82, 22, 26, 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[[-49, 46, 38, 63, 36, 46],\n [34, 4, -28, -38, -16, -16],\n [-31, -102, 30, 19, -10, -29],\n [10, 84, -12, 2, 16, 32],\n [79, 30, -66, -85, -32, -28],\n [54, -4, -44, -62, -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 6x6 matrix:\n[[-50, -41, -67, -8, 43, 87],\n [-57, 7, -84, -78, 32, 22],\n [-71, -49, -66, -22, 52, 96],\n [15, -14, 21, 36, -4, 13],\n [-43, 1, 24, -50, 8, -18],\n [14, -30, 40, 56, -2, 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[[33, -15, -55, 52, -122, 134],\n [73, -81, 15, 18, -38, 66],\n [-40, 85, 55, 18, 52, -64],\n [42, -25, 125, 0, 100, -80],\n [91, -61, -5, 76, -126, 162],\n [78, -80, -70, 53, -158, 186]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[-61, 70, -23, -83, -9, -27],\n [26, 101, -14, 52, -28, 125],\n [14, -9, 65, -4, 100, -161],\n [-32, -62, 53, 29, 85, 31],\n [-54, -7, 43, -46, 114, -61],\n [-34, 49, -14, -8, -8, 89]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-66, -8, -76, 85, -38, 65],\n [44, -25, 19, -104, 12, -5],\n [-66, 34, -39, 135, -18, 32],\n [-36, -130, -119, -28, -88, 37],\n [-58, 106, 8, 153, 26, 41],\n [0, -41, -34, -44, -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 6x6 matrix:\n[[109, 38, 95, 63, -62, -130],\n [58, 101, 161, 147, 22, -112],\n [-84, 39, -12, -19, 86, 45],\n [-107, -6, -20, 45, 90, 129],\n [-103, -10, -63, -41, 74, 104],\n [80, -28, -24, -68, -88, -76]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[-19, 4, -36, 17, -8, 12],\n [-32, 74, -41, 105, -49, -74],\n [-39, 58, -47, 80, -43, -58],\n [-19, -34, -44, -29, 12, 62],\n [0, 19, 4, 23, -10, -25],\n [25, 62, 67, 54, -25, -110]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[14, -19, 75, -45, -98, -94],\n [-54, -84, 2, -21, 53, 106],\n [66, 114, 6, 66, -42, -36],\n [-97, -68, -70, -3, 104, -10],\n [-68, -100, -17, -34, 71, 94],\n [-68, 58, 41, 177, 46, 92]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[10, -31, 7, 45, 23, 15],\n [-22, 51, -18, -44, -35, -30],\n [-12, -77, -1, 56, 33, 51],\n [-154, 20, -110, 77, -56, -18],\n [-98, 111, -86, 54, -71, -90],\n [-82, -26, -61, 126, -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 6x6 matrix:\n[[76, 28, -104, -37, 8, 53],\n [-25, -135, 6, -27, 35, 95],\n [27, 169, -22, 5, -20, -54],\n [100, -64, -47, -72, -6, 120],\n [77, -111, -66, 39, 44, 68],\n [-17, 114, -57, 101, 13, -140]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-11, 97, 3, 30, 11, -18],\n [74, -34, -30, 24, 34, 18],\n [-41, -5, 17, -22, -23, -6],\n [95, -13, -39, 42, 49, 18],\n [-46, -64, 20, -46, -36, 3],\n [58, 4, -24, 30, 32, 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[[-117, 147, -96, 3, -155, 42],\n [-58, -30, -44, 136, 69, 68],\n [20, 55, -31, -43, -51, 128],\n [-108, 7, -31, 183, 11, -24],\n [20, 63, 41, 39, -88, 32],\n [115, -150, 85, 30, 170, 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[[-71, -104, -121, 32, 142, 78],\n [52, 50, 4, 46, 0, 40],\n [5, -13, -53, 45, 64, 66],\n [27, 63, 87, -19, -91, -84],\n [24, 41, 64, -33, -78, -52],\n [105, 113, 13, 115, 7, 68]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[-106, -33, -92, -87, 61, 12],\n [2, -51, -80, -112, -88, -60],\n [-46, 66, -35, -88, 112, 29],\n [56, -143, -108, 34, -57, 37],\n [70, -18, -33, 72, 158, 81],\n [-88, 22, 88, 69, -47, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-69, -52, 53, -149, 2, -24],\n [-26, 71, -155, -130, -35, 62],\n [-11, -143, 89, -25, -53, -94],\n [15, 115, 6, -89, 87, 112],\n [146, -67, 61, -94, 79, -4],\n [28, -70, -114, -20, -18, -84]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-78, -135, 18, -24, 78, -143],\n [-48, -108, -156, -66, 54, -194],\n [-30, -34, 70, 86, 96, -92],\n [49, 87, 20, -21, -131, 198],\n [-34, -67, -94, -25, -25, -62],\n [-32, -47, 88, 13, 79, -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[[33, 36, 18, 93, 90, -111],\n [171, -184, -33, -61, -70, -66],\n [-72, 54, -14, 84, 39, 5],\n [37, 24, 68, -45, -36, -23],\n [44, -58, -30, 29, 5, -39],\n [40, -48, 47, -183, -144, 91]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[71, -144, -59, 41, -88, 53],\n [-56, 18, -4, -62, -2, 34],\n [24, -45, -18, 15, -27, 15],\n [-47, 99, 41, -26, 61, -38],\n [-54, 36, 6, -54, 12, 18],\n [82, -132, -50, 58, -76, 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[[72, -10, -162, -89, 86, 32],\n [-12, 18, 58, 4, -6, 10],\n [-47, -38, 17, 91, -81, -65],\n [-35, 47, 100, 62, -50, -8],\n [13, 37, 22, -24, 24, 30],\n [-21, 25, 160, -45, 22, 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[[56, 187, 71, -5, 79, -142],\n [-80, -88, 4, 20, -40, 40],\n [-31, 0, -46, 142, 77, -101],\n [-94, -60, 48, -8, -50, 30],\n [112, 49, -52, -28, 29, 8],\n [34, 62, 36, -52, 0, -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[[-40, 60, -100, 50, 90, -40],\n [47, -63, 62, -49, -57, 26],\n [11, -9, -28, -4, 24, -10],\n [47, -53, -12, -36, 8, -2],\n [40, -50, 26, -37, -25, 12],\n [30, -20, -110, -5, 95, -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[[-25, 26, 66, -28, 51, 22],\n [130, -92, 40, 4, 78, -168],\n [39, 158, 61, -16, 10, 110],\n [-115, -56, -32, -29, 127, -25],\n [21, -114, -12, 24, -81, -82],\n [-55, 78, -24, 12, -121, 130]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-14, -6, -3, -4, -17, 17],\n [-26, 0, 18, -10, -8, 14],\n [-56, -24, -12, -16, -68, 68],\n [-69, -24, -3, -21, -72, 75],\n [11, -38, -88, 13, -77, 54],\n [-15, -38, -70, 3, -85, 68]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-80, -132, 48, 62, -20, 50],\n [15, 27, -3, -27, -30, -30],\n [-22, -30, 30, -26, -100, -44],\n [54, 90, -30, -48, 0, -42],\n [9, 9, -21, 33, 90, 48],\n [18, 24, -26, 25, 90, 41]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[-168, -78, -123, -53, -68, 107],\n [5, -59, 166, -15, 6, 19],\n [5, 56, -87, 32, 43, -37],\n [-172, -63, 64, -180, -73, -43],\n [-81, -95, -36, -68, 21, 46],\n [-136, -19, -31, -102, -70, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[75, -18, 47, 78, -92, -127],\n [-53, -11, 45, -7, -36, 87],\n [-76, -1, -3, -17, 63, 168],\n [85, 28, -34, 36, -17, -131],\n [13, 31, -25, 87, 54, 105],\n [32, -43, -40, 11, 111, -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[[-39, 42, 9, -84, 274, -75],\n [-31, 8, 37, -24, 198, -57],\n [-47, -24, 77, 80, 22, -46],\n [-84, 4, 108, 64, 96, -101],\n [-65, 20, -85, 40, -110, 10],\n [-15, 0, -19, 54, -188, 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[[18, -135, 144, 18, 36, 27],\n [-6, 3, 0, 0, -48, 9],\n [-10, 110, -120, -15, 10, -30],\n [-8, 67, -72, -9, -10, -15],\n [16, -1, -8, -1, 134, -27],\n [-2, -20, 24, 3, -34, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[36, -24, 0, -32, 40, -32],\n [-72, -6, -24, 10, 40, -32],\n [-45, 66, 16, 76, -130, 104],\n [27, -63, -20, -69, 130, -104],\n [-180, 30, -40, 70, 0, 0],\n [99, -48, 8, -70, 70, -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 6x6 matrix:\n[[-22, 2, -104, 17, -22, -70],\n [-90, 163, 31, 60, 48, 10],\n [-9, 76, -4, -49, 18, -86],\n [-1, 7, 99, 57, -7, 142],\n [-35, 35, 87, 63, 34, 116],\n [-109, -60, -114, 40, 161, -78]]\n\nPresent the 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, -17, 75, -58, -65, 37],\n [-9, 21, 85, -51, -31, 63],\n [-8, -40, 78, 58, -88, 80],\n [-57, 83, 118, -10, -37, 153],\n [143, -72, 119, -114, -154, 34],\n [0, -87, -82, 45, 37, -117]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-77, -38, 31, 129, 108, -93],\n [-9, -20, -89, 92, 32, -60],\n [60, -46, -28, -7, -6, 85],\n [-3, 110, -41, -82, -151, -83],\n [48, -106, 32, 21, 110, 149],\n [-74, 92, 24, -46, 9, -87]]\n\nPresent the 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, 42, -60, -2, -3, -75],\n [-110, -10, -100, -30, 115, -5],\n [-4, -8, 10, 0, 2, 14],\n [20, -44, 100, 12, -34, 86],\n [-42, 14, -70, -14, 49, -35],\n [32, 64, -80, 0, -16, -112]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-80, 60, -64, -32, 40, 76],\n [50, 0, 34, -10, -22, -28],\n [-10, 45, -14, -34, 8, 29],\n [110, 30, 70, -46, -46, -46],\n [-15, 30, -15, -21, 9, 24],\n [-20, 115, -32, -88, 18, 71]]?\n\nPresent the 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, 71, -57, 27, -69, 14],\n [-9, 3, 58, 44, 29, -39],\n [-54, 88, -24, 18, -84, 32],\n [-6, -47, 51, -75, 21, 44],\n [11, -45, 38, -32, 37, 5],\n [-4, -26, 44, -26, 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 6x6 matrix:\n[[44, 127, -7, -90, 13, 14],\n [50, 156, 30, -96, -40, 16],\n [24, 82, -17, -18, 28, -100],\n [-18, 155, 18, -100, 46, 44],\n [28, 76, 6, 32, 8, -140],\n [-74, 39, -51, -193, -10, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[39, -25, 62, 88, 91, -67],\n [-43, -22, 26, 41, -50, -104],\n [39, -73, -20, -83, 18, 17],\n [12, 107, -24, 19, 11, 71],\n [-15, 82, -60, -54, -57, 84],\n [-3, 73, -22, 6, -19, 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[[-2, -28, 78, -26, 116, -28],\n [108, 20, -20, 6, 10, 38],\n [108, 35, -85, 73, -136, 84],\n [-17, 61, -38, 73, 82, 39],\n [37, -77, 58, -44, -100, -22],\n [-127, -61, 70, -56, 0, -78]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[74, 65, -56, -81, -95, 39],\n [-11, 37, 48, 15, -20, -43],\n [84, 28, -64, -8, -60, -32],\n [76, 122, -16, -92, -140, 12],\n [-68, 26, 112, 52, 20, -68],\n [13, 141, 64, -88, -125, 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[[39, 19, -10, 37, 0, -48],\n [-22, -12, 5, -22, -1, 28],\n [-60, 40, 50, 4, 54, 24],\n [34, -86, -60, -58, -80, 32],\n [36, -44, -40, -20, -48, 0],\n [-31, -51, -10, -61, -28, 64]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[-42, -28, -84, -27, 24, -25],\n [2, 34, 177, 45, -12, 44],\n [48, -69, -106, -37, 44, -40],\n [136, -106, -20, -24, 72, -34],\n [68, -32, 137, 13, 76, 58],\n [-37, 64, 93, 34, -44, 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[[52, 115, -24, 64, 113, 18],\n [49, 115, -77, 124, 9, 77],\n [50, 136, -22, 46, 127, 31],\n [110, 218, -2, 50, 143, 77],\n [117, 98, 99, -52, 16, 45],\n [-48, -57, -32, 29, 38, -61]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-90, 36, 90, -18, 54, 54],\n [100, -132, -170, 66, -98, 2],\n [6, -30, -27, 15, -15, 15],\n [58, -60, -86, 30, -50, -10],\n [-10, 4, 10, -2, 6, 6],\n [-36, -4, 22, 2, 14, 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[[94, -162, -123, -303, -87, 90],\n [60, 68, 16, 9, 25, 42],\n [-47, 15, 61, -2, 0, 5],\n [-80, 58, 40, 65, -12, -74],\n [-12, -46, -144, 93, 45, -63],\n [48, -128, -167, -176, -77, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[-34, -142, 134, 160, 74, -34],\n [-9, -30, 33, 23, -5, 0],\n [3, 32, -22, -59, -57, 11],\n [8, 48, -45, -64, -36, -9],\n [-52, -151, 152, 115, 2, -97],\n [-3, -3, 15, -18, -45, 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[[117, 60, 51, -184, -8, -30],\n [-18, 8, -44, 62, 10, -40],\n [-11, 86, 102, -40, -67, 15],\n [74, -57, -66, -119, 82, 23],\n [0, 13, 5, 1, -1, -20],\n [64, -46, 92, 18, -94, -40]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[17, -6, 23, -34, -33, 17],\n [-3, -6, -7, 46, 37, -23],\n [44, -24, 56, -40, -48, 20],\n [34, -36, 36, 68, 40, -34],\n [-19, 18, -21, -26, -13, 13],\n [-3, -6, -7, 46, 37, -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[[39, 135, 26, 55, 92, 21],\n [154, 78, -81, 70, 82, 65],\n [-56, 186, 46, 7, 77, -51],\n [68, 30, -50, 67, 45, -17],\n [-52, 116, 78, -8, 48, 4],\n [75, -25, -14, 25, 14, 69]]\n\nPresent the 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, -68, 80, -20, -4, -56],\n [5, -45, 30, -20, -25, -25],\n [-18, 57, -12, 33, 57, 18],\n [-41, 89, 10, 60, 117, 13],\n [-33, -53, 122, 2, 55, -75],\n [-27, -2, 62, 17, 58, -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[[10, -50, 6, -8, 76, -40],\n [52, -44, -36, 40, 16, -40],\n [14, 2, -14, 16, -20, 0],\n [-25, 35, 13, -14, -32, 30],\n [93, -51, -73, 82, -20, -50],\n [-13, 11, 9, -10, -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[[94, 8, -13, -30, -13, -68],\n [2, -54, 44, 88, -50, -177],\n [5, -61, 11, 76, -57, -186],\n [-52, 52, 53, -2, 17, 147],\n [50, 66, -22, -56, -38, 78],\n [-77, 21, 114, 118, -104, -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[[-133, 31, -41, -36, 61, 52],\n [-108, -7, -69, 24, 0, 76],\n [111, 8, 2, -9, 18, 14],\n [153, -81, 15, 82, 2, -11],\n [-141, 65, -52, 24, 84, 80],\n [-94, -57, -82, 158, 137, 120]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-221, 36, 129, 110, -71, -113],\n [-35, 121, 105, -29, 26, 36],\n [-157, 2, 131, 94, -20, -116],\n [117, -5, -153, -79, 13, 62],\n [-48, 84, -36, -12, -11, 0],\n [-5, 83, -4, -57, -59, 92]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, -62, -82, -68, -4, 74],\n [36, 11, -84, -56, -53, 98],\n [26, 60, -48, -18, -46, 67],\n [25, 9, -125, -80, -52, 138],\n [-14, -62, -76, -62, 8, 65],\n [-30, 10, 176, 118, 64, -189]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-44, -39, 47, 1, -45, 30],\n [10, 70, 26, -130, -43, -97],\n [67, 48, -74, -22, 26, -119],\n [-14, 66, 48, -125, -53, -67],\n [-42, -135, -17, 152, -47, -94],\n [-81, 58, 36, -29, -100, -19]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-61, -29, 23, 43, 70, 69],\n [58, 47, 10, -18, -36, -63],\n [47, 31, -13, -49, -112, -60],\n [94, 77, 14, -38, -84, -105],\n [92, 100, 44, -36, -120, -108],\n [56, 82, 72, 32, 40, -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[[197, 0, 61, 13, 69, 112],\n [-134, 79, -65, -9, -113, -73],\n [-125, 66, -136, -163, -9, -79],\n [-55, -82, 38, 21, 7, -43],\n [-65, 78, -61, -10, -62, -26],\n [50, -9, 26, 62, 24, 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[[-26, 29, -52, -1, 35, 18],\n [-35, -29, -75, -52, 26, 49],\n [-20, 88, -24, 29, 41, -26],\n [31, 19, 87, 5, -37, -71],\n [0, -85, -14, -50, -22, 42],\n [-19, 1, -23, -44, 10, -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, -81, -96, -10, -202, 33],\n [-33, -2, -77, -37, 11, 158],\n [38, -156, 67, 35, -113, -176],\n [62, -42, -6, 29, 7, 119],\n [42, 42, 0, 4, 91, 138],\n [-83, -42, -20, -79, 18, -27]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-36, 100, -24, -84, -14, -54],\n [-13, 61, 3, -56, -8, -86],\n [-56, 7, 21, 14, 22, -7],\n [0, 9, -15, -8, -5, 24],\n [-120, 80, 0, -32, 24, 0],\n [-41, 57, -9, -40, 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[[93, 106, -46, -73, 7, -39],\n [-19, -82, 31, 68, -31, 18],\n [4, -69, 46, 39, -44, -15],\n [92, 34, -114, 88, 8, 84],\n [61, -80, -23, 132, -51, 54],\n [137, -61, 91, -1, -127, -117]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[50, -24, 38, -106, -29, -37],\n [-67, 101, 18, 142, 47, 78],\n [34, 30, 70, -71, -17, -5],\n [39, 117, 68, 22, -56, 27],\n [-27, -1, -22, 49, 27, 10],\n [91, 49, 20, -36, -108, -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[[128, -120, -16, 16, -64, 24],\n [-7, 44, 32, -97, 1, -21],\n [-26, 28, -7, 27, 3, -18],\n [-39, -25, -5, 30, 54, 60],\n [11, -95, 15, -40, 64, 120],\n [44, -74, 1, -11, 5, 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[[15, -5, -86, 87, -61, 65],\n [-84, 129, -78, -15, 18, 75],\n [60, -95, 40, 30, -25, -40],\n [55, -145, 50, 75, -45, -35],\n [-14, -83, 76, 16, 7, -38],\n [-85, 164, -94, -35, 26, 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[[-6, 80, -52, -44, -82, 126],\n [-53, 25, -105, -26, -56, 78],\n [136, 64, 112, 0, -72, 24],\n [-88, 0, -162, -22, -62, 70],\n [30, 41, -59, -1, -105, 63],\n [-29, 40, -72, -20, -53, 79]]\n\nPresent the 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, 16, -101, -44, 158, 24],\n [-58, 11, -105, 2, 37, -9],\n [160, 78, 47, 63, 48, -67],\n [-70, -55, 12, -23, -55, 36],\n [91, -32, 42, 33, 120, -16],\n [149, -5, 100, 107, 7, -94]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 16, -22, -16, -156, -56],\n [-11, 59, -49, -16, -125, -36],\n [-3, 3, 15, -7, -28, 2],\n [27, -48, -22, 20, -163, -46],\n [30, -105, 41, 52, 130, 58],\n [6, -42, 52, 1, 49, 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[[57, 86, -43, 30, 21, 58],\n [-26, 92, -72, 155, -31, -4],\n [-45, -110, 75, -39, -22, -24],\n [56, 37, 1, -22, 29, 65],\n [107, -115, 85, -35, -53, 126],\n [-48, 226, -178, 93, 55, -104]]?\n\nPresent the answer 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, -6, -12, -11, 37, -9],\n [67, 74, 38, 10, 84, 105],\n [16, 57, -6, 140, -29, 19],\n [32, 17, 67, -22, 45, 77],\n [-58, -20, -45, 92, -36, -92],\n [121, 114, 61, 132, 48, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-96, 41, -122, 8, -59, 90],\n [-23, -78, 89, 36, 37, -123],\n [20, -82, -16, 29, -86, -164],\n [-20, -45, 219, 53, 176, -131],\n [9, 71, -46, 4, -25, 22],\n [-26, -67, -17, 4, 28, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[87, -96, -60, 0, 3, 16],\n [-41, 90, 14, -39, -36, -96],\n [-37, -70, -51, 43, -88, 27],\n [30, -80, 115, 48, 37, -85],\n [-49, 129, 19, -2, 105, 115],\n [33, -15, 3, -63, -62, -83]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-11, 16, -20, 49, -46, -46],\n [83, -5, 90, -53, 73, 73],\n [-44, 7, -50, 40, -49, -49],\n [52, 9, 50, 0, 17, 17],\n [57, -19, 70, -79, 87, 87],\n [46, -22, 60, -82, 86, 86]]?\n\nPresent the 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, -37, -54, -28, -41, 67],\n [30, -11, -33, 4, -24, 61],\n [0, -28, -48, -16, -36, 68],\n [20, -5, -18, 4, -13, 35],\n [-30, -31, -39, -28, -30, 41],\n [60, 55, 66, 52, 51, -65]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[-39, -51, 132, -60, -24, -45],\n [-16, 1, 38, -5, 34, -15],\n [-26, -72, 116, -74, -92, -36],\n [-14, 8, 28, 2, 44, -12],\n [6, 2, -16, 4, -8, 6],\n [17, 31, -64, 34, 28, 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[[29, 20, 16, -2, 6, -66],\n [14, 8, 16, -30, 6, -82],\n [91, 76, 41, 74, -6, -53],\n [39, 60, 81, -22, -54, -61],\n [2, 8, 28, -44, -12, -64],\n [50, 56, 43, 46, -30, 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, 48, -12, -77, -27, 103],\n [-82, 78, 60, 34, -35, 80],\n [125, -71, 15, -103, -56, 58],\n [-145, 74, -2, -5, -57, 140],\n [-135, 68, 95, 37, -46, 102],\n [94, -59, 100, 70, -85, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[51, 0, 32, -4, -28, 48],\n [-1, -1, -133, 107, 119, -134],\n [-135, 39, -19, -23, 10, 79],\n [12, -35, -53, 136, 50, 19],\n [-203, -1, -23, -1, -24, -91],\n [85, 6, 13, -49, -5, -67]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-60, 4, -124, -6, -11, 46],\n [-11, -29, 97, -7, 50, -56],\n [28, 23, 101, 43, 12, -42],\n [132, 90, 19, 136, -2, 17],\n [46, 68, -71, 61, -67, 65],\n [-2, 79, -16, 82, -51, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-55, -30, 40, -70, -170, 50],\n [88, 6, -13, 49, 62, 1],\n [24, 106, -56, -6, 140, -72],\n [56, 42, -8, -22, -20, 8],\n [-70, -14, 25, -61, -114, 23],\n [-8, 86, -2, -116, -120, 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[[-24, -31, 53, -8, 35, -43],\n [-7, -63, 9, 16, -90, -14],\n [28, 104, -104, -64, -28, 52],\n [-9, -81, 67, 76, 9, -18],\n [-33, -38, 50, -36, 4, -59],\n [-30, -85, 95, 40, 35, -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[[36, -58, -86, 41, 30, -164],\n [-31, 146, -49, -24, 17, 14],\n [-155, 12, 147, -78, 0, 19],\n [-41, -126, 44, -192, -118, -160],\n [10, 128, -54, 29, 8, -66],\n [35, 179, -103, 25, 23, 54]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-18, -118, 30, -19, 28, -13],\n [13, -4, 133, -49, 9, -42],\n [18, -29, 72, 6, 67, -95],\n [66, -40, -44, 99, 195, 54],\n [3, -103, -49, 20, 63, 121],\n [22, 122, -36, 36, -9, -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[[-101, -57, -70, 64, 4, -93],\n [69, 1, -50, -2, 16, 21],\n [47, -33, -8, -58, 56, 51],\n [92, 76, 36, -16, -32, 64],\n [78, 30, 33, -45, 6, 63],\n [-3, 51, -65, 107, -74, -71]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[126, -44, 18, -71, 81, 17],\n [3, 85, -52, 31, 30, 63],\n [-3, 7, 64, 43, 24, -5],\n [-42, -66, 132, 44, -22, -76],\n [-96, 26, -20, 45, -68, -17],\n [24, 162, -160, 17, 50, 135]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[80, 63, 108, 6, -46, -96],\n [51, 11, 38, 25, 2, -6],\n [-30, -14, -23, -4, -2, 15],\n [-61, -47, -78, -3, 30, 70],\n [-51, -9, -59, -43, 24, 11],\n [-27, -39, -150, -57, 150, 102]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[-5, -63, -38, -19, -1, -9],\n [-72, 111, 39, 45, 90, 75],\n [24, -7, 22, 14, -25, -26],\n [-53, 73, 113, 89, 161, -38],\n [55, 60, 14, 57, 60, 73],\n [102, -16, -89, -73, -67, 43]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-72, -132, -18, -140, -78, 40],\n [-9, -49, 75, -30, -11, -71],\n [12, 31, -15, 27, 14, 11],\n [-8, 58, -82, 18, 12, 82],\n [-75, -104, 0, -127, -61, 22],\n [-59, 100, 14, -3, 45, -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 6x6 matrix:\n[[-21, -29, -32, -50, 28, 47],\n [104, -58, -10, -12, 16, 2],\n [61, 46, 61, 96, -52, -92],\n [-1, -57, -48, -74, 44, 67],\n [-121, 38, -13, -24, 4, 32],\n [71, -41, -8, -10, 12, 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 6x6 matrix:\n[[-4, -4, 44, -67, -42, 49],\n [25, 2, 38, -127, -65, 113],\n [62, 48, -48, -55, -48, 53],\n [-49, -34, 74, -17, -7, -1],\n [-50, -57, 42, 32, 55, -18],\n [54, 129, 6, -98, -191, 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 6x6 matrix:\n[[8, 24, 38, 29, -8, 8],\n [-3, -6, -8, -4, 2, -1],\n [2, 36, 72, 76, -12, 22],\n [-13, -42, -68, -54, 14, -15],\n [-72, -96, -92, 14, 32, 8],\n [100, 120, 100, -50, -40, -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 6x6 matrix:\n[[20, -8, -66, 83, -37, 31],\n [55, 47, -9, -65, 88, -70],\n [25, 5, -45, 40, -5, 5],\n [35, 31, -3, -46, 59, -47],\n [45, 13, -71, 55, 2, 0],\n [55, 23, -69, 37, 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[[-30, 23, 4, 40, -20, -35],\n [-53, 52, -13, 64, 4, 11],\n [95, -93, 96, -71, 52, -33],\n [-98, 92, -43, 105, -28, -1],\n [61, -64, 51, -54, 4, -45],\n [-88, 88, -45, 93, -4, 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, -88, -84, 81, -128, 153],\n [128, 20, 28, 22, 32, -14],\n [-58, -47, -74, 37, -51, 66],\n [177, 15, 91, -32, 5, -24],\n [7, -8, -13, 12, -4, 9],\n [89, -67, -44, -84, 10, -56]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-48, -16, 8, 48, 12, -56],\n [44, -18, -33, -9, -67, 56],\n [76, 2, -31, -51, -59, 92],\n [40, -38, -47, 15, -98, 54],\n [-12, -4, 2, 12, 3, -14],\n [116, 34, -23, -111, -37, 136]]\n\nPresent the answer 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, 110, 15, -48, 84, 176],\n [40, 6, -55, 52, -14, -50],\n [6, 84, 21, -30, 87, 135],\n [-50, -54, 34, -84, -110, -2],\n [-106, -30, 146, -120, 44, 104],\n [93, 55, -141, 42, -105, -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[[-76, -24, 119, -36, -29, -16],\n [68, -223, 7, 11, 193, -65],\n [36, 48, -33, 3, -95, 111],\n [34, -47, 11, -11, 75, -7],\n [68, -75, 13, -15, 51, 61],\n [9, 87, -93, 33, -44, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[-15, -77, 46, -110, -81, 33],\n [0, -33, 14, -52, -35, 23],\n [-20, 84, -39, 148, 93, -84],\n [-75, -95, -15, -90, -80, -25],\n [30, -55, -57, -108, -52, 85],\n [-130, -111, 135, -76, -108, -99]]\n\nPresent 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, 120, -107, -71, -24, -66],\n [10, 80, -78, -34, -46, -64],\n [7, 56, -23, -87, 110, 50],\n [0, 0, 8, -16, 36, 24],\n [6, 48, -58, 2, -78, -72],\n [-9, -72, 85, 1, 108, 102]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-73, -8, -84, -113, -27, -90],\n [0, 24, 82, -162, 34, 76],\n [44, 56, -29, 55, -90, 55],\n [103, 100, 31, 94, -52, -14],\n [56, 92, 64, -34, -55, 15],\n [-47, -68, -6, 64, 53, -119]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-74, 99, 55, -79, 91, -169],\n [54, 117, -24, 73, -95, 91],\n [32, -28, 2, 74, -42, 28],\n [-22, 40, 27, -134, 74, -26],\n [-11, -177, -7, -6, 35, -1],\n [17, -110, -87, 94, -79, 106]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-60, 0, -68, 54, -40, 0],\n [37, -154, -106, -67, 171, -14],\n [-87, 144, 19, 108, -231, -21],\n [-15, 88, 119, 27, -13, 17],\n [9, -62, -38, -36, 71, -100],\n [58, 46, 107, -40, -8, 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[[-14, -6, -22, 0, 12, -14],\n [-86, -74, -124, -130, -60, -8],\n [36, 24, 54, 30, 0, 18],\n [19, 21, 26, 45, 30, -8],\n [66, 54, 96, 90, 36, 12],\n [-40, -20, -62, -10, 24, -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[[42, 12, -54, -20, 0, -16],\n [30, -120, 30, 148, -54, 8],\n [-97, 130, 36, -117, 69, 49],\n [24, 102, -75, -183, 36, -75],\n [69, -78, -30, 39, -45, -63],\n [88, 14, -100, -84, -9, -88]]\n\nPresent 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, -61, 38, -4, -43, 20],\n [-61, -83, 92, 19, -99, -37],\n [101, -73, -30, -10, 30, 89],\n [19, 119, -104, -1, 128, 6],\n [88, -118, -14, -13, -108, 19],\n [114, -29, -83, -17, 27, 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[[30, 57, 226, 26, -109, 85],\n [46, 50, 182, 8, -86, 62],\n [127, 101, 2, 7, 65, -73],\n [-143, -132, -190, 58, 82, -55],\n [-18, 11, -60, -38, 9, 9],\n [2, -12, 120, -41, -100, 81]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-18, -220, -116, 150, -106, -96],\n [-11, 53, 6, -104, -69, 79],\n [-13, -14, -66, 95, 63, -124],\n [-50, -166, -172, 76, -78, -102],\n [18, 29, 80, -77, 60, 89],\n [15, -112, -6, 121, 24, -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[[21, -66, -77, -252, 61, -124],\n [-14, 85, -126, -129, 39, -40],\n [44, 123, -141, -25, -17, -69],\n [65, -147, 149, 28, 78, 6],\n [-120, -21, -32, -167, 43, 12],\n [27, 43, -97, -34, -42, -102]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-13, 120, -88, -15, 30, 29],\n [-41, 23, -55, 63, 33, 57],\n [-27, -16, 74, 28, 16, -53],\n [30, -128, 56, -30, -84, -46],\n [-49, -84, 30, 67, -26, -19],\n [53, 8, 12, -51, 6, 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[[-72, 40, 16, 40, 8, 56],\n [148, -130, -45, -55, 104, -62],\n [-95, 155, 20, 31, -92, -71],\n [45, -85, -5, -25, -12, 102],\n [108, -50, -87, -11, 133, 58],\n [51, 45, -41, -19, 1, -82]]\n\nPresent the answer 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, 105, 35, 21, -105, -14],\n [-18, 24, 32, 54, -12, 16],\n [-6, -87, -41, -42, 81, 2],\n [12, 117, 51, 48, -111, -6],\n [59, -9, -67, -133, -23, -50],\n [-6, -87, -41, -42, 81, 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[[3, -40, -38, 17, 43, -57],\n [68, -101, 162, -15, -100, 143],\n [59, 45, 7, 14, 134, -32],\n [1, -89, 46, 16, -57, 36],\n [30, 33, 36, -9, 21, 30],\n [42, -2, 11, -36, 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[[36, -83, 6, 89, -75, -72],\n [-17, 28, -80, 5, -87, -55],\n [-61, 111, -31, -108, 78, 64],\n [-121, 80, -45, -63, 95, -36],\n [-14, 61, -34, -53, -1, 34],\n [104, -46, 80, 10, -6, 100]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[63, -42, -56, 0, -42, -56],\n [-67, 70, 58, 14, 48, 86],\n [35, -74, -28, -28, -30, -84],\n [27, -18, -24, 0, -18, -24],\n [3, 36, -5, 21, 3, 37],\n [119, 22, -112, 56, -66, 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, -33, -9, 20, -12, 21],\n [38, 11, -17, 28, 14, 14],\n [41, 62, -14, 16, 38, -7],\n [-135, -9, 63, -108, -36, -63],\n [12, -50, -10, 24, -20, 28],\n [-142, -1, 67, -116, -34, -70]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[-24, 34, 104, -125, -22, 11],\n [8, -16, -48, 58, 8, -6],\n [-42, -7, -8, 14, -29, -14],\n [46, -43, -136, 162, 39, -10],\n [-54, -11, -16, 25, -37, -19],\n [18, -1, -8, 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[[-90, -32, 60, 74, -25, -36],\n [-116, 78, 48, 25, -72, -55],\n [39, -202, 62, 64, -28, 33],\n [102, 48, -34, -96, 101, 6],\n [-76, 158, -102, 15, 18, -5],\n [-41, 54, 44, -14, 18, -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[[84, -64, -124, -56, 100, 34],\n [4, 37, 23, 11, 35, 55],\n [-14, -40, 27, -20, 64, 54],\n [-16, 39, 53, 17, 29, 59],\n [-48, 71, 77, 49, -83, -29],\n [42, 42, -54, 10, -20, -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[[41, 17, 35, 75, -45, -71],\n [-58, -52, 190, 131, -247, -48],\n [68, -107, -6, 64, 174, 18],\n [-46, -24, 158, 92, -264, -19],\n [103, -66, 3, 59, 58, 41],\n [-8, 49, -26, -90, 62, 52]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[13, 3, 67, -23, -28, 26],\n [53, -14, -38, 116, -49, 19],\n [-86, 43, 59, -102, 78, 25],\n [63, -58, -78, 46, -65, -81],\n [-59, 64, 64, -28, 75, 93],\n [185, -113, 77, 30, -247, -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[[55, 97, -34, -24, 69, 34],\n [10, 16, -166, -18, -96, 50],\n [-51, -94, 147, 25, 5, -63],\n [-27, -39, -60, 18, -69, 4],\n [-16, -19, 115, 27, 66, -39],\n [49, 44, -115, -85, -71, 55]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[-88, -12, -59, -17, 83, 70],\n [-20, -7, -25, -25, 120, 155],\n [-88, 24, 65, 11, -53, -48],\n [20, 57, -111, -123, 22, 73],\n [-66, 29, 84, 18, -91, -87],\n [77, 39, -42, -78, 20, 81]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[16, 62, -29, 42, -76, 47],\n [-77, -60, -61, 9, 144, -108],\n [-18, -102, 33, -12, -24, -9],\n [-72, -34, -26, -60, 15, 17],\n [105, 113, 34, -132, -174, 180],\n [20, 47, -46, -8, 31, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[23, -46, -1, 7, -78, 33],\n [-77, 20, -119, 66, 68, -68],\n [55, 22, 115, -70, 0, 36],\n [-2, -10, 12, -2, 16, 10],\n [13, -47, -6, 12, -58, 30],\n [10, 37, 1, -13, -12, -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[[51, -20, -31, 42, 49, -55],\n [93, -28, -11, 17, 19, 40],\n [9, -70, -39, 18, -7, -146],\n [-62, -70, 12, -54, -152, -19],\n [69, 2, -27, 55, 101, -98],\n [-222, -140, 2, -161, -246, -124]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[201, -34, -89, 106, 26, -81],\n [-41, 50, 38, -81, -126, -48],\n [100, 61, 10, 52, 42, 10],\n [37, -36, -35, 32, 22, -15],\n [36, -207, -144, 90, 90, -36],\n [112, -72, -82, 86, 56, -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 6x6 matrix:\n[[78, 150, 33, -7, -29, -84],\n [-51, -25, -72, 36, -11, -5],\n [-6, 30, -11, 9, 13, -12],\n [9, -9, 26, -14, 13, 15],\n [27, -15, 98, -50, 73, 57],\n [24, -112, 91, -57, 17, 82]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[141, -18, 56, 245, -85, -28],\n [-7, 74, 118, 109, -9, -24],\n [-18, 150, 75, 48, -32, -60],\n [177, -12, 153, 143, -143, -120],\n [19, -110, 53, -89, 2, -9],\n [50, 32, 69, 212, -26, 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[[76, 20, -16, 48, -60, -100],\n [4, -47, -2, -38, 9, 26],\n [-62, 106, 16, 64, 18, 2],\n [-76, -20, 16, -48, 60, 100],\n [76, -63, -18, -22, -39, -46],\n [3, -56, -2, -46, 12, 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[[2, -27, 102, 0, 75, 39],\n [30, -36, 90, -18, 72, 18],\n [26, -160, -10, -14, -60, -102],\n [-4, -44, 80, 4, 48, 20],\n [-13, -61, -60, 9, -78, -61],\n [46, -83, 25, -28, 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[[60, -87, -25, 108, -63, -89],\n [78, -57, 0, -35, -106, 6],\n [-148, 121, 11, 8, 137, -68],\n [-112, 5, -145, -136, 89, 28],\n [16, 109, -45, -44, -15, 3],\n [-102, -67, -40, -73, 142, 133]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[58, -21, 78, -11, -2, 125],\n [21, 2, -68, 65, 0, -67],\n [50, 5, 8, 19, 40, 80],\n [-33, -87, 4, -72, -5, 113],\n [44, 66, 4, 56, 23, -42],\n [118, 36, 24, 70, 64, 110]]\n\nPresent the answer 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, 72, -4, 38, -9, 74],\n [-37, -6, 94, -92, -13, -1],\n [-32, -40, 54, -124, 38, -14],\n [1, 78, -26, 4, 37, 105],\n [-46, 24, 102, -120, 8, 46],\n [-5, 22, 30, 16, -33, 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[[35, 38, -35, 72, -45, -21],\n [64, -72, 81, -51, 63, 78],\n [91, -11, 54, 34, 12, 68],\n [-83, 131, -65, 87, -81, -54],\n [-57, 105, 34, 46, -24, 44],\n [-112, 105, 39, 6, -9, 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[[-117, 21, -82, 60, 69, 1],\n [2, 42, -41, 3, -53, -8],\n [224, -80, 10, 20, 66, 24],\n [77, -27, -31, -56, -116, 17],\n [-57, 164, 16, 59, 160, 32],\n [-141, -48, -100, 48, 10, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[39, -103, 103, -161, 103, 45],\n [-71, 5, -36, -94, 29, 9],\n [-31, 13, 8, 58, 39, 59],\n [-131, -63, -41, 220, 27, 152],\n [-76, -13, 38, -109, 121, 53],\n [7, 161, -100, -88, -116, -202]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-58, -4, 66, -8, -22, 56],\n [-5, -12, 81, -11, -79, 12],\n [-36, -21, 142, -18, -121, 46],\n [12, -29, 86, -8, -117, 6],\n [-68, 18, -32, 4, 94, 52],\n [9, -5, -67, 13, 42, -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, -136, -125, -21, 72, -82],\n [27, -48, -26, 56, -38, -38],\n [-20, -8, -37, -105, 108, 10],\n [7, -32, -32, -14, 26, -18],\n [42, -96, -68, 56, -20, -68],\n [-14, -32, -60, -112, 124, -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 6x6 matrix:\n[[88, -42, 58, 40, 26, -92],\n [-20, -214, -64, 55, -78, 28],\n [13, -5, 208, -17, -73, -69],\n [43, 87, 200, -116, 105, -233],\n [-70, 22, 150, -71, -88, -6],\n [-8, 32, -166, 1, -15, 106]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-51, 129, 9, 89, -3, -59],\n [-135, -63, 96, 30, 93, -90],\n [91, -65, -44, 32, 31, 42],\n [-102, 42, 56, 110, 72, -98],\n [-62, 22, 30, 128, 74, -86],\n [170, -10, -100, -120, -108, 146]]?\n\nPresent 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, 51, 1, 141, 123, 66],\n [-18, -51, 69, 6, 17, -2],\n [-111, -36, 34, 45, -9, 63],\n [0, -15, 75, -102, -28, 7],\n [38, 36, -126, 4, -55, -37],\n [142, -6, -59, 53, 48, -115]]\n\nPresent the 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, -49, -129, -99, 116, 55],\n [92, 54, -86, -112, 132, -118],\n [-58, 14, -151, -64, 102, 2],\n [-80, -43, -32, 25, -22, 89],\n [-10, -7, 25, 19, -60, -47],\n [6, 54, 97, 68, -74, -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[[133, -98, -42, -47, 22, 108],\n [-89, 161, 58, -91, -50, -7],\n [-18, 10, 102, 18, 84, 80],\n [43, 57, 35, -27, 22, 88],\n [111, -96, -123, 123, -6, -45],\n [-127, 22, 127, 9, 62, -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[[38, -86, 5, -65, 64, 30],\n [-30, 66, -85, -33, 36, -108],\n [-49, 70, -40, -32, 10, -48],\n [-58, 14, 35, -95, 24, 74],\n [62, -60, -20, 28, 20, -32],\n [49, -44, -40, 5, 36, -53]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[51, -70, -45, 9, -8, -39],\n [75, 20, -39, 21, 7, -36],\n [82, 70, -32, 26, 15, -31],\n [118, -80, -86, 26, -6, -76],\n [57, 0, -33, 15, 3, -30],\n [-30, -160, -18, -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[[78, 18, -133, 42, -67, -80],\n [2, -18, -36, -26, -82, -110],\n [130, -73, 3, 27, 37, 88],\n [125, -88, 53, 32, 82, 123],\n [58, -66, 26, 8, 3, -36],\n [56, 112, -225, 72, -73, -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[[43, -2, 44, 34, -48, -49],\n [-73, -52, -68, -58, 12, 109],\n [-39, 88, -37, -12, 119, 5],\n [-85, 89, -46, 4, 76, 60],\n [18, 64, -13, -18, 119, -52],\n [24, 86, 13, 18, 85, -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[[-134, 36, 48, 173, -30, 27],\n [52, -114, -55, -107, 84, -113],\n [61, 39, 18, -99, -26, 22],\n [50, -30, -98, -40, 84, -58],\n [111, 48, 12, -97, -28, 56],\n [-9, 1, 22, -53, -2, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-5, -29, -1, 90, -40, 47],\n [68, 116, -51, -37, -88, -28],\n [-28, 60, -37, -9, -76, 56],\n [56, 110, -38, -65, -51, -46],\n [89, 119, -51, -79, -67, -61],\n [75, -79, 25, 34, 49, -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[[-30, 99, 100, 35, 51, -100],\n [-130, -56, -12, -187, -113, 56],\n [-36, 58, 20, -46, 86, -40],\n [2, -58, -10, 7, -105, 40],\n [10, -97, -116, -81, -25, 108],\n [8, -21, 38, 56, -100, -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[[22, 124, 88, -106, -65, -86],\n [153, 137, 44, -37, 43, -78],\n [36, -76, 72, 126, 87, 76],\n [-39, -37, -73, 1, 7, 19],\n [57, 127, -11, -111, -91, -107],\n [-124, -138, -124, 40, -37, 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, -60, -144, -21, 165, 42],\n [-72, -18, -66, 52, 106, -36],\n [127, -13, -46, 81, -135, -52],\n [-29, 73, -48, 87, -45, -60],\n [8, 94, -95, 62, -37, -26],\n [50, -50, 73, 11, -31, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[71, -140, -8, 93, -62, -95],\n [11, -56, 52, -27, 46, -23],\n [36, -91, 27, 23, 1, -53],\n [21, -12, -48, 63, -66, -21],\n [36, -91, 27, 23, 1, -53],\n [-28, 16, 64, -84, 88, 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[[97, 108, 76, -13, 90, -26],\n [30, -6, -124, 96, 44, -4],\n [4, 33, 110, -73, -8, -4],\n [-83, -51, 90, -94, -94, 18],\n [39, 39, 14, 6, 38, -10],\n [80, 75, 10, 25, 80, -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[[-1, -47, -21, -22, -9, -59],\n [-96, 76, -97, -77, 31, 12],\n [91, -25, -4, -66, 52, 75],\n [131, -127, 11, -16, -75, 16],\n [10, 52, 51, 18, 85, 39],\n [16, -72, -100, -96, -58, -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[[55, 68, 12, -105, -38, 49],\n [80, -8, -139, 123, -135, -52],\n [21, 33, 26, -115, -17, 55],\n [-18, -101, -69, 33, -51, -14],\n [17, 59, 75, 60, 164, -81],\n [48, 49, -63, 141, -54, -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[[-29, -85, -56, -65, -24, -176],\n [2, -30, -80, -62, -1, -99],\n [-1, 36, 72, 71, 7, 123],\n [-7, -37, 24, -51, -29, -131],\n [10, 15, 80, -10, -20, -30],\n [-22, -69, -48, -58, -20, -150]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[59, -82, -96, 48, -63, 59],\n [-43, 32, 39, -30, 21, -43],\n [-39, 78, 90, -36, 63, -39],\n [74, -46, -57, 50, -28, 74],\n [-89, 10, 18, -52, -7, -89],\n [52, -26, -33, 34, -14, 52]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[-133, -138, -131, -109, 33, 45],\n [170, 162, -7, -47, -144, -42],\n [65, 47, -52, -51, -38, -65],\n [-39, -73, 4, 64, 51, -24],\n [-20, -30, -37, -110, -28, 50],\n [166, 97, 76, 32, -148, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-45, 15, 103, -45, 71, 42],\n [24, -54, -130, -17, -26, -37],\n [7, 15, 94, 40, -10, 10],\n [-52, -18, 59, -84, 91, 37],\n [-48, -42, 79, -86, 95, 35],\n [-18, 24, -74, -33, 14, 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[[-66, 27, 153, 14, 100, 134],\n [1, -77, 35, -42, -56, -51],\n [35, 29, -21, 63, 3, 77],\n [8, -102, 42, -42, -62, -86],\n [20, -42, 0, -7, -49, -12],\n [98, -68, -50, 91, -33, -103]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[2, -7, 16, 30, -82, -52],\n [-26, -50, 74, 80, -62, 18],\n [12, 24, -36, -40, 36, -4],\n [8, 14, -20, -20, 8, -12],\n [42, 72, -102, -100, 30, -70],\n [-52, -76, 100, 80, 68, 148]]\n\nPresent the answer 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, 58, -44, -13, -46],\n [-172, 151, -161, -54, -11, 116],\n [-186, 143, -44, 66, -171, -24],\n [-105, 66, -88, -173, 102, 127],\n [64, -38, 6, 7, 58, 21],\n [56, -58, 90, 11, 14, -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 6x6 matrix:\n[[96, 58, 104, 145, 48, 121],\n [-200, -27, 30, 47, -169, 75],\n [90, -31, 148, 126, 68, 39],\n [120, 35, 20, 49, 67, 21],\n [-84, -8, -35, -42, -53, -8],\n [8, 26, -105, -151, 71, -79]]\n\nPresent the answer 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, 64, -19, 67, 64, 56],\n [54, -60, 12, -68, -56, -64],\n [79, -60, -52, -44, -8, -110],\n [-5, -15, -7, -3, -6, -13],\n [42, -9, 24, -38, -26, -13],\n [60, -41, -93, -1, 38, -109]]\n\nPresent 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, 108, 22, 45, 17, 51],\n [-19, 56, 25, 20, -2, 61],\n [-27, -24, 21, 30, 18, -21],\n [132, 8, -154, -150, -50, -80],\n [58, 124, -103, -75, -23, -10],\n [11, 116, -38, -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[[-2, 17, -29, 10, 29, -24],\n [46, 34, 82, 44, -56, 66],\n [39, -80, 72, 53, -167, 12],\n [99, 4, -4, 118, -59, -59],\n [-24, 72, 20, -58, 96, 70],\n [77, 32, 28, 72, -25, 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[[39, 176, -27, -128, 7, 40],\n [38, -86, 88, -11, 70, -49],\n [-40, 63, -99, 56, -112, 35],\n [19, 55, 18, -140, 153, 73],\n [-24, -14, 5, -36, 54, 31],\n [-14, 91, -52, -133, -6, 91]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-60, -45, 26, -92, -23, 28],\n [0, -45, -36, 72, -27, -18],\n [-72, -93, 0, -48, -51, 18],\n [-6, 1, 7, -18, 1, 5],\n [30, 35, -3, 26, 19, -9],\n [84, 76, -26, 108, 40, -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[[-86, 5, 24, -59, -34, 10],\n [-115, 0, 40, -80, -50, 20],\n [123, -9, -96, 71, 8, -30],\n [92, -54, -32, 42, -36, 20],\n [35, -34, 44, 22, 2, 32],\n [155, -71, 54, 101, 34, 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[[94, 57, 117, 40, 111, -68],\n [66, 45, 78, 48, 63, -66],\n [-34, -21, -42, -16, -39, 26],\n [-22, -3, -36, 32, -57, -22],\n [-4, -12, 3, -40, 24, 38],\n [-52, -36, -61, -40, -48, 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[[-104, -48, -96, 32, 60, 68],\n [99, -27, 81, 48, -75, -3],\n [64, -48, 48, 64, -56, 24],\n [-30, 54, -18, -64, 34, -38],\n [9, -117, -9, 128, -35, 97],\n [-56, -84, -60, 80, 18, 86]]\n\nPresent the 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, 15, -6, -18, -42],\n [41, -76, 34, -80, 6, 58],\n [63, -35, -55, 78, 52, -88],\n [-46, 12, 62, -96, -48, 96],\n [78, -87, -17, -2, 46, -18],\n [0, -41, 49, -94, -18, 86]]?\n\nPresent 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, -136, -5, 31, -7, -5],\n [-73, 19, -49, -66, -70, -78],\n [-60, 30, -27, -47, -65, -49],\n [-43, -12, -68, -201, -137, -83],\n [50, 0, 29, 63, 71, 46],\n [-27, 83, -16, -147, -121, -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[[4, 45, -85, 37, 47, 57],\n [28, -21, 29, -13, -39, -1],\n [26, -12, 13, -6, -28, 8],\n [54, -54, 81, -36, -90, -18],\n [-92, 36, -34, 16, 92, -36],\n [44, -30, 40, -18, -58, 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[[-47, -64, 75, 22, 15, 51],\n [62, 46, -57, 55, -88, -6],\n [-36, -24, 30, -36, 54, 0],\n [-103, -8, 9, -94, 117, -33],\n [-51, 120, -147, -102, 57, -117],\n [-41, 80, -99, -62, 33, -75]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[39, 10, 19, 23, -35, -27],\n [16, -40, 31, -88, 21, -14],\n [-1, -45, 45, -42, 85, 72],\n [195, -103, 122, 18, -137, 90],\n [19, -51, 49, -56, 53, 50],\n [-51, 23, -78, -60, -60, -100]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[181, -73, -97, 6, 128, -83],\n [-143, 48, 172, 16, -107, 135],\n [81, 28, 78, -82, 2, -15],\n [4, 13, -194, -86, -83, -140],\n [-15, 44, -48, 60, -52, 30],\n [-55, -57, -152, -6, 10, -89]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[63, 9, 81, -45, 0, -45],\n [-19, 23, 135, -25, 0, -25],\n [-63, 11, 43, 15, 0, 15],\n [20, 20, 132, -40, 0, -40],\n [8, 4, 28, -10, 0, -10],\n [-80, 0, -32, 40, 0, 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[[29, -9, 46, -58, -57, 39],\n [71, 76, 9, 44, 0, -73],\n [90, 123, -50, 143, -7, -131],\n [30, 154, 77, -65, -96, -35],\n [-134, -97, 107, -180, -68, 53],\n [-109, -181, -30, -13, -9, 50]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[36, -8, -56, 40, 42, 22],\n [-34, 32, 72, 20, -33, 9],\n [-62, 67, -8, 20, 16, 28],\n [84, -51, -25, 50, 23, 11],\n [36, 2, -23, 70, 32, 34],\n [40, 12, -61, 90, 60, 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[[81, 38, 23, -57, 113, 0],\n [40, -126, -17, 65, -56, 60],\n [37, -146, 7, 43, -42, -63],\n [-169, 114, 5, 19, -73, -48],\n [78, -122, 57, 40, 55, -59],\n [-10, -74, -43, 18, -92, -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[[70, 24, 83, 8, 73, 43],\n [63, 12, 111, 6, 33, -54],\n [-35, 59, 8, 28, 3, -47],\n [89, -161, -26, -76, -15, 119],\n [56, 22, 73, 8, 57, 23],\n [-51, 37, -5, 20, -34, -90]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[54, -78, 122, -162, -81, 24],\n [18, 116, -42, 91, 41, -79],\n [80, -111, -55, -33, 99, 99],\n [132, 43, 19, -60, 67, -42],\n [-228, -30, 28, 56, -162, 22],\n [-16, -140, 73, -134, -65, 89]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-49, 88, 21, -135, 12, -3],\n [-94, 119, 132, -102, -68, 39],\n [-61, 62, 54, -142, 24, 62],\n [102, -35, -69, 58, -7, 44],\n [-30, 0, 29, 56, -51, -36],\n [12, 19, 0, -95, 59, 59]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, 81, 79, 50, -6, 11],\n [-12, 24, -35, 27, -96, -89],\n [-134, 4, 67, 9, -124, -115],\n [-20, 14, 34, -146, -59, 38],\n [12, -38, -28, -40, 29, 28],\n [-32, 59, 126, -75, -2, 74]]\n\nPresent 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, 41, 101, 61, -34, 9],\n [102, -18, 17, 19, 138, -3],\n [-38, -18, 14, -15, -61, -21],\n [31, 19, -31, -60, 75, 31],\n [135, 61, 10, -54, 140, 75],\n [112, 39, 33, 40, 37, 43]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[28, -47, -45, 13, 2, 72],\n [12, 4, -36, 52, 12, -36],\n [-11, 18, 18, -6, -1, -27],\n [-14, 4, 36, -44, -10, 18],\n [-30, 55, 45, -5, 0, -90],\n [-55, 51, 117, -105, -23, -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 6x6 matrix:\n[[-93, 70, -78, 51, -16, -36],\n [86, -5, 34, 59, 10, 56],\n [-21, 43, -152, 16, -108, 2],\n [107, -18, 103, -40, -28, 94],\n [37, -12, -47, -48, -78, 28],\n [-73, 11, 32, 30, 82, -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[[95, 123, -23, 20, -41, -72],\n [-67, -5, 66, -33, 5, -35],\n [37, -14, -18, -55, 86, 40],\n [76, 121, -117, -85, -71, 166],\n [94, 27, -88, -48, 48, 101],\n [98, 54, -126, 80, -136, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-27, 141, -124, -70, -104, 117],\n [34, 80, 26, -197, 35, -7],\n [-21, 60, -32, -46, -13, 35],\n [9, -87, -36, 176, -52, 11],\n [-42, 63, -4, -66, 35, 16],\n [-12, -27, 68, -34, 115, -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[[30, 32, -40, 16, 38, -50],\n [-29, -52, 0, -20, -47, 77],\n [-60, -8, 175, -22, -44, 20],\n [50, -12, -75, 42, -36, 60],\n [-31, -68, -15, -22, -61, 103],\n [85, -40, -130, 76, -91, 145]]\n\nPresent 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, -19, -2, 2, 5],\n [-73, -26, -120, 15, 69, 78],\n [25, 14, 67, 11, 1, -11],\n [-47, -10, -43, 31, 77, 71],\n [-24, -24, -118, -44, -52, -22],\n [-6, 0, 1, 8, 16, 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[[-190, -6, -18, 37, 16, 11],\n [-140, 12, -16, 4, 20, -22],\n [60, -74, 51, 27, -15, 103],\n [0, -70, 35, 50, -15, 105],\n [40, 54, -19, -53, 11, -85],\n [-50, 48, -27, -31, 17, -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 6x6 matrix:\n[[0, 1, -7, 6, 8, 3],\n [28, 12, 24, -24, -64, 0],\n [-35, -11, -58, 54, 112, 12],\n [-49, -37, 70, -54, -16, -48],\n [-7, -5, 8, -6, 0, -6],\n [42, 22, 8, -12, -64, 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[[-36, -20, 48, 12, -8, 56],\n [27, 48, -54, 0, 39, -30],\n [33, 44, -58, -4, 33, -42],\n [15, -10, -10, -10, -15, -30],\n [3, -46, 22, -14, -47, -22],\n [0, -44, 24, -12, -44, -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[[-26, -4, -12, -6, 7, -30],\n [-18, 0, -3, -15, 15, -27],\n [-16, -20, -41, 65, -60, 21],\n [-2, -16, -31, 61, -57, 33],\n [28, -4, -3, 39, -38, 51],\n [76, 32, 74, -62, 54, 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 6x6 matrix:\n[[-194, 196, -20, 38, 51, 171],\n [35, -101, -154, -74, -95, 12],\n [-54, 77, -50, 49, 7, 68],\n [49, 20, -37, 126, -22, -29],\n [-192, 194, -106, 142, -95, 234],\n [-72, 62, -50, 124, -164, 144]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[16, -111, -65, -20, -138, 17],\n [-12, 80, -18, -40, 108, -6],\n [18, -105, 0, 60, -132, -12],\n [-12, 98, -24, -20, 140, -32],\n [18, -102, 21, 80, -130, -17],\n [-6, 41, -90, -80, 68, -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[[124, -100, 57, 12, 6, 102],\n [146, -127, 64, 82, 28, 80],\n [72, -37, 20, 8, 56, -5],\n [-180, 148, -80, -52, -24, -122],\n [114, -52, 29, 2, 98, -17],\n [12, 34, -2, -148, 12, 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[[-32, -47, -9, 22, 11, 51],\n [-92, 44, 110, -81, -141, 110],\n [-49, -22, 4, 11, 19, 11],\n [-3, 10, 27, -75, -60, 14],\n [-58, -66, 13, -98, -21, 17],\n [46, -10, -35, 59, 40, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-25, 44, 54, -109, 75, 165],\n [-4, 83, -28, -49, -94, -22],\n [79, -36, -36, -5, 39, -3],\n [-54, 78, 2, -24, -94, -22],\n [81, -54, 14, -69, 161, 143],\n [7, 70, -36, -35, -93, -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[[-35, 30, 21, -12, 5, 38],\n [27, -15, -18, 6, -6, -21],\n [40, 20, -36, -8, -20, 12],\n [-100, -50, 90, 20, 50, -30],\n [3, 30, -9, -12, -9, 30],\n [-2, -20, 6, 8, 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[[72, 7, -58, -74, 3, 6],\n [-38, 37, 70, 140, 6, -32],\n [-30, 41, 148, 159, -86, 29],\n [-26, -35, -202, -96, 151, -140],\n [-18, 33, -80, 77, 63, -145],\n [42, 63, 288, 99, -160, 177]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-30, -40, 73, 46, 46, 42],\n [-96, 40, 8, 80, 80, 48],\n [94, -80, 47, -62, -62, -26],\n [-58, -5, 44, 60, 60, 44],\n [-74, 130, -127, 22, 22, -14],\n [-56, 70, -58, 28, 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 6x6 matrix:\n[[32, -20, 4, 20, 20, 60],\n [36, -9, 36, 27, 18, 117],\n [4, -13, -24, -1, 6, -31],\n [52, -31, 10, 33, 32, 103],\n [-108, 135, 144, -45, -90, 45],\n [4, -13, -24, -1, 6, -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[[-97, -86, -31, -29, 92, -76],\n [60, 53, -43, 129, -104, -13],\n [-46, -46, 36, -144, 110, 52],\n [65, 55, -40, 110, -95, 10],\n [-20, 6, 86, 2, -33, -97],\n [-10, 5, 39, 23, -30, -67]]\n\nPresent the answer 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, -27, -75, 77, -3, -14],\n [124, -9, -34, -61, -116, 122],\n [-20, -78, 22, -150, -66, 100],\n [-66, -5, 47, 13, 83, -82],\n [74, 57, -23, -81, -149, 162],\n [14, 189, 13, 103, 2, -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 6x6 matrix:\n[[110, -11, 120, -88, 10, -1],\n [31, 67, -16, -22, 69, 53],\n [-165, -95, -53, 173, 11, -82],\n [-25, -97, 97, 67, 51, -74],\n [-82, 53, -190, 2, -154, 33],\n [-25, -74, 24, 14, -83, -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, 27, -63, -63, -9, 9],\n [11, 87, -38, -38, 15, -26],\n [6, 66, -64, -64, 2, -8],\n [14, 96, -14, -14, 24, -38],\n [6, 30, 20, 20, 14, -20],\n [-5, -54, 51, 51, -2, 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[[92, 80, -52, -36, 18, -10],\n [92, 54, 4, -114, 126, 22],\n [-58, -31, -16, 3, -69, -43],\n [-106, -90, 46, -56, 1, -25],\n [68, 62, -40, 34, -14, 6],\n [-156, -123, 54, 21, -60, -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[[0, -19, 80, 26, -221, -14],\n [41, 100, 20, -21, 113, 24],\n [62, 0, 69, 40, -61, 34],\n [130, 20, 84, 74, -15, 51],\n [-52, 32, 33, -124, 116, 1],\n [42, 10, 40, 52, -85, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[30, -105, -131, 31, -27, 49],\n [109, 4, -30, 92, -26, -50],\n [-19, 139, -65, -30, 43, 43],\n [37, 209, -151, 114, -35, 113],\n [35, 132, -6, 48, 2, 28],\n [23, -55, -149, 16, -11, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, -37, -18, 52, 130, -50],\n [102, -22, -71, 90, 89, 13],\n [39, 14, -51, 13, -114, 97],\n [-111, 5, 61, -72, -53, -23],\n [-150, 16, 137, -120, 11, -115],\n [-75, 35, 50, -88, -150, 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 6x6 matrix:\n[[-18, 70, -96, 14, -92, 54],\n [60, 44, 0, 60, 8, 12],\n [-84, -20, -48, -68, -56, 12],\n [39, 104, -87, 68, -76, 60],\n [-24, -2, -18, -18, -20, 6],\n [9, -74, 93, -22, 88, -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[[64, -86, -46, -35, 36, -16],\n [56, 4, 60, 6, 36, 48],\n [-16, 92, 112, 62, -36, 22],\n [60, -120, -88, -42, 18, -62],\n [-36, 100, 98, 56, -36, 27],\n [76, -106, -90, -99, 126, 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[[-52, -38, 30, -21, 69, 4],\n [49, 11, -30, 12, -18, 17],\n [43, 43, -24, 21, -79, -13],\n [0, -86, -6, -27, 163, 72],\n [16, -28, -12, -6, 54, 32],\n [-32, -30, 18, -15, 55, 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[[56, 42, 36, 44, 6, -76],\n [114, 91, 78, 22, -31, -106],\n [49, 42, 36, -26, -36, -20],\n [98, 77, 66, 34, -17, -102],\n [39, 28, 24, 46, 14, -64],\n [-41, -35, -30, 20, 29, 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[[30, 21, 115, -35, -92, -27],\n [-42, -36, -121, 14, -46, 15],\n [-91, 139, -102, 3, 78, 81],\n [74, -150, -59, 60, -118, -55],\n [71, -55, -27, 51, -64, -12],\n [-54, -38, 27, -56, 78, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-104, -132, 72, 106, 4, 32],\n [-38, -46, -54, 22, -148, -24],\n [-4, -6, 36, 11, 62, 16],\n [103, 131, -81, -107, -22, -36],\n [26, 34, -54, -34, -68, -24],\n [-76, -96, 36, 74, -28, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[-12, 6, 63, -28, 25, 25],\n [25, 40, 70, -70, -20, -20],\n [48, 48, 24, -64, -56, -56],\n [-14, -26, -53, 48, 9, 9],\n [-110, -86, 37, 88, 143, 143],\n [24, 6, -57, 12, -39, -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[[57, 91, 19, -45, -63, 139],\n [13, -91, -43, -39, 25, -55],\n [-56, -63, -16, 51, 56, -128],\n [-17, 14, 35, 24, -5, 23],\n [-26, -133, -60, -3, 66, -152],\n [19, -98, -50, -48, 25, -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[[-76, 122, -10, -88, -186, 202],\n [-90, 38, -35, -74, -77, 139],\n [-18, 27, -28, -6, -24, 28],\n [98, -137, 54, 69, 28, -76],\n [-42, 84, 3, -42, -3, 21],\n [-86, 130, -59, -59, -59, 93]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-29, 196, -34, 104, -154, 78],\n [27, 70, 150, 116, -46, 145],\n [7, 82, 77, 95, -105, 73],\n [-44, 28, 1, -21, 35, -76],\n [1, -64, 66, -8, 126, 46],\n [-49, 74, -48, 17, -118, -96]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[39, -123, -12, 143, 36, -13],\n [-73, 93, -33, -91, -78, -101],\n [91, -24, 156, -43, -63, 15],\n [19, -45, 15, 103, 97, 109],\n [-10, 51, 109, -20, -12, 48],\n [149, 54, 121, -110, 20, 148]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, -84, 3, 5, 109, -133],\n [-8, 62, 49, -51, -59, 26],\n [75, 32, -75, -61, 38, -91],\n [63, 67, -132, -138, 8, -96],\n [-34, -23, 132, 64, -7, 41],\n [-52, -58, 179, -9, 55, -112]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-28, -88, 6, -69, -9, -1],\n [55, 27, 52, -47, -23, -63],\n [-99, -74, 11, -125, 84, -16],\n [38, 1, -125, -63, -71, -5],\n [-66, -159, 93, 25, -92, 130],\n [84, 4, -166, 63, -116, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[71, 56, 28, 15, 81, 41],\n [29, 2, -18, -11, -29, -25],\n [1, -8, -12, -7, -25, -17],\n [94, 28, -28, -18, -30, -38],\n [23, 50, 54, 31, 121, 77],\n [65, 65, 45, 25, 115, 65]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[121, 111, -48, -41, -42, -91],\n [50, 43, -109, 35, -81, 31],\n [-31, 11, 43, 67, 83, 153],\n [24, 18, 16, -100, -29, -165],\n [115, 39, 52, -35, 63, 55],\n [152, 6, -41, 6, -19, 86]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[60, -146, -8, 68, 12, 100],\n [-6, 27, 12, -6, 6, -18],\n [4, -18, -8, 4, -4, 12],\n [55, -139, -12, 62, 8, 95],\n [-31, 31, -36, -38, -32, -23],\n [-34, 29, -44, -42, -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[[8, 92, 15, -98, -114, -4],\n [-17, -5, -32, 18, -231, 47],\n [-70, -109, 31, 58, 8, -35],\n [38, -54, -119, 136, 94, -31],\n [71, 48, -78, 28, 103, -8],\n [7, 43, 94, -89, -2, 79]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-15, 90, 60, -95, -35, -100],\n [42, 9, 39, -13, -19, -26],\n [-42, -67, -85, 75, 45, 94],\n [-114, 17, -73, -9, 33, 22],\n [-39, 60, 18, -61, -13, -56],\n [0, 29, 23, -31, -13, -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[[50, 125, -48, -134, -35, -3],\n [-3, 7, -2, 1, -12, 7],\n [66, 3, 120, 17, 119, -144],\n [17, 94, -118, -146, -67, 65],\n [39, 117, -6, -80, -44, -12],\n [-18, -117, 48, 89, 83, -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[[67, -108, 20, 14, -82, -80],\n [-110, 27, -67, 36, 113, 101],\n [92, -95, 15, 10, -97, -83],\n [-18, -31, 143, 11, 25, 123],\n [50, -166, 30, 56, -58, -8],\n [37, -50, 250, -25, -42, 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[[-30, 64, -154, -32, -36, -48],\n [45, -96, 81, -42, 9, 147],\n [-79, 35, -48, -64, -73, -47],\n [104, -93, 133, 74, 97, 90],\n [70, -113, 157, 2, 44, 150],\n [39, -21, 154, 108, 75, -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[[-67, 69, -38, -110, 17, -102],\n [-47, 41, -10, -50, 25, -46],\n [6, -42, 48, 96, 42, 102],\n [-115, 81, 75, 19, 126, 2],\n [-59, -15, -3, 5, 72, 52],\n [-44, 60, -42, -106, -6, -104]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[41, -72, 124, -53, -90, -6],\n [-25, -80, -145, 201, 104, 86],\n [46, -110, 63, 7, -94, 54],\n [18, 30, -63, 66, -9, -59],\n [104, -146, 26, 84, -83, -63],\n [-34, 147, 93, -73, -77, -83]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-34, -6, 21, 45, 51, -80],\n [-16, 3, -10, 7, 1, -18],\n [-36, -6, 18, 36, 36, -60],\n [47, 11, -24, -18, -3, 9],\n [-58, -3, -1, 16, -8, -18],\n [-9, 9, -9, 63, 90, -153]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-25, 139, -15, -46, -220, 72],\n [51, -128, -38, 7, 129, 34],\n [-59, 106, 65, 77, -113, 0],\n [26, -120, -81, 110, 64, -24],\n [0, -44, -28, 163, 63, -43],\n [28, -113, -104, 176, 51, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[53, 7, -87, 75, 67, 12],\n [4, 40, 44, -30, 11, 23],\n [-15, 8, -81, 75, 63, -13],\n [20, 78, 14, 6, 26, 104],\n [23, -63, 128, -132, -104, -67],\n [-140, -35, -129, 123, -119, 158]]\n\nPresent 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, -3, 15, -9, 24],\n [-52, -118, 56, 142, -20, 102],\n [77, 108, -34, -148, 26, -133],\n [-64, 24, -96, 8, 16, 88],\n [54, 88, 19, -104, -21, -107],\n [-23, 87, -40, -59, -30, 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[[15, 23, 77, 67, 58, 14],\n [98, 35, 5, 97, -47, -89],\n [-12, -60, 200, 80, 21, 67],\n [-207, -92, 32, -142, -23, 139],\n [161, 8, 165, 133, 166, 21],\n [-73, -55, -72, -116, -74, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[96, 53, -15, -9, -149, -83],\n [-1, 73, -54, -92, -21, -15],\n [21, -13, 38, 32, -3, 4],\n [-70, 0, -141, -17, -53, 55],\n [5, 3, -45, -17, -30, 103],\n [120, 26, 54, 24, -108, 7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[11, -71, 138, -31, 73, -5],\n [-5, -98, -36, 19, -17, 168],\n [-24, -31, 73, -131, 21, 94],\n [-35, -40, 66, -63, 67, 124],\n [11, -106, -32, 206, -60, -73],\n [-69, -136, 29, 49, -16, 135]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, 45, 11, -13, 26, 27],\n [40, 157, 59, -45, 120, 71],\n [79, -15, -45, -89, -34, -81],\n [-65, 98, 30, 14, 50, 106],\n [-120, -127, -43, 91, -110, 7],\n [74, -62, -28, -38, -34, -94]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[78, -37, 146, 100, -41, -95],\n [-35, 86, -92, -19, 70, 62],\n [-4, -36, 121, 46, -38, -78],\n [-46, 90, -30, 7, 16, -7],\n [24, -100, 33, -19, 0, 19],\n [-38, -67, -10, -60, -15, 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[[66, 3, -8, 144, 1, -116],\n [-111, 69, 41, -84, -79, 86],\n [-65, 64, 42, 45, -78, -95],\n [-131, 70, 64, -37, -96, -93],\n [-62, 121, 35, 55, -117, 101],\n [103, -47, -38, 128, 57, -180]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[-79, -40, 12, -136, 64, 153],\n [-115, -94, -162, 5, -78, 80],\n [2, 27, -35, -3, 19, -142],\n [31, 0, -55, 27, -51, -76],\n [-139, -63, -76, 1, 6, 93],\n [60, -9, 45, -138, 7, 109]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[84, 0, 117, -61, -42, -62],\n [89, 18, 151, -59, -132, -65],\n [-36, -30, -30, -26, 56, 83],\n [24, 3, 117, -17, -173, -7],\n [-49, 14, -42, -10, -38, 95],\n [-110, -20, -111, 127, 2, 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[[63, -12, 18, 60, -36, -141],\n [55, -51, 58, -78, -5, 2],\n [36, -20, 24, -8, -12, -40],\n [-74, 36, -44, 0, 28, 98],\n [72, -40, 48, -16, -24, -80],\n [73, -61, 70, -82, -11, -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[[13, 28, -11, 51, -7, -58],\n [46, -7, -210, -102, -169, 126],\n [-109, -23, 49, 65, 36, -10],\n [-24, 30, 21, -2, 6, -11],\n [-183, 64, 55, 37, 7, -7],\n [16, -80, -40, 74, -2, -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[[126, 75, -22, -234, 52, -55],\n [-28, -33, 5, 14, -8, 26],\n [119, 159, 75, -70, 15, -159],\n [31, 161, -76, -9, -28, -125],\n [99, 105, -31, -29, 15, -224],\n [-77, -23, -134, -113, -38, 53]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[69, -35, -35, -101, 17, 74],\n [-145, -38, -1, 135, 11, 8],\n [-1, -8, -13, 55, -9, -124],\n [-8, -31, -23, 15, 7, -20],\n [-74, -9, 5, 87, -1, -36],\n [-124, -88, -39, 85, 31, 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[[-51, -41, -11, 38, -59, -37],\n [15, -27, 15, -6, -9, 9],\n [-57, 86, -52, 25, 23, -35],\n [100, -14, 50, -62, 52, 68],\n [-7, -87, 23, 16, -63, -9],\n [-22, 23, -17, 11, 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[[41, 15, -74, 44, 14, 55],\n [-30, -40, 84, -72, -26, -90],\n [28, 35, -76, 64, 23, 80],\n [-50, 15, 56, -8, 1, -10],\n [27, -20, -18, -12, -7, -15],\n [-25, -10, 46, -28, -9, -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[[72, -14, -5, 29, -92, -5],\n [-35, -5, -18, 3, 20, -26],\n [94, -2, 12, 0, -91, 30],\n [107, -13, 73, -28, -19, -37],\n [-97, 8, -80, 107, -31, 59],\n [-9, -12, 51, 12, 69, -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[[72, 111, -75, -60, -16, -45],\n [-19, -62, 10, -66, -145, -205],\n [2, -6, -4, 20, -46, -70],\n [-19, -45, 8, -72, -12, -17],\n [50, 35, -81, 2, -61, -137],\n [10, 42, 16, -62, -39, -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[[30, -60, -144, -172, -16, 78],\n [9, -7, 100, 102, 56, -55],\n [-4, -21, 92, 85, 67, -60],\n [7, -60, 44, 21, 81, -35],\n [22, -58, 38, -21, 59, -103],\n [34, -71, 48, -1, 81, -80]]\n\nPresent the 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, 85, 0, 40, -35, -30],\n [-30, -34, -51, -12, 53, 60],\n [-15, -61, -9, -28, 32, 30],\n [-45, -71, -69, -28, 82, 90],\n [21, 87, 12, 40, -45, -42],\n [6, 18, 6, 8, -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[[-37, 30, -6, -19, -13, 34],\n [27, 36, 18, -27, -171, -18],\n [-14, 38, 4, -26, -88, 16],\n [8, -46, -8, 32, 126, -12],\n [25, -46, -2, 31, 89, -26],\n [16, -24, 0, 16, 40, -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[[116, -144, -59, -20, -22, -64],\n [-76, 54, -17, 94, -7, 88],\n [69, -112, 149, -166, 36, -88],\n [21, -54, -84, 19, -20, -4],\n [-104, 244, 0, 124, -178, -72],\n [-1, -22, 84, -73, -59, -90]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-17, -41, 135, 37, -141, 32],\n [-23, 84, 20, -25, -38, -13],\n [90, -88, 44, 145, -28, -80],\n [83, -19, -125, -81, 173, -25],\n [104, -259, -99, 11, 97, 161],\n [90, 31, 111, -79, -46, -63]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[19, 23, 76, 35, -46, 4],\n [23, 25, -53, 92, 48, 78],\n [19, 37, -79, 32, 54, 34],\n [-27, -129, -77, 87, -8, 118],\n [-58, -156, 39, 5, -58, 34],\n [2, 40, 51, -21, 14, -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[[-71, -34, 58, -133, -56, 0],\n [-24, -33, 54, -101, -19, 28],\n [4, -17, 30, -41, 5, 28],\n [-58, -5, 50, -39, -21, 14],\n [-64, -20, 104, -74, -7, 63],\n [-11, -6, -22, -31, -29, -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[[28, 105, -42, 63, -21, -14],\n [108, -55, 54, 79, -133, -94],\n [42, -15, 18, 33, -51, -36],\n [-102, 20, -36, -86, 122, 86],\n [1, 90, -42, 33, 9, 7],\n [121, -35, 48, 98, -146, -103]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[85, -197, 69, -86, 35, -1],\n [77, -39, 24, -29, -68, -8],\n [-39, -67, -111, -43, 137, -59],\n [78, 44, -2, 67, -157, -153],\n [-25, -246, 106, -73, 139, 9],\n [-113, 45, -56, 7, 109, 41]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-61, 134, 12, 73, 60, -27],\n [169, -1, -178, 60, -134, 13],\n [-69, -112, 118, -82, 70, 29],\n [81, 101, -134, 77, -59, -40],\n [-65, -7, 68, -36, 51, -14],\n [18, 121, -76, 74, 2, -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[[50, 60, 48, -111, -70, 170],\n [-108, -99, -18, -54, -63, 0],\n [-6, 2, 20, -75, -56, 90],\n [4, -3, -18, 66, 49, -80],\n [-62, -61, -22, 9, -7, -50],\n [12, 6, -12, 54, 42, -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[[136, 150, -20, 128, 216, 26],\n [104, 104, -100, 66, 35, -22],\n [-106, -114, 29, -101, -108, 74],\n [-124, -163, 46, -136, -242, -33],\n [20, 101, 40, 6, 51, -109],\n [-212, -116, -74, -98, -24, 140]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 6x6 matrix:\n[[31, 10, 29, -34, -25, -18],\n [2, -2, -14, 56, -36, -21],\n [45, 14, 39, -38, -43, -30],\n [-51, -16, -45, 46, 47, 33],\n [70, 20, 50, -20, -90, -60],\n [-90, -28, -78, 76, 86, 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[[2, -74, 108, 54, 14, -96],\n [-17, 2, 33, 3, -11, -57],\n [-15, -2, -9, -3, -17, 17],\n [-37, -13, -18, -3, -42, 44],\n [-54, -32, 60, 18, -47, -64],\n [-124, -1, -3, -18, -126, 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 6x6 matrix:\n[[56, -24, -32, -2, -12, -84],\n [-56, 24, -16, -28, -24, 48],\n [-21, 9, 78, 42, 54, 81],\n [63, -27, -18, 9, 0, -81],\n [42, -18, -76, -34, -48, -102],\n [-56, 24, -24, -33, -30, 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[[19, -35, -67, 9, -15, -11],\n [-15, 56, 61, -76, 24, -44],\n [-8, -7, 22, 49, -3, 45],\n [-7, 21, 27, -23, 9, -11],\n [-24, 56, 88, -40, 24, -8],\n [-17, 28, 59, 0, 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[[-13, -104, -75, 65, 39, -25],\n [9, 59, 16, 1, -29, 96],\n [-13, -71, -50, 34, 21, -2],\n [-11, 5, -76, -31, 69, -94],\n [24, 28, 22, 48, -6, 0],\n [-51, -18, 23, -170, -19, -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[[-98, -63, -58, -16, 18, -114],\n [62, -51, -54, -70, 6, -10],\n [24, 0, 64, -120, 72, -216],\n [-79, 37, -62, 137, -35, 25],\n [-43, -104, -44, -70, 4, 4],\n [54, 125, 16, 101, -10, -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 6x6 matrix:\n[[80, 30, -25, -85, 120, -80],\n [-61, -15, -82, 53, 24, 82],\n [2, 0, 9, -1, -8, -4],\n [-70, -24, -7, 71, -72, 76],\n [25, 15, -80, -35, 120, -10],\n [0, -6, 77, 9, -88, -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, 158, 44, 14, 50, -152],\n [-58, 65, 5, -51, -27, -50],\n [46, 73, 27, 41, 49, -82],\n [49, -68, -4, 16, 20, 92],\n [-19, 52, 11, -30, -2, -28],\n [-5, 57, 11, 13, 9, -78]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[61, -1, -45, -141, 32, -97],\n [12, -9, 96, -46, -102, -57],\n [-19, 25, -62, 24, -7, 51],\n [-32, -30, 121, 87, 28, 32],\n [56, 84, -69, -85, -24, 69],\n [-16, -19, -50, 40, 60, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-17, -36, -22, 43, -1, -56],\n [-57, -95, 30, -113, 89, 37],\n [-150, 21, -52, -42, -125, -34],\n [-268, -23, -70, -80, -21, 70],\n [6, 53, -103, 100, -138, 32],\n [-10, 36, 39, -113, -39, 38]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}